Applied Mathematics
http://hdl.handle.net/10023/92
Sat, 21 Oct 2017 08:26:11 GMT
20171021T08:26:11Z
Applied Mathematics
http://researchrepository.standrews.ac.uk:80/bitstream/id/27/Mathematics and statistics.gif
http://hdl.handle.net/10023/92

Collisionless current sheet equilibria
http://hdl.handle.net/10023/11890
Current sheets are important for the structure and dynamics of many plasma systems. In space and astrophysical plasmas they play a crucial role in activity processes, for example by facilitating the release of magnetic energy via processes such as magnetic reconnection. In this contribution we will focus on collisionless plasma systems. A sensible first step in any investigation of physical processes involving current sheets is to find appropriate equilibrium solutions. The theory of collisionless plasma equilibria is well established, but over the past few years there has been a renewed interest in finding equilibrium distribution functions for collisionless current sheets with particular properties, for example for cases where the current density is parallel to the magnetic field (forcefree current sheets). This interest is due to a combination of scientific curiosity and potential applications to space and astrophysical plasmas. In this paper we will give an overview of some of the recent developments, discuss their potential applications and address a number of open questions.
The authors acknowledge financial support by the UK Science and Technology Facilities Council Consolidated Grants ST/K000950/1 and and ST/N000609/1, as well as Doctoral Training Grant ST/K502327/1. OA also acknowledges support by the UK Natural Environment Research Council Grant NE/P017274/1.
Mon, 01 Jan 2018 00:00:00 GMT
http://hdl.handle.net/10023/11890
20180101T00:00:00Z
Neukirch, Thomas
Wilson, Fiona
Allanson, Oliver Douglas
Current sheets are important for the structure and dynamics of many plasma systems. In space and astrophysical plasmas they play a crucial role in activity processes, for example by facilitating the release of magnetic energy via processes such as magnetic reconnection. In this contribution we will focus on collisionless plasma systems. A sensible first step in any investigation of physical processes involving current sheets is to find appropriate equilibrium solutions. The theory of collisionless plasma equilibria is well established, but over the past few years there has been a renewed interest in finding equilibrium distribution functions for collisionless current sheets with particular properties, for example for cases where the current density is parallel to the magnetic field (forcefree current sheets). This interest is due to a combination of scientific curiosity and potential applications to space and astrophysical plasmas. In this paper we will give an overview of some of the recent developments, discuss their potential applications and address a number of open questions.

Vertical structure of tropospheric winds on gas giants
http://hdl.handle.net/10023/11850
Zonal mean zonal velocity profiles from cloudtracking observations on Jupiter and Saturn are used to infer latitudinal variations of potential temperature consistent with a shear stable potential vorticity distribution. Immediately below the cloud tops, density stratification is weaker on the poleward and stronger on the equatorward flanks of midlatitude jets, while at greater depth the opposite relation holds. Thermal wind balance then yields the associated vertical shears of midlatitude jets in an altitude range bounded above by the cloudtops and bounded below by the level where the latitudinal gradient of static stability changes sign. The inferred vertical shear below the cloud tops is consistent with existing thermal profiling of the upper troposphere.The sense of the associated mean meridional circulation in the upper troposphere is discussed and expected magnitudes are given based on existing estimates of the radiative timescale on each planet.
Support for this work was generously provided by the National Science Foundation.
Sun, 16 Apr 2017 00:00:00 GMT
http://hdl.handle.net/10023/11850
20170416T00:00:00Z
Scott, R. K.
Dunkerton, T. J.
Zonal mean zonal velocity profiles from cloudtracking observations on Jupiter and Saturn are used to infer latitudinal variations of potential temperature consistent with a shear stable potential vorticity distribution. Immediately below the cloud tops, density stratification is weaker on the poleward and stronger on the equatorward flanks of midlatitude jets, while at greater depth the opposite relation holds. Thermal wind balance then yields the associated vertical shears of midlatitude jets in an altitude range bounded above by the cloudtops and bounded below by the level where the latitudinal gradient of static stability changes sign. The inferred vertical shear below the cloud tops is consistent with existing thermal profiling of the upper troposphere.The sense of the associated mean meridional circulation in the upper troposphere is discussed and expected magnitudes are given based on existing estimates of the radiative timescale on each planet.

Vortex merger near a topographic slope in a homogeneous rotating fluid
http://hdl.handle.net/10023/11779
The effect of a bottom slope on the merger of two identical Rankine vortices is investigated in a two dimensional, quasigeostrophic, incompressible fluid. When two cyclones initially lie parallel to the slope, and more than two vortex diameters away from the slope, the critical merger distance is unchanged. When the cyclones are closer to the slope, they can merge at larger distances, but they lose more mass into filaments, thus weakening the efficiency of merger. Several effects account for this: the topographic Rossby wave advects the cyclones, reduces their mutual distance and deforms them. This along shelf wave breaks into filaments and into secondary vortices which shear out the initial cyclones. The global motion of fluid towards the shallow domain and the erosion of the two cyclones are confirmed by the evolution of particles seeded both in the cyclone sand near the topographic slope. The addition of tracer to the flow indicates that diffusion is ballistic at early times. For two anticyclones, merger is also facilitated because one vortex is ejected offshore towards the other, via coupling with a topographic cyclone. Again two anticyclones can merge at large distance but they are eroded in the process. Finally, for taller topographies, the critical merger distance is again increased and the topographic influence can scatter or completely erode one of the two initial cyclones. Conclusions are drawn on possible improvements of the model configuration for an application to the ocean.
This work is a contribution to the PHYSINDIEN research program. It was supported by CNRSRFBR contract PRC 1069/1655150001.
Sun, 01 Oct 2017 00:00:00 GMT
http://hdl.handle.net/10023/11779
20171001T00:00:00Z
Carton, Xavier
Morvan, Mathieu
Reinaud, Jean Noel
Sokolovskiy, Mikhail
L'Hégaret, Pierre
Vic, Clément
The effect of a bottom slope on the merger of two identical Rankine vortices is investigated in a two dimensional, quasigeostrophic, incompressible fluid. When two cyclones initially lie parallel to the slope, and more than two vortex diameters away from the slope, the critical merger distance is unchanged. When the cyclones are closer to the slope, they can merge at larger distances, but they lose more mass into filaments, thus weakening the efficiency of merger. Several effects account for this: the topographic Rossby wave advects the cyclones, reduces their mutual distance and deforms them. This along shelf wave breaks into filaments and into secondary vortices which shear out the initial cyclones. The global motion of fluid towards the shallow domain and the erosion of the two cyclones are confirmed by the evolution of particles seeded both in the cyclone sand near the topographic slope. The addition of tracer to the flow indicates that diffusion is ballistic at early times. For two anticyclones, merger is also facilitated because one vortex is ejected offshore towards the other, via coupling with a topographic cyclone. Again two anticyclones can merge at large distance but they are eroded in the process. Finally, for taller topographies, the critical merger distance is again increased and the topographic influence can scatter or completely erode one of the two initial cyclones. Conclusions are drawn on possible improvements of the model configuration for an application to the ocean.

Emergence of spatial patterns in a mathematical model for the coculture dynamics of epitheliallike and mesenchymallike cells
http://hdl.handle.net/10023/11775
Accumulating evidence indicates that the interaction between epithelial and mesenchymal cells plays a pivotal role in cancer development and metastasis formation. Here we propose an integrodifferential model for the coculture dynamics of epitheliallike and mesenchymallike cells. Our model takes into account the effects of chemotaxis, adhesive interactions between epitheliallike cells, proliferation and competition for nutrients. We present a sample of numerical results which display the emergence of spots, stripes and honeycomb patterns, depending on parameters and initial data. These simulations also suggest that epitheliallike and mesenchymallike cells can segregate when there is little competition for nutrients. Furthermore, our computational results provide a possible explanation for how the concerted action between epithelialcell adhesion and mesenchymalcell spreading can precipitate the formation of ringlike structures, which resemble the fibrous capsules frequently observed in hepatic tumours.
Wed, 01 Feb 2017 00:00:00 GMT
http://hdl.handle.net/10023/11775
20170201T00:00:00Z
Delitala, Marcello
Lorenzi, Tommaso
Accumulating evidence indicates that the interaction between epithelial and mesenchymal cells plays a pivotal role in cancer development and metastasis formation. Here we propose an integrodifferential model for the coculture dynamics of epitheliallike and mesenchymallike cells. Our model takes into account the effects of chemotaxis, adhesive interactions between epitheliallike cells, proliferation and competition for nutrients. We present a sample of numerical results which display the emergence of spots, stripes and honeycomb patterns, depending on parameters and initial data. These simulations also suggest that epitheliallike and mesenchymallike cells can segregate when there is little competition for nutrients. Furthermore, our computational results provide a possible explanation for how the concerted action between epithelialcell adhesion and mesenchymalcell spreading can precipitate the formation of ringlike structures, which resemble the fibrous capsules frequently observed in hepatic tumours.

Spatiotemporal models of synthetic genetic oscillators
http://hdl.handle.net/10023/11774
Signal transduction pathways play a major role in many important aspects of cellular function e.g. cell division, apoptosis. One important class of signal transduction pathways is gene regulatory networks (GRNs). In many GRNs, proteins bind to gene sites in the nucleus thereby altering the transcription rate. Such proteins are known as transcription factors. If the binding reduces the transcription rate there is a negative feedback leading to oscillatory behaviour in mRNA and protein levels, both spatially (e.g. by observing fluorescently labelled molecules in single cells) and temporally (e.g. by observing protein/mRNA levels over time). Recent computational modelling has demonstrated that spatial movement of the molecules is a vital component of GRNs and may cause the oscillations. These numerical findings have subsequently been proved rigorously i.e. the diffusion coefficient of the protein/mRNA acts as a bifurcation parameter and gives rise to a Hopf bifurcation. In this paper we first present a model of the canonical GRN (the Hes1 protein) and show the effect of varying the spatial location of gene and protein production sites on the oscillations. We then extend the approach to examine spatiotemporal models of synthetic gene regulatory networks e.g. ngene repressilators and activatorrepressor systems.
Wed, 01 Feb 2017 00:00:00 GMT
http://hdl.handle.net/10023/11774
20170201T00:00:00Z
Macnamara, Cicely K.
Chaplain, Mark A. J.
Signal transduction pathways play a major role in many important aspects of cellular function e.g. cell division, apoptosis. One important class of signal transduction pathways is gene regulatory networks (GRNs). In many GRNs, proteins bind to gene sites in the nucleus thereby altering the transcription rate. Such proteins are known as transcription factors. If the binding reduces the transcription rate there is a negative feedback leading to oscillatory behaviour in mRNA and protein levels, both spatially (e.g. by observing fluorescently labelled molecules in single cells) and temporally (e.g. by observing protein/mRNA levels over time). Recent computational modelling has demonstrated that spatial movement of the molecules is a vital component of GRNs and may cause the oscillations. These numerical findings have subsequently been proved rigorously i.e. the diffusion coefficient of the protein/mRNA acts as a bifurcation parameter and gives rise to a Hopf bifurcation. In this paper we first present a model of the canonical GRN (the Hes1 protein) and show the effect of varying the spatial location of gene and protein production sites on the oscillations. We then extend the approach to examine spatiotemporal models of synthetic gene regulatory networks e.g. ngene repressilators and activatorrepressor systems.

The eruption of a smallscale emerging flux rope as the driver of an Mclass flare and of a coronal mass ejection
http://hdl.handle.net/10023/11761
Solar flares and coronal mass ejections are the most powerful explosions in the Sun. They are major sources of potentially destructive space weather conditions. However, the possible causes of their initiation remain controversial. Using highresolution data observed by the New Solar Telescope of Big Bear Solar Observatory, supplemented by Solar Dynamics Observatory observations, we present unusual observations of a smallscale emerging flux rope near a large sunspot, whose eruption produced an Mclass flare and a coronal mass ejection. The presence of the smallscale flux rope was indicated by static nonlinear forcefree field extrapolation as well as datadriven magnetohydrodynamics modeling of the dynamic evolution of the coronal threedimensional magnetic field. During the emergence of the flux rope, rotation of satellite sunspots at the footpoints of the flux rope was observed. Meanwhile, the Lorentz force, magnetic energy, vertical current, and transverse fields were increasing during this phase. The free energy from the magnetic flux emergence and twisting magnetic fields is sufficient to power the Mclass flare. These observations present, for the first time, the complete process, from the emergence of the smallscale flux rope, to the production of solar eruptions.
This work is sponsored by the National Science Foundation of China (NSFC) under the grant numbers 11373066, 11603071, 11503080, 11633008, 11533008, by the Key Laboratory of Solar Activity of CAS under numbers KLSA201603, KLSA201508, by the Yunnan Science Foundation of China under number 2013FB086, CAS "Light of West China" Program, by the Youth Innovation Promotion Association CAS (No.2011056), and the national basic research program of China (973 program, 2011CB811400). The BBSO operation is supported by NJIT, US NSF AGS1250818, and NASA NNX13AG14G grants, and the NST operation is partly supported by the Korea Astronomy and Space Science Institute and Seoul National University and by the strategic priority research program of CAS with Grant No. XDB09000000.
Thu, 10 Aug 2017 00:00:00 GMT
http://hdl.handle.net/10023/11761
20170810T00:00:00Z
Yan, X. L.
Jiang, C. W.
Xue, Z. K.
Wang, J. C.
Priest, E. R.
Yang, L. H.
Kong, D. F.
Cao, W. D.
Ji, H. S.
Solar flares and coronal mass ejections are the most powerful explosions in the Sun. They are major sources of potentially destructive space weather conditions. However, the possible causes of their initiation remain controversial. Using highresolution data observed by the New Solar Telescope of Big Bear Solar Observatory, supplemented by Solar Dynamics Observatory observations, we present unusual observations of a smallscale emerging flux rope near a large sunspot, whose eruption produced an Mclass flare and a coronal mass ejection. The presence of the smallscale flux rope was indicated by static nonlinear forcefree field extrapolation as well as datadriven magnetohydrodynamics modeling of the dynamic evolution of the coronal threedimensional magnetic field. During the emergence of the flux rope, rotation of satellite sunspots at the footpoints of the flux rope was observed. Meanwhile, the Lorentz force, magnetic energy, vertical current, and transverse fields were increasing during this phase. The free energy from the magnetic flux emergence and twisting magnetic fields is sufficient to power the Mclass flare. These observations present, for the first time, the complete process, from the emergence of the smallscale flux rope, to the production of solar eruptions.

Interaction between a surface quasigeostrophic buoyancy filament and an internal vortex
http://hdl.handle.net/10023/11727
This paper focuses on the nonlinear interaction between a surface quasigeostrophic buoyancy filament and an internal vortex. We first revisit the stability of an isolated buoyancy filament. The buoyancy profile considered is continuous and leads to a continuous velocity field, albeit one with infinite shear just outside its edge. The stability properties of an isolated filament help to interpret the unsteady interaction with a subsurface (internal) vortex studied next. We find that, in all cases, the filament breaks into billows, analogous in form to those occurring in KelvinHelmholtz shear instability. For intense buoyancy filaments, the vortex itself may undergo strong deformations, including being split into several pieces. Generally, the nonlinear interaction causes both the filament and the vortex to lose their respective ‘self’energies to the energy of interaction. The flow evolution depends sensitively on whether the vertical vorticity of the filament and the vortex have the same or opposite signs — termed “cooperative” and “adverse” shear respectively. In cooperative shear, the filament rolls up into a coherent surface eddy above a vortex initially placed below it, whereas in adverse shear, buoyancy is expelled above the vortex. Although sufficiently great shear induced by the buoyancy filament may split the vortex in both cases, adverse shear is significantly more destructive.
Fri, 23 Sep 2016 00:00:00 GMT
http://hdl.handle.net/10023/11727
20160923T00:00:00Z
Reinaud, Jean Noel
Dritschel, David Gerard
Carton, Xavier
This paper focuses on the nonlinear interaction between a surface quasigeostrophic buoyancy filament and an internal vortex. We first revisit the stability of an isolated buoyancy filament. The buoyancy profile considered is continuous and leads to a continuous velocity field, albeit one with infinite shear just outside its edge. The stability properties of an isolated filament help to interpret the unsteady interaction with a subsurface (internal) vortex studied next. We find that, in all cases, the filament breaks into billows, analogous in form to those occurring in KelvinHelmholtz shear instability. For intense buoyancy filaments, the vortex itself may undergo strong deformations, including being split into several pieces. Generally, the nonlinear interaction causes both the filament and the vortex to lose their respective ‘self’energies to the energy of interaction. The flow evolution depends sensitively on whether the vertical vorticity of the filament and the vortex have the same or opposite signs — termed “cooperative” and “adverse” shear respectively. In cooperative shear, the filament rolls up into a coherent surface eddy above a vortex initially placed below it, whereas in adverse shear, buoyancy is expelled above the vortex. Although sufficiently great shear induced by the buoyancy filament may split the vortex in both cases, adverse shear is significantly more destructive.

Particle acceleration with anomalous pitch angle scattering in 2D magnteohydrodynamic reconnection simulations
http://hdl.handle.net/10023/11714
The conversion of magnetic energy into other forms (such as plasma heating, bulk plasma flows, and nonthermal particles) during solar flares is one of the outstanding open problems in solar physics. It is generally accepted that magnetic reconnection plays a crucialrole in these conversion processes. In order to achieve the rapid energy release required in solar flares, an anomalous resistivity, which is orders of magnitude higher than the Spitzer resistivity, is often used in magnetohydrodynamic (MHD) simulations of reconnection in the corona. The origin of Spitzer resistivity is based on Coulomb scattering, which becomes negligible at the high energies achieved by accelerated particles. As a result, simulations of particle acceleration in reconnection events are often performed in the absence of any interaction between accelerated particles and any background plasma. This need not be the case for scattering associated with anomalous resistivity caused by turbulence within solar flares, as the higher resistivity implies an elevated scattering rate. We present results of test particle calculations, with and without pitch angle scattering, subject to fields derived from MHD simulations of twodimensional (2D) Xpoint reconnection. Scattering rates proportional to the ratio of the anomalous resistivity to the local Spitzer resistivity, as well as at fixed values, are considered. Pitch angle scattering, which is independent of the anomalous resistivity, causes higher maximum energies in comparison to those obtained without scattering. Scattering rates which are dependent on the local anomalous resistivity tend to produce fewer highly energised particles due to weaker scattering in the separatrices, even though scattering in the current sheet may be stronger when compared to resistivityindependent scattering. Strong scattering also causes an increase in the number of particles exiting the computational box in the reconnection outflow region, as opposed to along the separatrices as is the case in the absence of scattering.
A.B. would like to thank the University of St Andrews for financial support from the 7th Century Scholarship and the Scottish Government for support from the Saltire Scholarship. E.P.K.’s work is partially supported by a STFC consolidated grant ST/L000741/1. J.T. and T.N. gratefully acknowledge the support of the UK STFC (consolidated grant SN/N000609/1).
Fri, 01 Sep 2017 00:00:00 GMT
http://hdl.handle.net/10023/11714
20170901T00:00:00Z
Borissov, Alexei
Kontar, Eduard
Threlfall, James William
Neukirch, Thomas
The conversion of magnetic energy into other forms (such as plasma heating, bulk plasma flows, and nonthermal particles) during solar flares is one of the outstanding open problems in solar physics. It is generally accepted that magnetic reconnection plays a crucialrole in these conversion processes. In order to achieve the rapid energy release required in solar flares, an anomalous resistivity, which is orders of magnitude higher than the Spitzer resistivity, is often used in magnetohydrodynamic (MHD) simulations of reconnection in the corona. The origin of Spitzer resistivity is based on Coulomb scattering, which becomes negligible at the high energies achieved by accelerated particles. As a result, simulations of particle acceleration in reconnection events are often performed in the absence of any interaction between accelerated particles and any background plasma. This need not be the case for scattering associated with anomalous resistivity caused by turbulence within solar flares, as the higher resistivity implies an elevated scattering rate. We present results of test particle calculations, with and without pitch angle scattering, subject to fields derived from MHD simulations of twodimensional (2D) Xpoint reconnection. Scattering rates proportional to the ratio of the anomalous resistivity to the local Spitzer resistivity, as well as at fixed values, are considered. Pitch angle scattering, which is independent of the anomalous resistivity, causes higher maximum energies in comparison to those obtained without scattering. Scattering rates which are dependent on the local anomalous resistivity tend to produce fewer highly energised particles due to weaker scattering in the separatrices, even though scattering in the current sheet may be stronger when compared to resistivityindependent scattering. Strong scattering also causes an increase in the number of particles exiting the computational box in the reconnection outflow region, as opposed to along the separatrices as is the case in the absence of scattering.

The theoretical foundation of 3D Alfvén resonances : time dependent solutions
http://hdl.handle.net/10023/11706
We present results from a 3D numerical simulation which investigates the coupling of fast and Alfvén magnetohydrodynamic (MHD) waves in a nonuniform dipole equilibrium. This represents the time dependent extension of the normal mode (∝ exp(−iωt)) analysis of Wright and Elsden [2016], and provides a theoretical basis for understanding 3D Alfvén resonances. Wright and Elsden [2016] show that these are fundamentally different to resonances in 1D and 2D. We demonstrate the temporal behaviour of the Alfvén resonance, which is formed within the ‘Resonant Zone’; a channel of the domain where a family of solutions exists such that the natural Alfvén frequency matches the fast mode frequency. At early times, phase mixing leads to the production of prominent ridges in the energy density, whose shape is determined by the Alfvén speed profile and the chosen background magnetic field geometry. These off resonant ridges decay in time, leaving only a main 3D resonant sheet in the steady state. We show that the width of the 3D resonance in time and in space can be accurately estimated by adapting previous analytical estimates from 1D theory. We further provide an analytical estimate for the resonance amplitude in 3D, based upon extending 2D theory.
Both authors were funded in part by STFC (through Consolidated Grant ST/N000609/1) and The Leverhulme Trust (through Research Grant RPG2016071).
Mon, 20 Mar 2017 00:00:00 GMT
http://hdl.handle.net/10023/11706
20170320T00:00:00Z
Elsden, T.
Wright, A. N.
We present results from a 3D numerical simulation which investigates the coupling of fast and Alfvén magnetohydrodynamic (MHD) waves in a nonuniform dipole equilibrium. This represents the time dependent extension of the normal mode (∝ exp(−iωt)) analysis of Wright and Elsden [2016], and provides a theoretical basis for understanding 3D Alfvén resonances. Wright and Elsden [2016] show that these are fundamentally different to resonances in 1D and 2D. We demonstrate the temporal behaviour of the Alfvén resonance, which is formed within the ‘Resonant Zone’; a channel of the domain where a family of solutions exists such that the natural Alfvén frequency matches the fast mode frequency. At early times, phase mixing leads to the production of prominent ridges in the energy density, whose shape is determined by the Alfvén speed profile and the chosen background magnetic field geometry. These off resonant ridges decay in time, leaving only a main 3D resonant sheet in the steady state. We show that the width of the 3D resonance in time and in space can be accurately estimated by adapting previous analytical estimates from 1D theory. We further provide an analytical estimate for the resonance amplitude in 3D, based upon extending 2D theory.

Wave of chaos in a spatial ecoepidemiological system : generating realistic patterns of patchiness in rabbitlynx dynamics
http://hdl.handle.net/10023/11666
In the present paper, we propose and analyse an ecoepidemiological model with diffusion to study the dynamics of rabbit populations which are consumed by lynx populations. Existence, boundedness, stability and bifurcation analyses of solutions for the proposed rabbitlynx model are performed. Results show that in the presence of diffusion the model has the potential of exhibiting Turing instability. Numerical results (finite difference and finite element methods) reveal the existence of the wave of chaos and this appears to be a dominant mode of disease dispersal. We also show the mechanism of spatiotemporal pattern formation resulting from the Hopf bifurcation analysis, which can be a potential candidate for understanding the complex spatiotemporal dynamics of ecoepidemiological systems. Implications of the asymptotic transmission rate on disease eradication among rabbit population which in turn enhances the survival of Iberian lynx are discussed.
AM and CV would like to acknowledge support from the Engineering and Physical Sciences Research Council grant (EP/J016780/1) and the Leverhulme Trust Research Project Grant (RPG2014149).
Tue, 01 Nov 2016 00:00:00 GMT
http://hdl.handle.net/10023/11666
20161101T00:00:00Z
Upadhyay, Ranjit
Roy, Parimita
Venkataraman, C.
Madzvamuse, Anotida
In the present paper, we propose and analyse an ecoepidemiological model with diffusion to study the dynamics of rabbit populations which are consumed by lynx populations. Existence, boundedness, stability and bifurcation analyses of solutions for the proposed rabbitlynx model are performed. Results show that in the presence of diffusion the model has the potential of exhibiting Turing instability. Numerical results (finite difference and finite element methods) reveal the existence of the wave of chaos and this appears to be a dominant mode of disease dispersal. We also show the mechanism of spatiotemporal pattern formation resulting from the Hopf bifurcation analysis, which can be a potential candidate for understanding the complex spatiotemporal dynamics of ecoepidemiological systems. Implications of the asymptotic transmission rate on disease eradication among rabbit population which in turn enhances the survival of Iberian lynx are discussed.

On the energetics of a twolayer baroclinic flow
http://hdl.handle.net/10023/11637
The formation, evolution and coexistence of jets and vortices in turbulent planetary atmospheres is examined using a twolayer quasigeostrophic β channel shallowwater model. The study in particular focuses on the vertical structure of jets. Following Panetta & Held (J. Atmos. Sci., vol. 45 (22), 1988, pp. 3354–3365), a vertical shear arising from latitudinal heating variations is imposed on the flow and maintained by thermal damping. Idealised convection between the upper and lower layers is implemented by adding cyclonic/anticyclonic pairs, called hetons, to the flow, though the qualitative flow evolution is evidently not sensitive to this or other smallscale stochastic forcing. A very wide range of simulations have been conducted. A characteristic simulation which exhibits alternation between two different phases, quiescent and turbulent, is examined in detail. We study the energy transfers between different components and modes, and find the classical picture of barotropic/baroclinic energy transfers to be too simplistic. We also discuss the dependence on thermal damping and on the imposed vertical shear. Both have a strong influence on the flow evolution. Thermal damping is a major factor affecting the stability of the flow while vertical shear controls the number of jets in the domain, qualitatively through the Rhines scale LRh = √U/β.
Sat, 01 Apr 2017 00:00:00 GMT
http://hdl.handle.net/10023/11637
20170401T00:00:00Z
Jougla, Thibault
Dritschel, David Gerard
The formation, evolution and coexistence of jets and vortices in turbulent planetary atmospheres is examined using a twolayer quasigeostrophic β channel shallowwater model. The study in particular focuses on the vertical structure of jets. Following Panetta & Held (J. Atmos. Sci., vol. 45 (22), 1988, pp. 3354–3365), a vertical shear arising from latitudinal heating variations is imposed on the flow and maintained by thermal damping. Idealised convection between the upper and lower layers is implemented by adding cyclonic/anticyclonic pairs, called hetons, to the flow, though the qualitative flow evolution is evidently not sensitive to this or other smallscale stochastic forcing. A very wide range of simulations have been conducted. A characteristic simulation which exhibits alternation between two different phases, quiescent and turbulent, is examined in detail. We study the energy transfers between different components and modes, and find the classical picture of barotropic/baroclinic energy transfers to be too simplistic. We also discuss the dependence on thermal damping and on the imposed vertical shear. Both have a strong influence on the flow evolution. Thermal damping is a major factor affecting the stability of the flow while vertical shear controls the number of jets in the domain, qualitatively through the Rhines scale LRh = √U/β.

Exact VlasovMaxwell equilibria for asymmetric current sheets
http://hdl.handle.net/10023/11626
The NASA Magnetospheric Multiscale mission has made insitu diffusion region and kineticscale resolution measurements of asymmetric magnetic reconnection for the first time [Burch et al., 2016], in the Earth’s magnetopause. The principal theoretical tool currently used to model collisionless asymmetric reconnection is particleincell simulations. Many particleincell simulations of asymmetric collisionless reconnection start from an asymmetric Harristype magnetic field, but with distribution functions that are not exact equilibrium solutions of the Vlasov equation. We present new and exact equilibrium solutions of the VlasovMaxwell system that are selfconsistent with onedimensional asymmetric current sheets, with an asymmetric Harristype magnetic field profile, plus a constant nonzero guide field. The distribution functions can be represented as a combination of four shifted Maxwellian distribution functions. This equilibrium describes a magnetic field configuration with more freedom than the previously known exact solution [Alpers, 1969], and has different bulk flow properties.
Funding: Science and Technology Facilities Council Consolidated Grant Nos. ST/K000950/1 and ST/N000609/1 (O.A., T.N., J.D.B.H.and F.W.), the Science and Technology Facilities Council Doctoral Training Grant No. ST/K502327/1 (O.A. and J.D.B.H), the Natural Environment Research Council Grant No. NE/P017274/1 (RadSat) (O.A.)
Sat, 16 Sep 2017 00:00:00 GMT
http://hdl.handle.net/10023/11626
20170916T00:00:00Z
Allanson, O.
Wilson, F.
Neukirch, T.
Liu, YiHsin
Hodgson, J. D. B.
The NASA Magnetospheric Multiscale mission has made insitu diffusion region and kineticscale resolution measurements of asymmetric magnetic reconnection for the first time [Burch et al., 2016], in the Earth’s magnetopause. The principal theoretical tool currently used to model collisionless asymmetric reconnection is particleincell simulations. Many particleincell simulations of asymmetric collisionless reconnection start from an asymmetric Harristype magnetic field, but with distribution functions that are not exact equilibrium solutions of the Vlasov equation. We present new and exact equilibrium solutions of the VlasovMaxwell system that are selfconsistent with onedimensional asymmetric current sheets, with an asymmetric Harristype magnetic field profile, plus a constant nonzero guide field. The distribution functions can be represented as a combination of four shifted Maxwellian distribution functions. This equilibrium describes a magnetic field configuration with more freedom than the previously known exact solution [Alpers, 1969], and has different bulk flow properties.

Spatial variation in boundary conditions can govern selection and location of eyespots in butterfly wings
http://hdl.handle.net/10023/11618
Despite being the subject of widespread study, many aspects of the development of eyespot patterns in butterfly wings remain poorly understood. In this work, we examine, through numerical simulations, a mathematical model for eyespot focus point formation in which a reactiondiffusion system is assumed to play the role of the patterning mechanism. In the model, changes in the boundary conditions at the veins at the proximal boundary alone are capable of determining whether or not an eyespot focus forms in a given wing cell and the eventual position of focus points within the wing cell. Furthermore, an auxiliary surface reaction diffusion system posed along the entire proximal boundary of the wing cells is proposed as the mechanism that generates the necessary changes in the proximal boundary profiles. In order to illustrate the robustness of the model, we perform simulations on a curved wing geometry that is somewhat closer to a biological realistic domain than the rectangular wing cells previously considered, and we also illustrate the ability of the model to reproduce experimental results on artificial selection of eyespots.
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10023/11618
20170101T00:00:00Z
Venkataraman, Chandrasekhar
Sekimura, Toshio
Despite being the subject of widespread study, many aspects of the development of eyespot patterns in butterfly wings remain poorly understood. In this work, we examine, through numerical simulations, a mathematical model for eyespot focus point formation in which a reactiondiffusion system is assumed to play the role of the patterning mechanism. In the model, changes in the boundary conditions at the veins at the proximal boundary alone are capable of determining whether or not an eyespot focus forms in a given wing cell and the eventual position of focus points within the wing cell. Furthermore, an auxiliary surface reaction diffusion system posed along the entire proximal boundary of the wing cells is proposed as the mechanism that generates the necessary changes in the proximal boundary profiles. In order to illustrate the robustness of the model, we perform simulations on a curved wing geometry that is somewhat closer to a biological realistic domain than the rectangular wing cells previously considered, and we also illustrate the ability of the model to reproduce experimental results on artificial selection of eyespots.

Forcefree collisionless current sheet models with nonuniform temperature and density profiles
http://hdl.handle.net/10023/11614
We present a class of onedimensional, strictly neutral, VlasovMaxwell equilibrium distribution functions for forcefree current sheets, with magnetic fields defined in terms of Jacobian elliptic functions, extending the results of AbrahamShrauner48 to allow for nonuniform density and temperature pro les. To achieve this, we use an approach previously applied to the forcefree Harris sheet by Kolotkov et al.49. In one limit of the parameters, we recover the model of Kolotkov et al.49, while another limit gives a linear forcefree field. We discuss conditions on the parameters such that the distribution functions are always positive, and give expressions for the pressure, density, temperature and bulk ow velocities of the equilibrium, discussing differences from previous models. We also present some illustrative plots of the distribution function in velocity space.
The authors acknowledge the support of the Science and Technology Facilities Council via the consolidated grants ST/K000950/1 and ST/N000609/1 and the doctoral training grant ST/K502327/1 (O. A.), and the Natural Environment Research Council via grant no. NE/P017274/1 (RadSat) (O. A.). F. W. and T. N. would also like to thank the University of St Andrews for general financial support
Thu, 17 Aug 2017 00:00:00 GMT
http://hdl.handle.net/10023/11614
20170817T00:00:00Z
Wilson, Fiona
Neukirch, Thomas
Allanson, Oliver Douglas
We present a class of onedimensional, strictly neutral, VlasovMaxwell equilibrium distribution functions for forcefree current sheets, with magnetic fields defined in terms of Jacobian elliptic functions, extending the results of AbrahamShrauner48 to allow for nonuniform density and temperature pro les. To achieve this, we use an approach previously applied to the forcefree Harris sheet by Kolotkov et al.49. In one limit of the parameters, we recover the model of Kolotkov et al.49, while another limit gives a linear forcefree field. We discuss conditions on the parameters such that the distribution functions are always positive, and give expressions for the pressure, density, temperature and bulk ow velocities of the equilibrium, discussing differences from previous models. We also present some illustrative plots of the distribution function in velocity space.

Erwin Schrödinger and quantum wave mechanics
http://hdl.handle.net/10023/11543
The fathers of matrix quantum mechanics believed that the quantum particles are unanschaulich (unvisualizable) and that quantum particles pop into existence only when we measure them. Challenging the orthodoxy, in 1926 Erwin Schrödinger developed his wave equation that describes the quantum particles as a packet of quantum probability amplitudes evolving in space and time. Thus, Schrödinger visualized the unvisualizable and lifted the veil that has been obscuring the wonders of the quantum world.
Tue, 22 Aug 2017 00:00:00 GMT
http://hdl.handle.net/10023/11543
20170822T00:00:00Z
O'Connor, John J.
Robertson, Edmund F.
The fathers of matrix quantum mechanics believed that the quantum particles are unanschaulich (unvisualizable) and that quantum particles pop into existence only when we measure them. Challenging the orthodoxy, in 1926 Erwin Schrödinger developed his wave equation that describes the quantum particles as a packet of quantum probability amplitudes evolving in space and time. Thus, Schrödinger visualized the unvisualizable and lifted the veil that has been obscuring the wonders of the quantum world.

The stability of Mars' annular polar vortex
http://hdl.handle.net/10023/11541
The Martian polar atmosphere is known to have a persistent local minimum in potential vorticity (PV) near the winter pole, with a region of high PV encircling it. This finding is surprising since an isolated band of PV is barotropically unstable, a result going back to Rayleigh. Here we investigate the stability of a Marslike annular vortex using numerical integrations of the rotating shallow water equations. We show how the mode of instability and its growth rate depends upon the latitude and width of the annulus. By introducing thermal relaxation towards an annular equilibrium profile with a time scale similar to that of the instability, we are able to simulate a persistent annular vortex with similar characteristics as that observed in the Martian atmosphere. This time scale, typically 0.52 sols, is similar to radiative relaxation time scales for Mars’ polar atmosphere. We also demonstrate that the persistence of an annular vortex is robust to topographic forcing, as long as it is below a certain amplitude. We hence propose that the persistence of this barotropically unstable annular vortex is permitted due to the combination of short radiative relaxation time scales and relatively weak topographic forcing in the Martian polar atmosphere.
This research was partially supported by a NASA grant from the Mars Fundamental Research Program (NNX14AG53G).
Mon, 01 May 2017 00:00:00 GMT
http://hdl.handle.net/10023/11541
20170501T00:00:00Z
Seviour, William
Waugh, Darryn
Scott, Richard Kirkness
The Martian polar atmosphere is known to have a persistent local minimum in potential vorticity (PV) near the winter pole, with a region of high PV encircling it. This finding is surprising since an isolated band of PV is barotropically unstable, a result going back to Rayleigh. Here we investigate the stability of a Marslike annular vortex using numerical integrations of the rotating shallow water equations. We show how the mode of instability and its growth rate depends upon the latitude and width of the annulus. By introducing thermal relaxation towards an annular equilibrium profile with a time scale similar to that of the instability, we are able to simulate a persistent annular vortex with similar characteristics as that observed in the Martian atmosphere. This time scale, typically 0.52 sols, is similar to radiative relaxation time scales for Mars’ polar atmosphere. We also demonstrate that the persistence of an annular vortex is robust to topographic forcing, as long as it is below a certain amplitude. We hence propose that the persistence of this barotropically unstable annular vortex is permitted due to the combination of short radiative relaxation time scales and relatively weak topographic forcing in the Martian polar atmosphere.

Multimodality imaging and mathematical modelling of drug delivery to glioblastomas
http://hdl.handle.net/10023/11513
Patients diagnosed with glioblastoma, an aggressive brain tumour, have a poor prognosis, with a median overall survival of less than 15 months. Vasculature within these tumours is typically abnormal, with increased tortuosity, dilation and disorganization and they typically exhibit a disrupted blood brain barrier. Although it has been hypothesized that the “normalization” of the vasculature resulting from antiangiogenic therapies could improve drug delivery through improved blood flow, there is also evidence that suggests that the restoration of blood brain barrier integrity might limit the delivery of therapeutic agents and hence their effectiveness. In this paper we apply mathematical models of blood flow, vascular permeability and diffusion within the tumour microenvironment to investigate the effect of these competing factors on drug delivery. Preliminary results from the modelling indicate that all three physiological parameters investigated – flow rate, vessel permeability, and tissue diffusion coefficient – interact nonlinearly to produce the observed average drug concentration in the microenvironment.
MAJC would like to thank the Isaac Newton Institute for Mathematical Sciences for its hospitality during the programme “Coupling Geometric PDEs with Physics for Cell Morphology, Motility and Pattern Formation” supported by EPSRC Grant Number EP/K032208/1.
Thu, 06 Oct 2016 00:00:00 GMT
http://hdl.handle.net/10023/11513
20161006T00:00:00Z
Boujelben, Ahmed
Watson, Michael
McDougall, Steven
Yen, YiFen
Gerstner, Elizabeth
Catana, Ciprian
Deisboeck, Thomas
Batchelor, Tracy
Boas, David
Rosen, Bruce
KalpathyCramer, Jayashree
Chaplain, Mark Andrew Joseph
Patients diagnosed with glioblastoma, an aggressive brain tumour, have a poor prognosis, with a median overall survival of less than 15 months. Vasculature within these tumours is typically abnormal, with increased tortuosity, dilation and disorganization and they typically exhibit a disrupted blood brain barrier. Although it has been hypothesized that the “normalization” of the vasculature resulting from antiangiogenic therapies could improve drug delivery through improved blood flow, there is also evidence that suggests that the restoration of blood brain barrier integrity might limit the delivery of therapeutic agents and hence their effectiveness. In this paper we apply mathematical models of blood flow, vascular permeability and diffusion within the tumour microenvironment to investigate the effect of these competing factors on drug delivery. Preliminary results from the modelling indicate that all three physiological parameters investigated – flow rate, vessel permeability, and tissue diffusion coefficient – interact nonlinearly to produce the observed average drug concentration in the microenvironment.

Pressure moderation and effective pressure in NavierStokes flows
http://hdl.handle.net/10023/11499
We study the Cauchy problem of the Navier–Stokes equations by both semianalytic and classical energy methods. The former approach provides a physical picture of how viscous effects may or may not be able to suppress singularity development. In the latter approach, we examine the pressure term that drives the dynamics of the velocity norms uLq , for q ≥ 3. A key idea behind this investigation is due to the fact that the pressure p in this term is determined upto a function of both space and u, say Ƥ(x, u), which may assume relatively broad forms. This allows us to use Ƥ as a pressure moderator in the evolution equation for uLq , whereby optimal regularity criteria can be sought by varying Ƥ within its admissible classes. New regularity criteria are derived with and without making use of the moderator. The results obtained in the absence of the moderator feature some improvement over existing criteria in the literature. Several criteria are derived in terms of the moderated (effective) pressure p+Ƥ. A simple moderation scheme and the plausibility of the present approach to the problem of Navier–Stokes regularity are discussed.
Wed, 17 Aug 2016 00:00:00 GMT
http://hdl.handle.net/10023/11499
20160817T00:00:00Z
Tran, Chuong Van
Yu, Xinwei
We study the Cauchy problem of the Navier–Stokes equations by both semianalytic and classical energy methods. The former approach provides a physical picture of how viscous effects may or may not be able to suppress singularity development. In the latter approach, we examine the pressure term that drives the dynamics of the velocity norms uLq , for q ≥ 3. A key idea behind this investigation is due to the fact that the pressure p in this term is determined upto a function of both space and u, say Ƥ(x, u), which may assume relatively broad forms. This allows us to use Ƥ as a pressure moderator in the evolution equation for uLq , whereby optimal regularity criteria can be sought by varying Ƥ within its admissible classes. New regularity criteria are derived with and without making use of the moderator. The results obtained in the absence of the moderator feature some improvement over existing criteria in the literature. Several criteria are derived in terms of the moderated (effective) pressure p+Ƥ. A simple moderation scheme and the plausibility of the present approach to the problem of Navier–Stokes regularity are discussed.

Energetics of the KelvinHelmholtz instability induced by transverse waves in twisted coronal loops
http://hdl.handle.net/10023/11444
Aims. We quantify the effects of twisted magnetic fields on the development of the magnetic KelvinHelmholtz instability (KHI) in transversely oscillating coronal loops. Methods. We modelled a fundamental standing kink mode in a straight, densityenhanced magnetic flux tube using the magnetohydrodynamics code, Lare3d. In order to evaluate the impact of an azimuthal component of the magnetic field, various degrees of twist were included within the flux tube’s magnetic field. Results. The process of resonant absorption is only weakly affected by the presence of a twisted magnetic field. However, the subsequent evolution of the KHI is sensitive to the strength of the azimuthal component of the field. Increased twist values inhibit the deformation of the loop’s density profile, which is associated with the growth of the instability. Despite this, much smaller scales in the magnetic field are generated when there is a nonzero azimuthal component present. Hence, the instability is more energetic in cases with (even weakly) twisted fields. Field aligned flows at the loop apex are established in a twisted regime once the instability has formed. Further, in the straight field case, there is no net vertical component of vorticity when integrated across the loop. However, the inclusion of azimuthal magnetic field generates a preferred direction for the vorticity which oscillates during the kink mode. Conclusions. The KHI may have implications for wave heating in the solar atmosphere due to the creation of small length scales and the generation of a turbulent regime. Whilst magnetic twist does suppress the development of the vortices associated with the instability, the formation of the KHI in a twisted regime will be accompanied by greater Ohmic dissipation due to the larger currents that are produced, even if only weak twist is present. The presence of magnetic twist will likely make the instability more difficult to detect in the corona, but will enhance its contribution to heating the solar atmosphere. Further, the development of velocities along the loop may have observational applications for inferring the presence of magnetic twist within coronal structures.
The research leading to these results has received funding from the UK Science and Technology Facilities Council (consolidated grant ST/N000609/1) and the European Union Horizon 2020 research and innovation programme (grant agreement No. 647214).
Fri, 28 Jul 2017 00:00:00 GMT
http://hdl.handle.net/10023/11444
20170728T00:00:00Z
Howson, Thomas Alexander
De Moortel, Ineke
Antolin, Patrick
Aims. We quantify the effects of twisted magnetic fields on the development of the magnetic KelvinHelmholtz instability (KHI) in transversely oscillating coronal loops. Methods. We modelled a fundamental standing kink mode in a straight, densityenhanced magnetic flux tube using the magnetohydrodynamics code, Lare3d. In order to evaluate the impact of an azimuthal component of the magnetic field, various degrees of twist were included within the flux tube’s magnetic field. Results. The process of resonant absorption is only weakly affected by the presence of a twisted magnetic field. However, the subsequent evolution of the KHI is sensitive to the strength of the azimuthal component of the field. Increased twist values inhibit the deformation of the loop’s density profile, which is associated with the growth of the instability. Despite this, much smaller scales in the magnetic field are generated when there is a nonzero azimuthal component present. Hence, the instability is more energetic in cases with (even weakly) twisted fields. Field aligned flows at the loop apex are established in a twisted regime once the instability has formed. Further, in the straight field case, there is no net vertical component of vorticity when integrated across the loop. However, the inclusion of azimuthal magnetic field generates a preferred direction for the vorticity which oscillates during the kink mode. Conclusions. The KHI may have implications for wave heating in the solar atmosphere due to the creation of small length scales and the generation of a turbulent regime. Whilst magnetic twist does suppress the development of the vortices associated with the instability, the formation of the KHI in a twisted regime will be accompanied by greater Ohmic dissipation due to the larger currents that are produced, even if only weak twist is present. The presence of magnetic twist will likely make the instability more difficult to detect in the corona, but will enhance its contribution to heating the solar atmosphere. Further, the development of velocities along the loop may have observational applications for inferring the presence of magnetic twist within coronal structures.

A new approach for modelling chromospheric evaporation in response to enhanced coronal heating : II. Nonuniform heating
http://hdl.handle.net/10023/11427
We proposed that the use of an approximate “jump condition” at the solar transition region permits fast and accurate numerical solutions of the one dimensional hydrodynamic equations when the corona undergoes impulsive heating. In particular, it eliminates the need for the very short timesteps imposed by a highly resolved numerical grid. This paper presents further examples of the applicability of the method for cases of nonuniform heating, in particular, nanoflare trains (uniform in space but nonuniform in time) and spatially localised impulsive heating, including at the loop apex and base of the transition region. In all cases the overall behaviour of the coronal density and temperature shows good agreement with a fully resolved one dimensional model and is significantly better than the equivalent results from a 1D code run without using the jump condition but with the same coarse grid. A detailed assessment of the errors introduced by the jump condition is presented showing that the causes of discrepancy with the fully resolved code are (i) the neglect of the terms corresponding to the rate of change of total energy in the unresolved atmosphere; (ii) mass motions at the base of the transition region and (iii) for some cases with footpoint heating, an overestimation of the radiative losses in the transition region.
This project has received funding from the Science and Technology Facilities Council (UK) through the consolidated grant ST/N000609/1 and the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (grant agreement No 647214).
Fri, 01 Sep 2017 00:00:00 GMT
http://hdl.handle.net/10023/11427
20170901T00:00:00Z
Johnston, C. D.
Hood, A. W.
Cargill, P. J.
De Moortel, I.
We proposed that the use of an approximate “jump condition” at the solar transition region permits fast and accurate numerical solutions of the one dimensional hydrodynamic equations when the corona undergoes impulsive heating. In particular, it eliminates the need for the very short timesteps imposed by a highly resolved numerical grid. This paper presents further examples of the applicability of the method for cases of nonuniform heating, in particular, nanoflare trains (uniform in space but nonuniform in time) and spatially localised impulsive heating, including at the loop apex and base of the transition region. In all cases the overall behaviour of the coronal density and temperature shows good agreement with a fully resolved one dimensional model and is significantly better than the equivalent results from a 1D code run without using the jump condition but with the same coarse grid. A detailed assessment of the errors introduced by the jump condition is presented showing that the causes of discrepancy with the fully resolved code are (i) the neglect of the terms corresponding to the rate of change of total energy in the unresolved atmosphere; (ii) mass motions at the base of the transition region and (iii) for some cases with footpoint heating, an overestimation of the radiative losses in the transition region.

Nbody dynamics on closed surfaces : the axioms of mechanics
http://hdl.handle.net/10023/11426
A major challenge for our understanding of the mathematical basis of particle dynamics is the formulation of Nbody and Nvortex dynamics on Riemann surfaces. In this paper, we show how the two problems are, in fact, closely related when considering the role played by the intrinsic geometry of the surface. This enables a straightforward deduction of the dynamics of point masses, using recently derived results for point vortices on general closed differentiable surfaces M endowed with a metric g. We find, generally, that Kepler's Laws do not hold. What is more, even Newton's First Law (the law of inertia) fails on closed surfaces with variable curvature (e.g. the ellipsoid).
D.G.D. gratefully acknowledges support for this research from CNPq (Conselho Nacional de Desenvolvimento Cientifico e Tecnologico ) and FINEP (Inovação e Pesquisa) in Brazil, and from the UK Engineering and Physical Sciences Research Council (grant no. EP/H001794/1)
Mon, 01 Aug 2016 00:00:00 GMT
http://hdl.handle.net/10023/11426
20160801T00:00:00Z
Boatto, Stefanella
Dritschel, David Gerard
Schaefer, Rodrigo G
A major challenge for our understanding of the mathematical basis of particle dynamics is the formulation of Nbody and Nvortex dynamics on Riemann surfaces. In this paper, we show how the two problems are, in fact, closely related when considering the role played by the intrinsic geometry of the surface. This enables a straightforward deduction of the dynamics of point masses, using recently derived results for point vortices on general closed differentiable surfaces M endowed with a metric g. We find, generally, that Kepler's Laws do not hold. What is more, even Newton's First Law (the law of inertia) fails on closed surfaces with variable curvature (e.g. the ellipsoid).

Interaction of a mode2 internal solitary wave with narrow isolated topography
http://hdl.handle.net/10023/11406
Numerical and experimental studies of the transit of a mode2 internal solitary wave over an isolated ridge are presented. All studies used a quasitwolayer fluid with a pycnocline centred at the middepth. The wave amplitude and total fluid depth were both varied, while the topography remained fixed. The strength of the interaction between the internal solitary waves and the hill was found to be characterized by three regimes: weak, moderate, and strong interactions. The weak interaction exhibited negligible wave modulation and bottom surface stress. The moderate interaction generated weak and persistent vorticity in the lower layer, in addition to negligible wave modulation. The strong interaction clearly showed material from the trapped core of the mode2 wave extracted in the form of a thin filament while generating a strong vortex at the hill. A criterion for the strength of the interaction was found by nondimensionalizing the wave amplitude by the lower layer depth, a/ℓ. A passive tracer was used to measure the conditions for resuspension of boundary material due to the interaction. The speed and prevalence of cross boundary layer transport increased with a/ℓ.
This research was supported by the Natural Sciences and Engineering Research Council of Canada through a Discovery Grant (MS), and the Government of Ontario through a Queen Elizabeth II Graduate Scholarship in Science and Technology (DD). The experimental work was conducted at The University of Dundee by DD and MC with the aid of grants provided by The University of Dundee, the University of St Andrews, and the University of Waterloo.
Mon, 31 Jul 2017 00:00:00 GMT
http://hdl.handle.net/10023/11406
20170731T00:00:00Z
Deepwell, David
Stastna, Marek
Carr, Magda
Davies, Peter A.
Numerical and experimental studies of the transit of a mode2 internal solitary wave over an isolated ridge are presented. All studies used a quasitwolayer fluid with a pycnocline centred at the middepth. The wave amplitude and total fluid depth were both varied, while the topography remained fixed. The strength of the interaction between the internal solitary waves and the hill was found to be characterized by three regimes: weak, moderate, and strong interactions. The weak interaction exhibited negligible wave modulation and bottom surface stress. The moderate interaction generated weak and persistent vorticity in the lower layer, in addition to negligible wave modulation. The strong interaction clearly showed material from the trapped core of the mode2 wave extracted in the form of a thin filament while generating a strong vortex at the hill. A criterion for the strength of the interaction was found by nondimensionalizing the wave amplitude by the lower layer depth, a/ℓ. A passive tracer was used to measure the conditions for resuspension of boundary material due to the interaction. The speed and prevalence of cross boundary layer transport increased with a/ℓ.

Interaction between a surface quasigeostrophic buoyancy anomaly jet and internal vortices
http://hdl.handle.net/10023/11404
This paper addresses the dynamical coupling of the ocean's surface and the ocean's interior. In particular, we investigate the dynamics of an oceanic surface jet, and its interaction with vortices at depth. The jet is induced by buoyancy (density) anomalies at the surface. We first focus on the jet alone. The linear stability indicates there are two modes of instability: the sinuous and the varicose modes. When a vortex in present below the jet, it interacts with it. The velocity field induced by the vortex perturbs the jet and triggers its destabilisation. The jet also influences the vortex by pushing it under a region of cooperative shear. Strong jets may also partially shear out the vortex. We also investigate the interaction between a surface jet and a vortex dipole in the interior. Again, strong jets may partially shear out the vortex structure. The jet also modifies the trajectory of the dipole. Dipoles travelling towards the jet at shallow incidence angles may be reflected by the jet. Vortices travelling at moderate incidence angles normally cross below the jet. This is related to the displacement of the two vortices of the dipole by the shear induced by the jet. Intense jets may also destabilise early and form streets of billows. These billows can pair with the vortices and separate the dipole.
Tue, 01 Aug 2017 00:00:00 GMT
http://hdl.handle.net/10023/11404
20170801T00:00:00Z
Reinaud, Jean Noel
Dritschel, David Gerard
Carton, Xavier
This paper addresses the dynamical coupling of the ocean's surface and the ocean's interior. In particular, we investigate the dynamics of an oceanic surface jet, and its interaction with vortices at depth. The jet is induced by buoyancy (density) anomalies at the surface. We first focus on the jet alone. The linear stability indicates there are two modes of instability: the sinuous and the varicose modes. When a vortex in present below the jet, it interacts with it. The velocity field induced by the vortex perturbs the jet and triggers its destabilisation. The jet also influences the vortex by pushing it under a region of cooperative shear. Strong jets may also partially shear out the vortex. We also investigate the interaction between a surface jet and a vortex dipole in the interior. Again, strong jets may partially shear out the vortex structure. The jet also modifies the trajectory of the dipole. Dipoles travelling towards the jet at shallow incidence angles may be reflected by the jet. Vortices travelling at moderate incidence angles normally cross below the jet. This is related to the displacement of the two vortices of the dipole by the shear induced by the jet. Intense jets may also destabilise early and form streets of billows. These billows can pair with the vortices and separate the dipole.

Observations and numerical models of coronal heating associated with spicules
http://hdl.handle.net/10023/11358
Spicules have been proposed as significant contributors to the mass and energy balance of the corona. While previous observations have provided a glimpse of shortlived transient brightenings in the corona that are associated with spicules,these observations have been contested and are the subject of a vigorous debate both on the modeling and the observational side. Therefore, it remains unclear whether plasma is heated to coronal temperatures in association with spicules.We use highresolution observations of the chromosphere and transition region with the Interface Region Imaging Spectrograph (IRIS) and of the corona with the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamics Observatory (SDO) to show evidence of the formation of coronal structures associated with spicular mass ejections and heating of plasma to transition region and coronal temperatures. Our observations suggest that a significant fraction of the highly dynamic loop fan environment associated with plage regions may be the result of the formation of such new coronal strands, a process that previously had been interpreted as the propagation of transient propagating coronal disturbances (PCD)s. Our observations are supported by 2.5D radiative MHD simulations that show heating to coronal temperatures in association with spicules. Our results suggest that heating and strong flows play an important role in maintaining the substructure of loop fans, in addition to the waves that permeate this low coronal environment.
Sun, 20 Aug 2017 00:00:00 GMT
http://hdl.handle.net/10023/11358
20170820T00:00:00Z
De Pontieu, Bart
De Moortel, Ineke
MartinezSykora, Juan
McIntosh, Scott
Spicules have been proposed as significant contributors to the mass and energy balance of the corona. While previous observations have provided a glimpse of shortlived transient brightenings in the corona that are associated with spicules,these observations have been contested and are the subject of a vigorous debate both on the modeling and the observational side. Therefore, it remains unclear whether plasma is heated to coronal temperatures in association with spicules.We use highresolution observations of the chromosphere and transition region with the Interface Region Imaging Spectrograph (IRIS) and of the corona with the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamics Observatory (SDO) to show evidence of the formation of coronal structures associated with spicular mass ejections and heating of plasma to transition region and coronal temperatures. Our observations suggest that a significant fraction of the highly dynamic loop fan environment associated with plage regions may be the result of the formation of such new coronal strands, a process that previously had been interpreted as the propagation of transient propagating coronal disturbances (PCD)s. Our observations are supported by 2.5D radiative MHD simulations that show heating to coronal temperatures in association with spicules. Our results suggest that heating and strong flows play an important role in maintaining the substructure of loop fans, in addition to the waves that permeate this low coronal environment.

Evolutionary dynamics of phenotypestructured populations : from individuallevel mechanisms to populationlevel consequences
http://hdl.handle.net/10023/11328
Epigenetic mechanisms are increasingly recognised as integral to the adaptation of species that face environmental changes. In particular, empirical work has provided important insights into the contribution of epigenetic mechanisms to the persistence of clonal species, from which a number of verbal explanations have emerged that are suited to logical testing by proofofconcept mathematical models. Here, we present a stochastic agentbased model and a related deterministic integrodifferential equation model for the evolution of a phenotypestructured population composed of asexuallyreproducing and competing organisms which are exposed to novel environmental conditions. This setting has relevance to the study of biological systems where colonising asexual populations must survive and rapidly adapt to hostile environments, like pathogenesis, invasion and tumour metastasis. We explore how evolution might proceed when epigenetic variation in gene expression can change the reproductive capacity of individuals within the population in the new environment. Simulations and analyses of our models clarify the conditions under which certain evolutionary paths are possible, and illustrate that whilst epigenetic mechanisms may facilitate adaptation in asexual species faced with environmental change, they can also lead to a type of “epigenetic load” and contribute to extinction. Moreover, our results offer a formal basis for the claim that constant environments favour individuals with low rates of stochastic phenotypic variation. Finally, our model provides a “proof of concept” of the verbal hypothesis that phenotypic stability is a key driver in rescuing the adaptive potential of an asexual lineage, and supports the notion that intense selection pressure can, to an extent, offset the deleterious effects of high phenotypic instability and biased epimutations, and steer an asexual population back from the brink of an evolutionary dead end.
This research was supported in part by the Australian Research Council (DP140100339) and by the French National Research Agency through the ANR blanche project Kibord [ANR13BS010004] and the “ANR JC” project Modevol [ANR13JS010009]. TL was also supported in part by the Hadamard Mathematics Labex, backed by the Fondation Mathématique Jacques Hadamard, through a grant overseen by the French National Research Agency [ANR11LABX0056LMH]. LD was also supported in part by Université Sorbonne Paris Cité “Investissements d’Avenir”[ANR11IDEX0005].
Mon, 01 Aug 2016 00:00:00 GMT
http://hdl.handle.net/10023/11328
20160801T00:00:00Z
Chisholm, Rebecca H.
Lorenzi, Tommaso
Desvillettes, Laurent
Hughes, Barry D.
Epigenetic mechanisms are increasingly recognised as integral to the adaptation of species that face environmental changes. In particular, empirical work has provided important insights into the contribution of epigenetic mechanisms to the persistence of clonal species, from which a number of verbal explanations have emerged that are suited to logical testing by proofofconcept mathematical models. Here, we present a stochastic agentbased model and a related deterministic integrodifferential equation model for the evolution of a phenotypestructured population composed of asexuallyreproducing and competing organisms which are exposed to novel environmental conditions. This setting has relevance to the study of biological systems where colonising asexual populations must survive and rapidly adapt to hostile environments, like pathogenesis, invasion and tumour metastasis. We explore how evolution might proceed when epigenetic variation in gene expression can change the reproductive capacity of individuals within the population in the new environment. Simulations and analyses of our models clarify the conditions under which certain evolutionary paths are possible, and illustrate that whilst epigenetic mechanisms may facilitate adaptation in asexual species faced with environmental change, they can also lead to a type of “epigenetic load” and contribute to extinction. Moreover, our results offer a formal basis for the claim that constant environments favour individuals with low rates of stochastic phenotypic variation. Finally, our model provides a “proof of concept” of the verbal hypothesis that phenotypic stability is a key driver in rescuing the adaptive potential of an asexual lineage, and supports the notion that intense selection pressure can, to an extent, offset the deleterious effects of high phenotypic instability and biased epimutations, and steer an asexual population back from the brink of an evolutionary dead end.

Our dynamic sun : 2017 Hannes Alfvén Medal lecture at the EGU
http://hdl.handle.net/10023/11320
This lecture summarises how our understanding of many aspects of the Sun has been revolutionised over the past few years by new observations and models. Much of the dynamic behaviour of the Sun is driven by the magnetic field since, in the outer atmosphere, it represents the largest source of energy by far. The interior of the Sun possesses a strong shear layer at the base of the convection zone, where sunspot magnetic fields are generated. A smallscale dynamo may also be operating near the surface of the Sun, generating magnetic fields that thread the lowest layer of the solar atmosphere, the turbulent photosphere. Above the photosphere lies the highly dynamic finescale chromosphere, and beyond that is the rare corona at high temperatures exceeding 1 million degrees K. Possible magnetic mechanisms for heating the corona and driving the solar wind (two intriguing and unsolved puzzles) are described. Other puzzles include the structure of giant flux ropes, known as prominences, which have complex fine structure. Occasionally, they erupt and produce huge ejections of mass and magnetic fields (coronal mass ejections), which can disrupt the space environment of the Earth. When such eruptions originate in active regions around sunspots, they are also associated with solar flares, in which magnetic energy is converted to kinetic energy, heat and fastparticle energy. A new theory will be presented for the origin of the twist that is observed in erupting prominences and for the nature of reconnection in the rise phase of an eruptive flare or coronal mass ejection.
Fri, 14 Jul 2017 00:00:00 GMT
http://hdl.handle.net/10023/11320
20170714T00:00:00Z
Priest, Eric
This lecture summarises how our understanding of many aspects of the Sun has been revolutionised over the past few years by new observations and models. Much of the dynamic behaviour of the Sun is driven by the magnetic field since, in the outer atmosphere, it represents the largest source of energy by far. The interior of the Sun possesses a strong shear layer at the base of the convection zone, where sunspot magnetic fields are generated. A smallscale dynamo may also be operating near the surface of the Sun, generating magnetic fields that thread the lowest layer of the solar atmosphere, the turbulent photosphere. Above the photosphere lies the highly dynamic finescale chromosphere, and beyond that is the rare corona at high temperatures exceeding 1 million degrees K. Possible magnetic mechanisms for heating the corona and driving the solar wind (two intriguing and unsolved puzzles) are described. Other puzzles include the structure of giant flux ropes, known as prominences, which have complex fine structure. Occasionally, they erupt and produce huge ejections of mass and magnetic fields (coronal mass ejections), which can disrupt the space environment of the Earth. When such eruptions originate in active regions around sunspots, they are also associated with solar flares, in which magnetic energy is converted to kinetic energy, heat and fastparticle energy. A new theory will be presented for the origin of the twist that is observed in erupting prominences and for the nature of reconnection in the rise phase of an eruptive flare or coronal mass ejection.

Diffusion driven oscillations in gene regulatory networks
http://hdl.handle.net/10023/11258
Gene regulatory networks (GRNs) play an important role in maintaining cellular function by correctly timing key processes such as cell division and apoptosis. GRNs are known to contain similar structural components, which describe how genes and proteins within a network interact  typically by feedback. In many GRNs, proteins bind to genesites in the nucleus thereby altering the transcription rate. If the binding reduces the transcription rate there is a negative feedback leading to oscillatory behaviour in mRNA and protein levels, both spatially (e.g. by observing fluorescently labelled molecules in single cells) and temporally (e.g. by observing protein/mRNA levels over time). Mathematical modelling of GRNs has focussed on such oscillatory behaviour. Recent computational modelling has demonstrated that spatial movement of the molecules is a vital component of GRNs, while it has been proved rigorously that the diffusion coefficient of the protein/mRNA acts as a bifurcation parameter and gives rise to a Hopfbifurcation. In this paper we consider the spatial aspect further by considering the specific location of gene and protein production, showing that there is an optimum range for the distance between an mRNA genesite and a protein production site in order to achieve oscillations. We first present a model of a wellknown GRN, the Hes1 system, and then extend the approach to examine spatiotemporal models of synthetic GRNs e.g. ngene repressilator and activatorrepressor systems. By incorporating the idea of production sites into such models we show that the spatial component is vital to fully understand GRN dynamics.
Fri, 21 Oct 2016 00:00:00 GMT
http://hdl.handle.net/10023/11258
20161021T00:00:00Z
Macnamara, Cicely Krystyna
Chaplain, Mark Andrew Joseph
Gene regulatory networks (GRNs) play an important role in maintaining cellular function by correctly timing key processes such as cell division and apoptosis. GRNs are known to contain similar structural components, which describe how genes and proteins within a network interact  typically by feedback. In many GRNs, proteins bind to genesites in the nucleus thereby altering the transcription rate. If the binding reduces the transcription rate there is a negative feedback leading to oscillatory behaviour in mRNA and protein levels, both spatially (e.g. by observing fluorescently labelled molecules in single cells) and temporally (e.g. by observing protein/mRNA levels over time). Mathematical modelling of GRNs has focussed on such oscillatory behaviour. Recent computational modelling has demonstrated that spatial movement of the molecules is a vital component of GRNs, while it has been proved rigorously that the diffusion coefficient of the protein/mRNA acts as a bifurcation parameter and gives rise to a Hopfbifurcation. In this paper we consider the spatial aspect further by considering the specific location of gene and protein production, showing that there is an optimum range for the distance between an mRNA genesite and a protein production site in order to achieve oscillations. We first present a model of a wellknown GRN, the Hes1 system, and then extend the approach to examine spatiotemporal models of synthetic GRNs e.g. ngene repressilator and activatorrepressor systems. By incorporating the idea of production sites into such models we show that the spatial component is vital to fully understand GRN dynamics.

MapMySmoke : feasibility of a new quit cigarette smoking mobile phone application using integrated geopositioning technology, and motivational messaging within a primary care setting
http://hdl.handle.net/10023/11205
Background: Approximately 11,000 people die in Scotland each year as a result of smokingrelated causes. Quitting smoking is relatively easy; maintaining a quit attempt is a very difficult task with success rates for unaided quit attempts stubbornly remaining in the single digits. Pharmaceutical treatment can improve these rates by lowering the overall reward factor of nicotine. However, these and related nicotine replacement therapies do not operate on, or address, the spatial and contextual aspects of smoking behaviour. With the ubiquity of smartphones that can log spatial, quantitative and qualitative data related to smoking behaviour, there exists a personcentred clinical opportunity to support smokers attempting to quit by first understanding their smoking behaviour and subsequently sending them dynamic messages to encourage health behaviour change within a situational context. Methods: We have built a smartphone app—MapMySmoke—that works on Android and iOS platforms. The deployment of this app within a clinical National Health Service (NHS) setting has two distinct phases: (1) a 2week logging phase where prequit patients log all of their smoking and craving events; and (2) a postquit phase where users receive dynamic support messages and can continue to log craving events, and should they occur, relapse events. Following the initial logging phase, patients consult with their general practitioner (GP) or healthcare provider to review their smoking patterns and to outline a precise, individualised quit attempt plan. Our feasibility study consists of assessment of an initial app version during and after use by eight patients recruited from an NHS Fife GP practice. In addition to evaluation of the app as a potential smoking cessation aid, we have assessed the user experience, technological requirements and security of the data flow. Results: In an initial feasibility study, we have deployed the app for a small number of patients within one GP practice in NHS Fife. We recruited eight patients within one surgery, four of whom actively logged information about their smoking behaviour. Initial feedback was very positive, and users indicated a willingness to log their craving and smoking events. In addition, two out of three patients who completed followup interviews noted that the app helped them reduce the number of cigarettes they smoked per day, while the third indicated that it had helped them quit. The study highlighted the use of pushed notifications as a potential technology for maintaining quit attempts, and the security of collection of data was audited. These initial results influenced the design of a planned second larger study, comprised of 100 patients, the primary objectives of which are to use statistical modelling to identify times and places of probable switches into smoking states, and to target these times with dynamic health behaviour messaging. Conclusions: While the health benefits of quitting smoking are unequivocal, such behaviour change is very difficult to achieve. Many factors are likely to contribute to maintaining smoking behaviour, yet the precise role of cues derived from the spatial environment remains unclear. The rise of smartphones, therefore, allows clinicians the opportunity to better understand the spatial aspects of smoking behaviour and affords them the opportunity to push targeted individualised health support messages at vulnerable times and places.
This work was funded in part by an NHS Fife Research and Development Bursary Award to all authors. In addition, we have received funding from the University of St Andrews’ EPSRC Impact Acceleration Account. In 2013, Schick received a LEADERS award from the Scottish Universities Life Sciences Alliance that started this project.
Fri, 14 Jul 2017 00:00:00 GMT
http://hdl.handle.net/10023/11205
20170714T00:00:00Z
Schick, Robert S.
Kelsey, Thomas W.
Marston, John
Sampson, Kay
Humphris, Gerald M.
Background: Approximately 11,000 people die in Scotland each year as a result of smokingrelated causes. Quitting smoking is relatively easy; maintaining a quit attempt is a very difficult task with success rates for unaided quit attempts stubbornly remaining in the single digits. Pharmaceutical treatment can improve these rates by lowering the overall reward factor of nicotine. However, these and related nicotine replacement therapies do not operate on, or address, the spatial and contextual aspects of smoking behaviour. With the ubiquity of smartphones that can log spatial, quantitative and qualitative data related to smoking behaviour, there exists a personcentred clinical opportunity to support smokers attempting to quit by first understanding their smoking behaviour and subsequently sending them dynamic messages to encourage health behaviour change within a situational context. Methods: We have built a smartphone app—MapMySmoke—that works on Android and iOS platforms. The deployment of this app within a clinical National Health Service (NHS) setting has two distinct phases: (1) a 2week logging phase where prequit patients log all of their smoking and craving events; and (2) a postquit phase where users receive dynamic support messages and can continue to log craving events, and should they occur, relapse events. Following the initial logging phase, patients consult with their general practitioner (GP) or healthcare provider to review their smoking patterns and to outline a precise, individualised quit attempt plan. Our feasibility study consists of assessment of an initial app version during and after use by eight patients recruited from an NHS Fife GP practice. In addition to evaluation of the app as a potential smoking cessation aid, we have assessed the user experience, technological requirements and security of the data flow. Results: In an initial feasibility study, we have deployed the app for a small number of patients within one GP practice in NHS Fife. We recruited eight patients within one surgery, four of whom actively logged information about their smoking behaviour. Initial feedback was very positive, and users indicated a willingness to log their craving and smoking events. In addition, two out of three patients who completed followup interviews noted that the app helped them reduce the number of cigarettes they smoked per day, while the third indicated that it had helped them quit. The study highlighted the use of pushed notifications as a potential technology for maintaining quit attempts, and the security of collection of data was audited. These initial results influenced the design of a planned second larger study, comprised of 100 patients, the primary objectives of which are to use statistical modelling to identify times and places of probable switches into smoking states, and to target these times with dynamic health behaviour messaging. Conclusions: While the health benefits of quitting smoking are unequivocal, such behaviour change is very difficult to achieve. Many factors are likely to contribute to maintaining smoking behaviour, yet the precise role of cues derived from the spatial environment remains unclear. The rise of smartphones, therefore, allows clinicians the opportunity to better understand the spatial aspects of smoking behaviour and affords them the opportunity to push targeted individualised health support messages at vulnerable times and places.

Mathematical modelling of cancer invasion : the multiple roles of TGFβ pathway on tumour proliferation and cell adhesion
http://hdl.handle.net/10023/11162
In this paper, we develop a nonlocal mathematical model describing cancer cell invasion and movement as a result of integrincontrolled cell–cell adhesion and cell–matrix adhesion, and transforming growth factorbeta (TGFβ) effect on cell proliferation and adhesion, for two cancer cell populations with different levels of mutation. The model consists of partial integrodifferential equations describing the dynamics of two cancer cell populations, coupled with ordinary differential equations describing the extracellular matrix (ECM) degradation and the production and decay of integrins, and with a parabolic PDE governing the evolution of TGFβ concentration. We prove the global existence of weak solutions to the model. We then use our model to explore numerically the role of TGFβ in cell aggregation and movement.
VB acknowledges support from an Engineering and Physical Sciences Research Council (UK) grant number EP/L504932/1. RE was partially supported by an Engineering and Physical Sciences Research Council (UK) grant number EP/K033689/1.
Thu, 06 Jul 2017 00:00:00 GMT
http://hdl.handle.net/10023/11162
20170706T00:00:00Z
Bitsouni, Vasiliki
Chaplain, Mark Andrew Joseph
Eftimie, Raluca
In this paper, we develop a nonlocal mathematical model describing cancer cell invasion and movement as a result of integrincontrolled cell–cell adhesion and cell–matrix adhesion, and transforming growth factorbeta (TGFβ) effect on cell proliferation and adhesion, for two cancer cell populations with different levels of mutation. The model consists of partial integrodifferential equations describing the dynamics of two cancer cell populations, coupled with ordinary differential equations describing the extracellular matrix (ECM) degradation and the production and decay of integrins, and with a parabolic PDE governing the evolution of TGFβ concentration. We prove the global existence of weak solutions to the model. We then use our model to explore numerically the role of TGFβ in cell aggregation and movement.

The characteristics of billows generated by internal solitary waves
http://hdl.handle.net/10023/11156
The spatial and temporal development of shearinduced overturning billows associated with breaking internal solitary waves is studied by means of a combined laboratory and numerical investigation. The waves are generated in the laboratory by a lock exchange mechanism and they are simulated numerically via a contouradvective semiLagrangian method. The properties of individual billows (maximum height attained, time of collapse, growth rate, speed, wavelength, Thorpe scale) are determined in each case, and the billow interaction processes are studied and classified. For broad flat waves, similar characteristics are seen to those in parallel shear flow, but, for waves not at the conjugate flow limit, billow characteristics are affected by the spatially varying waveinduced shear flow. Wave steepness and wave amplitude are shown to have a crucial influence on determining the type of interaction that occurs between billows and whether billow overturning can be arrested. Examples are given in which billows (i) evolve independently of one another, (ii) pair with one another, (iii) engulf/entrain one another and (iv) fail to completely overturn. It is shown that the vertical extent a billow can attain (and the associated Thorpe scale of the billow) is dependent on wave amplitude but that its value saturates once a given amplitude is reached. It is interesting to note that this amplitude is less than the conjugate flow limit amplitude. The number of billows that form on a wave is shown to be dependent on wavelength; shorter waves support fewer but larger billows than their longwave counterparts for a given stratification.
Wed, 01 Feb 2017 00:00:00 GMT
http://hdl.handle.net/10023/11156
20170201T00:00:00Z
Carr, Magda
Franklin, James
King, Stuart Edward
Davies, Peter
Grue, John
Dritschel, David Gerard
The spatial and temporal development of shearinduced overturning billows associated with breaking internal solitary waves is studied by means of a combined laboratory and numerical investigation. The waves are generated in the laboratory by a lock exchange mechanism and they are simulated numerically via a contouradvective semiLagrangian method. The properties of individual billows (maximum height attained, time of collapse, growth rate, speed, wavelength, Thorpe scale) are determined in each case, and the billow interaction processes are studied and classified. For broad flat waves, similar characteristics are seen to those in parallel shear flow, but, for waves not at the conjugate flow limit, billow characteristics are affected by the spatially varying waveinduced shear flow. Wave steepness and wave amplitude are shown to have a crucial influence on determining the type of interaction that occurs between billows and whether billow overturning can be arrested. Examples are given in which billows (i) evolve independently of one another, (ii) pair with one another, (iii) engulf/entrain one another and (iv) fail to completely overturn. It is shown that the vertical extent a billow can attain (and the associated Thorpe scale of the billow) is dependent on wave amplitude but that its value saturates once a given amplitude is reached. It is interesting to note that this amplitude is less than the conjugate flow limit amplitude. The number of billows that form on a wave is shown to be dependent on wavelength; shorter waves support fewer but larger billows than their longwave counterparts for a given stratification.

Solar coronal jets : observations, theory, and modeling
http://hdl.handle.net/10023/11148
Coronal jets represent important manifestations of ubiquitous solar transients, which may be the source of significant mass and energy input to the upper solar atmosphere and the solar wind. While the energy involved in a jetlike event is smaller than that of “nominal” solar flares and coronal mass ejections (CMEs), jets share many common properties with these phenomena, in particular, the explosive magnetically driven dynamics. Studies of jets could, therefore, provide critical insight for understanding the larger, more complex drivers of the solar activity. On the other side of the sizespectrum, the study of jets could also supply important clues on the physics of transients close or at the limit of the current spatial resolution such as spicules. Furthermore, jet phenomena may hint to basic process for heating the corona and accelerating the solar wind; consequently their study gives us the opportunity to attack a broad range of solarheliospheric problems.
S. Patsourakos acknowledges support from an FP7 Marie Curie Grant (FP7PEOPLE2010RG/268288) as well as European Union (European Social Fund—ESF) and Greek national funds through the Operational Program “Education and Lifelong Learning” of the National Strategic Reference Framework (NSRF)—Research Funding Program: Thales. A.C. Sterling was supported by funding from the Heliophysics Division of NASA’s Science Mission Directorate through the Living With a Star Targeted Research and Technology Program, and by funding from the Hinode Project Office at NASA/MSFC. P.R. Young acknowledges funding from National Science Foundation grant AGS1159353. T. Török was supported by NASA’s HSR and LWS programs. K. Dalmasse acknowledges support from the Computational and Information Systems Laboratory and from the HAO, as well as support from the AFOSR under award FA95501510030.
Tue, 01 Nov 2016 00:00:00 GMT
http://hdl.handle.net/10023/11148
20161101T00:00:00Z
Raouafi, N. E.
Patsourakos, S.
Pariat, E.
Young, P. R.
Sterling, A. C.
Savcheva, A.
Shimojo, M.
MorenoInsertis, F.
DeVore, C. R.
Archontis, V.
Török, T.
Mason, H.
Curdt, W.
Meyer, K.
Dalmasse, K.
Matsui, Y.
Coronal jets represent important manifestations of ubiquitous solar transients, which may be the source of significant mass and energy input to the upper solar atmosphere and the solar wind. While the energy involved in a jetlike event is smaller than that of “nominal” solar flares and coronal mass ejections (CMEs), jets share many common properties with these phenomena, in particular, the explosive magnetically driven dynamics. Studies of jets could, therefore, provide critical insight for understanding the larger, more complex drivers of the solar activity. On the other side of the sizespectrum, the study of jets could also supply important clues on the physics of transients close or at the limit of the current spatial resolution such as spicules. Furthermore, jet phenomena may hint to basic process for heating the corona and accelerating the solar wind; consequently their study gives us the opportunity to attack a broad range of solarheliospheric problems.

Interaction between a quasigeostrophic buoyancy filament and a heton
http://hdl.handle.net/10023/11138
We investigate the interaction between a heton and a current generated by a filament of buoyancy anomaly at the surface. Hetons are baroclinic dipoles consisting of a pair of vortices of opposite sign lying at different depths. Such structures have a selfinduced motion whenever the pair of vortices are offset horizontally. A surface buoyancy filament generates a shear flow since the density perturbation modifies locally the pressure field. The vertical shear induced by the filament offsets the vortices of the heton if vertically aligned initially. Moreover, if the vortex nearer the surface is in adverse horizontal shear with the buoyancy filament the heton tends to move towards the filament. Conversely, if the upper vortex is in cooperative horizontal shear with the buoyancy filament, the heton moves away from it. The filament is also naturally unstable and eventually breaks into a series of billows as it is perturbed by the heton. Moderate to large intensity surface buoyancy distributions separate the vortices of the heton, limiting its advection as a baroclinic dipole. Instead, the vortices of the heton start to interact strongly with surface billows. Additionally, the vortices of the heton can be partially destroyed by the filament if the shear it induces is sufficiently large.
Fri, 01 Sep 2017 00:00:00 GMT
http://hdl.handle.net/10023/11138
20170901T00:00:00Z
Reinaud, Jean Noel
Carton, Xavier
Dritschel, David Gerard
We investigate the interaction between a heton and a current generated by a filament of buoyancy anomaly at the surface. Hetons are baroclinic dipoles consisting of a pair of vortices of opposite sign lying at different depths. Such structures have a selfinduced motion whenever the pair of vortices are offset horizontally. A surface buoyancy filament generates a shear flow since the density perturbation modifies locally the pressure field. The vertical shear induced by the filament offsets the vortices of the heton if vertically aligned initially. Moreover, if the vortex nearer the surface is in adverse horizontal shear with the buoyancy filament the heton tends to move towards the filament. Conversely, if the upper vortex is in cooperative horizontal shear with the buoyancy filament, the heton moves away from it. The filament is also naturally unstable and eventually breaks into a series of billows as it is perturbed by the heton. Moderate to large intensity surface buoyancy distributions separate the vortices of the heton, limiting its advection as a baroclinic dipole. Instead, the vortices of the heton start to interact strongly with surface billows. Additionally, the vortices of the heton can be partially destroyed by the filament if the shear it induces is sufficiently large.

Heating by transverse waves in simulated coronal loops
http://hdl.handle.net/10023/11122
Context. Recent numerical studies of oscillating flux tubes have established the significance of resonant absorption in the damping of propagating transverse oscillations in coronal loops. The nonlinear nature of the mechanism has been examined alongside the KelvinHelmholtz instability,which is expected to manifest in the resonant layers at the edges of the flux tubes. While these two processes have been hypothesized to heat coronal loops through the dissipation of wave energy into smaller scales, the occurring mixing with the hotter surroundings can potentially hide this effect. Aims. We aim to study the effects of wave heating from driven and standing kink waves in a coronal loop. Methods. Using the MPIAMRVAC code, we perform ideal, three dimensional magnetohydrodynamic (MHD) simulations of both (a) footpoint driven and (b) free standing oscillations in a straight coronal flux tube, in the presence of numerical resistivity. Results. We have observed the development of KelvinHelmholtz eddies at the loop boundary layer of all three models considered here, as well as an increase of the volume averaged temperature inside the loop. The main heating mechanism in our setups was Ohmic dissipation, as indicated by the higher values for the temperatures and current densities located near the footpoints. The introduction of a temperature gradient between the inner tube and the surrounding plasma, suggests that the mixing of the two regions, in the case of hotter environment, greatly increases the temperature of the tube at the site of the strongest turbulence, beyond the contribution of the aforementioned wave heating mechanism.
K.K. was funded by GOA2015014 (KU Leuven). T.V.D was supported by the IAP P7/08 CHARM (Belspo) and the GOA2015014 (KU Leuven). P.A. acknowledges funding from the UK Science and Technology Facilities Council and the European Union Horizon 2020 research and innovation programme (grant agreement No. 647214).
Fri, 25 Aug 2017 00:00:00 GMT
http://hdl.handle.net/10023/11122
20170825T00:00:00Z
Karampelas, K.
Van Doorsselaere, T.
Antolin, P.
Context. Recent numerical studies of oscillating flux tubes have established the significance of resonant absorption in the damping of propagating transverse oscillations in coronal loops. The nonlinear nature of the mechanism has been examined alongside the KelvinHelmholtz instability,which is expected to manifest in the resonant layers at the edges of the flux tubes. While these two processes have been hypothesized to heat coronal loops through the dissipation of wave energy into smaller scales, the occurring mixing with the hotter surroundings can potentially hide this effect. Aims. We aim to study the effects of wave heating from driven and standing kink waves in a coronal loop. Methods. Using the MPIAMRVAC code, we perform ideal, three dimensional magnetohydrodynamic (MHD) simulations of both (a) footpoint driven and (b) free standing oscillations in a straight coronal flux tube, in the presence of numerical resistivity. Results. We have observed the development of KelvinHelmholtz eddies at the loop boundary layer of all three models considered here, as well as an increase of the volume averaged temperature inside the loop. The main heating mechanism in our setups was Ohmic dissipation, as indicated by the higher values for the temperatures and current densities located near the footpoints. The introduction of a temperature gradient between the inner tube and the surrounding plasma, suggests that the mixing of the two regions, in the case of hotter environment, greatly increases the temperature of the tube at the site of the strongest turbulence, beyond the contribution of the aforementioned wave heating mechanism.

Comparison of variational balance models for the rotating shallow water equations
http://hdl.handle.net/10023/11100
We present an extensive numerical comparison of a family of balance models appropriate to the semigeostrophic limit of the rotating shallow water equations, and derived by variational asymptotics in Oliver (J. Fluid Mech., vol. 551, 2006, pp. 197–234) for small Rossby numbers Ro . This family of generalized largescale semigeostrophic (GLSG) models contains the L 1model introduced by Simon (J. Fluid. Mech., vol. 132, pp. 431444) as a special case. We use these models to produce balanced initial states for the full shallow water equations. We then numerically investigate how well these models capture the dynamics of an initially balanced shallow water flow. It is shown that, whereas the L 1member of the GLSG family is able to reproduce the balanced dynamics of the full shallow water equations on time scales of O ( 1/Ro ) very well, all other members develop significant unphysical high wave number contributions in the ageostrophic vorticity which spoil the dynamics.
Funding through the TRR 181 is gratefully acknowledged. GAG’s initial work was funded by the Australian Research Council grant DP0452147. All three authors received support for this research from the UK Engineering and Physical Sciences Research Council (grant number EP/H001794/1).
Sat, 01 Jul 2017 00:00:00 GMT
http://hdl.handle.net/10023/11100
20170701T00:00:00Z
Dritschel, David Gerard
Gottwald, Georg
Oliver, Marcel
We present an extensive numerical comparison of a family of balance models appropriate to the semigeostrophic limit of the rotating shallow water equations, and derived by variational asymptotics in Oliver (J. Fluid Mech., vol. 551, 2006, pp. 197–234) for small Rossby numbers Ro . This family of generalized largescale semigeostrophic (GLSG) models contains the L 1model introduced by Simon (J. Fluid. Mech., vol. 132, pp. 431444) as a special case. We use these models to produce balanced initial states for the full shallow water equations. We then numerically investigate how well these models capture the dynamics of an initially balanced shallow water flow. It is shown that, whereas the L 1member of the GLSG family is able to reproduce the balanced dynamics of the full shallow water equations on time scales of O ( 1/Ro ) very well, all other members develop significant unphysical high wave number contributions in the ageostrophic vorticity which spoil the dynamics.

3D pic simulations of collisionless shocks at lunar magnetic anomalies and their role in forming lunar swirls
http://hdl.handle.net/10023/11067
Investigation of the lunar crustal magnetic anomalies offers a comprehensive longterm data set of observations of smallscale magnetic fields and their interaction with the solar wind. In this paper a review of the observations of lunar minimagnetospheres is compared quantifiably with theoretical kineticscale plasma physics and 3D particleincell simulations. The aim of this paper is to provide a complete picture of all the aspects of the phenomena and to show how the observations from all the different and international missions interrelate. The analysis shows that the simulations are consistent with the formation of miniature (smaller than the ion Larmor orbit) collisionless shocks and miniature magnetospheric cavities, which has not been demonstrated previously. The simulations reproduce the finesse and form of the differential proton patterns that are believed to be responsible for the creation of both the "lunar swirls" and "dark lanes." Using a mature plasma physics code like OSIRIS allows us, for the first time, to make a sidebyside comparison between model and space observations. This is shown for all of the key plasma parameters observed to date by spacecraft, including the spectral imaging data of the lunar swirls. The analysis of miniature magnetic structures offers insight into multiscale mechanisms and kineticscale aspects of planetary magnetospheres.
The authors would like to thank the Science and Technology Facilities Council for fundamental physics and computing resources that were provided by funding from STFC’s Scientific Computing Department, and would like to thank the European Research Council (ERC 2010 AdG Grant 267841) and FCT (Portugal) grants SFRH/BD/75558/2010 for support.
Tue, 18 Oct 2016 00:00:00 GMT
http://hdl.handle.net/10023/11067
20161018T00:00:00Z
Bamford, R. A.
Alves, E. P.
Cruz, F.
Kellett, B. J.
Fonsesca, R. A.
Silva, L. O.
Trines, R. M. G. M.
Halekas, J. S.
Kamer, G.
Harnett, E.
Cairns, Robert Alan
Bingham, R.
Investigation of the lunar crustal magnetic anomalies offers a comprehensive longterm data set of observations of smallscale magnetic fields and their interaction with the solar wind. In this paper a review of the observations of lunar minimagnetospheres is compared quantifiably with theoretical kineticscale plasma physics and 3D particleincell simulations. The aim of this paper is to provide a complete picture of all the aspects of the phenomena and to show how the observations from all the different and international missions interrelate. The analysis shows that the simulations are consistent with the formation of miniature (smaller than the ion Larmor orbit) collisionless shocks and miniature magnetospheric cavities, which has not been demonstrated previously. The simulations reproduce the finesse and form of the differential proton patterns that are believed to be responsible for the creation of both the "lunar swirls" and "dark lanes." Using a mature plasma physics code like OSIRIS allows us, for the first time, to make a sidebyside comparison between model and space observations. This is shown for all of the key plasma parameters observed to date by spacecraft, including the spectral imaging data of the lunar swirls. The analysis of miniature magnetic structures offers insight into multiscale mechanisms and kineticscale aspects of planetary magnetospheres.

Cell population heterogeneity and evolution towards drug resistance in cancer : biological and mathematical assessment, theoretical treatment optimisation
http://hdl.handle.net/10023/11036
Background. Druginduced drug resistance in cancer has been attributed to diverse biological mechanisms at the individual cell or cell population scale, relying on stochastically or epigenetically varying expression of phenotypes at the single cell level, and on the adaptability of tumours at the cell population level. Scope of review. We focus on intratumour heterogeneity, namely betweencell variability within cancer cell populations, to account for drug resistance. To shed light on such heterogeneity, we review evolutionary mechanisms that encompass the great evolution that has designed multicellular organisms, as well as smaller windows of evolution on the time scale of human disease. We also present mathematical models used to predict drug resistance in cancer and optimal control methods that can circumvent it in combined therapeutic strategies. Major conclusions. Plasticity in cancer cells, i.e., partial reversal to a stemlike status in individual cells and resulting adaptability of cancer cell populations, may be viewed as backward evolution making cancer cell populations resistant to drug insult. This reversible plasticity is captured by mathematical models that incorporate betweencell heterogeneity through continuous phenotypic variables. Such models have the benefit of being compatible with optimal control methods for the design of optimised therapeutic protocols involving combinations of cytotoxic and cytostatic treatments with epigenetic drugs and immunotherapies. General significance. Gathering knowledge from cancer and evolutionary biology with physiologically based mathematical models of cell population dynamics should provide oncologists with a rationale to design optimised therapeutic strategies to circumvent drug resistance, that still remains a major pitfall of cancer therapeutics. This article is part of a Special Issue entitled "System Genetics" Guest Editor: Dr. Yudong Cai and Dr. Tao Huang.
Tue, 01 Nov 2016 00:00:00 GMT
http://hdl.handle.net/10023/11036
20161101T00:00:00Z
Chisholm, Rebecca H.
Lorenzi, Tommaso
Clairambault, Jean
Background. Druginduced drug resistance in cancer has been attributed to diverse biological mechanisms at the individual cell or cell population scale, relying on stochastically or epigenetically varying expression of phenotypes at the single cell level, and on the adaptability of tumours at the cell population level. Scope of review. We focus on intratumour heterogeneity, namely betweencell variability within cancer cell populations, to account for drug resistance. To shed light on such heterogeneity, we review evolutionary mechanisms that encompass the great evolution that has designed multicellular organisms, as well as smaller windows of evolution on the time scale of human disease. We also present mathematical models used to predict drug resistance in cancer and optimal control methods that can circumvent it in combined therapeutic strategies. Major conclusions. Plasticity in cancer cells, i.e., partial reversal to a stemlike status in individual cells and resulting adaptability of cancer cell populations, may be viewed as backward evolution making cancer cell populations resistant to drug insult. This reversible plasticity is captured by mathematical models that incorporate betweencell heterogeneity through continuous phenotypic variables. Such models have the benefit of being compatible with optimal control methods for the design of optimised therapeutic protocols involving combinations of cytotoxic and cytostatic treatments with epigenetic drugs and immunotherapies. General significance. Gathering knowledge from cancer and evolutionary biology with physiologically based mathematical models of cell population dynamics should provide oncologists with a rationale to design optimised therapeutic strategies to circumvent drug resistance, that still remains a major pitfall of cancer therapeutics. This article is part of a Special Issue entitled "System Genetics" Guest Editor: Dr. Yudong Cai and Dr. Tao Huang.

Scaling theory for vortices in the twodimensional inverse energy cascade
http://hdl.handle.net/10023/11014
We propose a new similarity theory for the twodimensional inverse energy cascade and the coherent vortex population it contains when forced at intermediate scales. Similarity arguments taking into account enstrophy conservation and a prescribed constant energy injection rate such that E∼t yield three length scales, lω, lE and lψ, associated with the vorticity field, energy peak and streamfunction, and predictions for their temporal evolutions, t1/2, t and t3/2, respectively. We thus predict that vortex areas grow linearly in time, A∼l2ω∼t, while the spectral peak wavenumber kE ≡ 2πl−1E ∼ t−1. We construct a theoretical framework involving a threepart, timeevolving vortex number density distribution, n(A) ∼ tαiA−ri, i ∈ 1,2,3. Just above the forcing scale (i =1) there is a forcingequilibrated scaling range in which the number of vortices at fixed A is constant and vortex ‘selfenergy’ Evcm = (2D)−1∫ωv2A2n(A) dA is conserved in Aspace intervals [μA0(t), A0(t)] comoving with the growth in vortex area, A0(t) ∼ t. In this range, α1 = 0 and n(A) ∼ A−3. At intermediate scales (i = 2) sufficiently far from the forcing and the largest vortex, there is a range with a scaleinvariant vortex size distribution. We predict that in this range the vortex enstrophy Zvcm = (2D)−1∫ ωv2An(A)dA is conserved and n(A) ∼ t−1A−1. The final range (i = 3), which extends over the largest vortexcontaining scales, conserves σvcm = (2D)−1∫ ωv2n(A)dA. If ωv2 is constant in time, this is equivalent to conservation of vortex number Nvcm =∫ n(A)dA. This regime represents a ‘front’ of sparse vortices, which are effectively pointlike; in this range we predict n(A) ∼ tr3−1A−r3. Allowing for timevarying ωv2 results in a small but significant correction to these temporal dependences. Highresolution numerical simulations verify the predicted vortex and spectral peak growth rates, as well as the theoretical picture of the three scaling ranges in the vortex population. Vortices steepen the energy spectrum E(k) past the classical k−5/3 scaling in the range k ∈ [kf , kv], where kv is the wavenumber associated with the largest vortex, while at larger scales the slope approaches −5/3. Though vortices disrupt the classical scaling, their number density distribution and evolution reveal deeper and more complex scale invariance, and suggest an effective theory of the inverse cascade in terms of vortex interactions.
B.H.B. is supported by the Natural Environment Research Council grant NE/M014983/1.
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10023/11014
20170101T00:00:00Z
Burgess, B. H.
Scott, R. K.
We propose a new similarity theory for the twodimensional inverse energy cascade and the coherent vortex population it contains when forced at intermediate scales. Similarity arguments taking into account enstrophy conservation and a prescribed constant energy injection rate such that E∼t yield three length scales, lω, lE and lψ, associated with the vorticity field, energy peak and streamfunction, and predictions for their temporal evolutions, t1/2, t and t3/2, respectively. We thus predict that vortex areas grow linearly in time, A∼l2ω∼t, while the spectral peak wavenumber kE ≡ 2πl−1E ∼ t−1. We construct a theoretical framework involving a threepart, timeevolving vortex number density distribution, n(A) ∼ tαiA−ri, i ∈ 1,2,3. Just above the forcing scale (i =1) there is a forcingequilibrated scaling range in which the number of vortices at fixed A is constant and vortex ‘selfenergy’ Evcm = (2D)−1∫ωv2A2n(A) dA is conserved in Aspace intervals [μA0(t), A0(t)] comoving with the growth in vortex area, A0(t) ∼ t. In this range, α1 = 0 and n(A) ∼ A−3. At intermediate scales (i = 2) sufficiently far from the forcing and the largest vortex, there is a range with a scaleinvariant vortex size distribution. We predict that in this range the vortex enstrophy Zvcm = (2D)−1∫ ωv2An(A)dA is conserved and n(A) ∼ t−1A−1. The final range (i = 3), which extends over the largest vortexcontaining scales, conserves σvcm = (2D)−1∫ ωv2n(A)dA. If ωv2 is constant in time, this is equivalent to conservation of vortex number Nvcm =∫ n(A)dA. This regime represents a ‘front’ of sparse vortices, which are effectively pointlike; in this range we predict n(A) ∼ tr3−1A−r3. Allowing for timevarying ωv2 results in a small but significant correction to these temporal dependences. Highresolution numerical simulations verify the predicted vortex and spectral peak growth rates, as well as the theoretical picture of the three scaling ranges in the vortex population. Vortices steepen the energy spectrum E(k) past the classical k−5/3 scaling in the range k ∈ [kf , kv], where kv is the wavenumber associated with the largest vortex, while at larger scales the slope approaches −5/3. Though vortices disrupt the classical scaling, their number density distribution and evolution reveal deeper and more complex scale invariance, and suggest an effective theory of the inverse cascade in terms of vortex interactions.

A robust and efficient adaptive multigrid solver for the optimal control of phase field formulations of geometric evolution laws
http://hdl.handle.net/10023/10909
We propose and investigate a novel solution strategy to efficiently and accurately compute approximate solutions to semilinear optimal control problems, focusing on the optimal control of phase field formulations of geometric evolution laws. The optimal control of geometric evolution laws arises in a number of applications in fields including material science, image processing, tumour growth and cell motility. Despite this, many open problems remain in the analysis and approximation of such problems. In the current work we focus on a phase field formulation of the optimal control problem, hence exploiting the well developed mathematical theory for the optimal control of semilinear parabolic partial differential equations. Approximation of the resulting optimal control problem is computationally challenging, requiring massive amounts of computational time and memory storage. The main focus of this work is to propose, derive, implement and test an efficient solution method for such problems. The solver for the discretised partial differential equations is based upon a geometric multigrid method incorporating advanced techniques to deal with the nonlinearities in the problem and utilising adaptive mesh refinement. An inhouse two grid solution strategy for the forward and adjoint problems, that significantly reduces memory requirements and CPU time, is proposed and investigated computationally. Furthermore, parallelisation as well as an adaptivestep gradient update for the control are employed to further improve efficiency. Along with a detailed description of our proposed solution method together with its implementation we present a number of computational results that demonstrate and evaluate our algorithms with respect to accuracy and efficiency. A highlight of the present work is simulation results on the optimal control of phase field formulations of geometric evolution laws in 3D which would be computationally infeasible without the solution strategies proposed in the present work.
All authors acknowledge support from the Leverhulme Trust Research Project Grant (RPG2014149). The work of CV, VS and AMwas partially supported by the Engineering and Physical Sciences Research Council, UK grant (EP/J016780/1). This work (AM) has also received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie SklodowskaCurie grant agreement No 642866. The work of CV is partially supported by an EPSRC Impact Accelerator Account award. The authors (FWY, CV, VS, AM) thank the Isaac Newton Institute for Mathematical Sciences for its hospitality during the programme (Coupling Geometric PDEs with Physics for Cell Morphology, Motility and Pattern Formation; EPSRC EP/K032208/1). AM was partially supported by Fellowships from the Simons Foundation.
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10023/10909
20170101T00:00:00Z
Yang, Feng Wei
Venkataraman, Chandrasekhar
Styles, Vanessa
Madzvamuse, Anotida
We propose and investigate a novel solution strategy to efficiently and accurately compute approximate solutions to semilinear optimal control problems, focusing on the optimal control of phase field formulations of geometric evolution laws. The optimal control of geometric evolution laws arises in a number of applications in fields including material science, image processing, tumour growth and cell motility. Despite this, many open problems remain in the analysis and approximation of such problems. In the current work we focus on a phase field formulation of the optimal control problem, hence exploiting the well developed mathematical theory for the optimal control of semilinear parabolic partial differential equations. Approximation of the resulting optimal control problem is computationally challenging, requiring massive amounts of computational time and memory storage. The main focus of this work is to propose, derive, implement and test an efficient solution method for such problems. The solver for the discretised partial differential equations is based upon a geometric multigrid method incorporating advanced techniques to deal with the nonlinearities in the problem and utilising adaptive mesh refinement. An inhouse two grid solution strategy for the forward and adjoint problems, that significantly reduces memory requirements and CPU time, is proposed and investigated computationally. Furthermore, parallelisation as well as an adaptivestep gradient update for the control are employed to further improve efficiency. Along with a detailed description of our proposed solution method together with its implementation we present a number of computational results that demonstrate and evaluate our algorithms with respect to accuracy and efficiency. A highlight of the present work is simulation results on the optimal control of phase field formulations of geometric evolution laws in 3D which would be computationally infeasible without the solution strategies proposed in the present work.

Particle acceleration in collapsing magnetic traps with a braking plasma jet
http://hdl.handle.net/10023/10896
Collapsing magnetic traps (CMTs) are one proposed mechanism for generating nonthermal particle populations in solar flares. CMTs occur if an initially stretched magnetic field structure relaxes rapidly into a lowerenergy configuration, which is believed to happen as a byproduct of magnetic reconnection. A similar mechanism for energising particles has also been found to operate in the Earth's magnetotail. One particular feature proposed to be of importance for particle acceleration in the magnetotail is that of a braking plasma jet, i.e. a localised region of strong flow encountering stronger magnetic field which causes the jet to slow down and stop. Such a feature has not been included in previously proposed analytical models of CMTs for solar flares. In this work we incorporate a braking plasma jet into a well studied CMT model for the first time. We present results of test particle calculations in this new CMT model. We observe and characterise new types of particle behaviour caused by the magnetic structure of the jet braking region, which allows electrons to be trapped both in the braking jet region and the loop legs. We compare and contrast the behaviour of particle orbits for various parameter regimes of the underlying trap by examining particle trajectories, energy gains and the frequency with which different types of particle orbit are found for each parameter regime.
Fri, 01 Jan 2016 00:00:00 GMT
http://hdl.handle.net/10023/10896
20160101T00:00:00Z
Borissov, Alexei
Neukirch, Thomas
Threlfall, James William
Collapsing magnetic traps (CMTs) are one proposed mechanism for generating nonthermal particle populations in solar flares. CMTs occur if an initially stretched magnetic field structure relaxes rapidly into a lowerenergy configuration, which is believed to happen as a byproduct of magnetic reconnection. A similar mechanism for energising particles has also been found to operate in the Earth's magnetotail. One particular feature proposed to be of importance for particle acceleration in the magnetotail is that of a braking plasma jet, i.e. a localised region of strong flow encountering stronger magnetic field which causes the jet to slow down and stop. Such a feature has not been included in previously proposed analytical models of CMTs for solar flares. In this work we incorporate a braking plasma jet into a well studied CMT model for the first time. We present results of test particle calculations in this new CMT model. We observe and characterise new types of particle behaviour caused by the magnetic structure of the jet braking region, which allows electrons to be trapped both in the braking jet region and the loop legs. We compare and contrast the behaviour of particle orbits for various parameter regimes of the underlying trap by examining particle trajectories, energy gains and the frequency with which different types of particle orbit are found for each parameter regime.

A complex solar coronal jet with two phases
http://hdl.handle.net/10023/10893
Jets often occur repeatedly from almost the same location. In this paper, a complex solar jet was observed with two phases to the west of NOAA AR 11513 on 2012 July 2. If it had been observed at only moderate resolution, the two phases and their points of origin would have been regarded as identical. However, at high resolution we find that the two phases merge into one another and the accompanying footpoint brightenings occur at different locations. The phases originate from different magnetic patches rather than being one phase originating from the same patch. Photospheric line of sight (LOS) magnetograms show that the bases of the two phases lie in two different patches of magnetic flux that decrease in size during the occurrence of the two phases. Based on these observations, we suggest that the driving mechanism of the two successive phases is magnetic cancellation of two separate magnetic fragments with an oppositepolarity fragment between them.
This work was partly supported by National Natural Science Foundation of China (grant Nos. 11303048, 11673033, 11373040, 11427901). This work was also partly supported by an International Exchanges cost share award with NSFC for overseas travel between collaborators in the UK and China, and State Key Laboratory for Space Weather, Center for Space Science and Applied Research, Chinese Academy of Sciences.
Thu, 04 May 2017 00:00:00 GMT
http://hdl.handle.net/10023/10893
20170504T00:00:00Z
Chen, Jie
Su, Jiangtao
Deng, Yuanyong
Priest, E. R.
Jets often occur repeatedly from almost the same location. In this paper, a complex solar jet was observed with two phases to the west of NOAA AR 11513 on 2012 July 2. If it had been observed at only moderate resolution, the two phases and their points of origin would have been regarded as identical. However, at high resolution we find that the two phases merge into one another and the accompanying footpoint brightenings occur at different locations. The phases originate from different magnetic patches rather than being one phase originating from the same patch. Photospheric line of sight (LOS) magnetograms show that the bases of the two phases lie in two different patches of magnetic flux that decrease in size during the occurrence of the two phases. Based on these observations, we suggest that the driving mechanism of the two successive phases is magnetic cancellation of two separate magnetic fragments with an oppositepolarity fragment between them.

A new class of vacillations of the stratospheric polar vortex
http://hdl.handle.net/10023/10887
A new class of persistent vacillations of the winter polar vortex, under the action of topographic wave forcing and radiative cooling, is identified in numerical integrations of the rotating shallow water equations. The vacillations are obtained provided only that care is taken to prevent the unconstrained growth of tropical easterlies that otherwise develop as the result of persistent angular momentum deposition at low latitudes. The vacillation cycle involves purely barotropic dynamics and is characterized by a dynamically controlled rapid splitting and rapid reformation of the vortex followed by a more gradual period of vortex intensification under the influence of radiative relaxation. The onset of the splitting occurs when the frequency of the free mode of the vortex approaches that of the forcing and resembles a resonant excitation. Experiments with an alternative basic state suggest that the vacillations are a robust feature of the topographically forced and radiatively relaxed vortex. In contrast to the behavior found in models with vertical structure, the period of the vacillation cycles here increases with increasing forcing amplitude. A wide range of forcing amplitude exists over which the vortex exhibits distinct regime transitions between a strong, vacillating state and a state in which the vortex is weak and the zonal mean polar flow nearly zero. Comparison with observational reanalysis suggest that the vacillation cycles obtained here may be relevant to the dynamics of some sudden warming events and that the onset of a radiatively dominated regime may be usefully linked to the loss of vortex area following such an event.
Fri, 01 Jul 2016 00:00:00 GMT
http://hdl.handle.net/10023/10887
20160701T00:00:00Z
Scott, Richard Kirkness
A new class of persistent vacillations of the winter polar vortex, under the action of topographic wave forcing and radiative cooling, is identified in numerical integrations of the rotating shallow water equations. The vacillations are obtained provided only that care is taken to prevent the unconstrained growth of tropical easterlies that otherwise develop as the result of persistent angular momentum deposition at low latitudes. The vacillation cycle involves purely barotropic dynamics and is characterized by a dynamically controlled rapid splitting and rapid reformation of the vortex followed by a more gradual period of vortex intensification under the influence of radiative relaxation. The onset of the splitting occurs when the frequency of the free mode of the vortex approaches that of the forcing and resembles a resonant excitation. Experiments with an alternative basic state suggest that the vacillations are a robust feature of the topographically forced and radiatively relaxed vortex. In contrast to the behavior found in models with vertical structure, the period of the vacillation cycles here increases with increasing forcing amplitude. A wide range of forcing amplitude exists over which the vortex exhibits distinct regime transitions between a strong, vacillating state and a state in which the vortex is weak and the zonal mean polar flow nearly zero. Comparison with observational reanalysis suggest that the vacillation cycles obtained here may be relevant to the dynamics of some sudden warming events and that the onset of a radiatively dominated regime may be usefully linked to the loss of vortex area following such an event.

Bombs and flares at the surface and lower atmosphere of the Sun
http://hdl.handle.net/10023/10741
A spectacular manifestation of solar activity is the appearance of transient brightenings in the far wings of the Hα line, known as Ellerman bombs (EBs). Recent observations obtained by the Interface Region Imaging Spectrograph have revealed another type of plasma "bombs" (UV bursts) with high temperatures of perhaps up to 8 ×104 K within the cooler lower solar atmosphere. Realistic numerical modeling showing such events is needed to explain their nature. Here, we report on 3D radiative magnetohydrodynamic simulations of magnetic flux emergence in the solar atmosphere. We find that ubiquitous reconnection between emerging bipolar magnetic fields can trigger EBs in the photosphere, UV bursts in the mid/low chromosphere and small (nano/micro) flares (106 K) in the upper chromosphere. These results provide new insights into the emergence and build up of the coronal magnetic field and the dynamics and heating of the solar surface and lower atmosphere.
This research was supported by the Research Council of Norway and by the European Research Council under the European Union's Seventh Framework Programme (FP7/2007–2013)/ERC Grant agreement no. 291058.
Mon, 10 Apr 2017 00:00:00 GMT
http://hdl.handle.net/10023/10741
20170410T00:00:00Z
Hansteen, V. H.
Archontis, V.
Pereira, T. M. D.
Carlsson, M.
Rouppe van der Voort, L.
Leenaarts, J.
A spectacular manifestation of solar activity is the appearance of transient brightenings in the far wings of the Hα line, known as Ellerman bombs (EBs). Recent observations obtained by the Interface Region Imaging Spectrograph have revealed another type of plasma "bombs" (UV bursts) with high temperatures of perhaps up to 8 ×104 K within the cooler lower solar atmosphere. Realistic numerical modeling showing such events is needed to explain their nature. Here, we report on 3D radiative magnetohydrodynamic simulations of magnetic flux emergence in the solar atmosphere. We find that ubiquitous reconnection between emerging bipolar magnetic fields can trigger EBs in the photosphere, UV bursts in the mid/low chromosphere and small (nano/micro) flares (106 K) in the upper chromosphere. These results provide new insights into the emergence and build up of the coronal magnetic field and the dynamics and heating of the solar surface and lower atmosphere.

Elongation of flare ribbons
http://hdl.handle.net/10023/10686
We present an analysis of the apparent elongation motion of flare ribbons along the polarity inversion line (PIL), as well as the shear of flare loops in several tworibbon flares. Flare ribbons and loops spread along the PIL at a speed ranging from a few to a hundred km s1. The shear measured from conjugate footpoints is consistent with the measurement from flare loops, and both show the decrease of shear toward a potential field as a flare evolves and ribbons and loops spread along the PIL. Flares exhibiting fast bidirectional elongation appear to have a strong shear, which may indicate a large magnetic guide field relative to the reconnection field in the coronal current sheet. We discuss how the analysis of ribbon motion could help infer properties in the corona where reconnection takes place.
J.Q., D.W.L., and P.A.C. gratefully acknowledge support by NSF SHINE collaborative grant AGS1460059.
Mon, 20 Mar 2017 00:00:00 GMT
http://hdl.handle.net/10023/10686
20170320T00:00:00Z
Qiu, Jiong
Longcope, Dana W.
Cassak, Paul A.
Priest, Eric R.
We present an analysis of the apparent elongation motion of flare ribbons along the polarity inversion line (PIL), as well as the shear of flare loops in several tworibbon flares. Flare ribbons and loops spread along the PIL at a speed ranging from a few to a hundred km s1. The shear measured from conjugate footpoints is consistent with the measurement from flare loops, and both show the decrease of shear toward a potential field as a flare evolves and ribbons and loops spread along the PIL. Flares exhibiting fast bidirectional elongation appear to have a strong shear, which may indicate a large magnetic guide field relative to the reconnection field in the coronal current sheet. We discuss how the analysis of ribbon motion could help infer properties in the corona where reconnection takes place.

The role of spatial variations of abiotic factors in mediating intratumour phenotypic heterogeneity
http://hdl.handle.net/10023/10685
A growing body of evidence indicates that the progression of cancer can be viewed as an ecoevolutionary process. Under this perspective, we present here a space and phenotypestructured model of selection dynamics between cancer cells within a solid tumour. In the framework of this model, we combine formal analyses with numerical simulations to investigate in silico the role played by the spatial distribution of abiotic components of the tumour microenvironment in mediating phenotypic selection of cancer cells. Numerical simulations are performed both on the 3D geometry of an in silico multicellular tumour spheroid and on the 3D geometry of an in vivo human hepatic tumour, which was imaged using computerised tomography. The results obtained show that inhomogeneities in the spatial distribution of oxygen, currently observed in solid tumours, can promote the creation of distinct local niches and lead to the selection of different phenotypic variants within the same tumour. This process fosters the emergence of stable phenotypic heterogeneity and supports the presence of hypoxic cells resistant to cytotoxic therapy prior to treatment. Our theoretical results demonstrate the importance of integrating spatial data with ecological principles when evaluating the therapeutic response of solid tumours.
CV wishes to acknowledge partial support from the European Union's Horizon 2020 research and innovation programme under the Marie SklodowskaCurie grant agreement No 642866. AL was supported by King Abdullah University of Science and Technology (KAUST) baseline and startup funds (BAS/1/16480101 and BAS/1/16480102). MAJC gratefully acknowledge support of EPSRC grant no. EP/N014642/1.
Thu, 20 Apr 2017 00:00:00 GMT
http://hdl.handle.net/10023/10685
20170420T00:00:00Z
Lorenzi, Tommaso
Venkataraman, Chandrasekhar
Lorz, Alexander
Chaplain, Mark A. J.
A growing body of evidence indicates that the progression of cancer can be viewed as an ecoevolutionary process. Under this perspective, we present here a space and phenotypestructured model of selection dynamics between cancer cells within a solid tumour. In the framework of this model, we combine formal analyses with numerical simulations to investigate in silico the role played by the spatial distribution of abiotic components of the tumour microenvironment in mediating phenotypic selection of cancer cells. Numerical simulations are performed both on the 3D geometry of an in silico multicellular tumour spheroid and on the 3D geometry of an in vivo human hepatic tumour, which was imaged using computerised tomography. The results obtained show that inhomogeneities in the spatial distribution of oxygen, currently observed in solid tumours, can promote the creation of distinct local niches and lead to the selection of different phenotypic variants within the same tumour. This process fosters the emergence of stable phenotypic heterogeneity and supports the presence of hypoxic cells resistant to cytotoxic therapy prior to treatment. Our theoretical results demonstrate the importance of integrating spatial data with ecological principles when evaluating the therapeutic response of solid tumours.

Extrapolating cetacean densities to quantitatively assess human impacts on populations in the high seas
http://hdl.handle.net/10023/10682
As human activities expand beyond national jurisdictions to the high seas, there is an increasing need to consider anthropogenic impacts to species inhabiting these waters. The current scarcity of scientific observations of cetaceans in the high seas impedes the assessment of populationlevel impacts of these activities. We developed plausible density estimates to facilitate a quantitative assessment of anthropogenic impacts on cetacean populations in these waters. Our study region extended from a wellsurveyed region within the U.S. Exclusive Economic Zone into a large region of the western North Atlantic sparsely surveyed for cetaceans. We modeled densities of 15 cetacean taxa with available line transect survey data and habitat covariates and extrapolated predictions to sparsely surveyed regions. We formulated models to reduce the extent of extrapolation beyond covariate ranges, and constrained them to model simple and generalizable relationships. To evaluate confidence in the predictions, we mapped where predictions were made outside sampled covariate ranges, examined alternate models, and compared predicted densities with maps of sightings from sources that could not be integrated into our models. Confidence levels in model results depended on the taxon and geographic area and highlighted the need for additional surveying in environmentally distinct areas. With application of necessary caution, our density estimates can inform management needs in the high seas, such as the quantification of potential cetacean interactions with military training exercises, shipping, fisheries, and deepsea mining and be used to delineate areas of special biological significance in international waters. Our approach is generally applicable to other marine taxa and geographic regions for which management will be implemented but data are sparse.
Funding for this study came from the U.S. Fleet Forces Command (Cooperative Agreement N624701328008), NASA (NNX08AK73G) and NOAA/NMFS (EE133F14SE3558).
Thu, 01 Jun 2017 00:00:00 GMT
http://hdl.handle.net/10023/10682
20170601T00:00:00Z
Mannocci, Laura
Roberts, Jason J.
Miller, David L.
Halpin, Patrick N.
As human activities expand beyond national jurisdictions to the high seas, there is an increasing need to consider anthropogenic impacts to species inhabiting these waters. The current scarcity of scientific observations of cetaceans in the high seas impedes the assessment of populationlevel impacts of these activities. We developed plausible density estimates to facilitate a quantitative assessment of anthropogenic impacts on cetacean populations in these waters. Our study region extended from a wellsurveyed region within the U.S. Exclusive Economic Zone into a large region of the western North Atlantic sparsely surveyed for cetaceans. We modeled densities of 15 cetacean taxa with available line transect survey data and habitat covariates and extrapolated predictions to sparsely surveyed regions. We formulated models to reduce the extent of extrapolation beyond covariate ranges, and constrained them to model simple and generalizable relationships. To evaluate confidence in the predictions, we mapped where predictions were made outside sampled covariate ranges, examined alternate models, and compared predicted densities with maps of sightings from sources that could not be integrated into our models. Confidence levels in model results depended on the taxon and geographic area and highlighted the need for additional surveying in environmentally distinct areas. With application of necessary caution, our density estimates can inform management needs in the high seas, such as the quantification of potential cetacean interactions with military training exercises, shipping, fisheries, and deepsea mining and be used to delineate areas of special biological significance in international waters. Our approach is generally applicable to other marine taxa and geographic regions for which management will be implemented but data are sparse.

Bystander effects and their implications for clinical radiation therapy : insights from multiscale in silico experiments
http://hdl.handle.net/10023/10615
Radiotherapy is a commonly used treatment for cancer and is usually given in varying doses. At low radiation doses relatively few cells die as a direct response to radiation but secondary radiation effects, such as DNA mutation or bystander phenomena, may affect many cells. Consequently it is at low radiation levels where an understanding of bystander effects is essential in designing novel therapies with superior clinical outcomes. In this article, we use a hybrid multiscale mathematical model to study the direct effects of radiation as well as radiationinduced bystander effects on both tumour cells and normal cells. We show that bystander responses play a major role in mediating radiation damage to cells at lowdoses of radiotherapy, doing more damage than that due to direct radiation. The survival curves derived from our computational simulations showed an area of hyperradiosensitivity at lowdoses that are not obtained using a traditional radiobiological model.
GGP and MAJC thank University of Dundee, where this research was carried out. The authors gratefully acknowledge the support of the ERC Advanced Investigator Grant 227619, M5CGS  From Mutations to Metastases: Multiscale Mathematical Modelling of Cancer Growth and Spread. AJM Acknowledges support from EU BIOMICS Project DGCNECT Contract 318202.
Thu, 21 Jul 2016 00:00:00 GMT
http://hdl.handle.net/10023/10615
20160721T00:00:00Z
Powathil, Gibin
Munro, Alastair John
Chaplain, Mark Andrew Joseph
Swat, Maciej
Radiotherapy is a commonly used treatment for cancer and is usually given in varying doses. At low radiation doses relatively few cells die as a direct response to radiation but secondary radiation effects, such as DNA mutation or bystander phenomena, may affect many cells. Consequently it is at low radiation levels where an understanding of bystander effects is essential in designing novel therapies with superior clinical outcomes. In this article, we use a hybrid multiscale mathematical model to study the direct effects of radiation as well as radiationinduced bystander effects on both tumour cells and normal cells. We show that bystander responses play a major role in mediating radiation damage to cells at lowdoses of radiotherapy, doing more damage than that due to direct radiation. The survival curves derived from our computational simulations showed an area of hyperradiosensitivity at lowdoses that are not obtained using a traditional radiobiological model.

Particle acceleration due to coronal nonnull magnetic reconnection
http://hdl.handle.net/10023/10551
Various topological features, for example magnetic nullpoints and separators, have been inferred as likely sites of magnetic reconnection and particle acceleration in the solar atmosphere. In fact, magnetic reconnection is not constrained to solely take place at or near such topological features and may also take place in the absence of such features. Studies of particle acceleration using nontopological reconnection experiments embedded in the solar atmosphere are uncommon. We aim to investigate and characterise particle behaviour in a model of magnetic reconnection which causes an arcade of solar coronal magnetic field to twist and form an erupting flux rope, crucially in the absence of any common topological features where reconnection is often thought to occur. We use a numerical scheme which evolves the gyroaveraged orbit equations of single electrons and protons in time and space, and simulate the gyromotion of particles in a fully analytical global field model. We observe and discuss how the magnetic and electric fields of the model and the initial conditions of each orbit may lead to acceleration of protons and electrons up to 2 MeV in energy (depending on model parameters). We describe the morphology of timedependent acceleration and impact sites for each particle species and compare our findings to those recovered by topologically based studies of threedimensional (3D) reconnection and particle acceleration. We also broadly compare aspects of our findings to general observational features typically seen during tworibbon flare events.
Wed, 01 Mar 2017 00:00:00 GMT
http://hdl.handle.net/10023/10551
20170301T00:00:00Z
Threlfall, James William
Neukirch, Thomas
Parnell, Clare Elizabeth
Various topological features, for example magnetic nullpoints and separators, have been inferred as likely sites of magnetic reconnection and particle acceleration in the solar atmosphere. In fact, magnetic reconnection is not constrained to solely take place at or near such topological features and may also take place in the absence of such features. Studies of particle acceleration using nontopological reconnection experiments embedded in the solar atmosphere are uncommon. We aim to investigate and characterise particle behaviour in a model of magnetic reconnection which causes an arcade of solar coronal magnetic field to twist and form an erupting flux rope, crucially in the absence of any common topological features where reconnection is often thought to occur. We use a numerical scheme which evolves the gyroaveraged orbit equations of single electrons and protons in time and space, and simulate the gyromotion of particles in a fully analytical global field model. We observe and discuss how the magnetic and electric fields of the model and the initial conditions of each orbit may lead to acceleration of protons and electrons up to 2 MeV in energy (depending on model parameters). We describe the morphology of timedependent acceleration and impact sites for each particle species and compare our findings to those recovered by topologically based studies of threedimensional (3D) reconnection and particle acceleration. We also broadly compare aspects of our findings to general observational features typically seen during tworibbon flare events.

Blockage of saline intrusions in restricted, twolayer exchange flows across a submerged sill obstruction
http://hdl.handle.net/10023/10543
Results are presented from a series of largescale experiments investigating the internal and nearbed dynamics of bidirectional stratified flows with a netbarotropic component across a submerged, trapezoidal, sill obstruction. Highresolution velocity and density profiles are obtained in the vicinity of the obstruction to observe internalflow dynamics under a range of parametric forcing conditions (i.e. variable saline and fresh water volume fluxes; density differences; sill obstruction submergence depths). Detailed synoptic velocity fields are measured across the sill crest using 2D particle image velocimetry, while the density structure of the twolayer exchange flows is measured using microconductivity probes at several sill locations. These measurements are designed to aid qualitative and quantitative interpretation of the internalflow processes associated with the lower saline intrusion layer blockage conditions, and indicate that the primary mechanism for this blockage is mass exchange from the saline intrusion layer due to significant interfacial mixing and entrainment under dominant, netbarotropic, flow conditions in the upper freshwater layer. This interfacial mixing is quantified by considering both the isopycnal separation of verticallysorted density profiles across the sill, as well as calculation of corresponding Thorpe overturning length scales. Analysis of the synoptic velocity fields and density profiles also indicates that the net exchange flow conditions remain subcritical (G < 1) across the sill for all parametric conditions tested. An analytical twolayer exchange flow model is then developed to include frictional and entrainment effects, both of which are needed to account for turbulent stresses and saline entrainment into the upper freshwater layer. The experimental results are used to validate two key model parameters: (1) the internalflow head loss associated with boundary friction and interfacial shear; and (2) the mass exchange from the lower saline layer into the upper fresh layer due to entrainment.
The work has been supported by European Community’s Seventh Framework Programme through the grant to the budget of the Integrating Activity HYDRALAB IV within the Transnational Access Activities, Contract No. 261520.
Thu, 23 Mar 2017 00:00:00 GMT
http://hdl.handle.net/10023/10543
20170323T00:00:00Z
Cuthbertson, Alan
Laanearu, Janek
Carr, Magda
Sommeria, Joel
Viboud, Samuel
Results are presented from a series of largescale experiments investigating the internal and nearbed dynamics of bidirectional stratified flows with a netbarotropic component across a submerged, trapezoidal, sill obstruction. Highresolution velocity and density profiles are obtained in the vicinity of the obstruction to observe internalflow dynamics under a range of parametric forcing conditions (i.e. variable saline and fresh water volume fluxes; density differences; sill obstruction submergence depths). Detailed synoptic velocity fields are measured across the sill crest using 2D particle image velocimetry, while the density structure of the twolayer exchange flows is measured using microconductivity probes at several sill locations. These measurements are designed to aid qualitative and quantitative interpretation of the internalflow processes associated with the lower saline intrusion layer blockage conditions, and indicate that the primary mechanism for this blockage is mass exchange from the saline intrusion layer due to significant interfacial mixing and entrainment under dominant, netbarotropic, flow conditions in the upper freshwater layer. This interfacial mixing is quantified by considering both the isopycnal separation of verticallysorted density profiles across the sill, as well as calculation of corresponding Thorpe overturning length scales. Analysis of the synoptic velocity fields and density profiles also indicates that the net exchange flow conditions remain subcritical (G < 1) across the sill for all parametric conditions tested. An analytical twolayer exchange flow model is then developed to include frictional and entrainment effects, both of which are needed to account for turbulent stresses and saline entrainment into the upper freshwater layer. The experimental results are used to validate two key model parameters: (1) the internalflow head loss associated with boundary friction and interfacial shear; and (2) the mass exchange from the lower saline layer into the upper fresh layer due to entrainment.

Contribution of modecoupling and phasemixing of Alfvén waves to coronal heating
http://hdl.handle.net/10023/10517
Context. Phasemixing of Alfvén waves in the solar corona has been identified as one possible candidate to explain coronal heating. While this scenario is supported by observations of ubiquitous oscillations in the corona carrying sufficient wave energy and by theoretical models that have described the concentration of energy in smallscale structures, it is still unclear whether this wave energy can be converted into thermal energy in order to maintain the milliondegree hot solar corona. Aims. The aim of this work is to assess how much energy can be converted into thermal energy by a phasemixing process triggered by the propagation of Alfvénic waves in a cylindric coronal structure, such as a coronal loop, and to estimate the impact of this conversion on the coronal heating and thermal structure of the solar corona. Methods. To this end, we ran 3D MHD simulations of a magnetised cylinder where the Alfvén speed varies through a boundary shell, and a footpoint driver is set to trigger kink modes that mode couple to torsional Alfvén modes in the boundary shell. These Alfvén waves are expected to phasemix, and the system allows us to study the subsequent thermal energy deposition. We ran a reference simulation to explain the main process and then we varied the simulation parameters, such as the size of the boundary shell, its structure, and the persistence of the driver. Results. When we take high values of magnetic resistivity and strong footpoint drivers into consideration, we find that i) phasemixing leads to a temperature increase of the order of 105 K or less, depending on the structure of the boundary shell, ii) this energy is able to balance the radiative losses only in the localised region involved in the heating, and iii) we can determine the influence of the boundary layer and the persistence of the driver on the thermal structure of the system. Conclusions. Our conclusion is that as a result of the extreme physical parameters we adopted and the moderate impact on the heating of the system, it is unlikely that phasemixing can contribute on a global scale to the heating of the solar corona.
This research has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 647214) and from the UK Science and Technology Facilities Council. This work used the DiRAC Data Centric system at Durham University, operated by the Institute for Computational Cosmology on behalf of the STFC DiRAC HPC Facility (www.dirac.ac.uk. This equipment was funded by a BIS National Einfrastructure capital grant ST/K00042X/1, STFC capital grant ST/K00087X/1, DiRAC Operations grant ST/K003267/1 and Durham University.
Fri, 12 May 2017 00:00:00 GMT
http://hdl.handle.net/10023/10517
20170512T00:00:00Z
Pagano, P.
De Moortel, I.
Context. Phasemixing of Alfvén waves in the solar corona has been identified as one possible candidate to explain coronal heating. While this scenario is supported by observations of ubiquitous oscillations in the corona carrying sufficient wave energy and by theoretical models that have described the concentration of energy in smallscale structures, it is still unclear whether this wave energy can be converted into thermal energy in order to maintain the milliondegree hot solar corona. Aims. The aim of this work is to assess how much energy can be converted into thermal energy by a phasemixing process triggered by the propagation of Alfvénic waves in a cylindric coronal structure, such as a coronal loop, and to estimate the impact of this conversion on the coronal heating and thermal structure of the solar corona. Methods. To this end, we ran 3D MHD simulations of a magnetised cylinder where the Alfvén speed varies through a boundary shell, and a footpoint driver is set to trigger kink modes that mode couple to torsional Alfvén modes in the boundary shell. These Alfvén waves are expected to phasemix, and the system allows us to study the subsequent thermal energy deposition. We ran a reference simulation to explain the main process and then we varied the simulation parameters, such as the size of the boundary shell, its structure, and the persistence of the driver. Results. When we take high values of magnetic resistivity and strong footpoint drivers into consideration, we find that i) phasemixing leads to a temperature increase of the order of 105 K or less, depending on the structure of the boundary shell, ii) this energy is able to balance the radiative losses only in the localised region involved in the heating, and iii) we can determine the influence of the boundary layer and the persistence of the driver on the thermal structure of the system. Conclusions. Our conclusion is that as a result of the extreme physical parameters we adopted and the moderate impact on the heating of the system, it is unlikely that phasemixing can contribute on a global scale to the heating of the solar corona.

Imaging observations of magnetic reconnection in a solar eruptive flare
http://hdl.handle.net/10023/10486
Solar flares are among the most energetic events in the solar atmosphere. It is widely accepted that flares are powered by magnetic reconnection in the corona. An eruptive flare is usually accompanied by a coronal mass ejection, both of which are probably driven by the eruption of a magnetic flux rope (MFR). Here we report an eruptive flare on 2016 March 23 observed by the Atmospheric Imaging Assembly on board the Solar Dynamics Observatory. The extremeultraviolet imaging observations exhibit the clear rise and eruption of an MFR. In particular, the observations reveal solid evidence of magnetic reconnection from both the corona and chromosphere during the flare. Moreover, weak reconnection is observed before the start of the flare. We find that the preflare weak reconnection is of tethercutting type and helps the MFR to rise slowly. Induced by a further rise of the MFR, strong reconnection occurs in the rise phases of the flare, which is temporally related to the MFR eruption. We also find that the magnetic reconnection is more of 3Dtype in the early phase, as manifested in a strongtoweak shear transition in flare loops, and becomes more 2Dlike in the later phase, as shown by the apparent rising motion of an arcade of flare loops.
Tue, 31 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10023/10486
20170131T00:00:00Z
Li, Y.
Sun, X.
Ding, M. D.
Qiu, J.
Priest, E. R.
Solar flares are among the most energetic events in the solar atmosphere. It is widely accepted that flares are powered by magnetic reconnection in the corona. An eruptive flare is usually accompanied by a coronal mass ejection, both of which are probably driven by the eruption of a magnetic flux rope (MFR). Here we report an eruptive flare on 2016 March 23 observed by the Atmospheric Imaging Assembly on board the Solar Dynamics Observatory. The extremeultraviolet imaging observations exhibit the clear rise and eruption of an MFR. In particular, the observations reveal solid evidence of magnetic reconnection from both the corona and chromosphere during the flare. Moreover, weak reconnection is observed before the start of the flare. We find that the preflare weak reconnection is of tethercutting type and helps the MFR to rise slowly. Induced by a further rise of the MFR, strong reconnection occurs in the rise phases of the flare, which is temporally related to the MFR eruption. We also find that the magnetic reconnection is more of 3Dtype in the early phase, as manifested in a strongtoweak shear transition in flare loops, and becomes more 2Dlike in the later phase, as shown by the apparent rising motion of an arcade of flare loops.

The effects of resistivity and viscosity on the KelvinHelmholtz instability in oscillating coronal loops
http://hdl.handle.net/10023/10450
Aims. Investigate the effects of resistivity and viscosity on the onset and growth of the KelvinHelmholtz instability (KHI) in an oscillating coronal loop. Methods. We modelled a standing kink wave in a densityenhanced loop with the three dimensional (3D), resistive magnetohydrodynamics code, Lare3d. We conducted a parameter study on the viscosity and resistivity coefficients to examine the effects of dissipation on the KHI. Results. Enhancing the viscosity (ν) and resistivity (η) acts to suppress the KHI. Larger values of ν and η delay the formation of the instability and, in some cases, prevent the onset completely. This leads to the earlier onset of heating for smaller values of the transport coefficients. We note that viscosity has a greater effect on the development of the KHI than resistivity. Furthermore, when using anomalous resistivity, the Ohmic heating rate associated with the KHI may be greater than that associated with the phase mixing that occurs in an instabilitysuppressed regime (using uniform resistivity). Conclusions. From our study, it is clear that the heating rate crucially depends on the formation of small length scales (influenced by the numerical resolution) as well as the values of resistivity and viscosity. As larger values of the transport coefficients suppress the KHI, the onset of heating is delayed but the heating rate is larger. As increased numerical resolution allows smaller length scales to develop, the heating rate will be higher even for the same values of η and ν.
The research leading to these results has received funding from the UK Science and Technology Facilities Council and the European Union Horizon 2020 research and innovation programme (grant agreement No. 647214).
Fri, 16 Jun 2017 00:00:00 GMT
http://hdl.handle.net/10023/10450
20170616T00:00:00Z
Howson, T. A.
De Moortel, I.
Antolin, P.
Aims. Investigate the effects of resistivity and viscosity on the onset and growth of the KelvinHelmholtz instability (KHI) in an oscillating coronal loop. Methods. We modelled a standing kink wave in a densityenhanced loop with the three dimensional (3D), resistive magnetohydrodynamics code, Lare3d. We conducted a parameter study on the viscosity and resistivity coefficients to examine the effects of dissipation on the KHI. Results. Enhancing the viscosity (ν) and resistivity (η) acts to suppress the KHI. Larger values of ν and η delay the formation of the instability and, in some cases, prevent the onset completely. This leads to the earlier onset of heating for smaller values of the transport coefficients. We note that viscosity has a greater effect on the development of the KHI than resistivity. Furthermore, when using anomalous resistivity, the Ohmic heating rate associated with the KHI may be greater than that associated with the phase mixing that occurs in an instabilitysuppressed regime (using uniform resistivity). Conclusions. From our study, it is clear that the heating rate crucially depends on the formation of small length scales (influenced by the numerical resolution) as well as the values of resistivity and viscosity. As larger values of the transport coefficients suppress the KHI, the onset of heating is delayed but the heating rate is larger. As increased numerical resolution allows smaller length scales to develop, the heating rate will be higher even for the same values of η and ν.

Geostrophic tripolar vortices in a twolayer fluid : linear stability and nonlinear evolution of equilibria
http://hdl.handle.net/10023/10411
We investgate equilibrium solutions for tripolar vortices in a twolayer quasigeostrophic flow. Two of the vortices are likesigned and lie in one layer. An oppositesigned vortex lies in the other layer. The families of equilibria can be spanned by the distance (called separation) between the two likesigned vortices. Two equilibrium configurations are possible when the oppositesigned vortex lies between the two other vortices. In the first configuration (called ordinary roundabout), the opposite signed vortex is equidistant to the two other vortices. In the second configuration (eccentric roundabouts), the distances are unequal. We determine the equilibria numerically and describe their characteristics for various internal deformation radii. The two branches of equilibria can coexist and intersect for small deformation radii. Then, the eccentric roundabouts are stable while unstable ordinary roundabouts can be found. Indeed, ordinary roundabouts exist at smaller separations than eccentric roundabouts do, thus inducing stronger vortex interactions. However, for larger deformation radii, eccentric roundabouts can also be unstable. Then, the two branches of equilibria do not cross. The branch of eccentric roundabouts only exists for large separations. Near the end of the branch of eccentric roundabouts (at the smallest separation), one of the likesigned vortices exhibits a sharp inner corner where instabilities can be triggered. Finally, we investigate of the nonlinear evolution of a few selected cases of tripoles.
Wed, 01 Mar 2017 00:00:00 GMT
http://hdl.handle.net/10023/10411
20170301T00:00:00Z
Reinaud, Jean Noel
Sokolovskiy, Mikhail
Carton, Xavier
We investgate equilibrium solutions for tripolar vortices in a twolayer quasigeostrophic flow. Two of the vortices are likesigned and lie in one layer. An oppositesigned vortex lies in the other layer. The families of equilibria can be spanned by the distance (called separation) between the two likesigned vortices. Two equilibrium configurations are possible when the oppositesigned vortex lies between the two other vortices. In the first configuration (called ordinary roundabout), the opposite signed vortex is equidistant to the two other vortices. In the second configuration (eccentric roundabouts), the distances are unequal. We determine the equilibria numerically and describe their characteristics for various internal deformation radii. The two branches of equilibria can coexist and intersect for small deformation radii. Then, the eccentric roundabouts are stable while unstable ordinary roundabouts can be found. Indeed, ordinary roundabouts exist at smaller separations than eccentric roundabouts do, thus inducing stronger vortex interactions. However, for larger deformation radii, eccentric roundabouts can also be unstable. Then, the two branches of equilibria do not cross. The branch of eccentric roundabouts only exists for large separations. Near the end of the branch of eccentric roundabouts (at the smallest separation), one of the likesigned vortices exhibits a sharp inner corner where instabilities can be triggered. Finally, we investigate of the nonlinear evolution of a few selected cases of tripoles.

A general setting for symmetric distributions and their relationship to general distributions
http://hdl.handle.net/10023/10370
A standard method of obtaining nonsymmetrical distributions is that of modulating symmetrical distributions by multiplying the densities by a perturbation factor. This has been considered mainly for central symmetry of a Euclidean space in the origin. This paper enlarges the concept of modulation to the general setting of symmetry under the action of a compact topological group on the sample space. The main structural result relates the density of an arbitrary distribution to the density of the corresponding symmetrised distribution. Some general methods for constructing modulating functions are considered. The effect that transformations of the sample space have on symmetry of distributions is investigated. The results are illustrated by general examples, many of them in the setting of directional statistics.
Wed, 01 Jun 2016 00:00:00 GMT
http://hdl.handle.net/10023/10370
20160601T00:00:00Z
Jupp, P.E.
Regoli, G.
Azzalini, A.
A standard method of obtaining nonsymmetrical distributions is that of modulating symmetrical distributions by multiplying the densities by a perturbation factor. This has been considered mainly for central symmetry of a Euclidean space in the origin. This paper enlarges the concept of modulation to the general setting of symmetry under the action of a compact topological group on the sample space. The main structural result relates the density of an arbitrary distribution to the density of the corresponding symmetrised distribution. Some general methods for constructing modulating functions are considered. The effect that transformations of the sample space have on symmetry of distributions is investigated. The results are illustrated by general examples, many of them in the setting of directional statistics.

Logarithmic improvement of regularity criteria for the NavierStokes equations in terms of pressure
http://hdl.handle.net/10023/10319
In this article we prove a logarithmic improvement of regularity criteria in the multiplier spaces for the Cauchy problem of the incompressible NavierStokes equations in terms of pressure. This improves the main result in [S. Benbernou, A note on the regularity criterion in terms of pressure for the NavierStokes equations, Applied Mathematics Letters 22 (2009) 1438–1443].
XY is partially supported by a grant from NSERC.
Mon, 01 Aug 2016 00:00:00 GMT
http://hdl.handle.net/10023/10319
20160801T00:00:00Z
Tran, Chuong Van
Yu, Xinwei
In this article we prove a logarithmic improvement of regularity criteria in the multiplier spaces for the Cauchy problem of the incompressible NavierStokes equations in terms of pressure. This improves the main result in [S. Benbernou, A note on the regularity criterion in terms of pressure for the NavierStokes equations, Applied Mathematics Letters 22 (2009) 1438–1443].

A combined theory for magnetohydrodynamic equilibria with anisotropic pressure and magnetic shear
http://hdl.handle.net/10023/10305
We present a new approach to the theory of magnetohydrodynamic equilibria with anisotropic pressure, magnetic shear and translational/rotational invariance. This approach involves combining two existing formalisms in order to eliminate their individual weaknesses. The theoretical aspects of the method are explored in detail along with numerical solutions which make use of the method. Eventually, this method could be applied to model various plasma systems, such as planetary magnetospheres.
Grant numbers: Science and Technology Facilities Council via Doctoral Training Grant [ST/K502327/1], Consolidated Grant [ST/K000950/1] and Consolidated Grant [ST/N000609/1].
Fri, 10 Mar 2017 00:00:00 GMT
http://hdl.handle.net/10023/10305
20170310T00:00:00Z
Hodgson, Jonathan David Brockie
Neukirch, Thomas
We present a new approach to the theory of magnetohydrodynamic equilibria with anisotropic pressure, magnetic shear and translational/rotational invariance. This approach involves combining two existing formalisms in order to eliminate their individual weaknesses. The theoretical aspects of the method are explored in detail along with numerical solutions which make use of the method. Eventually, this method could be applied to model various plasma systems, such as planetary magnetospheres.

Observations and modelling of the preflare period of the 29 March 2014 X1 flare
http://hdl.handle.net/10023/10298
On the 29 March 2014 NOAA active region (AR) 12017 produced an X1 flare which was simultaneously observed by an unprecedented number of observatories. We have investigated the preflare period of this flare from 14:00 UT until 19:00 UT using joint observations made by the Interface Region Imaging Spectrometer (IRIS) and the Hinode Extreme Ultraviolet Imaging Spectrometer (EIS). Spectral lines providing coverage of the solar atmosphere from chromosphere to the corona were analysed to investigate preflare activity within the AR. The results of the investigation have revealed evidence of strongly blueshifted plasma flows, with velocities up to 200 km1, being observed 40 minutes prior to flaring. These flows are located along the filament present in the active region and are both spatially discrete and transient. In order to constrain the possible explanations for this activity, we undertake nonpotential magnetic field modelling of the active region. This modelling indicates the existence of a weakly twisted flux rope along the polarity inversion line in the region where a filament and the strong preflare flows are observed. We then discuss how these observations relate to the current models of flare triggering. We conclude that the most likely drivers of the observed activity are internal reconnection in the flux rope, early onset of the flare reconnection, or tether cutting reconnection along the filament.
MMW and SD acknowledge STFC for support via their PhD Studentships. DML is an EarlyCareer Fellow, funded by the Leverhulme Trust.
Wed, 01 Feb 2017 00:00:00 GMT
http://hdl.handle.net/10023/10298
20170201T00:00:00Z
Woods, M. M.
Harra, L. K.
Matthews, S. A.
Mackay, D. H.
Dacie, S.
Long, D. M.
On the 29 March 2014 NOAA active region (AR) 12017 produced an X1 flare which was simultaneously observed by an unprecedented number of observatories. We have investigated the preflare period of this flare from 14:00 UT until 19:00 UT using joint observations made by the Interface Region Imaging Spectrometer (IRIS) and the Hinode Extreme Ultraviolet Imaging Spectrometer (EIS). Spectral lines providing coverage of the solar atmosphere from chromosphere to the corona were analysed to investigate preflare activity within the AR. The results of the investigation have revealed evidence of strongly blueshifted plasma flows, with velocities up to 200 km1, being observed 40 minutes prior to flaring. These flows are located along the filament present in the active region and are both spatially discrete and transient. In order to constrain the possible explanations for this activity, we undertake nonpotential magnetic field modelling of the active region. This modelling indicates the existence of a weakly twisted flux rope along the polarity inversion line in the region where a filament and the strong preflare flows are observed. We then discuss how these observations relate to the current models of flare triggering. We conclude that the most likely drivers of the observed activity are internal reconnection in the flux rope, early onset of the flare reconnection, or tether cutting reconnection along the filament.

Forward modeling of standing slow modes in flaring coronal loops
http://hdl.handle.net/10023/10295
Standing slowmode waves in hot flaring loops are exclusively observed in spectrometers and are used to diagnose the magnetic field strength and temperature of the loop structure. Owing to the lack of spatial information, the longitudinal mode cannot be effectively identified. In this study, we simulate standing slowmode waves in flaring loops and compare the synthesized line emission properties with Solar Ultraviolet Measurements of Emitted Radiation spectrographic and Solar Dynamics Observatory/Atmospheric Imaging Assembly imaging observations. We find that the emission intensity and line width oscillations are a quarter period out of phase with Doppler shift velocity in both time and spatial domain, which can be used to identify a standing slowmode wave from spectroscopic observations. However, the longitudinal overtones could only be measured with the assistance of imagers. We find emission intensity asymmetry in the positive and negative modulations; this is because the contribution function pertaining to the atomic emission process responds differently to positive and negative temperature variations. One may detect half periodicity close to the loop apex, where emission intensity modulation is relatively small. The lineofsight projection affects the observation of Doppler shift significantly. A more accurate estimate of the amplitude of velocity perturbation is obtained by deprojecting the Doppler shift by a factor of 1–2θ/π rather than the traditionally used cosθ. If a loop is heated to the hotter wing, the intensity modulation could be overwhelmed by background emission, while the Doppler shift velocity could still be detected to a certain extent.
Thu, 02 Jul 2015 00:00:00 GMT
http://hdl.handle.net/10023/10295
20150702T00:00:00Z
Yuan, D.
Van Doorsselaere, T.
Banerjee, D.
Antolin, P.
Standing slowmode waves in hot flaring loops are exclusively observed in spectrometers and are used to diagnose the magnetic field strength and temperature of the loop structure. Owing to the lack of spatial information, the longitudinal mode cannot be effectively identified. In this study, we simulate standing slowmode waves in flaring loops and compare the synthesized line emission properties with Solar Ultraviolet Measurements of Emitted Radiation spectrographic and Solar Dynamics Observatory/Atmospheric Imaging Assembly imaging observations. We find that the emission intensity and line width oscillations are a quarter period out of phase with Doppler shift velocity in both time and spatial domain, which can be used to identify a standing slowmode wave from spectroscopic observations. However, the longitudinal overtones could only be measured with the assistance of imagers. We find emission intensity asymmetry in the positive and negative modulations; this is because the contribution function pertaining to the atomic emission process responds differently to positive and negative temperature variations. One may detect half periodicity close to the loop apex, where emission intensity modulation is relatively small. The lineofsight projection affects the observation of Doppler shift significantly. A more accurate estimate of the amplitude of velocity perturbation is obtained by deprojecting the Doppler shift by a factor of 1–2θ/π rather than the traditionally used cosθ. If a loop is heated to the hotter wing, the intensity modulation could be overwhelmed by background emission, while the Doppler shift velocity could still be detected to a certain extent.

Resonant absorption of transverse oscillations and associated heating in a solar prominence. I. Observational aspects
http://hdl.handle.net/10023/10294
Transverse magnetohydrodynamic waves have been shown to be ubiquitous in the solar atmosphere and can, in principle, carry sufficient energy to generate and maintain the Sun's milliondegree outer atmosphere or corona. However, direct evidence of the dissipation process of these waves and subsequent heating has not yet been directly observed. Here we report on high spatial, temporal, and spectral resolution observations of a solar prominence that show a compelling signature of socalled resonant absorption, a long hypothesized mechanism to efficiently convert and dissipate transverse wave energy into heat. Aside from coherence in the transverse direction, our observations show telltale phase differences around 180° between transverse motions in the planeofsky and lineofsight velocities of the oscillating fine structures or threads, and also suggest significant heating from chromospheric to higher temperatures. Comparison with advanced numerical simulations support a scenario in which transverse oscillations trigger a Kelvin–Helmholtz instability (KHI) at the boundaries of oscillating threads via resonant absorption. This instability leads to numerous thin current sheets in which wave energy is dissipated and plasma is heated. Our results provide direct evidence for waverelated heating in action, one of the candidate coronal heating mechanisms.
Tue, 11 Aug 2015 00:00:00 GMT
http://hdl.handle.net/10023/10294
20150811T00:00:00Z
Okamoto, Takenori J.
Antolin, Patrick
De Pontieu, Bart
Uitenbroek, Han
Van Doorsselaere, Tom
Yokoyama, Takaaki
Transverse magnetohydrodynamic waves have been shown to be ubiquitous in the solar atmosphere and can, in principle, carry sufficient energy to generate and maintain the Sun's milliondegree outer atmosphere or corona. However, direct evidence of the dissipation process of these waves and subsequent heating has not yet been directly observed. Here we report on high spatial, temporal, and spectral resolution observations of a solar prominence that show a compelling signature of socalled resonant absorption, a long hypothesized mechanism to efficiently convert and dissipate transverse wave energy into heat. Aside from coherence in the transverse direction, our observations show telltale phase differences around 180° between transverse motions in the planeofsky and lineofsight velocities of the oscillating fine structures or threads, and also suggest significant heating from chromospheric to higher temperatures. Comparison with advanced numerical simulations support a scenario in which transverse oscillations trigger a Kelvin–Helmholtz instability (KHI) at the boundaries of oscillating threads via resonant absorption. This instability leads to numerous thin current sheets in which wave energy is dissipated and plasma is heated. Our results provide direct evidence for waverelated heating in action, one of the candidate coronal heating mechanisms.

Resonant absorption of transverse oscillations and associated heating in a solar prominence. II. Numerical aspects
http://hdl.handle.net/10023/10293
Transverse magnetohydrodynamic (MHD) waves are ubiquitous in the solar atmosphere and may be responsible for generating the Sun's milliondegree outer atmosphere. However, direct evidence of the dissipation process and heating from these waves remains elusive. Through advanced numerical simulations combined with appropriate forward modeling of a prominence flux tube, we provide the observational signatures of transverse MHD waves in prominence plasmas. We show that these signatures are characterized by a threadlike substructure, strong transverse dynamical coherence, an outofphase difference between planeofthesky motions and lineofsight velocities, and enhanced line broadening and heating around most of the flux tube. A complex combination between resonant absorption and Kelvin–Helmholtz instabilities (KHIs) takes place in which the KHI extracts the energy from the resonant layer and dissipates it through vortices and current sheets, which rapidly degenerate into turbulence. An inward enlargement of the boundary is produced in which the turbulent flows conserve the characteristic dynamics from the resonance, therefore guaranteeing detectability of the resonance imprints. We show that the features described in the accompanying paper through coordinated Hinode and Interface Region Imaging Spectrograph observations match the numerical results well.
Tue, 11 Aug 2015 00:00:00 GMT
http://hdl.handle.net/10023/10293
20150811T00:00:00Z
Antolin, P.
Okamoto, T. J.
De Pontieu, B.
Uitenbroek, H.
Van Doorsselaere, T.
Yokoyama, T.
Transverse magnetohydrodynamic (MHD) waves are ubiquitous in the solar atmosphere and may be responsible for generating the Sun's milliondegree outer atmosphere. However, direct evidence of the dissipation process and heating from these waves remains elusive. Through advanced numerical simulations combined with appropriate forward modeling of a prominence flux tube, we provide the observational signatures of transverse MHD waves in prominence plasmas. We show that these signatures are characterized by a threadlike substructure, strong transverse dynamical coherence, an outofphase difference between planeofthesky motions and lineofsight velocities, and enhanced line broadening and heating around most of the flux tube. A complex combination between resonant absorption and Kelvin–Helmholtz instabilities (KHIs) takes place in which the KHI extracts the energy from the resonant layer and dissipates it through vortices and current sheets, which rapidly degenerate into turbulence. An inward enlargement of the boundary is produced in which the turbulent flows conserve the characteristic dynamics from the resonance, therefore guaranteeing detectability of the resonance imprints. We show that the features described in the accompanying paper through coordinated Hinode and Interface Region Imaging Spectrograph observations match the numerical results well.

Hα and EUV observations of a partial CME
http://hdl.handle.net/10023/10291
We have obtained Hα high spatial and time resolution observations of the upper solar chromosphere and supplemented these with multiwavelength observations from the Solar Dynamics Observatory (SDO) and the Hinode Extremeultraviolet Imaging Spectrometer. The Hα observations were conducted on 2012 February 11 with the HydrogenAlpha Rapid Dynamics Camera instrument at the National Solar Observatory's Dunn Solar Telescope. Our Hα observations found large downflows of chromospheric material returning from coronal heights following a failed prominence eruption. We have detected several large condensations ("blobs") returning to the solar surface at velocities of ≈200 km s−1 in both Hα and several SDO Atmospheric Imaging Assembly band passes. The average derived size of these "blobs" in Hα is 500 by 3000 km2 in the directions perpendicular and parallel to the direction of travel, respectively. A comparison of our "blob" widths to those found from coronal rain, indicate that there are additional, smaller, unresolved "blobs" in agreement with previous studies and recent numerical simulations. Our observed velocities and decelerations of the "blobs" in both Hα and SDO bands are less than those expected for gravitational freefall and imply additional magnetic or gas pressure impeding the flow. We derived a kinetic energy of ≈2 orders of magnitude lower for the main eruption than a typical coronal mass ejection, which may explain its partial nature.
Tue, 12 May 2015 00:00:00 GMT
http://hdl.handle.net/10023/10291
20150512T00:00:00Z
Christian, Damian J.
Jess, David B.
Antolin, Patrick
Mathioudakis, Mihalis
We have obtained Hα high spatial and time resolution observations of the upper solar chromosphere and supplemented these with multiwavelength observations from the Solar Dynamics Observatory (SDO) and the Hinode Extremeultraviolet Imaging Spectrometer. The Hα observations were conducted on 2012 February 11 with the HydrogenAlpha Rapid Dynamics Camera instrument at the National Solar Observatory's Dunn Solar Telescope. Our Hα observations found large downflows of chromospheric material returning from coronal heights following a failed prominence eruption. We have detected several large condensations ("blobs") returning to the solar surface at velocities of ≈200 km s−1 in both Hα and several SDO Atmospheric Imaging Assembly band passes. The average derived size of these "blobs" in Hα is 500 by 3000 km2 in the directions perpendicular and parallel to the direction of travel, respectively. A comparison of our "blob" widths to those found from coronal rain, indicate that there are additional, smaller, unresolved "blobs" in agreement with previous studies and recent numerical simulations. Our observed velocities and decelerations of the "blobs" in both Hα and SDO bands are less than those expected for gravitational freefall and imply additional magnetic or gas pressure impeding the flow. We derived a kinetic energy of ≈2 orders of magnitude lower for the main eruption than a typical coronal mass ejection, which may explain its partial nature.

The multithermal and multistranded nature of coronal rain
http://hdl.handle.net/10023/10290
We analyze coordinated observations of coronal rain in loops, spanning chromospheric, transition region (TR), and coronal temperatures with subarcsecond spatial resolution. Coronal rain is found to be a highly multithermal phenomenon with a high degree of cospatiality in the multiwavelength emission. EUV darkening and quasiperiodic intensity variations are found to be strongly correlated with coronal rain showers. Progressive cooling of coronal rain is observed, leading to a height dependence of the emission. A fastslow twostep catastrophic cooling progression is found, which may reflect the transition to optically thick plasma states. The intermittent and clumpy appearance of coronal rain at coronal heights becomes more continuous and persistent at chromospheric heights just before impact, mainly due to a funnel effect from the observed expansion of the magnetic field. Strong density inhomogeneities of 0.″20.″5 are found, in which a transition from temperatures of 105 to 104 K occurs. The 0.″20.″8 width of the distribution of coronal rain is found to be independent of temperature. The sharp increase in the number of clumps at the coolest temperatures, especially at higher resolution, suggests that the bulk distribution of the rain remains undetected. Rain clumps appear organized in strands in both chromospheric and TR temperatures. We further find structure reminiscent of the magnetohydrodynamic (MHD) thermal mode (also known as entropy mode), thereby suggesting an important role of thermal instability in shaping the basic loop substructure. Rain core densities are estimated to vary between 2 × 1010 and 2.5 × 1011cm−3, leading to significant downward mass fluxes per loop of 1–5 × 109 g s−1, thus suggesting a major role in the chromospherecorona mass cycle.
Tue, 09 Jun 2015 00:00:00 GMT
http://hdl.handle.net/10023/10290
20150609T00:00:00Z
Antolin, P.
Vissers, G.
Pereira, T. M. D.
Rouppe van der Voort, L.
Scullion, E.
We analyze coordinated observations of coronal rain in loops, spanning chromospheric, transition region (TR), and coronal temperatures with subarcsecond spatial resolution. Coronal rain is found to be a highly multithermal phenomenon with a high degree of cospatiality in the multiwavelength emission. EUV darkening and quasiperiodic intensity variations are found to be strongly correlated with coronal rain showers. Progressive cooling of coronal rain is observed, leading to a height dependence of the emission. A fastslow twostep catastrophic cooling progression is found, which may reflect the transition to optically thick plasma states. The intermittent and clumpy appearance of coronal rain at coronal heights becomes more continuous and persistent at chromospheric heights just before impact, mainly due to a funnel effect from the observed expansion of the magnetic field. Strong density inhomogeneities of 0.″20.″5 are found, in which a transition from temperatures of 105 to 104 K occurs. The 0.″20.″8 width of the distribution of coronal rain is found to be independent of temperature. The sharp increase in the number of clumps at the coolest temperatures, especially at higher resolution, suggests that the bulk distribution of the rain remains undetected. Rain clumps appear organized in strands in both chromospheric and TR temperatures. We further find structure reminiscent of the magnetohydrodynamic (MHD) thermal mode (also known as entropy mode), thereby suggesting an important role of thermal instability in shaping the basic loop substructure. Rain core densities are estimated to vary between 2 × 1010 and 2.5 × 1011cm−3, leading to significant downward mass fluxes per loop of 1–5 × 109 g s−1, thus suggesting a major role in the chromospherecorona mass cycle.

Unresolved finescale structure in solar coronal looptops
http://hdl.handle.net/10023/10288
New and advanced spacebased observing facilities continue to lower the resolution limit and detect solar coronal loops in greater detail. We continue to discover even finer substructures within coronal loop crosssections, in order to understand the nature of the solar corona. Here, we push this lower limit further to search for the finest coronal loop substructures, through taking advantage of the resolving power of the Swedish 1 m Solar Telescope/CRisp Imaging SpectroPolarimeter (CRISP), together with coobservations from the Solar Dynamics Observatory/Atmospheric Image Assembly (AIA). Highresolution imaging of the chromospheric Hα 656.28 nm spectral line core and wings can, under certain circumstances, allow one to deduce the topology of the local magnetic environment of the solar atmosphere where its observed. Here, we study postflare coronal loops, which become filled with evaporated chromosphere that rapidly condenses into chromospheric clumps of plasma (detectable in Hα) known as a coronal rain, to investigate their finescale structure. We identify, through analysis of three data sets, largescale catastrophic cooling in coronal looptops and the existence of multithermal, multistranded substructures. Many cool strands even extend fully intact from looptop to footpoint. We discover that coronal loop finescale strands can appear bunched with as many as eight parallel strands within an AIA coronal loop crosssection. The strand number density versus crosssectional width distribution, as detected by CRISP within AIAdefined coronal loops, most likely peaks at well below 100 km, and currently, 69% of the substructure strands are statistically unresolved in AIA coronal loops.
Mon, 24 Nov 2014 00:00:00 GMT
http://hdl.handle.net/10023/10288
20141124T00:00:00Z
Scullion, E.
Rouppe van der Voort, L.
Wedemeyer, S.
Antolin, P.
New and advanced spacebased observing facilities continue to lower the resolution limit and detect solar coronal loops in greater detail. We continue to discover even finer substructures within coronal loop crosssections, in order to understand the nature of the solar corona. Here, we push this lower limit further to search for the finest coronal loop substructures, through taking advantage of the resolving power of the Swedish 1 m Solar Telescope/CRisp Imaging SpectroPolarimeter (CRISP), together with coobservations from the Solar Dynamics Observatory/Atmospheric Image Assembly (AIA). Highresolution imaging of the chromospheric Hα 656.28 nm spectral line core and wings can, under certain circumstances, allow one to deduce the topology of the local magnetic environment of the solar atmosphere where its observed. Here, we study postflare coronal loops, which become filled with evaporated chromosphere that rapidly condenses into chromospheric clumps of plasma (detectable in Hα) known as a coronal rain, to investigate their finescale structure. We identify, through analysis of three data sets, largescale catastrophic cooling in coronal looptops and the existence of multithermal, multistranded substructures. Many cool strands even extend fully intact from looptop to footpoint. We discover that coronal loop finescale strands can appear bunched with as many as eight parallel strands within an AIA coronal loop crosssection. The strand number density versus crosssectional width distribution, as detected by CRISP within AIAdefined coronal loops, most likely peaks at well below 100 km, and currently, 69% of the substructure strands are statistically unresolved in AIA coronal loops.

First highresolution spectroscopic observations of an erupting prominence within a coronal mass ejection by the Interface Region Imaging Spectrograph (IRIS)
http://hdl.handle.net/10023/10287
Spectroscopic observations of prominence eruptions associated with coronal mass ejections (CMEs), although relatively rare, can provide valuable plasma and threedimensional geometry diagnostics. We report the first observations by the Interface Region Imaging Spectrograph mission of a spectacular fast CME/prominence eruption associated with an equivalent X1.6 flare on 2014 May 9. The maximum planeofsky and Doppler velocities of the eruption are 1200 and 460 km s−1, respectively. There are two eruption components separated by ~200 km s−1 in Doppler velocity: a primary, bright component and a secondary, faint component, suggesting a hollow, rather than solid, coneshaped distribution of material. The eruption involves a lefthanded helical structure undergoing counterclockwise (viewed topdown) unwinding motion. There is a temporal evolution from upward eruption to downward fallback with lessthanfreefall speeds and decreasing nonthermal line widths. We find a wide range of Mg ii k/h line intensity ratios (less than ~2 expected for opticallythin thermal emission): the lowest ever reported median value of 1.17 found in the fallback material, a comparably high value of 1.63 in nearby coronal rain, and intermediate values of 1.53 and 1.41 in the two eruption components. The fallback material exhibits a strong (>5α ) linear correlation between the k/h ratio and the Doppler velocity as well as the line intensity. We demonstrate that Doppler dimming of scattered chromospheric emission by the erupted material can potentially explain such characteristics.
Tue, 21 Apr 2015 00:00:00 GMT
http://hdl.handle.net/10023/10287
20150421T00:00:00Z
Liu, Wei
De Pontieu, Bart
Vial, JeanClaude
Title, Alan M.
Carlsson, Mats
Uitenbroek, Han
Okamoto, Takenori J.
Berger, Thomas E.
Antolin, Patrick
Spectroscopic observations of prominence eruptions associated with coronal mass ejections (CMEs), although relatively rare, can provide valuable plasma and threedimensional geometry diagnostics. We report the first observations by the Interface Region Imaging Spectrograph mission of a spectacular fast CME/prominence eruption associated with an equivalent X1.6 flare on 2014 May 9. The maximum planeofsky and Doppler velocities of the eruption are 1200 and 460 km s−1, respectively. There are two eruption components separated by ~200 km s−1 in Doppler velocity: a primary, bright component and a secondary, faint component, suggesting a hollow, rather than solid, coneshaped distribution of material. The eruption involves a lefthanded helical structure undergoing counterclockwise (viewed topdown) unwinding motion. There is a temporal evolution from upward eruption to downward fallback with lessthanfreefall speeds and decreasing nonthermal line widths. We find a wide range of Mg ii k/h line intensity ratios (less than ~2 expected for opticallythin thermal emission): the lowest ever reported median value of 1.17 found in the fallback material, a comparably high value of 1.63 in nearby coronal rain, and intermediate values of 1.53 and 1.41 in the two eruption components. The fallback material exhibits a strong (>5α ) linear correlation between the k/h ratio and the Doppler velocity as well as the line intensity. We demonstrate that Doppler dimming of scattered chromospheric emission by the erupted material can potentially explain such characteristics.

Simulating the in situ condensation process of solar prominences
http://hdl.handle.net/10023/10285
Prominences in the solar corona are a hundredfold cooler and denser than their surroundings, with a total mass of 1013 up to 1015 g. Here, we report on the first comprehensive simulations of threedimensional, thermally and gravitationally stratified magnetic flux ropes where in situ condensation to a prominence occurs due to radiative losses. After a gradual thermodynamic adjustment, we witness a phase where runaway cooling occurs while counterstreaming shearing flows drain off mass along helical field lines. After this drainage, a prominencelike condensation resides in concave upward field regions, and this prominence retains its overall characteristics for more than two hours. While condensing, the prominence establishes a prominencecorona transition region where magnetic fieldaligned thermal conduction is operative during the runaway cooling. The prominence structure represents a forcebalanced state in a helical flux rope. The simulated condensation demonstrates a rightbearing barb, as a remnant of the drainage. Synthetic images at extreme ultraviolet wavelengths follow the onset of the condensation, and confirm the appearance of horns and a threepart structure for the stable prominence state, as often seen in erupting prominences. This naturally explains recent Solar Dynamics Observatory views with the Atmospheric Imaging Assembly on prominences in coronal cavities demonstrating horns.
Wed, 27 Aug 2014 00:00:00 GMT
http://hdl.handle.net/10023/10285
20140827T00:00:00Z
Xia, C.
Keppens, R.
Antolin, P.
Porth, O.
Prominences in the solar corona are a hundredfold cooler and denser than their surroundings, with a total mass of 1013 up to 1015 g. Here, we report on the first comprehensive simulations of threedimensional, thermally and gravitationally stratified magnetic flux ropes where in situ condensation to a prominence occurs due to radiative losses. After a gradual thermodynamic adjustment, we witness a phase where runaway cooling occurs while counterstreaming shearing flows drain off mass along helical field lines. After this drainage, a prominencelike condensation resides in concave upward field regions, and this prominence retains its overall characteristics for more than two hours. While condensing, the prominence establishes a prominencecorona transition region where magnetic fieldaligned thermal conduction is operative during the runaway cooling. The prominence structure represents a forcebalanced state in a helical flux rope. The simulated condensation demonstrates a rightbearing barb, as a remnant of the drainage. Synthetic images at extreme ultraviolet wavelengths follow the onset of the condensation, and confirm the appearance of horns and a threepart structure for the stable prominence state, as often seen in erupting prominences. This naturally explains recent Solar Dynamics Observatory views with the Atmospheric Imaging Assembly on prominences in coronal cavities demonstrating horns.

Detection of supersonic downflows and associated heating events in the transition region above sunspots
http://hdl.handle.net/10023/10282
Interface Region Imaging Spectrograph data allow us to study the solar transition region (TR) with an unprecedented spatial resolution of 0″33. On 2013 August 30, we observed bursts of high Doppler shifts suggesting strong supersonic downflows of up to 200 km s–1 and weaker, slightly slower upflows in the spectral lines Mg II h and k, C II 1336, Si IV 1394 Å, and 1403 Å, that are correlated with brightenings in the slitjaw images (SJIs). The bursty behavior lasts throughout the 2 hr observation, with average burst durations of about 20 s. The locations of these shortlived events appear to be the umbral and penumbral footpoints of EUV loops. Fast apparent downflows are observed along these loops in the SJIs and in the Atmospheric Imaging Assembly, suggesting that the loops are thermally unstable. We interpret the observations as cool material falling from coronal heights, and especially coronal rain produced along the thermally unstable loops, which leads to an increase of intensity at the loop footpoints, probably indicating an increase of density and temperature in the TR. The rain speeds are on the higher end of previously reported speeds for this phenomenon, and possibly higher than the freefall velocity along the loops. On other observing days, similar bright dots are sometimes aligned into ribbons, resembling small flare ribbons. These observations provide a first insight into smallscale heating events in sunspots in the TR.
Fri, 27 Jun 2014 00:00:00 GMT
http://hdl.handle.net/10023/10282
20140627T00:00:00Z
Kleint, L.
Antolin, P.
Tian, H.
Judge, P.
Testa, P.
De Pontieu, B.
MartínezSykora, J.
Reeves, K. K.
Wuelser, J. P.
McKillop, S.
Saar, S.
Carlsson, M.
Boerner, P.
Hurlburt, N.
Lemen, J.
Tarbell, T. D.
Title, A.
Golub, L.
Hansteen, V.
Jaeggli, S.
Kankelborg, C.
Interface Region Imaging Spectrograph data allow us to study the solar transition region (TR) with an unprecedented spatial resolution of 0″33. On 2013 August 30, we observed bursts of high Doppler shifts suggesting strong supersonic downflows of up to 200 km s–1 and weaker, slightly slower upflows in the spectral lines Mg II h and k, C II 1336, Si IV 1394 Å, and 1403 Å, that are correlated with brightenings in the slitjaw images (SJIs). The bursty behavior lasts throughout the 2 hr observation, with average burst durations of about 20 s. The locations of these shortlived events appear to be the umbral and penumbral footpoints of EUV loops. Fast apparent downflows are observed along these loops in the SJIs and in the Atmospheric Imaging Assembly, suggesting that the loops are thermally unstable. We interpret the observations as cool material falling from coronal heights, and especially coronal rain produced along the thermally unstable loops, which leads to an increase of intensity at the loop footpoints, probably indicating an increase of density and temperature in the TR. The rain speeds are on the higher end of previously reported speeds for this phenomenon, and possibly higher than the freefall velocity along the loops. On other observing days, similar bright dots are sometimes aligned into ribbons, resembling small flare ribbons. These observations provide a first insight into smallscale heating events in sunspots in the TR.

Forward modeling of gyrosynchrotron intensity perturbations by sausage modes
http://hdl.handle.net/10023/10280
To determine the observable radio signatures of the fast sausagestanding wave, we examine gyrosynchrotron (GS) emission modulation usinga linear threedimensional magnetohydrodynamic model of a plasmacylinder. Effects of the lineofsight angle and instrumental resolutionon perturbations of the GS intensity are analyzed for two models: a basemodel with strong Razin suppression and a lowdensity model in which theRazin effect was unimportant. Our finding contradicts previouspredictions made with simpler models: an inphase variation of intensitybetween low (f <fpeak) and high (f > fpeak) frequencies is found for the lowdensity model and anantiphase variation for the base model in the case of a viewing angleof 45°. The spatially inhomogeneous character of the oscillatingemission source and the spatial resolution of the model are found tohave a significant effect on the resulting intensity.
Fri, 28 Mar 2014 00:00:00 GMT
http://hdl.handle.net/10023/10280
20140328T00:00:00Z
Reznikova, V. E.
Antolin, P.
Van Doorsselaere, T.
To determine the observable radio signatures of the fast sausagestanding wave, we examine gyrosynchrotron (GS) emission modulation usinga linear threedimensional magnetohydrodynamic model of a plasmacylinder. Effects of the lineofsight angle and instrumental resolutionon perturbations of the GS intensity are analyzed for two models: a basemodel with strong Razin suppression and a lowdensity model in which theRazin effect was unimportant. Our finding contradicts previouspredictions made with simpler models: an inphase variation of intensitybetween low (f <fpeak) and high (f > fpeak) frequencies is found for the lowdensity model and anantiphase variation for the base model in the case of a viewing angleof 45°. The spatially inhomogeneous character of the oscillatingemission source and the spatial resolution of the model are found tohave a significant effect on the resulting intensity.

Fine strandlike structure in the solar corona from magnetohydrodynamic transverse oscillations
http://hdl.handle.net/10023/10279
Current analytical and numerical modeling suggest the existence of ubiquitous thin current sheets in the corona that could explain the observed heating requirements. On the other hand, new high resolution observations of the corona indicate that its magnetic field may tend to organize itself in fine strandlike structures of few hundred kilometers widths. The link between small structure in models and the observed widths of strandlike structure several orders of magnitude larger is still not clear. A popular theoretical scenario is the nanoflare model, in which each strand is the product of an ensemble of heating events. Here, we suggest an alternative mechanism for strand generation. Through forward modeling of threedimensional MHD simulations we show that small amplitude transverse MHD waves can lead in a few periods time to strandlike structure in loops in EUV intensity images. Our model is based on previous numerical work showing that transverse MHD oscillations can lead to KelvinHelmholtz instabilities that deform the crosssectional area of loops. While previous work has focused on large amplitude oscillations, here we show that the instability can occur even for low wave amplitudes for long and thin loops, matching those presently observed in the corona. We show that the vortices generated from the instability are velocity sheared regions with enhanced emissivity hosting current sheets. Strands result as a complex combination of the vortices and the lineofsight angle, last for timescales of a period, and can be observed for spatial resolutions of a tenth of loop radius.
Tue, 13 May 2014 00:00:00 GMT
http://hdl.handle.net/10023/10279
20140513T00:00:00Z
Antolin, P.
Yokoyama, T.
Van Doorsselaere, T.
Current analytical and numerical modeling suggest the existence of ubiquitous thin current sheets in the corona that could explain the observed heating requirements. On the other hand, new high resolution observations of the corona indicate that its magnetic field may tend to organize itself in fine strandlike structures of few hundred kilometers widths. The link between small structure in models and the observed widths of strandlike structure several orders of magnitude larger is still not clear. A popular theoretical scenario is the nanoflare model, in which each strand is the product of an ensemble of heating events. Here, we suggest an alternative mechanism for strand generation. Through forward modeling of threedimensional MHD simulations we show that small amplitude transverse MHD waves can lead in a few periods time to strandlike structure in loops in EUV intensity images. Our model is based on previous numerical work showing that transverse MHD oscillations can lead to KelvinHelmholtz instabilities that deform the crosssectional area of loops. While previous work has focused on large amplitude oscillations, here we show that the instability can occur even for low wave amplitudes for long and thin loops, matching those presently observed in the corona. We show that the vortices generated from the instability are velocity sheared regions with enhanced emissivity hosting current sheets. Strands result as a complex combination of the vortices and the lineofsight angle, last for timescales of a period, and can be observed for spatial resolutions of a tenth of loop radius.

Forward modeling of EUV and gyrosynchrotron emission from coronal plasmas with FoMo
http://hdl.handle.net/10023/10275
The FOMO code was developed to calculate the EUV and UV emission from optically thin coronal plasmas. The input data for FOMO consists of the plasma density, temperature and velocity on a 3D grid. This is translated to emissivity on the 3D grid, using CHIANTI data. Then, the emissivity is integrated along the lineofsight (LOS) to calculate the emergent spectral line for synthetic spectrometer observations. The code also generates the emission channels for synthetic AIA imaging observations. Moreover, the code has been extended to model also the gyrosynchrotron emission from plasmas with a population of nonthermal particles. In this case, also optically thick plasmas may be modeled. The radio spectrum is calculated over a large wavelength range, allowing for the comparison with data from a wide range of radio telescopes.
Odysseus funding (FWOVlaanderen), IAPP7/08CHARM (Belspo), GOA2015014 (KULeuven), NAOJ Visiting Fellows Program. N Misa PhD student of the FWOVlaanderen.
Fri, 26 Feb 2016 00:00:00 GMT
http://hdl.handle.net/10023/10275
20160226T00:00:00Z
Van Doorsselaere, Tom
Antolin, Patrick
Yuan, Ding
Reznikova, Veronika
Magyar, Norbert
The FOMO code was developed to calculate the EUV and UV emission from optically thin coronal plasmas. The input data for FOMO consists of the plasma density, temperature and velocity on a 3D grid. This is translated to emissivity on the 3D grid, using CHIANTI data. Then, the emissivity is integrated along the lineofsight (LOS) to calculate the emergent spectral line for synthetic spectrometer observations. The code also generates the emission channels for synthetic AIA imaging observations. Moreover, the code has been extended to model also the gyrosynchrotron emission from plasmas with a population of nonthermal particles. In this case, also optically thick plasmas may be modeled. The radio spectrum is calculated over a large wavelength range, allowing for the comparison with data from a wide range of radio telescopes.

Observational signatures of transverse magnetohydrodynamic waves and associated dynamic instabilities in coronal flux tubes
http://hdl.handle.net/10023/10256
MHD waves permeate the solar atmosphere and constitute potential coronal heating agents. Yet, the waves detected so far may be but a small subset of the true existing wave power. Detection is limited by instrumental constraints, but also by wave processes that localise the wave power in undetectable spatial scales. In this study we conduct 3D MHD simulations and forward modelling of standing transverse MHD waves in coronal loops with uniform and nonuniform temperature variation in the perpendicular crosssection. The observed signatures are largely dominated by the combination of the KelvinHelmholtz instability (KHI), resonant absorption and phase mixing. In the presence of a crossloop temperature gradient we find that emission lines sensitive to the loop core catch different signatures than those more sensitive to the loop boundary and the surrounding corona, leading to an outofphase intensity modulation produced by the KHI mixing. Common signatures to all considered models include an intensity and loop width modulation at half the kink period, fine strandlike structure, a characteristic arrowshaped structure in the Doppler maps, overall line broadening in time but particularly at the loop edges. For our model, most of these features can be captured with a spatial resolution of 0.33″ and spectral resolution of 25 km s1, although severe overestimation of the line width is obtained. Resonant absorption leads to a significant decrease of the observed kinetic energy from Doppler motions over time, which is not recovered by a corresponding increase in the line width from phase mixing and the KHI motions. We estimate this hidden wave energy to be a factor of 510 of the observed value.
This research has received funding from the UK Science and Technology Facilities Council and the European Union Horizon 2020 research and innovation programme (grant agreement No. 647214), and also from JSPS KAKENHI Grant Numbers 25220703 (PI: S. Tsuneta) and 15H03640 (PI: T. Yokoyama). T.V.D. was supported by FWO Vlaanderen’s Odysseus programme, GOA2015014 (KU Leuven) and the IAP P7/08 CHARM (Belspo).
Wed, 22 Feb 2017 00:00:00 GMT
http://hdl.handle.net/10023/10256
20170222T00:00:00Z
Antolin, Patrick
Moortel, Ineke De
Doorsselaere, Tom Van
Yokoyama, Takaaki
MHD waves permeate the solar atmosphere and constitute potential coronal heating agents. Yet, the waves detected so far may be but a small subset of the true existing wave power. Detection is limited by instrumental constraints, but also by wave processes that localise the wave power in undetectable spatial scales. In this study we conduct 3D MHD simulations and forward modelling of standing transverse MHD waves in coronal loops with uniform and nonuniform temperature variation in the perpendicular crosssection. The observed signatures are largely dominated by the combination of the KelvinHelmholtz instability (KHI), resonant absorption and phase mixing. In the presence of a crossloop temperature gradient we find that emission lines sensitive to the loop core catch different signatures than those more sensitive to the loop boundary and the surrounding corona, leading to an outofphase intensity modulation produced by the KHI mixing. Common signatures to all considered models include an intensity and loop width modulation at half the kink period, fine strandlike structure, a characteristic arrowshaped structure in the Doppler maps, overall line broadening in time but particularly at the loop edges. For our model, most of these features can be captured with a spatial resolution of 0.33″ and spectral resolution of 25 km s1, although severe overestimation of the line width is obtained. Resonant absorption leads to a significant decrease of the observed kinetic energy from Doppler motions over time, which is not recovered by a corresponding increase in the line width from phase mixing and the KHI motions. We estimate this hidden wave energy to be a factor of 510 of the observed value.

Balanced solutions for an ellipsoidal vortex in a rotating stratified flow
http://hdl.handle.net/10023/10227
We consider the motion of a single ellipsoidal vortex with uniform potential vorticity in a rotating stratified fluid at finite Rossby number . Building on previous solutions obtained under the quasigeostrophic approximation (at first order in ), we obtain analytical solutions for the balanced part of the flow at . These solutions capture important ageostrophic effects giving rise to an asymmetry in the evolution of cyclonic and anticyclonic vortices. Previous work has shown that, if the velocity field induced by an ellipsoidal vortex only depends linearly on spatial coordinates inside the vortex, i.e. , then the dynamics reduces markedly to a simple matrix equation. The instantaneous vortex shape and orientation are encapsulated in a symmetric matrix , which is acted upon by the flow matrix to provide the vortex evolution. Under the quasigeostrophic approximation, the flow matrix is determined by inverting the potential vorticity to obtain the streamfunction via Poisson's equation, which has a known analytical solution depending on elliptic integrals. Here we show that higherorder balanced solutions, up to second order in the Rossby number, can also be calculated analytically. However, in this case there is a vector potential that requires the solution of three Poisson equations for each of its components. The source terms for these equations are independent of spatial coordinates within the ellipsoid, depending only on the elliptic integrals solved at the leading, quasigeostrophic order. Unlike the quasigeostrophic case, these source terms do not in general vanish outside the ellipsoid and have an inordinately complicated dependence on spatial coordinates. In the special case of an ellipsoid whose axes are aligned with the coordinate axes, we are able to derive these source terms and obtain the full analytical solution to the three Poisson equations. However, if one considers the homogeneous case, whereby the outer source terms are neglected, one can obtain an approximate solution having a compact matrix form analogous to the leadingorder quasigeostrophic case. This approximate solution proves to be highly accurate for the general case of an arbitrarily oriented ellipsoid, as verified through comparisons of the solutions with solutions obtained from numerical simulations of an ellipsoid using an accurate nonlinear balance model, even at moderate Rossby numbers.
Support for this research has come from the UK Engineering and Physical Sciences Research Council (grant number EP/H001794/1).
Thu, 01 Sep 2016 00:00:00 GMT
http://hdl.handle.net/10023/10227
20160901T00:00:00Z
Mckiver, William J.
Dritschel, David G.
We consider the motion of a single ellipsoidal vortex with uniform potential vorticity in a rotating stratified fluid at finite Rossby number . Building on previous solutions obtained under the quasigeostrophic approximation (at first order in ), we obtain analytical solutions for the balanced part of the flow at . These solutions capture important ageostrophic effects giving rise to an asymmetry in the evolution of cyclonic and anticyclonic vortices. Previous work has shown that, if the velocity field induced by an ellipsoidal vortex only depends linearly on spatial coordinates inside the vortex, i.e. , then the dynamics reduces markedly to a simple matrix equation. The instantaneous vortex shape and orientation are encapsulated in a symmetric matrix , which is acted upon by the flow matrix to provide the vortex evolution. Under the quasigeostrophic approximation, the flow matrix is determined by inverting the potential vorticity to obtain the streamfunction via Poisson's equation, which has a known analytical solution depending on elliptic integrals. Here we show that higherorder balanced solutions, up to second order in the Rossby number, can also be calculated analytically. However, in this case there is a vector potential that requires the solution of three Poisson equations for each of its components. The source terms for these equations are independent of spatial coordinates within the ellipsoid, depending only on the elliptic integrals solved at the leading, quasigeostrophic order. Unlike the quasigeostrophic case, these source terms do not in general vanish outside the ellipsoid and have an inordinately complicated dependence on spatial coordinates. In the special case of an ellipsoid whose axes are aligned with the coordinate axes, we are able to derive these source terms and obtain the full analytical solution to the three Poisson equations. However, if one considers the homogeneous case, whereby the outer source terms are neglected, one can obtain an approximate solution having a compact matrix form analogous to the leadingorder quasigeostrophic case. This approximate solution proves to be highly accurate for the general case of an arbitrarily oriented ellipsoid, as verified through comparisons of the solutions with solutions obtained from numerical simulations of an ellipsoid using an accurate nonlinear balance model, even at moderate Rossby numbers.

High Gaussicity feedhorns for sub/ millimeter wave applications
http://hdl.handle.net/10023/10171
In feedhorn design, the power coupling to the fundamental freespace LG00 mode, or Gaussicity, is a good proxy for high performance, particularly the sidelobe and crosspolar levels and the nearfield behavior. Gaussicity can be maximized by ensuring that the first few horn modes reach the aperture with the appropriate phase and amplitude relationship. We present two feedhorn designs for which the Gaussicity was maximized in order to achieve high performance. The first is a 94 GHz corrugated horn with a tanhlinear profile, manufactured by electroforming, which achieves a Gaussicity of 99.92% at band center and sidelobes at the 60 dB level. The second is a 340 GHz smoothwalled spline horn which achieves a Gaussicity of >99.2% over a 10% bandwidth, sidelobes below 30 dB and excellent nearfield behavior. This design has been successfully fabricated in Eplane split block suitable for low volume manufacture, for example for imaging arrays.
Mon, 28 Nov 2016 00:00:00 GMT
http://hdl.handle.net/10023/10171
20161128T00:00:00Z
Robertson, Duncan A.
McKay, Johannes E.
Hunter, Robert I.
Speirs, Peter J.
Smith, Graham M.
In feedhorn design, the power coupling to the fundamental freespace LG00 mode, or Gaussicity, is a good proxy for high performance, particularly the sidelobe and crosspolar levels and the nearfield behavior. Gaussicity can be maximized by ensuring that the first few horn modes reach the aperture with the appropriate phase and amplitude relationship. We present two feedhorn designs for which the Gaussicity was maximized in order to achieve high performance. The first is a 94 GHz corrugated horn with a tanhlinear profile, manufactured by electroforming, which achieves a Gaussicity of 99.92% at band center and sidelobes at the 60 dB level. The second is a 340 GHz smoothwalled spline horn which achieves a Gaussicity of >99.2% over a 10% bandwidth, sidelobes below 30 dB and excellent nearfield behavior. This design has been successfully fabricated in Eplane split block suitable for low volume manufacture, for example for imaging arrays.

Solar science with the Atacama Large Millimeter/Submillimeter Array — a new view of our sun
http://hdl.handle.net/10023/10156
The Atacama Large Millimeter/submillimeter Array (ALMA) is a new powerful tool for observing the Sun at high spatial, temporal, and spectral resolution. These capabilities can address a broad range of fundamental scientific questions in solar physics. The radiation observed by ALMA originates mostly from the chromosphere—a complex and dynamic region between the photosphere and corona, which plays a crucial role in the transport of energy and matter and, ultimately, the heating of the outer layers of the solar atmosphere. Based on first solar test observations, strategies for regular solar campaigns are currently being developed. Stateoftheart numerical simulations of the solar atmosphere and modeling of instrumental effects can help constrain and optimize future observing modes for ALMA. Here we present a short technical description of ALMA and an overview of past efforts and future possibilities for solar observations at submillimeter and millimeter wavelengths. In addition, selected numerical simulations and observations at other wavelengths demonstrate ALMA's scientific potential for studying the Sun for a large range of science cases.
Fri, 01 Apr 2016 00:00:00 GMT
http://hdl.handle.net/10023/10156
20160401T00:00:00Z
Wedemeyer, S.
Bastian, T.
Brajša, R.
Hudson, H.
Fleishman, G.
Loukitcheva, M.
Fleck, B.
Kontar, E. P.
De Pontieu, B.
Yagoubov, P.
Tiwari, S. K.
Soler, R.
Black, J. H.
Antolin, P.
Scullion, E.
Gunár, S.
Labrosse, N.
Ludwig, H.G.
Benz, A. O.
White, S. M.
Hauschildt, P.
Doyle, J. G.
Nakariakov, V. M.
Ayres, T.
Heinzel, P.
Karlicky, M.
Van Doorsselaere, T.
Gary, D.
Alissandrakis, C. E.
Nindos, A.
Solanki, S. K.
Rouppe van der Voort, L.
Shimojo, M.
Kato, Y.
Zaqarashvili, T.
Perez, E.
Selhorst, C. L.
Barta, M.
The Atacama Large Millimeter/submillimeter Array (ALMA) is a new powerful tool for observing the Sun at high spatial, temporal, and spectral resolution. These capabilities can address a broad range of fundamental scientific questions in solar physics. The radiation observed by ALMA originates mostly from the chromosphere—a complex and dynamic region between the photosphere and corona, which plays a crucial role in the transport of energy and matter and, ultimately, the heating of the outer layers of the solar atmosphere. Based on first solar test observations, strategies for regular solar campaigns are currently being developed. Stateoftheart numerical simulations of the solar atmosphere and modeling of instrumental effects can help constrain and optimize future observing modes for ALMA. Here we present a short technical description of ALMA and an overview of past efforts and future possibilities for solar observations at submillimeter and millimeter wavelengths. In addition, selected numerical simulations and observations at other wavelengths demonstrate ALMA's scientific potential for studying the Sun for a large range of science cases.

Global sausage oscillation of solar flare loops detected by the Interface Region Imaging Spectrograph
http://hdl.handle.net/10023/10140
An observation from the Interface Region Imaging Spectrograph reveals coherent oscillations in the loops of an M1.6 flare on 2015 March 12. Both the intensity and Doppler shift of Fe xxi 1354.08 Å show clear oscillations with a period of ˜25 s. Remarkably similar oscillations were also detected in the soft Xray flux recorded by the Geostationary Operational Environmental Satellites (GOES). With an estimated phase speed of ˜2420 km s1 and a derived electron density of at least 5.4 × 1010cm3, the observed shortperiod oscillation is most likely the global fast sausage mode of a hot flare loop. We find a phase shift of ˜π/2 (1/4 period) between the Doppler shift oscillation and the intensity/GOES oscillations, which is consistent with a recent forward modeling study of the sausage mode. The observed oscillation requires a density contrast between the flare loop and coronal background of a factor ≥42. The estimated phase speed of the global mode provides a lower limit of the Alfvén speed outside the flare loop. We also find an increase of the oscillation period,which might be caused by the separation of the loop footpoints with time.
Fri, 20 May 2016 00:00:00 GMT
http://hdl.handle.net/10023/10140
20160520T00:00:00Z
Tian, Hui
Young, Peter R.
Reeves, Katharine K.
Wang, Tongjiang
Antolin, Patrick
Chen, Bin
He, Jiansen
An observation from the Interface Region Imaging Spectrograph reveals coherent oscillations in the loops of an M1.6 flare on 2015 March 12. Both the intensity and Doppler shift of Fe xxi 1354.08 Å show clear oscillations with a period of ˜25 s. Remarkably similar oscillations were also detected in the soft Xray flux recorded by the Geostationary Operational Environmental Satellites (GOES). With an estimated phase speed of ˜2420 km s1 and a derived electron density of at least 5.4 × 1010cm3, the observed shortperiod oscillation is most likely the global fast sausage mode of a hot flare loop. We find a phase shift of ˜π/2 (1/4 period) between the Doppler shift oscillation and the intensity/GOES oscillations, which is consistent with a recent forward modeling study of the sausage mode. The observed oscillation requires a density contrast between the flare loop and coronal background of a factor ≥42. The estimated phase speed of the global mode provides a lower limit of the Alfvén speed outside the flare loop. We also find an increase of the oscillation period,which might be caused by the separation of the loop footpoints with time.

Numerical simulations of sunspot rotation driven by magnetic flux emergence
http://hdl.handle.net/10023/10129
Magnetic flux continually emerges from the Sun, rising through the solar interior, emerging at the photosphere in the form of sunspots and expanding into the atmosphere. Observations of sunspot rotations have been reported for over a century and are often accompanied by solar eruptions and flaring activity. In this thesis, we present 3D numerical simulations of the emergence of twisted flux tubes from the uppermost layers of the solar interior, examining the rotational movements of sunspots in the photospheric plane. The basic experiment introduces the mechanism and characteristics of sunspot rotation by a clear calculation of rotation angle, vorticity, magnetic helicity and energy, whereby we find an untwisting of the interior portion of the field, accompanied by an injection of twist into the atmospheric field. We extend this model by altering the initial field strength and twist of the subphotospheric tube. This comparison reveals the rotation angle, helicity and current show a direct dependence on field strength. An increase in field strength increases the rotation angle, the length of fieldlines extending into the atmosphere, and the magnetic energy transported to the atmosphere. The fieldline length is crucial as we predict the twist per unit length
equilibrates to a lower value on longer fieldlines, and hence possesses a larger rotation angle. No such direct dependence is found when varying the twist but there is a clear ordering in rotation angle, helicity, and energy, with more highly twisted tubes undergoing larger rotation angles. We believe the final angle of rotation is reached when the system achieves a constant degree of twist along the length of fieldlines. By extrapolating the size of the modelled active region, we find rotation angles and rates comparable with those observed. In addition, we explore sunspot rotation caused by subphotospheric velocities twisting the
footpoints of flux tubes.
Fri, 23 Jun 2017 00:00:00 GMT
http://hdl.handle.net/10023/10129
20170623T00:00:00Z
Sturrock, Zoe
Magnetic flux continually emerges from the Sun, rising through the solar interior, emerging at the photosphere in the form of sunspots and expanding into the atmosphere. Observations of sunspot rotations have been reported for over a century and are often accompanied by solar eruptions and flaring activity. In this thesis, we present 3D numerical simulations of the emergence of twisted flux tubes from the uppermost layers of the solar interior, examining the rotational movements of sunspots in the photospheric plane. The basic experiment introduces the mechanism and characteristics of sunspot rotation by a clear calculation of rotation angle, vorticity, magnetic helicity and energy, whereby we find an untwisting of the interior portion of the field, accompanied by an injection of twist into the atmospheric field. We extend this model by altering the initial field strength and twist of the subphotospheric tube. This comparison reveals the rotation angle, helicity and current show a direct dependence on field strength. An increase in field strength increases the rotation angle, the length of fieldlines extending into the atmosphere, and the magnetic energy transported to the atmosphere. The fieldline length is crucial as we predict the twist per unit length
equilibrates to a lower value on longer fieldlines, and hence possesses a larger rotation angle. No such direct dependence is found when varying the twist but there is a clear ordering in rotation angle, helicity, and energy, with more highly twisted tubes undergoing larger rotation angles. We believe the final angle of rotation is reached when the system achieves a constant degree of twist along the length of fieldlines. By extrapolating the size of the modelled active region, we find rotation angles and rates comparable with those observed. In addition, we explore sunspot rotation caused by subphotospheric velocities twisting the
footpoints of flux tubes.

Fluxrope twist in eruptive flares and CMEs : due to zipper and mainphase reconnection
http://hdl.handle.net/10023/10114
The nature of threedimensional reconnection when a twisted flux tube erupts during an eruptive flare or coronal mass ejection is considered. The reconnection has two phases: first of all, 3D “zipper reconnection” propagates along the initial coronal arcade, parallel to the polarity inversion line (PIL); then subsequent quasi2D “main phase reconnection” in the low corona around a flux rope during its eruption produces coronal loops and chromospheric ribbons that propagate away from the PIL in a direction normal to it. One scenario starts with a sheared arcade: the zipper reconnection creates a twisted flux rope of roughly one turn (2π radians of twist), and then main phase reconnection builds up the bulk of the erupting flux rope with a relatively uniform twist of a few turns. A second scenario starts with a preexisting flux rope under the arcade. Here the zipper phase can create a core with many turns that depend on the ratio of the magnetic fluxes in the newly formed flare ribbons and the new flux rope. Main phase reconnection then adds a layer of roughly uniform twist to the twisted central core. Both phases and scenarios are modeled in a simple way that assumes the initial magnetic flux is fragmented along the PIL. The model uses conservation of magnetic helicity and flux, together with equipartition of magnetic helicity, to deduce the twist of the erupting flux rope in terms the geometry of the initial configuration. Interplanetary observations show some flux ropes have a fairly uniform twist, which could be produced when the zipper phase and any preexisting flux rope possess small or moderate twist (up to one or two turns). Other interplanetary flux ropes have highly twisted cores (up to five turns), which could be produced when there is a preexisting flux rope and an active zipper phase that creates substantial extra twist.
Funding: UK Science and Technology Facilities Council
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10023/10114
20170101T00:00:00Z
Priest, Eric Ronald
Longcope, D.W.
The nature of threedimensional reconnection when a twisted flux tube erupts during an eruptive flare or coronal mass ejection is considered. The reconnection has two phases: first of all, 3D “zipper reconnection” propagates along the initial coronal arcade, parallel to the polarity inversion line (PIL); then subsequent quasi2D “main phase reconnection” in the low corona around a flux rope during its eruption produces coronal loops and chromospheric ribbons that propagate away from the PIL in a direction normal to it. One scenario starts with a sheared arcade: the zipper reconnection creates a twisted flux rope of roughly one turn (2π radians of twist), and then main phase reconnection builds up the bulk of the erupting flux rope with a relatively uniform twist of a few turns. A second scenario starts with a preexisting flux rope under the arcade. Here the zipper phase can create a core with many turns that depend on the ratio of the magnetic fluxes in the newly formed flare ribbons and the new flux rope. Main phase reconnection then adds a layer of roughly uniform twist to the twisted central core. Both phases and scenarios are modeled in a simple way that assumes the initial magnetic flux is fragmented along the PIL. The model uses conservation of magnetic helicity and flux, together with equipartition of magnetic helicity, to deduce the twist of the erupting flux rope in terms the geometry of the initial configuration. Interplanetary observations show some flux ropes have a fairly uniform twist, which could be produced when the zipper phase and any preexisting flux rope possess small or moderate twist (up to one or two turns). Other interplanetary flux ropes have highly twisted cores (up to five turns), which could be produced when there is a preexisting flux rope and an active zipper phase that creates substantial extra twist.

On the stability of homogeneous steady states of a chemotaxis system with logistic growth term
http://hdl.handle.net/10023/10087
We consider a nonlinear PDEs system of ParabolicElliptic type with chemotactic terms. The system models the movement of a population “n” towards a higher concentration of a chemical “c” in a bounded domain Ω. We consider constant chemotactic sensitivity χ and an elliptic equation to describe the distribution of the chemicalnt − dnΔn = −χdiv(n∇c) + μn(1−n), −dcΔc + c = h(n) for a monotone increasing and lipschitz function h. We study the asymptotic behavior of solutions under the assumption of 2χ∣h′∣ < μ. As a result of the asymptotic stability we obtain the uniqueness of the strictly positive steady states.
Fri, 01 Jul 2016 00:00:00 GMT
http://hdl.handle.net/10023/10087
20160701T00:00:00Z
Chaplain, Mark Andrew Joseph
Tello, J. I.
We consider a nonlinear PDEs system of ParabolicElliptic type with chemotactic terms. The system models the movement of a population “n” towards a higher concentration of a chemical “c” in a bounded domain Ω. We consider constant chemotactic sensitivity χ and an elliptic equation to describe the distribution of the chemicalnt − dnΔn = −χdiv(n∇c) + μn(1−n), −dcΔc + c = h(n) for a monotone increasing and lipschitz function h. We study the asymptotic behavior of solutions under the assumption of 2χ∣h′∣ < μ. As a result of the asymptotic stability we obtain the uniqueness of the strictly positive steady states.

Magnetostatic modeling from SUNRISE/IMaX : application to an active region observed with SUNRISE II
http://hdl.handle.net/10023/10083
Magnetostatic models may overcome some of the issues facing forcefree magnetic field extrapolations. So far they have seen limited use and have faced problems when applied to quietSun data. Here we present a first application to an active region. We use solar vector magnetic field measurements gathered by the IMaX polarimeter during the flight of the \sunrise{} balloonborne solar observatory in June 2013 as boundary condition for a magnetostatic model of the higher solar atmosphere above an active region. The IMaX data are embedded in active region vector magnetograms observed with SDO/HMI. This work continues our magnetostatic extrapolation approach, which has been applied earlier ({\it Paper I}) to a quiet Sun region observed with \sunrise{} I. In an active region the signaltonoiseratio in the measured Stokes parameters is considerably higher than in the quiet Sun and consequently the IMaX measurements of the horizontal photospheric magnetic field allow us to specify the free parameters of the model in a special class of linear magnetostatic equilibria. The high spatial resolution of IMaX (110130 km, pixel size 40 km) enables us to model the nonforcefree layer between the photosphere and the mid chromosphere vertically by about 50 grid points. In our approach we can incorporate some aspects of the mixed beta layer of photosphere and chromosphere, e.g., taking a finite Lorentz force into account, which was not possible with lower resolution photospheric measurements in the past. The linear model does not, however, permit to model intrinsic nonlinear structures like strongly localized electric currents.
Wed, 22 Mar 2017 00:00:00 GMT
http://hdl.handle.net/10023/10083
20170322T00:00:00Z
Wiegelmann, T.
Neukirch, Thomas
Nickeler, D. H.
Solanki, S. K.
Barthol, P.
Gandorfer, A.
Gizon, L.
Hirzberger, J.
Riethmüller, T. L.
Noort, M. van
Rodríguez, J. Blanco
Del Toro Iniesta, J. C.
Suárez, D. Orozco
Schmidt, W.
Pillet, V. Martínez
Knölker, M.
Magnetostatic models may overcome some of the issues facing forcefree magnetic field extrapolations. So far they have seen limited use and have faced problems when applied to quietSun data. Here we present a first application to an active region. We use solar vector magnetic field measurements gathered by the IMaX polarimeter during the flight of the \sunrise{} balloonborne solar observatory in June 2013 as boundary condition for a magnetostatic model of the higher solar atmosphere above an active region. The IMaX data are embedded in active region vector magnetograms observed with SDO/HMI. This work continues our magnetostatic extrapolation approach, which has been applied earlier ({\it Paper I}) to a quiet Sun region observed with \sunrise{} I. In an active region the signaltonoiseratio in the measured Stokes parameters is considerably higher than in the quiet Sun and consequently the IMaX measurements of the horizontal photospheric magnetic field allow us to specify the free parameters of the model in a special class of linear magnetostatic equilibria. The high spatial resolution of IMaX (110130 km, pixel size 40 km) enables us to model the nonforcefree layer between the photosphere and the mid chromosphere vertically by about 50 grid points. In our approach we can incorporate some aspects of the mixed beta layer of photosphere and chromosphere, e.g., taking a finite Lorentz force into account, which was not possible with lower resolution photospheric measurements in the past. The linear model does not, however, permit to model intrinsic nonlinear structures like strongly localized electric currents.

A relaxation model of coronal heating in multiple interacting flux ropes
http://hdl.handle.net/10023/10070
Context: Heating the solar corona requires dissipation of stored magnetic energy, which may occur in twisted magnetic fields. Recently published numerical simulations show that the ideal kink instability in a twisted magnetic thread may trigger energy release in stable twisted neighbours, and demonstrate an avalanche of heating events. Aims: We aim to construct a Taylor relaxation model for the energy release from two flux ropes and compare this with the outcomes of the simulations. We then aim to extend the model to large numbers of flux ropes, allowing the possibility of modelling a heating avalanche, and calculation of the energy release for ensembles of twisted threads with varying twist profiles. Methods: The final state is calculated by assuming a helicityconserving relaxation to a minimum energy state. Multiple scenarios are examined, which include kinkunstable flux ropes relaxing on their own, as well as stable and unstable flux ropes merging into a single rope as a result of magnetic reconnection. We consider alternative constraints that determine the spatial extent of the final relaxed state. Results: Good agreement is found between the relaxation model and the magnetohydrodynamic simulations, both for interactions of two twisted threads and for a multithread avalanche. The model can predict the energy release for flux ropes of varying degrees of twist, which relax individually or which merge through reconnection into a single flux rope. It is found that the energy output of merging flux ropes is dominated by the energy of the most strongly twisted rope. Conclusions: The relaxation approach provides a very good estimate of the energy release in an ensemble of twisted threads of which one is kinkunstable.
The authors wish to recognise funding from EPSRC through the Fusion Centre for Doctoral Training (FusionCDT  grant code: EP/K504178/1) through which this project is possible. Support from STFC for PKB and AWH is also acknowledged (grant numbers ST/L000768/1 and ST/N000609/1).
Sat, 01 Apr 2017 00:00:00 GMT
http://hdl.handle.net/10023/10070
20170401T00:00:00Z
Hussain, A. S.
Browning, P. K.
Hood, A. W.
Context: Heating the solar corona requires dissipation of stored magnetic energy, which may occur in twisted magnetic fields. Recently published numerical simulations show that the ideal kink instability in a twisted magnetic thread may trigger energy release in stable twisted neighbours, and demonstrate an avalanche of heating events. Aims: We aim to construct a Taylor relaxation model for the energy release from two flux ropes and compare this with the outcomes of the simulations. We then aim to extend the model to large numbers of flux ropes, allowing the possibility of modelling a heating avalanche, and calculation of the energy release for ensembles of twisted threads with varying twist profiles. Methods: The final state is calculated by assuming a helicityconserving relaxation to a minimum energy state. Multiple scenarios are examined, which include kinkunstable flux ropes relaxing on their own, as well as stable and unstable flux ropes merging into a single rope as a result of magnetic reconnection. We consider alternative constraints that determine the spatial extent of the final relaxed state. Results: Good agreement is found between the relaxation model and the magnetohydrodynamic simulations, both for interactions of two twisted threads and for a multithread avalanche. The model can predict the energy release for flux ropes of varying degrees of twist, which relax individually or which merge through reconnection into a single flux rope. It is found that the energy output of merging flux ropes is dominated by the energy of the most strongly twisted rope. Conclusions: The relaxation approach provides a very good estimate of the energy release in an ensemble of twisted threads of which one is kinkunstable.

A new approach for modelling chromospheric evaporation in response to enhanced coronal heating. I. The method
http://hdl.handle.net/10023/10063
We present a new computational approach that addresses the difficulty of obtaining the correct interaction between the solar corona and the transition region in response to rapid heating events. In the coupled corona, transition region and chromosphere system, an enhanced downward conductive flux results in an upflow (chromospheric evaporation).However, obtaining the correct upflow generally requires high spatial resolution in order to resolve the transition region. With an unresolved transition region, artificially low coronal densities are obtained because the downward heat flux ‘jumps’ across the unresolved region to the chromosphere, underestimating the upflows. Here, we treat the lower transition region as a discontinuity that responds to changing coronal conditions through the imposition of a jump condition that is derived from an integrated form of energy conservation. To illustrate and benchmark this approach against a fully resolved onedimensional model, we present fieldaligned simulations of coronal loops in response to a range of impulsive (spatially uniform) heating events. We show that our approach leads to a significant improvement in the coronal density evolution than just when using coarse spatial resolutions insufficient to resolve the lower transition region. Our approach compensates for the jumping of the heat flux by imposing a velocity correction that ensures that the energy from the heat flux goes into driving the transition region dynamics, rather than being lost through radiation. Hence, it is possible to obtain improved coronal densities. The advantages of using this approach in both onedimensional hydrodynamic and threedimensional magnetohydrodynamic simulations are discussed.
C.D.J. acknowledges the financial support of the Carnegie Trust for the Universities of Scotland. This project has received funding from the Science and Technology Facilities Council (UK) through the consolidated grant ST/N000609/1 and the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (grant agreement No 647214).
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10023/10063
20170101T00:00:00Z
Johnston, Craig David
Hood, Alan William
Cargill, Peter
De Moortel, Ineke
We present a new computational approach that addresses the difficulty of obtaining the correct interaction between the solar corona and the transition region in response to rapid heating events. In the coupled corona, transition region and chromosphere system, an enhanced downward conductive flux results in an upflow (chromospheric evaporation).However, obtaining the correct upflow generally requires high spatial resolution in order to resolve the transition region. With an unresolved transition region, artificially low coronal densities are obtained because the downward heat flux ‘jumps’ across the unresolved region to the chromosphere, underestimating the upflows. Here, we treat the lower transition region as a discontinuity that responds to changing coronal conditions through the imposition of a jump condition that is derived from an integrated form of energy conservation. To illustrate and benchmark this approach against a fully resolved onedimensional model, we present fieldaligned simulations of coronal loops in response to a range of impulsive (spatially uniform) heating events. We show that our approach leads to a significant improvement in the coronal density evolution than just when using coarse spatial resolutions insufficient to resolve the lower transition region. Our approach compensates for the jumping of the heat flux by imposing a velocity correction that ensures that the energy from the heat flux goes into driving the transition region dynamics, rather than being lost through radiation. Hence, it is possible to obtain improved coronal densities. The advantages of using this approach in both onedimensional hydrodynamic and threedimensional magnetohydrodynamic simulations are discussed.

Spectral nonlocality, absolute equilibria and KraichnanLeithBatchelor phenomenology in twodimensional turbulent energy cascades
http://hdl.handle.net/10023/10062
We study the degree to which KraichnanLeithBatchelor (KLB) phenomenology describes twodimensional energy cascades in alpha turbulence, governed by δθ/δt + J(ψ, θ) = ν ∇2θ + f, where θ = (Δ)α/2ψ is generalized vorticity, and ψ over bar (k)= kα θ over bar (k) in Fourier space. These models differ in spectral nonlocality, and include surface quasigeostrophic flow (alpha = 1), regular twodimensional flow (α = 2) and rotating shallow flow (α = 3), which is the isotropic limit of a mantle convection model. We reexamine arguments for dual inverse energy and direct enstrophy cascades, including Fjørtoft analysis, which we extend to general α, and point out their limitations. Using an αdependent eddydamped quasinormal Markovian (EDQNM) closure, we seek selfsimilar inertial range solutions and study their characteristics. Our present focus is not on coherent structures, which the EDQNM filters out, but on any selfsimilar and approximately Gaussian turbulent component that may exist in the flow and be described by KLB phenomenology. For this, the EDQNM is an appropriate tool. Nonlocal triads contribute increasingly to the energy flux as α increases. More importantly, the energy cascade is downscale in the selfsimilar inertial range for 2.5 <α <10. At α = 2.5 and α = 10, the KLB spectra correspond, respectively, to enstrophy and energy equipartition, and the triad energy transfers and flux vanish identically. Eddy turnover time and strain rate arguments suggest the inverse energy cascade should obey KLB phenomenology and be selfsimilar for α <4. However, downscale energy flux in the EDQNM selfsimilar inertial range for α > 2.5 leads us to predict that any inverse cascade for α ≥ 2.5 will not exhibit KLB phenomenology, and specifically the KLB energy spectrum. Numerical simulations confirm this: the inverse cascade energy spectrum for α ≥ 2.5 is significantly steeper than the KLB prediction, while for α <2.5 we obtain the KLB spectrum.
Sat, 01 Jun 2013 00:00:00 GMT
http://hdl.handle.net/10023/10062
20130601T00:00:00Z
Burgess, B. H.
Shepherd, T. G.
We study the degree to which KraichnanLeithBatchelor (KLB) phenomenology describes twodimensional energy cascades in alpha turbulence, governed by δθ/δt + J(ψ, θ) = ν ∇2θ + f, where θ = (Δ)α/2ψ is generalized vorticity, and ψ over bar (k)= kα θ over bar (k) in Fourier space. These models differ in spectral nonlocality, and include surface quasigeostrophic flow (alpha = 1), regular twodimensional flow (α = 2) and rotating shallow flow (α = 3), which is the isotropic limit of a mantle convection model. We reexamine arguments for dual inverse energy and direct enstrophy cascades, including Fjørtoft analysis, which we extend to general α, and point out their limitations. Using an αdependent eddydamped quasinormal Markovian (EDQNM) closure, we seek selfsimilar inertial range solutions and study their characteristics. Our present focus is not on coherent structures, which the EDQNM filters out, but on any selfsimilar and approximately Gaussian turbulent component that may exist in the flow and be described by KLB phenomenology. For this, the EDQNM is an appropriate tool. Nonlocal triads contribute increasingly to the energy flux as α increases. More importantly, the energy cascade is downscale in the selfsimilar inertial range for 2.5 <α <10. At α = 2.5 and α = 10, the KLB spectra correspond, respectively, to enstrophy and energy equipartition, and the triad energy transfers and flux vanish identically. Eddy turnover time and strain rate arguments suggest the inverse energy cascade should obey KLB phenomenology and be selfsimilar for α <4. However, downscale energy flux in the EDQNM selfsimilar inertial range for α > 2.5 leads us to predict that any inverse cascade for α ≥ 2.5 will not exhibit KLB phenomenology, and specifically the KLB energy spectrum. Numerical simulations confirm this: the inverse cascade energy spectrum for α ≥ 2.5 is significantly steeper than the KLB prediction, while for α <2.5 we obtain the KLB spectrum.

Note on ProdiSerrinLadyzhenskaya type regularity criteria for the NavierStokes equations
http://hdl.handle.net/10023/10048
In this article we prove new regularity criteria of the ProdiSerrinLadyzhenskaya type for the Cauchy problem of the threedimensional NavierStokes equations. Our results improve the classical Lr(0,T;Ls) regularity criteria for both velocity and pressure by factors of certain nagative powers of the scaling invariant norm uL3 and uH1/2.
X.Y. is partially supported by the Discovery Grant No. RES0020476 from NSERC.
Wed, 18 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10023/10048
20170118T00:00:00Z
Tran, Chuong Van
Yu, Xinwei
In this article we prove new regularity criteria of the ProdiSerrinLadyzhenskaya type for the Cauchy problem of the threedimensional NavierStokes equations. Our results improve the classical Lr(0,T;Ls) regularity criteria for both velocity and pressure by factors of certain nagative powers of the scaling invariant norm uL3 and uH1/2.

Vortex merger in surface quasigeostrophy
http://hdl.handle.net/10023/10016
The merger of two identical surface temperature vortices is studied in the surface quasi geostrophic model. The motivation for this study is the observation of the merger of sub mesoscale vortices in the ocean. Firstly, the interaction between two point vortices, in the absence or in the presence of an external deformation field, is investigated. The rotation rate of the vortices, their stationary positions and the stability of these positions are determined. Then, a numerical model provides the steady states of two finitearea, constanttemperature, vortices. Such states are less deformed than their counterparts in twodimensional incom pressible flows. Finally, numerical simulations of the nonlinear surface quasigeostrophic equations are used to investigate the finitetime evolution of initially identical and sym metric, constant temperature vortices. The critical merger distance is obtained and the deformation of the vortices before or after merger is determined. The addition of external deformation is shown to favor or to oppose merger depending on the orientation of the vor tex pair with respect to the strain axes. An explanation for this observation is proposed. Conclusions are drawn towards an application of this study to oceanic vortices.
Fri, 01 Jan 2016 00:00:00 GMT
http://hdl.handle.net/10023/10016
20160101T00:00:00Z
Carton, Xavier
Ciani, Daniele
Verron, Jacques
Reinaud, Jean Noel
Sokolovskiy, Mikhail
The merger of two identical surface temperature vortices is studied in the surface quasi geostrophic model. The motivation for this study is the observation of the merger of sub mesoscale vortices in the ocean. Firstly, the interaction between two point vortices, in the absence or in the presence of an external deformation field, is investigated. The rotation rate of the vortices, their stationary positions and the stability of these positions are determined. Then, a numerical model provides the steady states of two finitearea, constanttemperature, vortices. Such states are less deformed than their counterparts in twodimensional incom pressible flows. Finally, numerical simulations of the nonlinear surface quasigeostrophic equations are used to investigate the finitetime evolution of initially identical and sym metric, constant temperature vortices. The critical merger distance is obtained and the deformation of the vortices before or after merger is determined. The addition of external deformation is shown to favor or to oppose merger depending on the orientation of the vor tex pair with respect to the strain axes. An explanation for this observation is proposed. Conclusions are drawn towards an application of this study to oceanic vortices.

Observing the formation of flaredriven coronal rain
http://hdl.handle.net/10023/10001
Flaredriven coronal rain can manifest from rapidly cooled plasma condensations near coronal looptops in thermally unstable postflare arcades. We detect 5 phases that characterise the postflare decay:heating, evaporation, conductive cooling dominance for ~120 s, radiative/ enthalpy cooling dominance for ~4700 s and finally catastrophic cooling occurring within 35124 s leading to rain strands with s periodicity of 5570 s. We find an excellent agreement between the observations and model predictions of the dominant cooling timescales and the onset of catastrophic cooling. At the rain formation site we detect comoving, multithermal rain clumps that undergo catastrophic cooling from ~1 MK to ~22000 K. During catastrophic cooling the plasma cools at a maximum rate of 22700 K s1 in multiple looptop sources. We calculated the density of the EUV plasma from the DEM of the multithermal source employing regularised inversion. Assuming a pressure balance, we estimate the density of the chromospheric component of rain to be 9.21x1011 ±1.76x1011 cm3 which is comparable with quiescent coronal rain densities. With up to 8 parallel strands in the EUV loop cross section, we calculate the mass loss rate from the postflare arcade to be as much as 1.98x1012 ± 4.95x1011 g s1. Finally, we reveal a close proximity between the model predictions of 105.8 K and the observed properties between 105.9 K and 106.2 K, that defines the temperature onset of catastrophic cooling. The close correspondence between the observations and numerical models suggests that indeed acoustic waves (with a sound travel time of 68 s) could play an important role in redistributing energy and sustaining the enthalpybased radiative cooling.
PA. GV are funded by the European Research Council under the European Union Seventh Framework Programme (FP7/20072013) / ERC grant agreement nr. 291058
Tue, 20 Dec 2016 00:00:00 GMT
http://hdl.handle.net/10023/10001
20161220T00:00:00Z
Scullion, E.
Rouppe Van Der Voort, L.
Antolin, P.
Wedemeyer, S.
Vissers, G.
Kontar, E. P.
Gallagher, P.
Flaredriven coronal rain can manifest from rapidly cooled plasma condensations near coronal looptops in thermally unstable postflare arcades. We detect 5 phases that characterise the postflare decay:heating, evaporation, conductive cooling dominance for ~120 s, radiative/ enthalpy cooling dominance for ~4700 s and finally catastrophic cooling occurring within 35124 s leading to rain strands with s periodicity of 5570 s. We find an excellent agreement between the observations and model predictions of the dominant cooling timescales and the onset of catastrophic cooling. At the rain formation site we detect comoving, multithermal rain clumps that undergo catastrophic cooling from ~1 MK to ~22000 K. During catastrophic cooling the plasma cools at a maximum rate of 22700 K s1 in multiple looptop sources. We calculated the density of the EUV plasma from the DEM of the multithermal source employing regularised inversion. Assuming a pressure balance, we estimate the density of the chromospheric component of rain to be 9.21x1011 ±1.76x1011 cm3 which is comparable with quiescent coronal rain densities. With up to 8 parallel strands in the EUV loop cross section, we calculate the mass loss rate from the postflare arcade to be as much as 1.98x1012 ± 4.95x1011 g s1. Finally, we reveal a close proximity between the model predictions of 105.8 K and the observed properties between 105.9 K and 106.2 K, that defines the temperature onset of catastrophic cooling. The close correspondence between the observations and numerical models suggests that indeed acoustic waves (with a sound travel time of 68 s) could play an important role in redistributing energy and sustaining the enthalpybased radiative cooling.

Toward a PVbased algorithm for the dynamical core of hydrostatic global models
http://hdl.handle.net/10023/9957
The diabatic contouradvective semiLagrangian (DCASL) algorithms previously constructed for the shallowwater and multilayer Boussinesq primitive equations are extended to multilayer nonBoussinesq equations on the sphere using a hybrid terrainfollowingisentropic (sigma) vertical coordinate. It is shown that the DCASL algorithms face challenges beyond more conventional algorithms in that various types of damping, filtering, and regularization are required for computational stability, and the nonlinearity of the hydrostatic equation in the sigma coordinate causes convergence problems with setting up a semiimplicit timestepping scheme to reduce computational cost. The prognostic variables are an approximation to the RossbyErtel potential vorticity Q, a scaled pressure thickness, the horizontal divergence, and the surface potential temperature. Results from the DCASL algorithm in two formulations of the sigma coordinate, differing only in the rate at which the vertical coordinate tends to with increasing height, are assessed using the baroclinic instability test case introduced by Jablonowski and Williamson in 2006. The assessment is based on comparisons with available reference solutions as well as results from two other algorithms derived from the DCASL algorithm: one with a semiLagrangian solution for Q and another with an Eulerian gridbased solution procedure with relative vorticity replacing Q as the prognostic variable. It is shown that at intermediate resolutions, results comparable to the reference solutions can be obtained.
Wed, 01 Jun 2016 00:00:00 GMT
http://hdl.handle.net/10023/9957
20160601T00:00:00Z
Mohebalhojeh, Ali R.
Joghataei, Mohammad
Dritschel, David G.
The diabatic contouradvective semiLagrangian (DCASL) algorithms previously constructed for the shallowwater and multilayer Boussinesq primitive equations are extended to multilayer nonBoussinesq equations on the sphere using a hybrid terrainfollowingisentropic (sigma) vertical coordinate. It is shown that the DCASL algorithms face challenges beyond more conventional algorithms in that various types of damping, filtering, and regularization are required for computational stability, and the nonlinearity of the hydrostatic equation in the sigma coordinate causes convergence problems with setting up a semiimplicit timestepping scheme to reduce computational cost. The prognostic variables are an approximation to the RossbyErtel potential vorticity Q, a scaled pressure thickness, the horizontal divergence, and the surface potential temperature. Results from the DCASL algorithm in two formulations of the sigma coordinate, differing only in the rate at which the vertical coordinate tends to with increasing height, are assessed using the baroclinic instability test case introduced by Jablonowski and Williamson in 2006. The assessment is based on comparisons with available reference solutions as well as results from two other algorithms derived from the DCASL algorithm: one with a semiLagrangian solution for Q and another with an Eulerian gridbased solution procedure with relative vorticity replacing Q as the prognostic variable. It is shown that at intermediate resolutions, results comparable to the reference solutions can be obtained.

On the theory of symmetric MHD equilibria with anisotropic pressure
http://hdl.handle.net/10023/9908
In this thesis we discuss the theory of symmetric MHD equilibria with anisotropic pressure. More
specifically, we focus on gyrotropic pressures, where the pressure tensor can be split into components along
and across the magnetic field. We first explore 2D solutions, which can be found using total field type
formalisms. These formalisms rely on treating quantities as functions of both the magnetic flux function
and the magnetic field strength, and reduce the equilibrium equations to a single GradShafranov equation
that can be solved to find the magnetic flux function. However, these formalisms are not appropriate
when one includes a shear field component of magnetic flux, since they lead to a set of equations which
are implicitly coupled. Therefore, in order to solve the equilibrium problem with a magnetic shear field
component, we introduce the poloidal formalism. This new formalism considers quantities as functions
of the poloidal magnetic field strength (instead of the total magnetic field strength), and yields a set
of two equations which are not coupled, and can be solved to find the magnetic flux function and the
shear field. There are some situations where the poloidal formalism is difficult to use, however, such as
in rotationally symmetric systems. Thus we require a further formalism, which we call the combined
approach, which allows a more general use of the poloidal formalism. One finds that the combined
formalism leads to multivalued functions, which must be dealt with appropriately. Finally, we present
some numerical examples of MHD equilibria, which have been found using each of the three formalisms
mentioned above.
Fri, 01 Jan 2016 00:00:00 GMT
http://hdl.handle.net/10023/9908
20160101T00:00:00Z
Hodgson, Jonathan David Brockie
In this thesis we discuss the theory of symmetric MHD equilibria with anisotropic pressure. More
specifically, we focus on gyrotropic pressures, where the pressure tensor can be split into components along
and across the magnetic field. We first explore 2D solutions, which can be found using total field type
formalisms. These formalisms rely on treating quantities as functions of both the magnetic flux function
and the magnetic field strength, and reduce the equilibrium equations to a single GradShafranov equation
that can be solved to find the magnetic flux function. However, these formalisms are not appropriate
when one includes a shear field component of magnetic flux, since they lead to a set of equations which
are implicitly coupled. Therefore, in order to solve the equilibrium problem with a magnetic shear field
component, we introduce the poloidal formalism. This new formalism considers quantities as functions
of the poloidal magnetic field strength (instead of the total magnetic field strength), and yields a set
of two equations which are not coupled, and can be solved to find the magnetic flux function and the
shear field. There are some situations where the poloidal formalism is difficult to use, however, such as
in rotationally symmetric systems. Thus we require a further formalism, which we call the combined
approach, which allows a more general use of the poloidal formalism. One finds that the combined
formalism leads to multivalued functions, which must be dealt with appropriately. Finally, we present
some numerical examples of MHD equilibria, which have been found using each of the three formalisms
mentioned above.

A comparison of global magnetic field skeletons and activeregion upflows
http://hdl.handle.net/10023/9875
Plasma upflows have been detected in active regions using Doppler velocity maps. The origin and nature of these upflows is not well known with many of their characteristics determined from the examination of single events. In particular, some studies suggest these upflows occur along open field lines and, hence, are linked to sources of the solar wind. To investigate the relationship these upflows may have with the solar wind, and to probe what may be driving them, this paper considers seven active regions observed on the solar disc using the Extreme ultraviolet Imaging Spectrometer aboard Hinode between August 2011 and September 2012. Plasma upflows are observed in all these active regions. The locations of these upflows are compared to the global potential magnetic field extrapolated from the Solar Dynamics Observatory, Helioseismic and Magnetic Imager daily synoptic magnetogram taken on the day the upflows were observed. The structure of the magnetic field is determined by constructing its magnetic skeleton in order to help identify openfield regions and also sites where magnetic reconnection at global features is likely to occur. As a further comparison, measurements of the temperature, density and composition of the plasma are taken from regions with activeregion upflows. In most cases the locations of the upflows in the active regions do not correspond to areas of open field, as predicted by a global coronal potentialfield model, and therefore these upflows are not always sources of the slow solar wind. The locations of the upflows are, in general, intersected by separatrix surfaces associated with null points located high in the corona; these could be important sites of reconnection with global consequences.
Fri, 01 Jan 2016 00:00:00 GMT
http://hdl.handle.net/10023/9875
20160101T00:00:00Z
Edwards, S. J.
Parnell, C. E.
Harra, L. K.
Culhane, J. L.
Brooks, D. H.
Plasma upflows have been detected in active regions using Doppler velocity maps. The origin and nature of these upflows is not well known with many of their characteristics determined from the examination of single events. In particular, some studies suggest these upflows occur along open field lines and, hence, are linked to sources of the solar wind. To investigate the relationship these upflows may have with the solar wind, and to probe what may be driving them, this paper considers seven active regions observed on the solar disc using the Extreme ultraviolet Imaging Spectrometer aboard Hinode between August 2011 and September 2012. Plasma upflows are observed in all these active regions. The locations of these upflows are compared to the global potential magnetic field extrapolated from the Solar Dynamics Observatory, Helioseismic and Magnetic Imager daily synoptic magnetogram taken on the day the upflows were observed. The structure of the magnetic field is determined by constructing its magnetic skeleton in order to help identify openfield regions and also sites where magnetic reconnection at global features is likely to occur. As a further comparison, measurements of the temperature, density and composition of the plasma are taken from regions with activeregion upflows. In most cases the locations of the upflows in the active regions do not correspond to areas of open field, as predicted by a global coronal potentialfield model, and therefore these upflows are not always sources of the slow solar wind. The locations of the upflows are, in general, intersected by separatrix surfaces associated with null points located high in the corona; these could be important sites of reconnection with global consequences.

The energy budget of stellar magnetic fields : comparing nonpotential simulations and observations
http://hdl.handle.net/10023/9869
The magnetic geometry of the surface magnetic fields of more than 55 cool stars have now been mapped using spectropolarimetry. In order to better understand these observations, we compare the magnetic fieldt opology at different surface scale sizes of observed and simulated cool stars. For ease of comparison between the highresolution nonpotential magnetofrictional simulations and the relatively lowresolution observations, we filter out the smallscale field in the simulations using a spherical harmonics decomposition. We show that the largescalefield topologies of the solarbased simulations produce values of poloidal/toroidal fields and fractions of energy in axisymmetric modes that are similar to the observations. These global nonpotential evolution model simulations capture key magnetic features of the observed solarlike stars through the processes of surface flux transport and magnetic flux emergence. They do not, however, reproduce the magnetic field of Mdwarfs or stars with dominantly toroidal field.Furthermore, we analyse the magnetic field topologies of individual spherical harmonics for the simulations and discover that the dipole is predominately poloidal, while the quadrupole shows the highest fraction of toroidal fields. Magnetic field structures smaller than a quadrupole display a fixed ratio between the poloidal and toroidal magnetic energies.
LTL acknowledges support from the Scottish Universities Physics Alliance (SUPA) prize studentship and the University of St Andrews Higgs studentship. MMJ and VS acknowledge a Science & Technology Facilities Council (STFC) postdoctoral fellowship.
Thu, 27 Oct 2016 00:00:00 GMT
http://hdl.handle.net/10023/9869
20161027T00:00:00Z
Lehmann, L. T.
Jardine, M. M.
Vidotto, A. A.
Mackay, D. H.
See, V.
Donati, J.F.
Folsom, C. P.
Jeffers, S. V.
Marsden, S. C.
Morin, J.
Petit, P.
The magnetic geometry of the surface magnetic fields of more than 55 cool stars have now been mapped using spectropolarimetry. In order to better understand these observations, we compare the magnetic fieldt opology at different surface scale sizes of observed and simulated cool stars. For ease of comparison between the highresolution nonpotential magnetofrictional simulations and the relatively lowresolution observations, we filter out the smallscale field in the simulations using a spherical harmonics decomposition. We show that the largescalefield topologies of the solarbased simulations produce values of poloidal/toroidal fields and fractions of energy in axisymmetric modes that are similar to the observations. These global nonpotential evolution model simulations capture key magnetic features of the observed solarlike stars through the processes of surface flux transport and magnetic flux emergence. They do not, however, reproduce the magnetic field of Mdwarfs or stars with dominantly toroidal field.Furthermore, we analyse the magnetic field topologies of individual spherical harmonics for the simulations and discover that the dipole is predominately poloidal, while the quadrupole shows the highest fraction of toroidal fields. Magnetic field structures smaller than a quadrupole display a fixed ratio between the poloidal and toroidal magnetic energies.

Theoretical foundation of 3D Alfvén resonances : normal modes
http://hdl.handle.net/10023/9847
We consider the resonant coupling of fast and Alfvén magnetohydrodynamic (MHD) waves in a 3D equilibrium. Numerical solutions to normal modes (∝ exp(−iωt)) are presented along with a theoretical framework to interpret them. The solutions we find are fundamentally different to those in 1D and 2D. In 3D there exists an infinite number of possible resonant solutions within a “Resonant Zone", and we show how boundary conditions and locally 2D regions can favour particular solutions. A unique feature of the resonance in 3D is switching between different permissible solutions when the boundary of the Resonant Zone is encountered. The theoretical foundation we develop relies upon recognising that in 3D the orientation of the resonant surface will not align in a simple fashion with an equilibrium coordinate. We present a method for generating the Alfvén wave natural frequencies for an arbitrarily oriented Alfvén wave, which requires a careful treatment of scale factors describing the background magnetic field geometry.
Tue, 20 Dec 2016 00:00:00 GMT
http://hdl.handle.net/10023/9847
20161220T00:00:00Z
Wright, Andrew Nicholas
Elsden, Thomas William
We consider the resonant coupling of fast and Alfvén magnetohydrodynamic (MHD) waves in a 3D equilibrium. Numerical solutions to normal modes (∝ exp(−iωt)) are presented along with a theoretical framework to interpret them. The solutions we find are fundamentally different to those in 1D and 2D. In 3D there exists an infinite number of possible resonant solutions within a “Resonant Zone", and we show how boundary conditions and locally 2D regions can favour particular solutions. A unique feature of the resonance in 3D is switching between different permissible solutions when the boundary of the Resonant Zone is encountered. The theoretical foundation we develop relies upon recognising that in 3D the orientation of the resonant surface will not align in a simple fashion with an equilibrium coordinate. We present a method for generating the Alfvén wave natural frequencies for an arbitrarily oriented Alfvén wave, which requires a careful treatment of scale factors describing the background magnetic field geometry.

Coupled bulksurface free boundary problems arising from a mathematical model of receptorligand dynamics
http://hdl.handle.net/10023/9779
We consider a coupled bulksurface system of partial differential equations with nonlinear coupling modelling receptorligand dynamics. The model arises as a simplification of a mathematical model for the reaction between cell surface resident receptors and ligands present in the extracellular medium. We prove the existence and uniqueness of solutions. We also consider a number of biologically relevant asymptotic limits of the model. We prove convergence to limiting problems which take the form of free boundary problems posed on the cell surface. We also report on numerical simulations illustrating convergence to one of the limiting problems as well as the spatiotemporal distributions of the receptors and ligands in a realistic geometry.
This work was started whilst the authors were participants in the Isaac Newton Institute programme: “Free Boundary Problems and Related Topics” and finalised whilst the authors were participants in the Isaac Newton Institute programme: “Coupling Geometric PDEs with Physics for Cell Morphology, Motility and Pattern Formation” supported by EPSRC Grant Number EP/K032208/1. The work of CV received support from the Leverhulme Trust Research Project Grant (RPG2014149).
Wed, 08 Feb 2017 00:00:00 GMT
http://hdl.handle.net/10023/9779
20170208T00:00:00Z
Elliot, Charles M.
Ranner, Thomas
Venkataraman, Chandrasekhar
We consider a coupled bulksurface system of partial differential equations with nonlinear coupling modelling receptorligand dynamics. The model arises as a simplification of a mathematical model for the reaction between cell surface resident receptors and ligands present in the extracellular medium. We prove the existence and uniqueness of solutions. We also consider a number of biologically relevant asymptotic limits of the model. We prove convergence to limiting problems which take the form of free boundary problems posed on the cell surface. We also report on numerical simulations illustrating convergence to one of the limiting problems as well as the spatiotemporal distributions of the receptors and ligands in a realistic geometry.

Kinematics of coronal rain in a transversely oscillating loop : ponderomotive force and rainexcited oscillations
http://hdl.handle.net/10023/9777
Context. Coronal rain are cool dense blobs that form in solar coronal loops and are a manifestation of catastrophic cooling linked to thermal instability. Once formed, rain falls towards the solar surface at subballistic speeds, which is not wellunderstood. Pressure forces seem to be the prime candidate to explain this. In many observations rain is accompanied by transverse oscillations and the interaction between the two needs to be explored. Aims. Therefore, an alternative kinematic model for coronal rain kinematics in transversely oscillating loops is developed to understand the physical nature of the observed subballistic falling motion of rain. It explicitly explores the role of the ponderomotive force arising from the transverse oscillation on the rain motion as well as the capacity of rain to excite wave motion. Methods. An analytical model is presented that describes a rain blob guided by the coronal magnetic field supporting a one dimensional shear Alfvén wave as a point mass on an oscillating string. The model includes gravity and the ponderomotive force from the oscillation acting on the mass, as well as the inertia of the mass acting on the oscillation. Results. The kinematics of rain in the limit of negligible rain mass are explored and falling and trapped regimes are found, depending on wave amplitude. In the trapped regime for the fundamental mode, the rain blob bounces back and forth around the loop top at a long period inversely proportional to the oscillation amplitude. The model is compared with several observational rain studies, including one indepth comparison with an observation that shows rain with upand down bobbing motion. The role of rain inertia in exciting transverse oscillations is explored in inclined loops. Conclusions. It is found that the model requires displacement amplitudes of the transverse oscillation that are typically an order of magnitude larger than observed to explain the measured subballistic motion of the rain. Therefore, it is concluded that the ponderomotive force is not the primary reason for understanding subballistic motion, but it plays a role in cases of large loop oscillations.The appearance of rain causes the excitation of smallamplitude transverse oscillations that may explain observed events and provide a seismological tool to measure rain mass.
E.V. acknowledges support from the Warwick STFC Consolidated Grant ST/L000733/I. P.A. acknowledges support from the EU Horizon 2020 Research and Innovation programme (grant agreement No. 647214). P.K. acknowledges support from a UK STFC PhD studentship. T.N. acknowledges support from the St Andrews STFC Consolidated Grant SN/N000609/1.
Wed, 01 Feb 2017 00:00:00 GMT
http://hdl.handle.net/10023/9777
20170201T00:00:00Z
Verwichte, E.
Antolin, P.
Rowlands, G.
Kohutova, P.
Neukirch, T.
Context. Coronal rain are cool dense blobs that form in solar coronal loops and are a manifestation of catastrophic cooling linked to thermal instability. Once formed, rain falls towards the solar surface at subballistic speeds, which is not wellunderstood. Pressure forces seem to be the prime candidate to explain this. In many observations rain is accompanied by transverse oscillations and the interaction between the two needs to be explored. Aims. Therefore, an alternative kinematic model for coronal rain kinematics in transversely oscillating loops is developed to understand the physical nature of the observed subballistic falling motion of rain. It explicitly explores the role of the ponderomotive force arising from the transverse oscillation on the rain motion as well as the capacity of rain to excite wave motion. Methods. An analytical model is presented that describes a rain blob guided by the coronal magnetic field supporting a one dimensional shear Alfvén wave as a point mass on an oscillating string. The model includes gravity and the ponderomotive force from the oscillation acting on the mass, as well as the inertia of the mass acting on the oscillation. Results. The kinematics of rain in the limit of negligible rain mass are explored and falling and trapped regimes are found, depending on wave amplitude. In the trapped regime for the fundamental mode, the rain blob bounces back and forth around the loop top at a long period inversely proportional to the oscillation amplitude. The model is compared with several observational rain studies, including one indepth comparison with an observation that shows rain with upand down bobbing motion. The role of rain inertia in exciting transverse oscillations is explored in inclined loops. Conclusions. It is found that the model requires displacement amplitudes of the transverse oscillation that are typically an order of magnitude larger than observed to explain the measured subballistic motion of the rain. Therefore, it is concluded that the ponderomotive force is not the primary reason for understanding subballistic motion, but it plays a role in cases of large loop oscillations.The appearance of rain causes the excitation of smallamplitude transverse oscillations that may explain observed events and provide a seismological tool to measure rain mass.

A test case for the inviscid shallowwater equations on the sphere
http://hdl.handle.net/10023/9761
A numerically converged solution to the inviscid global shallowwater equations for a predefined time interval is documented to provide a convenient benchmark for model validation. The solution is based on the same initial conditions as a previously documented solution for the viscous equations. The solution is computed using two independent numerical schemes, one a pseudospectral scheme based on an expansion in spherical harmonics and the other a finitevolume scheme on a cubedsphere grid. Flow fields and various integral norms are documented to facilitate model comparison and validation. Attention is drawn to the utility of the potential vorticity supremum as a convenient and sensitive test of numerical convergence, in which the exact value is known a priori over the entire time interval.
Partial support for this work was provided through the National Science Foundation award AGS1333029.
Fri, 01 Jan 2016 00:00:00 GMT
http://hdl.handle.net/10023/9761
20160101T00:00:00Z
Scott, R. K.
Harris, L. M.
Polvani, L. M.
A numerically converged solution to the inviscid global shallowwater equations for a predefined time interval is documented to provide a convenient benchmark for model validation. The solution is based on the same initial conditions as a previously documented solution for the viscous equations. The solution is computed using two independent numerical schemes, one a pseudospectral scheme based on an expansion in spherical harmonics and the other a finitevolume scheme on a cubedsphere grid. Flow fields and various integral norms are documented to facilitate model comparison and validation. Attention is drawn to the utility of the potential vorticity supremum as a convenient and sensitive test of numerical convergence, in which the exact value is known a priori over the entire time interval.

Models of interacting pairs of thin, quasigeostrophic vortices: steadystate solutions and nonlinear stability
http://hdl.handle.net/10023/9744
We study pairwise interactions of elliptical quasigeostrophic vortices as the limiting case of vanishingly thin uniform potential vorticity ellipsoids. In this limit, the product of the vertical extent of the ellipsoid and the potential vorticity within it is held fixed to a finite nonzero constant. Such elliptical 'lenses' inherit the property that, in isolation, they steadily rotate without changing shape. Here, we use this property to extend both standard moment models and Hamiltonian ellipsoidal models to approximate the dynamical interaction of such elliptical lenses. By neglecting nonelliptical deformations, the simplified models reduce the dynamics to just four degrees of freedom per vortex. For simplicity, we focus on pairwise interactions between identical elliptical vortices initially separated in both the horizontal and vertical directions. The dynamics of the simplified models are compared with the full quasigeostrophic (QG) dynamics of the system, and show good agreement as expected for sufficiently distant lenses. The results reveal the existence of families of steadily rotating equilibria in the initial horizontal and vertical separation parameter space. For sufficiently large vertical separations, equilibria with varying shape exist for all horizontal separations. Below a critical vertical separation (stretched by the constant ratio of buoyancy to Coriolis frequencies N/f), comparable to the mean radius of either vortex, a gap opens in horizontal separation where no equilibria are possible. Solutions near the edge of this gap are unstable. In the full QG system, equilibria at the edge of the gap exhibit corners (infinite curvature) along their boundaries. Comparisons of the model results with the full nonlinear QG evolution show that the early stages of the instability are captured by the Hamiltonian elliptical model but not by the moment model that inaccurately estimates shorterrange interactions.
This work was supported by the Office of Naval Research under Grant N0001411 10087; the National Science Foundation under Grant 1107307; and the UK Engineering and Physical Sciences Research Council under grant EP/H001794/1.
Fri, 01 Jan 2016 00:00:00 GMT
http://hdl.handle.net/10023/9744
20160101T00:00:00Z
Bersanelli, Matteo
Dritschel, David G.
Lancellotti, Carlo
Poje, Andrew C.
We study pairwise interactions of elliptical quasigeostrophic vortices as the limiting case of vanishingly thin uniform potential vorticity ellipsoids. In this limit, the product of the vertical extent of the ellipsoid and the potential vorticity within it is held fixed to a finite nonzero constant. Such elliptical 'lenses' inherit the property that, in isolation, they steadily rotate without changing shape. Here, we use this property to extend both standard moment models and Hamiltonian ellipsoidal models to approximate the dynamical interaction of such elliptical lenses. By neglecting nonelliptical deformations, the simplified models reduce the dynamics to just four degrees of freedom per vortex. For simplicity, we focus on pairwise interactions between identical elliptical vortices initially separated in both the horizontal and vertical directions. The dynamics of the simplified models are compared with the full quasigeostrophic (QG) dynamics of the system, and show good agreement as expected for sufficiently distant lenses. The results reveal the existence of families of steadily rotating equilibria in the initial horizontal and vertical separation parameter space. For sufficiently large vertical separations, equilibria with varying shape exist for all horizontal separations. Below a critical vertical separation (stretched by the constant ratio of buoyancy to Coriolis frequencies N/f), comparable to the mean radius of either vortex, a gap opens in horizontal separation where no equilibria are possible. Solutions near the edge of this gap are unstable. In the full QG system, equilibria at the edge of the gap exhibit corners (infinite curvature) along their boundaries. Comparisons of the model results with the full nonlinear QG evolution show that the early stages of the instability are captured by the Hamiltonian elliptical model but not by the moment model that inaccurately estimates shorterrange interactions.

The energy budget of stellar magnetic fields : comparing nonpotential simulations and observations
http://hdl.handle.net/10023/9742
The magnetic geometry of the surface magnetic fields of more than 55 cool stars have now been mapped using spectropolarimetry. In order to better understand these observations, we compare the magnetic field topology at different surface scale sizes of observed and simulated cool stars. For ease of comparison between the highresolution nonpotential magnetofrictional simulations and the relatively lowresolution observations, we filter out the smallscale field in the simulations using a spherical harmonics decomposition. We show that the largescale field topologies of the solarbased simulations produce values of poloidal/toroidal fields and fractions of energy in axisymmetric modes that are similar to the observations. These global nonpotential evolution model simulations capture key magnetic features of the observed solarlike stars through the processes of surface flux transport and magnetic flux emergence. They do not, however, reproduce the magnetic field of Mdwarfs or stars with dominantly toroidal field. Furthermore, we analyse the magnetic field topologies of individual spherical harmonics for the simulations and discover that the dipole is predominately poloidal, while the quadrupole shows the highest fraction of toroidal fields. Magnetic field structures smaller than a quadrupole display a fixed ratio between the poloidal and toroidal magnetic energies.
LTL acknowledges support from the Scottish Universities Physics Alliance (SUPA) prize studentship and the University of St Andrews Higgs studentship. MMJ and VS acknowledge a Science & Technology Facilities Council (STFC) postdoctoral fellowship.
Tue, 21 Mar 2017 00:00:00 GMT
http://hdl.handle.net/10023/9742
20170321T00:00:00Z
Lehmann, L. T.
Jardine, M. M.
Vidotto, A. A.
Mackay, D. H.
See, Wyke Chun Victor
Donati, J. F.
Folsom, C. P.
Jeffers, S. V.
Marsden, Steve
Morin, J.
Petit, P.
The magnetic geometry of the surface magnetic fields of more than 55 cool stars have now been mapped using spectropolarimetry. In order to better understand these observations, we compare the magnetic field topology at different surface scale sizes of observed and simulated cool stars. For ease of comparison between the highresolution nonpotential magnetofrictional simulations and the relatively lowresolution observations, we filter out the smallscale field in the simulations using a spherical harmonics decomposition. We show that the largescale field topologies of the solarbased simulations produce values of poloidal/toroidal fields and fractions of energy in axisymmetric modes that are similar to the observations. These global nonpotential evolution model simulations capture key magnetic features of the observed solarlike stars through the processes of surface flux transport and magnetic flux emergence. They do not, however, reproduce the magnetic field of Mdwarfs or stars with dominantly toroidal field. Furthermore, we analyse the magnetic field topologies of individual spherical harmonics for the simulations and discover that the dipole is predominately poloidal, while the quadrupole shows the highest fraction of toroidal fields. Magnetic field structures smaller than a quadrupole display a fixed ratio between the poloidal and toroidal magnetic energies.

Influence of nonpotential coronal magnetic topology on solar wind models
http://hdl.handle.net/10023/9729
By comparing a magnetofrictional model of the low coronal magnetic field to a potential field source surface model, we investigate the possible impact of nonpotential magnetic structure on empirical solar wind models. These empirical models (such as WangSheeleyArge) estimate the distribution of solar wind speed solely from the magnetic field structure in the low corona. Our models are computed in a domain between the solar surface and 2.5 solar radii, and are extended to 0.1 AU using a Schatten current sheet model. The nonpotential field has a more complex magnetic skeleton and quasiseparatrix structures than the potential field, leading to different substructure in the solar wind speed proxies. It contains twisted magnetic structures which can perturb the separatrix surfaces traced down from the base of the heliospheric current sheet. A significant difference between the models is the greater amount of open magnetic flux in the nonpotential model. Using existing empirical formulae this leads to higher predicted wind speeds for two reasons: partly because magnetic flux tubes expand less rapidly with height, but more importantly because more open field lines are further from coronal hole boundaries.
Thu, 01 Oct 2015 00:00:00 GMT
http://hdl.handle.net/10023/9729
20151001T00:00:00Z
Edwards, Sarah Jane
Yeates, Anthony Robinson
Bocquet, Francois
Mackay, Duncan Hendry
By comparing a magnetofrictional model of the low coronal magnetic field to a potential field source surface model, we investigate the possible impact of nonpotential magnetic structure on empirical solar wind models. These empirical models (such as WangSheeleyArge) estimate the distribution of solar wind speed solely from the magnetic field structure in the low corona. Our models are computed in a domain between the solar surface and 2.5 solar radii, and are extended to 0.1 AU using a Schatten current sheet model. The nonpotential field has a more complex magnetic skeleton and quasiseparatrix structures than the potential field, leading to different substructure in the solar wind speed proxies. It contains twisted magnetic structures which can perturb the separatrix surfaces traced down from the base of the heliospheric current sheet. A significant difference between the models is the greater amount of open magnetic flux in the nonpotential model. Using existing empirical formulae this leads to higher predicted wind speeds for two reasons: partly because magnetic flux tubes expand less rapidly with height, but more importantly because more open field lines are further from coronal hole boundaries.

Quiescent prominences in the era of ALMA : simulated observations using 3D wholeprominence fine structure model
http://hdl.handle.net/10023/9710
We use the detailed 3D wholeprominence fine structure model to produce the first simulated highresolution ALMA observations of a modeled quiescent solar prominence. The synthetic brightness temperature and optical thickness maps shown in the present paper are produced using a visualization method for the submillimeter/millimeter radio continua synthesis. We have obtained the simulated observations of both the prominence at the limb and the filament on the disk at wavelengths covering a broad range which encompasses the full potential of ALMA.We demonstrate here to what extent the smallscale and largescale prominence and filament structures will be visible in the ALMA observations spanning both the optically thin and thick regimes. We analyze the relationship between the brightness and kinetic temperature of the prominence plasma. We also illustrate the opportunities ALMA will provide for studying the thermal structure of the prominence plasma from the cool prominence fine structure cores to the prominencecorona transition region. In addition, we show that the detailed 3D modeling of entire prominences with their numerous fine structures will be important for the correct interpretation of future ALMA prominence observations.
Tue, 20 Dec 2016 00:00:00 GMT
http://hdl.handle.net/10023/9710
20161220T00:00:00Z
Gunar, Stanislav
Heinzel, Petr
Mackay, Duncan Hendry
Anzer, Ulrich
We use the detailed 3D wholeprominence fine structure model to produce the first simulated highresolution ALMA observations of a modeled quiescent solar prominence. The synthetic brightness temperature and optical thickness maps shown in the present paper are produced using a visualization method for the submillimeter/millimeter radio continua synthesis. We have obtained the simulated observations of both the prominence at the limb and the filament on the disk at wavelengths covering a broad range which encompasses the full potential of ALMA.We demonstrate here to what extent the smallscale and largescale prominence and filament structures will be visible in the ALMA observations spanning both the optically thin and thick regimes. We analyze the relationship between the brightness and kinetic temperature of the prominence plasma. We also illustrate the opportunities ALMA will provide for studying the thermal structure of the prominence plasma from the cool prominence fine structure cores to the prominencecorona transition region. In addition, we show that the detailed 3D modeling of entire prominences with their numerous fine structures will be important for the correct interpretation of future ALMA prominence observations.

Deciphering satellite observations of compressional ULF waveguide modes
http://hdl.handle.net/10023/9702
We present an analytical method for determining incident and reflection co efficients for flank ULF compressional waveguide modes in Earth’s magnetosphere. In the flank magnetosphere, compressional waves propagate azimuthally, but exhibit a mixed standing/propagating nature radially. Understanding this radial dependence will yield information on the energy absorption and transport of these waves. We provide a step by step method that can be applied to observations of flank ULF waves, which separates these fluctuations into incident and reflected parts. As a means of testing, we apply the method to data from a numerical waveguide simulation, which shows the effect on the reflection coefficient when energy is absorbed at a field line resonance.
T. Elsden would like to thank STFC for financial support for a doctoral training grant, number AMC3 STFC12. A.N. Wright was supported by STFC grant ST/N000609/1.
Fri, 01 Apr 2016 00:00:00 GMT
http://hdl.handle.net/10023/9702
20160401T00:00:00Z
Elsden, Tom
Wright, Andrew Nicholas
Hartinger, Michael
We present an analytical method for determining incident and reflection co efficients for flank ULF compressional waveguide modes in Earth’s magnetosphere. In the flank magnetosphere, compressional waves propagate azimuthally, but exhibit a mixed standing/propagating nature radially. Understanding this radial dependence will yield information on the energy absorption and transport of these waves. We provide a step by step method that can be applied to observations of flank ULF waves, which separates these fluctuations into incident and reflected parts. As a means of testing, we apply the method to data from a numerical waveguide simulation, which shows the effect on the reflection coefficient when energy is absorbed at a field line resonance.

Transverse, propagating velocity perturbations in solar coronal loops
http://hdl.handle.net/10023/9684
As waves and oscillations carry both energy and information, they have enormous potential as a plasma heating mechanism and, through seismology, to provide estimates of local plasma properties which are hard to obtain from direct measurements. Being sufficiently near to allow highresolution observations, the atmosphere of the Sun forms a natural plasma laboratory. Recent observations have revealed that an abundance of waves and oscillations is present in the solar atmosphere, leading to a renewed interest in wave heating mechanisms. This short review paper gives an overview of recently observed transverse, propagating velocity perturbations in coronal loops. These ubiquitous perturbations are observed to undergo strong damping as they propagate. Using 3D numerical simulations of footpointdriven transverse waves propagating in a coronal plasma with a cylindrical density structure, in combination with analytical modelling, it is demonstrated that the observed velocity perturbations can be understood in terms of coupling of different wave modes in the inhomogeneous boundaries of the loops. Mode coupling in the inhomogeneous boundary layers of the loops leads to the coupling of the transversal (kink) mode to the azimuthal (Alfven) mode, observed as the decay of the transverse kink oscillations. Both the numerical and analytical results show the spatial profile of the damped wave has a Gaussian shape to begin with, before switching to exponential decay at large heights. In addition, recent analysis of CoMP (Coronal Multichannel Polarimeter) Doppler shift observations of large, offlimb, transequatorial loops shows that Fourier power at the apex appears to be higher in the highfrequency part of the spectrum than expected from theoretical models. This excess highfrequency FFT power could be tentative evidence for the onset of a cascade of the lowtomid frequency waves into (Alfvenic) turbulence.
Fri, 01 Jan 2016 00:00:00 GMT
http://hdl.handle.net/10023/9684
20160101T00:00:00Z
De Moortel, Ineke
Pascoe, David James
Wright, Andrew Nicholas
Hood, Alan William
As waves and oscillations carry both energy and information, they have enormous potential as a plasma heating mechanism and, through seismology, to provide estimates of local plasma properties which are hard to obtain from direct measurements. Being sufficiently near to allow highresolution observations, the atmosphere of the Sun forms a natural plasma laboratory. Recent observations have revealed that an abundance of waves and oscillations is present in the solar atmosphere, leading to a renewed interest in wave heating mechanisms. This short review paper gives an overview of recently observed transverse, propagating velocity perturbations in coronal loops. These ubiquitous perturbations are observed to undergo strong damping as they propagate. Using 3D numerical simulations of footpointdriven transverse waves propagating in a coronal plasma with a cylindrical density structure, in combination with analytical modelling, it is demonstrated that the observed velocity perturbations can be understood in terms of coupling of different wave modes in the inhomogeneous boundaries of the loops. Mode coupling in the inhomogeneous boundary layers of the loops leads to the coupling of the transversal (kink) mode to the azimuthal (Alfven) mode, observed as the decay of the transverse kink oscillations. Both the numerical and analytical results show the spatial profile of the damped wave has a Gaussian shape to begin with, before switching to exponential decay at large heights. In addition, recent analysis of CoMP (Coronal Multichannel Polarimeter) Doppler shift observations of large, offlimb, transequatorial loops shows that Fourier power at the apex appears to be higher in the highfrequency part of the spectrum than expected from theoretical models. This excess highfrequency FFT power could be tentative evidence for the onset of a cascade of the lowtomid frequency waves into (Alfvenic) turbulence.

Dynamical patterns of coexisting strategies in a hybrid discretecontinuum spatial evolutionary game model
http://hdl.handle.net/10023/9625
We present a novel hybrid modelling framework that takes into account two aspects which have been largely neglected in previous models of spatial evolutionary games: random motion and chemotaxis. A stochastic individualbased model is used to describe the player dynamics,whereas the evolution of the chemoattractant is governed by a reactiondiffusion equation. The two models are coupled by deriving individual movement rules via the discretisation of a taxisdiffusion equation which describes the evolution of the local number of players. In this framework, individuals occupying the same position can engage in a twoplayer game, and are awarded a payoff, interms of reproductive fitness, according to their strategy. As an example, we let individuals play the HawkDove game. Numerical simulations illustrate how random motion and chemotactic response can bring about selfgenerated dynamical patterns that create favourable conditions for the coexistence of hawks and doves in situations in which the two strategies cannot coexist otherwise.In this sense, our work offers a new perspective of research on spatial evolutionary games, and provides a general formalism to study the dynamics of spatiallystructured populations in biological and social contexts where individual motion is likely to affect natural selection of behavioural traits.
Wed, 07 Dec 2016 00:00:00 GMT
http://hdl.handle.net/10023/9625
20161207T00:00:00Z
Burgess, A. E. F
Schofield, P. G.
Hubbard, S. F.
Chaplain, Mark A. J.
Lorenzi, T.
We present a novel hybrid modelling framework that takes into account two aspects which have been largely neglected in previous models of spatial evolutionary games: random motion and chemotaxis. A stochastic individualbased model is used to describe the player dynamics,whereas the evolution of the chemoattractant is governed by a reactiondiffusion equation. The two models are coupled by deriving individual movement rules via the discretisation of a taxisdiffusion equation which describes the evolution of the local number of players. In this framework, individuals occupying the same position can engage in a twoplayer game, and are awarded a payoff, interms of reproductive fitness, according to their strategy. As an example, we let individuals play the HawkDove game. Numerical simulations illustrate how random motion and chemotactic response can bring about selfgenerated dynamical patterns that create favourable conditions for the coexistence of hawks and doves in situations in which the two strategies cannot coexist otherwise.In this sense, our work offers a new perspective of research on spatial evolutionary games, and provides a general formalism to study the dynamics of spatiallystructured populations in biological and social contexts where individual motion is likely to affect natural selection of behavioural traits.

The usage of a threecompartment model to investigate the metabolic differences between hepatic reductase null and wildtype mice
http://hdl.handle.net/10023/9611
The Cytochrome P450 (CYP) system is involved in 90% of the human body’s interactions with xenobiotics and due to this, it has become an area of avid research including the creation of transgenic mice. This paper proposes a threecompartment model which is used to explain the drug metabolism in the Hepatic Reductase Null (HRN) mouse developed by the University of Dundee (Henderson, C. J., Otto, D. M. E., Carrie, D., Magnuson, M. A., McLaren, A. W., Rosewell, I. and Wolf, C. R. (2003) Inactivation of the hepatic cytochrome p450 system by conditional deletion of hepatic cytochrome p450 reductase. J. Biol. Chem. 278, 13480–13486). The model is compared with a twocompartment model using experimental data from studies using wildtype and HRN mice. This comparison allowed for metabolic differences between the two types of mice to be isolated. The three sets of drug data (Gefitinib, Midazolam and Thalidomide) showed that the transgenic mouse has a decreased rate of metabolism.
L.H. is currently funded by the Research Foundation Flanders (FWO) and the Belgian Science Policy Office under Grant No. IAPVI/10.
Mon, 05 Oct 2015 00:00:00 GMT
http://hdl.handle.net/10023/9611
20151005T00:00:00Z
Hill, Lydia
Chaplain, Mark Andrew Joseph
Wolf, Roland
Kapelyukh, Yury
The Cytochrome P450 (CYP) system is involved in 90% of the human body’s interactions with xenobiotics and due to this, it has become an area of avid research including the creation of transgenic mice. This paper proposes a threecompartment model which is used to explain the drug metabolism in the Hepatic Reductase Null (HRN) mouse developed by the University of Dundee (Henderson, C. J., Otto, D. M. E., Carrie, D., Magnuson, M. A., McLaren, A. W., Rosewell, I. and Wolf, C. R. (2003) Inactivation of the hepatic cytochrome p450 system by conditional deletion of hepatic cytochrome p450 reductase. J. Biol. Chem. 278, 13480–13486). The model is compared with a twocompartment model using experimental data from studies using wildtype and HRN mice. This comparison allowed for metabolic differences between the two types of mice to be isolated. The three sets of drug data (Gefitinib, Midazolam and Thalidomide) showed that the transgenic mouse has a decreased rate of metabolism.

On the connection between propagating solar coronal disturbances and chromospheric footpoints
http://hdl.handle.net/10023/9600
The Interface Region Imaging Spectrograph (IRIS) provides an unparalleled opportunity to explore the (thermal) interface between the chromosphere, transition region, and the coronal plasma observed by the Atmospheric Imaging Assembly (AIA) of the Solar Dynamics Observatory (SDO). The SDO/AIA observations of coronal loop footpoints show strong recurring upward propagating signals—“propagating coronal disturbances” (PCDs) with apparent speeds of the order of 100–120 km/s1. That signal has a clear signature in the slitjaw images of IRIS in addition to identifiable spectral signatures and diagnostics in the Mg IIh (2803 Å) line. In analyzing the Mg IIh line, we are able to observe the presence of magnetoacoustic shock waves that are also present in the vicinity of the coronal loop footpoints. We see there is enough of a correspondence between the shock propagation in Mg IIh, the evolution of the Si IV line profiles, and the PCD evolution to indicate that these waves are an important ingredient for PCDs. In addition, the strong flows in the jetlike features in the IRIS Si IV slitjaw images are also associated with PCDs, such that waves and flows both appear to be contributing to the signals observed at the footpoints of PCDs.
Thu, 01 Sep 2016 00:00:00 GMT
http://hdl.handle.net/10023/9600
20160901T00:00:00Z
Bryans, Paul
McIntosh, Scott W.
De Moortel, Ineke
De Pontieu, Bart
The Interface Region Imaging Spectrograph (IRIS) provides an unparalleled opportunity to explore the (thermal) interface between the chromosphere, transition region, and the coronal plasma observed by the Atmospheric Imaging Assembly (AIA) of the Solar Dynamics Observatory (SDO). The SDO/AIA observations of coronal loop footpoints show strong recurring upward propagating signals—“propagating coronal disturbances” (PCDs) with apparent speeds of the order of 100–120 km/s1. That signal has a clear signature in the slitjaw images of IRIS in addition to identifiable spectral signatures and diagnostics in the Mg IIh (2803 Å) line. In analyzing the Mg IIh line, we are able to observe the presence of magnetoacoustic shock waves that are also present in the vicinity of the coronal loop footpoints. We see there is enough of a correspondence between the shock propagation in Mg IIh, the evolution of the Si IV line profiles, and the PCD evolution to indicate that these waves are an important ingredient for PCDs. In addition, the strong flows in the jetlike features in the IRIS Si IV slitjaw images are also associated with PCDs, such that waves and flows both appear to be contributing to the signals observed at the footpoints of PCDs.

The interaction between two oppositely travelling, horizontally offset, antisymmetric quasigeostrophic hetons
http://hdl.handle.net/10023/9593
We investigate numerically the nonlinear interactions between hetons. Hetons are baroclinic structures consisting of two vortices of opposite sign lying at different depths. Hetons are longlived. They most often translate (they can sometimes rotate) and therefore they can noticeably contribute to the transport of scalar properties in the oceans. Heton interactions can interrupt this translation and thus this transport, by inducing a reconfiguration of interacting hetons into more complex baroclinic multipoles. More specifically, we study here the general case of two hetons, which collide with an offset between their translation axes. For this purpose, we use the point vortex theory, the ellipsoidal vortex model and direct simulations in the threedimensional quasigeostrophic, contour surgery model. More specifically, this paper shows that there are in general three regimes for the interaction. For small horizontal offsets between the hetons, their vortices recombine as samedepth dipoles which escape at an angle. The angle depends in particular on the horizontal offset. It is a right angle for no offset, and the angle is shallower for small but finite offsets. The second limiting regime is for large horizontal offsets where the two hetons remain the same hetonic structures but are deflected by the weaker mutual interaction. Finally the intermediate regime is for moderate offsets. This is the regime where the formation of a metastable quadrupole is possible. The formation of this quadrupole greatly restrains transport. Indeed, it constrains the vortices to reside in a closed area. It is shown that the formation of such structures is enhanced by the quasi periodic deformation of the vortices. Indeed, these structures are nearly unobtainable for singular vortices (point vortices) but may be obtained using deformable, finitecore vortices.
Sun, 01 May 2016 00:00:00 GMT
http://hdl.handle.net/10023/9593
20160501T00:00:00Z
Reinaud, Jean Noel
Carton, Xavier
We investigate numerically the nonlinear interactions between hetons. Hetons are baroclinic structures consisting of two vortices of opposite sign lying at different depths. Hetons are longlived. They most often translate (they can sometimes rotate) and therefore they can noticeably contribute to the transport of scalar properties in the oceans. Heton interactions can interrupt this translation and thus this transport, by inducing a reconfiguration of interacting hetons into more complex baroclinic multipoles. More specifically, we study here the general case of two hetons, which collide with an offset between their translation axes. For this purpose, we use the point vortex theory, the ellipsoidal vortex model and direct simulations in the threedimensional quasigeostrophic, contour surgery model. More specifically, this paper shows that there are in general three regimes for the interaction. For small horizontal offsets between the hetons, their vortices recombine as samedepth dipoles which escape at an angle. The angle depends in particular on the horizontal offset. It is a right angle for no offset, and the angle is shallower for small but finite offsets. The second limiting regime is for large horizontal offsets where the two hetons remain the same hetonic structures but are deflected by the weaker mutual interaction. Finally the intermediate regime is for moderate offsets. This is the regime where the formation of a metastable quadrupole is possible. The formation of this quadrupole greatly restrains transport. Indeed, it constrains the vortices to reside in a closed area. It is shown that the formation of such structures is enhanced by the quasi periodic deformation of the vortices. Indeed, these structures are nearly unobtainable for singular vortices (point vortices) but may be obtained using deformable, finitecore vortices.

Modeling observed decayless oscillations as resonantly enhanced KelvinHelmholtz vortices from transverse MHD waves and their seismological application
http://hdl.handle.net/10023/9577
In the highly structured solar corona, resonant absorption is an unavoidable mechanism of energy transfer from global transverse MHD waves to local azimuthal Alfvén waves. Due to its localised nature, a direct detection of this mechanism is extremely difficult. Yet, it is the leading theory explaining the observed fast damping of the global transverse waves. However, at odds with this theoretical prediction, recent observations indicate that in the low amplitude regime such transverse MHD waves can also appear decayless, a yet unsolved phenomenon. Recent numerical work has shown that KelvinHelmholtz instabilities (KHI) often accompany transverse MHD waves. In this work, we combine 3D MHD simulations and forward modelling to show that for currently achieved spatial resolution and observed small amplitudes, an apparent decayless oscillation is obtained. This effect results from the combination of periodic brightenings produced by the KHI and the coherent motion of the KHI vortices amplified by resonant absorption. Such effect is especially clear in emission lines forming at temperatures that capture the boundary dynamics rather than the core, and reflects the low damping character of the local azimuthal Alfvén waves resonantly coupled to the kink mode. Due to phase mixing, the detected period can vary depending on the emission line, with those sensitive to the boundary having shorter periods than those sensitive to the loop core. This allows to estimate the density contrast at the boundary.
Wed, 12 Oct 2016 00:00:00 GMT
http://hdl.handle.net/10023/9577
20161012T00:00:00Z
Antolin, P.
De Moortel, Ineke
Van Doorsselaere, T.
Yokoyama, T.
In the highly structured solar corona, resonant absorption is an unavoidable mechanism of energy transfer from global transverse MHD waves to local azimuthal Alfvén waves. Due to its localised nature, a direct detection of this mechanism is extremely difficult. Yet, it is the leading theory explaining the observed fast damping of the global transverse waves. However, at odds with this theoretical prediction, recent observations indicate that in the low amplitude regime such transverse MHD waves can also appear decayless, a yet unsolved phenomenon. Recent numerical work has shown that KelvinHelmholtz instabilities (KHI) often accompany transverse MHD waves. In this work, we combine 3D MHD simulations and forward modelling to show that for currently achieved spatial resolution and observed small amplitudes, an apparent decayless oscillation is obtained. This effect results from the combination of periodic brightenings produced by the KHI and the coherent motion of the KHI vortices amplified by resonant absorption. Such effect is especially clear in emission lines forming at temperatures that capture the boundary dynamics rather than the core, and reflects the low damping character of the local azimuthal Alfvén waves resonantly coupled to the kink mode. Due to phase mixing, the detected period can vary depending on the emission line, with those sensitive to the boundary having shorter periods than those sensitive to the loop core. This allows to estimate the density contrast at the boundary.

Neutral and nonneutral collisionless plasma equilibria for twisted flux tubes : the GoldHoyle model in a background field
http://hdl.handle.net/10023/9539
We calculate exact onedimensional collisionless plasma equilibria for a continuum of flux tube models, for which the total magnetic field is made up of the `forcefree' GoldHoyle magnetic flux tube embedded in a uniform and antiparallel background magnetic field. For a sufficiently weak background magnetic field, the axial component of the total magnetic field reverses at some finite radius. The presence of the background magnetic field means that the total system is not exactly forcefree, but by reducing its magnitude the departure from forcefree can be made as small as desired. The distribution function for each species is a function of the three constants of motion; namely the Hamiltonian and the canonical momenta in the axial and azimuthal directions. Poisson's Equation and Amp ere's Law are solved exactly, and the solution allows either electrically neutral or nonneutral configurations, depending on the values of the bulk ion and electron flows. These equilibria have possible applications in various solar, space and astrophysical contexts, as well as in the laboratory.
The authors gratefully acknowledge the support of the Science and Technology Facilities Council Consolidated Grants ST/K000950/1 and ST/N000609/1, as well as Doctoral Training Grant ST/K502327/1. We also gratefully acknowledge funding from Leverhulme Trust Research Project Grant F/00268/BB.
Thu, 01 Sep 2016 00:00:00 GMT
http://hdl.handle.net/10023/9539
20160901T00:00:00Z
Allanson, Oliver Douglas
Wilson, Fiona
Neukirch, Thomas
We calculate exact onedimensional collisionless plasma equilibria for a continuum of flux tube models, for which the total magnetic field is made up of the `forcefree' GoldHoyle magnetic flux tube embedded in a uniform and antiparallel background magnetic field. For a sufficiently weak background magnetic field, the axial component of the total magnetic field reverses at some finite radius. The presence of the background magnetic field means that the total system is not exactly forcefree, but by reducing its magnitude the departure from forcefree can be made as small as desired. The distribution function for each species is a function of the three constants of motion; namely the Hamiltonian and the canonical momenta in the axial and azimuthal directions. Poisson's Equation and Amp ere's Law are solved exactly, and the solution allows either electrically neutral or nonneutral configurations, depending on the values of the bulk ion and electron flows. These equilibria have possible applications in various solar, space and astrophysical contexts, as well as in the laboratory.

The role of planetary waves in the tropospheric jet response to stratospheric cooling
http://hdl.handle.net/10023/9528
An idealized general circulation model is used to assess the importance of planetaryscale waves in determining the position of the tropospheric jet, specifically its tendency to shift poleward as winter stratospheric cooling is increased. Full model integrations are compared against integrations in which planetary waves are truncated in the zonal direction, and only synopticscale waves are retained. Two series of truncated integrations are considered, using (i) a modified radiative equilibrium temperature or (ii) a nudgedbias correction technique. Both produce tropospheric climatologies that are similar to the full model when stratospheric cooling is weak. When stratospheric cooling is increased, the results indicate that the interaction between planetary and synopticscale waves plays an important role in determining the structure of the tropospheric mean flow and rule out the possibility that the jet shift occurs purely as a response to changes in the planetary or synopticscale wave fields alone.
K.L.S. is funded in part by a Natural Sciences and Engineering Council of Canada Postdoctoral Fellowship. R.K.S. acknowledges support from the National Science Foundation.
Mon, 28 Mar 2016 00:00:00 GMT
http://hdl.handle.net/10023/9528
20160328T00:00:00Z
Smith, Karen L.
Scott, Richard K.
An idealized general circulation model is used to assess the importance of planetaryscale waves in determining the position of the tropospheric jet, specifically its tendency to shift poleward as winter stratospheric cooling is increased. Full model integrations are compared against integrations in which planetary waves are truncated in the zonal direction, and only synopticscale waves are retained. Two series of truncated integrations are considered, using (i) a modified radiative equilibrium temperature or (ii) a nudgedbias correction technique. Both produce tropospheric climatologies that are similar to the full model when stratospheric cooling is weak. When stratospheric cooling is increased, the results indicate that the interaction between planetary and synopticscale waves plays an important role in determining the structure of the tropospheric mean flow and rule out the possibility that the jet shift occurs purely as a response to changes in the planetary or synopticscale wave fields alone.

Modeling the sun's smallscale global photospheric magnetic field
http://hdl.handle.net/10023/9511
We present a new model for the Sun's global photospheric magnetic field during a deep minimum of activity, in which no active regions emerge. The emergence and subsequent evolution of smallscale magnetic features across the full solar surface is simulated, subject to the influence of a global supergranular flow pattern. Visually, the resulting simulated magnetograms reproduce the typical structure and scale observed in quiet Sun magnetograms. Quantitatively, the simulation quickly reaches a steady state, resulting in a mean field and flux distribution that are in good agreement with those determined from observations. A potential coronal magnetic field is extrapolated from the simulated full Sun magnetograms to consider the implications of such a quiet photospheric magnetic field on the corona and inner heliosphere. The bulk of the coronal magnetic field closes very low down, in short connections between smallscale features in the simulated magnetic network. Just 0.1% of the photospheric magnetic flux is found to be open at 2.5 R⊙, around 10–100 times less than that determined for typical Helioseismic and Magnetic Imager synoptic map observations. If such conditions were to exist on the Sun, this would lead to a significantly weaker interplanetary magnetic field than is currently observed, and hence a much higher cosmic ray flux at Earth.
Wed, 19 Oct 2016 00:00:00 GMT
http://hdl.handle.net/10023/9511
20161019T00:00:00Z
Meyer, Karen Alison
Mackay, Duncan Hendry
We present a new model for the Sun's global photospheric magnetic field during a deep minimum of activity, in which no active regions emerge. The emergence and subsequent evolution of smallscale magnetic features across the full solar surface is simulated, subject to the influence of a global supergranular flow pattern. Visually, the resulting simulated magnetograms reproduce the typical structure and scale observed in quiet Sun magnetograms. Quantitatively, the simulation quickly reaches a steady state, resulting in a mean field and flux distribution that are in good agreement with those determined from observations. A potential coronal magnetic field is extrapolated from the simulated full Sun magnetograms to consider the implications of such a quiet photospheric magnetic field on the corona and inner heliosphere. The bulk of the coronal magnetic field closes very low down, in short connections between smallscale features in the simulated magnetic network. Just 0.1% of the photospheric magnetic flux is found to be open at 2.5 R⊙, around 10–100 times less than that determined for typical Helioseismic and Magnetic Imager synoptic map observations. If such conditions were to exist on the Sun, this would lead to a significantly weaker interplanetary magnetic field than is currently observed, and hence a much higher cosmic ray flux at Earth.

The possible impact of L5 magnetograms on nonpotential solar coronal magnetic field simulations
http://hdl.handle.net/10023/9480
The proposed CarringtonL5 mission would bring instruments to the L5 Lagrange point to provide us with crucial data for space weather prediction. To assess the importance of including a magnetograph, we consider the possible differences in nonpotential solar coronal magnetic field simulations when magnetograph observations are available from the L5 point, compared to an L1based field of view. A time series of synoptic radial magnetic field maps is constructed to capture the emergence of two active regions from the L5 field of view. These regions are initially absent in the L1 magnetic field maps, but are included once they rotate into the L1 field of view. Nonpotential simulations for the two sets of input data are compared in detail. Within the bipolar active regions themselves, differences in the magnetic field structure can exist between the two simulations once the active regions are included in both. These differences tend to reduce within 5 days of the active region being included in L1. The delayed emergence in L1 can however lead to significant persistent differences in long range connectivity between the active regions and the surrounding fields, and also in the global magnetic energy. In particular, the open magnetic flux, and the location of open magnetic foot points, are sensitive to capturing the real time of emergence. These results suggest that a magnetograph at L5 could significantly improve predictions of the nonpotential corona, interplanetary magnetic field and of solar wind source regions on the Sun.
Sat, 10 Sep 2016 00:00:00 GMT
http://hdl.handle.net/10023/9480
20160910T00:00:00Z
Weinzierl, Marion
Mackay, Duncan Hendry
Yeates, Anthony Robinson
Pevtsov, Alexei
The proposed CarringtonL5 mission would bring instruments to the L5 Lagrange point to provide us with crucial data for space weather prediction. To assess the importance of including a magnetograph, we consider the possible differences in nonpotential solar coronal magnetic field simulations when magnetograph observations are available from the L5 point, compared to an L1based field of view. A time series of synoptic radial magnetic field maps is constructed to capture the emergence of two active regions from the L5 field of view. These regions are initially absent in the L1 magnetic field maps, but are included once they rotate into the L1 field of view. Nonpotential simulations for the two sets of input data are compared in detail. Within the bipolar active regions themselves, differences in the magnetic field structure can exist between the two simulations once the active regions are included in both. These differences tend to reduce within 5 days of the active region being included in L1. The delayed emergence in L1 can however lead to significant persistent differences in long range connectivity between the active regions and the surrounding fields, and also in the global magnetic energy. In particular, the open magnetic flux, and the location of open magnetic foot points, are sensitive to capturing the real time of emergence. These results suggest that a magnetograph at L5 could significantly improve predictions of the nonpotential corona, interplanetary magnetic field and of solar wind source regions on the Sun.

3D MHD modeling of twisted coronal loops
http://hdl.handle.net/10023/9475
We perform MHD modeling of a single bright coronal loop to include the interaction with a nonuniform magnetic field. The field is stressed by random footpoint rotation in the central region and its energy is dissipated into heating by growing currents through anomalous magnetic diffusivity that switches on in the corona above a current density threshold. We model an entire single magnetic flux tube, in the solar atmosphere extending from the highbeta chromosphere to the lowbetacorona through the steep transition region. The magnetic field expands from the chromosphere to the corona. The maximum resolution is ~30 km. We obtain an overall evolution typical of loop models and realistic loop emission in the EUV and Xray bands. The plasma confined in the fluxtube is heated to active region temperatures (~3 MK) after ~2/3 hr. Upflows from the chromosphere up to ~100 km/s fill the core of the fluxtube to densities above 109 cm3. More heating is released in the low corona than the high corona and is finely structured both in space and time.
Mon, 10 Oct 2016 00:00:00 GMT
http://hdl.handle.net/10023/9475
20161010T00:00:00Z
Reale, F.
Orlando, S.
Guarrasi, M.
Mignone, A.
Peres, G.
Hood, A. W.
Priest, E. R.
We perform MHD modeling of a single bright coronal loop to include the interaction with a nonuniform magnetic field. The field is stressed by random footpoint rotation in the central region and its energy is dissipated into heating by growing currents through anomalous magnetic diffusivity that switches on in the corona above a current density threshold. We model an entire single magnetic flux tube, in the solar atmosphere extending from the highbeta chromosphere to the lowbetacorona through the steep transition region. The magnetic field expands from the chromosphere to the corona. The maximum resolution is ~30 km. We obtain an overall evolution typical of loop models and realistic loop emission in the EUV and Xray bands. The plasma confined in the fluxtube is heated to active region temperatures (~3 MK) after ~2/3 hr. Upflows from the chromosphere up to ~100 km/s fill the core of the fluxtube to densities above 109 cm3. More heating is released in the low corona than the high corona and is finely structured both in space and time.

Threedimensional forceddamped dynamical systems with rich dynamics : bifurcations, chaos and unbounded solutions
http://hdl.handle.net/10023/9468
We consider certain autonomous threedimensional dynamical systems that can arise in mechanical and fluiddynamical contexts. Extending a previous study in Craik and Okamoto (2002), to include linear forcing and damping, we find that the fourleaf structure discovered in that paper, and unbounded orbits, persist, but may now be accompanied by three distinct perioddoubling cascades to chaos, and by orbits that approach stable equilibrium points. This rich structure is investigated both analytically and numerically, distinguishing three main cases determined by the damping and forcing parameter values.
T.M. is supported by the GrantinAid for JSPS Fellow No. 24·5312. H.O. is partially supported by JSPS KAKENHI 24244007.
Thu, 01 Jan 2015 00:00:00 GMT
http://hdl.handle.net/10023/9468
20150101T00:00:00Z
Miyaji, Tomoyuki
Okamoto, Hisashi
Craik, Alexander Duncan Davidson
We consider certain autonomous threedimensional dynamical systems that can arise in mechanical and fluiddynamical contexts. Extending a previous study in Craik and Okamoto (2002), to include linear forcing and damping, we find that the fourleaf structure discovered in that paper, and unbounded orbits, persist, but may now be accompanied by three distinct perioddoubling cascades to chaos, and by orbits that approach stable equilibrium points. This rich structure is investigated both analytically and numerically, distinguishing three main cases determined by the damping and forcing parameter values.

Sunspot rotation : II. Effects of varying the field strength and twist of an emerging flux tube
http://hdl.handle.net/10023/9442
Context. Observations of flux emergence indicate that rotational velocities may develop within sunspots. However, the dependence of this rotation on subphotospheric field strength and twist remains largely unknown. Aims. We investigate the effects of varying the initial field strength and twist of an emerging subphotospheric magnetic flux tube onthe rotation of the sunspots at the photosphere. Methods. We consider a simple model of a stratified domain with a subphotospheric interior layer and three overlying atmospheric layers. A twisted arched flux tube is inserted in the interior and is allowed to rise into the atmosphere. To achieve this, the MHD equations are solved using the Lagrangianremap code, Lare3d. We perform a parameter study by independently varying the subphotospheric magnetic field strength and twist. Results. Altering the initial magnetic field strength and twist of the flux tube significantly affects the tube’s evolution and the rotational motions that develop at the photosphere. The rotation angle, vorticity, and current show a direct dependence on the initial field strength. We find that an increase in field strength increases the angle through which the fieldlines rotate, the length of the fieldlines extending into the atmosphere, and the magnetic energy transported to the atmosphere. This also affects the amount of residual twist in the interior. The length of the fieldlines is crucial as we predict the twist per unit length equilibrates to a lower value on longer fieldlines. No such direct dependence is found when we modify the twist of the magnetic field owing to the complex effect this has on the tension force acting on the tube. However, there is still a clear ordering in quantities such as the rotation angle, helicity, and free energy with higher initial twist cases being related to sunspots that rotate more rapidly, transporting more helicity and magnetic energy to the atmosphere.
ZS acknowledges the financial support of the Carnegie Trust for Scotland. This work used the DIRAC 1, UKMHD Consortium machine at the University of St Andrews and the DiRAC Data Centric system at Durham University, operated by the Institute for Computational Cosmology on behalf of the STFC DiRAC HPC Facility (www.dirac.ac.uk). This equipment was funded by BIS National Einfrastructure capital grant ST/K00042X/1, STFC capital grant ST/H008519/1, and STFC DiRAC Operations grant ST/K003267/1 and Durham University. DiRAC is part of the National EInfrastructure.
Thu, 01 Sep 2016 00:00:00 GMT
http://hdl.handle.net/10023/9442
20160901T00:00:00Z
Sturrock, Zoe
Hood, Alan William
Context. Observations of flux emergence indicate that rotational velocities may develop within sunspots. However, the dependence of this rotation on subphotospheric field strength and twist remains largely unknown. Aims. We investigate the effects of varying the initial field strength and twist of an emerging subphotospheric magnetic flux tube onthe rotation of the sunspots at the photosphere. Methods. We consider a simple model of a stratified domain with a subphotospheric interior layer and three overlying atmospheric layers. A twisted arched flux tube is inserted in the interior and is allowed to rise into the atmosphere. To achieve this, the MHD equations are solved using the Lagrangianremap code, Lare3d. We perform a parameter study by independently varying the subphotospheric magnetic field strength and twist. Results. Altering the initial magnetic field strength and twist of the flux tube significantly affects the tube’s evolution and the rotational motions that develop at the photosphere. The rotation angle, vorticity, and current show a direct dependence on the initial field strength. We find that an increase in field strength increases the angle through which the fieldlines rotate, the length of the fieldlines extending into the atmosphere, and the magnetic energy transported to the atmosphere. This also affects the amount of residual twist in the interior. The length of the fieldlines is crucial as we predict the twist per unit length equilibrates to a lower value on longer fieldlines. No such direct dependence is found when we modify the twist of the magnetic field owing to the complex effect this has on the tension force acting on the tube. However, there is still a clear ordering in quantities such as the rotation angle, helicity, and free energy with higher initial twist cases being related to sunspots that rotate more rapidly, transporting more helicity and magnetic energy to the atmosphere.

Uncovering the birth of a coronal mass ejection from twoviewpoint SECCHI observations
http://hdl.handle.net/10023/9428
We investigate the initiation and formation of Coronal Mass Ejections (CMEs) via a detailed twoviewpoint analysis of low corona observations of a relatively fast CME acquired by the SECCHI instruments aboard the STEREO mission. The event which occurred on 2 January 2008, was chosen because of several unique characteristics. It shows upward motions for at least four hours before the flare peak. Its speed and acceleration profiles exhibit a number of inflections which seem to have a direct counterpart in the GOES light curves. We detect and measure, in 3D, loops that collapse toward the erupting channel while the CME is increasing in size and accelerates. We suggest that these collapsing loops are our first evidence of magnetic evacuation behind the forming CME flux rope. We report the detection of a hot structure which becomes the core of the white light CME. We observe and measure unidirectional flows along the erupting filament channel which may be associated with the eruption process. Finally, we compare these observations to the predictions from the standard flareCME model and find a very satisfactory agreement. We conclude that the standard flareCME concept is a reliable representation of the initial stages of CMEs and that multiviewpoint, high cadence EUV observations can be extremely useful in understanding the formation of CMEs.
Mon, 01 Oct 2012 00:00:00 GMT
http://hdl.handle.net/10023/9428
20121001T00:00:00Z
Vourlidas, A.
Syntelis, P.
Tsinganos, K.
We investigate the initiation and formation of Coronal Mass Ejections (CMEs) via a detailed twoviewpoint analysis of low corona observations of a relatively fast CME acquired by the SECCHI instruments aboard the STEREO mission. The event which occurred on 2 January 2008, was chosen because of several unique characteristics. It shows upward motions for at least four hours before the flare peak. Its speed and acceleration profiles exhibit a number of inflections which seem to have a direct counterpart in the GOES light curves. We detect and measure, in 3D, loops that collapse toward the erupting channel while the CME is increasing in size and accelerates. We suggest that these collapsing loops are our first evidence of magnetic evacuation behind the forming CME flux rope. We report the detection of a hot structure which becomes the core of the white light CME. We observe and measure unidirectional flows along the erupting filament channel which may be associated with the eruption process. Finally, we compare these observations to the predictions from the standard flareCME model and find a very satisfactory agreement. We conclude that the standard flareCME concept is a reliable representation of the initial stages of CMEs and that multiviewpoint, high cadence EUV observations can be extremely useful in understanding the formation of CMEs.

Study of the threedimensional shape and dynamics of coronal loops observed by Hinode/EIS
http://hdl.handle.net/10023/9426
We study plasma flows along selected coronal loops in NOAA Active Region 10926, observed on 3 December 2006 with Hinode’sEUVImaging Spectrograph (EIS). From the shape of the loops traced on intensity images and the Doppler shifts measured along their length we compute their threedimensional (3D) shape and plasma flow velocity using a simple geometrical model. This calculation was performed for loops visible in the Fe viii 185 Å, Fe x 184 Å, Fe xii 195 Å, Fe xiii202 Å, and Fe xv 284 Å spectral lines. In most cases the flow is unidirectional from one footpoint to the other but there are also cases of draining motions from the top of the loops to their footpoints. Our results indicate that the same loop may show different flow patterns when observed in different spectral lines, suggesting a dynamically complex rather than a monolithic structure. We have also carried out magnetic extrapolations in the linear forcefree field approximation using SOHO/MDI magnetograms, aiming toward a firstorder identification of extrapolated magnetic field lines corresponding to the reconstructed loops. In all cases, the bestfit extrapolated lines exhibit lefthanded twist (α<0), in agreement with the dominant twist of the region.
Mon, 01 Oct 2012 00:00:00 GMT
http://hdl.handle.net/10023/9426
20121001T00:00:00Z
Syntelis, P.
Gontikakis, C.
Georgoulis, M. K.
Alissandrakis, C. E.
Tsinganos, K.
We study plasma flows along selected coronal loops in NOAA Active Region 10926, observed on 3 December 2006 with Hinode’sEUVImaging Spectrograph (EIS). From the shape of the loops traced on intensity images and the Doppler shifts measured along their length we compute their threedimensional (3D) shape and plasma flow velocity using a simple geometrical model. This calculation was performed for loops visible in the Fe viii 185 Å, Fe x 184 Å, Fe xii 195 Å, Fe xiii202 Å, and Fe xv 284 Å spectral lines. In most cases the flow is unidirectional from one footpoint to the other but there are also cases of draining motions from the top of the loops to their footpoints. Our results indicate that the same loop may show different flow patterns when observed in different spectral lines, suggesting a dynamically complex rather than a monolithic structure. We have also carried out magnetic extrapolations in the linear forcefree field approximation using SOHO/MDI magnetograms, aiming toward a firstorder identification of extrapolated magnetic field lines corresponding to the reconstructed loops. In all cases, the bestfit extrapolated lines exhibit lefthanded twist (α<0), in agreement with the dominant twist of the region.

The spectroscopic imprint of the preeruptive configuration resulting into two major coronal mass ejections
http://hdl.handle.net/10023/9425
Aims: We present a spectroscopic analysis of the preeruptive configuration of active region NOAA 11429, prior to two very fast coronal mass ejections (CMEs) on March 7, 2012 that are associated with this active region. We study the thermal components and the dynamics associated with the ejected flux ropes. Methods: Using differential emission measure (DEM) analysis of Hinode/EIS and SDO/AIA observations, we identify the emission components of both the flux rope and the host active region. We then follow the time evolution of the flux rope emission components by using AIA observations. The plasma density and the Doppler and nonthermal velocities associated with the flux ropes are also calculated from the EIS data. Results: The eastern and western parts of the active region, in which the two different fast CMEs originated during two Xclass flares, were studied separately. In both regions we identified an emission component in the temperature range of log T = 6.87.1 associated with the presence of flux ropes. The time evolution of the eastern region showed an increase in the mean DEM in this temperature range by an order of magnitude, 5 h prior to the first CME. This was associated with a gradual rise and heating of the flux rope as manifested by blueshifts and increased nonthermal velocities in Ca xv 200.97 Å, respectively. An overall upward motion of the flux ropes was measured (relative blueshifts of ~12 km s1). The measured electron density was found to be 4× 1092 × 1010 cm3 (using the ratio of Ca xv 181.90 Å over Ca xv 200.97 Å). We compare our findings with other works on the same AR to provide a unified picture of its evolution.
P.S acknowledges financial support from the programme Aristotelis/SIEMENS at the NOA.
Fri, 01 Apr 2016 00:00:00 GMT
http://hdl.handle.net/10023/9425
20160401T00:00:00Z
Syntelis, P.
Gontikakis, C.
Patsourakos, S.
Tsinganos, K.
Aims: We present a spectroscopic analysis of the preeruptive configuration of active region NOAA 11429, prior to two very fast coronal mass ejections (CMEs) on March 7, 2012 that are associated with this active region. We study the thermal components and the dynamics associated with the ejected flux ropes. Methods: Using differential emission measure (DEM) analysis of Hinode/EIS and SDO/AIA observations, we identify the emission components of both the flux rope and the host active region. We then follow the time evolution of the flux rope emission components by using AIA observations. The plasma density and the Doppler and nonthermal velocities associated with the flux ropes are also calculated from the EIS data. Results: The eastern and western parts of the active region, in which the two different fast CMEs originated during two Xclass flares, were studied separately. In both regions we identified an emission component in the temperature range of log T = 6.87.1 associated with the presence of flux ropes. The time evolution of the eastern region showed an increase in the mean DEM in this temperature range by an order of magnitude, 5 h prior to the first CME. This was associated with a gradual rise and heating of the flux rope as manifested by blueshifts and increased nonthermal velocities in Ca xv 200.97 Å, respectively. An overall upward motion of the flux ropes was measured (relative blueshifts of ~12 km s1). The measured electron density was found to be 4× 1092 × 1010 cm3 (using the ratio of Ca xv 181.90 Å over Ca xv 200.97 Å). We compare our findings with other works on the same AR to provide a unified picture of its evolution.

The major geoeffective solar eruptions of 2012 March 7: comprehensive SuntoEarth analysis
http://hdl.handle.net/10023/9421
During the interval 2012 March 711 the geospace experienced a barrage of intense space weather phenomena including the second largest geomagnetic storm of solar cycle 24 so far. Significant ultralowfrequency wave enhancements and relativisticelectron dropouts in the radiation belts, as well as strong energeticelectron injection events in the magnetosphere were observed. These phenomena were ultimately associated with two ultrafast (>2000 kms1) coronal mass ejections (CMEs), linked to two Xclass flares launched on early 2012 March 7. Given that both powerful events originated from solar active region NOAA 11429 and their onsets were separated by less than an hour, the analysis of the two events and the determination of solar causes and geospace effects are rather challenging. Using satellite data from a flotilla of solar, heliospheric and magnetospheric missions a synergistic SuntoEarth study of diverse observational solar, interplanetary and magnetospheric data sets was performed. It was found that only the second CME was Earthdirected. Using a novel method, we estimated its nearSun magnetic field at 13R⊙ to be in the range [0.01, 0.16] G. Steep radial falloffs of the nearSun CME magnetic field are required to match the magnetic fields of the corresponding interplanetary CME (ICME) at 1 AU. Perturbed upstream solarwind conditions, as resulting from the shock associated with the Earthdirected CME, offer a decent description of its kinematics. The magnetospheric compression caused by the arrival at 1 AU of the shock associated with the ICME was a key factor for radiationbelt dynamics.
Tue, 19 Jan 2016 00:00:00 GMT
http://hdl.handle.net/10023/9421
20160119T00:00:00Z
Patsourakos, S.
Georgoulis, M. K.
Vourlidas, A.
Nindos, A.
Sarris, T.
Anagnostopoulos, G.
Anastasiadis, A.
Chintzoglou, G.
Daglis, I. A.
Gontikakis, C.
Hatzigeorgiu, N.
Iliopoulos, A. C.
Katsavrias, C.
Kouloumvakos, A.
Moraitis, K.
NievesChinchilla, T.
Pavlos, G.
Sarafopoulos, D.
Syntelis, P.
Tsironis, C.
Tziotziou, K.
Vogiatzis, I. I.
Balasis, G.
Georgiou, M.
Karakatsanis, L. P.
Malandraki, O. E.
Papadimitriou, C.
Odstrčil, D.
Pavlos, E. G.
Podlachikova, O.
Sandberg, I.
Turner, D. L.
Xenakis, M. N.
Sarris, E.
Tsinganos, K.
Vlahos, L.
During the interval 2012 March 711 the geospace experienced a barrage of intense space weather phenomena including the second largest geomagnetic storm of solar cycle 24 so far. Significant ultralowfrequency wave enhancements and relativisticelectron dropouts in the radiation belts, as well as strong energeticelectron injection events in the magnetosphere were observed. These phenomena were ultimately associated with two ultrafast (>2000 kms1) coronal mass ejections (CMEs), linked to two Xclass flares launched on early 2012 March 7. Given that both powerful events originated from solar active region NOAA 11429 and their onsets were separated by less than an hour, the analysis of the two events and the determination of solar causes and geospace effects are rather challenging. Using satellite data from a flotilla of solar, heliospheric and magnetospheric missions a synergistic SuntoEarth study of diverse observational solar, interplanetary and magnetospheric data sets was performed. It was found that only the second CME was Earthdirected. Using a novel method, we estimated its nearSun magnetic field at 13R⊙ to be in the range [0.01, 0.16] G. Steep radial falloffs of the nearSun CME magnetic field are required to match the magnetic fields of the corresponding interplanetary CME (ICME) at 1 AU. Perturbed upstream solarwind conditions, as resulting from the shock associated with the Earthdirected CME, offer a decent description of its kinematics. The magnetospheric compression caused by the arrival at 1 AU of the shock associated with the ICME was a key factor for radiationbelt dynamics.

Tracking the evolution of cancer cell populations through the mathematical lens of phenotypestructured equations
http://hdl.handle.net/10023/9363
Background: A thorough understanding of the ecological and evolutionary mechanisms that drive the phenotypic evolution of neoplastic cells is a timely and key challenge for the cancer research community. In this respect, mathematical modelling can complement experimental cancer research by offering alternative means of understanding the results of in vitro and in vivo experiments, and by allowing for a quick and easy exploration of a variety of biological scenarios through in silico studies. Results: To elucidate the roles of phenotypic plasticity and selection pressures in tumour relapse, we present here a phenotypestructured model of evolutionary dynamics in a cancer cell population which is exposed to the action of a cytotoxic drug. The analytical tractability of our model allows us to investigate how the phenotype distribution, the level of phenotypic heterogeneity, and the size of the cell population are shaped by the strength of natural selection, the rate of random epimutations, the intensity of the competition for limited resources between cells, and the drug dose in use. Conclusions: Our analytical results clarify the conditions for the successful adaptation of cancer cells faced with environmental changes. Furthermore, the results of our analyses demonstrate that the same cell population exposed to different concentrations of the same cytotoxic drug can take different evolutionary trajectories, which culminate in the selection of phenotypic variants characterised by different levels of drug tolerance. This suggests that the response of cancer cells to cytotoxic agents is more complex than a simple binary outcome, i.e., extinction of sensitive cells and selection of highly resistant cells. Also, our mathematical results formalise the idea that the use of cytotoxic agents at high doses can act as a doubleedged sword by promoting the outgrowth of drug resistant cellular clones. Overall, our theoretical work offers a formal basis for the development of anticancer therapeutic protocols that go beyond the ‘maximumtolerateddose paradigm’, as they may be more effective than traditional protocols at keeping the size of cancer cell populations under control while avoiding the expansion of drug tolerant clones.
This work was supported in part by the French National Research Agency through the “ANR blanche” project Kibord [ANR13BS010004].
Tue, 23 Aug 2016 00:00:00 GMT
http://hdl.handle.net/10023/9363
20160823T00:00:00Z
Lorenzi, Tommaso
Chisholm, Rebecca H.
Clairambault, Jean
Background: A thorough understanding of the ecological and evolutionary mechanisms that drive the phenotypic evolution of neoplastic cells is a timely and key challenge for the cancer research community. In this respect, mathematical modelling can complement experimental cancer research by offering alternative means of understanding the results of in vitro and in vivo experiments, and by allowing for a quick and easy exploration of a variety of biological scenarios through in silico studies. Results: To elucidate the roles of phenotypic plasticity and selection pressures in tumour relapse, we present here a phenotypestructured model of evolutionary dynamics in a cancer cell population which is exposed to the action of a cytotoxic drug. The analytical tractability of our model allows us to investigate how the phenotype distribution, the level of phenotypic heterogeneity, and the size of the cell population are shaped by the strength of natural selection, the rate of random epimutations, the intensity of the competition for limited resources between cells, and the drug dose in use. Conclusions: Our analytical results clarify the conditions for the successful adaptation of cancer cells faced with environmental changes. Furthermore, the results of our analyses demonstrate that the same cell population exposed to different concentrations of the same cytotoxic drug can take different evolutionary trajectories, which culminate in the selection of phenotypic variants characterised by different levels of drug tolerance. This suggests that the response of cancer cells to cytotoxic agents is more complex than a simple binary outcome, i.e., extinction of sensitive cells and selection of highly resistant cells. Also, our mathematical results formalise the idea that the use of cytotoxic agents at high doses can act as a doubleedged sword by promoting the outgrowth of drug resistant cellular clones. Overall, our theoretical work offers a formal basis for the development of anticancer therapeutic protocols that go beyond the ‘maximumtolerateddose paradigm’, as they may be more effective than traditional protocols at keeping the size of cancer cell populations under control while avoiding the expansion of drug tolerant clones.

Evolution of magnetic helicity during eruptive flares and coronal mass ejections
http://hdl.handle.net/10023/9320
During eruptive solar flares and coronal mass ejections, a nonpotential magnetic arcade with much excess magnetic energy goes unstable and reconnects. It produces a twisted erupting flux rope and leaves behind a sheared arcade of hot coronal loops. We suggest that: the twist of the erupting flux rope can be determined from conservation of magnetic flux and magnetic helicity and equipartition of magnetic helicity. It depends on the geometry of the initial preeruptive structure. Two cases are considered, in the first of which a flux rope is not present initially but is created during the eruption by the reconnection. In the second case, a flux rope is present under the arcade in the preeruptive state,and the e.ect of the eruption and reconnection is to add an amount of magnetic helicity that depends on the fluxes of the rope and arcade and the geometry.
Funding: UK STFC, High Altitude Observatory and Montana State University.
Mon, 01 Aug 2016 00:00:00 GMT
http://hdl.handle.net/10023/9320
20160801T00:00:00Z
Priest, Eric Ronald
Longcope, D W
Janvier, M
During eruptive solar flares and coronal mass ejections, a nonpotential magnetic arcade with much excess magnetic energy goes unstable and reconnects. It produces a twisted erupting flux rope and leaves behind a sheared arcade of hot coronal loops. We suggest that: the twist of the erupting flux rope can be determined from conservation of magnetic flux and magnetic helicity and equipartition of magnetic helicity. It depends on the geometry of the initial preeruptive structure. Two cases are considered, in the first of which a flux rope is not present initially but is created during the eruption by the reconnection. In the second case, a flux rope is present under the arcade in the preeruptive state,and the e.ect of the eruption and reconnection is to add an amount of magnetic helicity that depends on the fluxes of the rope and arcade and the geometry.

Properties of the prominence magnetic field and plasma distributions as obtained from 3D wholeprominence fine structure modeling
http://hdl.handle.net/10023/9203
Aims. We analyze distributions of the magnetic field strength and prominence plasma (temperature, pressure, plasma beta, and mass) using the 3D wholeprominence fine structure model. Methods. The model combines a 3D magnetic field configuration of an entire prominence, obtained from nonlinear forcefree field simulations, with a detailed semiempirically derived description of the prominence plasma. The plasma is located in magnetic dips in hydrostatic equilibrium and is distributed along multiple fine structures within the 3D magnetic model. Results. We show that in the modeled prominence, the variations of the magnetic field strength and its orientation are insignificant on scales comparable to the smallest dimensions of the observed prominence fine structures. We also show the ability of the 3D wholeprominence fine structure model to reveal the distribution of the prominence plasma, with respect to its temperature within the prominence volume. This provides new insights into the composition of the prominencecorona transition region. We further demonstrate that the values of the plasma beta are small throughout the majority of the modeled prominence when realistic photospheric magnetic flux distributions and prominence plasma parameters are assumed. While this is generally true, we also find that in the region with the deepest magnetic dips, the plasma beta may increase towards unity. Finally, we show that the mass of the modeled prominence plasma is in good agreement with the mass of observed noneruptive prominences.
Mon, 01 Aug 2016 00:00:00 GMT
http://hdl.handle.net/10023/9203
20160801T00:00:00Z
Gunar, Stanislav
Mackay, Duncan Hendry
Aims. We analyze distributions of the magnetic field strength and prominence plasma (temperature, pressure, plasma beta, and mass) using the 3D wholeprominence fine structure model. Methods. The model combines a 3D magnetic field configuration of an entire prominence, obtained from nonlinear forcefree field simulations, with a detailed semiempirically derived description of the prominence plasma. The plasma is located in magnetic dips in hydrostatic equilibrium and is distributed along multiple fine structures within the 3D magnetic model. Results. We show that in the modeled prominence, the variations of the magnetic field strength and its orientation are insignificant on scales comparable to the smallest dimensions of the observed prominence fine structures. We also show the ability of the 3D wholeprominence fine structure model to reveal the distribution of the prominence plasma, with respect to its temperature within the prominence volume. This provides new insights into the composition of the prominencecorona transition region. We further demonstrate that the values of the plasma beta are small throughout the majority of the modeled prominence when realistic photospheric magnetic flux distributions and prominence plasma parameters are assumed. While this is generally true, we also find that in the region with the deepest magnetic dips, the plasma beta may increase towards unity. Finally, we show that the mass of the modeled prominence plasma is in good agreement with the mass of observed noneruptive prominences.

Motives and tensions in the release of open educational resources : the UKOER program
http://hdl.handle.net/10023/9166
Open educational resources (OER) have been promoted as a path to universal education, supporting economic development and intercultural dialogue. However, to realise these benefits requires greater understanding of the factors that influence both OER supply and use. This paper examines an aspect of the supply side of the OER lifecycle – the motives prompting release – and the resultant tensions in the release process. It draws evidence from a major program of OER release projects (UKOER) funded by the UK government. The paper sets the UKOER program within the global context of OER initiatives. It uses grounded theory to identify five candidate motive types. Then, by mapping the actions evident in the UKOER program against an organisational framework derived from an activity system, it examines tensions or contradictions encountered by the projects, revealing unstated motives. The findings will be of interest to funders, institutions and educators releasing OER as they reveal potential limitations and barriers to realising the benefits of OER
It gives us pleasure to acknowledge the support of the UK Joint Information Systems Committee and Higher Education Academy, who funded the UKOER projects upon which this paper is based.
Fri, 01 Jan 2016 00:00:00 GMT
http://hdl.handle.net/10023/9166
20160101T00:00:00Z
Falconer, Isobel Jessie
Littlejohn, Allison
McGill, Lou
Beetham, Helen
Open educational resources (OER) have been promoted as a path to universal education, supporting economic development and intercultural dialogue. However, to realise these benefits requires greater understanding of the factors that influence both OER supply and use. This paper examines an aspect of the supply side of the OER lifecycle – the motives prompting release – and the resultant tensions in the release process. It draws evidence from a major program of OER release projects (UKOER) funded by the UK government. The paper sets the UKOER program within the global context of OER initiatives. It uses grounded theory to identify five candidate motive types. Then, by mapping the actions evident in the UKOER program against an organisational framework derived from an activity system, it examines tensions or contradictions encountered by the projects, revealing unstated motives. The findings will be of interest to funders, institutions and educators releasing OER as they reveal potential limitations and barriers to realising the benefits of OER

Impact of an L5 magnetograph on nonpotential solar global magnetic field modeling
http://hdl.handle.net/10023/9154
We present the first theoretical study to consider what improvement could be obtained in global nonpotential modeling of the solar corona if magnetograph data were available from the L5 Lagrange point, in addition to from the direction of Earth. To consider this, we first carry out a "reference Sun'' simulation over two solar cycles. An important property of this simulation is that random bipole emergences are allowed across the entire solar surface at any given time (such as can occur on the Sun). Next we construct two "limited data'' simulations, where bipoles are only included when they could be seen from (i) an Earthbased magnetograph and (ii) either Earth or L5 based magnetographs. The improvement in reproducing the reference Sun simulation when an L5 view is available is quantified through considering global quantities in the limited data simulations. These include surface and polar flux, total magnetic energy, volume electric current, open flux and the number of flux ropes. Results show that when an L5 observational viewpoint is included, the accuracy of the global quantities in the limited data simulations can increase by 2640%. This clearly shows that a magnetograph at the L5 point could significantly increase the accuracy of global nonpotential modeling and with this the accuracy of future space weather forecasts.
Tue, 12 Jul 2016 00:00:00 GMT
http://hdl.handle.net/10023/9154
20160712T00:00:00Z
Mackay, Duncan Hendry
Yeates, Anthony Robinson
Bocquet, FrancoisXavier
We present the first theoretical study to consider what improvement could be obtained in global nonpotential modeling of the solar corona if magnetograph data were available from the L5 Lagrange point, in addition to from the direction of Earth. To consider this, we first carry out a "reference Sun'' simulation over two solar cycles. An important property of this simulation is that random bipole emergences are allowed across the entire solar surface at any given time (such as can occur on the Sun). Next we construct two "limited data'' simulations, where bipoles are only included when they could be seen from (i) an Earthbased magnetograph and (ii) either Earth or L5 based magnetographs. The improvement in reproducing the reference Sun simulation when an L5 view is available is quantified through considering global quantities in the limited data simulations. These include surface and polar flux, total magnetic energy, volume electric current, open flux and the number of flux ropes. Results show that when an L5 observational viewpoint is included, the accuracy of the global quantities in the limited data simulations can increase by 2640%. This clearly shows that a magnetograph at the L5 point could significantly increase the accuracy of global nonpotential modeling and with this the accuracy of future space weather forecasts.

Explosive fragmentation of liquids in spherical geometry
http://hdl.handle.net/10023/9116
Rapid acceleration of a spherical shell of liquid following detonation of a high explosive causes the liquid to form fine jets that are similar in appearance to the particle jets that are formed during explosive dispersal of a packed layer of solid particles. Of particular interest is determining the dependence of the scale of the jetlike structures on the physical parameters of the system, including the fluid properties (e.g., density, viscosity, surface tension) and the ratio of the mass of the liquid to that of the explosive. The present paper presents computational results from a multimaterial hydrocode describing the dynamics of the explosive dispersal process. The computations are used to track the overall features of the dispersal of the liquid layer, including the wave dynamics, and motion of the spall and accretion layers. The results are compared with experimental results of spherical charges surrounded by a variety of different fluids, including water, glycerol, ethanol, and vegetable oil, which together encompass a significant range of fluid properties. The results show that the number of jet structures is not sensitive to the fluid properties, but primarily dependent on the mass ratio. Above a certain mass ratio of liquid fill to explosive burster (F/B), the number of jets is approximately constant and consistent with an empirical model based on the maximum thickness of the accretion layer. For small values of F/B, the number of liquid jets is reduced, in contrast with explosive powder dispersal, where small F/B yields a larger number of particle jets. A hypothetical explanation of these features based on nucleation of cavitation is explored numerically.
Fri, 08 Jul 2016 00:00:00 GMT
http://hdl.handle.net/10023/9116
20160708T00:00:00Z
Milne, Alexander Mitchell
Longbottom, Aaron William
Frost, David
Loiseau, Jason
Goroshin, Samuel
Petel, Oren
Rapid acceleration of a spherical shell of liquid following detonation of a high explosive causes the liquid to form fine jets that are similar in appearance to the particle jets that are formed during explosive dispersal of a packed layer of solid particles. Of particular interest is determining the dependence of the scale of the jetlike structures on the physical parameters of the system, including the fluid properties (e.g., density, viscosity, surface tension) and the ratio of the mass of the liquid to that of the explosive. The present paper presents computational results from a multimaterial hydrocode describing the dynamics of the explosive dispersal process. The computations are used to track the overall features of the dispersal of the liquid layer, including the wave dynamics, and motion of the spall and accretion layers. The results are compared with experimental results of spherical charges surrounded by a variety of different fluids, including water, glycerol, ethanol, and vegetable oil, which together encompass a significant range of fluid properties. The results show that the number of jet structures is not sensitive to the fluid properties, but primarily dependent on the mass ratio. Above a certain mass ratio of liquid fill to explosive burster (F/B), the number of jets is approximately constant and consistent with an empirical model based on the maximum thickness of the accretion layer. For small values of F/B, the number of liquid jets is reduced, in contrast with explosive powder dispersal, where small F/B yields a larger number of particle jets. A hypothetical explanation of these features based on nucleation of cavitation is explored numerically.

Impact of flux distribution on elementary heating events
http://hdl.handle.net/10023/9109
Context. The complex magnetic field on the solar surface has been shown to contain a range of sizes and distributions of magnetic flux structures. The dynamic evolution of this magnetic carpet by photospheric flows provides a continual source of free magnetic energy into the solar atmosphere, that can subsequently be released by magnetic reconnection. Aims. We investigate how the distribution and number of magnetic flux sources impact the energy release and locations of heating through magnetic reconnection driven by slow footpoint motions. Methods. 3D MHD simulations using Lare3D are carried out, where fluxtubes are formed between positive and negative sources placed symmetrically on the lower and upper boundaries of the domain, respectively. The fluxtubes are subjected to rotational driving velocities on the boundaries and are forced to interact and reconnect. Results. Initially, simple flux distributions with two and four sources are compared. In both cases, central current concentrations are formed between the fluxtubes and Ohmic heating occurs. The reconnection and subsequent energy release is delayed in the four source case and is shown to produce more locations of heating, but with smaller magnitudes. Increasing the values of background field between the fluxtubes is shown to delay the onset of reconnection and increases the efficiency of heating in both the two and four source cases. The two fluxtube cases are always more energetic than the corresponding four fluxtube case, however the addition of the background field makes this disparity less significant. A final experiment with a larger number of smaller flux sources is considered and the field evolution and energetics are shown to be remarkably similar to the two source case, indicating the importance of the size and separation of the flux sources relative to the spatial scales of the velocity driver.
This work used the COSMA Data Centric system at Durham University, operated by the Institute for Computational Cosmology on behalf of the STFC DiRAC HPC Facility (www.dirac.ac.uk. This equipment was funded by a BIS National Einfrastructure capital grant ST/K00042X/1, STFC capital grant ST/K00087X/1, DiRAC Operations grant ST/K003267/1 and Durham University. DiRAC is part of the National EInfrastructure. I.D.M was funded by the Science and Technology Facilities Council (UK). The research leading to these results has also received funding from the European Research Council (ERC) under the European Union Horizon 2020 research and innovation programme (grant agreement No. 647214). J.O was funded by the Science and Technology Facilities Council (UK) by Doctoral Grant [ST/K502327/1].
Sat, 01 Oct 2016 00:00:00 GMT
http://hdl.handle.net/10023/9109
20161001T00:00:00Z
O'Hara, Jennifer Patricia
De Moortel, Ineke
Context. The complex magnetic field on the solar surface has been shown to contain a range of sizes and distributions of magnetic flux structures. The dynamic evolution of this magnetic carpet by photospheric flows provides a continual source of free magnetic energy into the solar atmosphere, that can subsequently be released by magnetic reconnection. Aims. We investigate how the distribution and number of magnetic flux sources impact the energy release and locations of heating through magnetic reconnection driven by slow footpoint motions. Methods. 3D MHD simulations using Lare3D are carried out, where fluxtubes are formed between positive and negative sources placed symmetrically on the lower and upper boundaries of the domain, respectively. The fluxtubes are subjected to rotational driving velocities on the boundaries and are forced to interact and reconnect. Results. Initially, simple flux distributions with two and four sources are compared. In both cases, central current concentrations are formed between the fluxtubes and Ohmic heating occurs. The reconnection and subsequent energy release is delayed in the four source case and is shown to produce more locations of heating, but with smaller magnitudes. Increasing the values of background field between the fluxtubes is shown to delay the onset of reconnection and increases the efficiency of heating in both the two and four source cases. The two fluxtube cases are always more energetic than the corresponding four fluxtube case, however the addition of the background field makes this disparity less significant. A final experiment with a larger number of smaller flux sources is considered and the field evolution and energetics are shown to be remarkably similar to the two source case, indicating the importance of the size and separation of the flux sources relative to the spatial scales of the velocity driver.

Null point distribution in global coronal potential field extrapolations
http://hdl.handle.net/10023/9063
Magnetic null points are points in space where the magnetic field is zero. Thus, they can be important sites for magnetic reconnection by virtue of the fact that they are weak points in the magnetic field and also because they are associated with topological structures, such as separators, which lie on the boundary between four topologically distinct flux domains and therefore are also locations where reconnection occurs. The number and distribution of nulls in a magnetic field acts as a measure of the complexity of the field. In this article, the numbers and distributions of null points in global potential field extrapolations from highresolution synoptic magnetograms are examined. Extrapolations from magnetograms obtained with the Michelson Doppler Imager (MDI) are studied in depth and compared with those from highresolution SOlar Longtime Investigations of the Sun (SOLIS) and Heliospheric Magnetic Imager (HMI). The falloff in the density of null points with height is found to follow a power law with a slope that differs depending on whether the data are from solar maximum or solar minimum. The distribution of null points with latitude also varies with the cycle as null points form predominantly over quietSun regions and avoid activeregion fields. The exception to this rule are the null points that form high in the solar atmosphere, and these null points tend to form over large areas of strong flux in active regions. From case studies of data acquired with the MDI, SOLIS, and HMI, it is found that the distribution of null points is very similar between data sets, except, of course, that there are far fewer nulls observed in the SOLIS data than in the cases from MDI and HMI due to its lower resolution.
SJE would like to thank the Isle of Man Government for support during her PhD and also for the financial support of the STFC.
Sat, 18 Jul 2015 00:00:00 GMT
http://hdl.handle.net/10023/9063
20150718T00:00:00Z
Edwards, S.J.
Parnell, C.E.
Magnetic null points are points in space where the magnetic field is zero. Thus, they can be important sites for magnetic reconnection by virtue of the fact that they are weak points in the magnetic field and also because they are associated with topological structures, such as separators, which lie on the boundary between four topologically distinct flux domains and therefore are also locations where reconnection occurs. The number and distribution of nulls in a magnetic field acts as a measure of the complexity of the field. In this article, the numbers and distributions of null points in global potential field extrapolations from highresolution synoptic magnetograms are examined. Extrapolations from magnetograms obtained with the Michelson Doppler Imager (MDI) are studied in depth and compared with those from highresolution SOlar Longtime Investigations of the Sun (SOLIS) and Heliospheric Magnetic Imager (HMI). The falloff in the density of null points with height is found to follow a power law with a slope that differs depending on whether the data are from solar maximum or solar minimum. The distribution of null points with latitude also varies with the cycle as null points form predominantly over quietSun regions and avoid activeregion fields. The exception to this rule are the null points that form high in the solar atmosphere, and these null points tend to form over large areas of strong flux in active regions. From case studies of data acquired with the MDI, SOLIS, and HMI, it is found that the distribution of null points is very similar between data sets, except, of course, that there are far fewer nulls observed in the SOLIS data than in the cases from MDI and HMI due to its lower resolution.

The dependence of coronal loop heating on the characteristics of slow photospheric motions
http://hdl.handle.net/10023/9044
The Parker hypothesis assumes that heating of coronal loops occurs due to reconnection, induced when photospheric motions braid field lines to the point of current sheet formation. In this contribution we address the question of how the nature of photospheric motions affects the heating of braided coronal loops. We design a series of boundary drivers and quantify their properties in terms of complexity and helicity injection. We examine a series of longduration full resistive MHD simulations in which a simulated coronal loop, consisting of initially uniform field lines, is subject to these photospheric flows. Braiding of the loop is continually driven until differences in behavior induced by the drivers can be characterized. It is shown that heating is crucially dependent on the nature of the photospheric driver—coherent motions typically lead to fewer large energy release events, while more complex motions result in more frequent but less energetic heating events.
Mon, 06 Jun 2016 00:00:00 GMT
http://hdl.handle.net/10023/9044
20160606T00:00:00Z
Ritchie, M. L.
WilmotSmith, A. L.
Hornig, G.
The Parker hypothesis assumes that heating of coronal loops occurs due to reconnection, induced when photospheric motions braid field lines to the point of current sheet formation. In this contribution we address the question of how the nature of photospheric motions affects the heating of braided coronal loops. We design a series of boundary drivers and quantify their properties in terms of complexity and helicity injection. We examine a series of longduration full resistive MHD simulations in which a simulated coronal loop, consisting of initially uniform field lines, is subject to these photospheric flows. Braiding of the loop is continually driven until differences in behavior induced by the drivers can be characterized. It is shown that heating is crucially dependent on the nature of the photospheric driver—coherent motions typically lead to fewer large energy release events, while more complex motions result in more frequent but less energetic heating events.

A new technique for the photospheric driving of nonpotential solar coronal magnetic field simulations
http://hdl.handle.net/10023/9043
In this paper, we develop a new technique for driving global nonpotential simulations of the Sun's coronal magnetic field solely from sequences of radial magnetic maps of the solar photosphere. A primary challenge to driving such global simulations is that the required horizontal electric field cannot be uniquely determined from such maps. We show that an "inductive" electric field solution similar to that used by previous authors successfully reproduces specific features of the coronal field evolution in both single and multiple bipole simulations. For these cases, the true solution is known because the electric field was generated from a surface fluxtransport model. The match for these cases is further improved by including the noninductive electric field contribution from surface differential rotation. Then, using this reconstruction method for the electric field, we show that a coronal nonpotential simulation can be successfully driven from a sequence of ADAPT maps of the photospheric radial field, without including additional physical observations which are not routinely available.
Mon, 23 May 2016 00:00:00 GMT
http://hdl.handle.net/10023/9043
20160523T00:00:00Z
Weinzierl, Marion
Yeates, Anthony
Mackay, Duncan Hendry
Henney, Carl
Arge, C. Nick
In this paper, we develop a new technique for driving global nonpotential simulations of the Sun's coronal magnetic field solely from sequences of radial magnetic maps of the solar photosphere. A primary challenge to driving such global simulations is that the required horizontal electric field cannot be uniquely determined from such maps. We show that an "inductive" electric field solution similar to that used by previous authors successfully reproduces specific features of the coronal field evolution in both single and multiple bipole simulations. For these cases, the true solution is known because the electric field was generated from a surface fluxtransport model. The match for these cases is further improved by including the noninductive electric field contribution from surface differential rotation. Then, using this reconstruction method for the electric field, we show that a coronal nonpotential simulation can be successfully driven from a sequence of ADAPT maps of the photospheric radial field, without including additional physical observations which are not routinely available.

Solar cycle variation of magnetic flux ropes in a quasistatic coronal evolution model
http://hdl.handle.net/10023/9037
The structure of electric current and magnetic helicity in the solar corona is closely linked to solar activity over the 11year cycle, yet is poorly understood. As an alternative to traditional currentfree "potential field" extrapolations, we investigate a model for the global coronal magnetic field which is nonpotential and timedependent, following the buildup and transport of magnetic helicity due to flux emergence and largescale photospheric motions. This helicity concentrates into twisted magnetic flux ropes, which may lose equilibrium and be ejected. Here, we consider how the magnetic structure predicted by this modelin particular the flux ropesvaries over the solar activity cycle, based on photospheric input data from six periods of cycle 23. The number of flux ropes doubles from minimum to maximum, following the total length of photospheric polarity inversion lines. However, the number of flux rope ejections increases by a factor of eight, following the emergence rate of active regions. This is broadly consistent with the observed cycle modulation of coronal mass ejections, although the actual rate of ejections in the simulation is about a fifth of the rate of observed events. The model predicts that, even at minimum, differential rotation will produce sheared, nonpotential, magnetic structure at all latitudes.
Sat, 01 May 2010 00:00:00 GMT
http://hdl.handle.net/10023/9037
20100501T00:00:00Z
Yeates, A. R.
Constable, J. A.
Martens, P. C. H.
The structure of electric current and magnetic helicity in the solar corona is closely linked to solar activity over the 11year cycle, yet is poorly understood. As an alternative to traditional currentfree "potential field" extrapolations, we investigate a model for the global coronal magnetic field which is nonpotential and timedependent, following the buildup and transport of magnetic helicity due to flux emergence and largescale photospheric motions. This helicity concentrates into twisted magnetic flux ropes, which may lose equilibrium and be ejected. Here, we consider how the magnetic structure predicted by this modelin particular the flux ropesvaries over the solar activity cycle, based on photospheric input data from six periods of cycle 23. The number of flux ropes doubles from minimum to maximum, following the total length of photospheric polarity inversion lines. However, the number of flux rope ejections increases by a factor of eight, following the emergence rate of active regions. This is broadly consistent with the observed cycle modulation of coronal mass ejections, although the actual rate of ejections in the simulation is about a fifth of the rate of observed events. The model predicts that, even at minimum, differential rotation will produce sheared, nonpotential, magnetic structure at all latitudes.

Coronal density structure and its role in wave damping in loops
http://hdl.handle.net/10023/9020
It has long been established that gradients in the Alfvén speed, and in particular the plasma density, are an essential part of the damping of waves in the magnetically closed solar corona by mechanisms such as resonant absorption or phase mixing. While models of wave damping often assume a fixed density gradient, in this paper the selfconsistency of such calculations is assessed by examining the temporal evolution of the coronal density. It is shown conceptually that for some coronal structures, density gradients can evolve in a way that the wave damping processes are inhibited. For the case of phase mixing we argue that: (a) wave heating cannot sustain the assumed density structure and (b) inclusion of feedback of the heating on the density gradient can lead to a highly structured density, although on long timescales. In addition, transport coefficients well in excess of classical are required to maintain the observed coronal density. Hence, the heating of closed coronal structures by global oscillations may face problems arising from the assumption of a fixed density gradient and the rapid damping of oscillations may have to be accompanied by a separate (nonwave based) heating mechanism to sustain the required density structuring.
This project has received funding from the Science and Technology Facilities Council (UK) and the European Research Council (ERC) under the European Unionʼs Horizon 2020 research and innovation program (grant agreement No 647214). The research leading to these results has also received funding from the European Commission Seventh Framework Programme (FP7/20072013) under the grant agreement SOLSPANET (project No. 269299, www.solspanet.eu/about).
Thu, 19 May 2016 00:00:00 GMT
http://hdl.handle.net/10023/9020
20160519T00:00:00Z
Cargill, Peter
De Moortel, Ineke
Kiddie, Greg
It has long been established that gradients in the Alfvén speed, and in particular the plasma density, are an essential part of the damping of waves in the magnetically closed solar corona by mechanisms such as resonant absorption or phase mixing. While models of wave damping often assume a fixed density gradient, in this paper the selfconsistency of such calculations is assessed by examining the temporal evolution of the coronal density. It is shown conceptually that for some coronal structures, density gradients can evolve in a way that the wave damping processes are inhibited. For the case of phase mixing we argue that: (a) wave heating cannot sustain the assumed density structure and (b) inclusion of feedback of the heating on the density gradient can lead to a highly structured density, although on long timescales. In addition, transport coefficients well in excess of classical are required to maintain the observed coronal density. Hence, the heating of closed coronal structures by global oscillations may face problems arising from the assumption of a fixed density gradient and the rapid damping of oscillations may have to be accompanied by a separate (nonwave based) heating mechanism to sustain the required density structuring.

From onedimensional fields to Vlasov equilibria : Theory and application of Hermite Polynomials
http://hdl.handle.net/10023/8992
We consider the theory and application of a solution method for the inverse problem in collisionless equilibria, namely that of calculating a VlasovMaxwell equilibrium for a given macroscopic (fluid) equilibrium. Using Jeans' Theorem, the equilibria are expressed as functions of the constants of motion, in the form of a Maxwellian multiplied by an unknown function of the canonical momenta. In this case it is possible to reduce the inverse problem to inverting Weierstrass transforms, which we achieve by using expansions over Hermite Polynomials. Sufficient conditions are found which guarantee the convergence,boundedness and nonnegativity of the candidate solution, when satisfied. These conditions are obtained by elementary means, and it is clear how to put them into practice. Illustrative examples of the use of this method with both forcefree and non forcefree macroscopic equilibria are presented, including the full verification of a recently derived distribution function for the ForceFree Harris Sheet (Allanson et al. (2015)). In the effort to model equilibria with lower values of the plasma beta, solutions for the same macroscopic equilibrium in a new gauge are calculated, with numerical results presented for βpl = 0:05.
Wed, 01 Jun 2016 00:00:00 GMT
http://hdl.handle.net/10023/8992
20160601T00:00:00Z
Allanson, Oliver Douglas
Neukirch, Thomas
Troscheit, Sascha
Wilson, Fiona
We consider the theory and application of a solution method for the inverse problem in collisionless equilibria, namely that of calculating a VlasovMaxwell equilibrium for a given macroscopic (fluid) equilibrium. Using Jeans' Theorem, the equilibria are expressed as functions of the constants of motion, in the form of a Maxwellian multiplied by an unknown function of the canonical momenta. In this case it is possible to reduce the inverse problem to inverting Weierstrass transforms, which we achieve by using expansions over Hermite Polynomials. Sufficient conditions are found which guarantee the convergence,boundedness and nonnegativity of the candidate solution, when satisfied. These conditions are obtained by elementary means, and it is clear how to put them into practice. Illustrative examples of the use of this method with both forcefree and non forcefree macroscopic equilibria are presented, including the full verification of a recently derived distribution function for the ForceFree Harris Sheet (Allanson et al. (2015)). In the effort to model equilibria with lower values of the plasma beta, solutions for the same macroscopic equilibrium in a new gauge are calculated, with numerical results presented for βpl = 0:05.

Emergence of nontwisted magnetic fields in the Sun : jets and atmospheric response
http://hdl.handle.net/10023/8990
Aims. We study the emergence of a nontwisted flux tube from the solar interior into the solar atmosphere. We investigate whether the length of the buoyant part of the flux tube (i.e. λ) affects the emergence of the field and the dynamics of the evolving magnetic flux system. Methods. We perform threedimensional (3D), timedependent, resistive, compressible magnetohydrodynamic (MHD) simulations using the Lare3D code. Results. We find that there are considerable differences in the dynamics of the emergence of a magnetic flux tube when λ is varied. In the solar interior, for larger values of λ, the rising magnetic field emerges faster and expands more due to its lower magnetic tension. As a result, its field strength decreases and its emergence above the photosphere occurs later than in the smaller λ case. However, in both cases, the emerging field at the photosphere becomes unstable in two places, forming two magnetic bipoles that interact dynamically during the evolution of the system. Most of the dynamic phenomena occur at the current layer, which is formed at the interface between the interacting bipoles. We find the formation and ejection of plasmoids, the onset of successive jets from the interface, and the impulsive heating of the plasma in the solar atmosphere. We discuss the triggering mechanism of the jets and the atmospheric response to the emergence of magnetic flux in the two cases.
The authors acknowledge support by the EU (IEF272549 grant) and the Royal Society. The present research has been cofinanced by the European Union (European Social FundESF) and Greek national funds through the Operational Program “Education and Lifelong Learning” of the National Strategic Reference Framework (NSRF) – Research Funding Program: Thales. Investing in knowledge society through the European Social Fund. This research has also been carried out in the frame of the research program of the RCAAM of the Academy of Athens and has been cofinanced by the Program “IKY Scholarships” of the Greek national funds through the Operational Program Education and Lifelong Learning of the NSRF through the European Social Fund of ESPA 20072013. Finally, the work reported in this article was additionally supported by the SOLARNET project, funded by the European Commisions FP7 Capacities Program, under the Grant Agreement 312495. The simulations were performed on the STFC and SRIF funded UKMHD cluster, at the University of St Andrews.
Tue, 01 Dec 2015 00:00:00 GMT
http://hdl.handle.net/10023/8990
20151201T00:00:00Z
Syntelis, P.
Archontis, V.
Gontikakis, C.
Tsinganos, K.
Aims. We study the emergence of a nontwisted flux tube from the solar interior into the solar atmosphere. We investigate whether the length of the buoyant part of the flux tube (i.e. λ) affects the emergence of the field and the dynamics of the evolving magnetic flux system. Methods. We perform threedimensional (3D), timedependent, resistive, compressible magnetohydrodynamic (MHD) simulations using the Lare3D code. Results. We find that there are considerable differences in the dynamics of the emergence of a magnetic flux tube when λ is varied. In the solar interior, for larger values of λ, the rising magnetic field emerges faster and expands more due to its lower magnetic tension. As a result, its field strength decreases and its emergence above the photosphere occurs later than in the smaller λ case. However, in both cases, the emerging field at the photosphere becomes unstable in two places, forming two magnetic bipoles that interact dynamically during the evolution of the system. Most of the dynamic phenomena occur at the current layer, which is formed at the interface between the interacting bipoles. We find the formation and ejection of plasmoids, the onset of successive jets from the interface, and the impulsive heating of the plasma in the solar atmosphere. We discuss the triggering mechanism of the jets and the atmospheric response to the emergence of magnetic flux in the two cases.

Spontaneous reconnection at a separator current layer : 2. Nature of the waves and flows
http://hdl.handle.net/10023/8960
Sudden destabilisations of the magnetic field, such as those caused by spontaneous reconnection, will produce waves and/or flows. Here, we investigate the nature of the plasma motions resulting from spontaneous reconnection at a 3D separator. In order to clearly see the perturbations generated by the reconnection, we start from a magnetohydrostatic equilibrium containing two oppositelysigned null points joined by a generic separator along which lies a twisted current layer. The nature of the magnetic reconnection initiated in this equilibrium as a result of an anomalous resistivity is discussed in detail in \cite{Stevenson15_jgra}. The resulting sudden loss of force balance inevitably generates waves that propagate away from the diffusion region carrying the dissipated current. In their wake a twisting stagnationflow, in planes perpendicular to the separator, feeds flux back into the original diffusion site (the separator) in order to try to regain equilibrium. This flow drives a phase of slow weak impulsivebursty reconnection that follows on after the initial fastreconnection phase.
JEHS would like to thank STFC for financial support during her Ph.D and continued support after on the St Andrews SMTG’s STFC consortium grant. CEP also acknowledges support from this same grant.
Thu, 10 Dec 2015 00:00:00 GMT
http://hdl.handle.net/10023/8960
20151210T00:00:00Z
E. H. Stevenson, Julie
E. Parnell, Clare
Sudden destabilisations of the magnetic field, such as those caused by spontaneous reconnection, will produce waves and/or flows. Here, we investigate the nature of the plasma motions resulting from spontaneous reconnection at a 3D separator. In order to clearly see the perturbations generated by the reconnection, we start from a magnetohydrostatic equilibrium containing two oppositelysigned null points joined by a generic separator along which lies a twisted current layer. The nature of the magnetic reconnection initiated in this equilibrium as a result of an anomalous resistivity is discussed in detail in \cite{Stevenson15_jgra}. The resulting sudden loss of force balance inevitably generates waves that propagate away from the diffusion region carrying the dissipated current. In their wake a twisting stagnationflow, in planes perpendicular to the separator, feeds flux back into the original diffusion site (the separator) in order to try to regain equilibrium. This flow drives a phase of slow weak impulsivebursty reconnection that follows on after the initial fastreconnection phase.

Spontaneous reconnection at a separator current layer : I. Nature of the reconnection
http://hdl.handle.net/10023/8959
Magnetic separators, which lie on the boundary between four topologicallydistinct flux domains, are prime locations in threedimensional magnetic fields for reconnection, especially in the magnetosphere between the planetary and interplanetary magnetic field and also in the solar atmosphere. Little is known about the details of separator reconnection and so the aim of this paper, which is the first of two, is to study the properties of magnetic reconnection at a single separator. Threedimensional, resistive magnetohydrodynamic numerical experiments are run to study separator reconnection starting from a magnetohydrostatic equilibrium which contains a twisted current layer along a single separator linking a pair of oppositepolarity null points. The resulting reconnection occurs in two phases. The first is short involving rapidreconnection in which the current at the separator is reduced by a factor of around 2.3. Most ($75\%$) of the magnetic energy is converted during this phase, via Ohmic dissipation, directly into internal energy, with just $0.1\%$ going into kinetic energy. During this phase the reconnection occurs along most of the separator away from its ends (the nulls), but in an asymmetric manner which changes both spatially and temporally over time. The second phase is much longer and involves slow impulsivebursty reconnection. Again Ohmic heating dominates over viscous damping. Here, the reconnection occurs in small localised bursts at random anywhere along the separator.
Wed, 27 Jan 2016 00:00:00 GMT
http://hdl.handle.net/10023/8959
20160127T00:00:00Z
E. H. Stevenson, Julie
E. Parnell, Clare
Magnetic separators, which lie on the boundary between four topologicallydistinct flux domains, are prime locations in threedimensional magnetic fields for reconnection, especially in the magnetosphere between the planetary and interplanetary magnetic field and also in the solar atmosphere. Little is known about the details of separator reconnection and so the aim of this paper, which is the first of two, is to study the properties of magnetic reconnection at a single separator. Threedimensional, resistive magnetohydrodynamic numerical experiments are run to study separator reconnection starting from a magnetohydrostatic equilibrium which contains a twisted current layer along a single separator linking a pair of oppositepolarity null points. The resulting reconnection occurs in two phases. The first is short involving rapidreconnection in which the current at the separator is reduced by a factor of around 2.3. Most ($75\%$) of the magnetic energy is converted during this phase, via Ohmic dissipation, directly into internal energy, with just $0.1\%$ going into kinetic energy. During this phase the reconnection occurs along most of the separator away from its ends (the nulls), but in an asymmetric manner which changes both spatially and temporally over time. The second phase is much longer and involves slow impulsivebursty reconnection. Again Ohmic heating dominates over viscous damping. Here, the reconnection occurs in small localised bursts at random anywhere along the separator.

SSALMON  the Solar Simulations for the Atacama Large Millimeter Observatory Network
http://hdl.handle.net/10023/8874
The Solar Simulations for the Atacama Large Millimeter Observatory Network (SSALMON) was initiated in 2014 in connection with two ALMA development studies. The Atacama Large Millimeter/submillimeter Array (ALMA) is a powerful new tool, which can also observe the Sun at high spatial, temporal, and spectral resolution. The international SSALMONetwork aims at coordinating the further development of solar observing modes for ALMA and at promoting scientific opportunities for solar physics with particular focus on numerical simulations, which can provide important constraints for the observing modes and can aid the interpretation of future observations. The radiation detected by ALMA originates mostly in the solar chromosphere – a complex and dynamic layer between the photosphere and corona, which plays an important role in the transport of energy and matter and the heating of the outer layers of the solar atmosphere. Potential targets include active regions, prominences, quiet Sun regions, flares. Here, we give a brief overview over the network and potential science cases for future solar observations with ALMA.
Tue, 01 Dec 2015 00:00:00 GMT
http://hdl.handle.net/10023/8874
20151201T00:00:00Z
Wedemeyer, S.
Bastian, T.
Brajša, R.
Barta, M.
Hudson, H.
Fleishman, G.
Loukitcheva, M.
Fleck, B.
Kontar, E.
De Pontieu, B.
Tiwari, S.
Kato, Y.
Soler, R.
Yagoubov, P.
Black, J. H.
Antolin, P.
Gunár, S.
Labrosse, N.
Benz, A. O.
Nindos, A.
Steffen, M.
Scullion, E.
Doyle, J. G.
Zaqarashvili, T.
Hanslmeier, A.
Nakariakov, V. M.
Heinzel, P.
Ayres, T.
Karlicky, M.
The Solar Simulations for the Atacama Large Millimeter Observatory Network (SSALMON) was initiated in 2014 in connection with two ALMA development studies. The Atacama Large Millimeter/submillimeter Array (ALMA) is a powerful new tool, which can also observe the Sun at high spatial, temporal, and spectral resolution. The international SSALMONetwork aims at coordinating the further development of solar observing modes for ALMA and at promoting scientific opportunities for solar physics with particular focus on numerical simulations, which can provide important constraints for the observing modes and can aid the interpretation of future observations. The radiation detected by ALMA originates mostly in the solar chromosphere – a complex and dynamic layer between the photosphere and corona, which plays an important role in the transport of energy and matter and the heating of the outer layers of the solar atmosphere. Potential targets include active regions, prominences, quiet Sun regions, flares. Here, we give a brief overview over the network and potential science cases for future solar observations with ALMA.

Numerical simulations of footpoint driven coronal heating
http://hdl.handle.net/10023/8871
Magnetic field permeates the solar atmosphere and plays a crucial role in the dynamics, energetics and structures observed. In particular, magnetic flux tubes provide the structure for coronal loops that extend from the solar surface into the corona. In this thesis, we present 3D numerical simulations examining the heating produced by reconnection between flux tubes driven by rotational footpoint motions. The basic model consists of two, initially aligned, flux tubes that are forced to interact by rotational driving velocities on the flux concentrations on the boundaries. A single, twisted current layer is created in the centre of the domain and strong, localised heating is produced. We extend this model by altering the number, distribution and strength of the sources, while maintaining the same total magnetic flux on the boundaries. The dynamical evolution and the resultant magnitude, distribution and timing of the heating events are examined for the different flux distributions. In all cases, the magnetic field is stressed by the boundary motions and a current grows within the domain. A comparison of cases with two and four sources shows that there are more locations of current concentrations, but with reduced maximum current density values, for the four source case. This produces weaker reconnection and less efficient heating. In addition, for the case with two sources, we also consider the effect of splitting up one of the sources into many smaller flux fragments. The evolution and heating are shown to be very similar to the two source case. The impact of increasing the strength of the background field between the flux tubes is also examined and we find that it delays and increases the strength of the heating, although by how much depends on the distribution of the flux sources.
Fri, 24 Jun 2016 00:00:00 GMT
http://hdl.handle.net/10023/8871
20160624T00:00:00Z
O'Hara, Jennifer
Magnetic field permeates the solar atmosphere and plays a crucial role in the dynamics, energetics and structures observed. In particular, magnetic flux tubes provide the structure for coronal loops that extend from the solar surface into the corona. In this thesis, we present 3D numerical simulations examining the heating produced by reconnection between flux tubes driven by rotational footpoint motions. The basic model consists of two, initially aligned, flux tubes that are forced to interact by rotational driving velocities on the flux concentrations on the boundaries. A single, twisted current layer is created in the centre of the domain and strong, localised heating is produced. We extend this model by altering the number, distribution and strength of the sources, while maintaining the same total magnetic flux on the boundaries. The dynamical evolution and the resultant magnitude, distribution and timing of the heating events are examined for the different flux distributions. In all cases, the magnetic field is stressed by the boundary motions and a current grows within the domain. A comparison of cases with two and four sources shows that there are more locations of current concentrations, but with reduced maximum current density values, for the four source case. This produces weaker reconnection and less efficient heating. In addition, for the case with two sources, we also consider the effect of splitting up one of the sources into many smaller flux fragments. The evolution and heating are shown to be very similar to the two source case. The impact of increasing the strength of the background field between the flux tubes is also examined and we find that it delays and increases the strength of the heating, although by how much depends on the distribution of the flux sources.

A computational framework for particle and whole cell tracking applied to a real biological dataset
http://hdl.handle.net/10023/8783
Cell tracking is becoming increasingly important in cell biology as it provides a valuable tool for analysing experimental data and hence furthering our understanding of dynamic cellular phenomena. The advent of highthroughput, highresolution microscopy and imaging techniques means that a wealth of large data is routinely generated in many laboratories. Due to the sheer magnitude of the data involved manual tracking is often cumbersome and the development of computer algorithms for automated cell tracking is thus highly desirable. In this work, we describe two approaches for automated cell tracking. Firstly, we consider particle tracking. We propose a few segmentation techniques for the detection of cells migrating in a nonuniform background, centroids of the segmented cells are then calculated and linked from frame to frame via a nearestneighbour approach. Secondly, we consider the problem of whole cell tracking in which one wishes to reconstruct in time whole cell morphologies. Our approach is based on fitting a mathematical model to the experimental imaging data with the goal being that the physics encoded in the model is rejected in the reconstructed data. The resulting mathematical problem involves the optimal control of a phasefield formulation of a geometric evolution law. Efficient approximation of this challenging optimal control problem is achieved via advanced numerical methods for the solution of semilinear parabolic partial differential equations (PDEs) coupled with parallelisation and adaptive resolution techniques. Along with a detailed description of our algorithms, a number of simulation results are reported on. We focus on illustrating the effectivity of our approaches by applying the algorithms to the tracking of migrating cells in a dataset which reflects many of the challenges typically encountered in microscopy data.
FY, CV, VS and AM acknowledge support from the Leverhulme Trust Research Project Grant (RPG2014149). The work of CV, VS and AM was partially supported by the Engineering and Physical Sciences Research Council, UK grant (EP/J016780/1). This work (AM, ZG, EH, RZ) has also received funding from the European Union's Horizon 2020 research and innovation programme under the Marie SklodowskaCurie grant agreement No 642866. The work of CV is partially supported by an EPSRC Impact Accelerator Account award.
Tue, 24 May 2016 00:00:00 GMT
http://hdl.handle.net/10023/8783
20160524T00:00:00Z
Yang, Feng Wei
Venkataraman, Chandrasekhar
Styles, Vanessa
Kuttenberger, Verena
Horn, Elias
von Guttenberg, Zeno
Madzvamuse, Anotida
Cell tracking is becoming increasingly important in cell biology as it provides a valuable tool for analysing experimental data and hence furthering our understanding of dynamic cellular phenomena. The advent of highthroughput, highresolution microscopy and imaging techniques means that a wealth of large data is routinely generated in many laboratories. Due to the sheer magnitude of the data involved manual tracking is often cumbersome and the development of computer algorithms for automated cell tracking is thus highly desirable. In this work, we describe two approaches for automated cell tracking. Firstly, we consider particle tracking. We propose a few segmentation techniques for the detection of cells migrating in a nonuniform background, centroids of the segmented cells are then calculated and linked from frame to frame via a nearestneighbour approach. Secondly, we consider the problem of whole cell tracking in which one wishes to reconstruct in time whole cell morphologies. Our approach is based on fitting a mathematical model to the experimental imaging data with the goal being that the physics encoded in the model is rejected in the reconstructed data. The resulting mathematical problem involves the optimal control of a phasefield formulation of a geometric evolution law. Efficient approximation of this challenging optimal control problem is achieved via advanced numerical methods for the solution of semilinear parabolic partial differential equations (PDEs) coupled with parallelisation and adaptive resolution techniques. Along with a detailed description of our algorithms, a number of simulation results are reported on. We focus on illustrating the effectivity of our approaches by applying the algorithms to the tracking of migrating cells in a dataset which reflects many of the challenges typically encountered in microscopy data.

Existence, stability and formation of baroclinic triples in quasigeostrophic flows
http://hdl.handle.net/10023/8770
Hetons are baroclinic vortices able to transport tracers or species, and which have been observed at sea. This paper studies the offset collision of two identical hetons, often resulting in the formation of a baroclinic tripole, in a continuously stratified quasigeostrophic model. This process is of interest since it (temporarily or definitely) stops the transport of tracers contained in the hetons. Firstly, the structure, stationarity and nonlinear stability of baroclinic tripoles composed of an upper core and of two lower (symmetric) satellites are studied analytically for point vortices and numerically for finitearea vortices. The condition for stationarity of the point vortices is obtained and it is proven that the baroclinic point tripoles are neutral. Finitevolume stationary tripoles exist with marginal states having very elongated (figure8) upper core. In the case of vertically distant upper and lower cores, these latter can nearly joint near the center of the plane. These steady states are compared with their twolayer counterparts. Then, the nonlinear evolution of the steady states shows when they are often neutral (showing an oscillatory evolution); when they are unstable, they can either split into two hetons (by breaking of the upper core) or form a single heton (by merger of the lower satellites). These evolutions reflect the linearly unstable modes which can grow on the vorticity poles. Very tall tripoles can break up vertically due to the vertical shear mutually induced by the poles. Finally, the formation of such baroclinic tripoles from the offset collision of two identical hetons is investigated numerically. This formation occurs for hetons offset by less than the internal separation between their poles. The velocity shear during the interaction can lead to substantial filamentation by the upper core, thus forming small, upper satellites, vertically aligned with the lower ones. Finally, in the case of close and flat poles, this shear (or the baroclinic instability of the tripole) can be strong enough that the formed baroclinic tripole is shortlived and that hetons eventually emerge from the collision and drift away.
Tue, 01 Dec 2015 00:00:00 GMT
http://hdl.handle.net/10023/8770
20151201T00:00:00Z
Reinaud, Jean Noel
Carton, Xavier
Hetons are baroclinic vortices able to transport tracers or species, and which have been observed at sea. This paper studies the offset collision of two identical hetons, often resulting in the formation of a baroclinic tripole, in a continuously stratified quasigeostrophic model. This process is of interest since it (temporarily or definitely) stops the transport of tracers contained in the hetons. Firstly, the structure, stationarity and nonlinear stability of baroclinic tripoles composed of an upper core and of two lower (symmetric) satellites are studied analytically for point vortices and numerically for finitearea vortices. The condition for stationarity of the point vortices is obtained and it is proven that the baroclinic point tripoles are neutral. Finitevolume stationary tripoles exist with marginal states having very elongated (figure8) upper core. In the case of vertically distant upper and lower cores, these latter can nearly joint near the center of the plane. These steady states are compared with their twolayer counterparts. Then, the nonlinear evolution of the steady states shows when they are often neutral (showing an oscillatory evolution); when they are unstable, they can either split into two hetons (by breaking of the upper core) or form a single heton (by merger of the lower satellites). These evolutions reflect the linearly unstable modes which can grow on the vorticity poles. Very tall tripoles can break up vertically due to the vertical shear mutually induced by the poles. Finally, the formation of such baroclinic tripoles from the offset collision of two identical hetons is investigated numerically. This formation occurs for hetons offset by less than the internal separation between their poles. The velocity shear during the interaction can lead to substantial filamentation by the upper core, thus forming small, upper satellites, vertically aligned with the lower ones. Finally, in the case of close and flat poles, this shear (or the baroclinic instability of the tripole) can be strong enough that the formed baroclinic tripole is shortlived and that hetons eventually emerge from the collision and drift away.

On the stability of continuously stratified quasigeostrophic hetons
http://hdl.handle.net/10023/8709
In this paper we examine the stability of quasigeostrophic hetons in a stably, continuously stratified fluid. To this purpose we first determinate numerically equilibrium states. Equilibrium hetons consist of two vortices of equal and opposite strength lying at different depths that are steadily translating without deforming. The situation is studied through a parameter space comprising the vertical offset between the vortices, their horizontal separation distance and their aspect ratio. The study first shows that the equilibrium vortices are not only strongly deformed in the vertical but that their instability modes are also varying within the height of the structures. The main purpose of the present contribution is to study families of equilibria which stem from the case of two vertically aligned cylindrical vortices. It is however shown that other branches of solutions exist with different properties. The paper concludes that hetons may be sensitive to baroclinic instabilities provided the separation distance between the poles of the hetons is moderate both in the horizontal and in the vertical directions. The hetons become stable and efficient ways to transport properties as fas as the poles are distant from one another. The critical separation distance in a nontrivial function of the radiustoheight aspect ratio of the poles.
Thu, 30 Apr 2015 00:00:00 GMT
http://hdl.handle.net/10023/8709
20150430T00:00:00Z
Reinaud, Jean Noel
In this paper we examine the stability of quasigeostrophic hetons in a stably, continuously stratified fluid. To this purpose we first determinate numerically equilibrium states. Equilibrium hetons consist of two vortices of equal and opposite strength lying at different depths that are steadily translating without deforming. The situation is studied through a parameter space comprising the vertical offset between the vortices, their horizontal separation distance and their aspect ratio. The study first shows that the equilibrium vortices are not only strongly deformed in the vertical but that their instability modes are also varying within the height of the structures. The main purpose of the present contribution is to study families of equilibria which stem from the case of two vertically aligned cylindrical vortices. It is however shown that other branches of solutions exist with different properties. The paper concludes that hetons may be sensitive to baroclinic instabilities provided the separation distance between the poles of the hetons is moderate both in the horizontal and in the vertical directions. The hetons become stable and efficient ways to transport properties as fas as the poles are distant from one another. The critical separation distance in a nontrivial function of the radiustoheight aspect ratio of the poles.

Solar prominences embedded in flux ropes : morphological features and dynamics from 3D MHD simulations
http://hdl.handle.net/10023/8702
The temporal evolution of a solar prominence inserted in a threedimensional magnetic flux rope is investigated numerically. Using the model of Titov & Démoulin (1999) under the regime of weak twist, the cold and dense prominence counteracts gravity by modifying the initially forcefree magnetic configuration. In some cases a quasistationary situation is achieved after the relaxation phase, characterized by the excitation of standing vertical oscillations. These oscillations show a strong attenuation with time produced by the mechanism of continuum damping due to the in homogeneous transition between the prominence and solar corona. The characteristic period of the vertical oscillations does not depend strongly on the twist of the flux rope. Nonlinearity is the responsible for triggering the KelvinHelmholtz instability associated to the vertical oscillations and that eventually produces horizontal structures. Contrary to other configurations in which the longitudinal axis of the prominence is permeated by a perpendicular magnetic field, like in unsheared arcades, the orientation of the prominence along the flux rope axis prevents the development of RayleighTaylor instabilities and therefore the appearance of vertical structuring along this axis.
J.T. and R.S. acknowledge support from MINECO and UIB through a Ramón y Cajal grant. The authors acknowledge support by the Spanish MINECO and FEDER funds through project AYA201454485P. M.L. acknowledges the support by the Spanish Ministry of Economy and Competitiveness through projects AYA201124808, AYA201018029, and AYA201455078P. This work contributes to the deliverables identified in FP7 European Research Council grant agreement 277829, “Magnetic Connectivity through the Solar Partially Ionized Atmosphere” (PI: E. Khomenko). M.L., J.T., and J.L.B. also acknowledge support from the International Space Science Institute (ISSI) to the Team 314 on “LargeAmplitude Oscillation in prominences” led by M. Luna.
Wed, 30 Mar 2016 00:00:00 GMT
http://hdl.handle.net/10023/8702
20160330T00:00:00Z
Terradas, J.
Soler, R.
Luna, M.
Oliver, R.
Ballester, J. L.
Wright, Andrew Nicholas
The temporal evolution of a solar prominence inserted in a threedimensional magnetic flux rope is investigated numerically. Using the model of Titov & Démoulin (1999) under the regime of weak twist, the cold and dense prominence counteracts gravity by modifying the initially forcefree magnetic configuration. In some cases a quasistationary situation is achieved after the relaxation phase, characterized by the excitation of standing vertical oscillations. These oscillations show a strong attenuation with time produced by the mechanism of continuum damping due to the in homogeneous transition between the prominence and solar corona. The characteristic period of the vertical oscillations does not depend strongly on the twist of the flux rope. Nonlinearity is the responsible for triggering the KelvinHelmholtz instability associated to the vertical oscillations and that eventually produces horizontal structures. Contrary to other configurations in which the longitudinal axis of the prominence is permeated by a perpendicular magnetic field, like in unsheared arcades, the orientation of the prominence along the flux rope axis prevents the development of RayleighTaylor instabilities and therefore the appearance of vertical structuring along this axis.

Copulae on products of compact Riemannian manifolds
http://hdl.handle.net/10023/8672
Abstract One standard way of considering a probability distribution on the unit n cube, [0 , 1]n , due to Sklar (1959), is to decompose it into its marginal distributions and a copula, i.e. a probability distribution on [0 , 1]n with uniform marginals. The definition of copula was extended by Jones et al. (2014) to probability distributions on products of circles. This paper defines a copula as a probability distribution on a product of compact Riemannian manifolds that has uniform marginals. Basic properties of such copulae are established. Two fairly general constructions of copulae on products of compact homogeneous manifolds are given; one is based on convolution in the isometry group, the other using equivariant functions from compact Riemannian manifolds to their spaces of square integrable functions. Examples illustrate the use of copulae to analyse bivariate spherical data and bivariate rotational data.
Tue, 01 Sep 2015 00:00:00 GMT
http://hdl.handle.net/10023/8672
20150901T00:00:00Z
Jupp, P.E.
Abstract One standard way of considering a probability distribution on the unit n cube, [0 , 1]n , due to Sklar (1959), is to decompose it into its marginal distributions and a copula, i.e. a probability distribution on [0 , 1]n with uniform marginals. The definition of copula was extended by Jones et al. (2014) to probability distributions on products of circles. This paper defines a copula as a probability distribution on a product of compact Riemannian manifolds that has uniform marginals. Basic properties of such copulae are established. Two fairly general constructions of copulae on products of compact homogeneous manifolds are given; one is based on convolution in the isometry group, the other using equivariant functions from compact Riemannian manifolds to their spaces of square integrable functions. Examples illustrate the use of copulae to analyse bivariate spherical data and bivariate rotational data.

The effect of interstitial pressure on therapeutic agent transport : coupling with the tumor blood and lymphatic vascular systems
http://hdl.handle.net/10023/8648
Vascularized tumor growth is characterized by both abnormal interstitial fluid flow and the associated interstitial fluid pressure (IFP). Here, we study the effect that these conditions have on the transport of therapeutic agents during chemotherapy. We apply our recently developed vascular tumor growth model which couples a continuous growth component with a discrete angiogenesis model to show that hypertensive IFP is a physical barrier that may hinder vascular extravasation of agents through transvascular fluid flux convection, which drives the agents away from the tumor. This result is consistent with previous work using simpler models without blood flow or lymphatic drainage. We consider the vascular/interstitial/lymphatic fluid dynamics to show that tumors with larger lymphatic resistance increase the agent concentration more rapidly while also experiencing faster washout. In contrast, tumors with smaller lymphatic resistance accumulate less agents but are able to retain them for a longer time. The agent availability (areaunderthe curve, or AUC) increases for less permeable agents as lymphatic resistance increases, and correspondingly decreases for more permeable agents. We also investigate the effect of vascular pathologies on agent transport. We show that elevated vascular hydraulic conductivity contributes to the highest AUC when the agent is less permeable, but to lower AUC when the agent is more permeable. We find that elevated interstitial hydraulic conductivity contributes to low AUC in general regardless of the transvascular agent transport capability. We also couple the agent transport with the tumor dynamics to simulate chemotherapy with the same vascularized tumor under different vascular pathologies. We show that tumors with an elevated interstitial hydraulic conductivity alone require the strongest dosage to shrink. We further show that tumors with elevated vascular hydraulic conductivity are more hypoxic during therapy and that the response slows down as the tumor shrinks due to the heterogeneity and low concentration of agents in the tumor interior compared with the cases where other pathological effects may combine to flatten the IFP and thus reduce the heterogeneity. We conclude that dual normalizations of the micronevironment ? both the vasculature and the interstitium ? are needed to maximize the effects of chemotherapy, while normalization of only one of these may be insufficient to overcome the physical resistance and may thus lead to suboptimal outcomes.
Thu, 21 Aug 2014 00:00:00 GMT
http://hdl.handle.net/10023/8648
20140821T00:00:00Z
Wu, Min
Frieboes, Hermann B.
Chaplain, Mark A. J.
McDougall, Steven R.
Cristini, Vittorio
Lowengrub, John S.
Vascularized tumor growth is characterized by both abnormal interstitial fluid flow and the associated interstitial fluid pressure (IFP). Here, we study the effect that these conditions have on the transport of therapeutic agents during chemotherapy. We apply our recently developed vascular tumor growth model which couples a continuous growth component with a discrete angiogenesis model to show that hypertensive IFP is a physical barrier that may hinder vascular extravasation of agents through transvascular fluid flux convection, which drives the agents away from the tumor. This result is consistent with previous work using simpler models without blood flow or lymphatic drainage. We consider the vascular/interstitial/lymphatic fluid dynamics to show that tumors with larger lymphatic resistance increase the agent concentration more rapidly while also experiencing faster washout. In contrast, tumors with smaller lymphatic resistance accumulate less agents but are able to retain them for a longer time. The agent availability (areaunderthe curve, or AUC) increases for less permeable agents as lymphatic resistance increases, and correspondingly decreases for more permeable agents. We also investigate the effect of vascular pathologies on agent transport. We show that elevated vascular hydraulic conductivity contributes to the highest AUC when the agent is less permeable, but to lower AUC when the agent is more permeable. We find that elevated interstitial hydraulic conductivity contributes to low AUC in general regardless of the transvascular agent transport capability. We also couple the agent transport with the tumor dynamics to simulate chemotherapy with the same vascularized tumor under different vascular pathologies. We show that tumors with an elevated interstitial hydraulic conductivity alone require the strongest dosage to shrink. We further show that tumors with elevated vascular hydraulic conductivity are more hypoxic during therapy and that the response slows down as the tumor shrinks due to the heterogeneity and low concentration of agents in the tumor interior compared with the cases where other pathological effects may combine to flatten the IFP and thus reduce the heterogeneity. We conclude that dual normalizations of the micronevironment ? both the vasculature and the interstitium ? are needed to maximize the effects of chemotherapy, while normalization of only one of these may be insufficient to overcome the physical resistance and may thus lead to suboptimal outcomes.

Recent advances in coronal heating
http://hdl.handle.net/10023/8643
The solar corona, the tenuous outer atmosphere of the Sun, is orders of magnitude hotter than the solar surface. This 'coronal heating problem' requires the identification of a heat source to balance losses due to thermal conduction, radiation and (in some locations) convection. The review papers in this Theo Murphy meeting issue present an overview of recent observational findings, large and smallscale numerical modelling of physical processes occurring in the solar atmosphere and other aspects which may affect our understanding of the proposed heating mechanisms. At the same time, they also set out the directions and challenges which must be tackled by future research. In this brief introduction, we summarize some of the issues and themes which reoccur throughout this issue.
Thu, 28 May 2015 00:00:00 GMT
http://hdl.handle.net/10023/8643
20150528T00:00:00Z
De Moortel, I.
Browning, P.
The solar corona, the tenuous outer atmosphere of the Sun, is orders of magnitude hotter than the solar surface. This 'coronal heating problem' requires the identification of a heat source to balance losses due to thermal conduction, radiation and (in some locations) convection. The review papers in this Theo Murphy meeting issue present an overview of recent observational findings, large and smallscale numerical modelling of physical processes occurring in the solar atmosphere and other aspects which may affect our understanding of the proposed heating mechanisms. At the same time, they also set out the directions and challenges which must be tackled by future research. In this brief introduction, we summarize some of the issues and themes which reoccur throughout this issue.

Is magnetic topology important for heating the solar atmosphere?
http://hdl.handle.net/10023/8642
Magnetic fields permeate the entire solar atmosphere weaving an extremely complex pattern on both local and global scales. In order to understand the nature of this tangled web of magnetic fields, its magnetic skeleton, which forms the boundaries between topologically distinct flux domains, may be determined. The magnetic skeleton consists of null points, separatrix surfaces, spines and separators. The skeleton is often used to clearly visualize key elements of the magnetic configuration, but parts of the skeleton are also locations where currents and waves may collect and dissipate. In this review, the nature of the magnetic skeleton on both global and local scales, over solar cycle time scales, is explained. The behaviour of wave pulses in the vicinity of both nulls and separators is discussed and so too is the formation of current layers and reconnection at the same features. Each of these processes leads to heating of the solar atmosphere, but collectively do they provide enough heat, spread over a wide enough area, to explain the energy losses throughout the solar atmosphere? Here, we consider this question for the three different solar regions: active regions, openfield regions and the quiet Sun. We find that the heating of active regions and openfield regions is highly unlikely to be due to reconnection or wave dissipation at topological features, but it is possible that these may play a role in the heating of the quiet Sun. In active regions, the absence of a complex topology may play an important role in allowing large energies to build up and then, subsequently, be explosively released in the form of a solar flare. Additionally, knowledge of the intricate boundaries of openfield regions (which the magnetic skeleton provides) could be very important in determining the main acceleration mechanism(s) of the solar wind.
CEP and JT acknowledge the support of STFC through the St Andrew’s SMTG consolidated grant. JEHS is supported by STFC as a PhD student. SJE is supported STFC through the Durham University Impact Acceleration Account.
Thu, 21 May 2015 00:00:00 GMT
http://hdl.handle.net/10023/8642
20150521T00:00:00Z
E. Parnell, C.
E. H. Stevenson, J.
Threlfall, J.
J. Edwards, S.
Magnetic fields permeate the entire solar atmosphere weaving an extremely complex pattern on both local and global scales. In order to understand the nature of this tangled web of magnetic fields, its magnetic skeleton, which forms the boundaries between topologically distinct flux domains, may be determined. The magnetic skeleton consists of null points, separatrix surfaces, spines and separators. The skeleton is often used to clearly visualize key elements of the magnetic configuration, but parts of the skeleton are also locations where currents and waves may collect and dissipate. In this review, the nature of the magnetic skeleton on both global and local scales, over solar cycle time scales, is explained. The behaviour of wave pulses in the vicinity of both nulls and separators is discussed and so too is the formation of current layers and reconnection at the same features. Each of these processes leads to heating of the solar atmosphere, but collectively do they provide enough heat, spread over a wide enough area, to explain the energy losses throughout the solar atmosphere? Here, we consider this question for the three different solar regions: active regions, openfield regions and the quiet Sun. We find that the heating of active regions and openfield regions is highly unlikely to be due to reconnection or wave dissipation at topological features, but it is possible that these may play a role in the heating of the quiet Sun. In active regions, the absence of a complex topology may play an important role in allowing large energies to build up and then, subsequently, be explosively released in the form of a solar flare. Additionally, knowledge of the intricate boundaries of openfield regions (which the magnetic skeleton provides) could be very important in determining the main acceleration mechanism(s) of the solar wind.

Depletion of nonlinearity in the pressure force driving NavierStokes flows : nonlinear depletion in NS flows
http://hdl.handle.net/10023/8620
The dynamics of the velocity norms uLq for q ≥ 3, in NavierStokes flows is studied. The pressure term that drives this dynamics has a high degree of nonlinear depletion, which owes its origin to a genuine negative correlation between u and ∇u, among other things. Under viscous effects, such depletion may give rise to mild growth of uLq. We explore the possibility of nonsingular growth of uLq.
Fri, 17 Apr 2015 00:00:00 GMT
http://hdl.handle.net/10023/8620
20150417T00:00:00Z
Tran, Chuong Van
Yu, Xinwei
The dynamics of the velocity norms uLq for q ≥ 3, in NavierStokes flows is studied. The pressure term that drives this dynamics has a high degree of nonlinear depletion, which owes its origin to a genuine negative correlation between u and ∇u, among other things. Under viscous effects, such depletion may give rise to mild growth of uLq. We explore the possibility of nonsingular growth of uLq.

Memory versus effector immune responses in oncolytic virotherapies
http://hdl.handle.net/10023/8604
The main priority when designing cancer immunotherapies has been to seek viable biological mechanisms that lead to permanent cancer eradication or cancer control. Understanding the delicate balance between the role of effector and memory cells on eliminating cancer cells remains an elusive problem in immunology. Here we make an initial investigation into this problem with the help of a mathematical model for oncolytic virotherapy; although the model can in fact be made general enough to be applied also to other immunological problems. Our results show that longterm cancer control is associated with a large number of persistent effector cells (irrespective of the initial peak in effector cell numbers). However, this large number of persistent effector cells is sustained by a relatively large number of memory cells. Moreover, we show that cancer control from a dormant state cannot be predicted by the size of the memory population.
R.E. acknowledges support from an Engineering and Physical Sciences Research Council (UK) First Grant number EP/K033689/1
Tue, 21 Jul 2015 00:00:00 GMT
http://hdl.handle.net/10023/8604
20150721T00:00:00Z
Macnamara, Cicely Krystyna
Eftimie, Raluca
The main priority when designing cancer immunotherapies has been to seek viable biological mechanisms that lead to permanent cancer eradication or cancer control. Understanding the delicate balance between the role of effector and memory cells on eliminating cancer cells remains an elusive problem in immunology. Here we make an initial investigation into this problem with the help of a mathematical model for oncolytic virotherapy; although the model can in fact be made general enough to be applied also to other immunological problems. Our results show that longterm cancer control is associated with a large number of persistent effector cells (irrespective of the initial peak in effector cell numbers). However, this large number of persistent effector cells is sustained by a relatively large number of memory cells. Moreover, we show that cancer control from a dormant state cannot be predicted by the size of the memory population.

On the latetime behaviour of a bounded, inviscid twodimensional flow
http://hdl.handle.net/10023/8603
Using complementary numerical approaches at high resolution, we study the latetime behaviour of an inviscid incompressible twodimensional flow on the surface of a sphere. Starting from a random initial vorticity field comprised of a small set of intermediatewavenumber spherical harmonics, we find that, contrary to the predictions of equilibrium statistical mechanics, the flow does not evolve into a largescale steady state. Instead, significant unsteadiness persists, characterised by a population of persistent smallscale vortices interacting with a largescale oscillating quadrupolar vorticity field. Moreover, the vorticity develops a stepped, staircase distribution, consisting of nearly homogeneous regions separated by sharp gradients. The persistence of unsteadiness is explained by a simple pointvortex model characterising the interactions between the four main vortices which emerge.
We thank the Kavli Institute for Theoretical Physics for supporting our participation in the 2014 Program “WaveFlow Interaction in Geophysics, Climate, Astrophysics, and Plasmas” where this work was initiated. The KITP is supported in part by the NSF Grant No. NSF PHY1125915. This work was also supported in part by the NSF under grant Nos. DMR1306806 and CCF1048701 (JBM and WQ).
Sun, 01 Nov 2015 00:00:00 GMT
http://hdl.handle.net/10023/8603
20151101T00:00:00Z
Dritschel, David Gerard
Qi, Wanming
Marston, J.B.
Using complementary numerical approaches at high resolution, we study the latetime behaviour of an inviscid incompressible twodimensional flow on the surface of a sphere. Starting from a random initial vorticity field comprised of a small set of intermediatewavenumber spherical harmonics, we find that, contrary to the predictions of equilibrium statistical mechanics, the flow does not evolve into a largescale steady state. Instead, significant unsteadiness persists, characterised by a population of persistent smallscale vortices interacting with a largescale oscillating quadrupolar vorticity field. Moreover, the vorticity develops a stepped, staircase distribution, consisting of nearly homogeneous regions separated by sharp gradients. The persistence of unsteadiness is explained by a simple pointvortex model characterising the interactions between the four main vortices which emerge.

Whole cell tracking through the optimal control of geometric evolution laws
http://hdl.handle.net/10023/8582
Cell tracking algorithms which automate and systematise the analysis of time lapse image data sets of cells are an indispensable tool in the modelling and understanding of cellular phenomena. In this study we present a theoretical framework and an algorithm for whole cell tracking. Within this work we consider that "tracking" is equivalent to a dynamic reconstruction of the whole cell data (morphologies) from static image data sets. The novelty of our work is that the tracking algorithm is driven by a model for the motion of the cell. This model may be regarded as a simplification of a recently developed physically meaningful model for cell motility. The resulting problem is the optimal control of a geometric evolution law and we discuss the formulation and numerical approximation of the optimal control problem. The overall goal of this work is to design a framework for cell tracking within which the recovered data reflects the physics of the forward model. A number of numerical simulations are presented that illustrate the applicability of our approach.
This work (A.M., V.S. and C.V.) is supported by the Engineering and Physical Sciences Research Council, UK grant (EP/J016780/1) and the Leverhulme Trust Research Project Grant (RPG2014149). K.B. was partially supported by the Embirikion Foundation Grant (20112014) – Greece.
Tue, 15 Sep 2015 00:00:00 GMT
http://hdl.handle.net/10023/8582
20150915T00:00:00Z
Blazakis, Konstantinos N.
Madzvamuse, Anotida
ReyesAldasoro, Constantino Carlos
Styles, Vanessa
Venkataraman, Chandrasekhar
Cell tracking algorithms which automate and systematise the analysis of time lapse image data sets of cells are an indispensable tool in the modelling and understanding of cellular phenomena. In this study we present a theoretical framework and an algorithm for whole cell tracking. Within this work we consider that "tracking" is equivalent to a dynamic reconstruction of the whole cell data (morphologies) from static image data sets. The novelty of our work is that the tracking algorithm is driven by a model for the motion of the cell. This model may be regarded as a simplification of a recently developed physically meaningful model for cell motility. The resulting problem is the optimal control of a geometric evolution law and we discuss the formulation and numerical approximation of the optimal control problem. The overall goal of this work is to design a framework for cell tracking within which the recovered data reflects the physics of the forward model. A number of numerical simulations are presented that illustrate the applicability of our approach.

Solar coronal electron heating by shortwavelength dispersive shear Alfvén waves
http://hdl.handle.net/10023/8581
The electron heating of the solar coronal plasma has remained one of the most important problems in solar physics. An explanation of the electron heating rests on the identification of the energy source and appropriate physical mechanisms via which the energy can be channelled to the electrons. Our objective here is to present an estimate for the electron heating rate in the presence of finite amplitude shortwavelength (in comparison with the ion gyroradius) dispersive shear Alfven (SWDSA) waves that propagate obliquely to the ambient magnetic field direction in the solar corona. Specifically, it is demonstrated that SWDSA waves can significantly contribute to the solar coronal electron heating via collisionless heating involving SWDSA waveelectron interactions.
This work was partially supported by the STFC through the Centre for Fundamental Physics (CfFP) at Rutherford Appleton Laboratory, Chilton, Didcot, UK. BE acknowledges support by the Engineering and Physical Sciences Research Council (EPSRC), UK, Grant no EP/M009386/1.
Tue, 15 Sep 2015 00:00:00 GMT
http://hdl.handle.net/10023/8581
20150915T00:00:00Z
Bingham, R.
Shukla, P. K.
Eliasson, B.
Cairns, A.
Cairns, R Alan
The electron heating of the solar coronal plasma has remained one of the most important problems in solar physics. An explanation of the electron heating rests on the identification of the energy source and appropriate physical mechanisms via which the energy can be channelled to the electrons. Our objective here is to present an estimate for the electron heating rate in the presence of finite amplitude shortwavelength (in comparison with the ion gyroradius) dispersive shear Alfven (SWDSA) waves that propagate obliquely to the ambient magnetic field direction in the solar corona. Specifically, it is demonstrated that SWDSA waves can significantly contribute to the solar coronal electron heating via collisionless heating involving SWDSA waveelectron interactions.

The role of dimerisation and nuclear transport in the Hes1 gene regulatory network
http://hdl.handle.net/10023/8458
Hes1 is a member of the family of basic helixloophelix transcription factors and the Hes1 gene regulatory network (GRN) may be described as the canonical example of transcriptional control in eukaryotic cells, since it involves only the Hes1 protein and its own mRNA. Recently, the Hes1 protein has been established as an excellent target for an anticancer drug treatment, with the design of a small molecule Hes1 dimerisation inhibitor representing a promising if challenging approach to therapy. In this paper, we extend a previous spatial stochastic model of the Hes1 GRN to include nuclear transport and dimerisation of Hes1 monomers. Initially, we assume that dimerisation occurs only in the cytoplasm, with only dimers being imported into the nucleus. Stochastic simulations of this novel model using the URDME software show that oscillatory dynamics in agreement with experimental studies are retained. Furthermore, we find that our model is robust to changes in the nuclear transport and dimerisation parameters. However, since the precise dynamics of the nuclear import of Hes1 and the localisation of the dimerisation reaction are not known, we consider a second modelling scenario in which we allow for both Hes1 monomers and dimers to be imported into the nucleus, and we allow dimerisation of Hes1 to occur everywhere in the cell. Once again, computational solutions of this second model produce oscillatory dynamics in agreement with experimental studies. We also explore sensitivity of the numerical solutions to nuclear transport and dimerisation parameters. Finally, we compare and contrast the two different modelling scenarios using numerical experiments that simulate dimer disruption, and suggest a biological experiment that could distinguish which model more faithfully captures the Hes1 GRN.
Tue, 01 Apr 2014 00:00:00 GMT
http://hdl.handle.net/10023/8458
20140401T00:00:00Z
Sturrock, Marc
Hellander, Andreas
Aldakheel, Sahar
Petzold, Linda
Chaplain, Mark A. J.
Hes1 is a member of the family of basic helixloophelix transcription factors and the Hes1 gene regulatory network (GRN) may be described as the canonical example of transcriptional control in eukaryotic cells, since it involves only the Hes1 protein and its own mRNA. Recently, the Hes1 protein has been established as an excellent target for an anticancer drug treatment, with the design of a small molecule Hes1 dimerisation inhibitor representing a promising if challenging approach to therapy. In this paper, we extend a previous spatial stochastic model of the Hes1 GRN to include nuclear transport and dimerisation of Hes1 monomers. Initially, we assume that dimerisation occurs only in the cytoplasm, with only dimers being imported into the nucleus. Stochastic simulations of this novel model using the URDME software show that oscillatory dynamics in agreement with experimental studies are retained. Furthermore, we find that our model is robust to changes in the nuclear transport and dimerisation parameters. However, since the precise dynamics of the nuclear import of Hes1 and the localisation of the dimerisation reaction are not known, we consider a second modelling scenario in which we allow for both Hes1 monomers and dimers to be imported into the nucleus, and we allow dimerisation of Hes1 to occur everywhere in the cell. Once again, computational solutions of this second model produce oscillatory dynamics in agreement with experimental studies. We also explore sensitivity of the numerical solutions to nuclear transport and dimerisation parameters. Finally, we compare and contrast the two different modelling scenarios using numerical experiments that simulate dimer disruption, and suggest a biological experiment that could distinguish which model more faithfully captures the Hes1 GRN.

Effects of thermal conduction and compressive viscosity on the period ratio of the slow mode
http://hdl.handle.net/10023/8423
Aims: Increasing observational evidence of wave modes brings us to a closer understanding of the solar corona. Coronal seismology allows us to combine wave observations and theory to determine otherwise unknown parameters. The period ratio, P1/2P2, between the period P1 of the fundamental mode and the period P2 of its first overtone, is one such tool of coronal seismology and its departure from unity provides information about the structure of the corona. Methods: We consider analytically the effects of thermal conduction and compressive viscosity on the period ratio for a longitudinally propagating sound wave. Results: For coronal values of thermal conduction the effect on the period ratio is negligible. For compressive viscosity the effect on the period ratio may become important for some short hot loops. Conclusions: Damping typically has a small effect on the period ratio, suggesting that longitudinal structuring remains the most significant effect.
C.K.M. acknowledges financial support from the CarnegieTrust. Discussions with Dr. I. De Moortel and Prof. A. W. Hood are gratefully acknowledged
Tue, 01 Jun 2010 00:00:00 GMT
http://hdl.handle.net/10023/8423
20100601T00:00:00Z
Macnamara, Cicely Krystyna
Roberts, Bernard
Aims: Increasing observational evidence of wave modes brings us to a closer understanding of the solar corona. Coronal seismology allows us to combine wave observations and theory to determine otherwise unknown parameters. The period ratio, P1/2P2, between the period P1 of the fundamental mode and the period P2 of its first overtone, is one such tool of coronal seismology and its departure from unity provides information about the structure of the corona. Methods: We consider analytically the effects of thermal conduction and compressive viscosity on the period ratio for a longitudinally propagating sound wave. Results: For coronal values of thermal conduction the effect on the period ratio is negligible. For compressive viscosity the effect on the period ratio may become important for some short hot loops. Conclusions: Damping typically has a small effect on the period ratio, suggesting that longitudinal structuring remains the most significant effect.

Particleincell simulations of collisionless magnetic reconnection with a nonuniform guide field
http://hdl.handle.net/10023/8386
Results are presented of a first study of collisionless magnetic reconnection starting from a recently found exact nonlinear forcefree VlasovMaxwell equilibrium. The initial state has a Harris sheet magnetic field profile in one direction and a nonuniform guide field in a second direction, resulting in a spatially constant magnetic field strength as well as a constant initial plasma density and plasma pressure. It is found that the reconnection process initially resembles guide field reconnection, but that a gradual transition to antiparallel reconnection happens as the system evolves. The time evolution of a number of plasma parameters is investigated, and the results are compared with simulations starting from a Harris sheet equilibrium and a Harris sheet plus constant guide field equilibrium.
Tue, 01 Mar 2016 00:00:00 GMT
http://hdl.handle.net/10023/8386
20160301T00:00:00Z
Wilson, Fiona
Neukirch, Thomas
Hesse, Michael
Harrison, Michael G.
Stark, Craig R.
Results are presented of a first study of collisionless magnetic reconnection starting from a recently found exact nonlinear forcefree VlasovMaxwell equilibrium. The initial state has a Harris sheet magnetic field profile in one direction and a nonuniform guide field in a second direction, resulting in a spatially constant magnetic field strength as well as a constant initial plasma density and plasma pressure. It is found that the reconnection process initially resembles guide field reconnection, but that a gradual transition to antiparallel reconnection happens as the system evolves. The time evolution of a number of plasma parameters is investigated, and the results are compared with simulations starting from a Harris sheet equilibrium and a Harris sheet plus constant guide field equilibrium.

Apparent crossfield superslow propagation of magnetohydrodynamic waves in solar plasmas
http://hdl.handle.net/10023/8377
In this paper we show that the phase mixing of continuum Alfvén waves and/or continuum slow waves in magnetic structures of the solar atmosphere as, e.g., coronal arcades, can create the illusion of wave propagation across the magnetic eld. This phenomenon could be erroneously interpreted as fast mag netosonic waves. The crossfield propagation due to phase mixing of continuum waves is apparent because there is no real propagation of energy across the magnetic surfaces. We investigate the continuous Alfvén and slow spectra in 2D Cartesian equilibrium models with a purely poloidal magnetic field. We show that apparent superslow propagation across the magnetic surfaces in solar coronal structures is a consequence of the existence of continuum Alfvén waves and continuum slow waves that naturally live on those structures and phase mix as time evolves. The apparent crossfield phase velocity is related to the spatial variation of the local Alfvén/slow frequency across the magnetic surfaces and is slower than the Alfvén/sound velocities for typical coronal conditions. Understanding the nature of the apparent crossfield propagation is important for the correct analysis of numerical simulations and the correct interpretation of observations.
TK was supported by the Program for Leading Graduate School, MEXT, Japan. This work was supported by JSPS KAKENHI Grant Number 15H03640. RS acknowledges support from MINECO through project AYA201454485P and from FEDER funds. RS also acknowledges support from MINECO through a ‘Juan de la Cierva’ grant, from MECD through project CEF110012, and from the ‘Vicerectorat d’Investigació Postgrau’ of the UIB. JT acknowledges support from the Spanish Ministerio de Educación y Ciencia through a Ramón y Cajal grant. JT acknowledges support from MINECO through project AYA201454485P and from FEDER funds. MG was supported by IAP P7/08 CHARM (Belspo) and the GOA2015014 (KU Leuven). TVD was supported by an Odysseus grant of the FWO Vlaanderen, the IAP P7/08 CHARM (Belspo) and the GOA2015014 (KU Leuven)
Thu, 15 Oct 2015 00:00:00 GMT
http://hdl.handle.net/10023/8377
20151015T00:00:00Z
Kaneko, T
Goossens, Marcel
Soler, Roberto
Terradas, Jaume
Van Doorsselaere, Tom
Yokoyama, T
Wright, Andrew Nicholas
In this paper we show that the phase mixing of continuum Alfvén waves and/or continuum slow waves in magnetic structures of the solar atmosphere as, e.g., coronal arcades, can create the illusion of wave propagation across the magnetic eld. This phenomenon could be erroneously interpreted as fast mag netosonic waves. The crossfield propagation due to phase mixing of continuum waves is apparent because there is no real propagation of energy across the magnetic surfaces. We investigate the continuous Alfvén and slow spectra in 2D Cartesian equilibrium models with a purely poloidal magnetic field. We show that apparent superslow propagation across the magnetic surfaces in solar coronal structures is a consequence of the existence of continuum Alfvén waves and continuum slow waves that naturally live on those structures and phase mix as time evolves. The apparent crossfield phase velocity is related to the spatial variation of the local Alfvén/slow frequency across the magnetic surfaces and is slower than the Alfvén/sound velocities for typical coronal conditions. Understanding the nature of the apparent crossfield propagation is important for the correct analysis of numerical simulations and the correct interpretation of observations.

Stability analysis and simulations of coupled bulksurface reactiondiffusion systems
http://hdl.handle.net/10023/8349
In this article, we formulate new models for coupled systems of bulksurface reactiondiffusion equations on stationary volumes. The bulk reactiondiffusion equations are coupled to the surface reactiondiffusion equations through linear Robintype boundary conditions. We then state and prove the necessary conditions for diffusiondriven instability for the coupled system. Owing to the nature of the coupling between bulk and surface dynamics, we are able to decouple the stability analysis of the bulk and surface dynamics. Under a suitable choice of model parameter values, the bulk reactiondiffusion system can induce patterning on the surface independent of whether the surface reactiondiffusion system produces or not, patterning. On the other hand, the surface reactiondiffusion system cannot generate patterns everywhere in the bulk in the absence of patterning from the bulk reactiondiffusion system. For this case, patterns can be induced only in regions close to the surface membrane. Various numerical experiments are presented to support our theoretical findings. Our most revealing numerical result is that, Robintype boundary conditions seem to introduce a boundary layer coupling the bulk and surface dynamics.
Sun, 08 Mar 2015 00:00:00 GMT
http://hdl.handle.net/10023/8349
20150308T00:00:00Z
Madzvamuse, Anotida
Chung, Andy H. W.
Venkataraman, Chandrasekhar
In this article, we formulate new models for coupled systems of bulksurface reactiondiffusion equations on stationary volumes. The bulk reactiondiffusion equations are coupled to the surface reactiondiffusion equations through linear Robintype boundary conditions. We then state and prove the necessary conditions for diffusiondriven instability for the coupled system. Owing to the nature of the coupling between bulk and surface dynamics, we are able to decouple the stability analysis of the bulk and surface dynamics. Under a suitable choice of model parameter values, the bulk reactiondiffusion system can induce patterning on the surface independent of whether the surface reactiondiffusion system produces or not, patterning. On the other hand, the surface reactiondiffusion system cannot generate patterns everywhere in the bulk in the absence of patterning from the bulk reactiondiffusion system. For this case, patterns can be induced only in regions close to the surface membrane. Various numerical experiments are presented to support our theoretical findings. Our most revealing numerical result is that, Robintype boundary conditions seem to introduce a boundary layer coupling the bulk and surface dynamics.

Stellar coronal response to differential rotation and flux emergence
http://hdl.handle.net/10023/8298
We perform a numerical parameter study to determine what effect varying differential rotation and flux emergence has on a star's nonpotential coronal magnetic field. In particular we consider the effects on the star's surface magnetic flux, open magnetic flux, mean azimuthal field strength, coronal free magnetic energy, coronal heating and flux rope eruptions. To do this, we apply a magnetic flux transport model to describe the photospheric evolution, and couple this to the nonpotential coronal evolution using a magnetofrictional technique. A flux emergence model is applied to add new magnetic flux on to the photosphere and into the corona. The parameters of this flux emergence model are derived from the solar flux emergence profile, however the rate of emergence can be increased to represent higher flux emergence rates than the Sun's. Overall we find that flux emergence has a greater effect on the nonpotential coronal properties compared to differential rotation, with all the aforementioned properties increasing with increasing flux emergence rate. Although differential rotation has a lesser effect on the overall coronal properties compared to flux emergence, varying differential rotation does alter the coronal structure. As the differential rotation rate increases, the corona becomes more open, and more nonpotential.
GPSG would like to thank the STFC for financial support. DHM would like to thank the STFC and the Leverhulme Trust for financial support. Simulations were carried out on a STFC/SRIF funded UKMHD cluster at St Andrews.
Thu, 14 Jan 2016 00:00:00 GMT
http://hdl.handle.net/10023/8298
20160114T00:00:00Z
Gibb, Gordon Peter Samuel
Mackay, Duncan Hendry
Jardine, Moira Mary
Yeates, A. R.
We perform a numerical parameter study to determine what effect varying differential rotation and flux emergence has on a star's nonpotential coronal magnetic field. In particular we consider the effects on the star's surface magnetic flux, open magnetic flux, mean azimuthal field strength, coronal free magnetic energy, coronal heating and flux rope eruptions. To do this, we apply a magnetic flux transport model to describe the photospheric evolution, and couple this to the nonpotential coronal evolution using a magnetofrictional technique. A flux emergence model is applied to add new magnetic flux on to the photosphere and into the corona. The parameters of this flux emergence model are derived from the solar flux emergence profile, however the rate of emergence can be increased to represent higher flux emergence rates than the Sun's. Overall we find that flux emergence has a greater effect on the nonpotential coronal properties compared to differential rotation, with all the aforementioned properties increasing with increasing flux emergence rate. Although differential rotation has a lesser effect on the overall coronal properties compared to flux emergence, varying differential rotation does alter the coronal structure. As the differential rotation rate increases, the corona becomes more open, and more nonpotential.

Head on collisions between two quasigeostrophic hetons in a continuously stratified fluid
http://hdl.handle.net/10023/8219
We examine the interactions between two threedimensional quasigeostrophic hetons. The hetons are initially translating towards one another. We address the effect of the vertical distance between the two poles (vortices) constituting each heton, on the interaction. We also examine the influence of the horizontal separation between the poles within each heton. In this investigation, the two hetons are facing each other. Two configurations are possible depending on the respective location of the likesigned poles of the hetons. When they lie at the same depth, we refer to the configuration as symmetric; the antisymmetric configuration corresponds to oppositesigned poles at the same depth. The first step in the investigation uses point vortices to represent the poles of the hetons. This approach allows to rapidly browse the parameter space and to estimate the possible heton trajectories. For a symmetric pair, hetons either reverse their trajectory or recombine and escape perpendicularly depending of their horizontal and vertical offsets. On the other hand, antisymmetric hetons recombine and escape perpendicularly as samedepth dipoles. In a second part, we focus on finite core hetons (with finite volume poles). These hetons can deform and may be sensitive to horizontal shear induced deformations, or to baroclinic instability. These destabilisations depend on the vertical and horizontal offsets between the various poles, as well as on their widthtoheight aspect ratios. They can modify the volume of the poles via vortex merger, breaking and/or shearing out; they compete with the advective evolution observed for singular (point) vortices. Importantly, hetons can break down or reconfigure before they can drift away as expected from a point vortex approach. Thus a large variety of behaviours is observed in the parameter space. Finally, we briefly illustrate the behaviour of tall hetons which can be unstable to an azimuthal mode l=1 when many vertical modes of deformation are present on the heton.
Date of Acceptance : 21/07/2015
Tue, 01 Sep 2015 00:00:00 GMT
http://hdl.handle.net/10023/8219
20150901T00:00:00Z
Reinaud, Jean Noel
Carton, Xavier
We examine the interactions between two threedimensional quasigeostrophic hetons. The hetons are initially translating towards one another. We address the effect of the vertical distance between the two poles (vortices) constituting each heton, on the interaction. We also examine the influence of the horizontal separation between the poles within each heton. In this investigation, the two hetons are facing each other. Two configurations are possible depending on the respective location of the likesigned poles of the hetons. When they lie at the same depth, we refer to the configuration as symmetric; the antisymmetric configuration corresponds to oppositesigned poles at the same depth. The first step in the investigation uses point vortices to represent the poles of the hetons. This approach allows to rapidly browse the parameter space and to estimate the possible heton trajectories. For a symmetric pair, hetons either reverse their trajectory or recombine and escape perpendicularly depending of their horizontal and vertical offsets. On the other hand, antisymmetric hetons recombine and escape perpendicularly as samedepth dipoles. In a second part, we focus on finite core hetons (with finite volume poles). These hetons can deform and may be sensitive to horizontal shear induced deformations, or to baroclinic instability. These destabilisations depend on the vertical and horizontal offsets between the various poles, as well as on their widthtoheight aspect ratios. They can modify the volume of the poles via vortex merger, breaking and/or shearing out; they compete with the advective evolution observed for singular (point) vortices. Importantly, hetons can break down or reconfigure before they can drift away as expected from a point vortex approach. Thus a large variety of behaviours is observed in the parameter space. Finally, we briefly illustrate the behaviour of tall hetons which can be unstable to an azimuthal mode l=1 when many vertical modes of deformation are present on the heton.

Particle dynamics in a nonflaring solar active region model
http://hdl.handle.net/10023/8203
The aim of this work is to investigate and characterise particle behaviour in a (observationallydriven) 3D MHD model of the solar atmosphere above a slowly evolving, nonflaring active region. We use a relativistic guidingcentre particle code to investigate particle acceleration in a single snapshot of the 3D MHD simulation. Despite the lack of flarelike behaviour in the active region, direct acceleration of electrons and protons to nonthermal energies (≲ 42 MeV) was found, yielding spectra with highenergy tails which conform to a power law. Examples of particle dynamics, including particle trapping caused by local electric rather than magnetic field effects, are observed and discussed, together with implications for future experiments which simulate nonflaring active region heating and reconnection.
Tue, 01 Mar 2016 00:00:00 GMT
http://hdl.handle.net/10023/8203
20160301T00:00:00Z
Threlfall, J.
A. Bourdin, Ph.
Neukirch, T.
E. Parnell, C.
The aim of this work is to investigate and characterise particle behaviour in a (observationallydriven) 3D MHD model of the solar atmosphere above a slowly evolving, nonflaring active region. We use a relativistic guidingcentre particle code to investigate particle acceleration in a single snapshot of the 3D MHD simulation. Despite the lack of flarelike behaviour in the active region, direct acceleration of electrons and protons to nonthermal energies (≲ 42 MeV) was found, yielding spectra with highenergy tails which conform to a power law. Examples of particle dynamics, including particle trapping caused by local electric rather than magnetic field effects, are observed and discussed, together with implications for future experiments which simulate nonflaring active region heating and reconnection.

Magnetohydrostatic modelling of stellar coronae
http://hdl.handle.net/10023/8067
We introduce to the stellar physics community a method of modelling stellar coronae that can be considered to be an extension of the potential field. In this approach, the magnetic field is coupled to the background atmosphere. The model is magnetohydrostatic and is a balance between the Lorentz force, the pressure gradient and gravity. Analytical solutions are possible and we consider a particular class of equilibria in this paper. The model contains two free parameters and the effects of these on both the geometry and topology of the coronal magnetic field are investigated. A demonstration of the approach is given using a magnetogram derived from Zeeman–Doppler imaging of the 0.75 M⊙ Mdwarf star GJ 182.
Thu, 11 Feb 2016 00:00:00 GMT
http://hdl.handle.net/10023/8067
20160211T00:00:00Z
MacTaggart, David
Gregory, Scott
Neukirch, Thomas
Donati, JeanFrancois
We introduce to the stellar physics community a method of modelling stellar coronae that can be considered to be an extension of the potential field. In this approach, the magnetic field is coupled to the background atmosphere. The model is magnetohydrostatic and is a balance between the Lorentz force, the pressure gradient and gravity. Analytical solutions are possible and we consider a particular class of equilibria in this paper. The model contains two free parameters and the effects of these on both the geometry and topology of the coronal magnetic field are investigated. A demonstration of the approach is given using a magnetogram derived from Zeeman–Doppler imaging of the 0.75 M⊙ Mdwarf star GJ 182.

Particle acceleration at reconnecting separator current layers
http://hdl.handle.net/10023/8001
The aim of this work is to investigate and characterise particle behaviour in a 3D MHD model of a reconnecting magnetic separator. We use a relativistic guidingcentre testparticle code to investigate electron and proton acceleration in snapshots from 3D MHD separator reconnection experiments, and compare the results with findings from an analytical separator reconnection model studied in a previous investigation. The behaviour (and acceleration) of large distributions of particles are examined in detail for both analytical and numerical separator reconnection models. Differences in acceleration sites are recovered and discussed, together with the dependence of final particle energy ranges upon the dimensions of the models and the stage of the (timedependent) MHD reconnection event. We discuss the implications of these results for observed magnetic separators in the solar corona.
Fri, 01 Jan 2016 00:00:00 GMT
http://hdl.handle.net/10023/8001
20160101T00:00:00Z
Threlfall, J.
E. H. Stevenson, J.
E. Parnell, C.
Neukirch, T.
The aim of this work is to investigate and characterise particle behaviour in a 3D MHD model of a reconnecting magnetic separator. We use a relativistic guidingcentre testparticle code to investigate electron and proton acceleration in snapshots from 3D MHD separator reconnection experiments, and compare the results with findings from an analytical separator reconnection model studied in a previous investigation. The behaviour (and acceleration) of large distributions of particles are examined in detail for both analytical and numerical separator reconnection models. Differences in acceleration sites are recovered and discussed, together with the dependence of final particle energy ranges upon the dimensions of the models and the stage of the (timedependent) MHD reconnection event. We discuss the implications of these results for observed magnetic separators in the solar corona.

A model for selection of eyespots on butterfly wings
http://hdl.handle.net/10023/7904
Unsolved Problem The development of eyespots on the wing surface of butterflies of the family Nympalidae is one of the most studied examples of biological pattern formation. However, little is known about the mechanism that determines the number and precise locations of eyespots on the wing. Eyespots develop around signaling centers, called foci, that are located equidistant from wing veins along the midline of a wing cell (an area bounded by veins). A fundamental question that remains unsolved is, why a certain wing cell develops an eyespot, while other wing cells do not. Key Idea and Model We illustrate that the key to understanding focus point selection may be in the venation system of the wing disc. Our main hypothesis is that changes in morphogen concentration along the proximal boundary veins of wing cells govern focus point selection. Based on previous studies, we focus on a spatially twodimensional reactiondiffusion system model posed in the interior of each wing cell that describes the formation of focus points. Using finite element based numerical simulations, we demonstrate that variation in the proximal boundary condition is sufficient to robustly select whether an eyespot focus point forms in otherwise identical wing cells. We also illustrate that this behavior is robust to small perturbations in the parameters and geometry and moderate levels of noise. Hence, we suggest that an anteriorposterior pattern of morphogen concentration along the proximal vein may be the main determinant of the distribution of focus points on the wing surface. In order to complete our model, we propose a two stage reactiondiffusion system model, in which an onedimensional surface reactiondiffusion system, posed on the proximal vein, generates the morphogen concentrations that act as nonhomogeneous Dirichlet (i.e., fixed) boundary conditions for the twodimensional reactiondiffusion model posed in the wing cells. The twostage model appears capable of generating focus point distributions observed in nature. Result We therefore conclude that changes in the proximal boundary conditions are sufficient to explain the empirically observed distribution of eyespot focus points on the entire wing surface. The model predicts, subject to experimental verification, that the source strength of the activator at the proximal boundary should be lower in wing cells in which focus points form than in those that lack focus points. The model suggests that the number and locations of eyespot foci on the wing disc could be largely controlled by two kinds of gradients along two different directions, that is, the first one is the gradient in spatially varying parameters such as the reaction rate along the anteriorposterior direction on the proximal boundary of the wing cells, and the second one is the gradient in source values of the activator along the veins in the proximaldistal direction of the wing cell.
The authors acknowledge financial support from the EPSRC grant EP/J016780/1. AM and CV acknowledge financial support from the Leverhulme Trust Research Project Grant (RPG2014149). This research was started while CV was visiting Japan as a 2013 Japanese Society for the Promotion of Science (JSPS) Summer Fellow (http://www.jsps.go.jp/). This research was finalized whilst TS, CV and AM were participants in the Isaac Newton Institute Program, Coupling Geometric PDEs with Physics for Cell Morphology, Motility and Pattern Formation. This work (AM) has received funding from the European Union Horizon 2020 research and innovation programme under the Marie SklodowskaCurie grant agreement No 642866. AM was partially supported by a grant from the Simons Foundation.
Wed, 04 Nov 2015 00:00:00 GMT
http://hdl.handle.net/10023/7904
20151104T00:00:00Z
Sekimura, Toshio
Venkataraman, Chandrasekhar
Madzvamuse, Anotida
Unsolved Problem The development of eyespots on the wing surface of butterflies of the family Nympalidae is one of the most studied examples of biological pattern formation. However, little is known about the mechanism that determines the number and precise locations of eyespots on the wing. Eyespots develop around signaling centers, called foci, that are located equidistant from wing veins along the midline of a wing cell (an area bounded by veins). A fundamental question that remains unsolved is, why a certain wing cell develops an eyespot, while other wing cells do not. Key Idea and Model We illustrate that the key to understanding focus point selection may be in the venation system of the wing disc. Our main hypothesis is that changes in morphogen concentration along the proximal boundary veins of wing cells govern focus point selection. Based on previous studies, we focus on a spatially twodimensional reactiondiffusion system model posed in the interior of each wing cell that describes the formation of focus points. Using finite element based numerical simulations, we demonstrate that variation in the proximal boundary condition is sufficient to robustly select whether an eyespot focus point forms in otherwise identical wing cells. We also illustrate that this behavior is robust to small perturbations in the parameters and geometry and moderate levels of noise. Hence, we suggest that an anteriorposterior pattern of morphogen concentration along the proximal vein may be the main determinant of the distribution of focus points on the wing surface. In order to complete our model, we propose a two stage reactiondiffusion system model, in which an onedimensional surface reactiondiffusion system, posed on the proximal vein, generates the morphogen concentrations that act as nonhomogeneous Dirichlet (i.e., fixed) boundary conditions for the twodimensional reactiondiffusion model posed in the wing cells. The twostage model appears capable of generating focus point distributions observed in nature. Result We therefore conclude that changes in the proximal boundary conditions are sufficient to explain the empirically observed distribution of eyespot focus points on the entire wing surface. The model predicts, subject to experimental verification, that the source strength of the activator at the proximal boundary should be lower in wing cells in which focus points form than in those that lack focus points. The model suggests that the number and locations of eyespot foci on the wing disc could be largely controlled by two kinds of gradients along two different directions, that is, the first one is the gradient in spatially varying parameters such as the reaction rate along the anteriorposterior direction on the proximal boundary of the wing cells, and the second one is the gradient in source values of the activator along the veins in the proximaldistal direction of the wing cell.

Magnetostatic modeling of the mixed plasma Beta solar atmosphere based on SUNRISE/IMaX data
http://hdl.handle.net/10023/7887
Our aim is to model the 3D magnetic field structure of the upper solar atmosphere, including regions of nonnegligible plasma beta. We use highresolution photospheric magnetic field measurements from SUNRISE/IMaX as boundary condition for a magnetostatic magnetic field model. The high resolution of IMaX allows us to resolve the interface region between photosphere and corona, but modelling this region is challenging for the following reasons. While the coronal magnetic field is thought to be forcefree (the Lorentzforce vanishes), this is not the case in the mixed plasma β environment in the photosphere and lower chromosphere. In our model, pressure gradients and gravity forces are taken selfconsistently into account and compensate the nonvanishing Lorentzforce. Above a certain height (about 2 Mm) the nonmagnetic forces become very weak and consequently the magnetic field becomes almost forcefree. Here we apply a linear approach, where the electric current density consists of a superposition of a fieldline parallel current and a current perpendicular to the Sun’s gravity field. We illustrate the prospects and limitations of this approach and give an outlook for an extension towards a nonlinear model.
TN acknowledges support by the U.K.’s Science and Technology Facilities Council and would like to thank the MPS for its hospitality during a visit in December 2014.
Tue, 01 Dec 2015 00:00:00 GMT
http://hdl.handle.net/10023/7887
20151201T00:00:00Z
Wiegelmann, Thomas
Neukirch, Thomas
Nickeler, Dieter
Solanki, Sami
Martinez Pillet, Valentin
Borrero, Juan Manule
Our aim is to model the 3D magnetic field structure of the upper solar atmosphere, including regions of nonnegligible plasma beta. We use highresolution photospheric magnetic field measurements from SUNRISE/IMaX as boundary condition for a magnetostatic magnetic field model. The high resolution of IMaX allows us to resolve the interface region between photosphere and corona, but modelling this region is challenging for the following reasons. While the coronal magnetic field is thought to be forcefree (the Lorentzforce vanishes), this is not the case in the mixed plasma β environment in the photosphere and lower chromosphere. In our model, pressure gradients and gravity forces are taken selfconsistently into account and compensate the nonvanishing Lorentzforce. Above a certain height (about 2 Mm) the nonmagnetic forces become very weak and consequently the magnetic field becomes almost forcefree. Here we apply a linear approach, where the electric current density consists of a superposition of a fieldline parallel current and a current perpendicular to the Sun’s gravity field. We illustrate the prospects and limitations of this approach and give an outlook for an extension towards a nonlinear model.

The appearance, motion, and disappearance of threedimensional magnetic null points
http://hdl.handle.net/10023/7868
While theoretical models and simulations of magnetic reconnection often assume symmetry such that the magnetic null point when present is colocated with a flow stagnation point, the introduction of asymmetry typically leads to nonideal flows across the null point. To understand this behavior, we present exact expressions for the motion of threedimensional linear null points. The most general expression shows that linear null points move in the direction along which the magnetic field and its time derivative are antiparallel. Null point motion in resistive magnetohydrodynamics results from advection by the bulk plasma flow and resistive diffusion of the magnetic field, which allows nonideal flows across topological boundaries. Null point motion is described intrinsically by parameters evaluated locally; however, global dynamics help set the local conditions at the null point. During a bifurcation of a degenerate null point into a nullnull pair or the reverse, the instantaneous velocity of separation or convergence of the nullnull pair will typically be infinite along the null space of the Jacobian matrix of the magnetic field, but with finite components in the directions orthogonal to the null space. Not all bifurcating nullnull pairs are connected by a separator. Furthermore, except under special circumstances, there will not exist a straight line separator connecting a bifurcating nullnull pair. The motion of separators cannot be described using solely local parameters because the identification of a particular field line as a separator may change as a result of nonideal behavior elsewhere along the field line.
N.A.M. acknowledges support from NASA grants NNX11AB61G, NNX12AB25G, and NNX15AF43G; NASA contract NNM07AB07C; and NSF SHINE grants AGS1156076 and AGS1358342 to SAO. C.E.P. acknowledges support from the St Andrews 2013 STFC Consolidated grant.
Fri, 30 Oct 2015 00:00:00 GMT
http://hdl.handle.net/10023/7868
20151030T00:00:00Z
A. Murphy, Nicholas
Parnell, Clare Elizabeth
Haynes, Andrew Lewis
While theoretical models and simulations of magnetic reconnection often assume symmetry such that the magnetic null point when present is colocated with a flow stagnation point, the introduction of asymmetry typically leads to nonideal flows across the null point. To understand this behavior, we present exact expressions for the motion of threedimensional linear null points. The most general expression shows that linear null points move in the direction along which the magnetic field and its time derivative are antiparallel. Null point motion in resistive magnetohydrodynamics results from advection by the bulk plasma flow and resistive diffusion of the magnetic field, which allows nonideal flows across topological boundaries. Null point motion is described intrinsically by parameters evaluated locally; however, global dynamics help set the local conditions at the null point. During a bifurcation of a degenerate null point into a nullnull pair or the reverse, the instantaneous velocity of separation or convergence of the nullnull pair will typically be infinite along the null space of the Jacobian matrix of the magnetic field, but with finite components in the directions orthogonal to the null space. Not all bifurcating nullnull pairs are connected by a separator. Furthermore, except under special circumstances, there will not exist a straight line separator connecting a bifurcating nullnull pair. The motion of separators cannot be described using solely local parameters because the identification of a particular field line as a separator may change as a result of nonideal behavior elsewhere along the field line.

Nearthreshold electron injection in the laserplasma wakefield accelerator leading to femtosecond bunches
http://hdl.handle.net/10023/7750
The laserplasma wakefield accelerator is a compact source of high brightness, ultrashort duration electron bunches. Selfinjection occurs when electrons from the background plasma gain sufficient momentum at the back of the bubbleshaped accelerating structure to experience sustained acceleration. The shortest duration and highest brightness electron bunches result from selfinjection close to the threshold for injection. Here we show that in this case injection is due to the localized charge density buildup in the sheath crossing region at the rear of the bubble, which has the effect of increasing the accelerating potential to above a critical value. Bunch duration is determined by the dwell time above this critical value, which explains why single or multiple ultrashort electron bunches with little dark current are formed in the first bubble. We confirm experimentally, using coherent optical transition radiation measurements, that single or multiple bunches with femtosecond duration and peak currents of several kiloAmpere, and femtosecond intervals between bunches, emerge from the accelerator.
We gratefully acknowledge the support of the UK EPSRC (grant no. EP/J018171/1), the EU FP7 programmes: the Extreme Light Infrastructure (ELI) project, the LaserlabEurope (no. 284464), and the EUCARD2 project (no. 312453).
Thu, 17 Sep 2015 00:00:00 GMT
http://hdl.handle.net/10023/7750
20150917T00:00:00Z
Islam, M.R.
Brunetti, E.
Shanks, R.P.
Ersfeld, B.
Issac, R.C.
Cipiccia, S.
Anania, M.P.
Welsh, G.H.
Wiggins, S.M.
Noble, A.
Cairns, R Alan
Raj, G.
Jaroszynski, D.A.
The laserplasma wakefield accelerator is a compact source of high brightness, ultrashort duration electron bunches. Selfinjection occurs when electrons from the background plasma gain sufficient momentum at the back of the bubbleshaped accelerating structure to experience sustained acceleration. The shortest duration and highest brightness electron bunches result from selfinjection close to the threshold for injection. Here we show that in this case injection is due to the localized charge density buildup in the sheath crossing region at the rear of the bubble, which has the effect of increasing the accelerating potential to above a critical value. Bunch duration is determined by the dwell time above this critical value, which explains why single or multiple ultrashort electron bunches with little dark current are formed in the first bubble. We confirm experimentally, using coherent optical transition radiation measurements, that single or multiple bunches with femtosecond duration and peak currents of several kiloAmpere, and femtosecond intervals between bunches, emerge from the accelerator.

Future capabilities of CME polarimetric 3D reconstructions with the METIS instrument : a numerical test
http://hdl.handle.net/10023/7748
Context. Understanding the 3D structure of coronal mass ejections (CMEs) is crucial for understanding the nature and origin of solar eruptions. However, owing to the optical thinness of the solar corona we can only observe the line of sight integrated emission. As a consequence the resulting projection effects hide the true 3D structure of CMEs. To derive information on the 3D structure of CMEs from whitelight (total and polarized brightness) images, the polarization ratio technique is widely used. The soontobelaunched METIS coronagraph on board Solar Orbiter will use this technique to produce new polarimetric images. Aims. This work considers the application of the polarization ratio technique to synthetic CME observations from METIS. In particular we determine the accuracy at which the position of the centre of mass, direction and speed of propagation, and the column density of the CME can be determined along the line of sight. Methods. We perform a 3D MHD simulation of a flux rope ejection where a CME is produced. From the simulation we (i) synthesize the corresponding METIS whitelight (total and polarized brightness) images and (ii) apply the polarization ratio technique to these synthesized images and compare the results with the known density distribution from the MHD simulation. In addition, we use recent results that consider how the position of a single blob of plasma is measured depending on its projected position in the plane of the sky. From this we can interpret the results of the polarization ratio technique and give an estimation of the error associated with derived parameters. Results. We find that the polarization ratio technique reproduces with high accuracy the position of the centre of mass along the line of sight. However, some errors are inherently associated with this determination. The polarization ratio technique also allows information to be derived on the real 3D direction of propagation of the CME. The determination of this is of fundamental importance for future space weather forecasting. In addition, we find that the column density derived from whitelight images is accurate and we propose an improved technique where the combined use of the polarization ratio technique and whitelight images minimizes the error in the estimation of column densities. Moreover, by applying the comparison to a set of snapshots of the simulation we can also assess the errors related to the trajectory and the expansion of the CME. Conclusions. Our method allows us to thoroughly test the performance of the polarization ratio technique and allows a determination of the errors associated with it, which means that it can be used to quantify the results from the analysis of the forthcoming METIS observations in white light (total and polarized brightness). Finally, we describe a satellite observing configuration relative to the Earth that can allow the technique to be efficiently used for space weather predictions.
D.H.M. would like to thank STFC and the Leverhulme Trust for their financial support. P.P. would like to thank STFC and the Leverhulme Trust. The computational work for this paper was carried out on the joint STFC and SFC (SRIF) funded cluster at the University of St Andrews (Scotland, UK).
Thu, 01 Oct 2015 00:00:00 GMT
http://hdl.handle.net/10023/7748
20151001T00:00:00Z
Pagano, Paolo
Bemporad, A
Mackay, Duncan Hendry
Context. Understanding the 3D structure of coronal mass ejections (CMEs) is crucial for understanding the nature and origin of solar eruptions. However, owing to the optical thinness of the solar corona we can only observe the line of sight integrated emission. As a consequence the resulting projection effects hide the true 3D structure of CMEs. To derive information on the 3D structure of CMEs from whitelight (total and polarized brightness) images, the polarization ratio technique is widely used. The soontobelaunched METIS coronagraph on board Solar Orbiter will use this technique to produce new polarimetric images. Aims. This work considers the application of the polarization ratio technique to synthetic CME observations from METIS. In particular we determine the accuracy at which the position of the centre of mass, direction and speed of propagation, and the column density of the CME can be determined along the line of sight. Methods. We perform a 3D MHD simulation of a flux rope ejection where a CME is produced. From the simulation we (i) synthesize the corresponding METIS whitelight (total and polarized brightness) images and (ii) apply the polarization ratio technique to these synthesized images and compare the results with the known density distribution from the MHD simulation. In addition, we use recent results that consider how the position of a single blob of plasma is measured depending on its projected position in the plane of the sky. From this we can interpret the results of the polarization ratio technique and give an estimation of the error associated with derived parameters. Results. We find that the polarization ratio technique reproduces with high accuracy the position of the centre of mass along the line of sight. However, some errors are inherently associated with this determination. The polarization ratio technique also allows information to be derived on the real 3D direction of propagation of the CME. The determination of this is of fundamental importance for future space weather forecasting. In addition, we find that the column density derived from whitelight images is accurate and we propose an improved technique where the combined use of the polarization ratio technique and whitelight images minimizes the error in the estimation of column densities. Moreover, by applying the comparison to a set of snapshots of the simulation we can also assess the errors related to the trajectory and the expansion of the CME. Conclusions. Our method allows us to thoroughly test the performance of the polarization ratio technique and allows a determination of the errors associated with it, which means that it can be used to quantify the results from the analysis of the forthcoming METIS observations in white light (total and polarized brightness). Finally, we describe a satellite observing configuration relative to the Earth that can allow the technique to be efficiently used for space weather predictions.

Corotating interaction regions as seen by the STEREO Heliospheric Imagers 2007 – 2010
http://hdl.handle.net/10023/7746
NASA’s Solar Terrestrial Relations Observatory (STEREO) mission has coincided with a pronounced solar minimum. This allowed for easier detection of corotating interaction regions (CIRs). CIRs are formed by the interaction between fast and slow solarwind streams ejected from source regions on the solar surface that rotate with the Sun. Highdensity plasma blobs that have become entrained at the stream interface can be tracked out to large elongations in data from the Heliospheric Imager (HI) instruments onboard STEREO. These blobs act as tracers of the CIR itself such that their HI signatures can be used to estimate CIR source location and radial speed. We estimate the kinematic properties of solarwind transients associated with 40 CIRs detected by the HI instrument onboard the STEREOA spacecraft between 2007 and 2010. We identify insitu signatures of these transients at L1 using the Advanced Composition Explorer (ACE) and compare the insitu parameters with the HI results. We note that solarwind transients associated with CIRs appear to travel at or close to the slow solarwind speed preceding the event as measured in situ. We also highlight limitations in the commonly used analysis techniques of solarwind transients by considering variability in the solar wind.
T.M. Conlon and A.O. Williams were supported by an STFC, UK studentship and S.E. Milan was supported by STFC grant ST/K001000/1. Date of Acceptance: 08/08/2015
Sat, 01 Aug 2015 00:00:00 GMT
http://hdl.handle.net/10023/7746
20150801T00:00:00Z
Conlon, Thomas Michael
Milan, S.E.
Davies, J.A.
Williams, A.O.
NASA’s Solar Terrestrial Relations Observatory (STEREO) mission has coincided with a pronounced solar minimum. This allowed for easier detection of corotating interaction regions (CIRs). CIRs are formed by the interaction between fast and slow solarwind streams ejected from source regions on the solar surface that rotate with the Sun. Highdensity plasma blobs that have become entrained at the stream interface can be tracked out to large elongations in data from the Heliospheric Imager (HI) instruments onboard STEREO. These blobs act as tracers of the CIR itself such that their HI signatures can be used to estimate CIR source location and radial speed. We estimate the kinematic properties of solarwind transients associated with 40 CIRs detected by the HI instrument onboard the STEREOA spacecraft between 2007 and 2010. We identify insitu signatures of these transients at L1 using the Advanced Composition Explorer (ACE) and compare the insitu parameters with the HI results. We note that solarwind transients associated with CIRs appear to travel at or close to the slow solarwind speed preceding the event as measured in situ. We also highlight limitations in the commonly used analysis techniques of solarwind transients by considering variability in the solar wind.

Observational signatures of waves and flows in the solar corona
http://hdl.handle.net/10023/7722
Propagating perturbations have been observed in extended coronal loop structures for a number of years, but the interpretation in terms of slow (propagating) magnetoacoustic waves and/or as quasiperiodic upflows remains unresolved. We used forwardmodelling to construct observational signatures associated with a simple slow magnetoacoustic wave or periodic flow model. Observational signatures were computed for the 171 Å Fe ix and the 193 Å Fe xii spectral lines. Although there are many differences between the flow and wave models, we did not find any clear, robust observational characteristics that can be used in isolation (i.e. that do not rely on a comparison between the models). For the waves model, a relatively rapid change of the average line widths as a function of (shallow) lineofsight angles was found, whereas the ratio of the line width amplitudes to the Doppler velocity amplitudes is relatively high for the flow model. The most robust observational signature found is that the ratio of the mean to the amplitudes of the Doppler velocity is always higher than one for the flow model. This ratio is substantially higher for flows than for waves, and for the flows model used in the study is exactly the same in the 171 Å Fe ix and the 193 Å Fe xii spectral lines. However, these potential observational signatures need to be treated cautiously because they are likely to be modeldependent.
DM acknowledges support of a Royal Society University Research Fellowship and a KU Leuven Research Council senior research fellowship (SF/12/008). The research leading to these results has also received funding from the European Commission Seventh Framework Programme (FP7/20072013) under the grant agreement SOLSPANET (project No. 269299, www.solspanet.eu/solspanet ). TVD has been sponsored by an Odysseus grant of the FWO Vlaanderen. The research was performed in the context of the IAP P7/08 CHARM (Belspo) and the GOA2015014 (KU Leuven). TVD acknowledges the funding from the FP7 ERG grant with number 276808.
Sun, 01 Feb 2015 00:00:00 GMT
http://hdl.handle.net/10023/7722
20150201T00:00:00Z
De Moortel, I.
Antolin, Patrick
Van Doorsselaere, T.
Propagating perturbations have been observed in extended coronal loop structures for a number of years, but the interpretation in terms of slow (propagating) magnetoacoustic waves and/or as quasiperiodic upflows remains unresolved. We used forwardmodelling to construct observational signatures associated with a simple slow magnetoacoustic wave or periodic flow model. Observational signatures were computed for the 171 Å Fe ix and the 193 Å Fe xii spectral lines. Although there are many differences between the flow and wave models, we did not find any clear, robust observational characteristics that can be used in isolation (i.e. that do not rely on a comparison between the models). For the waves model, a relatively rapid change of the average line widths as a function of (shallow) lineofsight angles was found, whereas the ratio of the line width amplitudes to the Doppler velocity amplitudes is relatively high for the flow model. The most robust observational signature found is that the ratio of the mean to the amplitudes of the Doppler velocity is always higher than one for the flow model. This ratio is substantially higher for flows than for waves, and for the flows model used in the study is exactly the same in the 171 Å Fe ix and the 193 Å Fe xii spectral lines. However, these potential observational signatures need to be treated cautiously because they are likely to be modeldependent.

Multiscale modelling of cancer progression and treatment control : the role of intracellular heterogeneities in chemotherapy treatment
http://hdl.handle.net/10023/7714
Cancer is a complex, multiscale process involving interactions at intracellular, intercellular and tissue scales that are in turn susceptible to microenvironmental changes. Each individual cancer cell within a cancer cell mass is unique, with its own internal cellular pathways and biochemical interactions. These interactions contribute to the functional changes at the cellular and tissue scale, creating a heterogenous cancer cell population. Anticancer drugs are effective in controlling cancer growth by inflicting damage to various target molecules and thereby triggering multiple cellular and intracellular pathways, leading to cell death or cellcycle arrest. One of the major impediments in the chemotherapy treatment of cancer is drug resistance driven by multiple mechanisms, including multidrug and cellcycle mediated resistance to chemotherapy drugs. In this article, we discuss two hybrid multiscale modelling approaches, incorporating multiple interactions involved in the subcellular, cellular and microenvironmental levels to study the effects of cellcycle, phasespecific chemotherapy on the growth and progression of cancer cells.
Mon, 01 Jun 2015 00:00:00 GMT
http://hdl.handle.net/10023/7714
20150601T00:00:00Z
Chaplain, Mark Andrew Joseph
Powathil, Gibin
Cancer is a complex, multiscale process involving interactions at intracellular, intercellular and tissue scales that are in turn susceptible to microenvironmental changes. Each individual cancer cell within a cancer cell mass is unique, with its own internal cellular pathways and biochemical interactions. These interactions contribute to the functional changes at the cellular and tissue scale, creating a heterogenous cancer cell population. Anticancer drugs are effective in controlling cancer growth by inflicting damage to various target molecules and thereby triggering multiple cellular and intracellular pathways, leading to cell death or cellcycle arrest. One of the major impediments in the chemotherapy treatment of cancer is drug resistance driven by multiple mechanisms, including multidrug and cellcycle mediated resistance to chemotherapy drugs. In this article, we discuss two hybrid multiscale modelling approaches, incorporating multiple interactions involved in the subcellular, cellular and microenvironmental levels to study the effects of cellcycle, phasespecific chemotherapy on the growth and progression of cancer cells.

Systems oncology : towards patientspecific treatment regimes informed by multiscale mathematical modelling
http://hdl.handle.net/10023/7713
The multiscale complexity of cancer as a disease necessitates a corresponding multiscale modelling approach to produce truly predictive mathematical models capable of improving existing treatment protocols. To capture all the dynamics of solid tumour growth and its progression, mathematical modellers need to couple biological processes occurring at various spatial and temporal scales (from genes to tissues). Because effectiveness of cancer therapy is considerably affected by intracellular and extracellular heterogeneities as well as by the dynamical changes in the tissue microenvironment, any model attempt to optimise existing protocols must consider these factors ultimately leading to improved multimodal treatment regimes. By improving existing and building new mathematical models of cancer, modellers can play important role in preventing the use of potentially suboptimal treatment combinations. In this paper, we analyse a multiscale computational mathematical model for cancer growth and spread, incorporating the multiple effects of radiation therapy and chemotherapy in the patient survival probability and implement the model using two different cell based modelling techniques. We show that the insights provided by such multiscale modelling approaches can ultimately help in designing optimal patientspecific multimodality treatment protocols that may increase patients quality of life.
Sun, 01 Feb 2015 00:00:00 GMT
http://hdl.handle.net/10023/7713
20150201T00:00:00Z
Powathil, Gibin G.
Swat, Maciej
Chaplain, Mark A. J.
The multiscale complexity of cancer as a disease necessitates a corresponding multiscale modelling approach to produce truly predictive mathematical models capable of improving existing treatment protocols. To capture all the dynamics of solid tumour growth and its progression, mathematical modellers need to couple biological processes occurring at various spatial and temporal scales (from genes to tissues). Because effectiveness of cancer therapy is considerably affected by intracellular and extracellular heterogeneities as well as by the dynamical changes in the tissue microenvironment, any model attempt to optimise existing protocols must consider these factors ultimately leading to improved multimodal treatment regimes. By improving existing and building new mathematical models of cancer, modellers can play important role in preventing the use of potentially suboptimal treatment combinations. In this paper, we analyse a multiscale computational mathematical model for cancer growth and spread, incorporating the multiple effects of radiation therapy and chemotherapy in the patient survival probability and implement the model using two different cell based modelling techniques. We show that the insights provided by such multiscale modelling approaches can ultimately help in designing optimal patientspecific multimodality treatment protocols that may increase patients quality of life.

Mathematical modelling of cancer invasion : implications of cell adhesion variability for tumour infiltrative growth patterns
http://hdl.handle.net/10023/7712
Cancer invasion, recognised as one of the hallmarks of cancer, is a complex, multiscale phenomenon involving many interrelated genetic, biochemical, cellular and tissue processes at different spatial and temporal scales. Central to invasion is the ability of cancer cells to alter and degrade an extracellular matrix. Combined with abnormal excessive proliferation and migration which is enabled and enhanced by altered cellcell and cellmatrix adhesion, the cancerous mass can invade the neighbouring tissue. Along with tumourinduced angiogenesis, invasion is a key component of metastatic spread, ultimately leading to the formation of secondary tumours in other parts of the host body. In this paper we explore the spatiotemporal dynamics of a model of cancer invasion, where cellcell and cellmatrix adhesion is accounted for through nonlocal interaction terms in a system of partial integrodifferential equations. The change of adhesion properties during cancer growth and development is investigated here through timedependent adhesion characteristics within the cell population as well as those between the cells and the components of the extracellular matrix. Our computational simulation results demonstrate a range of heterogeneous dynamics which are qualitatively similar to the invasive growth patterns observed in a number of different types of cancer, such as tumour infiltrative growth patterns (INF).
Fri, 21 Nov 2014 00:00:00 GMT
http://hdl.handle.net/10023/7712
20141121T00:00:00Z
Domschke, Pia
Trucu, Dumitru
Gerisch, Alf
Chaplain, Mark A. J.
Cancer invasion, recognised as one of the hallmarks of cancer, is a complex, multiscale phenomenon involving many interrelated genetic, biochemical, cellular and tissue processes at different spatial and temporal scales. Central to invasion is the ability of cancer cells to alter and degrade an extracellular matrix. Combined with abnormal excessive proliferation and migration which is enabled and enhanced by altered cellcell and cellmatrix adhesion, the cancerous mass can invade the neighbouring tissue. Along with tumourinduced angiogenesis, invasion is a key component of metastatic spread, ultimately leading to the formation of secondary tumours in other parts of the host body. In this paper we explore the spatiotemporal dynamics of a model of cancer invasion, where cellcell and cellmatrix adhesion is accounted for through nonlocal interaction terms in a system of partial integrodifferential equations. The change of adhesion properties during cancer growth and development is investigated here through timedependent adhesion characteristics within the cell population as well as those between the cells and the components of the extracellular matrix. Our computational simulation results demonstrate a range of heterogeneous dynamics which are qualitatively similar to the invasive growth patterns observed in a number of different types of cancer, such as tumour infiltrative growth patterns (INF).

Stochastic modelling of chromosomal segregation : errors can introduce correction
http://hdl.handle.net/10023/7711
Cell division is a complex process requiring the cell to have many internal checks so that division may proceed and be completed correctly. Failure to divide correctly can have serious consequences, including progression to cancer. During mitosis, chromosomal segregation is one such process that is crucial for successful progression. Accurate segregation of chromosomes during mitosis requires regulation of the interactions between chromosomes and spindle microtubules. If left uncorrected, chromosome attachment errors can cause chromosome segregation defects which have serious effects on cell fates. In early prometaphase, where kinetochores are exposed to multiple microtubules originating from the two poles, there are frequent errors in kinetochoremicrotubule attachment. Erroneous attachments are classified into two categories, syntelic and merotelic. In this paper, we consider a stochastic model for a possible function of syntelic and merotelic kinetochores, and we provide theoretical evidence that merotely can contribute to lessening the stochastic noise in the time for completion of the mitotic process in eukaryotic cells.
Tue, 01 Jul 2014 00:00:00 GMT
http://hdl.handle.net/10023/7711
20140701T00:00:00Z
Matzavinos, Anastasios
Roitershtein, Alexander
Shtylla, Blerta
Voller, Zachary
Liu, Sijia
Chaplain, Mark A.J.
Cell division is a complex process requiring the cell to have many internal checks so that division may proceed and be completed correctly. Failure to divide correctly can have serious consequences, including progression to cancer. During mitosis, chromosomal segregation is one such process that is crucial for successful progression. Accurate segregation of chromosomes during mitosis requires regulation of the interactions between chromosomes and spindle microtubules. If left uncorrected, chromosome attachment errors can cause chromosome segregation defects which have serious effects on cell fates. In early prometaphase, where kinetochores are exposed to multiple microtubules originating from the two poles, there are frequent errors in kinetochoremicrotubule attachment. Erroneous attachments are classified into two categories, syntelic and merotelic. In this paper, we consider a stochastic model for a possible function of syntelic and merotelic kinetochores, and we provide theoretical evidence that merotely can contribute to lessening the stochastic noise in the time for completion of the mitotic process in eukaryotic cells.

Mathematical modeling of tumor growth and treatment
http://hdl.handle.net/10023/7710
Using mathematical models to simulate dynamic biological processes has a long history. Over the past couple of decades or so, quantitative approaches have also made their way into cancer research. An increasing number of mathematical, physical, computational and engineering techniques have been applied to various aspects of tumor growth, with the ultimate goal of understanding the response of the cancer population to clinical intervention. Socalled in silico trials that predict patientspecific response to various dose schedules or treatment combinations and sequencing are on the way to becoming an invaluable tool to optimize patient care. Herein we describe fundamentals of mathematical modeling of tumor growth and tumorhost interactions, and summarize some of the seminal and most prominent approaches.
Wed, 01 Jan 2014 00:00:00 GMT
http://hdl.handle.net/10023/7710
20140101T00:00:00Z
Enderling, Heiko
Chaplain, Mark A. J.
Using mathematical models to simulate dynamic biological processes has a long history. Over the past couple of decades or so, quantitative approaches have also made their way into cancer research. An increasing number of mathematical, physical, computational and engineering techniques have been applied to various aspects of tumor growth, with the ultimate goal of understanding the response of the cancer population to clinical intervention. Socalled in silico trials that predict patientspecific response to various dose schedules or treatment combinations and sequencing are on the way to becoming an invaluable tool to optimize patient care. Herein we describe fundamentals of mathematical modeling of tumor growth and tumorhost interactions, and summarize some of the seminal and most prominent approaches.

Mean field analysis of a spatial stochastic model of a gene regulatory network
http://hdl.handle.net/10023/7709
A gene regulatory network may be defined as a collection of DNA segments which interact with each other indirectly through their RNA and protein products. Such a network is said to contain a negative feedback loop if its products inhibit gene transcription, and a positive feedback loop if a gene product promotes its own production. Negative feedback loops can create oscillations in mRNA and protein levels while positive feedback loops are primarily responsible for signal amplification. It is often the case in real biological systems that both negative and positive feedback loops operate in parameter regimes that result in low copy numbers of gene products. In this paper we investigate the spatiotemporal dynamics of a single feedback loop in a eukaryotic cell. We first develop a simplified spatial stochastic model of a canonical feedback system (either positive or negative). Using a Gillespie's algorithm, we compute sample trajectories and analyse their corresponding statistics. We then derive a system of equations that describe the spatiotemporal evolution of the stochastic means. Subsequently, we examine the spatially homogeneous case and compare the results of numerical simulations with the spatially explicit case. Finally, using a combination of steadystate analysis and data clustering techniques, we explore model behaviour across a subregion of the parameter space that is difficult to access experimentally and compare the parameter landscape of our spatiotemporal and spatiallyhomogeneous models.
Thu, 01 Oct 2015 00:00:00 GMT
http://hdl.handle.net/10023/7709
20151001T00:00:00Z
Sturrock, M.
Murray, P. J.
Matzavinos, A.
Chaplain, M. A. J.
A gene regulatory network may be defined as a collection of DNA segments which interact with each other indirectly through their RNA and protein products. Such a network is said to contain a negative feedback loop if its products inhibit gene transcription, and a positive feedback loop if a gene product promotes its own production. Negative feedback loops can create oscillations in mRNA and protein levels while positive feedback loops are primarily responsible for signal amplification. It is often the case in real biological systems that both negative and positive feedback loops operate in parameter regimes that result in low copy numbers of gene products. In this paper we investigate the spatiotemporal dynamics of a single feedback loop in a eukaryotic cell. We first develop a simplified spatial stochastic model of a canonical feedback system (either positive or negative). Using a Gillespie's algorithm, we compute sample trajectories and analyse their corresponding statistics. We then derive a system of equations that describe the spatiotemporal evolution of the stochastic means. Subsequently, we examine the spatially homogeneous case and compare the results of numerical simulations with the spatially explicit case. Finally, using a combination of steadystate analysis and data clustering techniques, we explore model behaviour across a subregion of the parameter space that is difficult to access experimentally and compare the parameter landscape of our spatiotemporal and spatiallyhomogeneous models.

An exact collisionless equilibrium for the ForceFree Harris Sheet with low plasma beta
http://hdl.handle.net/10023/7691
We present a first discussion and analysis of the physical properties of a new exact collisionless equilibrium for a onedimensional nonlinear forcefree magnetic field, namely, the forcefree Harris sheet. The solution allows any value of the plasma beta, and crucially below unity, which previous nonlinear forcefree collisionless equilibria could not. The distribution function involves infinite series of Hermite polynomials in the canonical momenta, of which the important mathematical properties of convergence and nonnegativity have recently been proven. Plots of the distribution function are presented for the plasma beta modestly below unity, and we compare the shape of the distribution function in two of the velocity directions to a Maxwellian distribution.
Funding: STFC Consolidated Grant [ST/K000950/1] (OA, TN & FW) and a Doctoral Training Grant [ST/K502327/1] (OA). EPSRC Doctoral Training Grant [EP/K503162/1] (ST).
Thu, 01 Oct 2015 00:00:00 GMT
http://hdl.handle.net/10023/7691
20151001T00:00:00Z
Allanson, Oliver Douglas
Neukirch, Thomas
Wilson, Fiona
Troscheit, Sascha
We present a first discussion and analysis of the physical properties of a new exact collisionless equilibrium for a onedimensional nonlinear forcefree magnetic field, namely, the forcefree Harris sheet. The solution allows any value of the plasma beta, and crucially below unity, which previous nonlinear forcefree collisionless equilibria could not. The distribution function involves infinite series of Hermite polynomials in the canonical momenta, of which the important mathematical properties of convergence and nonnegativity have recently been proven. Plots of the distribution function are presented for the plasma beta modestly below unity, and we compare the shape of the distribution function in two of the velocity directions to a Maxwellian distribution.

3D wholeprominence fine structure modeling. II. Prominence evolution
http://hdl.handle.net/10023/7683
We use the new threedimensional (3D) wholeprominence fine structure model to study the evolution of prominences and their fine structures in response to changes in the underlying photospheric magnetic flux distribution. The applied model combines a detailed 3D prominence magnetic field configuration with a realistic description of the prominence plasma distributed along multiple fine structures. In addition, we utilize an approximate Hα visualization technique to study the evolution of the visible cool prominence plasma both in emission (prominence) and absorption (filament). We show that the initial magnetic field configuration of the modeled prominence is significantly disturbed by the changing position of a single polarity of a magnetic bipole as the bipole is advected toward the main body of the filament. This leads to the creation of a barb, which becomes the dominant feature visible in the synthetic Hα images of both the prominence and filament views. The evolution of the bipole also creates conditions that lead to the disappearance and reappearance of large portions of the main body. We also show that an archlike region containing a dark void (a bubble) can be naturally produced in the synthetic prominence Hα images. While not visible in terms of the magnetic field lines, it is due to a lack of Hα emission from lowpressure, lowdensity plasma located in shallow magnetic dips lying along the lines of sight intersecting the dark void. In addition, a quasivertical smallscale feature consisting of short and deep dips, piled one above the other, is produced.
Tue, 20 Oct 2015 00:00:00 GMT
http://hdl.handle.net/10023/7683
20151020T00:00:00Z
Gunar, Stanislav
Mackay, Duncan Hendry
We use the new threedimensional (3D) wholeprominence fine structure model to study the evolution of prominences and their fine structures in response to changes in the underlying photospheric magnetic flux distribution. The applied model combines a detailed 3D prominence magnetic field configuration with a realistic description of the prominence plasma distributed along multiple fine structures. In addition, we utilize an approximate Hα visualization technique to study the evolution of the visible cool prominence plasma both in emission (prominence) and absorption (filament). We show that the initial magnetic field configuration of the modeled prominence is significantly disturbed by the changing position of a single polarity of a magnetic bipole as the bipole is advected toward the main body of the filament. This leads to the creation of a barb, which becomes the dominant feature visible in the synthetic Hα images of both the prominence and filament views. The evolution of the bipole also creates conditions that lead to the disappearance and reappearance of large portions of the main body. We also show that an archlike region containing a dark void (a bubble) can be naturally produced in the synthetic prominence Hα images. While not visible in terms of the magnetic field lines, it is due to a lack of Hα emission from lowpressure, lowdensity plasma located in shallow magnetic dips lying along the lines of sight intersecting the dark void. In addition, a quasivertical smallscale feature consisting of short and deep dips, piled one above the other, is produced.

Formation and largescale patterns of filament channels and filaments
http://hdl.handle.net/10023/7673
The properties and largescale patterns of filament channels and filaments are considered. Initially, the global formation locations of filament channels and filaments are discussed, along with their hemispheric pattern. Next, observations of the formation of filament channels and filaments are described where two opposing views are considered. Finally, the wide range of models that have been constructed to consider the formation of filament channels and filaments over long timescales are described, along with the origin of the hemispheric pattern of filaments.
2015ASSL..415..355M
Thu, 01 Jan 2015 00:00:00 GMT
http://hdl.handle.net/10023/7673
20150101T00:00:00Z
Mackay, Duncan Hendry
The properties and largescale patterns of filament channels and filaments are considered. Initially, the global formation locations of filament channels and filaments are discussed, along with their hemispheric pattern. Next, observations of the formation of filament channels and filaments are described where two opposing views are considered. Finally, the wide range of models that have been constructed to consider the formation of filament channels and filaments over long timescales are described, along with the origin of the hemispheric pattern of filaments.

Particle energisation in a collapsing magnetic trap model : the relativistic regime
http://hdl.handle.net/10023/7603
Context. In solar flares, a large number of charged particles is accelerated to high energies. By which physical processes this is achieved is one of the main open problems in solar physics. It has been suggested that during a flare, regions of the rapidly relaxing magnetic field can form a collapsing magnetic trap (CMT) and that this trap may contribute to particle energisation. Aims. In this Research Note we focus on a particular analytical CMT model based on kinematic magnetohydrodynamics. Previous investigations of particle acceleration for this CMT model focused on the nonrelativistic energy regime. It is the specific aim of this Research Note to extend the previous work to relativistic particle energies. Methods. Particle orbits were calculated numerically using the relativistic guiding centre equations. We also calculated particle orbits using the nonrelativistic guiding centre equations for comparison. Results. For mildly relativistic energies the relativistic and nonrelativistic particle orbits mainly agree well, but clear deviations are seen for higher energies. In particular, the final particle energies obtained from the relativistic calculations are systematically lower than the energies reached from the corresponding nonrelativistic calculations, and the mirror points of the relativistic orbits are systematically higher than for the corresponding nonrelativistic orbits. Conclusions. While the overall behaviour of particle orbits in CMTs does not differ qualitatively when using the relativistic guiding centre equations, there are a few systematic quantitative differences between relativistic and nonrelativistic particle dynamics.
The authors acknowledge financial support by the UK’s Science and Technology Facilities Council through a Doctoral Training Grant (SEO) and Consolidated Grant ST/K000950/1 (SEO and TN).
Tue, 01 Jul 2014 00:00:00 GMT
http://hdl.handle.net/10023/7603
20140701T00:00:00Z
Eradat Oskoui, S.
Neukirch, T.
Context. In solar flares, a large number of charged particles is accelerated to high energies. By which physical processes this is achieved is one of the main open problems in solar physics. It has been suggested that during a flare, regions of the rapidly relaxing magnetic field can form a collapsing magnetic trap (CMT) and that this trap may contribute to particle energisation. Aims. In this Research Note we focus on a particular analytical CMT model based on kinematic magnetohydrodynamics. Previous investigations of particle acceleration for this CMT model focused on the nonrelativistic energy regime. It is the specific aim of this Research Note to extend the previous work to relativistic particle energies. Methods. Particle orbits were calculated numerically using the relativistic guiding centre equations. We also calculated particle orbits using the nonrelativistic guiding centre equations for comparison. Results. For mildly relativistic energies the relativistic and nonrelativistic particle orbits mainly agree well, but clear deviations are seen for higher energies. In particular, the final particle energies obtained from the relativistic calculations are systematically lower than the energies reached from the corresponding nonrelativistic calculations, and the mirror points of the relativistic orbits are systematically higher than for the corresponding nonrelativistic orbits. Conclusions. While the overall behaviour of particle orbits in CMTs does not differ qualitatively when using the relativistic guiding centre equations, there are a few systematic quantitative differences between relativistic and nonrelativistic particle dynamics.

Multiscale modelling of the dynamics of cell colonies : insights into celladhesion forces and cancer invasion from in silico simulations
http://hdl.handle.net/10023/7571
Studying the biophysical interactions between cells is crucial to understanding how normal tissue develops, how it is structured and also when malfunctions occur. Traditional experiments try to infer events at the tissue level after observing the behaviour of and interactions between individual cells. This approach assumes that cells behave in the same biophysical manner in isolated experiments as they do within colonies and tissues. In this paper, we develop a multiscale multicompartment mathematical model that accounts for the principal biophysical interactions and adhesion pathways not only at a cell?cell level but also at the level of cell colonies (in contrast to the traditional approach). Our results suggest that adhesion/separation forces between cells may be lower in cell colonies than traditional isolated singlecell experiments infer. As a consequence, isolated singlecell experiments may be insufficient to deduce important biological processes such as singlecell invasion after detachment from a solid tumour. The simulations further show that kinetic rates and cell biophysical characteristics such as pressurerelated cellcycle arrest have a major influence on cell colony patterns and can allow for the development of protrusive cellular structures as seen in invasive cancer cell lines independent of expression levels of proinvasion molecules.
Sun, 01 Feb 2015 00:00:00 GMT
http://hdl.handle.net/10023/7571
20150201T00:00:00Z
Schluter, Daniela K.
RamisConde, Ignacio
Chaplain, Mark A. J.
Studying the biophysical interactions between cells is crucial to understanding how normal tissue develops, how it is structured and also when malfunctions occur. Traditional experiments try to infer events at the tissue level after observing the behaviour of and interactions between individual cells. This approach assumes that cells behave in the same biophysical manner in isolated experiments as they do within colonies and tissues. In this paper, we develop a multiscale multicompartment mathematical model that accounts for the principal biophysical interactions and adhesion pathways not only at a cell?cell level but also at the level of cell colonies (in contrast to the traditional approach). Our results suggest that adhesion/separation forces between cells may be lower in cell colonies than traditional isolated singlecell experiments infer. As a consequence, isolated singlecell experiments may be insufficient to deduce important biological processes such as singlecell invasion after detachment from a solid tumour. The simulations further show that kinetic rates and cell biophysical characteristics such as pressurerelated cellcycle arrest have a major influence on cell colony patterns and can allow for the development of protrusive cellular structures as seen in invasive cancer cell lines independent of expression levels of proinvasion molecules.

Hopf bifurcation in a gene regulatory network model : molecular movement causes oscillations
http://hdl.handle.net/10023/7564
Gene regulatory networks, i.e. DNA segments in a cell which interact with each other indirectly through their RNA and protein products, lie at the heart of many important intracellular signal transduction processes. In this paper, we analyze a mathematical model of a canonical gene regulatory network consisting of a single negative feedback loop between a protein and its mRNA (e.g. the Hes1 transcription factor system). The model consists of two partial differential equations describing the spatiotemporal inter actions between the protein and its mRNA in a 1dimensional domain. Such intracellular negative feedback systems are known to exhibit oscillatory behavior and this is the case for our model, shown initially via computational simulations. In order to investigate this behavior more deeply, we undertake a linearized stability analysis of the steady states of the model. Our results show that the diffusion coefficient of the protein/mRNA acts as a bifurcation parameter and gives rise to a Hopf bifurcation. This shows that the spatial movement of the mRNA and protein molecules alone is sufficient to cause the oscillations. Our result has implications for transcription factors such as p53, NFκB and heat shock proteins which are involved in regulating important cellular processes such as inflammation, meiosis, apoptosis and the heat shock response, and are linked to diseases such as arthritis and cancer.
M.A.J.C. and M.S. gratefully acknowledge the support of the ERC Advanced Investigator Grant 227619, “M5CGS — From Mutations to Metastases: Multiscale Mathematical Modelling of Cancer Growth and Spread”. M.S. would also like to thank the support from the Mathematical Biosciences Institute at the Ohio State University and NSF Grant DMS0931642.
Mon, 15 Jun 2015 00:00:00 GMT
http://hdl.handle.net/10023/7564
20150615T00:00:00Z
Chaplain, Mark
Ptashnyk, Mariya
Sturrock, Marc
Gene regulatory networks, i.e. DNA segments in a cell which interact with each other indirectly through their RNA and protein products, lie at the heart of many important intracellular signal transduction processes. In this paper, we analyze a mathematical model of a canonical gene regulatory network consisting of a single negative feedback loop between a protein and its mRNA (e.g. the Hes1 transcription factor system). The model consists of two partial differential equations describing the spatiotemporal inter actions between the protein and its mRNA in a 1dimensional domain. Such intracellular negative feedback systems are known to exhibit oscillatory behavior and this is the case for our model, shown initially via computational simulations. In order to investigate this behavior more deeply, we undertake a linearized stability analysis of the steady states of the model. Our results show that the diffusion coefficient of the protein/mRNA acts as a bifurcation parameter and gives rise to a Hopf bifurcation. This shows that the spatial movement of the mRNA and protein molecules alone is sufficient to cause the oscillations. Our result has implications for transcription factors such as p53, NFκB and heat shock proteins which are involved in regulating important cellular processes such as inflammation, meiosis, apoptosis and the heat shock response, and are linked to diseases such as arthritis and cancer.

Magnetospheric signatures of ionospheric density cavities observed by Cluster
http://hdl.handle.net/10023/7509
We present Cluster measurements of large amplitude electric fields corre lated with intense downward fieldaligned currents, observed during a nightside crossing of the auroral zone. The data are reproduced by a simple model of magnetosphereionosphere coupling which, under different conditions, can also produce a divergent electric field signature in the downward current region, or correlation between the electric and perturbed magnetic fields. We conclude that strong electric field associated with intense downward fieldaligned current, such as this observation, is a signature of ionospheric plasma depletion caused by the downward current. It is also shown that the electric field in the downward current region correlates with downward current density if a background field is present, e.g. due to magnetospheric convection.
AJBR ackowledges support from STFC under consolidated grant ST/K000993/1.
Sun, 01 Mar 2015 00:00:00 GMT
http://hdl.handle.net/10023/7509
20150301T00:00:00Z
Russell, Alexander John Barkway
Karlsson, Tomas
Wright, Andrew Nicholas
We present Cluster measurements of large amplitude electric fields corre lated with intense downward fieldaligned currents, observed during a nightside crossing of the auroral zone. The data are reproduced by a simple model of magnetosphereionosphere coupling which, under different conditions, can also produce a divergent electric field signature in the downward current region, or correlation between the electric and perturbed magnetic fields. We conclude that strong electric field associated with intense downward fieldaligned current, such as this observation, is a signature of ionospheric plasma depletion caused by the downward current. It is also shown that the electric field in the downward current region correlates with downward current density if a background field is present, e.g. due to magnetospheric convection.

Strategies of eradicating glioma cells : a multiscale mathematical model with miR451AMPKmTOR control
http://hdl.handle.net/10023/7503
The cellular dispersion and therapeutic control of glioblastoma, the most aggressive type of primary brain cancer, depends critically on the migration patterns after surgery and intracellular responses of the individual cancer cells in response to external biochemical and biomechanical cues in the microenvironment. Recent studies have shown that a particular microRNA, miR451, regulates downstream molecules including AMPK and mTOR to determine the balance between rapid proliferation and invasion in response to metabolic stress in the harsh tumor microenvironment. Surgical removal of main tumor is inevitably followed by recurrence of the tumor due to inaccessibility of dispersed tumor cells in normal brain tissue. In order to address this multiscale nature of glioblastoma proliferation and invasion and its response to conventional treatment, we propose a hybrid model of glioblastoma that analyses spatiotemporal dynamics at the cellular level, linking individual tumor cells with the macroscopic behaviour of cell organization and the microenvironment, and with the intracellular dynamics of miR451AMPKmTOR signaling within a tumour cell. The model identifies a key mechanism underlying the molecular switches between proliferative phase and migratory phase in response to metabolic stress and biophysical interaction between cells in response to fluctuating glucose levels in the presence of blood vessels (BVs). The model predicts that cell migration, therefore efficacy of the treatment, not only depends on oxygen and glucose availability but also on the relative balance between random motility and strength of chemoattractants. Effective control of growing cells near BV sites in addition to relocalization of invisible migratory cells back to the resection site was suggested as a way of eradicating these migratory cells.
Wed, 28 Jan 2015 00:00:00 GMT
http://hdl.handle.net/10023/7503
20150128T00:00:00Z
Kim, Yangjin
Powathil, Gibin
Kang, Hyunji
Trucu, Dumitru
Kim, Hyeongi
Lawler, Sean
Chaplain, Mark
The cellular dispersion and therapeutic control of glioblastoma, the most aggressive type of primary brain cancer, depends critically on the migration patterns after surgery and intracellular responses of the individual cancer cells in response to external biochemical and biomechanical cues in the microenvironment. Recent studies have shown that a particular microRNA, miR451, regulates downstream molecules including AMPK and mTOR to determine the balance between rapid proliferation and invasion in response to metabolic stress in the harsh tumor microenvironment. Surgical removal of main tumor is inevitably followed by recurrence of the tumor due to inaccessibility of dispersed tumor cells in normal brain tissue. In order to address this multiscale nature of glioblastoma proliferation and invasion and its response to conventional treatment, we propose a hybrid model of glioblastoma that analyses spatiotemporal dynamics at the cellular level, linking individual tumor cells with the macroscopic behaviour of cell organization and the microenvironment, and with the intracellular dynamics of miR451AMPKmTOR signaling within a tumour cell. The model identifies a key mechanism underlying the molecular switches between proliferative phase and migratory phase in response to metabolic stress and biophysical interaction between cells in response to fluctuating glucose levels in the presence of blood vessels (BVs). The model predicts that cell migration, therefore efficacy of the treatment, not only depends on oxygen and glucose availability but also on the relative balance between random motility and strength of chemoattractants. Effective control of growing cells near BV sites in addition to relocalization of invisible migratory cells back to the resection site was suggested as a way of eradicating these migratory cells.

Sunspot rotation. I : A consequence of flux emergence
http://hdl.handle.net/10023/7497
Context. Solar eruptions and high flare activity often accompany the rapid rotation of sunspots. The study of sunspot rotation and the mechanisms driving this motion are therefore key to our understanding of how the solar atmosphere attains the conditions necessary for large energy release. Aims. We aim to demonstrate and investigate the rotation of sunspots in a 3D numerical experiment of the emergence of a magnetic flux tube as it rises through the solar interior and emerges into the atmosphere. Furthermore, we seek to show that the subphotospheric twist stored in the interior is injected into the solar atmosphere by means of a definitive rotation of the sunspots. Methods. A numerical experiment is performed to solve the 3D resistive magnetohydrodynamic (MHD) equations using a LagrangianRemap code. We track the emergence of a toroidal flux tube as it rises through the solar interior and emerges into the atmosphere investigating various quantities related to both the magnetic field and plasma. Results. Through detailed analysis of the numerical experiment, we find clear evidence that the photospheric footprints or sunspots of the flux tube undergo a rotation. Significant vertical vortical motions are found to develop within the two polarity sources after the field emerges. These rotational motions are found to leave the interior portion of the field untwisted and twist up the atmospheric portion of the field. This is shown by our analysis of the relative magnetic helicity as a significant portion of the interior helicity is transported to the atmosphere. In addition, there is a substantial transport of magnetic energy to the atmosphere. Rotation angles are also calculated by tracing selected fieldlines; the fieldlines threading through the sunspot are found to rotate through angles of up to 353º over the course of the experiment. We explain the rotation by an unbalanced torque produced by the magnetic tension force, rather than an apparent effect.
ZS acknowledges the financial support of the Carnegie Trust for Scotland and CMM the support of the Royal Society of Edinburgh. This work used the DIRAC 1, UKMHD Consortium machine at the University of St Andrews and the DiRAC Data Centric system at Durham University, operated by the Institute for Computational Cosmology on behalf of the STFC DiRAC HPC Facility (www.dirac.ac.uk). This equipment was funded by BIS National Einfrastructure capital grant ST/K00042X/1, STFC capital grant ST/H008519/1, and STFC DiRAC Operations grant ST/K003267/1 and Durham University. DiRAC is part of the National EInfrastructure.
Mon, 12 Oct 2015 00:00:00 GMT
http://hdl.handle.net/10023/7497
20151012T00:00:00Z
Sturrock, Zoe
Hood, Alan William
Archontis, Vasilis
McNeill, Craig
Context. Solar eruptions and high flare activity often accompany the rapid rotation of sunspots. The study of sunspot rotation and the mechanisms driving this motion are therefore key to our understanding of how the solar atmosphere attains the conditions necessary for large energy release. Aims. We aim to demonstrate and investigate the rotation of sunspots in a 3D numerical experiment of the emergence of a magnetic flux tube as it rises through the solar interior and emerges into the atmosphere. Furthermore, we seek to show that the subphotospheric twist stored in the interior is injected into the solar atmosphere by means of a definitive rotation of the sunspots. Methods. A numerical experiment is performed to solve the 3D resistive magnetohydrodynamic (MHD) equations using a LagrangianRemap code. We track the emergence of a toroidal flux tube as it rises through the solar interior and emerges into the atmosphere investigating various quantities related to both the magnetic field and plasma. Results. Through detailed analysis of the numerical experiment, we find clear evidence that the photospheric footprints or sunspots of the flux tube undergo a rotation. Significant vertical vortical motions are found to develop within the two polarity sources after the field emerges. These rotational motions are found to leave the interior portion of the field untwisted and twist up the atmospheric portion of the field. This is shown by our analysis of the relative magnetic helicity as a significant portion of the interior helicity is transported to the atmosphere. In addition, there is a substantial transport of magnetic energy to the atmosphere. Rotation angles are also calculated by tracing selected fieldlines; the fieldlines threading through the sunspot are found to rotate through angles of up to 353º over the course of the experiment. We explain the rotation by an unbalanced torque produced by the magnetic tension force, rather than an apparent effect.

Evolution of field line helicity during magnetic reconnection
http://hdl.handle.net/10023/7485
We investigate the evolution of field line helicity for magnetic fields that connect two boundaries without null points, with emphasis on localized finiteB magnetic reconnection. Total ( relative) magnetic helicity is already recognized as an important topological constraint on magnetohydrodynamic processes. Field line helicity offers further advantages because it preserves all topological information and can distinguish between different magnetic fields with the same total helicity. Magnetic reconnection changes field connectivity and field line helicity reflects these changes; the goal of this paper is to characterize that evolution. We start by deriving the evolution equation for field line helicity and examining its terms, also obtaining a simplified form for cases where dynamics are localized within the domain. The main result, which we support using kinematic examples, is that during localized reconnection in a complex magnetic field, the evolution of field line helicity is dominated by a worklike term that is evaluated at the field line endpoints, namely, the scalar product of the generalized field line velocity and the vector potential. Furthermore, the flux integral of this term over certain areas is very small compared to the integral of the unsigned quantity, which indicates that changes of field line helicity happen in a wellorganized pairwise manner. It follows that reconnection is very efficient at redistributing helicity in complex magnetic fields despite having little effect on the total helicity.
This work was supported by the Science and Technology Facilities Council (UK) through consortium Grant Nos. ST/K000993/1 and ST/K001043 to the University of Dundee and Durham University.
Sun, 01 Mar 2015 00:00:00 GMT
http://hdl.handle.net/10023/7485
20150301T00:00:00Z
Russell, A. J. B.
Yeates, A. R.
Hornig, G.
WilmotSmith, A. L.
We investigate the evolution of field line helicity for magnetic fields that connect two boundaries without null points, with emphasis on localized finiteB magnetic reconnection. Total ( relative) magnetic helicity is already recognized as an important topological constraint on magnetohydrodynamic processes. Field line helicity offers further advantages because it preserves all topological information and can distinguish between different magnetic fields with the same total helicity. Magnetic reconnection changes field connectivity and field line helicity reflects these changes; the goal of this paper is to characterize that evolution. We start by deriving the evolution equation for field line helicity and examining its terms, also obtaining a simplified form for cases where dynamics are localized within the domain. The main result, which we support using kinematic examples, is that during localized reconnection in a complex magnetic field, the evolution of field line helicity is dominated by a worklike term that is evaluated at the field line endpoints, namely, the scalar product of the generalized field line velocity and the vector potential. Furthermore, the flux integral of this term over certain areas is very small compared to the integral of the unsigned quantity, which indicates that changes of field line helicity happen in a wellorganized pairwise manner. It follows that reconnection is very efficient at redistributing helicity in complex magnetic fields despite having little effect on the total helicity.

On the theory of translationally invariant magnetohydrodynamic equilibria with anisotropic pressure and magnetic shear
http://hdl.handle.net/10023/7484
We present an improved formalism for translationally invariant magnetohydrodynamic equilibria with anisotropic pressure and currents with a field aligned component. The derivation of a GradShafranov type equation is given along with a constraint which links the shear field to the parallel pressure. The difficulties of the formalism are discussed and various methods of circumventing these difficulties are given. A simple example is then used to highlight the methods and difficulties involved.
Funding: STFC Doctoral Training Grant ST/K502327/1 (Jonathan Hodgson) and STFC Consolidated Grant ST/K000950/1 (Thomas Neukirch)
Thu, 01 Jan 2015 00:00:00 GMT
http://hdl.handle.net/10023/7484
20150101T00:00:00Z
Hodgson, Jonathan David Brockie
Neukirch, Thomas
We present an improved formalism for translationally invariant magnetohydrodynamic equilibria with anisotropic pressure and currents with a field aligned component. The derivation of a GradShafranov type equation is given along with a constraint which links the shear field to the parallel pressure. The difficulties of the formalism are discussed and various methods of circumventing these difficulties are given. A simple example is then used to highlight the methods and difficulties involved.

Coronal heating in multiple magnetic threads
http://hdl.handle.net/10023/7259
Context. Heating the solar corona to several million degrees requires the conversion of magnetic energy into thermal energy. In this paper, we investigate whether an unstable magnetic thread within a coronal loop can destabilise a neighbouring magnetic thread. Aims. By running a series of simulations, we aim to understand under what conditions the destabilisation of a single magnetic thread can also trigger a release of energy in a nearby thread. Methods. The 3D magnetohydrodynamics code, Lare3d, is used to simulate the temporal evolution of coronal magnetic fields during a kink instability and the subsequent relaxation process. We assume that a coronal magnetic loop consists of nonpotential magnetic threads that are initially in an equilibrium state. Results. The nonlinear kink instability in one magnetic thread forms a helical current sheet and initiates magnetic reconnection. The current sheet fragments, and magnetic energy is released throughout that thread. We find that, under certain conditions, this event can destabilise a nearby thread, which is a necessary requirement for starting an avalanche of energy release in magnetic threads. Conclusions. It is possible to initiate an energy release in a nearby, nonpotential magnetic thread, because the energy released from one unstable magnetic thread can trigger energy release in nearby threads, provided that the nearby structures are close to marginal stability.
We acknowledge the financial support of STFC through the Consolidated grant to the University of St Andrews.
Sat, 01 Aug 2015 00:00:00 GMT
http://hdl.handle.net/10023/7259
20150801T00:00:00Z
Tam, Kuan Vai
Hood, Alan William
Browning, Philippa
Cargill, Peter
Context. Heating the solar corona to several million degrees requires the conversion of magnetic energy into thermal energy. In this paper, we investigate whether an unstable magnetic thread within a coronal loop can destabilise a neighbouring magnetic thread. Aims. By running a series of simulations, we aim to understand under what conditions the destabilisation of a single magnetic thread can also trigger a release of energy in a nearby thread. Methods. The 3D magnetohydrodynamics code, Lare3d, is used to simulate the temporal evolution of coronal magnetic fields during a kink instability and the subsequent relaxation process. We assume that a coronal magnetic loop consists of nonpotential magnetic threads that are initially in an equilibrium state. Results. The nonlinear kink instability in one magnetic thread forms a helical current sheet and initiates magnetic reconnection. The current sheet fragments, and magnetic energy is released throughout that thread. We find that, under certain conditions, this event can destabilise a nearby thread, which is a necessary requirement for starting an avalanche of energy release in magnetic threads. Conclusions. It is possible to initiate an energy release in a nearby, nonpotential magnetic thread, because the energy released from one unstable magnetic thread can trigger energy release in nearby threads, provided that the nearby structures are close to marginal stability.

Are tornadolike magnetic structures able to support solar prominence plasma?
http://hdl.handle.net/10023/7202
Recent highresolution and highcadence observations have surprisingly suggested that prominence barbs exhibit apparent rotating motions suggestive of a tornadolike structure. Additional evidence has been provided by Doppler measurements. The observations reveal opposite velocities for both hot and cool plasma on the two sides of a prominence barb. This motion is persistent for several hours and has been interpreted in terms of rotational motion of prominence feet. Several authors suggest that such barb motions are rotating helical structures around a vertical axis similar to tornadoes on Earth. One of the difficulties of such a proposal is how to support cool prominence plasma in almostvertical structures against gravity. In this work we model analytically a tornadolike structure and try to determine possible mechanisms to support the prominence plasma. We have found that the Lorentz force can indeed support the barb plasma provided the magnetic structure is sufficiently twisted and/or significant poloidal flows are present.
M. Luna and F. MorenoInsertis acknowledge support by the Spanish Ministry of Economy and Competitiveness through projects AYA201124808 and AYA201455078P. M.L. is also grateful to ERC2011StG 277829SPIA. E.R.P. is grateful to the UK STFC and the Leverhulme Trust for financial support.
Mon, 20 Jul 2015 00:00:00 GMT
http://hdl.handle.net/10023/7202
20150720T00:00:00Z
Luna, M.
MorenoInsertis, F.
Priest, E.
Recent highresolution and highcadence observations have surprisingly suggested that prominence barbs exhibit apparent rotating motions suggestive of a tornadolike structure. Additional evidence has been provided by Doppler measurements. The observations reveal opposite velocities for both hot and cool plasma on the two sides of a prominence barb. This motion is persistent for several hours and has been interpreted in terms of rotational motion of prominence feet. Several authors suggest that such barb motions are rotating helical structures around a vertical axis similar to tornadoes on Earth. One of the difficulties of such a proposal is how to support cool prominence plasma in almostvertical structures against gravity. In this work we model analytically a tornadolike structure and try to determine possible mechanisms to support the prominence plasma. We have found that the Lorentz force can indeed support the barb plasma provided the magnetic structure is sufficiently twisted and/or significant poloidal flows are present.

Effect of Prandtl's ration on balance in geophysical turbulence
http://hdl.handle.net/10023/7201
The fluid dynamics of the atmosphere and oceans are to a large extent controlled by the slow evolution of a scalar field called ‘potential vorticity’, with relatively fast motions such as inertiagravity waves playing only a minor role. This state of affairs is commonly referred to as ‘balance’. Potential vorticity (PV) is a special scalar field which is materially conserved in the absence of diabatic effects and dissipation, effects which are generally weak in the atmosphere and oceans. Moreover, in a balanced flow, PV induces the entire fluid motion and its thermodynamic structure (Hoskins et al. 1985). While exact balance is generally not achievable, it is now well established that balance holds to a high degree of accuracy in rapidly rotating and strongly stratified flows. Such flows are characterised by both a small Rossby number, Ro ≡ ζmax/f, and a small Froude number, Fr ≡ .hmax/N, where ζ and .h are the relative vertical and horizontal vorticity components, while f and N are the Coriolis and buoyancy frequencies. In fact, balance can even be a good approximation when Fr < ∼ Ro ∼ O(1). In this study, we examine how balance depends specifically on Prandtl’s ratio, f/N, in unforced freelyevolving turbulence. We examine a wide variety of turbulent flows, at a mature and complex stage of their evolution, making use of the fully nonhydrostatic equations under the Boussinesq and incompressible approximations. We perform numerical simulations at exceptionally high resolution in order to carefully assess the degree to which balance holds, and to determine when it breaks down. For this purpose, it proves most useful to employ an invariant, PVbased Rossby number ε, together with f/N. For a given ε, our key finding is that — for at least tens of characteristic vortex rotation periods — the flow is insensitive to f/N for all values for which the flow remains statically stable (typically f/N < ∼1). Only the vertical velocity varies in proportion to f/N, in line with quasigeostrophic scaling for which Fr2 ≪ Ro ≪ 1. We also find that as ε increases toward unity, the maximum f/N attainable decreases toward 0. No statically stable flows occur for ε > ∼ 1. For all stable flows, balance is found to hold to a remarkably high degree: as measured by an energy norm, imbalance never exceeds more than a few percent of the balance, even in flows where Ro > 1. The vertical velocity w remains a tiny fraction of the horizontal velocity uh, even when w is dominantly balanced. Finally, typical vertical to horizontal scale ratios H/L remain close to f/N, as found previously in quasigeostrophic turbulence for which Fr ∼ Ro ≪ 1.
Support for this research has come from the UK Engineering and Physical Sciences Research Council (grant no. EP/H001794/1).
Tue, 21 Jul 2015 00:00:00 GMT
http://hdl.handle.net/10023/7201
20150721T00:00:00Z
Dritschel, David Gerard
McKiver, William Joseph
The fluid dynamics of the atmosphere and oceans are to a large extent controlled by the slow evolution of a scalar field called ‘potential vorticity’, with relatively fast motions such as inertiagravity waves playing only a minor role. This state of affairs is commonly referred to as ‘balance’. Potential vorticity (PV) is a special scalar field which is materially conserved in the absence of diabatic effects and dissipation, effects which are generally weak in the atmosphere and oceans. Moreover, in a balanced flow, PV induces the entire fluid motion and its thermodynamic structure (Hoskins et al. 1985). While exact balance is generally not achievable, it is now well established that balance holds to a high degree of accuracy in rapidly rotating and strongly stratified flows. Such flows are characterised by both a small Rossby number, Ro ≡ ζmax/f, and a small Froude number, Fr ≡ .hmax/N, where ζ and .h are the relative vertical and horizontal vorticity components, while f and N are the Coriolis and buoyancy frequencies. In fact, balance can even be a good approximation when Fr < ∼ Ro ∼ O(1). In this study, we examine how balance depends specifically on Prandtl’s ratio, f/N, in unforced freelyevolving turbulence. We examine a wide variety of turbulent flows, at a mature and complex stage of their evolution, making use of the fully nonhydrostatic equations under the Boussinesq and incompressible approximations. We perform numerical simulations at exceptionally high resolution in order to carefully assess the degree to which balance holds, and to determine when it breaks down. For this purpose, it proves most useful to employ an invariant, PVbased Rossby number ε, together with f/N. For a given ε, our key finding is that — for at least tens of characteristic vortex rotation periods — the flow is insensitive to f/N for all values for which the flow remains statically stable (typically f/N < ∼1). Only the vertical velocity varies in proportion to f/N, in line with quasigeostrophic scaling for which Fr2 ≪ Ro ≪ 1. We also find that as ε increases toward unity, the maximum f/N attainable decreases toward 0. No statically stable flows occur for ε > ∼ 1. For all stable flows, balance is found to hold to a remarkably high degree: as measured by an energy norm, imbalance never exceeds more than a few percent of the balance, even in flows where Ro > 1. The vertical velocity w remains a tiny fraction of the horizontal velocity uh, even when w is dominantly balanced. Finally, typical vertical to horizontal scale ratios H/L remain close to f/N, as found previously in quasigeostrophic turbulence for which Fr ∼ Ro ≪ 1.

On the parallel and perpendicular propagating motions visible in polar plumes : an incubator for (fast) solar wind acceleration?
http://hdl.handle.net/10023/7190
We combine observations of the Coronal Multichannel Polarimeter and the Atmospheric Imaging Assembly on board the Solar Dynamics Observatory to study the characteristic properties of (propagating) Alfvenic motions and quasiperiodic intensity disturbances in polar plumes. This unique combination of instruments highlights the physical richness of the processes taking place at the base of the (fast) solar wind. The (parallel) intensity perturbations with intensity enhancements around 1% have an apparent speed of 120 km s(1) (in both the 171 and 193 angstrom passbands) and a periodicity of 15 minutes, while the (perpendicular) Alfvenic wave motions have a velocity amplitude of 0.5 km s(1), a phase speed of 830 km s(1), and a shorter period of 5 minutes on the same structures. These observations illustrate a scenario where the excited Alfvenic motions are propagating along an inhomogeneously loaded magnetic field structure such that the combination could be a potential progenitor of the magnetohydrodynamic turbulence required to accelerate the fast solar wind.
J.L. was a student visitor at HAO. J.L. acknowledges the financial support for his visit to HAO from the Chinese Scholarship Council (CSC). The authors acknowledge support from NSFC 41131065, 41121003, 973 Key Project 2011CB811403, and CAS Key Research Program KZZDEW014. We also acknowledge support from NASA contracts NNX08BA99G, NNX11AN98G, NNM12AB40P, NNG09FA40C (IRIS), and NNM07AA01C (Hinode). The research leading to these results has also received funding from the European Commission Seventh Framework Programme (FP7/ 20072013) under the grant agreement SOLSPANET (project No. 269299, www.solspanet.eu/solspanet) Date of Acceptance: 25/05/2015
Sat, 20 Jun 2015 00:00:00 GMT
http://hdl.handle.net/10023/7190
20150620T00:00:00Z
Liu, Jiajia
McIntosh, Scott W.
De Moortel, Ineke
Wang, Yuming
We combine observations of the Coronal Multichannel Polarimeter and the Atmospheric Imaging Assembly on board the Solar Dynamics Observatory to study the characteristic properties of (propagating) Alfvenic motions and quasiperiodic intensity disturbances in polar plumes. This unique combination of instruments highlights the physical richness of the processes taking place at the base of the (fast) solar wind. The (parallel) intensity perturbations with intensity enhancements around 1% have an apparent speed of 120 km s(1) (in both the 171 and 193 angstrom passbands) and a periodicity of 15 minutes, while the (perpendicular) Alfvenic wave motions have a velocity amplitude of 0.5 km s(1), a phase speed of 830 km s(1), and a shorter period of 5 minutes on the same structures. These observations illustrate a scenario where the excited Alfvenic motions are propagating along an inhomogeneously loaded magnetic field structure such that the combination could be a potential progenitor of the magnetohydrodynamic turbulence required to accelerate the fast solar wind.

Uncertainties in polarimetric 3D reconstructions of coronal mass ejections
http://hdl.handle.net/10023/7178
Aims. The aim of this work is to quantify the uncertainties in the threedimensional (3D) reconstruction of the location of coronal mass ejections (CMEs) obtained with the socalled polarization ratio technique. The method takes advantage of the different distributions along the line of sight of total (tB) and polarized (pB) brightnesses emitted by Thomson scattering to estimate the average location of the emitting plasma. This is particularly important to correctly identify of CME propagation angles and unprojected velocities, thus allowing better capabilities for space weather forecastings. Methods. To this end, we assumed two simple electron density distributions along the line of sight (a constant density and Gaussian density profiles) for a plasma blob and synthesized the expected tB and pB for different distances z of the blob from the plane of the sky and different projected altitudes.. Reconstructed locations of the blob along the line of sight were thus compared with the real ones, allowing a precise determination of uncertainties in the method. Results. Results show that, independently of the analytical density profile, when the blob is centered at a small distance from the plane of the sky (i. e. for limb CMEs) the distance from the plane of the sky starts to be significantly overestimated. Polarization ratio technique provides the lineofsight position of the center of mass of what we call folded density distribution, given by reflecting and summing in front of the plane of the sky the fraction of density profile located behind that plane. On the other hand, when the blob is far from the plane of the sky, but with very small projected altitudes (i. e. for halo CMEs, rho< 1.4 Rcircle dot), the inferred distance from that plane is significantly underestimated. Better determination of the real blob position along the line of sight is given for intermediate locations, and in particular when the blob is centered at an angle of 20 degrees from the plane of the sky. Conclusions. These result have important consequences not only for future 3D reconstruction of CMEs with polarization ratio technique, but also for the design of future coronagraphs aimed at providing a continuous monitoring of haloCMEs for space weather prediction purposes.
P.P. acknowledges STFC for financial support. Date of Acceptance: 21/01/2015
Mon, 06 Apr 2015 00:00:00 GMT
http://hdl.handle.net/10023/7178
20150406T00:00:00Z
Bemporad, A.
Pagano, P.
Aims. The aim of this work is to quantify the uncertainties in the threedimensional (3D) reconstruction of the location of coronal mass ejections (CMEs) obtained with the socalled polarization ratio technique. The method takes advantage of the different distributions along the line of sight of total (tB) and polarized (pB) brightnesses emitted by Thomson scattering to estimate the average location of the emitting plasma. This is particularly important to correctly identify of CME propagation angles and unprojected velocities, thus allowing better capabilities for space weather forecastings. Methods. To this end, we assumed two simple electron density distributions along the line of sight (a constant density and Gaussian density profiles) for a plasma blob and synthesized the expected tB and pB for different distances z of the blob from the plane of the sky and different projected altitudes.. Reconstructed locations of the blob along the line of sight were thus compared with the real ones, allowing a precise determination of uncertainties in the method. Results. Results show that, independently of the analytical density profile, when the blob is centered at a small distance from the plane of the sky (i. e. for limb CMEs) the distance from the plane of the sky starts to be significantly overestimated. Polarization ratio technique provides the lineofsight position of the center of mass of what we call folded density distribution, given by reflecting and summing in front of the plane of the sky the fraction of density profile located behind that plane. On the other hand, when the blob is far from the plane of the sky, but with very small projected altitudes (i. e. for halo CMEs, rho< 1.4 Rcircle dot), the inferred distance from that plane is significantly underestimated. Better determination of the real blob position along the line of sight is given for intermediate locations, and in particular when the blob is centered at an angle of 20 degrees from the plane of the sky. Conclusions. These result have important consequences not only for future 3D reconstruction of CMEs with polarization ratio technique, but also for the design of future coronagraphs aimed at providing a continuous monitoring of haloCMEs for space weather prediction purposes.

NonLTE modelling of prominence fine structures using hydrogen Lymanline profiles
http://hdl.handle.net/10023/7177
Aims. We perform a detailed statistical analysis of the spectral Lymanline observations of the quiescent prominence observed on May 18, 2005. Methods. We used a profiletoprofile comparison of the synthetic Lyman spectra obtained by 2D singlethread prominence finestructure model as a starting point for a full statistical analysis of the observed Lyman spectra. We employed 2D multithread finestructure models with random positions and lineofsight velocities of each thread to obtain a statistically significant set of synthetic Lymanline profiles. We used for the first time multithread models composed of nonidentical threads and viewed at lineofsight angles different from perpendicular to the magnetic field. Results. We investigated the plasma properties of the prominence observed with the SoHO/SUMER spectrograph on May 18, 2005 by comparing the histograms of three statistical parameters characterizing the properties of the synthetic and observed line profiles. In this way, the integrated intensity, Lyman decrement ratio, and the ratio of intensity at the central reversal to the average intensity of peaks provided insight into the column mass and the central temperature of the prominence fine structures.
Date of Acceptance: 10/03/2015
Fri, 08 May 2015 00:00:00 GMT
http://hdl.handle.net/10023/7177
20150508T00:00:00Z
Schwartz, P.
Gunar, S.
Curdt, W.
Aims. We perform a detailed statistical analysis of the spectral Lymanline observations of the quiescent prominence observed on May 18, 2005. Methods. We used a profiletoprofile comparison of the synthetic Lyman spectra obtained by 2D singlethread prominence finestructure model as a starting point for a full statistical analysis of the observed Lyman spectra. We employed 2D multithread finestructure models with random positions and lineofsight velocities of each thread to obtain a statistically significant set of synthetic Lymanline profiles. We used for the first time multithread models composed of nonidentical threads and viewed at lineofsight angles different from perpendicular to the magnetic field. Results. We investigated the plasma properties of the prominence observed with the SoHO/SUMER spectrograph on May 18, 2005 by comparing the histograms of three statistical parameters characterizing the properties of the synthetic and observed line profiles. In this way, the integrated intensity, Lyman decrement ratio, and the ratio of intensity at the central reversal to the average intensity of peaks provided insight into the column mass and the central temperature of the prominence fine structures.

The formation and eruption of magnetic flux ropes in solar and stellar coronae
http://hdl.handle.net/10023/7069
Flux ropes are magnetic structures commonly found in the solar corona. They are thought to play an important role in solar flares and coronal mass ejections. Understanding their formation and eruption is of paramount importance for our understanding of space weather. In this thesis the magnetofrictional method is applied to simulate the formation of flux ropes and track their evolution up to eruption both in solar and stellar coronae.
Initially, the coronal magnetic field of a solar active region is simulated using observed magnetograms to drive the coronal evolution. From the sequence of magnetograms the formation of a flux rope is simulated, and compared with coronal observations.
Secondly a procedure to produce proxy SOLIS synoptic magnetograms from SDO/HMI and SOHO/MDI magnetograms is presented. This procedure allows SOLISlike synoptic magnetograms to be produced during times when SOLIS magnetograms are not available.
Thirdly, a series of scaling laws for the formation and lifetimes of flux ropes in stellar coronae are determined as a function of stellar differential rotation and surface diffusion. These scaling laws can be used to infer the response of stellar coronae to the transport of magnetic fields at their surface.
Finally, global longterm simulations of stellar corona are carried out to determine the coronal response to flux emergence and differential rotation. A bipole emergence model is developed and is used in conjunction with a surface flux transport model in order to drive the global coronal evolution. These global simulations allow the flux, energy and flux rope distributions to be studied as a function of a star’s differential rotation and flux emergence rate.
Mon, 30 Nov 2015 00:00:00 GMT
http://hdl.handle.net/10023/7069
20151130T00:00:00Z
Gibb, Gordon Peter Samuel
Flux ropes are magnetic structures commonly found in the solar corona. They are thought to play an important role in solar flares and coronal mass ejections. Understanding their formation and eruption is of paramount importance for our understanding of space weather. In this thesis the magnetofrictional method is applied to simulate the formation of flux ropes and track their evolution up to eruption both in solar and stellar coronae.
Initially, the coronal magnetic field of a solar active region is simulated using observed magnetograms to drive the coronal evolution. From the sequence of magnetograms the formation of a flux rope is simulated, and compared with coronal observations.
Secondly a procedure to produce proxy SOLIS synoptic magnetograms from SDO/HMI and SOHO/MDI magnetograms is presented. This procedure allows SOLISlike synoptic magnetograms to be produced during times when SOLIS magnetograms are not available.
Thirdly, a series of scaling laws for the formation and lifetimes of flux ropes in stellar coronae are determined as a function of stellar differential rotation and surface diffusion. These scaling laws can be used to infer the response of stellar coronae to the transport of magnetic fields at their surface.
Finally, global longterm simulations of stellar corona are carried out to determine the coronal response to flux emergence and differential rotation. A bipole emergence model is developed and is used in conjunction with a surface flux transport model in order to drive the global coronal evolution. These global simulations allow the flux, energy and flux rope distributions to be studied as a function of a star’s differential rotation and flux emergence rate.

Propagation and damping of MHD waves in the solar atmosphere
http://hdl.handle.net/10023/7054
Quasiperiodic disturbances have been observed in the outer solar atmosphere for many years. Although first interpreted as upflows (Schrijver et al. (1999)), they have been widely regarded as slow magnetoacoustic waves, due to their observed velocities and periods. Here we conduct a detailed analysis of the velocities of these disturbances across several wavelengths using the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamics Observatory (SDO). We analysed 41 examples, including both sunspot and nonsunspot regions of the Sun. We found that the velocities of propagating disturbances (PDs) located at sunspots are more likely to be temperature dependent, whereas the velocities of PDs at nonsunspot locations do not show a clear temperature dependence. This suggests an interpretation in terms of slow magnetoacoustic waves in sunspots but the nature of PDs in nonsunspot (plage) regions remains unclear. Finally, we found that removing the contribution due to the cooler ions in the 193 wavelength suggests that a substantial part of the 193 emission of sunspot PDs can be attributed to the cool component of 193. Phase mixing is a well known and studied phenomenon in the solar corona, to enhance the dissipation of Alfvén waves (Heyvaerts and Priest (1982)). In this study we run numerical simulations of a continuously driven Alfvén wave in a low beta plasma along a uniform magnetic field. We model phase mixing by introducing a density inhomogeneity. Thermal conduction is then added into the model in the form of Braginskii thermal conduction. This acts to transport heat along the magnetic field. A parameter study will be carried out to investigate how changing the density structure and other parameters changes the results. We go on to consider the effect of wave reflection on phase mixing. We found that wave reflection has no effect on the damping of Alfvén waves but increases the heat in the system. We also consider a more realistic experiment where we drive both boundaries and study how the loop is heated in this situation. We also study what effect changing the frequency of one of the drivers so there is a small difference between the frequencies (10%) and a large difference (50%). We find the general behaviour is similar, but the heat is tilted.
We have investigated basic phase mixing model which incorporates the mass exchange between the corona and the chromosphere. Chromospheric evaporation is approximated by using a non dimensional version of the RTV (Rosner et al. (1978)) scaling laws, relating heating (by phase mixing of Alfvén waves), density and temperature. By combining this scaling law with our numerical MHD model for phase mixing of Alfvén waves, we investigate the modification of the density profile through the mass up flow. We find a rapid modification of the density profile, leading to drifting of the heating layers. We also find that similar results are own seen in the propagating Alfvén wave case when we incorporate the effects of reflection.
Fri, 27 Jun 2014 00:00:00 GMT
http://hdl.handle.net/10023/7054
20140627T00:00:00Z
Kiddie, Greg
Quasiperiodic disturbances have been observed in the outer solar atmosphere for many years. Although first interpreted as upflows (Schrijver et al. (1999)), they have been widely regarded as slow magnetoacoustic waves, due to their observed velocities and periods. Here we conduct a detailed analysis of the velocities of these disturbances across several wavelengths using the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamics Observatory (SDO). We analysed 41 examples, including both sunspot and nonsunspot regions of the Sun. We found that the velocities of propagating disturbances (PDs) located at sunspots are more likely to be temperature dependent, whereas the velocities of PDs at nonsunspot locations do not show a clear temperature dependence. This suggests an interpretation in terms of slow magnetoacoustic waves in sunspots but the nature of PDs in nonsunspot (plage) regions remains unclear. Finally, we found that removing the contribution due to the cooler ions in the 193 wavelength suggests that a substantial part of the 193 emission of sunspot PDs can be attributed to the cool component of 193. Phase mixing is a well known and studied phenomenon in the solar corona, to enhance the dissipation of Alfvén waves (Heyvaerts and Priest (1982)). In this study we run numerical simulations of a continuously driven Alfvén wave in a low beta plasma along a uniform magnetic field. We model phase mixing by introducing a density inhomogeneity. Thermal conduction is then added into the model in the form of Braginskii thermal conduction. This acts to transport heat along the magnetic field. A parameter study will be carried out to investigate how changing the density structure and other parameters changes the results. We go on to consider the effect of wave reflection on phase mixing. We found that wave reflection has no effect on the damping of Alfvén waves but increases the heat in the system. We also consider a more realistic experiment where we drive both boundaries and study how the loop is heated in this situation. We also study what effect changing the frequency of one of the drivers so there is a small difference between the frequencies (10%) and a large difference (50%). We find the general behaviour is similar, but the heat is tilted.
We have investigated basic phase mixing model which incorporates the mass exchange between the corona and the chromosphere. Chromospheric evaporation is approximated by using a non dimensional version of the RTV (Rosner et al. (1978)) scaling laws, relating heating (by phase mixing of Alfvén waves), density and temperature. By combining this scaling law with our numerical MHD model for phase mixing of Alfvén waves, we investigate the modification of the density profile through the mass up flow. We find a rapid modification of the density profile, leading to drifting of the heating layers. We also find that similar results are own seen in the propagating Alfvén wave case when we incorporate the effects of reflection.

Extreme ultraviolet imaging of threedimensional magnetic reconnection in a solar eruption
http://hdl.handle.net/10023/7025
Magnetic reconnection, a change of magnetic field connectivity, is a fundamental physical process in which magnetic energy is released explosively, and it is responsible for various eruptive phenomena in the universe. However, this process is difficult to observe directly. Here, the magnetic topology associated with a solar reconnection event is studied in three dimensions using the combined perspectives of two spacecraft. The sequence of extreme ultraviolet images clearly shows that two groups of oppositely directed and noncoplanar magnetic loops gradually approach each other, forming a separator or quasiseparator and then reconnecting. The plasma near the reconnection site is subsequently heated from ∼ 1 to ≥ 5MK. Shortly afterwards, warm flare loops (∼3MK) appear underneath the hot plasma. Other observational signatures of reconnection, including plasma inflows and downflows, are unambiguously revealed and quantitatively measured. These observations provide direct evidence of magnetic reconnection in a threedimensional configuration and reveal its origin.
X.C., J.Q.S., M.D.D., Y.G., P.F.C. and C.F. are supported by NSFC through grants 11303016, 11373023, 11203014 and 11025314, and by NKBRSF through grants 2011CB811402 and 2014CB744203. C.E.P. and S.J.E. are supported by the UK STFC. J.Z. is supported by US NSF AGS1249270 and AGS1156120.
Fri, 26 Jun 2015 00:00:00 GMT
http://hdl.handle.net/10023/7025
20150626T00:00:00Z
Sun, J.Q.
Cheng, X.
Ding, M.D.
Guo, Y.
Priest, E.R.
Parnell, C.E.
Edwards, S.J.
Zhang, J.
Chen, P.F.
Fang, C.
Magnetic reconnection, a change of magnetic field connectivity, is a fundamental physical process in which magnetic energy is released explosively, and it is responsible for various eruptive phenomena in the universe. However, this process is difficult to observe directly. Here, the magnetic topology associated with a solar reconnection event is studied in three dimensions using the combined perspectives of two spacecraft. The sequence of extreme ultraviolet images clearly shows that two groups of oppositely directed and noncoplanar magnetic loops gradually approach each other, forming a separator or quasiseparator and then reconnecting. The plasma near the reconnection site is subsequently heated from ∼ 1 to ≥ 5MK. Shortly afterwards, warm flare loops (∼3MK) appear underneath the hot plasma. Other observational signatures of reconnection, including plasma inflows and downflows, are unambiguously revealed and quantitatively measured. These observations provide direct evidence of magnetic reconnection in a threedimensional configuration and reveal its origin.

Ergodicity and spectral cascades in point vortex flows on the sphere
http://hdl.handle.net/10023/7024
We present results for the equilibrium statistics and dynamic evolution of moderately large [n=O(102103)] numbers of interacting point vortices on the sphere under the constraint of zero mean angular momentum. For systems with equal numbers of positive and negative identical circulations, the density of rescaled energies, p(E), converges rapidly with n to a function with a single maximum with maximum entropy. Ensembleaveraged wavenumber spectra of the nonsingular velocity field induced by the vortices exhibit the expected k1 behavior at small scales for all energies. Spectra at the largest scales vary continuously with the inverse temperature of the system. For positive temperatures, spectra peak at finite intermediate wave numbers; for negative temperatures, spectra decrease everywhere. Comparisons of time and ensemble averages, over a large range of energies, strongly support ergodicity in the dynamics even for highly atypical initial vortex configurations. Crucially, rapid relaxation of spectra toward the microcanonical average implies that the direction of any spectral cascade process depends only on the relative difference between the initial spectrum and the ensemble mean spectrum at that energy, not on the energy, or temperature, of the system.
A.C.P. was supported under DOD (MURI) Grant No. N000141110087 ONR. The computations were supported by the CUNY HPCC under NSF Grants No. CNS0855217 and No. CNS0958379.
Mon, 29 Jun 2015 00:00:00 GMT
http://hdl.handle.net/10023/7024
20150629T00:00:00Z
Dritschel, D.G.
Lucia, M.
Poje, A.C.
We present results for the equilibrium statistics and dynamic evolution of moderately large [n=O(102103)] numbers of interacting point vortices on the sphere under the constraint of zero mean angular momentum. For systems with equal numbers of positive and negative identical circulations, the density of rescaled energies, p(E), converges rapidly with n to a function with a single maximum with maximum entropy. Ensembleaveraged wavenumber spectra of the nonsingular velocity field induced by the vortices exhibit the expected k1 behavior at small scales for all energies. Spectra at the largest scales vary continuously with the inverse temperature of the system. For positive temperatures, spectra peak at finite intermediate wave numbers; for negative temperatures, spectra decrease everywhere. Comparisons of time and ensemble averages, over a large range of energies, strongly support ergodicity in the dynamics even for highly atypical initial vortex configurations. Crucially, rapid relaxation of spectra toward the microcanonical average implies that the direction of any spectral cascade process depends only on the relative difference between the initial spectrum and the ensemble mean spectrum at that energy, not on the energy, or temperature, of the system.

Fast approximate radiative transfer method for visualizing the fine structure of prominences in the hydrogen Hα line
http://hdl.handle.net/10023/7020
Aims. We present a novel approximate radiative transfer method developed to visualize 3D wholeprominence models with multiple fine structures using the hydrogen Hα spectral line. Methods. This method employs a fast lineofsight synthesis of the Hα line profiles through the whole 3D prominence volume and realistically reflects the basic properties of the Hα line formation in the cool and lowdensity prominence medium. The method can be applied both to prominences seen above the limb and filaments seen against the disk. Results. We provide recipes for the use of this method for visualizing the prominence or filament models that have multiple fine structures. We also perform tests of the method that demonstrate its accuracy under prominence conditions. Conclusions. We demonstrate that this fast approximate radiative transfer method provides realistic synthetic Hα intensities useful for a reliable visualization of prominences and filaments. Such synthetic highresolution images of modeled prominences/filaments can be used for a direct comparison with highresolution observations.
P.H. acknowledges the support from grant 209/12/0906 of the Grant Agency of the Czech Republic. S.G. acknowledges support from the European Commission via the Marie Curie Actions – IntraEuropean Fellowships Project No. 328138. P.H. and S.G. acknowledge support from project RVO:67985815 of the Astronomical Institute of the Czech Academy of Sciences and from the MPA Garching. U.A. thanks for the support from the Astronomical Institute of the Czech Academy of Sciences.
Wed, 01 Jul 2015 00:00:00 GMT
http://hdl.handle.net/10023/7020
20150701T00:00:00Z
Heinzel, P.
Gunár, S.
Anzer, U.
Aims. We present a novel approximate radiative transfer method developed to visualize 3D wholeprominence models with multiple fine structures using the hydrogen Hα spectral line. Methods. This method employs a fast lineofsight synthesis of the Hα line profiles through the whole 3D prominence volume and realistically reflects the basic properties of the Hα line formation in the cool and lowdensity prominence medium. The method can be applied both to prominences seen above the limb and filaments seen against the disk. Results. We provide recipes for the use of this method for visualizing the prominence or filament models that have multiple fine structures. We also perform tests of the method that demonstrate its accuracy under prominence conditions. Conclusions. We demonstrate that this fast approximate radiative transfer method provides realistic synthetic Hα intensities useful for a reliable visualization of prominences and filaments. Such synthetic highresolution images of modeled prominences/filaments can be used for a direct comparison with highresolution observations.

The use of the Poynting vector in interpreting ULF waves in magnetospheric waveguides
http://hdl.handle.net/10023/6976
We numerically model ultralow frequency (ULF) waves in the magnetosphere assuming an ideal, lowbeta inhomogeneous plasma waveguide. The waveguide is based on the hydromagnetic box model. We develop a novel boundary condition that drives the magnetospheric boundary by pressure perturbations, in order to simulate solar wind dynamic pressure uctuations disturbing the magnetopause. The model is applied to observations from Cluster and THEMIS. Our model is able to reproduce similar wave signatures to those in the data, such as a unidirectional azimuthal Poynting vector, by interpreting the observations in terms of fast waveguide modes. Despite the simplicity of the model, we can shed light on the nature of these modes and the location of the energy source relative to the spacecraft. This is achieved by demonstrating that important information, such as phase shifts between components of the electric and magnetic fields and the balance of radial to azimuthal propagation of energy, may be extracted from a careful analysis of the components of the Poynting vector.
T.E. would like to thank STFC for financial support for a doctoral training grant. Date of Acceptance: 04/12/2014
Thu, 01 Jan 2015 00:00:00 GMT
http://hdl.handle.net/10023/6976
20150101T00:00:00Z
Elsden, Tom
Wright, Andrew Nicholas
We numerically model ultralow frequency (ULF) waves in the magnetosphere assuming an ideal, lowbeta inhomogeneous plasma waveguide. The waveguide is based on the hydromagnetic box model. We develop a novel boundary condition that drives the magnetospheric boundary by pressure perturbations, in order to simulate solar wind dynamic pressure uctuations disturbing the magnetopause. The model is applied to observations from Cluster and THEMIS. Our model is able to reproduce similar wave signatures to those in the data, such as a unidirectional azimuthal Poynting vector, by interpreting the observations in terms of fast waveguide modes. Despite the simplicity of the model, we can shed light on the nature of these modes and the location of the energy source relative to the spacecraft. This is achieved by demonstrating that important information, such as phase shifts between components of the electric and magnetic fields and the balance of radial to azimuthal propagation of energy, may be extracted from a careful analysis of the components of the Poynting vector.

Ellipsoidal vortices in rotating stratified fluids : beyond the quasigeostrophic approximation
http://hdl.handle.net/10023/6889
We examine the basic properties and stability of isolated vortices having uniform potential vorticity (PV) in a nonhydrostatic rotating stratified fluid, under the Boussinesq approximation. For simplicity, we consider a uniform background rotation and a linear basicstate stratification for which both the Coriolis and buoyancy frequencies, f and N, are constant. Moreover, we take ƒ/N≪1, as typically observed in the Earth’s atmosphere and oceans. In the small Rossby number ‘quasigeostrophic’ (QG) limit, when the flow is weak compared to the background rotation, there exist exact solutions for steadily rotating ellipsoidal volumes of uniform PV in an unbounded flow (Zhmur & Shchepetkin, Izv. Akad. Nauk SSSR Atmos. Ocean. Phys., vol. 27, 1991, pp. 492–503; Meacham, Dyn. Atmos. Oceans, vol. 16, 1992, pp. 189–223). Furthermore, a wide range of these solutions are stable as long as the horizontal and vertical aspect ratios λ and μ do not depart greatly from unity (Dritschel et al.,J. Fluid Mech., vol. 536, 2005, pp. 401–421). In the present study, we examine the behaviour of ellipsoidal vortices at Rossby numbers up to near unity in magnitude. We find that there is a monotonic increase in stability as one varies the Rossby number from nearly −1 (anticyclone) to nearly +1 (cyclone). That is, QG vortices are more stable than anticyclones at finite negative Rossby number, and generally less stable than cyclones at finite positive Rossby number. Ageostrophic effects strengthen both the rotation and the stratification within a cyclone, enhancing its stability. The converse is true for an anticyclone. For all Rossby numbers, stability is reinforced by increasing λ towards unity or decreasing μ. An unstable vortex often restabilises by developing a nearcircular crosssection, typically resulting in a roughly ellipsoidal vortex, but occasionally a binary system is formed. Throughout the nonlinear evolution of a vortex, the emission of inertia–gravity waves (IGWs) is negligible across the entire parameter space investigated. Thus, vortices at small to moderate Rossby numbers, and any associated instabilities, are (ageostrophically) balanced. A manifestation of this balance is that, at finite Rossby number, an anticyclone rotates faster than a cyclone.
Support for this research has come from the UK Engineering and Physical Sciences Research Council (grant number EP/H001794/1).
Thu, 01 Jan 2015 00:00:00 GMT
http://hdl.handle.net/10023/6889
20150101T00:00:00Z
Tsang, YueKin
Dritschel, David G.
We examine the basic properties and stability of isolated vortices having uniform potential vorticity (PV) in a nonhydrostatic rotating stratified fluid, under the Boussinesq approximation. For simplicity, we consider a uniform background rotation and a linear basicstate stratification for which both the Coriolis and buoyancy frequencies, f and N, are constant. Moreover, we take ƒ/N≪1, as typically observed in the Earth’s atmosphere and oceans. In the small Rossby number ‘quasigeostrophic’ (QG) limit, when the flow is weak compared to the background rotation, there exist exact solutions for steadily rotating ellipsoidal volumes of uniform PV in an unbounded flow (Zhmur & Shchepetkin, Izv. Akad. Nauk SSSR Atmos. Ocean. Phys., vol. 27, 1991, pp. 492–503; Meacham, Dyn. Atmos. Oceans, vol. 16, 1992, pp. 189–223). Furthermore, a wide range of these solutions are stable as long as the horizontal and vertical aspect ratios λ and μ do not depart greatly from unity (Dritschel et al.,J. Fluid Mech., vol. 536, 2005, pp. 401–421). In the present study, we examine the behaviour of ellipsoidal vortices at Rossby numbers up to near unity in magnitude. We find that there is a monotonic increase in stability as one varies the Rossby number from nearly −1 (anticyclone) to nearly +1 (cyclone). That is, QG vortices are more stable than anticyclones at finite negative Rossby number, and generally less stable than cyclones at finite positive Rossby number. Ageostrophic effects strengthen both the rotation and the stratification within a cyclone, enhancing its stability. The converse is true for an anticyclone. For all Rossby numbers, stability is reinforced by increasing λ towards unity or decreasing μ. An unstable vortex often restabilises by developing a nearcircular crosssection, typically resulting in a roughly ellipsoidal vortex, but occasionally a binary system is formed. Throughout the nonlinear evolution of a vortex, the emission of inertia–gravity waves (IGWs) is negligible across the entire parameter space investigated. Thus, vortices at small to moderate Rossby numbers, and any associated instabilities, are (ageostrophically) balanced. A manifestation of this balance is that, at finite Rossby number, an anticyclone rotates faster than a cyclone.

Excitation and damping of broadband kink waves in the solar corona
http://hdl.handle.net/10023/6839
Context. Observations such as those by the Coronal MultiChannel Polarimeter (CoMP) have revealed that broadband kink oscillations are ubiquitous in the solar corona. Aims. We consider footpointdriven kink waves propagating in a low β coronal plasma with a cylindrical density structure. We investigate the excitation and damping of propagating kink waves by a broadband driver, including the effects of different spatial profiles for the driver. Methods. We employ a general spatial damping profile in which the initial stage of the damping envelope is approximated by a Gaussian profile and the asymptotic state by an exponential one. We develop a method of accounting for the presence of these different damping regimes and test it using data from numerical simulations. Results. Strongly damped oscillations in low density coronal loops are more accurately described by a Gaussian spatial damping profile than an exponential profile. The consequences for coronal seismology are investigated and applied to observational data for the ubiquitous broadband waves observed by CoMP. Current data cannot distinguish between the exponential and Gaussian profiles because of the levels of noise. We demonstrate the importance of the spatial profile of the driver on the resulting damping profile. Furthermore, we show that a smallscale turbulent driver is inefficient at exciting propagating kink waves
D.J.P. acknowledges financial support from STFC. I.D.M. acknowledges support of a Royal Society University Research Fellowship. The research leading to these results has also received funding from the European Commission Seventh Framework Programme (FP7/ 2007−2013) under the grant agreement SOLSPANET (project No. 269299, www.solspanet.eu/solspanet).
Mon, 01 Jun 2015 00:00:00 GMT
http://hdl.handle.net/10023/6839
20150601T00:00:00Z
Pascoe, David James
Wright, Andrew Nicholas
De Moortel, Ineke
Hood, Alan William
Context. Observations such as those by the Coronal MultiChannel Polarimeter (CoMP) have revealed that broadband kink oscillations are ubiquitous in the solar corona. Aims. We consider footpointdriven kink waves propagating in a low β coronal plasma with a cylindrical density structure. We investigate the excitation and damping of propagating kink waves by a broadband driver, including the effects of different spatial profiles for the driver. Methods. We employ a general spatial damping profile in which the initial stage of the damping envelope is approximated by a Gaussian profile and the asymptotic state by an exponential one. We develop a method of accounting for the presence of these different damping regimes and test it using data from numerical simulations. Results. Strongly damped oscillations in low density coronal loops are more accurately described by a Gaussian spatial damping profile than an exponential profile. The consequences for coronal seismology are investigated and applied to observational data for the ubiquitous broadband waves observed by CoMP. Current data cannot distinguish between the exponential and Gaussian profiles because of the levels of noise. We demonstrate the importance of the spatial profile of the driver on the resulting damping profile. Furthermore, we show that a smallscale turbulent driver is inefficient at exciting propagating kink waves

On the properties of singleseparator MHS equilibria and the nature of separator reconnection
http://hdl.handle.net/10023/6678
This thesis considers the properties of MHS equilibria formed through nonresistive MHD relaxation of analytical nonpotential magnetic field models, which contain two null points connected by a generic separator. Four types of analytical magnetic fields are formulated, with different forms of current. The magnetic field model which has a uniform current directed along the separator, is used through the rest of this thesis to form MHS equilibria and to study reconnection.
This magnetic field, which is not forcefree, embedded in a highbeta plasma, relaxes nonresistively using a 3D MHD code. The relaxation causes the field about the separator to collapse leading to a twisted current layer forming along the separator. The MHS equilibrium current layer slowly becomes stronger, longer, wider and thinner with time. Its properties, and the properties of the plasma, are found to depend on the initial parameters of the magnetic field, which control the geometry of the magnetic configuration.
Such a MHS equilibria is used in a high plasmabeta reconnection experiment. An anomalous resistivity ensures that only the central strong current in the separator current layer is dissipated. The reconnection occurs in two phases characterised by fast and slow reconnection, respectively. Waves, launched from the diffusion site, communicate the loss of force balance at the current layer and set up flows in the system. The energy transport in this system is dominated by Ohmic dissipation.
Several methods are presented which allow a low plasmabeta value to be approached in the singleseparator model. One method is chosen and this model is relaxed nonresistively to form a MHS equilibrium. A twisted current layer grows along the separator, containing stronger current than in the high plasmabeta experiments, and has a local enhancement in pressure inside it. The growth rate of this current layer is similar to that found in the high plasmabeta experiments, however, the current layer becomes thinner and narrower over time.
Fri, 26 Jun 2015 00:00:00 GMT
http://hdl.handle.net/10023/6678
20150626T00:00:00Z
Stevenson, Julie E. H.
This thesis considers the properties of MHS equilibria formed through nonresistive MHD relaxation of analytical nonpotential magnetic field models, which contain two null points connected by a generic separator. Four types of analytical magnetic fields are formulated, with different forms of current. The magnetic field model which has a uniform current directed along the separator, is used through the rest of this thesis to form MHS equilibria and to study reconnection.
This magnetic field, which is not forcefree, embedded in a highbeta plasma, relaxes nonresistively using a 3D MHD code. The relaxation causes the field about the separator to collapse leading to a twisted current layer forming along the separator. The MHS equilibrium current layer slowly becomes stronger, longer, wider and thinner with time. Its properties, and the properties of the plasma, are found to depend on the initial parameters of the magnetic field, which control the geometry of the magnetic configuration.
Such a MHS equilibria is used in a high plasmabeta reconnection experiment. An anomalous resistivity ensures that only the central strong current in the separator current layer is dissipated. The reconnection occurs in two phases characterised by fast and slow reconnection, respectively. Waves, launched from the diffusion site, communicate the loss of force balance at the current layer and set up flows in the system. The energy transport in this system is dominated by Ohmic dissipation.
Several methods are presented which allow a low plasmabeta value to be approached in the singleseparator model. One method is chosen and this model is relaxed nonresistively to form a MHS equilibrium. A twisted current layer grows along the separator, containing stronger current than in the high plasmabeta experiments, and has a local enhancement in pressure inside it. The growth rate of this current layer is similar to that found in the high plasmabeta experiments, however, the current layer becomes thinner and narrower over time.

CALIFA, the Calar Alto Legacy Integral Field Area survey : III. Second public data release
http://hdl.handle.net/10023/6664
This paper describes the Second Public Data Release (DR2) of the Calar Alto Legacy Integral Field Area (CALIFA) survey. The data for 200 objects are made public, including the 100 galaxies of the First Public Data Release (DR1). Data were obtained with the integralfield spectrograph PMAS/PPak mounted on the 3.5 m telescope at the Calar Alto observatory. Two different spectral setups are available for each galaxy, (i) a lowresolution V500 setup covering the wavelength range 37457500 Å with a spectral resolution of 6.0 Å (FWHM); and (ii) a mediumresolution V1200 setup covering the wavelength range 36504840 Å with a spectral resolution of 2.3 Å (FWHM). The sample covers a redshift range between 0.005 and 0.03, with a wide range of properties in the colormagnitude diagram, stellar mass, ionization conditions, and morphological types. All the cubes in the data release were reduced with the latest pipeline, which includes improvedspectrophotometric calibration, spatial registration, and spatial resolution. The spectrophotometric calibration is better than 6% and the median spatial resolution is 2.4. In total, the second data release contains over 1.5 million spectra.
J.M.A. acknowledges support from the European Research Council Starting Grant (SEDmorph; P.I. V. Wild). V.W. acknowledges support from the European Research Council Starting Grant (SEDMorph P.I. V. Wild) and European Career Reintegration Grant (PhizEv P.I. V. Wild).
Wed, 01 Apr 2015 00:00:00 GMT
http://hdl.handle.net/10023/6664
20150401T00:00:00Z
GarcíaBenito, R.
Zibetti, S.
Sánchez, S. F.
Husemann, B.
de Amorim, A. L.
CastilloMorales, A.
Cid Fernandes, R.
Ellis, S. C.
FalcónBarroso, J.
Galbany, L.
Gil de Paz, A.
González Delgado, R. M.
Lacerda, E. A. D.
LópezFernandez, R.
de LorenzoCáceres, A.
Lyubenova, M.
Marino, R. A.
Mast, D.
Mendoza, M. A.
Pérez, E.
Vale Asari, N.
Aguerri, J. A. L.
Ascasibar, Y.
Bekerait*error*ė, S.
BlandHawthorn, J.
BarreraBallesteros, J. K.
Bomans, D. J.
CanoDíaz, M.
CatalánTorrecilla, C.
Cortijo, C.
DelgadoInglada, G.
Demleitner, M.
Dettmar, R.J.
Díaz, A. I.
Florido, E.
Gallazzi, A.
GarcíaLorenzo, B.
Gomes, J. M.
Holmes, L.
IglesiasPáramo, J.
Jahnke, K.
Kalinova, V.
Kehrig, C.
Kennicutt, R. C.
LópezSánchez, Á. R.
Márquez, I.
Masegosa, J.
Meidt, S. E.
MendezAbreu, J.
Mollá, M.
MonrealIbero, A.
Morisset, C.
del Olmo, A.
Papaderos, P.
Pérez, I.
Quirrenbach, A.
RosalesOrtega, F. F.
Roth, M. M.
RuizLara, T.
SánchezBlázquez, P.
SánchezMenguiano, L.
Singh, R.
Spekkens, K.
Stanishev, V.
TorresPapaqui, J. P.
van de Ven, G.
Vilchez, J. M.
Walcher, C. J.
Wild, V.
Wisotzki, L.
Ziegler, B.
Alves, J.
Barrado, D.
Quintana, J. M.
Aceituno, J.
This paper describes the Second Public Data Release (DR2) of the Calar Alto Legacy Integral Field Area (CALIFA) survey. The data for 200 objects are made public, including the 100 galaxies of the First Public Data Release (DR1). Data were obtained with the integralfield spectrograph PMAS/PPak mounted on the 3.5 m telescope at the Calar Alto observatory. Two different spectral setups are available for each galaxy, (i) a lowresolution V500 setup covering the wavelength range 37457500 Å with a spectral resolution of 6.0 Å (FWHM); and (ii) a mediumresolution V1200 setup covering the wavelength range 36504840 Å with a spectral resolution of 2.3 Å (FWHM). The sample covers a redshift range between 0.005 and 0.03, with a wide range of properties in the colormagnitude diagram, stellar mass, ionization conditions, and morphological types. All the cubes in the data release were reduced with the latest pipeline, which includes improvedspectrophotometric calibration, spatial registration, and spatial resolution. The spectrophotometric calibration is better than 6% and the median spatial resolution is 2.4. In total, the second data release contains over 1.5 million spectra.

Numerical simulations of a flux rope ejection
http://hdl.handle.net/10023/6650
Coronal mass ejections (CMEs) are the most violent phenomena observed on the Sun. One of the most successful models to explain CMEs is the flux rope ejection model, where a magnetic flux rope is expelled from the solar corona after a long phase along which the flux rope stays in equilibrium while magnetic energy is being accumulated. However, still many questions are outstanding on the detailed mechanism of the ejection and observations continuously provide new data to interpret and put in the context. Currently, extreme ultraviolet (EUV) images from the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamic Observatory (SDO) are providing new insights into the early phase of CME evolution. In particular, observations show the ejection of magnetic flux ropes from the solar corona and how they evolve into CMEs. However, these observations are difficult to interpret in terms of basic physical mechanisms and quantities, thus, we need to compare equivalent quantities to test and improve our models. In our work, we intend to bridge the gap between models and observations with our model of flux rope ejection where we consistently describe the full life span of a flux rope from its formation to ejection. This is done by coupling the global nonlinear forcefree model (GNLFFF) built to describe the slow low β formation phase, with a full MHD simulation run with the software MPIAMRVAC, suitable to describe the fast MHD evolution of the flux rope ejection that happens in a heterogeneous β regime. We also explore the parameter space to identify the conditions upon which the ejection is favoured (gravity stratification and magnetic field intensity) and we produce synthesised AIA observations (171 Å and 211 Å). To carry this out, we run 3D MHD simulation in spherical coordinates where we include the role of thermal conduction and radiative losses, both of which are important for determining the temperature distribution of the solar corona during a CME. Our model of flux rope ejection is successful in realistically describing the entire life span of a flux rope and we also set some conditions for the backgroud solar corona to favour the escape of the flux rope, so that it turns into a CME. Furthermore, our MHD simulation reproduces many of the features found in the AIA observations.
Sun, 01 Mar 2015 00:00:00 GMT
http://hdl.handle.net/10023/6650
20150301T00:00:00Z
Pagano, P.
Mackay, D.H.
Poedts, S.
Coronal mass ejections (CMEs) are the most violent phenomena observed on the Sun. One of the most successful models to explain CMEs is the flux rope ejection model, where a magnetic flux rope is expelled from the solar corona after a long phase along which the flux rope stays in equilibrium while magnetic energy is being accumulated. However, still many questions are outstanding on the detailed mechanism of the ejection and observations continuously provide new data to interpret and put in the context. Currently, extreme ultraviolet (EUV) images from the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamic Observatory (SDO) are providing new insights into the early phase of CME evolution. In particular, observations show the ejection of magnetic flux ropes from the solar corona and how they evolve into CMEs. However, these observations are difficult to interpret in terms of basic physical mechanisms and quantities, thus, we need to compare equivalent quantities to test and improve our models. In our work, we intend to bridge the gap between models and observations with our model of flux rope ejection where we consistently describe the full life span of a flux rope from its formation to ejection. This is done by coupling the global nonlinear forcefree model (GNLFFF) built to describe the slow low β formation phase, with a full MHD simulation run with the software MPIAMRVAC, suitable to describe the fast MHD evolution of the flux rope ejection that happens in a heterogeneous β regime. We also explore the parameter space to identify the conditions upon which the ejection is favoured (gravity stratification and magnetic field intensity) and we produce synthesised AIA observations (171 Å and 211 Å). To carry this out, we run 3D MHD simulation in spherical coordinates where we include the role of thermal conduction and radiative losses, both of which are important for determining the temperature distribution of the solar corona during a CME. Our model of flux rope ejection is successful in realistically describing the entire life span of a flux rope and we also set some conditions for the backgroud solar corona to favour the escape of the flux rope, so that it turns into a CME. Furthermore, our MHD simulation reproduces many of the features found in the AIA observations.

3D wholeprominence fine structure modeling
http://hdl.handle.net/10023/6541
We present the first 3D wholeprominence fine structure model. The model combines a 3D magnetic field configuration of an entire prominence obtained from nonlinear forcefree field simulations, with a detailed description of the prominence plasma. The plasma is located in magnetic dips in hydrostatic equilibrium and is distributed along multiple fine structures within the 3D magnetic model. Through the use of a novel radiative transfer visualization technique for the Halpha line such plasmaloaded magnetic field model produces synthetic images of the modeled prominence comparable with highresolution observations. This allows us for the first time to use a single technique to consistently study, in both emission on the limb and absorption against the solar disk, the fine structures of prominences/filaments produced by a magnetic field model.
Mon, 20 Apr 2015 00:00:00 GMT
http://hdl.handle.net/10023/6541
20150420T00:00:00Z
Gunar, Stanislav
Mackay, Duncan Hendry
We present the first 3D wholeprominence fine structure model. The model combines a 3D magnetic field configuration of an entire prominence obtained from nonlinear forcefree field simulations, with a detailed description of the prominence plasma. The plasma is located in magnetic dips in hydrostatic equilibrium and is distributed along multiple fine structures within the 3D magnetic model. Through the use of a novel radiative transfer visualization technique for the Halpha line such plasmaloaded magnetic field model produces synthetic images of the modeled prominence comparable with highresolution observations. This allows us for the first time to use a single technique to consistently study, in both emission on the limb and absorption against the solar disk, the fine structures of prominences/filaments produced by a magnetic field model.

Experiments on the structure and stability of mode2 internal solitarylike waves propagating on an offset pycnocline
http://hdl.handle.net/10023/6519
The structure and stability of mode2 internal solitarylike waves is investigated experimentally. A rankordered train of mode2 internal solitary waves is generated using a lock release configuration. The pycnocline is centred either on the middepth of the water column (the 0% offset case) or it is offset in the positive vertical direction by a fraction of 5%, 10% or 20% of the total fluid depth. It is found that offsetting the pycnocline has little effect on the basic wave properties (e.g wave speed, wave amplitude and wave length) but it does significantly affect wave stability. Instability takes the form of small KHlike billows in the rear of the wave and small scale overturning in the core of the wave. In the 0% offset case, instability occurs on both the upper and lower interfaces of the pycnocline and is similar in extent and vigour over the two interfaces. As the offset percentage is increased, however, instability is more pronounced on the lower interface with little or no evidence of instability being observed on the upper interface. In the 20% offset case a mode1 tail is associated with the wave and the wave characteristics resemble qualitatively the recent field observations of Shroyer et al [E. L. Shroyer, J. N. Moum and J. D. Nash, J. Geophys. Res. 115, C07001 (2010)].
Thu, 01 Jan 2015 00:00:00 GMT
http://hdl.handle.net/10023/6519
20150101T00:00:00Z
Carr, Magda
Davies, Peter
Hoebers, Ruud
The structure and stability of mode2 internal solitarylike waves is investigated experimentally. A rankordered train of mode2 internal solitary waves is generated using a lock release configuration. The pycnocline is centred either on the middepth of the water column (the 0% offset case) or it is offset in the positive vertical direction by a fraction of 5%, 10% or 20% of the total fluid depth. It is found that offsetting the pycnocline has little effect on the basic wave properties (e.g wave speed, wave amplitude and wave length) but it does significantly affect wave stability. Instability takes the form of small KHlike billows in the rear of the wave and small scale overturning in the core of the wave. In the 0% offset case, instability occurs on both the upper and lower interfaces of the pycnocline and is similar in extent and vigour over the two interfaces. As the offset percentage is increased, however, instability is more pronounced on the lower interface with little or no evidence of instability being observed on the upper interface. In the 20% offset case a mode1 tail is associated with the wave and the wave characteristics resemble qualitatively the recent field observations of Shroyer et al [E. L. Shroyer, J. N. Moum and J. D. Nash, J. Geophys. Res. 115, C07001 (2010)].

MHD simulations of coronal heating
http://hdl.handle.net/10023/6373
The problem of heating the solar corona requires the conversion of magnetic energy into thermal energy. Presently, there are two promising mechanisms for heating the solar corona: wave heating and nanoflare heating. In this thesis, we consider nanoflare heating only. Previous modelling has shown that the kink instability can trigger energy release and heating in large scale loops, as the field rapidly relaxes to a lower energy state under the Taylor relaxation theory. Two distinct experiments were developed to understand the coronal heating problem: the avalanche effect within a multiple loop system, and the importance of thermal conduction and optically thin radiation during the evolution of the kinkedunstable coronal magnetic field.
The first experiment showed that a kinkunstable thread can also destabilise nearby threads under some conditions. The second experiment showed that the inclusion of thermal conduction and optically thin radiation causes significant change to the internal energy of the coronal loop. After the initial instability occurs, there is continual heating throughout the relaxation process. Our simulation results show that the data is consistent with observation values, and the relaxation process can take over 200 seconds to reach the final relaxed state. The inclusion of both effects perhaps provides a more realistic and rapid heating experiment compared to previous investigations.
Mon, 01 Dec 2014 00:00:00 GMT
http://hdl.handle.net/10023/6373
20141201T00:00:00Z
Tam, Kuan V.
The problem of heating the solar corona requires the conversion of magnetic energy into thermal energy. Presently, there are two promising mechanisms for heating the solar corona: wave heating and nanoflare heating. In this thesis, we consider nanoflare heating only. Previous modelling has shown that the kink instability can trigger energy release and heating in large scale loops, as the field rapidly relaxes to a lower energy state under the Taylor relaxation theory. Two distinct experiments were developed to understand the coronal heating problem: the avalanche effect within a multiple loop system, and the importance of thermal conduction and optically thin radiation during the evolution of the kinkedunstable coronal magnetic field.
The first experiment showed that a kinkunstable thread can also destabilise nearby threads under some conditions. The second experiment showed that the inclusion of thermal conduction and optically thin radiation causes significant change to the internal energy of the coronal loop. After the initial instability occurs, there is continual heating throughout the relaxation process. Our simulation results show that the data is consistent with observation values, and the relaxation process can take over 200 seconds to reach the final relaxed state. The inclusion of both effects perhaps provides a more realistic and rapid heating experiment compared to previous investigations.

The motion of point vortices on closed surfaces
http://hdl.handle.net/10023/6297
We develop a mathematical framework for the dynamics of a set of point vortices on a class of differentiable surfaces conformal to the unit sphere. When the sum of the vortex circulations is nonzero, a compensating uniform vorticity field is required to satisfy the Gauss condition (that the integral of the LaplaceBeltrami operator must vanish). On variable Gaussian curvature surfaces, this results in selfinduced vortex motion, a feature entirely absent on the plane, the sphere or the hyperboloid.We derive explicit equations of motion for vortices on surfaces of revolution and compute their solutions for a variety of surfaces. We also apply these equations to study the linear stability of a ring of vortices on any surface of revolution. On an ellipsoid of revolution, as few as 2 vortices can be unstable on oblate surfaces or sufficiently prolate ones. This extends known results for the plane, where 7 vortices are marginally unstable [1,2], and the sphere, where 4 vortices may be unstable if sufficiently close to the equator [3].
Date of Acceptance: 29/01/2015
Wed, 25 Feb 2015 00:00:00 GMT
http://hdl.handle.net/10023/6297
20150225T00:00:00Z
Dritschel, David Gerard
Boatto, S
We develop a mathematical framework for the dynamics of a set of point vortices on a class of differentiable surfaces conformal to the unit sphere. When the sum of the vortex circulations is nonzero, a compensating uniform vorticity field is required to satisfy the Gauss condition (that the integral of the LaplaceBeltrami operator must vanish). On variable Gaussian curvature surfaces, this results in selfinduced vortex motion, a feature entirely absent on the plane, the sphere or the hyperboloid.We derive explicit equations of motion for vortices on surfaces of revolution and compute their solutions for a variety of surfaces. We also apply these equations to study the linear stability of a ring of vortices on any surface of revolution. On an ellipsoid of revolution, as few as 2 vortices can be unstable on oblate surfaces or sufficiently prolate ones. This extends known results for the plane, where 7 vortices are marginally unstable [1,2], and the sphere, where 4 vortices may be unstable if sufficiently close to the equator [3].

Understanding the Mg II and Hα spectra in a highly dynamical solar prominence
http://hdl.handle.net/10023/6190
Mg ii h and k and Hα spectra in a dynamical prominence have been obtained along the slit of the Interface Region Imaging Spectrograph (IRIS) and with the Meudon Multichannel Subtractive Double Pass spectrograph on 2013 September 24, respectively. Single Mg ii line profiles are not much reversed, while at some positions along the IRIS slit the profiles show several discrete peaks that are Dopplershifted. The intensity of these peaks is generally decreasing with their increasing Doppler shift. We interpret this unusual behavior as being due to the Doppler dimming effect. We discuss the possibility to interpret the unreversed single profiles by using a twodimensional (2D) model of the entire prominence body with specific radiative boundary conditions. We have performed new 2D isothermal–isobaric modeling of both Hα and Mg ii lines and show the ability of such models to account for the line profile variations as observed. However, the Mg ii linecenter intensities require the model with a temperature increase toward the prominence boundary. We show that even simple onedimensional (1D) models with a prominencetocorona transition region (PCTR) fit the observed Mg ii and Hα lines quite well, while the isothermal–isobaric models (1D or 2D) are inconsistent with simultaneous observations in the Mg ii h and k and Hα lines, meaning that the Hα line provides a strong additional constraint on the modeling. IRIS farUV detection of the C ii lines in this prominence seems to provide a direct constraint on the PCTR part of the model.
Date of Acceptance: 08/01/2015
Tue, 10 Feb 2015 00:00:00 GMT
http://hdl.handle.net/10023/6190
20150210T00:00:00Z
Heinzel, P.
Schmieder, B.
Mein, N.
Gunar, S.
Mg ii h and k and Hα spectra in a dynamical prominence have been obtained along the slit of the Interface Region Imaging Spectrograph (IRIS) and with the Meudon Multichannel Subtractive Double Pass spectrograph on 2013 September 24, respectively. Single Mg ii line profiles are not much reversed, while at some positions along the IRIS slit the profiles show several discrete peaks that are Dopplershifted. The intensity of these peaks is generally decreasing with their increasing Doppler shift. We interpret this unusual behavior as being due to the Doppler dimming effect. We discuss the possibility to interpret the unreversed single profiles by using a twodimensional (2D) model of the entire prominence body with specific radiative boundary conditions. We have performed new 2D isothermal–isobaric modeling of both Hα and Mg ii lines and show the ability of such models to account for the line profile variations as observed. However, the Mg ii linecenter intensities require the model with a temperature increase toward the prominence boundary. We show that even simple onedimensional (1D) models with a prominencetocorona transition region (PCTR) fit the observed Mg ii and Hα lines quite well, while the isothermal–isobaric models (1D or 2D) are inconsistent with simultaneous observations in the Mg ii h and k and Hα lines, meaning that the Hα line provides a strong additional constraint on the modeling. IRIS farUV detection of the C ii lines in this prominence seems to provide a direct constraint on the PCTR part of the model.

Simplyconnected vortexpatch shallowwater quasiequilibria
http://hdl.handle.net/10023/6179
We examine the form, properties, stability and evolution of simplyconnected vortexpatch relative quasiequilibria in the singlelayer ƒplane shallowwater model of geophysical fluid dynamics. We examine the effects of the size, shape and strength of vortices in this system, represented by three distinct parameters completely describing the families of the quasiequilibria. Namely, these are the ratio γ=L/LD between the horizontal size of the vortices and the Rossby deformation length; the aspect ratio λ between the minor to major axes of the vortex; and a potential vorticity (PV)based Rossby number Ro=q′/ƒ, the ratio of the PV anomaly q′ within the vortex to the Coriolis frequency ƒ. By defining an appropriate steadiness parameter, we find that the quasiequilibria remain steady for long times, enabling us to determine the boundary of stability λc=λc(γ, Ro), for 0.25≤γ≤6 and Ro≤1. By calling two states which share γ,Ro and λ ‘equivalent’, we find a clear asymmetry in the stability of cyclonic (Ro>0) and anticyclonic (Ro<0) equilibria, with cyclones being able to sustain greater deformations than anticyclones before experiencing an instability. We find that ageostrophic motions stabilise cyclones and destabilise anticyclones. Both types of vortices undergo the same main types of unstable evolution, albeit in different ranges of the parameter space, (a) vacillations for largeγ, largeRo states, (b) filamentation for smallγ states and (c) vortex splitting, asymmetric for intermediateγ and symmetric for largeγ states.
This work is supported by a UK Natural Environment Research Council studentship
Wed, 05 Mar 2014 00:00:00 GMT
http://hdl.handle.net/10023/6179
20140305T00:00:00Z
Plotka, Hanna
Dritschel, David Gerard
We examine the form, properties, stability and evolution of simplyconnected vortexpatch relative quasiequilibria in the singlelayer ƒplane shallowwater model of geophysical fluid dynamics. We examine the effects of the size, shape and strength of vortices in this system, represented by three distinct parameters completely describing the families of the quasiequilibria. Namely, these are the ratio γ=L/LD between the horizontal size of the vortices and the Rossby deformation length; the aspect ratio λ between the minor to major axes of the vortex; and a potential vorticity (PV)based Rossby number Ro=q′/ƒ, the ratio of the PV anomaly q′ within the vortex to the Coriolis frequency ƒ. By defining an appropriate steadiness parameter, we find that the quasiequilibria remain steady for long times, enabling us to determine the boundary of stability λc=λc(γ, Ro), for 0.25≤γ≤6 and Ro≤1. By calling two states which share γ,Ro and λ ‘equivalent’, we find a clear asymmetry in the stability of cyclonic (Ro>0) and anticyclonic (Ro<0) equilibria, with cyclones being able to sustain greater deformations than anticyclones before experiencing an instability. We find that ageostrophic motions stabilise cyclones and destabilise anticyclones. Both types of vortices undergo the same main types of unstable evolution, albeit in different ranges of the parameter space, (a) vacillations for largeγ, largeRo states, (b) filamentation for smallγ states and (c) vortex splitting, asymmetric for intermediateγ and symmetric for largeγ states.

The formation and stability of Petschek reconnection
http://hdl.handle.net/10023/6100
A combined analytical and numerical study of magnetic reconnection in twodimensional resistive magnetohydrodynamics is carried out by using different explicit spatial variations of the resistivity. A special emphasis on the existence of stable/unstable Petschek's solutions is taken, comparing with the recent analytical model given by Forbes et al. [Phys. Plasmas 20, 052902 (2013)]. Our results show good quantitative agreement between the analytical theory and the numerical solutions for a Petschektype solution to within an accuracy of about 10% or better. Our simulations also show that if the resistivity profile is relatively flat near the Xpoint, one of two possible asymmetric solutions will occur. Which solution occurs depends on small random perturbations of the initial conditions. The existence of two possible asymmetric solutions, in a system which is otherwise symmetric, constitutes an example of spontaneous symmetry breaking.
E. R. Priest is grateful to the Leverhulme Trust. T. G. Forbes received support from NASA grant NNX10AC04G to the University of New Hampshire. H. Baty acknowledges support by French National Research Agency (ANR) through Grant ANR13JS05000301 (Project EMPERE).
Sat, 01 Nov 2014 00:00:00 GMT
http://hdl.handle.net/10023/6100
20141101T00:00:00Z
Baty, H.
Forbes, T.G.
Priest, E.R.
A combined analytical and numerical study of magnetic reconnection in twodimensional resistive magnetohydrodynamics is carried out by using different explicit spatial variations of the resistivity. A special emphasis on the existence of stable/unstable Petschek's solutions is taken, comparing with the recent analytical model given by Forbes et al. [Phys. Plasmas 20, 052902 (2013)]. Our results show good quantitative agreement between the analytical theory and the numerical solutions for a Petschektype solution to within an accuracy of about 10% or better. Our simulations also show that if the resistivity profile is relatively flat near the Xpoint, one of two possible asymmetric solutions will occur. Which solution occurs depends on small random perturbations of the initial conditions. The existence of two possible asymmetric solutions, in a system which is otherwise symmetric, constitutes an example of spontaneous symmetry breaking.

Helical blowout jets in the sun : untwisting and propagation of waves
http://hdl.handle.net/10023/6097
We report on a numerical experiment of the recurrent onset of helical "blowout" jets in an emerging flux region. We find that these jets are running with velocities of ∼100250 km s1 and they transfer a vast amount of heavy plasma into the outer solar atmosphere. During their emission, they undergo an untwisting motion as a result of reconnection between the twisted emerging and the nontwisted preexisting magnetic field in the solar atmosphere. For the first time in the context of blowout jets, we provide direct evidence that their untwisting motion is associated with the propagation of torsional Alfvén waves in the corona.
Thu, 01 Jan 2015 00:00:00 GMT
http://hdl.handle.net/10023/6097
20150101T00:00:00Z
Lee, E.J.
Archontis, V.
Hood, A.W.
We report on a numerical experiment of the recurrent onset of helical "blowout" jets in an emerging flux region. We find that these jets are running with velocities of ∼100250 km s1 and they transfer a vast amount of heavy plasma into the outer solar atmosphere. During their emission, they undergo an untwisting motion as a result of reconnection between the twisted emerging and the nontwisted preexisting magnetic field in the solar atmosphere. For the first time in the context of blowout jets, we provide direct evidence that their untwisting motion is associated with the propagation of torsional Alfvén waves in the corona.

Statistical evidence for the existence of Alfvénic turbulence in solar coronal loops
http://hdl.handle.net/10023/5987
Recent observations have demonstrated that waves capable of carrying large amounts of energy are ubiquitous throughout the solar corona. However, the question of how this wave energy is dissipated (on which timescales and length scales) and released into the plasma remains largely unanswered. Both analytic and numerical models have previously shown that Alfvénic turbulence may play a key role not only in the generation of the fast solar wind, but in the heating of coronal loops. In an effort to bridge the gap between theory and observations, we expand on a recent study by analyzing 37 clearly isolated coronal loops using data from the Coronal Multichannel Polarimeter instrument.We observe Alfvénic perturbations with phase speeds which range from 250 to 750 km s1 and periods from 140 to 270 s for the chosen loops. While excesses of highfrequency wave power are observed near the apex of some loops (tentatively supporting the onset of Alfvénic turbulence), we show that this excess depends on loop length and the wavelength of the observed oscillations. In deriving a proportional relationship between the loop length/wavelength ratio and the enhanced wave power at the loop apex, and from the analysis of the line widths associated with these loops, our findings are supportive of the existence of Alfvénic turbulence in coronal loops.
The authors acknowledge support from NASA contracts NNX08BA99G, NNX11AN98G, NNM12AB40P, NNG09FA40C (IRIS), and NNM07AA01C (Hinode). The research leading to these results has also received funding from the European Commission Seventh Framework Programme (FP7/ 20072013) under the grant agreement SOLSPANET (project No. 269299, www.solspanet.eu/solspanet).
Wed, 10 Dec 2014 00:00:00 GMT
http://hdl.handle.net/10023/5987
20141210T00:00:00Z
Liu, J.
Mcintosh, S.W.
De Moortel, I.
Threlfall, J.
Bethge, C.
Recent observations have demonstrated that waves capable of carrying large amounts of energy are ubiquitous throughout the solar corona. However, the question of how this wave energy is dissipated (on which timescales and length scales) and released into the plasma remains largely unanswered. Both analytic and numerical models have previously shown that Alfvénic turbulence may play a key role not only in the generation of the fast solar wind, but in the heating of coronal loops. In an effort to bridge the gap between theory and observations, we expand on a recent study by analyzing 37 clearly isolated coronal loops using data from the Coronal Multichannel Polarimeter instrument.We observe Alfvénic perturbations with phase speeds which range from 250 to 750 km s1 and periods from 140 to 270 s for the chosen loops. While excesses of highfrequency wave power are observed near the apex of some loops (tentatively supporting the onset of Alfvénic turbulence), we show that this excess depends on loop length and the wavelength of the observed oscillations. In deriving a proportional relationship between the loop length/wavelength ratio and the enhanced wave power at the loop apex, and from the analysis of the line widths associated with these loops, our findings are supportive of the existence of Alfvénic turbulence in coronal loops.

On the topology of global coronal magnetic fields
http://hdl.handle.net/10023/5896
This thesis considers the magnetic topology of the global solar corona. To understand the magnetic topology we use the magnetic skeleton which provides us with a robust description of the magnetic field. To do this we use a Potential Field model extrapolated from observations of the photospheric magnetic field. Various measurements of the photospheric magnetic field are used from both groundbased observatories (KittPeak and SOLIS) and spacebased observatories (MDI and HMI).
Using the magnetic skeleton we characterise particular topological structures and discuss their variations throughout the solar cycle. We find that, from the topology, there are two types of solar minimum magnetic field and one type of solar maximum. The global structure of the coronal magnetic field depends on the relative strengths of the polar fields and the lowlatitude fields. During a strong solar dipole minimum the heliospheric current sheet sits near the equator and the heliospheric current sheet curtains enclose a large amount of mixed polarity field which is associated with many lowaltitude null points. In a weak solar dipole minimum the heliospheric current sheet becomes warped and large scale topological features can form that are associated with weak magnetic field regions. At solar maximum the heliospheric current sheet is highly warped and there are more null points at high altitudes than at solar minimum.
The number of null points in a magnetic field can be seen as a measure of the complexity of the field so this is investigated. We find that the number of nulls above 10Mm falls off with height as a power law whose slope depends on the phase of the solar cycle.
We compare the magnetic topology we found at particular times with observations of the Doppler velocity and intensity around particular active regions to see if it is possible to determine whether plasma upflows at the edge of active regions are linked to open field regions.
Mon, 01 Dec 2014 00:00:00 GMT
http://hdl.handle.net/10023/5896
20141201T00:00:00Z
Edwards, Sarah J.
This thesis considers the magnetic topology of the global solar corona. To understand the magnetic topology we use the magnetic skeleton which provides us with a robust description of the magnetic field. To do this we use a Potential Field model extrapolated from observations of the photospheric magnetic field. Various measurements of the photospheric magnetic field are used from both groundbased observatories (KittPeak and SOLIS) and spacebased observatories (MDI and HMI).
Using the magnetic skeleton we characterise particular topological structures and discuss their variations throughout the solar cycle. We find that, from the topology, there are two types of solar minimum magnetic field and one type of solar maximum. The global structure of the coronal magnetic field depends on the relative strengths of the polar fields and the lowlatitude fields. During a strong solar dipole minimum the heliospheric current sheet sits near the equator and the heliospheric current sheet curtains enclose a large amount of mixed polarity field which is associated with many lowaltitude null points. In a weak solar dipole minimum the heliospheric current sheet becomes warped and large scale topological features can form that are associated with weak magnetic field regions. At solar maximum the heliospheric current sheet is highly warped and there are more null points at high altitudes than at solar minimum.
The number of null points in a magnetic field can be seen as a measure of the complexity of the field so this is investigated. We find that the number of nulls above 10Mm falls off with height as a power law whose slope depends on the phase of the solar cycle.
We compare the magnetic topology we found at particular times with observations of the Doppler velocity and intensity around particular active regions to see if it is possible to determine whether plasma upflows at the edge of active regions are linked to open field regions.

Validation of the magnetic energy vs. helicity scaling in solar magnetic structures
http://hdl.handle.net/10023/5872
Aims. We assess the validity of the free magnetic energy  relative magnetic helicity diagram for solar magnetic structures. Methods. We used two different methods of calculating the free magnetic energy and the relative magnetic helicity budgets: a classical, volumecalculation nonlinear forcefree (NLFF) method applied to finite coronal magnetic structures and a surfacecalculation NLFF derivation that relies on a single photospheric or chromospheric vector magnetogram. Both methods were applied to two different data sets, namely synthetic activeregion cases obtained by threedimensional magnetohydrodynamic (MHD) simulations and observed activeregion cases, which include both eruptive and noneruptive magnetic structures. Results. The derived energyhelicity diagram shows a consistent monotonic scaling between relative helicity and free energy with a scaling index 0.84 ± 0.05 for both data sets and calculation methods. It also confirms the segregation between noneruptive and eruptive active regions and the existence of thresholds in both free energy and relative helicity for active regions to enter eruptive territory. Conclusions. We consider the previously reported energyhelicity diagram of solar magnetic structures as adequately validated and envision a significant role of the uncovered scaling in future studies of solar magnetism.
V.A. acknowledges support by the Royal Society. This work was supported from the EU’s Seventh Framework Program under grant agreement n° PIRG07GA2010268245. It has been also cofinanced by the European Union (European Social Fund – ESF) and Greek national funds through the Operational Program “Education and Lifelong Learning” of the National Strategic Reference Framework (NSRF) – Research Funding Program: Thales.
Wed, 01 Oct 2014 00:00:00 GMT
http://hdl.handle.net/10023/5872
20141001T00:00:00Z
Tziotziou, K.
Moraitis, K.
Georgoulis, M.K.
Archontis, V.
Aims. We assess the validity of the free magnetic energy  relative magnetic helicity diagram for solar magnetic structures. Methods. We used two different methods of calculating the free magnetic energy and the relative magnetic helicity budgets: a classical, volumecalculation nonlinear forcefree (NLFF) method applied to finite coronal magnetic structures and a surfacecalculation NLFF derivation that relies on a single photospheric or chromospheric vector magnetogram. Both methods were applied to two different data sets, namely synthetic activeregion cases obtained by threedimensional magnetohydrodynamic (MHD) simulations and observed activeregion cases, which include both eruptive and noneruptive magnetic structures. Results. The derived energyhelicity diagram shows a consistent monotonic scaling between relative helicity and free energy with a scaling index 0.84 ± 0.05 for both data sets and calculation methods. It also confirms the segregation between noneruptive and eruptive active regions and the existence of thresholds in both free energy and relative helicity for active regions to enter eruptive territory. Conclusions. We consider the previously reported energyhelicity diagram of solar magnetic structures as adequately validated and envision a significant role of the uncovered scaling in future studies of solar magnetism.

Simulating AIA observations of a flux rope ejection
http://hdl.handle.net/10023/5821
Context. Coronal mass ejections (CMEs) are the most violent phenomena observed on the Sun. Currently, extreme ultraviolet (EUV) images from the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamic Observatory (SDO) are providing new insights into the early phase of CME evolution. In particular, observations now show the ejection of magnetic flux ropes from the solar corona and how they evolve into CMEs. While this is the case, these observations are difficult to interpret in terms of basic physical mechanisms and quantities. To fully understand CMEs we need to compare equivalent quantities derived from both observations and theoretical models. This will aid in bridging the gap between observations and models. Aims: To this end, we aim to produce synthesised AIA observations from simulations of a flux rope ejection. To carry this out we include the role of thermal conduction and radiative losses, both of which are important for determining the temperature distribution of the solar corona during a CME. Methods: We perform a simulation where a flux rope is ejected from the solar corona. From the density and temperature of the plasma in the simulation we synthesise AIA observations. The emission is then integrated along the line of sight using the instrumental response function of AIA. Results: We sythesise observations of AIA in the channels at 304 Å, 171 Å, 335 Å, and 94 Å. The synthesised observations show a number of features similar to actual observations and in particular reproduce the general development of CMEs in the low corona as observed by AIA. In particular we reproduce an erupting and expanding arcade in the 304 Å and 171 Å channels with a high density core. Conclusions: The ejection of a flux rope reproduces many of the features found in the AIA observations. This work is therefore a step forward in bridging the gap between observations and models, and can lead to more direct interpretations of EUV observations in terms of flux rope ejections. We plan to improve the model in future studies in order to perform a more quantitative comparison. Movies associated with Figs. 3, 9, and 10 are available in electronic form at http://www.aanda.org
D.H.M. would like to thank STFC, the Leverhulme Trust and the European Commission’s Seventh Framework Programme (FP7/20072013) for their financial support. P.P. would like to thank the European Commission’s Seventh Framework Programme (FP7/20072013) under grant agreement SWIFF (project 263340, http://www.swiff.eu) and STFC for financial support. These results were obtained in the framework of the projects GOA/2009009 (KU Leuven), G.0729.11 (FWOVlaanderen) and C 90347 (ESA Prodex 9). The research leading to these results has also received funding from the European Commission’s Seventh Framework Programme (FP7/20072013) under the grant agreements SOLSPANET (project No. 269299, http:// www.solspanet.eu), SPACECAST (project No. 262468, fp7spacecast.eu), eHeroes (project n 284461, http://www.eheroes.eu). The computational work for this paper was carried out on the joint STFC and SFC (SRIF) funded cluster at the University of St Andrews (Scotland, UK).
Fri, 01 Aug 2014 00:00:00 GMT
http://hdl.handle.net/10023/5821
20140801T00:00:00Z
Pagano, Paolo
Mackay, Duncan Hendry
Poedts, Stephan
Context. Coronal mass ejections (CMEs) are the most violent phenomena observed on the Sun. Currently, extreme ultraviolet (EUV) images from the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamic Observatory (SDO) are providing new insights into the early phase of CME evolution. In particular, observations now show the ejection of magnetic flux ropes from the solar corona and how they evolve into CMEs. While this is the case, these observations are difficult to interpret in terms of basic physical mechanisms and quantities. To fully understand CMEs we need to compare equivalent quantities derived from both observations and theoretical models. This will aid in bridging the gap between observations and models. Aims: To this end, we aim to produce synthesised AIA observations from simulations of a flux rope ejection. To carry this out we include the role of thermal conduction and radiative losses, both of which are important for determining the temperature distribution of the solar corona during a CME. Methods: We perform a simulation where a flux rope is ejected from the solar corona. From the density and temperature of the plasma in the simulation we synthesise AIA observations. The emission is then integrated along the line of sight using the instrumental response function of AIA. Results: We sythesise observations of AIA in the channels at 304 Å, 171 Å, 335 Å, and 94 Å. The synthesised observations show a number of features similar to actual observations and in particular reproduce the general development of CMEs in the low corona as observed by AIA. In particular we reproduce an erupting and expanding arcade in the 304 Å and 171 Å channels with a high density core. Conclusions: The ejection of a flux rope reproduces many of the features found in the AIA observations. This work is therefore a step forward in bridging the gap between observations and models, and can lead to more direct interpretations of EUV observations in terms of flux rope ejections. We plan to improve the model in future studies in order to perform a more quantitative comparison. Movies associated with Figs. 3, 9, and 10 are available in electronic form at http://www.aanda.org

Stellar differential rotation and coronal timescales
http://hdl.handle.net/10023/5820
We investigate the timescales of evolution of stellar coronae in response to surface differential rotation and diffusion. To quantify this, we study both the formation time and lifetime of a magnetic flux rope in a decaying bipolar active region. We apply a magnetic flux transport model to prescribe the evolution of the stellar photospheric field, and use this to drive the evolution of the coronal magnetic field via a magnetofrictional technique. Increasing the differential rotation (i.e. decreasing the equatorpole lap time) decreases the flux rope formation time. We find that the formation time is dependent upon the lap time and the surface diffusion timescale through the relation tau_Form ∝ &surd;{tau_Laptau_Diff}. In contrast, the lifetimes of flux ropes are proportional to the lap time (tauLife∝tauLap). With this, flux ropes on stars with a differential rotation of more than eight times the solar value have a lifetime of less than 2 d. As a consequence, we propose that features such as solarlike quiescent prominences may not be easily observable on such stars, as the lifetimes of the flux ropes which host the cool plasma are very short. We conclude that such high differential rotation stars may have very dynamical coronae.
GPSG would like to thank the STFC for financial support. DHM would like to thank the STFC and the Leverhulme Trust for financial support.
Wed, 01 Oct 2014 00:00:00 GMT
http://hdl.handle.net/10023/5820
20141001T00:00:00Z
Gibb, Gordon Peter Samuel
Jardine, Moira Mary
Mackay, Duncan Hendry
We investigate the timescales of evolution of stellar coronae in response to surface differential rotation and diffusion. To quantify this, we study both the formation time and lifetime of a magnetic flux rope in a decaying bipolar active region. We apply a magnetic flux transport model to prescribe the evolution of the stellar photospheric field, and use this to drive the evolution of the coronal magnetic field via a magnetofrictional technique. Increasing the differential rotation (i.e. decreasing the equatorpole lap time) decreases the flux rope formation time. We find that the formation time is dependent upon the lap time and the surface diffusion timescale through the relation tau_Form ∝ &surd;{tau_Laptau_Diff}. In contrast, the lifetimes of flux ropes are proportional to the lap time (tauLife∝tauLap). With this, flux ropes on stars with a differential rotation of more than eight times the solar value have a lifetime of less than 2 d. As a consequence, we propose that features such as solarlike quiescent prominences may not be easily observable on such stars, as the lifetimes of the flux ropes which host the cool plasma are very short. We conclude that such high differential rotation stars may have very dynamical coronae.

Backward wave cyclotronmaser emission in the auroral magnetosphere
http://hdl.handle.net/10023/5802
In this Letter, we present theory and particleincell simulations describing cyclotron radio emission from Earth's auroral region and similar phenomena in other astrophysical environments. In particular, we find that the radiation, generated by a downgoing electron horseshoe distribution is due to a backward wave cyclotronmaser emission process. The backward wave nature of the radiation contributes to upward refraction of the radiation that is also enhanced by a density inhomogeneity. We also show that the radiation is preferentially amplified along the auroral oval rather than transversely. The results are in agreement with recent Cluster observations.
This work was supported by EPSRC Grant No. EP/G04239X/1.
Tue, 07 Oct 2014 00:00:00 GMT
http://hdl.handle.net/10023/5802
20141007T00:00:00Z
Speirs, D. C.
Bingham, R.
Cairns, R. A.
Vorgul, I.
Kellett, B. J.
Phelps, A. D. R.
Ronald, K.
In this Letter, we present theory and particleincell simulations describing cyclotron radio emission from Earth's auroral region and similar phenomena in other astrophysical environments. In particular, we find that the radiation, generated by a downgoing electron horseshoe distribution is due to a backward wave cyclotronmaser emission process. The backward wave nature of the radiation contributes to upward refraction of the radiation that is also enhanced by a density inhomogeneity. We also show that the radiation is preferentially amplified along the auroral oval rather than transversely. The results are in agreement with recent Cluster observations.

The nature of separator current layers in MHS equilibria I. Current parallel to the separator
http://hdl.handle.net/10023/5785
Separators, which are in many ways the threedimensional equivalent to twodimensional nulls, are important sites for magnetic reconnection. Magnetic reconnection occurs in strong current layers which have very short length scales. The aim of this work is to explore the nature of current layers around separators. A separator is a special field line which lies along the intersection of two separatrix surfaces and forms the boundary between four topologically distinct flux domains. In particular, here the current layer about a separator that joins two 3D nulls and lies along the intersection of their separatrix surfaces is investigated. A magnetic configuration containing a single separator embedded in a uniform plasma with a uniform electric current parallel to the separator is considered. This initial magnetic setup, which is not in equilibrium, relaxes in a nonresistive manner to form an equilibrium. The relaxation is achieved using the 3D MHD code, Lare3d, with resistivity set to zero. A series of experiments with varying initial current are run to investigate the characteristics of the resulting current layers present in the final (quasi) equilibrium states. In each experiment, the separator collapses and a current layer forms along it. The dimensions and strength of the current layer increase with initial current. It is found that separator current layers formed from current parallel to the separator are twisted. Also the collapse of the separator is a process that evolves like an infinitetime singularity where the length, width and peak current in the layer grow slowly whilst the depth of the current layer decreases.
JEHS would like to thank STFC for financial support during her Ph.D and CEP acknowledges support from the STFC consolidated grant.
Thu, 01 Jan 2015 00:00:00 GMT
http://hdl.handle.net/10023/5785
20150101T00:00:00Z
Stevenson, Julie Elizabeth Helen
Parnell, Clare Elizabeth
Priest, Eric Ronald
Haynes, Andrew Lewis
Separators, which are in many ways the threedimensional equivalent to twodimensional nulls, are important sites for magnetic reconnection. Magnetic reconnection occurs in strong current layers which have very short length scales. The aim of this work is to explore the nature of current layers around separators. A separator is a special field line which lies along the intersection of two separatrix surfaces and forms the boundary between four topologically distinct flux domains. In particular, here the current layer about a separator that joins two 3D nulls and lies along the intersection of their separatrix surfaces is investigated. A magnetic configuration containing a single separator embedded in a uniform plasma with a uniform electric current parallel to the separator is considered. This initial magnetic setup, which is not in equilibrium, relaxes in a nonresistive manner to form an equilibrium. The relaxation is achieved using the 3D MHD code, Lare3d, with resistivity set to zero. A series of experiments with varying initial current are run to investigate the characteristics of the resulting current layers present in the final (quasi) equilibrium states. In each experiment, the separator collapses and a current layer forms along it. The dimensions and strength of the current layer increase with initial current. It is found that separator current layers formed from current parallel to the separator are twisted. Also the collapse of the separator is a process that evolves like an infinitetime singularity where the length, width and peak current in the layer grow slowly whilst the depth of the current layer decreases.

Particle acceleration at a reconnecting magnetic separator
http://hdl.handle.net/10023/5782
While the exact acceleration mechanism of energetic particles during solar flares is (as yet) unknown, magnetic reconnection plays a key role both in the release of stored magnetic energy of the solar corona and the magnetic restructuring during a flare. Recent work has shown that special field lines, called separators, are common sites of reconnection in 3D numerical experiments. To date, 3D separator reconnection sites have received little attention as particle accelerators. We investigate the effectiveness of separator reconnection as a particle acceleration mechanism for electrons and protons. We study the particle acceleration using a relativistic guidingcentre particle code in a timedependent kinematic model of magnetic reconnection at a separator. The effect upon particle behaviour of initial position, pitch angle and initial kinetic energy are examined in detail, both for specific (single) particle examples and for large distributions of initial conditions. The separator reconnection model contains several free parameters and we study the effect of changing these parameters upon particle acceleration, in particular in view of the final particle energy ranges which agree with observed energy spectra.
Sun, 01 Feb 2015 00:00:00 GMT
http://hdl.handle.net/10023/5782
20150201T00:00:00Z
Threlfall, J.
Neukirch, T.
Parnell, Clare Elizabeth
Eradat Oskoui, S.
While the exact acceleration mechanism of energetic particles during solar flares is (as yet) unknown, magnetic reconnection plays a key role both in the release of stored magnetic energy of the solar corona and the magnetic restructuring during a flare. Recent work has shown that special field lines, called separators, are common sites of reconnection in 3D numerical experiments. To date, 3D separator reconnection sites have received little attention as particle accelerators. We investigate the effectiveness of separator reconnection as a particle acceleration mechanism for electrons and protons. We study the particle acceleration using a relativistic guidingcentre particle code in a timedependent kinematic model of magnetic reconnection at a separator. The effect upon particle behaviour of initial position, pitch angle and initial kinetic energy are examined in detail, both for specific (single) particle examples and for large distributions of initial conditions. The separator reconnection model contains several free parameters and we study the effect of changing these parameters upon particle acceleration, in particular in view of the final particle energy ranges which agree with observed energy spectra.

Alfvén wave boundary condition for responsive magnetosphere ionosphere coupling
http://hdl.handle.net/10023/5660
The solution of electric fields and currents in a heightresolved ionosphere is traditionally solved as an elliptic equation with Dirichlet or Neumann boundary condition in which the magnetosphere is represented as an unresponsive (prescribed) voltage generator or current source. In this paper we derive an alternative boundary condition based upon Alfvén waves in which only the Alfvén wave from the magnetosphere that is incident upon the ionosphere (E) is prescribed. For a uniform magnetosphere the new boundary condition reduces to ∂φ/∂z=(∂2φ/ ∂x2+2∂Exi/∂x)/(μ0VAσ≥) and is evaluated at the magnetosphereionosphere interface. The resulting solution is interpreted as a responsive magnetosphere and establishes a key stage in the full selfconsistent and nonlinear coupling of the magnetosphere and ionosphere.
A.J.B.R. thanks STFC for present support through consolidated grant ST/K000993/1 and gratefully acknowledges a Royal Commission for the Exhibition of 1851 Research Fellowship that also assisted this work.
Thu, 01 May 2014 00:00:00 GMT
http://hdl.handle.net/10023/5660
20140501T00:00:00Z
Wright, A.N.
Russell, A.J.B.
The solution of electric fields and currents in a heightresolved ionosphere is traditionally solved as an elliptic equation with Dirichlet or Neumann boundary condition in which the magnetosphere is represented as an unresponsive (prescribed) voltage generator or current source. In this paper we derive an alternative boundary condition based upon Alfvén waves in which only the Alfvén wave from the magnetosphere that is incident upon the ionosphere (E) is prescribed. For a uniform magnetosphere the new boundary condition reduces to ∂φ/∂z=(∂2φ/ ∂x2+2∂Exi/∂x)/(μ0VAσ≥) and is evaluated at the magnetosphereionosphere interface. The resulting solution is interpreted as a responsive magnetosphere and establishes a key stage in the full selfconsistent and nonlinear coupling of the magnetosphere and ionosphere.

Ultraviolet and extremeultraviolet emissions at the flare footpoints observed by atmosphere imaging assembly
http://hdl.handle.net/10023/5499
A solar flare is composed of impulsive energy release events by magnetic reconnection, which forms and heats flare loops. Recent studies have revealed a twophase evolution pattern of UV 1600 Å emission at the feet of these loops: a rapid pulse lasting for a few seconds to a few minutes, followed by a gradual decay on timescales of a few tens of minutes. Multiple band EUV observations by the Atmosphere Imaging Assembly further reveal very similar signatures. These two phases represent different but related signatures of an impulsive energy release in the corona. The rapid pulse is an immediate response of the lower atmosphere to an intense thermal conduction flux resulting from the sudden heating of the corona to high temperatures (we rule out energetic particles due to a lack of significant hard Xray emission). The gradual phase is associated with the cooling of hot plasma that has been evaporated into the corona. The observed footpoint emission is again powered by thermal conduction (and enthalpy), but now during a period when approximate steadystate conditions are established in the loop. UV and EUV light curves of individual pixels may therefore be separated into contributions from two distinct physical mechanisms to shed light on the nature of energy transport in a flare. We demonstrate this technique using coordinated, spatially resolved observations of UV and EUV emissions from the footpoints of a C3.2 thermal flare.
Sun, 01 Sep 2013 00:00:00 GMT
http://hdl.handle.net/10023/5499
20130901T00:00:00Z
Qiu, J.
Sturrock, Z.
Longcope, D.W.
Klimchuk, J.A.
Liu, W.J.
A solar flare is composed of impulsive energy release events by magnetic reconnection, which forms and heats flare loops. Recent studies have revealed a twophase evolution pattern of UV 1600 Å emission at the feet of these loops: a rapid pulse lasting for a few seconds to a few minutes, followed by a gradual decay on timescales of a few tens of minutes. Multiple band EUV observations by the Atmosphere Imaging Assembly further reveal very similar signatures. These two phases represent different but related signatures of an impulsive energy release in the corona. The rapid pulse is an immediate response of the lower atmosphere to an intense thermal conduction flux resulting from the sudden heating of the corona to high temperatures (we rule out energetic particles due to a lack of significant hard Xray emission). The gradual phase is associated with the cooling of hot plasma that has been evaporated into the corona. The observed footpoint emission is again powered by thermal conduction (and enthalpy), but now during a period when approximate steadystate conditions are established in the loop. UV and EUV light curves of individual pixels may therefore be separated into contributions from two distinct physical mechanisms to shed light on the nature of energy transport in a flare. We demonstrate this technique using coordinated, spatially resolved observations of UV and EUV emissions from the footpoints of a C3.2 thermal flare.

Nonlinear forcefree magnetic dip models of quiescent prominence fine structures
http://hdl.handle.net/10023/5476
Aims. We use 3D nonlinear forcefree magnetic field modeling of prominence/filament magnetic fields to develop the first 2D models of individual prominence fine structures based on the 3D configuration of the magnetic field of the whole prominence. Methods. We use an iterative technique to fill the magnetic dips produced by the 3D modeling with realistic prominence plasma in hydrostatic equilibrium and with a temperature structure that contains the prominencecorona transition region. With this welldefined plasma structure the radiative transfer can be treated in detail in 2D and the resulting synthetic emission can be compared with prominence/filament observations. Results. Newly developed nonlinear forcefree magnetic dip models are able to produce synthetic hydrogen Lyman spectra in a qualitative agreement with a range of quiescent prominence observations. Moreover, the plasma structure of these models agrees with the gravity induced prominence fine structure models which have already been shown to produce synthetic spectra in good qualitative agreement with several observed prominences. Conclusions. We describe in detail the iterative technique which can be used to produce realistic plasma models of prominence fine structures located in prominence magnetic field configurations containing dips, obtained using any kind of magnetic field modeling.
S.G. and P.H. acknowledge the support from grant 209/12/0906 of the Grant Agency of the Czech Republic. P.H. acknowledges the support from grant P209/10/1680 of the Grant Agency of the Czech Republic. S.G. and P.H. acknowledge the support from the MPA Garching; U.A. thanks for support from the Ondřejov Observatory. S.G. acknowledges the support from St Andrews University. Work of S.G. and P.H. was supported by the project RVO: 67985815. DHM acknowledges financial support from the STFC and the Leverhulme Trust. In addition research leading to these results has received funding from the European Commission’s Seventh Framework Programme (FP7/20072013) under the grant agreement SWIFF (project N° 263340, http://www.swiff.eu).
Fri, 01 Mar 2013 00:00:00 GMT
http://hdl.handle.net/10023/5476
20130301T00:00:00Z
Gunar, Stanislav
Mackay, Duncan Hendry
Anzer, U
Heinzel, Petr
Aims. We use 3D nonlinear forcefree magnetic field modeling of prominence/filament magnetic fields to develop the first 2D models of individual prominence fine structures based on the 3D configuration of the magnetic field of the whole prominence. Methods. We use an iterative technique to fill the magnetic dips produced by the 3D modeling with realistic prominence plasma in hydrostatic equilibrium and with a temperature structure that contains the prominencecorona transition region. With this welldefined plasma structure the radiative transfer can be treated in detail in 2D and the resulting synthetic emission can be compared with prominence/filament observations. Results. Newly developed nonlinear forcefree magnetic dip models are able to produce synthetic hydrogen Lyman spectra in a qualitative agreement with a range of quiescent prominence observations. Moreover, the plasma structure of these models agrees with the gravity induced prominence fine structure models which have already been shown to produce synthetic spectra in good qualitative agreement with several observed prominences. Conclusions. We describe in detail the iterative technique which can be used to produce realistic plasma models of prominence fine structures located in prominence magnetic field configurations containing dips, obtained using any kind of magnetic field modeling.

Effects of M dwarf magnetic fields on potentially habitable planets
http://hdl.handle.net/10023/5462
We investigate the effect of the magnetic fields of M dwarf (dM) stars on potentially habitable Earthlike planets. These fields can reduce the size of planetary magnetospheres to such an extent that a significant fraction of the planet’s atmosphere may be exposed to erosion by the stellar wind. We used a sample of 15 active dM stars, for which surface magneticfield maps were reconstructed, to determine the magnetic pressure at the planet orbit and hence the largest size of its magnetosphere, which would only be decreased by considering the stellar wind. Our method provides a fast means to assess which planets are most affected by the stellar magnetic field, which can be used as a first study to be followed by more sophisticated models. We show that hypothetical Earthlike planets with similar terrestrial magnetisation (~1 G) orbiting at the inner (outer) edge of the habitable zone of these stars would present magnetospheres that extend at most up to 6 (11.7) planetary radii. To be able to sustain an Earthsized magnetosphere, with the exception of only a few cases, the terrestrial planet would either (1) need to orbit significantly farther out than the traditional limits of the habitable zone; or else, (2) if it were orbiting within the habitable zone, it would require at least a magnetic field ranging from a few G to up to a few thousand G. By assuming a magnetospheric size that is more appropriate for the youngEarth (3.4 Gyr ago), the required planetary magnetic fields are one order of magnitude weaker. However, in this case, the polarcap area of the planet, which is unprotected from transport of particles to/from interplanetary space, is twice as large. At present, we do not know how small the smallest area of the planetary surface is that could be exposed and would still not affect the potential for formation and development of life in a planet. As the star becomes older and, therefore, its rotation rate and magnetic field reduce, the interplanetary magnetic pressure decreases and the magnetosphere of planets probably expands. Using an empirically derived rotationactivity/magnetism relation, we provide an analytical expression for estimating the shortest stellar rotation period for which an Earthanalogue in the habitable zone could sustain an Earthsized magnetosphere. We find that the required rotation rate of the early and middM stars (with periods ≳37–202 days) is slower than the solar one, and even slower for the latedM stars (≳63–263 days). Planets orbiting in the habitable zone of dM stars that rotate faster than this have smaller magnetospheric sizes than that of the Earth magnetosphere. Because many latedM stars are fast rotators, conditions for terrestrial planets to harbour Earthsized magnetospheres are more easily achieved for planets orbiting slowly rotating early and middM stars.
A.A.V. acknowledges support from the Royal Astronomical Society through a postdoctoral fellowship. J.M. acknowledges support from a fellowship of the Alexander von Humboldt foundation. P.L. acknowledges funding from a STFC scholarship. AJBR is a Research Fellow of the Royal Commission for the Exhibition of 1851.
Mon, 02 Sep 2013 00:00:00 GMT
http://hdl.handle.net/10023/5462
20130902T00:00:00Z
Vidotto, A.A.
Jardine, M.
Morin, J.
Donati, J.F.
Lang, P.
Russell, A.J.B.
We investigate the effect of the magnetic fields of M dwarf (dM) stars on potentially habitable Earthlike planets. These fields can reduce the size of planetary magnetospheres to such an extent that a significant fraction of the planet’s atmosphere may be exposed to erosion by the stellar wind. We used a sample of 15 active dM stars, for which surface magneticfield maps were reconstructed, to determine the magnetic pressure at the planet orbit and hence the largest size of its magnetosphere, which would only be decreased by considering the stellar wind. Our method provides a fast means to assess which planets are most affected by the stellar magnetic field, which can be used as a first study to be followed by more sophisticated models. We show that hypothetical Earthlike planets with similar terrestrial magnetisation (~1 G) orbiting at the inner (outer) edge of the habitable zone of these stars would present magnetospheres that extend at most up to 6 (11.7) planetary radii. To be able to sustain an Earthsized magnetosphere, with the exception of only a few cases, the terrestrial planet would either (1) need to orbit significantly farther out than the traditional limits of the habitable zone; or else, (2) if it were orbiting within the habitable zone, it would require at least a magnetic field ranging from a few G to up to a few thousand G. By assuming a magnetospheric size that is more appropriate for the youngEarth (3.4 Gyr ago), the required planetary magnetic fields are one order of magnitude weaker. However, in this case, the polarcap area of the planet, which is unprotected from transport of particles to/from interplanetary space, is twice as large. At present, we do not know how small the smallest area of the planetary surface is that could be exposed and would still not affect the potential for formation and development of life in a planet. As the star becomes older and, therefore, its rotation rate and magnetic field reduce, the interplanetary magnetic pressure decreases and the magnetosphere of planets probably expands. Using an empirically derived rotationactivity/magnetism relation, we provide an analytical expression for estimating the shortest stellar rotation period for which an Earthanalogue in the habitable zone could sustain an Earthsized magnetosphere. We find that the required rotation rate of the early and middM stars (with periods ≳37–202 days) is slower than the solar one, and even slower for the latedM stars (≳63–263 days). Planets orbiting in the habitable zone of dM stars that rotate faster than this have smaller magnetospheric sizes than that of the Earth magnetosphere. Because many latedM stars are fast rotators, conditions for terrestrial planets to harbour Earthsized magnetospheres are more easily achieved for planets orbiting slowly rotating early and middM stars.

Numerical simulation of a selfsimilar cascade of filament instabilities in the surface quasigeostrophic system
http://hdl.handle.net/10023/5436
We provide numerical evidence for the existence of a cascade of filament instabilities in the surface quasigeostrophic system for rotating, stratified flow near a horizontal boundary. The cascade involves geometrically shrinking spatial and temporal scales and implies the singular collapse of the filament width to zero in a finite time. The numerical method is both spatially and temporally adaptive, permitting the accurate simulation of the evolution over an unprecedented range of spatial scales spanning over ten orders of magnitude. It provides the first convincing demonstration of the cascade, in which the large separation of scales between subsequent instabilities has made previous numerical simulation difficult.
Fri, 11 Apr 2014 00:00:00 GMT
http://hdl.handle.net/10023/5436
20140411T00:00:00Z
Scott, R. K.
Dritschel, D. G.
We provide numerical evidence for the existence of a cascade of filament instabilities in the surface quasigeostrophic system for rotating, stratified flow near a horizontal boundary. The cascade involves geometrically shrinking spatial and temporal scales and implies the singular collapse of the filament width to zero in a finite time. The numerical method is both spatially and temporally adaptive, permitting the accurate simulation of the evolution over an unprecedented range of spatial scales spanning over ten orders of magnitude. It provides the first convincing demonstration of the cascade, in which the large separation of scales between subsequent instabilities has made previous numerical simulation difficult.

Inertialrange dynamics and scaling laws of twodimensional magnetic turbulence in the weakfield regime
http://hdl.handle.net/10023/5358
We study inertialrange dynamics and scaling laws in unforced twodimensional magnetohydrodynamic turbulence in the regime of moderately small and small initial magnetictokinetic energy ratio $r_0$, with an emphasis on the latter. The regime of small $r_0$ corresponds to a relatively weak field and strong magnetic stretching, whereby the turbulence is characterized by an intense conversion of kinetic into magnetic energy (dynamo action in the threedimensional context). This conversion is an inertialrange phenomenon and, upon becoming quasisaturated, deposits the converted energy within the inertial range rather than transferring it to the small scales. As a result, the magnetic energy spectrum $E_\b(k)$ in the inertial range can become quite shallow and may not be adequately explained or understood in terms of conventional cascade theories. It is demonstrated by numerical simulations at high Reynolds numbers (and unity magnetic Prandtl number) that the energetics and inertialrange scaling depend strongly on $r_0$. In particular, for fully developed turbulence with $r_0$ in the range $[1/4,1/4096]$, $E_\b(k)$ is found to scale as $k^{\alpha}$, where $\alpha\gtrsim1$, including $\alpha>0$. The extent of such a shallow spectrum is limited, becoming broader as $r_0$ is decreased. The slope $\alpha$ increases as $r_0$ is decreased, appearing to tend to $+1$ in the limit of small $r_0$. This implies equipartition of magnetic energy among the Fourier modes of the inertial range and the scaling $k^{1}$ of the magnetic potential variance, whose flux is direct rather than inverse. This behavior of the potential resembles that of a passive scalar. However, unlike a passive scalar whose variance dissipation rate slowly vanishes in the diffusionless limit, the dissipation rate of the magnetic potential variance scales linearly with the diffusivity in that limit. Meanwhile, the kinetic energy spectrum is relatively steep, followed by a much shallower tail due to strong antidynamo excitation. This gives rise to a total energy spectrum poorly obeying a powerlaw scaling.
The work reported here was partially supported by an EPSRC postgraduate studentship to L.A.K.B. L.A.K.B. was further supported by an EPSRC doctoral prize.
Thu, 21 Aug 2014 00:00:00 GMT
http://hdl.handle.net/10023/5358
20140821T00:00:00Z
Blackbourn, Luke Austen Kazimierz
Tran, Chuong Van
We study inertialrange dynamics and scaling laws in unforced twodimensional magnetohydrodynamic turbulence in the regime of moderately small and small initial magnetictokinetic energy ratio $r_0$, with an emphasis on the latter. The regime of small $r_0$ corresponds to a relatively weak field and strong magnetic stretching, whereby the turbulence is characterized by an intense conversion of kinetic into magnetic energy (dynamo action in the threedimensional context). This conversion is an inertialrange phenomenon and, upon becoming quasisaturated, deposits the converted energy within the inertial range rather than transferring it to the small scales. As a result, the magnetic energy spectrum $E_\b(k)$ in the inertial range can become quite shallow and may not be adequately explained or understood in terms of conventional cascade theories. It is demonstrated by numerical simulations at high Reynolds numbers (and unity magnetic Prandtl number) that the energetics and inertialrange scaling depend strongly on $r_0$. In particular, for fully developed turbulence with $r_0$ in the range $[1/4,1/4096]$, $E_\b(k)$ is found to scale as $k^{\alpha}$, where $\alpha\gtrsim1$, including $\alpha>0$. The extent of such a shallow spectrum is limited, becoming broader as $r_0$ is decreased. The slope $\alpha$ increases as $r_0$ is decreased, appearing to tend to $+1$ in the limit of small $r_0$. This implies equipartition of magnetic energy among the Fourier modes of the inertial range and the scaling $k^{1}$ of the magnetic potential variance, whose flux is direct rather than inverse. This behavior of the potential resembles that of a passive scalar. However, unlike a passive scalar whose variance dissipation rate slowly vanishes in the diffusionless limit, the dissipation rate of the magnetic potential variance scales linearly with the diffusivity in that limit. Meanwhile, the kinetic energy spectrum is relatively steep, followed by a much shallower tail due to strong antidynamo excitation. This gives rise to a total energy spectrum poorly obeying a powerlaw scaling.

Distribution of electric currents in solar active regions
http://hdl.handle.net/10023/5322
There has been a longstanding debate on the question of whether or not electric currents in solar active regions are neutralized. That is, whether or not the main (or direct) coronal currents connecting the active region polarities are surrounded by shielding (or return) currents of equal total value and opposite direction. Both theory and observations are not yet fully conclusive regarding this question, and numerical simulations have, surprisingly, barely been used to address it. Here we quantify the evolution of electric currents during the formation of a bipolar active region by considering a threedimensional magnetohydrodynamic simulation of the emergence of a subphotospheric, currentneutralized magnetic flux rope into the solar atmosphere. We find that a strong deviation from current neutralization develops simultaneously with the onset of significant flux emergence into the corona, accompanied by the development of substantial magnetic shear along the active region's polarity inversion line. After the region has formed and flux emergence has ceased, the strong magnetic fields in the region's center are connected solely by direct currents, and the total direct current is several times larger than the total return current. These results suggest that active regions, the main sources of coronal mass ejections and flares, are born with substantial net currents, in agreement with recent observations. Furthermore, they support eruption models that employ preeruption magnetic fields containing such currents.
The contributions of T.T., V.S.T., and Z.M. were supported by NASA's HTP, LWS, and SR&T programs. J.E.L and M.G.L. were supported by NASA/LWS. M.G.L. received support also from the ONR 6.1 program. The simulation was performed under grant of computer time from the D.o.D. HPC Program. B.K. was supported by the DFG. V.A. acknowledges support through the IEF272549 grant.
Mon, 10 Feb 2014 00:00:00 GMT
http://hdl.handle.net/10023/5322
20140210T00:00:00Z
Török, T.
Leake, J.E.
Titov, V.S.
Archontis, V.
Mikić, Z.
Linton, M.G.
Dalmasse, K.
Aulanier, G.
Kliem, B.
There has been a longstanding debate on the question of whether or not electric currents in solar active regions are neutralized. That is, whether or not the main (or direct) coronal currents connecting the active region polarities are surrounded by shielding (or return) currents of equal total value and opposite direction. Both theory and observations are not yet fully conclusive regarding this question, and numerical simulations have, surprisingly, barely been used to address it. Here we quantify the evolution of electric currents during the formation of a bipolar active region by considering a threedimensional magnetohydrodynamic simulation of the emergence of a subphotospheric, currentneutralized magnetic flux rope into the solar atmosphere. We find that a strong deviation from current neutralization develops simultaneously with the onset of significant flux emergence into the corona, accompanied by the development of substantial magnetic shear along the active region's polarity inversion line. After the region has formed and flux emergence has ceased, the strong magnetic fields in the region's center are connected solely by direct currents, and the total direct current is several times larger than the total return current. These results suggest that active regions, the main sources of coronal mass ejections and flares, are born with substantial net currents, in agreement with recent observations. Furthermore, they support eruption models that employ preeruption magnetic fields containing such currents.

Recurrent explosive eruptions and the "sigmoidtoarcade" transformation in the Sun driven by dynamical magnetic flux emergence
http://hdl.handle.net/10023/5319
We report on threedimensional MHD simulations of recurrent mini coronal mass ejection (CME)like eruptions in a small active region (AR), which is formed by the dynamical emergence of a twisted (not kink unstable) flux tube from the solar interior. The eruptions develop as a result of the repeated formation and expulsion of new flux ropes due to continuous emergence and reconnection of sheared field lines along the polarity inversion line of the AR. The acceleration of the eruptions is triggered by tethercutting reconnection at the current sheet underneath the erupting field. We find that each explosive eruption is followed by reformation of a sigmoidal structure and a subsequent "sigmoidtoflare arcade" transformation in the AR. These results might have implications for recurrent CMEs and eruptive sigmoids/flares observations and theoretical studies.
The authors acknowledge support by EU (IEF272549 grant) and the Royal Society.
Sat, 10 May 2014 00:00:00 GMT
http://hdl.handle.net/10023/5319
20140510T00:00:00Z
Archontis, V.
Hood, A.W.
Tsinganos, K.
We report on threedimensional MHD simulations of recurrent mini coronal mass ejection (CME)like eruptions in a small active region (AR), which is formed by the dynamical emergence of a twisted (not kink unstable) flux tube from the solar interior. The eruptions develop as a result of the repeated formation and expulsion of new flux ropes due to continuous emergence and reconnection of sheared field lines along the polarity inversion line of the AR. The acceleration of the eruptions is triggered by tethercutting reconnection at the current sheet underneath the erupting field. We find that each explosive eruption is followed by reformation of a sigmoidal structure and a subsequent "sigmoidtoflare arcade" transformation in the AR. These results might have implications for recurrent CMEs and eruptive sigmoids/flares observations and theoretical studies.

Observations of a hybrid doublestreamer/pseudostreamer in the solar corona
http://hdl.handle.net/10023/5318
We report on the first observation of a single hybrid magnetic structure that contains both a pseudostreamer and a double streamer. This structure was originally observed by the SWAP instrument on board the PROBA2 satellite between 2013 May 5 and 10. It consists of a pair of filament channels near the south pole of the Sun. On the western edge of the structure, the magnetic morphology above the filaments is that of a sidebyside double streamer, with open field between the two channels. On the eastern edge, the magnetic morphology is that of a coronal pseudostreamer without the central open field. We investigated this structure with multiple observations and modeling techniques. We describe the topology and dynamic consequences of such a unified structure.
D.B.S. and L.A.R. acknowledge support from the Belgian Federal Science Policy Office (BELSPO) through the ESAPRODEX program, grant No. 4000103240. S.J.P. acknowledges the financial support of the Isle of Man Government.
Tue, 20 May 2014 00:00:00 GMT
http://hdl.handle.net/10023/5318
20140520T00:00:00Z
Rachmeler, L.A.
Platten, S.J.
Bethge, C.
Seaton, D.B.
Yeates, A.R.
We report on the first observation of a single hybrid magnetic structure that contains both a pseudostreamer and a double streamer. This structure was originally observed by the SWAP instrument on board the PROBA2 satellite between 2013 May 5 and 10. It consists of a pair of filament channels near the south pole of the Sun. On the western edge of the structure, the magnetic morphology above the filaments is that of a sidebyside double streamer, with open field between the two channels. On the eastern edge, the magnetic morphology is that of a coronal pseudostreamer without the central open field. We investigated this structure with multiple observations and modeling techniques. We describe the topology and dynamic consequences of such a unified structure.

Clusters of small eruptive flares produced by magnetic reconnection in the Sun
http://hdl.handle.net/10023/5316
We report on the formation of small solar flares produced by patchy magnetic reconnection between interacting magnetic loops. A threedimensional (3D) magnetohydrodynamic (MHD) numerical experiment was performed, where a uniform magnetic flux sheet was injected into a fully developed convective layer. The gradual emergence of the field into the solar atmosphere results in a network of magnetic loops, which interact dynamically forming current layers at their interfaces. The formation and ejection of plasmoids out of the current layers leads to patchy reconnection and the spontaneous formation of several small (size ≈12 Mm) flares. We find that these flares are shortlived (30 s3 minutes) bursts of energy in the range O(10251027) erg, which is basically the nanoflaremicroflare range. Their persistent formation and cooperative action and evolution leads to recurrent emission of fast EUV/Xray jets and considerable plasma heating in the active corona.
This research was supported by the Research Council of Norway through the grant "Solar Atmospheric Modelling" and through grants of computing time from the Programme for Supercomputing, by the European Research Council under the European Union's Seventh Framework Programme (FP7/20072013)/ERC Grant agreement No. 291058 and by computing project s1061 from the High End Computing Division of NASA. The authors acknowledge support by the EU (IEF272549 grant) and the Royal Society.
Tue, 10 Jun 2014 00:00:00 GMT
http://hdl.handle.net/10023/5316
20140610T00:00:00Z
Archontis, V.
Hansteen, V.
We report on the formation of small solar flares produced by patchy magnetic reconnection between interacting magnetic loops. A threedimensional (3D) magnetohydrodynamic (MHD) numerical experiment was performed, where a uniform magnetic flux sheet was injected into a fully developed convective layer. The gradual emergence of the field into the solar atmosphere results in a network of magnetic loops, which interact dynamically forming current layers at their interfaces. The formation and ejection of plasmoids out of the current layers leads to patchy reconnection and the spontaneous formation of several small (size ≈12 Mm) flares. We find that these flares are shortlived (30 s3 minutes) bursts of energy in the range O(10251027) erg, which is basically the nanoflaremicroflare range. Their persistent formation and cooperative action and evolution leads to recurrent emission of fast EUV/Xray jets and considerable plasma heating in the active corona.

Loss cone evolution and particle escape in collapsing magnetic trap models in solar flares
http://hdl.handle.net/10023/5275
Context. Collapsing magnetic traps (CMTs) have been suggested as one possible mechanism responsible for the acceleration of highenergy particles during solar flares. An important question regarding the CMT acceleration mechanism is which particle orbits escape and which are trapped during the time evolution of a CMT. While some models predict the escape of the majority of particle orbits, other more sophisticated CMT models show that, in particular, the highestenergy particles remain trapped at all times. The exact prediction is not straightforward because both the loss cone angle and the particle orbit pitch angle evolve in time in a CMT. Aims. Our aim is to gain a better understanding of the conditions leading to either particle orbit escape or trapping in CMTs. Methods. We present a detailed investigation of the time evolution of particle orbit pitch angles in the CMT model of Giuliani and collaborators and compare this with the time evolution of the loss cone angle. The nonrelativistic guiding centre approximation is used to calculate the particle orbits. We also use simplified models to corroborate the findings of the particle orbit calculations. Results. We find that there is a critical initial pitch angle for each field line of a CMT that divides trapped and escaping particle orbits. This critical initial pitch angle is greater than the initial loss cone angle, but smaller than the asymptotic (final) loss cone angle for that field line. As the final loss cone angle in CMTs is larger than the initial loss cone angle, particle orbits with pitch angles that cross into the loss cone during their time evolution will escape whereas all other particle orbits are trapped. We find that in realistic CMT models, Fermi acceleration will only dominate in the initial phase of the CMT evolution and, in this case, can reduce the pitch angle, but that betatron acceleration will dominate for later stages of the CMT evolution leading to a systematic increase of the pitch angle. Whether a particle escapes or remains trapped depends critically on the relative importance of the two acceleration mechanisms, which cannot be decoupled in more sophisticated CMT models.
This work was financially supported by the UK’s Science and Technology Facilities Council.
Sat, 01 Mar 2014 00:00:00 GMT
http://hdl.handle.net/10023/5275
20140301T00:00:00Z
Eradat Oskoui, Solmaz
Neukirch, Thomas
Grady, Keith James
Context. Collapsing magnetic traps (CMTs) have been suggested as one possible mechanism responsible for the acceleration of highenergy particles during solar flares. An important question regarding the CMT acceleration mechanism is which particle orbits escape and which are trapped during the time evolution of a CMT. While some models predict the escape of the majority of particle orbits, other more sophisticated CMT models show that, in particular, the highestenergy particles remain trapped at all times. The exact prediction is not straightforward because both the loss cone angle and the particle orbit pitch angle evolve in time in a CMT. Aims. Our aim is to gain a better understanding of the conditions leading to either particle orbit escape or trapping in CMTs. Methods. We present a detailed investigation of the time evolution of particle orbit pitch angles in the CMT model of Giuliani and collaborators and compare this with the time evolution of the loss cone angle. The nonrelativistic guiding centre approximation is used to calculate the particle orbits. We also use simplified models to corroborate the findings of the particle orbit calculations. Results. We find that there is a critical initial pitch angle for each field line of a CMT that divides trapped and escaping particle orbits. This critical initial pitch angle is greater than the initial loss cone angle, but smaller than the asymptotic (final) loss cone angle for that field line. As the final loss cone angle in CMTs is larger than the initial loss cone angle, particle orbits with pitch angles that cross into the loss cone during their time evolution will escape whereas all other particle orbits are trapped. We find that in realistic CMT models, Fermi acceleration will only dominate in the initial phase of the CMT evolution and, in this case, can reduce the pitch angle, but that betatron acceleration will dominate for later stages of the CMT evolution leading to a systematic increase of the pitch angle. Whether a particle escapes or remains trapped depends critically on the relative importance of the two acceleration mechanisms, which cannot be decoupled in more sophisticated CMT models.

The solar cycle variation of topological structures in the global solar corona
http://hdl.handle.net/10023/5271
Context. The complicated distribution of magnetic flux across the solar photosphere results in a complex web of coronal magnetic field structures. To understand this complexity, the magnetic skeleton of the coronal field can be calculated. The skeleton highlights the (separatrix) surfaces that divide the field into topologically distinct regions, allowing openfield regions on the solar surface to be located. Furthermore, separatrix surfaces and their intersections with other separatrix surfaces (i.e., separators) are important likely energy release sites. Aims. The aim of this paper is to investigate, throughout the solar cycle, the nature of coronal magneticfield topologies that arise under the potentialfield sourcesurface approximation. In particular, we characterise the typical global fields at solar maximum and minimum. Methods. Global magnetic fields are extrapolated from observed Kitt Peak and SOLIS synoptic magnetograms, from Carrington rotations 1645 to 2144, using the potentialfield sourcesurface model. This allows the variations in the coronal skeleton to be studied over three solar cycles. Results. The main building blocks which make up magnetic fields are identified and classified according to the nature of their separatrix surfaces. The magnetic skeleton reveals that, at solar maximum, the global coronal field involves a multitude of topological structures at all latitudes crisscrossing throughout the atmosphere. Many openfield regions exist originating anywhere on the photosphere. At solar minimum, the coronal topology is heavily influenced by the solar magnetic dipole. A strong dipole results in a simple largescale structure involving just two large polar openfield regions, but, at short radial distances between ± 60° latitude, the smallscale topology is complex. If the solar magnetic dipole if weak, as in the recent minimum, then the lowlatitude quietsun magnetic fields may be globally significant enough to create many disconnected openfield regions between ± 60° latitude, in addition to the two polar openfield regions.
S.J.P. acknowledges financial support from the Isle of Man Government. E.R.P. is grateful to the Leverhulme Trust for his emeritus fellowship. The research leading to these results has received funding from the European Commission’s Seventh Framework Programme (FP7/20072013) under the grant agreement SWIFF (project No. 263340, www.swiff.eu).
Thu, 01 May 2014 00:00:00 GMT
http://hdl.handle.net/10023/5271
20140501T00:00:00Z
Platten, S.J.
Parnell, C.E.
Haynes, A.L.
Priest, E.R.
MacKay, D.H.
Context. The complicated distribution of magnetic flux across the solar photosphere results in a complex web of coronal magnetic field structures. To understand this complexity, the magnetic skeleton of the coronal field can be calculated. The skeleton highlights the (separatrix) surfaces that divide the field into topologically distinct regions, allowing openfield regions on the solar surface to be located. Furthermore, separatrix surfaces and their intersections with other separatrix surfaces (i.e., separators) are important likely energy release sites. Aims. The aim of this paper is to investigate, throughout the solar cycle, the nature of coronal magneticfield topologies that arise under the potentialfield sourcesurface approximation. In particular, we characterise the typical global fields at solar maximum and minimum. Methods. Global magnetic fields are extrapolated from observed Kitt Peak and SOLIS synoptic magnetograms, from Carrington rotations 1645 to 2144, using the potentialfield sourcesurface model. This allows the variations in the coronal skeleton to be studied over three solar cycles. Results. The main building blocks which make up magnetic fields are identified and classified according to the nature of their separatrix surfaces. The magnetic skeleton reveals that, at solar maximum, the global coronal field involves a multitude of topological structures at all latitudes crisscrossing throughout the atmosphere. Many openfield regions exist originating anywhere on the photosphere. At solar minimum, the coronal topology is heavily influenced by the solar magnetic dipole. A strong dipole results in a simple largescale structure involving just two large polar openfield regions, but, at short radial distances between ± 60° latitude, the smallscale topology is complex. If the solar magnetic dipole if weak, as in the recent minimum, then the lowlatitude quietsun magnetic fields may be globally significant enough to create many disconnected openfield regions between ± 60° latitude, in addition to the two polar openfield regions.

Dynamic properties of bright points in an active region
http://hdl.handle.net/10023/5264
Context. Bright points (BPs) are smallscale, magnetic features ubiquitous across the solar surface. Previously, we have observed and noted their properties for quiet Sun regions. Here, we determine the dynamic properties of BPs using simultaneous quiet Sun and active region data. Aims. The aim of this paper is to compare the properties of BPs in both active and quiet Sun regions and to determine any difference in the dynamics and general properties of BPs as a result of the varying magnetic activity within these two regions. Methods. High spatial and temporal resolution Gband observations of active region AR11372 were obtained with the Rapid Oscillations in the Solar Atmosphere instrument at the Dunn Solar Telescope. Three subfields of varying polarity and magnetic flux density were selected with the aid of magnetograms obtained from the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory. Bright points within these subfields were subsequently tracked and analysed. Results. It is found that BPs within active regions display attenuated velocity distributions with an average horizontal velocity of ∼0.6 km s1, compared to the quiet region which had an average velocity of 0.9 km s1. Active region BPs are also ∼21% larger than quiet region BPs and have longer average lifetimes (∼132 s) than their quiet region counterparts (88 s). No preferential flow directions are observed within the active region subfields. The diffusion index (γ) is estimated at ∼1.2 for the three regions. Conclusions. We confirm that the dynamic properties of BPs arise predominately from convective motions. The presence of stronger field strengths within active regions is the likely reason behind the varying properties observed. We believe that larger amounts of magnetic flux will attenuate BP velocities by a combination of restricting motion within the intergranular lanes and by increasing the number of stagnation points produced by inhibited convection. Larger BPs are found in regions of higher magnetic flux density and we believe that lifetimes increase in active regions as the magnetic flux stabilises the BPs.
This work has been supported by the UK Science and Technology Facilities Council (STFC). Observations were obtained at the National Solar Observatory, operated by the Association of Universities for Research in Astronomy, Inc. (AURA), under cooperative agreement with the National Science Foundation. D.B.J. would like to thank the STFC for an Ernest Rutherford Fellowship. We are also grateful for support sponsored by the Air Force Office of Scientific Research, Air Force Material Command, USAF under grant number FA86550913085.
Fri, 20 Jun 2014 00:00:00 GMT
http://hdl.handle.net/10023/5264
20140620T00:00:00Z
Keys, P.H.
Mathioudakis, M.
Jess, D.B.
MacKay, D.H.
Keenan, F.P.
Context. Bright points (BPs) are smallscale, magnetic features ubiquitous across the solar surface. Previously, we have observed and noted their properties for quiet Sun regions. Here, we determine the dynamic properties of BPs using simultaneous quiet Sun and active region data. Aims. The aim of this paper is to compare the properties of BPs in both active and quiet Sun regions and to determine any difference in the dynamics and general properties of BPs as a result of the varying magnetic activity within these two regions. Methods. High spatial and temporal resolution Gband observations of active region AR11372 were obtained with the Rapid Oscillations in the Solar Atmosphere instrument at the Dunn Solar Telescope. Three subfields of varying polarity and magnetic flux density were selected with the aid of magnetograms obtained from the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory. Bright points within these subfields were subsequently tracked and analysed. Results. It is found that BPs within active regions display attenuated velocity distributions with an average horizontal velocity of ∼0.6 km s1, compared to the quiet region which had an average velocity of 0.9 km s1. Active region BPs are also ∼21% larger than quiet region BPs and have longer average lifetimes (∼132 s) than their quiet region counterparts (88 s). No preferential flow directions are observed within the active region subfields. The diffusion index (γ) is estimated at ∼1.2 for the three regions. Conclusions. We confirm that the dynamic properties of BPs arise predominately from convective motions. The presence of stronger field strengths within active regions is the likely reason behind the varying properties observed. We believe that larger amounts of magnetic flux will attenuate BP velocities by a combination of restricting motion within the intergranular lanes and by increasing the number of stagnation points produced by inhibited convection. Larger BPs are found in regions of higher magnetic flux density and we believe that lifetimes increase in active regions as the magnetic flux stabilises the BPs.

Vortical control of forced twodimensional turbulence
http://hdl.handle.net/10023/5236
A new numerical technique for the simulation of forced twodimensional turbulence[D. Dritschel and J. Fontane, “The combined Lagrangian advection method,” J. Comput. Phys.229, 5408–5417 (Year: 2010)10.1016/j.jcp.2010.03.048] is used to examine the validity of KraichnanBatchelor scaling laws at higher Reynolds number than previously accessible with classical pseudospectral methods, making use of large simulation ensembles to allow a detailed consideration of the inverse cascade in a quasisteady state. Our results support the recent finding of Scott [R. Scott, “Nonrobustness of the twodimensional turbulent inverse cascade,” Phys. Rev. E75, 046301 (Year: 2007)10.1103/PhysRevE.75.046301], namely that when a direct enstrophy cascading range is wellrepresented numerically, a steeper energy spectrum proportional to k−2 is obtained in place of the classical k −5/3 prediction. It is further shown that this steep spectrum is associated with a faster growth of energy at large scales, scaling like t −1 rather than Kraichnan's prediction of t −3/2. The deviation from Kraichnan's theory is related to the emergence of a population of vortices that dominate the distribution of energy across scales, and whose number density and vorticity distribution with respect to vortex area are related to the shape of the enstrophy spectrum. An analytical model is proposed which closely matches the numerical spectra between the large scales and the forcing scale.
Jérôme Fontane is supported by the European Community in the framework of the CONVECT project under Grant No. PIEFGA2008221003.
Mon, 14 Jan 2013 00:00:00 GMT
http://hdl.handle.net/10023/5236
20130114T00:00:00Z
Fontane, Jerome Jacob Louis
Dritschel, David Gerard
Scott, Richard Kirkness
A new numerical technique for the simulation of forced twodimensional turbulence[D. Dritschel and J. Fontane, “The combined Lagrangian advection method,” J. Comput. Phys.229, 5408–5417 (Year: 2010)10.1016/j.jcp.2010.03.048] is used to examine the validity of KraichnanBatchelor scaling laws at higher Reynolds number than previously accessible with classical pseudospectral methods, making use of large simulation ensembles to allow a detailed consideration of the inverse cascade in a quasisteady state. Our results support the recent finding of Scott [R. Scott, “Nonrobustness of the twodimensional turbulent inverse cascade,” Phys. Rev. E75, 046301 (Year: 2007)10.1103/PhysRevE.75.046301], namely that when a direct enstrophy cascading range is wellrepresented numerically, a steeper energy spectrum proportional to k−2 is obtained in place of the classical k −5/3 prediction. It is further shown that this steep spectrum is associated with a faster growth of energy at large scales, scaling like t −1 rather than Kraichnan's prediction of t −3/2. The deviation from Kraichnan's theory is related to the emergence of a population of vortices that dominate the distribution of energy across scales, and whose number density and vorticity distribution with respect to vortex area are related to the shape of the enstrophy spectrum. An analytical model is proposed which closely matches the numerical spectra between the large scales and the forcing scale.

Resistive magnetohydrodynamic reconnection : resolving longterm, chaotic dynamics
http://hdl.handle.net/10023/5233
In this paper, we address the longterm evolution of an idealised double current system entering reconnection regimes where chaotic behavior plays a prominent role. Our aim is to quantify the energetics in high magnetic Reynolds number evolutions, enriched by secondary tearing events, multiple magnetic island coalescence, and compressive versus resistive heating scenarios. Our study will pay particular attention to the required numerical resolutions achievable by modern (gridadaptive) computations, and comment on the challenge associated with resolving chaotic island formation and interaction. We will use shockcapturing, conservative, gridadaptive simulations for investigating trends dominated by both physical (resistivity) and numerical (resolution) parameters, and confront them with (visco)resistive magnetohydrodynamic simulations performed with very different, but equally widely used discretization schemes. This will allow us to comment on the obtained evolutions in a manner irrespective of the adopted discretization strategy. Our findings demonstrate that all schemes used (finite volume based shockcapturing, high order finite differences, and particle in celllike methods) qualitatively agree on the various evolutionary stages, and that resistivity values of order 0.001 already can lead to chaotic island appearance. However, none of the methods exploited demonstrates convergence in the strong sense in these chaotic regimes. At the same time, nonperturbed tests for showing convergence over long time scales in ideal to resistive regimes are provided as well, where all methods are shown to agree. Both the advantages and disadvantages of specific discretizations as applied to this challenging problem are discussed.
We acknowledge financial support from the EC FP7/20072013 Grant Agreement SWIFF (No. 263340) and from project GOA/2009/009 (KU Leuven). This research has been funded by the Interuniversity Attraction Poles Programme initiated by the Belgian Science Policy Office (IAP P7/08 CHARM). Part of the simulations used the infrastructure of the VSCFlemish Supercomputer Center, funded by the Hercules Foundation and the Flemish GovernmentDepartment EWI. Another part of the simulations was done at the former Danish Center for Scientific Computing at Copenhagen University which is now part of DeIC Danish eInfrastructure Cooperation.
Fri, 13 Sep 2013 00:00:00 GMT
http://hdl.handle.net/10023/5233
20130913T00:00:00Z
Keppens, R.
Porth, O.
Galsgaard, K.
Frederiksen, J.T.
Restante, A.L.
Lapenta, G.
Parnell, C.
In this paper, we address the longterm evolution of an idealised double current system entering reconnection regimes where chaotic behavior plays a prominent role. Our aim is to quantify the energetics in high magnetic Reynolds number evolutions, enriched by secondary tearing events, multiple magnetic island coalescence, and compressive versus resistive heating scenarios. Our study will pay particular attention to the required numerical resolutions achievable by modern (gridadaptive) computations, and comment on the challenge associated with resolving chaotic island formation and interaction. We will use shockcapturing, conservative, gridadaptive simulations for investigating trends dominated by both physical (resistivity) and numerical (resolution) parameters, and confront them with (visco)resistive magnetohydrodynamic simulations performed with very different, but equally widely used discretization schemes. This will allow us to comment on the obtained evolutions in a manner irrespective of the adopted discretization strategy. Our findings demonstrate that all schemes used (finite volume based shockcapturing, high order finite differences, and particle in celllike methods) qualitatively agree on the various evolutionary stages, and that resistivity values of order 0.001 already can lead to chaotic island appearance. However, none of the methods exploited demonstrates convergence in the strong sense in these chaotic regimes. At the same time, nonperturbed tests for showing convergence over long time scales in ideal to resistive regimes are provided as well, where all methods are shown to agree. Both the advantages and disadvantages of specific discretizations as applied to this challenging problem are discussed.

The effect of slip length on vortex rebound from a rigid boundary
http://hdl.handle.net/10023/5232
The problem of a dipole incident normally on a rigid boundary, for moderate to large Reynolds numbers, has recently been treated numerically using a volume penalisation method by Nguyen van yen, Farge, and Schneider [Phys. Rev. Lett.106, 184502 (2011)]. Their results indicate that energy dissipating structures persist in the inviscid limit. They found that the use of penalisation methods intrinsically introduces some slip at the boundary wall, where the slip approaches zero as the Reynolds number goes to infinity, so reducing to the noslip case in this limit. We study the same problem, for both noslip and partial slip cases, using compact differences on a Chebyshev grid in the direction normal to the wall and Fourier methods in the direction along the wall. We find that for the noslip case there is no indication of the persistence of energy dissipating structures in the limit as viscosity approaches zero and that this also holds for any fixed slip length. However, when the slip length is taken to vary inversely with Reynolds number then the results of Nguyen van yen et al. are regained. It therefore appears that the prediction that energy dissipating structures persist in the inviscid limit follows from the two limits of wall slip length going to zero, and viscosity going to zero, not being treated independently in their use of the volume penalisation method.
Mon, 23 Sep 2013 00:00:00 GMT
http://hdl.handle.net/10023/5232
20130923T00:00:00Z
Sutherland, D.
Macaskill, C.
Dritschel, D.G.
The problem of a dipole incident normally on a rigid boundary, for moderate to large Reynolds numbers, has recently been treated numerically using a volume penalisation method by Nguyen van yen, Farge, and Schneider [Phys. Rev. Lett.106, 184502 (2011)]. Their results indicate that energy dissipating structures persist in the inviscid limit. They found that the use of penalisation methods intrinsically introduces some slip at the boundary wall, where the slip approaches zero as the Reynolds number goes to infinity, so reducing to the noslip case in this limit. We study the same problem, for both noslip and partial slip cases, using compact differences on a Chebyshev grid in the direction normal to the wall and Fourier methods in the direction along the wall. We find that for the noslip case there is no indication of the persistence of energy dissipating structures in the limit as viscosity approaches zero and that this also holds for any fixed slip length. However, when the slip length is taken to vary inversely with Reynolds number then the results of Nguyen van yen et al. are regained. It therefore appears that the prediction that energy dissipating structures persist in the inviscid limit follows from the two limits of wall slip length going to zero, and viscosity going to zero, not being treated independently in their use of the volume penalisation method.

Progress towards numerical and experimental simulations of fusion relevant beam instabilities
http://hdl.handle.net/10023/5186
In certain plasmas, nonthermal electron distributions can produce instabilities. These instabilities may be useful or potentially disruptive. Therefore the study of these instabilities is of importance in a variety of fields including fusion science and astrophysics. Following on from previous work conducted at the University of Strathclyde on the cyclotron resonance maser instability that was relevant to astrophysical radiowave generation, further instabilities are being investigated. Particular instabilities of interest are the anomalous Doppler instability which can occur in magnetic confinement fusion plasmas and the twostream instability that is of importance in fastignition inertial confinement fusion. To this end, computational simulations have been undertaken to investigate the behaviour of both the anomalous Doppler and twostream instabilities with the goal of designing an experiment to observe these behaviours in a laboratory.
Wed, 07 May 2014 00:00:00 GMT
http://hdl.handle.net/10023/5186
20140507T00:00:00Z
King, M.
Bryson, R.
Ronald, K.
Cairns, R. A.
McConville, S. L.
Speirs, D. C.
Phelps, A. D. R.
Bingham, R.
Gillespie, K. M.
Cross, A. W.
Vorgul, I.
Trines, R.
In certain plasmas, nonthermal electron distributions can produce instabilities. These instabilities may be useful or potentially disruptive. Therefore the study of these instabilities is of importance in a variety of fields including fusion science and astrophysics. Following on from previous work conducted at the University of Strathclyde on the cyclotron resonance maser instability that was relevant to astrophysical radiowave generation, further instabilities are being investigated. Particular instabilities of interest are the anomalous Doppler instability which can occur in magnetic confinement fusion plasmas and the twostream instability that is of importance in fastignition inertial confinement fusion. To this end, computational simulations have been undertaken to investigate the behaviour of both the anomalous Doppler and twostream instabilities with the goal of designing an experiment to observe these behaviours in a laboratory.

Scaled Experiment to Investigate Auroral Kilometric Radiation Mechanisms in the Presence of Background Electrons
http://hdl.handle.net/10023/5185
Auroral Kilometric Radiation (AKR) emissions occur at frequencies similar to 300kHz polarised in the Xmode with efficiencies similar to 12% [1,2] in the auroral density cavity in the polar regions of the Earth's magnetosphere, a region of low density plasma similar to 3200km above the Earth's surface, where electrons are accelerated down towards the Earth whilst undergoing magnetic compression. As a result of this magnetic compression the electrons acquire a horseshoe distribution function in velocity space. Previous theoretical studies have predicted that this distribution is capable of driving the cyclotron maser instability. To test this theory a scaled laboratory experiment was constructed to replicate this phenomenon in a controlled environment, [35] whilst 2D and 3D simulations are also being conducted to predict the experimental radiation power and mode, [69]. The experiment operates in the microwave frequency regime and incorporates a region of increasing magnetic field as found at the Earth's pole using magnet solenoids to encase the cylindrical interaction waveguide through which an initially rectilinear electron beam (12A) was accelerated by a 75keV pulse. Experimental results showed evidence of the formation of the horseshoe distribution function. The radiation was produced in the near cutoff TE01 mode, comparable with Xmode characteristics, at 4.42GHz. Peak microwave output power was measured similar to 35kW and peak efficiency of emission similar to 2%, [3]. A Penning trap was constructed and inserted into the interaction waveguide to enable generation of a background plasma which would lead to closer comparisons with the magnetospheric conditions. Initial design and measurements are presented showing the principle features of the new geometry.
Wed, 07 May 2014 00:00:00 GMT
http://hdl.handle.net/10023/5185
20140507T00:00:00Z
McConville, S. L.
Ronald, K.
Speirs, D. C.
Gillespie, K. M.
Phelps, A. D. R.
Cross, A. W.
Bingham, R.
Robertson, C. W.
Whyte, C. G.
He, W.
King, M.
Bryson, R.
Vorgul, I.
Cairns, R. A.
Kellett, B. J.
Auroral Kilometric Radiation (AKR) emissions occur at frequencies similar to 300kHz polarised in the Xmode with efficiencies similar to 12% [1,2] in the auroral density cavity in the polar regions of the Earth's magnetosphere, a region of low density plasma similar to 3200km above the Earth's surface, where electrons are accelerated down towards the Earth whilst undergoing magnetic compression. As a result of this magnetic compression the electrons acquire a horseshoe distribution function in velocity space. Previous theoretical studies have predicted that this distribution is capable of driving the cyclotron maser instability. To test this theory a scaled laboratory experiment was constructed to replicate this phenomenon in a controlled environment, [35] whilst 2D and 3D simulations are also being conducted to predict the experimental radiation power and mode, [69]. The experiment operates in the microwave frequency regime and incorporates a region of increasing magnetic field as found at the Earth's pole using magnet solenoids to encase the cylindrical interaction waveguide through which an initially rectilinear electron beam (12A) was accelerated by a 75keV pulse. Experimental results showed evidence of the formation of the horseshoe distribution function. The radiation was produced in the near cutoff TE01 mode, comparable with Xmode characteristics, at 4.42GHz. Peak microwave output power was measured similar to 35kW and peak efficiency of emission similar to 2%, [3]. A Penning trap was constructed and inserted into the interaction waveguide to enable generation of a background plasma which would lead to closer comparisons with the magnetospheric conditions. Initial design and measurements are presented showing the principle features of the new geometry.

3D PiC code investigations of Auroral Kilometric Radiation mechanisms
http://hdl.handle.net/10023/5184
Efficient (similar to 1%) electron cyclotron radio emissions are known to originate in the X mode from regions of locally depleted plasma in the Earths polar magnetosphere. These emissions are commonly referred to as the Auroral Kilometric Radiation (AKR). AKR occurs naturally in these polar regions where electrons are accelerated by electric fields into the increasing planetary magnetic dipole. Here conservation of the magnetic moment converts axial to rotational momentum forming a horseshoe distribution in velocity phase space. This distribution is unstable to cyclotron emission with radiation emitted in the Xmode. Initial studies were conducted in the form of 2D PiC code simulations [1] and a scaled laboratory experiment that was constructed to reproduce the mechanism of AKR. As studies progressed, 3D PiC code simulations were conducted to enable complete investigation of the complex interaction dimensions. A maximum efficiency of 1.25% is predicted from these simulations in the same mode and frequency as measured in the experiment. This is also consistent with geophysical observations and the predictions of theory.
Wed, 01 Jan 2014 00:00:00 GMT
http://hdl.handle.net/10023/5184
20140101T00:00:00Z
Gillespie, K. M.
McConville, S. L.
Speirs, D. C.
Ronald, K.
Phelps, A. D. R.
Bingham, R.
Cross, A. W.
Robertson, C. W.
Whyte, C. G.
He, W.
Vorgul, I.
Cairns, R. A.
Kellett, B. J.
Efficient (similar to 1%) electron cyclotron radio emissions are known to originate in the X mode from regions of locally depleted plasma in the Earths polar magnetosphere. These emissions are commonly referred to as the Auroral Kilometric Radiation (AKR). AKR occurs naturally in these polar regions where electrons are accelerated by electric fields into the increasing planetary magnetic dipole. Here conservation of the magnetic moment converts axial to rotational momentum forming a horseshoe distribution in velocity phase space. This distribution is unstable to cyclotron emission with radiation emitted in the Xmode. Initial studies were conducted in the form of 2D PiC code simulations [1] and a scaled laboratory experiment that was constructed to reproduce the mechanism of AKR. As studies progressed, 3D PiC code simulations were conducted to enable complete investigation of the complex interaction dimensions. A maximum efficiency of 1.25% is predicted from these simulations in the same mode and frequency as measured in the experiment. This is also consistent with geophysical observations and the predictions of theory.

Numerical simulation of unconstrained cyclotron resonant maser emission
http://hdl.handle.net/10023/5183
When a mainly rectilinear electron beam is subject to significant magnetic compression, conservation of magnetic moment results in the formation of a horseshoe shaped velocity distribution. It has been shown that such a distribution is unstable to cyclotron emission and may be responsible for the generation of Auroral Kilometric Radiation (AKR) an intense rf emission sourced at high altitudes in the terrestrial auroral magnetosphere. PiC code simulations have been undertaken to investigate the dynamics of the cyclotron emission process in the absence of cavity boundaries with particular consideration of the spatial growth rate, spectral output and rf conversion efficiency. Computations reveal that a welldefined cyclotron emission process occurs albeit with a low spatial growth rate compared to waveguide bounded simulations. The rf output is near perpendicular to the electron beam with a slight backwardwave character reflected in the spectral output with a well defined peak at 2.68GHz, just below the relativistic electron cyclotron frequency. The corresponding rf conversion efficiency of 1.1% is comparable to waveguide bounded simulations and consistent with the predictions of kinetic theory that suggest efficient, spectrally well defined radiation emission can be obtained from an electron horseshoe distribution in the absence of radiation boundaries.
Wed, 07 May 2014 00:00:00 GMT
http://hdl.handle.net/10023/5183
20140507T00:00:00Z
Speirs, D. C.
Gillespie, K. M.
Ronald, K.
McConville, S. L.
Phelps, A. D. R.
Cross, A. W.
Bingham, R.
Kellett, B. J.
Cairns, R. A.
Vorgul, I.
When a mainly rectilinear electron beam is subject to significant magnetic compression, conservation of magnetic moment results in the formation of a horseshoe shaped velocity distribution. It has been shown that such a distribution is unstable to cyclotron emission and may be responsible for the generation of Auroral Kilometric Radiation (AKR) an intense rf emission sourced at high altitudes in the terrestrial auroral magnetosphere. PiC code simulations have been undertaken to investigate the dynamics of the cyclotron emission process in the absence of cavity boundaries with particular consideration of the spatial growth rate, spectral output and rf conversion efficiency. Computations reveal that a welldefined cyclotron emission process occurs albeit with a low spatial growth rate compared to waveguide bounded simulations. The rf output is near perpendicular to the electron beam with a slight backwardwave character reflected in the spectral output with a well defined peak at 2.68GHz, just below the relativistic electron cyclotron frequency. The corresponding rf conversion efficiency of 1.1% is comparable to waveguide bounded simulations and consistent with the predictions of kinetic theory that suggest efficient, spectrally well defined radiation emission can be obtained from an electron horseshoe distribution in the absence of radiation boundaries.

Laminar shocks in high power laser plasma interactions
http://hdl.handle.net/10023/5180
We propose a theory to describe laminar ion sound structures in a collisionless plasma. Reflection of a small fraction of the upstream ions converts the well known ion acoustic soliton into a structure with a steep potential gradient upstream and with downstream oscillations. The theory provides a simple interpretation of results dating back more than forty years but, more importantly, is shown to provide an explanation for recent observations on laser produced plasmas relevant to inertial fusion and to ion acceleration. (C) 2014 AIP Publishing LLC.
Sat, 01 Feb 2014 00:00:00 GMT
http://hdl.handle.net/10023/5180
20140201T00:00:00Z
Cairns, R. A.
Bingham, R.
Norreys, P.
Trines, R.
We propose a theory to describe laminar ion sound structures in a collisionless plasma. Reflection of a small fraction of the upstream ions converts the well known ion acoustic soliton into a structure with a steep potential gradient upstream and with downstream oscillations. The theory provides a simple interpretation of results dating back more than forty years but, more importantly, is shown to provide an explanation for recent observations on laser produced plasmas relevant to inertial fusion and to ion acceleration. (C) 2014 AIP Publishing LLC.

Effect of collisions on amplification of laser beams by Brillouin scattering in plasmas
http://hdl.handle.net/10023/5173
We report on particle in cell simulations of energy transfer between a laser pump beam and a counterpropagating seed beam using the Brillouin scattering process in uniform plasma including collisions. The results presented show that the ion acoustic waves excited through naturally occurring Brillouin scattering of the pump field are preferentially damped without affecting the driven Brillouin scattering process resulting from the beating of the pump and seed fields together. We find that collisions, including the effects of Landau damping, allow for a more efficient transfer of energy between the laser beams, and a significant reduction in the amount of seed prepulse produced.
Authors KH, RT, DCS, RAC, RB were supported by EPSRC grant EP/G04239X/1.
Tue, 01 Oct 2013 00:00:00 GMT
http://hdl.handle.net/10023/5173
20131001T00:00:00Z
Humphrey, K. A.
Trines, R. M. G. M.
Fiuza, F.
Speirs, D. C.
Norreys, P.
Cairns, R. A.
Silva, L. O.
Bingham, R.
We report on particle in cell simulations of energy transfer between a laser pump beam and a counterpropagating seed beam using the Brillouin scattering process in uniform plasma including collisions. The results presented show that the ion acoustic waves excited through naturally occurring Brillouin scattering of the pump field are preferentially damped without affecting the driven Brillouin scattering process resulting from the beating of the pump and seed fields together. We find that collisions, including the effects of Landau damping, allow for a more efficient transfer of energy between the laser beams, and a significant reduction in the amount of seed prepulse produced.

Quasigeostrophic shallowwater doublyconnected vortex equilibria and their stability
http://hdl.handle.net/10023/5172
We examine the form, properties, stability and evolution of doublyconnected (twovortex) relative equilibria in the singlelayer ƒplane quasigeostrophic shallowwater model of geophysical fluid dynamics. Three parameters completely describe families of equilibria in this system: the ratio γ =L/LD between the horizontal size of the vortices and the Rossby deformation length; the area ratio α of the smaller to the larger vortex; and the minimum distance δ between the two vortices. We vary 0 < γ ≤ 10 and 0.1 ≤ α ≤ 1.0, determining the boundary of stability δ = δC(γ,α). We also examine the nonlinear development of the instabilities and the transitions to other nearequilibrium configurations. Two modes of instability occur when δ < δC: a small γ asymmetric (wave 3) mode, which is absent for α ≳ 0.6; and a large γ mode. In general, major structural changes take place during the nonlinear evolution of the vortices, which near δC may be classified as follows: (i) vacillations about equilibrium for γ ≳ 2.5; (ii) partial straining out, associated with the small γ mode, where either one or both of the vortices get smaller for γ ≲ 2.5 and α ≲ 0.6; (iii) partial merger, occurring at the transition region between the two modes of instability, where one of the vortices gets bigger, and (iv) complete merger, associated with the largeγ mode. We also find that although conservative inviscid transitions to equilibria with the same energy, angular momentum and circulation are possible, they are not the preferred evolutionary path.
H.P. acknowledges the support of a NERC studentship. D.G.D. received support for this research from the UK Engineering and Physical Sciences Research Council (grant EP/H001794/1).
Wed, 01 May 2013 00:00:00 GMT
http://hdl.handle.net/10023/5172
20130501T00:00:00Z
Plotka, Hanna
Dritschel, David Gerard
We examine the form, properties, stability and evolution of doublyconnected (twovortex) relative equilibria in the singlelayer ƒplane quasigeostrophic shallowwater model of geophysical fluid dynamics. Three parameters completely describe families of equilibria in this system: the ratio γ =L/LD between the horizontal size of the vortices and the Rossby deformation length; the area ratio α of the smaller to the larger vortex; and the minimum distance δ between the two vortices. We vary 0 < γ ≤ 10 and 0.1 ≤ α ≤ 1.0, determining the boundary of stability δ = δC(γ,α). We also examine the nonlinear development of the instabilities and the transitions to other nearequilibrium configurations. Two modes of instability occur when δ < δC: a small γ asymmetric (wave 3) mode, which is absent for α ≳ 0.6; and a large γ mode. In general, major structural changes take place during the nonlinear evolution of the vortices, which near δC may be classified as follows: (i) vacillations about equilibrium for γ ≳ 2.5; (ii) partial straining out, associated with the small γ mode, where either one or both of the vortices get smaller for γ ≲ 2.5 and α ≲ 0.6; (iii) partial merger, occurring at the transition region between the two modes of instability, where one of the vortices gets bigger, and (iv) complete merger, associated with the largeγ mode. We also find that although conservative inviscid transitions to equilibria with the same energy, angular momentum and circulation are possible, they are not the preferred evolutionary path.

The influence of the magnetic field on running penumbral waves in the solar chromosphere
http://hdl.handle.net/10023/5155
We use images of high spatial and temporal resolution, obtained using both ground and spacebased instrumentation, to investigate the role magnetic field inclination angles play in the propagation characteristics of running penumbral waves in the solar chromosphere. Analysis of a nearcircular sunspot, close to the center of the solar disk, reveals a smooth rise in oscillatory period as a function of distance from the umbral barycenter. However, in one directional quadrant, corresponding to the north direction, a pronounced kink in the perioddistance diagram is found. Utilizing a combination of the inversion of magnetic Stokes vectors and forcefree field extrapolations, we attribute this behavior to the cutoff frequency imposed by the magnetic field geometry in this location. A rapid, localized inclination of the magnetic field lines in the north direction results in a faster increase in the dominant periodicity due to an accelerated reduction in the cutoff frequency. For the first time, we reveal how the spatial distribution of dominant wave periods, obtained with one of the highest resolution solar instruments currently available, directly reflects the magnetic geometry of the underlying sunspot, thus opening up a wealth of possibilities in future magnetohydrodynamic seismology studies. In addition, the intrinsic relationships we find between the underlying magnetic field geometries connecting the photosphere to the chromosphere, and the characteristics of running penumbral waves observed in the upper chromosphere, directly supports the interpretation that running penumbral wave phenomena are the chromospheric signature of upwardly propagating magnetoacoustic waves generated in the photosphere.
D.B.J. acknowledges the European Commission and the Fonds Wetenschappelijk Onderzoek (FWO) for the award of a Marie Curie Pegasus Fellowship during which this work was initiated, in addition to the UK Science and Technology Facilities Council (STFC) for the award of an Ernest Rutherford Fellowship which allowed the completion of this project. The research carried out by V.E.R. is partly supported by grant MC FP7PEOPLE2011IRSES295272. T.V.D. acknowledges funding from the Odysseus Programme of the FWO Vlaanderen and from the EU's 7th Framework Programme as an ERG with grant number 276808. P.H.K. and D.H.M. are grateful to STFC for research support. This research has been funded by the Interuniversity Attraction Poles Programme initiated by the Belgian Science Policy Office (IAP P7/08 CHARM).
Tue, 03 Dec 2013 00:00:00 GMT
http://hdl.handle.net/10023/5155
20131203T00:00:00Z
Jess, David
Reznikova, V
Van Doorsselaere, Tom
Mackay, Duncan Hendry
Keys, Peter
We use images of high spatial and temporal resolution, obtained using both ground and spacebased instrumentation, to investigate the role magnetic field inclination angles play in the propagation characteristics of running penumbral waves in the solar chromosphere. Analysis of a nearcircular sunspot, close to the center of the solar disk, reveals a smooth rise in oscillatory period as a function of distance from the umbral barycenter. However, in one directional quadrant, corresponding to the north direction, a pronounced kink in the perioddistance diagram is found. Utilizing a combination of the inversion of magnetic Stokes vectors and forcefree field extrapolations, we attribute this behavior to the cutoff frequency imposed by the magnetic field geometry in this location. A rapid, localized inclination of the magnetic field lines in the north direction results in a faster increase in the dominant periodicity due to an accelerated reduction in the cutoff frequency. For the first time, we reveal how the spatial distribution of dominant wave periods, obtained with one of the highest resolution solar instruments currently available, directly reflects the magnetic geometry of the underlying sunspot, thus opening up a wealth of possibilities in future magnetohydrodynamic seismology studies. In addition, the intrinsic relationships we find between the underlying magnetic field geometries connecting the photosphere to the chromosphere, and the characteristics of running penumbral waves observed in the upper chromosphere, directly supports the interpretation that running penumbral wave phenomena are the chromospheric signature of upwardly propagating magnetoacoustic waves generated in the photosphere.

Simulating the formation of a sigmoidal flux rope in AR10977 from SOHO/MDI magnetograms
http://hdl.handle.net/10023/5154
The modeling technique of Mackay et al. is applied to simulate the coronal magnetic field of NOAA active region AR10977 over a seven day period (2007 December 210). The simulation is driven with a sequence of lineofsight component magnetograms from SOHO/MDI and evolves the coronal magnetic field though a continuous series of nonlinear forcefree states. Upon comparison with Hinode/XRT observations, results show that the simulation reproduces many features of the active region's evolution. In particular, it describes the formation of a flux rope across the polarity inversion line during flux cancellation. The flux rope forms at the same location as an observed Xray sigmoid. After five days of evolution, the free magnetic energy contained within the flux rope was found to be 3.9 × 1030 erg. This value is more than sufficient to account for the B1.4 GOES flare observed from the active region on 2007 December 7. At the time of the observed eruption, the flux rope was found to contain 20% of the active region flux. We conclude that the modeling technique proposed in Mackay et al.—which directly uses observed magnetograms to energize the coronal field—is a viable method to simulate the evolution of the coronal magnetic field.
G.P.S.G. acknowledges STFC for financial support. D.H.M. acknowledges the STFC, the Leverhulme Trust, and the EU FP7 funded project "SWIFF" (263340) for financial support. L.M.G. acknowledges to the Royal Society for a University Research Fellowship. K.A.M. acknowledges the Leverhulme Trust for financial support. Simulations were carried out on a STFC/SRIF funded UKMHD cluster at St Andrews.
Thu, 20 Feb 2014 00:00:00 GMT
http://hdl.handle.net/10023/5154
20140220T00:00:00Z
Gibb, Gordon Peter Samuel
Mackay, Duncan Hendry
Green, Lucie
Meyer, Karen Alison
The modeling technique of Mackay et al. is applied to simulate the coronal magnetic field of NOAA active region AR10977 over a seven day period (2007 December 210). The simulation is driven with a sequence of lineofsight component magnetograms from SOHO/MDI and evolves the coronal magnetic field though a continuous series of nonlinear forcefree states. Upon comparison with Hinode/XRT observations, results show that the simulation reproduces many features of the active region's evolution. In particular, it describes the formation of a flux rope across the polarity inversion line during flux cancellation. The flux rope forms at the same location as an observed Xray sigmoid. After five days of evolution, the free magnetic energy contained within the flux rope was found to be 3.9 × 1030 erg. This value is more than sufficient to account for the B1.4 GOES flare observed from the active region on 2007 December 7. At the time of the observed eruption, the flux rope was found to contain 20% of the active region flux. We conclude that the modeling technique proposed in Mackay et al.—which directly uses observed magnetograms to energize the coronal field—is a viable method to simulate the evolution of the coronal magnetic field.

First comparison of wave observations from CoMP and AIA/SDO
http://hdl.handle.net/10023/5153
Context. Waves have long been thought to contribute to the heating of the solar corona and the generation of the solar wind. Recent observations have demonstrated evidence of quasiperiodic longitudinal disturbances and ubiquitous transverse wave propagation in many different coronal environments. Aims. This paper investigates signatures of different types of oscillatory behaviour, both above the solar limb and ondisk, by comparing findings from the Coronal Multichannel Polarimeter (CoMP) and the Atmospheric Imaging Assembly (AIA) onboard the Solar Dynamics Observatory (SDO) for the same active region. Methods. We study both transverse and longitudinal motion by comparing and contrasting timedistance images of parallel and perpendicular cuts along/across active region fan loops. Comparisons between parallel spacetime diagram features in CoMP Doppler velocity and transverse oscillations in AIA images are made, together with spacetime analysis of propagating quasiperiodic intensity features seen near the base of loops in AIA. Results. Signatures of transverse motions are observed along the same magnetic structure using CoMP Doppler velocity (vphase = 600 → 750 km s1, P = 3 → 6 min) and in AIA/SDO above the limb (P = 3 → 8 min). Quasiperiodic intensity features (vphase = 100 → 200 km s1, P = 6 → 11 min) also travel along the base of the same structure. On the disk, signatures of both transverse and longitudinal intensity features were observed by AIA, and both show similar properties to signatures found along structures anchored in the same active region three days earlier above the limb. Correlated features are recovered by spacetime analysis of neighbouring tracks over perpendicular distances of ≲2.6 Mm.
I.D.M. acknowledges support of a Royal Society University Research Fellowship. The research leading to these results has also received funding from the European Commission Seventh Framework Programme (FP7/20072013) under the grant agreements SOLSPANET (project No. 269299, www.solspanet.eu/solspanet).
Thu, 01 Aug 2013 00:00:00 GMT
http://hdl.handle.net/10023/5153
20130801T00:00:00Z
Threlfall, James William
De Moortel, Ineke
McIntosh, Scott
Bethge, Christian
Context. Waves have long been thought to contribute to the heating of the solar corona and the generation of the solar wind. Recent observations have demonstrated evidence of quasiperiodic longitudinal disturbances and ubiquitous transverse wave propagation in many different coronal environments. Aims. This paper investigates signatures of different types of oscillatory behaviour, both above the solar limb and ondisk, by comparing findings from the Coronal Multichannel Polarimeter (CoMP) and the Atmospheric Imaging Assembly (AIA) onboard the Solar Dynamics Observatory (SDO) for the same active region. Methods. We study both transverse and longitudinal motion by comparing and contrasting timedistance images of parallel and perpendicular cuts along/across active region fan loops. Comparisons between parallel spacetime diagram features in CoMP Doppler velocity and transverse oscillations in AIA images are made, together with spacetime analysis of propagating quasiperiodic intensity features seen near the base of loops in AIA. Results. Signatures of transverse motions are observed along the same magnetic structure using CoMP Doppler velocity (vphase = 600 → 750 km s1, P = 3 → 6 min) and in AIA/SDO above the limb (P = 3 → 8 min). Quasiperiodic intensity features (vphase = 100 → 200 km s1, P = 6 → 11 min) also travel along the base of the same structure. On the disk, signatures of both transverse and longitudinal intensity features were observed by AIA, and both show similar properties to signatures found along structures anchored in the same active region three days earlier above the limb. Correlated features are recovered by spacetime analysis of neighbouring tracks over perpendicular distances of ≲2.6 Mm.

Erratum : "a numerical model of standard to blowout jets" (2013, ApJL, 769, L21)
http://hdl.handle.net/10023/5152
Mon, 10 Jun 2013 00:00:00 GMT
http://hdl.handle.net/10023/5152
20130610T00:00:00Z
Archontis, Vasilis
Hood, Alan William

The emergence of weakly twisted magnetic fields in the Sun
http://hdl.handle.net/10023/5151
We have studied the emergence of a weakly twisted magnetic flux tube from the upper convection zone into the solar atmosphere. It is found that the rising magnetized plasma does not undergo the classical, single Ωshaped loop emergence, but it becomes unstable in two places, forming two magnetic lobes that are anchored in smallscale bipolar structures at the photosphere, between the two main flux concentrations. The two magnetic lobes rise and expand into the corona, forming an overall undulating magnetic flux system. The dynamical interaction of the lobes results in the triggering of highspeed and hot jets and the formation of successive cool and hot loops that coexist in the emerging flux region. Although the initial emerging field is weakly twisted, a highly twisted magnetic flux rope is formed at the low atmosphere, due to shearing and reconnection. The new flux rope (hereafter postemergence flux rope) does not erupt. It remains confined by the overlying field. Although there is no ejective eruption of the postemergence rope, it is found that a considerable amount of axial and azimuthal flux is transferred into the solar atmosphere during the emergence of the magnetic field.
The simulations were performed on the STFC and SRIF funded UKMHD cluster, at the University of St Andrews. K.T. and V.A. acknowledge EU support (IEF272549 grant).
Fri, 01 Nov 2013 00:00:00 GMT
http://hdl.handle.net/10023/5151
20131101T00:00:00Z
Archontis, Vasilis
Hood, Alan William
Tsinganos, K
We have studied the emergence of a weakly twisted magnetic flux tube from the upper convection zone into the solar atmosphere. It is found that the rising magnetized plasma does not undergo the classical, single Ωshaped loop emergence, but it becomes unstable in two places, forming two magnetic lobes that are anchored in smallscale bipolar structures at the photosphere, between the two main flux concentrations. The two magnetic lobes rise and expand into the corona, forming an overall undulating magnetic flux system. The dynamical interaction of the lobes results in the triggering of highspeed and hot jets and the formation of successive cool and hot loops that coexist in the emerging flux region. Although the initial emerging field is weakly twisted, a highly twisted magnetic flux rope is formed at the low atmosphere, due to shearing and reconnection. The new flux rope (hereafter postemergence flux rope) does not erupt. It remains confined by the overlying field. Although there is no ejective eruption of the postemergence rope, it is found that a considerable amount of axial and azimuthal flux is transferred into the solar atmosphere during the emergence of the magnetic field.

Production of smallscale Alfvén waves by ionospheric depletion, nonlinear magnetosphereionosphere coupling and phase mixing
http://hdl.handle.net/10023/5150
Rockets and satellites have previously observed smallscale Alfven waves inside largescale downward fieldaligned currents, and numerical simulations have associated their formation with selfconsistent magnetosphereionosphere coupling. The origin of these waves was previously attributed to ionospheric feedback instability; however, we show that they arise in numerical experiments in which the instability is excluded. A new interpretation is proposed in which strong ionospheric depletion and associated current broadening (a nonlinear steepening/wavebreaking process) form magnetosphereionosphere waves inside a downward current region and these oscillations drive upgoing inertial Alfven waves in the overlying plasma. The resulting waves are governed by characteristic periods, which are a good match to previously observed periods for reasonable assumed conditions. Meanwhile, wavelengths perpendicular to the magnetic field initially map to an ionospheric scale comparable to the electron inertial length for the lowaltitude magnetosphere, but become shorter with time due to frequencybased phase mixing of boundary waves (a new manifestation of phase mixing). Under suitable conditions, these could act as seeds for the ionospheric feedback instability.
The authors acknowledge the International Space Science Institute (Switzerland) for funding the program that inspired this work. AJBR is grateful to the Royal Commission for the Exhibition of 1851 for present support and acknowledges an STFC studentship that funded part of this work.
Wed, 03 Apr 2013 00:00:00 GMT
http://hdl.handle.net/10023/5150
20130403T00:00:00Z
Russell, A. J. B.
Wright, Andrew Nicholas
Streltsov, A. V.
Rockets and satellites have previously observed smallscale Alfven waves inside largescale downward fieldaligned currents, and numerical simulations have associated their formation with selfconsistent magnetosphereionosphere coupling. The origin of these waves was previously attributed to ionospheric feedback instability; however, we show that they arise in numerical experiments in which the instability is excluded. A new interpretation is proposed in which strong ionospheric depletion and associated current broadening (a nonlinear steepening/wavebreaking process) form magnetosphereionosphere waves inside a downward current region and these oscillations drive upgoing inertial Alfven waves in the overlying plasma. The resulting waves are governed by characteristic periods, which are a good match to previously observed periods for reasonable assumed conditions. Meanwhile, wavelengths perpendicular to the magnetic field initially map to an ionospheric scale comparable to the electron inertial length for the lowaltitude magnetosphere, but become shorter with time due to frequencybased phase mixing of boundary waves (a new manifestation of phase mixing). Under suitable conditions, these could act as seeds for the ionospheric feedback instability.

A numerical model of standard to blowout jets
http://hdl.handle.net/10023/5140
We report on threedimensional (3D) MHD simulations of the formation of jets produced during the emergence and eruption of solar magnetic fields. The interaction between an emerging and an ambient magnetic field in the solar atmosphere leads to (external) reconnection and the formation of "standard" jets with an inverse Yshaped configuration. Eventually, lowatmosphere (internal) reconnection of sheared fieldlines in the emerging flux region produces an erupting magnetic flux rope and a reconnection jet underneath it. The erupting plasma blows out the ambient field and, moreover, it unwinds as it is ejected into the outer solar atmosphere. The fast emission of the cool material that erupts together with the hot outflows due to external/internal reconnection form a wider "blowout" jet. We show the transition from "standard" to "blowout" jets and report on their 3D structure. The physical plasma properties of the jets are consistent with observational studies.
Thu, 09 May 2013 00:00:00 GMT
http://hdl.handle.net/10023/5140
20130509T00:00:00Z
Archontis, Vasilis
Hood, A. W.
We report on threedimensional (3D) MHD simulations of the formation of jets produced during the emergence and eruption of solar magnetic fields. The interaction between an emerging and an ambient magnetic field in the solar atmosphere leads to (external) reconnection and the formation of "standard" jets with an inverse Yshaped configuration. Eventually, lowatmosphere (internal) reconnection of sheared fieldlines in the emerging flux region produces an erupting magnetic flux rope and a reconnection jet underneath it. The erupting plasma blows out the ambient field and, moreover, it unwinds as it is ejected into the outer solar atmosphere. The fast emission of the cool material that erupts together with the hot outflows due to external/internal reconnection form a wider "blowout" jet. We show the transition from "standard" to "blowout" jets and report on their 3D structure. The physical plasma properties of the jets are consistent with observational studies.

SWIFF : space weather integrated forecasting framework
http://hdl.handle.net/10023/5049
SWIFF is a project funded by the Seventh Framework Programme of the European Commission to study the mathematicalphysics models that form the basis for space weather forecasting. The phenomena of space weather span a tremendous scale of densities and temperature with scales ranging 10 orders of magnitude in space and time. Additionally even in local regions there are concurrent processes developing at the electron, ion and global scales strongly interacting with each other. The fundamental challenge in modelling space weather is the need to address multiple physics and multiple scales. Here we present our approach to take existing expertise in fluid and kinetic models to produce an integrated mathematical approach and software infrastructure that allows fluid and kinetic processes to be modelled together. SWIFF aims also at using this new infrastructure to model specific coupled processes at the Solar Corona, in the interplanetary space and in the interaction at the Earth magnetosphere.
This research has received funding from the European Commission’s FP7 Program with the grant agreement SWIFF (Project No. 2633430, swiff.eu). The KU Leuven simulations were conducted on the computational resources provided by the PRACE Tier0 Project No. 2011050747 (Curie supercomputer) and by the Flemish Supercomputer Center (VIC3). Additional computational support is provided at KU Leuven by the NASA NCCS (Discover) and NAS (Pleiades) Divisons, as part of the support to the NASA MMS Mission. UNIPI acknowledges the HPC resources of CINECA made available within the Distributed European Computing Initiative by the PRACE2IP, receiving funding from the European Community’s Seventh Framework Programme (FP7/ 20072013) under Grant Agreement No. nRI283493. Work at UNIPI was supported by the Italian Supercomputing Center – CINECA under the ISCRA initiative. Work at UNIPI was supported by the HPCEUROPA2 project (Project No. 228398) with the support of the European Commission – Capacities Area – Research Infrastructures. Work performed at IAP, ASCR was supported also by the Project RVO: 68378289.
Mon, 18 Feb 2013 00:00:00 GMT
http://hdl.handle.net/10023/5049
20130218T00:00:00Z
Lapenta, Giovanni
Pierrard, Viviane
Keppens, Rony
Markidis, Stefano
Poedts, Stefaan
Šebek, Ondřej
Trávníček, Pavel M
Henri, Pierre
Califano, Francesco
Pegoraro, Francesco
Faganello, Matteo
Olshevsky, Vyacheslav
Restante, Anna Lisa
Nordlund, Åke
Trier Frederiksen, Jacob
Mackay, Duncan Hendry
Parnell, Clare Elizabeth
Bemporad, Alessandro
Susino, Roberto
Borremans, Kris
SWIFF is a project funded by the Seventh Framework Programme of the European Commission to study the mathematicalphysics models that form the basis for space weather forecasting. The phenomena of space weather span a tremendous scale of densities and temperature with scales ranging 10 orders of magnitude in space and time. Additionally even in local regions there are concurrent processes developing at the electron, ion and global scales strongly interacting with each other. The fundamental challenge in modelling space weather is the need to address multiple physics and multiple scales. Here we present our approach to take existing expertise in fluid and kinetic models to produce an integrated mathematical approach and software infrastructure that allows fluid and kinetic processes to be modelled together. SWIFF aims also at using this new infrastructure to model specific coupled processes at the Solar Corona, in the interplanetary space and in the interaction at the Earth magnetosphere.

Frequency of behavior witnessed and conformity in an everyday social context
http://hdl.handle.net/10023/5024
Conformity is thought to be an important force in human evolution because it has the potential to stabilize cultural homogeneity within groups and cultural diversity between groups. However, the effects of such conformity on cultural and biological evolution will depend much on the particular way in which individuals are influenced by the frequency of alternative behavioral options they witness. In a previous study we found that in a natural situation people displayed a tendency to be 'linearconformist'. When visitors to a Zoo exhibit were invited to write or draw answers to questions on cards to win a small prize and we manipulated the proportion of text versus drawings on display, we found a strong and significant effect of the proportion of text displayed on the proportion of text in the answers, a conformist effect that was largely linear with a small nonlinear component. However, although this overall effect is important to understand cultural evolution, it might mask a greater diversity of behavioral responses shaped by variables such as age, sex, social environment and attention of the participants. Accordingly we performed a further study explicitly to analyze the effects of these variables, together with the quality of the information participants' responses made available to further visitors. Results again showed a largely linear conformity effect that varied little with the variables analyzed. © 2014 Claidière et al.
Fri, 20 Jun 2014 00:00:00 GMT
http://hdl.handle.net/10023/5024
20140620T00:00:00Z
Claidière, N.
Bowler, M.
Brookes, S.
Brown, R.
Whiten, A.
Conformity is thought to be an important force in human evolution because it has the potential to stabilize cultural homogeneity within groups and cultural diversity between groups. However, the effects of such conformity on cultural and biological evolution will depend much on the particular way in which individuals are influenced by the frequency of alternative behavioral options they witness. In a previous study we found that in a natural situation people displayed a tendency to be 'linearconformist'. When visitors to a Zoo exhibit were invited to write or draw answers to questions on cards to win a small prize and we manipulated the proportion of text versus drawings on display, we found a strong and significant effect of the proportion of text displayed on the proportion of text in the answers, a conformist effect that was largely linear with a small nonlinear component. However, although this overall effect is important to understand cultural evolution, it might mask a greater diversity of behavioral responses shaped by variables such as age, sex, social environment and attention of the participants. Accordingly we performed a further study explicitly to analyze the effects of these variables, together with the quality of the information participants' responses made available to further visitors. Results again showed a largely linear conformity effect that varied little with the variables analyzed. © 2014 Claidière et al.

The transterminator ion flow at Venus at solar minimum
http://hdl.handle.net/10023/4795
The transterminator ion flow in the Venusian ionosphere is observed at solar minimum for the first time. Such a flow, which transports ions from the day to the nightside, has been observed previously around solar maximum. At solar minimum this transport process is severely inhibited by the lower altitude of the ionopause. The observations presented were those made of the Venusian ionospheric plasma by the ASPERA4 experiment onboard the Venus Express spacecraft, and which constitute the first extensive insitu measurements of the plasma near solar minimum. Observations near the terminator of the energies of ions of ionospheric origin showed asymmetry between the noon and midnight sectors, which indicated an antisunward ion flow with a velocity of (2.5 +/ 1.5) km s(1). It is suggested that this ion flow contributes to maintaining the nightside ionosphere near the terminator region at solar minimum. The interpretation of the result was reinforced by observed asymmetries in the ion number counts. The observed dawndusk asymmetry was consistent with a nightward transport of ions while the noonmidnight observations indicated that the flow was highly variable but could contribute to the maintenance of the nightside ionosphere.
Financial support for this paper was provided by the UK Science and Technology Facilities Council under grant PP/E001157/1.
Sat, 01 Dec 2012 00:00:00 GMT
http://hdl.handle.net/10023/4795
20121201T00:00:00Z
Wood, A. G.
Pryse, S. E.
Grande, M.
Whittaker, I. C.
Coates, A. J.
Husband, K.
Baumjohann, W.
Zhang, T. L.
Mazelle, C.
Kallio, E.
Fraenz, M.
McKennaLawlor, S.
Wurz, P.
The transterminator ion flow in the Venusian ionosphere is observed at solar minimum for the first time. Such a flow, which transports ions from the day to the nightside, has been observed previously around solar maximum. At solar minimum this transport process is severely inhibited by the lower altitude of the ionopause. The observations presented were those made of the Venusian ionospheric plasma by the ASPERA4 experiment onboard the Venus Express spacecraft, and which constitute the first extensive insitu measurements of the plasma near solar minimum. Observations near the terminator of the energies of ions of ionospheric origin showed asymmetry between the noon and midnight sectors, which indicated an antisunward ion flow with a velocity of (2.5 +/ 1.5) km s(1). It is suggested that this ion flow contributes to maintaining the nightside ionosphere near the terminator region at solar minimum. The interpretation of the result was reinforced by observed asymmetries in the ion number counts. The observed dawndusk asymmetry was consistent with a nightward transport of ions while the noonmidnight observations indicated that the flow was highly variable but could contribute to the maintenance of the nightside ionosphere.

Shallowwater vortex equilibria and their stability
http://hdl.handle.net/10023/4762
We first describe the equilibrium form and stability of steadilyrotating simplyconnected vortex patches in the singlelayer quasigeostrophic model of geophysical fluid dynamics. This model, valid for rotating shallowwater flow in the limit of small Rossby and Froude numbers, has an intrinsic length scale L called the "Rossby deformation length" relating the strength of stratification to that of the background rotation rate. Specifically, L = c/f where c = √gH is a characteristic gravitywave speed, g is gravity (or "reduced" gravity in a twolayer context where one layer is infinitely deep), H is the mean active layer depth, and f is the Coriolis frequency (here constant). We next introduce ageostrophic effects by using the full shallowwater model to generate what we call "quasiequilibria". These equilibria are not strictly steady, but radiate such weak gravity waves that they are steady for all practical purposes. Through an artificial ramping procedure, we ramp up the potential vorticity anomaly of the fluid particles in our quasigeostrophic equilibria to obtain shallowwater quasiequilibria at finite Rossby number. We show a few examples of these states in this paper.
Sat, 01 Jan 2011 00:00:00 GMT
http://hdl.handle.net/10023/4762
20110101T00:00:00Z
Płotka, H.
Dritschel, D.G.
We first describe the equilibrium form and stability of steadilyrotating simplyconnected vortex patches in the singlelayer quasigeostrophic model of geophysical fluid dynamics. This model, valid for rotating shallowwater flow in the limit of small Rossby and Froude numbers, has an intrinsic length scale L called the "Rossby deformation length" relating the strength of stratification to that of the background rotation rate. Specifically, L = c/f where c = √gH is a characteristic gravitywave speed, g is gravity (or "reduced" gravity in a twolayer context where one layer is infinitely deep), H is the mean active layer depth, and f is the Coriolis frequency (here constant). We next introduce ageostrophic effects by using the full shallowwater model to generate what we call "quasiequilibria". These equilibria are not strictly steady, but radiate such weak gravity waves that they are steady for all practical purposes. Through an artificial ramping procedure, we ramp up the potential vorticity anomaly of the fluid particles in our quasigeostrophic equilibria to obtain shallowwater quasiequilibria at finite Rossby number. We show a few examples of these states in this paper.

Propagating coupled Alfvén and kink oscillations in an arbitrary inhomogeneous corona
http://hdl.handle.net/10023/4755
Observations have revealed ubiquitous transverse velocity perturbation waves propagating in the solar corona. We perform threedimensional numerical simulations of footpointdriven transverse waves propagating in a low β plasma. We consider the cases of distorted cylindrical flux tubes and a randomly generated inhomogeneous medium. When density structuring is present, mode coupling in inhomogeneous regions leads to the coupling of the kink mode to the Alfvén mode. The decay of the propagating kink wave is observed as energy is transferred to the local Alfvén mode. In all cases considered, modest changes in density were capable of efficiently converting energy from the driving footpoint motion to localized Alfv´en modes. We have demonstrated that mode coupling efficiently couples propagating kink perturbations to Alfvén modes in an arbitrary inhomogeneous medium. This has the consequence that transverse footpoint motions at the base of the corona will deposit energy to Alfvén modes in the corona.
D.J.P. acknowledges financial support from STFC. I.D.M. acknowledges support of a Royal Society University Research Fellowship.
Sun, 10 Apr 2011 00:00:00 GMT
http://hdl.handle.net/10023/4755
20110410T00:00:00Z
Pascoe, David James
Wright, Andrew Nicholas
De Moortel, Ineke
Observations have revealed ubiquitous transverse velocity perturbation waves propagating in the solar corona. We perform threedimensional numerical simulations of footpointdriven transverse waves propagating in a low β plasma. We consider the cases of distorted cylindrical flux tubes and a randomly generated inhomogeneous medium. When density structuring is present, mode coupling in inhomogeneous regions leads to the coupling of the kink mode to the Alfvén mode. The decay of the propagating kink wave is observed as energy is transferred to the local Alfvén mode. In all cases considered, modest changes in density were capable of efficiently converting energy from the driving footpoint motion to localized Alfv´en modes. We have demonstrated that mode coupling efficiently couples propagating kink perturbations to Alfvén modes in an arbitrary inhomogeneous medium. This has the consequence that transverse footpoint motions at the base of the corona will deposit energy to Alfvén modes in the corona.

Modeling the dispersal of an active region : quantifying energy input into the corona
http://hdl.handle.net/10023/4754
In this paper, a new technique for modeling nonlinear forcefree fields directly from lineofsight magnetogram observations is presented. The technique uses sequences of magnetograms directly as lower boundary conditions to drive the evolution of coronal magnetic fields between successive forcefree equilibria over long periods of time. It is illustrated by applying it to SOHO: MDI observations of a decaying active region, NOAA AR 8005. The active region is modeled during a fourday period around its central meridian passage. Over this time, the dispersal of the active region is dominated by random motions due to smallscale convective cells. Through studying the buildup of magnetic energy in the model, it is found that such smallscale motions may inject anywhere from (2.53) × 1025 erg s1 of free magnetic energy into the coronal field. Most of this energy is stored within the center of the active region in the low corona, below 30 Mm. After four days, the buildup of free energy is 10% that of the corresponding potential field. This energy buildup is sufficient to explain the radiative losses at coronal temperatures within the active region. Smallscale convective motions therefore play an integral part in the energy balance of the corona. This new technique has wide ranging applications with the new highresolution, highcadence observations from the SDO:HMI and SDO:AIA instruments.
Funding: UK STFC. Royal Society Research Grants Scheme.
Thu, 10 Mar 2011 00:00:00 GMT
http://hdl.handle.net/10023/4754
20110310T00:00:00Z
Mackay, Duncan Hendry
Green, Lucie
van Ballegooijen, Aad
In this paper, a new technique for modeling nonlinear forcefree fields directly from lineofsight magnetogram observations is presented. The technique uses sequences of magnetograms directly as lower boundary conditions to drive the evolution of coronal magnetic fields between successive forcefree equilibria over long periods of time. It is illustrated by applying it to SOHO: MDI observations of a decaying active region, NOAA AR 8005. The active region is modeled during a fourday period around its central meridian passage. Over this time, the dispersal of the active region is dominated by random motions due to smallscale convective cells. Through studying the buildup of magnetic energy in the model, it is found that such smallscale motions may inject anywhere from (2.53) × 1025 erg s1 of free magnetic energy into the coronal field. Most of this energy is stored within the center of the active region in the low corona, below 30 Mm. After four days, the buildup of free energy is 10% that of the corresponding potential field. This energy buildup is sufficient to explain the radiative losses at coronal temperatures within the active region. Smallscale convective motions therefore play an integral part in the energy balance of the corona. This new technique has wide ranging applications with the new highresolution, highcadence observations from the SDO:HMI and SDO:AIA instruments.

The effects of lineofsight integration on multistrand coronal loop oscillations
http://hdl.handle.net/10023/4752
IDM acknowledges support of a Royal Society University Research Fellowship.
Fri, 10 Feb 2012 00:00:00 GMT
http://hdl.handle.net/10023/4752
20120210T00:00:00Z
De Moortel, Ineke
Pascoe, David James

Standing kink modes in threedimensional coronal loops
http://hdl.handle.net/10023/4745
So far, the straight flux tube model proposed by Edwin & Roberts is the most commonly used tool in practical coronal seismology, in particular, to infer values of the (coronal) magnetic field from observed, standing kink mode oscillations. In this paper, we compare the period predicted by this basic model with threedimensional (3D) numerical simulations of standing kink mode oscillations, as the period is a crucial parameter in the seismological inversion to determine the magnetic field. We perform numerical simulations of standing kink modes in both straight and curved 3D coronal loops and consider excitation by internal and external drivers. The period of oscillation for the displacement of dense coronal loops is determined by the loop length and the kink speed, in agreement with the estimate based on analytical theory for straight flux tubes. For curved coronal loops embedded in a magnetic arcade and excited by an external driver, a secondary mode with a period determined by the loop length and external Alfvén speed is also present. When a low number of oscillations is considered, these two periods can result in a single, nonresolved (broad) peak in the power spectrum, particularly for low values of the density contrast for which the two periods will be relatively similar. In that case (and for this particular geometry), the presence of this additional mode would lead to ambiguous seismological estimates of the magnetic field strength.
I.D.M. acknowledges support from a Royal Society University Research Fellowship. The computational work for this paper was carried out at the joint STFC and SFC (SRIF)fundedclusterattheUniversityofStAndrews(UK). The research leading to these results has also received funding from the European Commissions Seventh Framework Programme (FP7/20072013) under the grant agreement SOLSPANET (project No. 269299;www.solspanet.eu/solspanet).
Tue, 11 Mar 2014 00:00:00 GMT
http://hdl.handle.net/10023/4745
20140311T00:00:00Z
De Moortel, Ineke
Pascoe, David James
So far, the straight flux tube model proposed by Edwin & Roberts is the most commonly used tool in practical coronal seismology, in particular, to infer values of the (coronal) magnetic field from observed, standing kink mode oscillations. In this paper, we compare the period predicted by this basic model with threedimensional (3D) numerical simulations of standing kink mode oscillations, as the period is a crucial parameter in the seismological inversion to determine the magnetic field. We perform numerical simulations of standing kink modes in both straight and curved 3D coronal loops and consider excitation by internal and external drivers. The period of oscillation for the displacement of dense coronal loops is determined by the loop length and the kink speed, in agreement with the estimate based on analytical theory for straight flux tubes. For curved coronal loops embedded in a magnetic arcade and excited by an external driver, a secondary mode with a period determined by the loop length and external Alfvén speed is also present. When a low number of oscillations is considered, these two periods can result in a single, nonresolved (broad) peak in the power spectrum, particularly for low values of the density contrast for which the two periods will be relatively similar. In that case (and for this particular geometry), the presence of this additional mode would lead to ambiguous seismological estimates of the magnetic field strength.

Simulating the "Sliding Doors" Effect Through Magnetic Flux Emergence
http://hdl.handle.net/10023/4742
Recent Hinode photospheric vector magnetogram observations have shown that the opposite polarities of a long arcade structure move apart and then come together. In addition to this "sliding doors" effect, orientations of horizontal magnetic fields along the polarity inversion line on the photosphere evolve from a normalpolarity configuration to an inverse one. To explain this behavior, a simple model by Okamoto et al. suggested that it is the result of the emergence of a twisted flux rope. Here, we model this scenario using a threedimensional megnatohydrodynamic simulation of a twisted flux rope emerging into a preexisting overlying arcade. We construct magnetograms from the simulation and compare them with the observations. The model produces the two signatures mentioned above. However, the cause of the "sliding doors" effect differs from the previous model.
D.M. acknowledges financial assistance from STFC. The computational work for this Letter was carried out on the joint STFC and SFC (SRIF) funded cluster at the University of St. Andrews. D.M. and A.W.H. acknowledge financial support form the European Commission through the SOLAIRE Network (MTRNCT2006035484).
Fri, 04 Jun 2010 00:00:00 GMT
http://hdl.handle.net/10023/4742
20100604T00:00:00Z
MacTaggart, David
Hood, Alan William
Recent Hinode photospheric vector magnetogram observations have shown that the opposite polarities of a long arcade structure move apart and then come together. In addition to this "sliding doors" effect, orientations of horizontal magnetic fields along the polarity inversion line on the photosphere evolve from a normalpolarity configuration to an inverse one. To explain this behavior, a simple model by Okamoto et al. suggested that it is the result of the emergence of a twisted flux rope. Here, we model this scenario using a threedimensional megnatohydrodynamic simulation of a twisted flux rope emerging into a preexisting overlying arcade. We construct magnetograms from the simulation and compare them with the observations. The model produces the two signatures mentioned above. However, the cause of the "sliding doors" effect differs from the previous model.

The storage and dissipation of magnetic energy in the quiet sun corona determined from SDO/HMI magnetograms
http://hdl.handle.net/10023/4741
In recent years, higher cadence, higher resolution observations have revealed the quietSun photosphere to be complex and rapidly evolving. Since magnetic fields anchored in the photosphere extend up into the solar corona, it is expected that the smallscale coronal magnetic field exhibits similar complexity. For the first time, the quietSun coronal magnetic field is continuously evolved through a series of nonpotential, quasistatic equilibria, deduced from magnetograms observed by the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory, where the photospheric boundary condition which drives the coronal evolution exactly reproduces the observed magnetograms. The buildup, storage, and dissipation of magnetic energy within the simulations is studied. We find that the free magnetic energy built up and stored within the field is sufficient to explain smallscale, impulsive events such as nanoflares. On comparing with coronal images of the same region, the energy storage and dissipation visually reproduces many of the observed features. The results indicate that the complex smallscale magnetic evolution of a large number of magnetic features is a key element in explaining the nature of the solar corona.
2013ApJ...770L..18M
Thu, 30 May 2013 00:00:00 GMT
http://hdl.handle.net/10023/4741
20130530T00:00:00Z
Meyer, Karen Alison
Sabol, Juraj
Mackay, Duncan Hendry
van Ballegooijen, Aad
In recent years, higher cadence, higher resolution observations have revealed the quietSun photosphere to be complex and rapidly evolving. Since magnetic fields anchored in the photosphere extend up into the solar corona, it is expected that the smallscale coronal magnetic field exhibits similar complexity. For the first time, the quietSun coronal magnetic field is continuously evolved through a series of nonpotential, quasistatic equilibria, deduced from magnetograms observed by the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory, where the photospheric boundary condition which drives the coronal evolution exactly reproduces the observed magnetograms. The buildup, storage, and dissipation of magnetic energy within the simulations is studied. We find that the free magnetic energy built up and stored within the field is sufficient to explain smallscale, impulsive events such as nanoflares. On comparing with coronal images of the same region, the energy storage and dissipation visually reproduces many of the observed features. The results indicate that the complex smallscale magnetic evolution of a large number of magnetic features is a key element in explaining the nature of the solar corona.

Potential Evidence for the Onset of Alfvénic Turbulence in Transequatorial Coronal Loops
http://hdl.handle.net/10023/4740
This study investigates Coronal Multichannel Polarimeter Dopplershift observations of a large, offlimb, transequatorial loop system observed on 2012 April 1011. Dopplershift oscillations with a broad range of frequencies are found to propagate along the loop with a speed of about 500 km s–1. The power spectrum of perturbations travelling up from both loop footpoints is remarkably symmetric, probably due to the almost perfect northsouth alignment of the loop system. Compared to the power spectrum at the footpoints of the loop, the Fourier power at the apex appears to be higher in the highfrequency part of the spectrum than expected from theoretical models. We suggest this excess highfrequency power could be tentative evidence for the onset of a cascade of the lowtomid frequency waves into (Alfvénic) turbulence.
Mon, 10 Feb 2014 00:00:00 GMT
http://hdl.handle.net/10023/4740
20140210T00:00:00Z
De Moortel, Ineke
McIntosh, Scott
Threlfall, James William
Bethge, Christian
Liu, J
This study investigates Coronal Multichannel Polarimeter Dopplershift observations of a large, offlimb, transequatorial loop system observed on 2012 April 1011. Dopplershift oscillations with a broad range of frequencies are found to propagate along the loop with a speed of about 500 km s–1. The power spectrum of perturbations travelling up from both loop footpoints is remarkably symmetric, probably due to the almost perfect northsouth alignment of the loop system. Compared to the power spectrum at the footpoints of the loop, the Fourier power at the apex appears to be higher in the highfrequency part of the spectrum than expected from theoretical models. We suggest this excess highfrequency power could be tentative evidence for the onset of a cascade of the lowtomid frequency waves into (Alfvénic) turbulence.

The detection of numerous magnetic separators in a threedimensional magnetohydrodynamic model of solar emerging flux
http://hdl.handle.net/10023/4739
Magnetic separators in threedimensional (3D) magnetic fields are believed to be often associated with locations of magnetic reconnection. In this preliminary study, we investigate this relationship using data from a numerical resistive 3D MHD experiment of a solar flux emergence event. For the first time separators are detected in complex magnetic fields resulting from a 3D resistive MHD model of flux emergence. Two snapshots of the model, taken from different stages of its evolution, are analyzed. Numerous separators are found in both snapshots, and their properties, including their geometry, length, relationship to the magnetic null points, and integrated parallel electric field are studied. The separators reside at the junctions between the emerging flux, the overlying field, and two other flux domains that are newly formed by reconnection. The long separators, which connect clusters of nulls that lie either side of the emerging flux, pass through spatially localized regions of high parallel electric field and correspond to local maxima in integrated parallel electric field. These factors indicate that strong magnetic reconnection takes place along many of the separators, and that separators play a key role during the interaction of emerging and overlying flux.
Mon, 20 Dec 2010 00:00:00 GMT
http://hdl.handle.net/10023/4739
20101220T00:00:00Z
Parnell, Clare Elizabeth
Maclean, Rhona Claire
Haynes, Andrew Lewis
Magnetic separators in threedimensional (3D) magnetic fields are believed to be often associated with locations of magnetic reconnection. In this preliminary study, we investigate this relationship using data from a numerical resistive 3D MHD experiment of a solar flux emergence event. For the first time separators are detected in complex magnetic fields resulting from a 3D resistive MHD model of flux emergence. Two snapshots of the model, taken from different stages of its evolution, are analyzed. Numerous separators are found in both snapshots, and their properties, including their geometry, length, relationship to the magnetic null points, and integrated parallel electric field are studied. The separators reside at the junctions between the emerging flux, the overlying field, and two other flux domains that are newly formed by reconnection. The long separators, which connect clusters of nulls that lie either side of the emerging flux, pass through spatially localized regions of high parallel electric field and correspond to local maxima in integrated parallel electric field. These factors indicate that strong magnetic reconnection takes place along many of the separators, and that separators play a key role during the interaction of emerging and overlying flux.

Globalscale consequences of magnetichelicity injection and condensation on the sun
http://hdl.handle.net/10023/4735
In the recent paper of Antiochos, a new concept for the injection of magnetic helicity into the solar corona by smallscale convective motions and its condensation onto polarity inversion lines (PILs) has been developed. We investigate this concept through global simulations of the Sun’s photospheric and coronal magnetic fields, and compare the results with the hemispheric pattern of solar filaments. Assuming that the vorticity of the cells is predominately counterclockwise/clockwise in the northern/southern hemisphere, the convective motions inject negative/positive helicity into each hemisphere. The simulations show that: (1) on a north–south oriented PIL, both differential rotation and convective motions inject the same sign of helicity, which matches that required to reproduce the hemispheric pattern of filaments. (2) On a highlatitude east–west oriented polar crown or subpolar crown PIL, the vorticity of the cells has to be approximately 2–3 times greater than the local differentialrotation gradient in order to overcome the incorrect sign of helicity injection from differential rotation. (3) In the declining phase of the cycle, as a bipole interacts with the polar field, in some cases, helicity condensation can reverse the effect of differential rotation along the east–west lead arm but not in all cases. The results show that this newly developed concept of magnetic helicity injection and condensation, in conjunction with the mechanisms used in Yeates et al., is a viable explanation for the hemispheric pattern of filaments. Future observational studies should focus on examining the vorticity component within convective motions to determine both its magnitude and latitudinal variation relative to the differentialrotation gradient on the Sun.
Tue, 01 Apr 2014 00:00:00 GMT
http://hdl.handle.net/10023/4735
20140401T00:00:00Z
Mackay, Duncan Hendry
DeVore, Rick
Antiochos, Spiro
In the recent paper of Antiochos, a new concept for the injection of magnetic helicity into the solar corona by smallscale convective motions and its condensation onto polarity inversion lines (PILs) has been developed. We investigate this concept through global simulations of the Sun’s photospheric and coronal magnetic fields, and compare the results with the hemispheric pattern of solar filaments. Assuming that the vorticity of the cells is predominately counterclockwise/clockwise in the northern/southern hemisphere, the convective motions inject negative/positive helicity into each hemisphere. The simulations show that: (1) on a north–south oriented PIL, both differential rotation and convective motions inject the same sign of helicity, which matches that required to reproduce the hemispheric pattern of filaments. (2) On a highlatitude east–west oriented polar crown or subpolar crown PIL, the vorticity of the cells has to be approximately 2–3 times greater than the local differentialrotation gradient in order to overcome the incorrect sign of helicity injection from differential rotation. (3) In the declining phase of the cycle, as a bipole interacts with the polar field, in some cases, helicity condensation can reverse the effect of differential rotation along the east–west lead arm but not in all cases. The results show that this newly developed concept of magnetic helicity injection and condensation, in conjunction with the mechanisms used in Yeates et al., is a viable explanation for the hemispheric pattern of filaments. Future observational studies should focus on examining the vorticity component within convective motions to determine both its magnitude and latitudinal variation relative to the differentialrotation gradient on the Sun.

The Sun's global photospheric and coronal magnetic fields : observations and models
http://hdl.handle.net/10023/4714
In this review, our present day understanding of the Sun's global photospheric and coronal magnetic fields is discussed from both observational and theoretical viewpoints. Firstly, the largescale properties of photospheric magnetic fields are described, along with recent advances in photospheric magnetic flux transport models. Following this, the wide variety of theoretical models used to simulate global coronal magnetic fields are described. From this, the combined application of both magnetic flux transport simulations and coronal modeling techniques to describe the phenomena of coronal holes, the Sun's open magnetic flux and the hemispheric pattern of solar filaments is discussed. Finally, recent advances in noneruptive global MHD models are described. While the review focuses mainly on solar magnetic fields, recent advances in measuring and modeling stellar magnetic fields are described where appropriate. In the final section key areas of future research are identified.
2012LRSP....9....6M Funding: STFC, the Leverhulme Trust and European Commission’s Seventh Framework Programme (FP7/20072013) under the grant agreement SWIFF (project no. 263340, http://www.swiff.eu).
Thu, 01 Nov 2012 00:00:00 GMT
http://hdl.handle.net/10023/4714
20121101T00:00:00Z
Mackay, Duncan Hendry
Yeates, Anthony Robinson
In this review, our present day understanding of the Sun's global photospheric and coronal magnetic fields is discussed from both observational and theoretical viewpoints. Firstly, the largescale properties of photospheric magnetic fields are described, along with recent advances in photospheric magnetic flux transport models. Following this, the wide variety of theoretical models used to simulate global coronal magnetic fields are described. From this, the combined application of both magnetic flux transport simulations and coronal modeling techniques to describe the phenomena of coronal holes, the Sun's open magnetic flux and the hemispheric pattern of solar filaments is discussed. Finally, recent advances in noneruptive global MHD models are described. While the review focuses mainly on solar magnetic fields, recent advances in measuring and modeling stellar magnetic fields are described where appropriate. In the final section key areas of future research are identified.

Laboratory astrophysics : investigation of planetary and astrophysical maser emission
http://hdl.handle.net/10023/4494
This paper describes a model for cyclotron maser emission applicable to planetary auroral radio emission, the stars UV Ceti and CU Virginus, blazar jets and astrophysical shocks. These emissions may be attributed to energetic electrons moving into convergent magnetic fields that are typically found in association with dipole like planetary magnetospheres or shocks. It is found that magnetic compression leads to the formation of a velocity distribution having a horseshoe shape as a result of conservation of the electron magnetic moment. Under certain plasma conditions where the local electron plasma frequency ωpe is much less than the cyclotron frequency ωce the distribution is found to be unstable to maser type radiation emission. We have established a laboratorybased facility that has verified many of the details of our original theoretical description and agrees well with numerical simulations. The experiment has demonstrated that the horseshoe distribution produces cyclotron emission at a frequency just below the local electron cyclotron frequency, with polarisation close to Xmode and propagating nearly perpendicularly to the electron beam motion. We discuss recent developments in the theory and simulation of the instability including addressing radiation escape problems, and relate these to the laboratory, space, and astrophysical observations. The experiments showed strong narrow band EM emissions at frequencies just below the coldplasma cyclotron frequency as predicted by the theory. Measurements of the conversion efficiency, mode and spectral content were in close agreement with the predictions of numerical simulations undertaken using a particleincell code and also with satellite observations confirming the horseshoe maser as an important emission mechanism in geophysical/astrophysical plasmas. In each case we address how the radiation can escape the plasma without suffering strong absorption at the second harmonic layer.
Tue, 01 Jan 2013 00:00:00 GMT
http://hdl.handle.net/10023/4494
20130101T00:00:00Z
Speirs, David
Cairns, R Alan
Kellett, Barry
Vorgul, Irena
McConville, Sandra
Cross, Adrian
Phelps, Alan
Ronald, Kevin
Bingham, Robert
This paper describes a model for cyclotron maser emission applicable to planetary auroral radio emission, the stars UV Ceti and CU Virginus, blazar jets and astrophysical shocks. These emissions may be attributed to energetic electrons moving into convergent magnetic fields that are typically found in association with dipole like planetary magnetospheres or shocks. It is found that magnetic compression leads to the formation of a velocity distribution having a horseshoe shape as a result of conservation of the electron magnetic moment. Under certain plasma conditions where the local electron plasma frequency ωpe is much less than the cyclotron frequency ωce the distribution is found to be unstable to maser type radiation emission. We have established a laboratorybased facility that has verified many of the details of our original theoretical description and agrees well with numerical simulations. The experiment has demonstrated that the horseshoe distribution produces cyclotron emission at a frequency just below the local electron cyclotron frequency, with polarisation close to Xmode and propagating nearly perpendicularly to the electron beam motion. We discuss recent developments in the theory and simulation of the instability including addressing radiation escape problems, and relate these to the laboratory, space, and astrophysical observations. The experiments showed strong narrow band EM emissions at frequencies just below the coldplasma cyclotron frequency as predicted by the theory. Measurements of the conversion efficiency, mode and spectral content were in close agreement with the predictions of numerical simulations undertaken using a particleincell code and also with satellite observations confirming the horseshoe maser as an important emission mechanism in geophysical/astrophysical plasmas. In each case we address how the radiation can escape the plasma without suffering strong absorption at the second harmonic layer.

Magnetohydrodynamics dynamical relaxation of coronal magnetic fields : I. Parallel untwisted magnetic fields in 2D
http://hdl.handle.net/10023/4378
Context. For the last thirty years, most of the studies on the relaxation of stressed magnetic fields in the solar environment have only considered the Lorentz force, neglecting plasma contributions, and therefore, limiting every equilibrium to that of a forcefree field. Aims: Here we begin a study of the nonresistive evolution of finite beta plasmas and their relaxation to magnetohydrostatic states, where magnetic forces are balanced by plasmapressure gradients, by using a simple 2D scenario involving a hydromagnetic disturbance to a uniform magnetic field. The final equilibrium state is predicted as a function of the initial disturbances, with aims to demonstrate what happens to the plasma during the relaxation process and to see what effects it has on the final equilibrium state. Methods: A set of numerical experiments are run using a full MHD code, with the relaxation driven by magnetoacoustic waves damped by viscous effects. The numerical results are compared with analytical calculations made within the linear regime, in which the whole process must remain adiabatic. Particular attention is paid to the thermodynamic behaviour of the plasma during the relaxation. Results: The analytical predictions for the final non forcefree equilibrium depend only on the initial perturbations and the total pressure of the system. It is found that these predictions hold surprisingly well even for amplitudes of the perturbation far outside the linear regime. Conclusions: Including the effects of a finite plasma beta in relaxation experiments leads to significant differences from the forcefree case.
Sat, 01 May 2010 00:00:00 GMT
http://hdl.handle.net/10023/4378
20100501T00:00:00Z
Fuentes Fernandez, Jorge
Parnell, Clare Elizabeth
Hood, Alan William
Context. For the last thirty years, most of the studies on the relaxation of stressed magnetic fields in the solar environment have only considered the Lorentz force, neglecting plasma contributions, and therefore, limiting every equilibrium to that of a forcefree field. Aims: Here we begin a study of the nonresistive evolution of finite beta plasmas and their relaxation to magnetohydrostatic states, where magnetic forces are balanced by plasmapressure gradients, by using a simple 2D scenario involving a hydromagnetic disturbance to a uniform magnetic field. The final equilibrium state is predicted as a function of the initial disturbances, with aims to demonstrate what happens to the plasma during the relaxation process and to see what effects it has on the final equilibrium state. Methods: A set of numerical experiments are run using a full MHD code, with the relaxation driven by magnetoacoustic waves damped by viscous effects. The numerical results are compared with analytical calculations made within the linear regime, in which the whole process must remain adiabatic. Particular attention is paid to the thermodynamic behaviour of the plasma during the relaxation. Results: The analytical predictions for the final non forcefree equilibrium depend only on the initial perturbations and the total pressure of the system. It is found that these predictions hold surprisingly well even for amplitudes of the perturbation far outside the linear regime. Conclusions: Including the effects of a finite plasma beta in relaxation experiments leads to significant differences from the forcefree case.

Flux emergence and coronal eruption
http://hdl.handle.net/10023/4376
Aims. Our aim is to study the photospheric flux distribution of a twisted flux tube that emerges from the solar interior. We also report on the eruption of a new flux rope when the emerging tube rises into a preexisting magnetic field in the corona. Methods. To study the evolution, we use 3D numerical simulations by solving the timedependent and resistive MHD equations. We qualitatively compare our numerical results with MDI magnetograms of emerging flux at the solar surface. Results. We find that the photospheric magnetic flux distribution consists of two regions of opposite polarities and elongated magnetic tails on the two sides of the polarity inversion line (PIL), depending on the azimuthal nature of the emerging field lines and the initial field strength of the rising tube. Their shape is progressively deformed due to plasma motions towards the PIL. Our results are in qualitative agreement with observational studies of magnetic flux emergence in active regions (ARs). Moreover, if the initial twist of the emerging tube is small, the photospheric magnetic field develops an undulating shape and does not possess tails. In all cases, we find that a new flux rope is formed above the original axis of the emerging tube that may erupt into the corona, depending on the strength of the ambient field.
Sat, 01 May 2010 00:00:00 GMT
http://hdl.handle.net/10023/4376
20100501T00:00:00Z
Archontis, Vasilis
Hood, Alan William
Aims. Our aim is to study the photospheric flux distribution of a twisted flux tube that emerges from the solar interior. We also report on the eruption of a new flux rope when the emerging tube rises into a preexisting magnetic field in the corona. Methods. To study the evolution, we use 3D numerical simulations by solving the timedependent and resistive MHD equations. We qualitatively compare our numerical results with MDI magnetograms of emerging flux at the solar surface. Results. We find that the photospheric magnetic flux distribution consists of two regions of opposite polarities and elongated magnetic tails on the two sides of the polarity inversion line (PIL), depending on the azimuthal nature of the emerging field lines and the initial field strength of the rising tube. Their shape is progressively deformed due to plasma motions towards the PIL. Our results are in qualitative agreement with observational studies of magnetic flux emergence in active regions (ARs). Moreover, if the initial twist of the emerging tube is small, the photospheric magnetic field develops an undulating shape and does not possess tails. In all cases, we find that a new flux rope is formed above the original axis of the emerging tube that may erupt into the corona, depending on the strength of the ambient field.

Magnetohydrodynamic kink waves in twodimensional nonuniform prominence threads
http://hdl.handle.net/10023/4374
Aims. We analyse the oscillatory properties of resonantly damped transverse kink oscillations in twodimensional prominence threads. Methods. The fine structures are modelled as cylindrically symmetric magnetic flux tubes with a dense central part with prominence plasma properties and an evacuated part, both surrounded by coronal plasma. The equilibrium density is allowed to vary nonuniformly in both the transverse and the longitudinal directions. We examine the influence of longitudinal density structuring on periods, damping times, and damping rates for transverse kink modes computed by numerically solving the linear resistive magnetohydrodynamic (MHD) equations. Results. The relevant parameters are the length of the thread and the density in the evacuated part of the tube, two quantities that are difficult to directly estimate from observations. We find that both of them strongly influence the oscillatory periods and damping times, and to a lesser extent the damping ratios. The analysis of the spatial distribution of perturbations and of the energy flux into the resonances allows us to explain the obtained damping times. Conclusions. Implications for prominence seismology, the physics of resonantly damped kink modes in twodimensional magnetic flux tubes, and the heating of prominence plasmas are discussed.
Thu, 01 Sep 2011 00:00:00 GMT
http://hdl.handle.net/10023/4374
20110901T00:00:00Z
Arregui, I
Soler, R
Ballester, J.
Wright, Andrew Nicholas
Aims. We analyse the oscillatory properties of resonantly damped transverse kink oscillations in twodimensional prominence threads. Methods. The fine structures are modelled as cylindrically symmetric magnetic flux tubes with a dense central part with prominence plasma properties and an evacuated part, both surrounded by coronal plasma. The equilibrium density is allowed to vary nonuniformly in both the transverse and the longitudinal directions. We examine the influence of longitudinal density structuring on periods, damping times, and damping rates for transverse kink modes computed by numerically solving the linear resistive magnetohydrodynamic (MHD) equations. Results. The relevant parameters are the length of the thread and the density in the evacuated part of the tube, two quantities that are difficult to directly estimate from observations. We find that both of them strongly influence the oscillatory periods and damping times, and to a lesser extent the damping ratios. The analysis of the spatial distribution of perturbations and of the energy flux into the resonances allows us to explain the obtained damping times. Conclusions. Implications for prominence seismology, the physics of resonantly damped kink modes in twodimensional magnetic flux tubes, and the heating of prominence plasmas are discussed.

Thermal conduction effects on the kink instability in coronal loops
http://hdl.handle.net/10023/4373
Context. Heating of the solar corona by nanoflares, which are small transient events in which stored magnetic energy is dissipated by magnetic reconnection, may occur as the result of the nonlinear phase of the kink instability (Hood et al. 2009). Because of the high temperatures reached through these reconnection events, thermal conduction cannot be ignored in the evolution of the kink instability. Aims. To study the effect of thermal conduction on the nonlinear evolution of the kink instability of a coronal loop. To assess the efficiency of loop heating and the role of thermal conduction, both during the kink instability and for the long time evolution of the loop. Methods. Numerically solve the 3D nonlinear magnetohydrodynamic equations to simulate the evolution of a coronal loop that is initially in an unstable equilibrium. The initial state has zero net current. A comparison is made of the time evolution of the loop with thermal conduction and without thermal conduction. Results. Thermal conduction along magnetic field lines reduces the local temperature. This leads to temperatures that are an order of magnitude lower than those obtained in the absence of thermal conductivity. Consequently, different spectral lines are activated with and without the inclusion of thermal conduction, which have consequences for observations of solar corona loops. The conduction process is also important on the timescale of the fast magnetohydrodynamic phenomena. It reduces the kinetic energy released by an order of magnitude. Conclusions. Thermal conduction plays an essential role in the kink instability of coronal loops and cannot be ignored in the forward modelling of such loops.
Sat, 01 Jan 2011 00:00:00 GMT
http://hdl.handle.net/10023/4373
20110101T00:00:00Z
Botha, G. J. J.
Arber, T. D.
Hood, A. W.
Context. Heating of the solar corona by nanoflares, which are small transient events in which stored magnetic energy is dissipated by magnetic reconnection, may occur as the result of the nonlinear phase of the kink instability (Hood et al. 2009). Because of the high temperatures reached through these reconnection events, thermal conduction cannot be ignored in the evolution of the kink instability. Aims. To study the effect of thermal conduction on the nonlinear evolution of the kink instability of a coronal loop. To assess the efficiency of loop heating and the role of thermal conduction, both during the kink instability and for the long time evolution of the loop. Methods. Numerically solve the 3D nonlinear magnetohydrodynamic equations to simulate the evolution of a coronal loop that is initially in an unstable equilibrium. The initial state has zero net current. A comparison is made of the time evolution of the loop with thermal conduction and without thermal conduction. Results. Thermal conduction along magnetic field lines reduces the local temperature. This leads to temperatures that are an order of magnitude lower than those obtained in the absence of thermal conductivity. Consequently, different spectral lines are activated with and without the inclusion of thermal conduction, which have consequences for observations of solar corona loops. The conduction process is also important on the timescale of the fast magnetohydrodynamic phenomena. It reduces the kinetic energy released by an order of magnitude. Conclusions. Thermal conduction plays an essential role in the kink instability of coronal loops and cannot be ignored in the forward modelling of such loops.

Alfven wave phasemixing and damping in the ion cyclotron range of frequencies
http://hdl.handle.net/10023/4372
Aims. We determine the effect of the Hall term in the generalised Ohm's law on the damping and phase mixing of Alfven waves in the ion cyclotron range of frequencies in uniform and nonuniform equilibrium plasmas. Methods. Wave damping in a uniform plasma is treated analytically, whilst a Lagrangian remap code (Lare2d) is used to study Hall effects on damping and phase mixing in the presence of an equilibrium density gradient. Results. The magnetic energy associated with an initially Gaussian field perturbation in a uniform resistive plasma is shown to decay algebraically at a rate that is unaffected by the Hall term to leading order in k(2)delta(2)(i) where k is wavenumber and delta(i) is ion skin depth. A similar algebraic decay law applies to whistler perturbations in the limit k(2)delta(2)(i) >> 1. In a nonuniform plasma it is found that the spatiallyintegrated damping rate due to phase mixing is lower in Hall MHD than it is in MHD, but the reduction in the damping rate, which can be attributed to the effects of wave dispersion, tends to zero in both the weak and strong phase mixing limits.
Sat, 01 Jan 2011 00:00:00 GMT
http://hdl.handle.net/10023/4372
20110101T00:00:00Z
Threlfall, J.
McClements, K. G.
De Moortel, I.
Aims. We determine the effect of the Hall term in the generalised Ohm's law on the damping and phase mixing of Alfven waves in the ion cyclotron range of frequencies in uniform and nonuniform equilibrium plasmas. Methods. Wave damping in a uniform plasma is treated analytically, whilst a Lagrangian remap code (Lare2d) is used to study Hall effects on damping and phase mixing in the presence of an equilibrium density gradient. Results. The magnetic energy associated with an initially Gaussian field perturbation in a uniform resistive plasma is shown to decay algebraically at a rate that is unaffected by the Hall term to leading order in k(2)delta(2)(i) where k is wavenumber and delta(i) is ion skin depth. A similar algebraic decay law applies to whistler perturbations in the limit k(2)delta(2)(i) >> 1. In a nonuniform plasma it is found that the spatiallyintegrated damping rate due to phase mixing is lower in Hall MHD than it is in MHD, but the reduction in the damping rate, which can be attributed to the effects of wave dispersion, tends to zero in both the weak and strong phase mixing limits.

Nonlinear wave propagation and reconnection at magnetic Xpoints in the Hall MHD regime
http://hdl.handle.net/10023/4368
Context: The highly dynamical, complex nature of the solar atmosphere naturally implies the presence of waves in a topologically varied magnetic environment. Here, the interaction of waves with topological features such as null points is inevitable and potentially important for energetics. The low resistivity of the solar coronal plasma implies that nonmagnetohydrodynamic (MHD) effects should be considered in studies of magnetic energy release in this environment. Aims: This paper investigates the role of the Hall term in the propagation and dissipation of waves, their interaction with 2D magnetic Xpoints and the nature of the resulting reconnection. Methods: A Lagrangian remap shockcapturing code (Lare2d) was used to study the evolution of an initial fast magnetoacoustic wave annulus for a range of values of the ion skin depth (δi) in resistive Hall MHD. A magnetic nullpoint finding algorithm was also used to locate and track the evolution of the multiple nullpoints that are formed in the system. Results: Depending on the ratio of ion skin depth to system size, our model demonstrates that Hall effects can play a key role in the wavenull interaction. In particular, the initial fastwave pulse now consists of whistler and ioncyclotron components; the dispersive nature of the whistler wave leads to (i) earlier interaction with the null; (ii) the creation of multiple additional, transient nulls and, hence, an increased number of energy release sites. In the Hall regime, the relevant timescales (such as the onset of reconnection and the period of the oscillatory relaxation) of the system are reduced significantly, and the reconnection rate is enhanced.
Sun, 01 Jul 2012 00:00:00 GMT
http://hdl.handle.net/10023/4368
20120701T00:00:00Z
Threlfall, James William
Parnell, Clare Elizabeth
De Moortel, Ineke
McClements, Ken
Arber, Tony D.
Context: The highly dynamical, complex nature of the solar atmosphere naturally implies the presence of waves in a topologically varied magnetic environment. Here, the interaction of waves with topological features such as null points is inevitable and potentially important for energetics. The low resistivity of the solar coronal plasma implies that nonmagnetohydrodynamic (MHD) effects should be considered in studies of magnetic energy release in this environment. Aims: This paper investigates the role of the Hall term in the propagation and dissipation of waves, their interaction with 2D magnetic Xpoints and the nature of the resulting reconnection. Methods: A Lagrangian remap shockcapturing code (Lare2d) was used to study the evolution of an initial fast magnetoacoustic wave annulus for a range of values of the ion skin depth (δi) in resistive Hall MHD. A magnetic nullpoint finding algorithm was also used to locate and track the evolution of the multiple nullpoints that are formed in the system. Results: Depending on the ratio of ion skin depth to system size, our model demonstrates that Hall effects can play a key role in the wavenull interaction. In particular, the initial fastwave pulse now consists of whistler and ioncyclotron components; the dispersive nature of the whistler wave leads to (i) earlier interaction with the null; (ii) the creation of multiple additional, transient nulls and, hence, an increased number of energy release sites. In the Hall regime, the relevant timescales (such as the onset of reconnection and the period of the oscillatory relaxation) of the system are reduced significantly, and the reconnection rate is enhanced.

Phase mixing of nonlinear viscoresistive Alfvén waves
http://hdl.handle.net/10023/4367
Aims: We investigate the behaviour of nonlinear, nonideal Alfvén wave propagation within an inhomogeneous magnetic environment. Methods: The governing MHD equations are solved in 1D and 2D using both analytical techniques and numerical simulations. Results: We find clear evidence for the ponderomotive effect and viscoresistive heating. The ponderomotive effect generates a longitudinal component to the transverse Alfvén wave, with a frequency twice that of the driving frequency. Analytical work shows the addition of resistive heating. This leads to a substantial increase in the local temperature and thus gas pressure of the plasma, resulting in material being pushed along the magnetic field. In 2D, our system exhibits phase mixing and we observe an evolution in the location of the maximum heating, i.e. we find a drifting of the heating layer. Conclusions: Considering Alfvén wave propagation in 2D with an inhomogeneous density gradient, we find that the equilibrium density profile is significantly modified by both the flow of density due to viscoresistive heating and the nonlinear response to the localised heating through phase mixing.
Tue, 01 Feb 2011 00:00:00 GMT
http://hdl.handle.net/10023/4367
20110201T00:00:00Z
McLaughlin, James Alexander
De Moortel, Ineke
Hood, Alan William
Aims: We investigate the behaviour of nonlinear, nonideal Alfvén wave propagation within an inhomogeneous magnetic environment. Methods: The governing MHD equations are solved in 1D and 2D using both analytical techniques and numerical simulations. Results: We find clear evidence for the ponderomotive effect and viscoresistive heating. The ponderomotive effect generates a longitudinal component to the transverse Alfvén wave, with a frequency twice that of the driving frequency. Analytical work shows the addition of resistive heating. This leads to a substantial increase in the local temperature and thus gas pressure of the plasma, resulting in material being pushed along the magnetic field. In 2D, our system exhibits phase mixing and we observe an evolution in the location of the maximum heating, i.e. we find a drifting of the heating layer. Conclusions: Considering Alfvén wave propagation in 2D with an inhomogeneous density gradient, we find that the equilibrium density profile is significantly modified by both the flow of density due to viscoresistive heating and the nonlinear response to the localised heating through phase mixing.

The period ratio for kink and sausage modes in a magnetic slab
http://hdl.handle.net/10023/4366
Aims. Increasing observational evidence of wave modes in the solar corona brings us to a closer understanding of that medium. Coronal seismology allows us to combine wave observations and theory to determine otherwise unknown parameters. The period ratio, P1/2P(2), between the period P1 of the fundamental mode and twice the period P2 of its first overtone, is one such tool of coronal seismology and its departure from unity provides information about the structure of the corona. Methods. We consider analytically the period ratio for the fast kink and sausage modes of a magnetic slab, discussing both an Epstein density profile and a simple step function profile. Results. Transverse density structuring in the form of an Epstein profile or a step function profile may contribute to the shift of the period ratio for long thin slablike structures.
A75 article number
Tue, 01 Feb 2011 00:00:00 GMT
http://hdl.handle.net/10023/4366
20110201T00:00:00Z
Macnamara, C. K.
Roberts, B.
Aims. Increasing observational evidence of wave modes in the solar corona brings us to a closer understanding of that medium. Coronal seismology allows us to combine wave observations and theory to determine otherwise unknown parameters. The period ratio, P1/2P(2), between the period P1 of the fundamental mode and twice the period P2 of its first overtone, is one such tool of coronal seismology and its departure from unity provides information about the structure of the corona. Methods. We consider analytically the period ratio for the fast kink and sausage modes of a magnetic slab, discussing both an Epstein density profile and a simple step function profile. Results. Transverse density structuring in the form of an Epstein profile or a step function profile may contribute to the shift of the period ratio for long thin slablike structures.

Coronal heating and nanoflares : current sheet formation and heating
http://hdl.handle.net/10023/4364
Aims: Solar photospheric footpoint motions can produce strong, localised currents in the corona. A detailed understanding of the formation process and the resulting heating is important in modelling nanoflares, as a mechanism for heating the solar corona. Methods: A 3D MHD simulation is described in which an initially straight magnetic field is sheared in two directions. Grid resolutions up to 5123 were used and two boundary drivers were considered; one where the boundaries are continuously driven and one where the driving is switched off once a current layer is formed. Results: For both drivers a twisted current layer is formed. After a long time we see that, when the boundary driving has been switched off, the system relaxes towards a lower energy equilibrium. For the driver which continuously shears the magnetic field we see a repeating cycle of strong current structures forming, fragmenting and decreasing in magnitude and then building up again. Realistic coronal temperatures are obtained.
Sun, 01 Dec 2013 00:00:00 GMT
http://hdl.handle.net/10023/4364
20131201T00:00:00Z
Bowness, Ruth
Hood, Alan William
Parnell, Clare Elizabeth
Aims: Solar photospheric footpoint motions can produce strong, localised currents in the corona. A detailed understanding of the formation process and the resulting heating is important in modelling nanoflares, as a mechanism for heating the solar corona. Methods: A 3D MHD simulation is described in which an initially straight magnetic field is sheared in two directions. Grid resolutions up to 5123 were used and two boundary drivers were considered; one where the boundaries are continuously driven and one where the driving is switched off once a current layer is formed. Results: For both drivers a twisted current layer is formed. After a long time we see that, when the boundary driving has been switched off, the system relaxes towards a lower energy equilibrium. For the driver which continuously shears the magnetic field we see a repeating cycle of strong current structures forming, fragmenting and decreasing in magnitude and then building up again. Realistic coronal temperatures are obtained.

Damping of kink waves by mode coupling. II. Parametric study and seismology
http://hdl.handle.net/10023/4363
Context: Recent observations of the corona reveal ubiquitous transverse velocity perturbations that undergo strong damping as they propagate. These can be understood in terms of propagating kink waves that undergo mode coupling in inhomogeneous regions. Aims: The use of these propagating waves as a seismological tool for the investigation of the solar corona depends upon an accurate understanding of how the mode coupling behaviour is determined by local plasma parameters. Our previous work suggests the exponential spatial damping profile provides a poor description of the behaviour of strongly damped kink waves. We aim to investigate the spatial damping profile in detail and provide a guide to the approximations most suitable for performing seismological inversions. Methods: We propose a general spatial damping profile based on analytical results that accounts for the initial Gaussian stage of damped kink waves as well as the asymptotic exponential stage considered by previous authors. The applicability of this profile is demonstrated by a full parametric study of the relevant physical parameters. The implication of this profile for seismological inversions is investigated. Results: The Gaussian damping profile is found to be most suitable for application as a seismological tool for observations of oscillations in loops with a low density contrast. This profile also provides accurate estimates for data in which only a few wavelengths or periods are observed.
Fri, 01 Feb 2013 00:00:00 GMT
http://hdl.handle.net/10023/4363
20130201T00:00:00Z
Pascoe, David James
Hood, Alan William
De Moortel, Ineke
Wright, Andrew Nicholas
Context: Recent observations of the corona reveal ubiquitous transverse velocity perturbations that undergo strong damping as they propagate. These can be understood in terms of propagating kink waves that undergo mode coupling in inhomogeneous regions. Aims: The use of these propagating waves as a seismological tool for the investigation of the solar corona depends upon an accurate understanding of how the mode coupling behaviour is determined by local plasma parameters. Our previous work suggests the exponential spatial damping profile provides a poor description of the behaviour of strongly damped kink waves. We aim to investigate the spatial damping profile in detail and provide a guide to the approximations most suitable for performing seismological inversions. Methods: We propose a general spatial damping profile based on analytical results that accounts for the initial Gaussian stage of damped kink waves as well as the asymptotic exponential stage considered by previous authors. The applicability of this profile is demonstrated by a full parametric study of the relevant physical parameters. The implication of this profile for seismological inversions is investigated. Results: The Gaussian damping profile is found to be most suitable for application as a seismological tool for observations of oscillations in loops with a low density contrast. This profile also provides accurate estimates for data in which only a few wavelengths or periods are observed.

Cyclotron maser radiation from inhomogeneous plasmas
http://hdl.handle.net/10023/4335
Cyclotron maser instabilities are important in space, astrophysical, and laboratory plasmas. While extensive work has been done on these instabilities, most of it deals with homogeneous plasmas with uniform magnetic fields while in practice, of course, the systems are generally inhomogeneous. Here we expand on our previous work [R. A. Cairns, I. Vorgul, and R. Bingham, Phys. Rev. Lett. 101, 215003 (2008)] in which we showed that localized regions of instability can exist in an inhomogeneous plasma and that the way in which waves propagate away from this region is not necessarily obvious from the homogeneous plasma dispersion relation. While we consider only a simple ring distribution in velocity space, because of its tractability, the ideas may point toward understanding the behavior in the presence of more realistic distributions. The main object of the present work is to move away from consideration of the local dispersion relation and show how global growing eigenmodes can be constructed.
Tue, 01 Feb 2011 00:00:00 GMT
http://hdl.handle.net/10023/4335
20110201T00:00:00Z
Cairns, R Alan
Vorgul, I.
Bingham, Robert
Ronald, K.
Speirs, D. C.
McConville, S. L.
Gillespie, K. M.
Bryson, R.
Phelps, A. D. R.
Kellett, B. J.
Cross, A. W.
Roberston, C. W.
Whyte, C. G.
He, W.
Cyclotron maser instabilities are important in space, astrophysical, and laboratory plasmas. While extensive work has been done on these instabilities, most of it deals with homogeneous plasmas with uniform magnetic fields while in practice, of course, the systems are generally inhomogeneous. Here we expand on our previous work [R. A. Cairns, I. Vorgul, and R. Bingham, Phys. Rev. Lett. 101, 215003 (2008)] in which we showed that localized regions of instability can exist in an inhomogeneous plasma and that the way in which waves propagate away from this region is not necessarily obvious from the homogeneous plasma dispersion relation. While we consider only a simple ring distribution in velocity space, because of its tractability, the ideas may point toward understanding the behavior in the presence of more realistic distributions. The main object of the present work is to move away from consideration of the local dispersion relation and show how global growing eigenmodes can be constructed.

Cyclotron maser emission : Stars, planets, and laboratory
http://hdl.handle.net/10023/4334
This paper is a review of results by the group over the past decade on auroral kilometric radiation and similar cyclotron emissions from stars and planets. These emissions are often attributed to a horseshoe or crescent shaped momentum distribution of energetic electrons moving into the convergent magnetic field which exists around polar regions of dipoletype stars and planets. We have established a laboratorybased facility that has verified many of the details of our original theoretical description and agrees well with numerical simulations. The experiment has demonstrated that the horseshoe distribution does indeed produce cyclotron emission at a frequency just below the local cyclotron frequency, with polarization close to Xmode and propagating nearly perpendicularly to the beam motion. We discuss recent developments in the theory and simulation of the instability including addressing a radiation escape problem and the effect of competing instabilities, relating these to the laboratory, space, and astrophysical observations.
Sun, 01 May 2011 00:00:00 GMT
http://hdl.handle.net/10023/4334
20110501T00:00:00Z
Vorgul, I.
Kellett, B. J.
Cairns, R Alan
Bingham, Robert
Ronald, K.
Speirs, D.C.
McConville, S. L.
Gillespie, K. M.
Phelps, A. D. R.
This paper is a review of results by the group over the past decade on auroral kilometric radiation and similar cyclotron emissions from stars and planets. These emissions are often attributed to a horseshoe or crescent shaped momentum distribution of energetic electrons moving into the convergent magnetic field which exists around polar regions of dipoletype stars and planets. We have established a laboratorybased facility that has verified many of the details of our original theoretical description and agrees well with numerical simulations. The experiment has demonstrated that the horseshoe distribution does indeed produce cyclotron emission at a frequency just below the local cyclotron frequency, with polarization close to Xmode and propagating nearly perpendicularly to the beam motion. We discuss recent developments in the theory and simulation of the instability including addressing a radiation escape problem and the effect of competing instabilities, relating these to the laboratory, space, and astrophysical observations.

Energy dissipation and resolution of steep gradients in onedimensional Burgers flows
http://hdl.handle.net/10023/4333
Travelingwave solutions of the inviscid Burgers equation having smooth initial wave profiles of suitable shapes are known to develop shocks (infinite gradients) in finite times. Such singular solutions are characterized by energy spectra that scale with the wave number k as k−2. In the presence of viscosity ν>0, no shocks can develop, and smooth solutions remain so for all times t>0, eventually decaying to zero as t→∞. At peak energy dissipation, say t = t∗, the spectrum of such a smooth solution extends to a finite dissipation wave number kν and falls off more rapidly, presumably exponentially, for k>kν. The number N of Fourier modes within the socalled inertial range is proportional to kν. This represents the number of modes necessary to resolve the dissipation scale and can be thought of as the system’s number of degrees of freedom. The peak energy dissipation rate ϵ remains positive and becomes independent of ν in the inviscid limit. In this study, we carry out an analysis which verifies the dynamical features described above and derive upper bounds for ϵ and N. It is found that ϵ satisfies ϵ ≤ ν2α−1‖u∗‖∞2(1−α)‖(−Δ)α/2u∗‖2, where α<1 and u∗ = u(x,t∗) is the velocity field at t = t∗. Given ϵ>0 in the limit ν→0, this implies that the energy spectrum remains no steeper than k−2 in that limit. For the critical k−2 scaling, the bound for ϵ reduces to ϵ ≤ k0‖u0‖∞‖u0‖2, where k0 marks the lower end of the inertial range and u0 = u(x,0). This implies N ≤ L‖u0‖∞/ν, where L is the domain size, which is shown to coincide with a rigorous estimate for the number of degrees of freedom defined in terms of local Lyapunov exponents. We demonstrate both analytically and numerically an instance, where the k−2 scaling is uniquely realizable. The numerics also return ϵ and t∗, consistent with analytic values derived from the corresponding limiting weak solution.
Mon, 01 Mar 2010 00:00:00 GMT
http://hdl.handle.net/10023/4333
20100301T00:00:00Z
Tran, Chuong Van
Dritschel, David Gerard
Travelingwave solutions of the inviscid Burgers equation having smooth initial wave profiles of suitable shapes are known to develop shocks (infinite gradients) in finite times. Such singular solutions are characterized by energy spectra that scale with the wave number k as k−2. In the presence of viscosity ν>0, no shocks can develop, and smooth solutions remain so for all times t>0, eventually decaying to zero as t→∞. At peak energy dissipation, say t = t∗, the spectrum of such a smooth solution extends to a finite dissipation wave number kν and falls off more rapidly, presumably exponentially, for k>kν. The number N of Fourier modes within the socalled inertial range is proportional to kν. This represents the number of modes necessary to resolve the dissipation scale and can be thought of as the system’s number of degrees of freedom. The peak energy dissipation rate ϵ remains positive and becomes independent of ν in the inviscid limit. In this study, we carry out an analysis which verifies the dynamical features described above and derive upper bounds for ϵ and N. It is found that ϵ satisfies ϵ ≤ ν2α−1‖u∗‖∞2(1−α)‖(−Δ)α/2u∗‖2, where α<1 and u∗ = u(x,t∗) is the velocity field at t = t∗. Given ϵ>0 in the limit ν→0, this implies that the energy spectrum remains no steeper than k−2 in that limit. For the critical k−2 scaling, the bound for ϵ reduces to ϵ ≤ k0‖u0‖∞‖u0‖2, where k0 marks the lower end of the inertial range and u0 = u(x,0). This implies N ≤ L‖u0‖∞/ν, where L is the domain size, which is shown to coincide with a rigorous estimate for the number of degrees of freedom defined in terms of local Lyapunov exponents. We demonstrate both analytically and numerically an instance, where the k−2 scaling is uniquely realizable. The numerics also return ϵ and t∗, consistent with analytic values derived from the corresponding limiting weak solution.

Boundary layer flow beneath an internal solitary wave of elevation
http://hdl.handle.net/10023/4331
The waveinduced flow over a fixed bottom boundary beneath an internal solitary wave of elevation propagating in an unsheared, twolayer, stably stratified fluid is investigated experimentally. Measurements of the velocity field close to the bottom boundary are presented to illustrate that in the lower layer the fluid velocity near the bottom reverses direction as the wave decelerates while higher in the water column the fluid velocity is in the same direction as the wave propagation. The observation is similar in nature to that for waveinduced flow beneath a surface solitary wave. Contrary to theoretical predictions for internal solitary waves, no evidence for either boundary layer separation or vortex formation is found beneath the front half of the wave in the adverse pressure gradient region of the flow.
Mon, 01 Feb 2010 00:00:00 GMT
http://hdl.handle.net/10023/4331
20100201T00:00:00Z
Carr, Magda
Davies, P A
The waveinduced flow over a fixed bottom boundary beneath an internal solitary wave of elevation propagating in an unsheared, twolayer, stably stratified fluid is investigated experimentally. Measurements of the velocity field close to the bottom boundary are presented to illustrate that in the lower layer the fluid velocity near the bottom reverses direction as the wave decelerates while higher in the water column the fluid velocity is in the same direction as the wave propagation. The observation is similar in nature to that for waveinduced flow beneath a surface solitary wave. Contrary to theoretical predictions for internal solitary waves, no evidence for either boundary layer separation or vortex formation is found beneath the front half of the wave in the adverse pressure gradient region of the flow.

An analytical, phenomenological and numerical study of geophysical and magnetohydrodynamic turbulence in two dimensions
http://hdl.handle.net/10023/4291
In this thesis I study a variety of twodimensional turbulent systems using a
mixed analytical, phenomenological and numerical approach. The systems under
consideration are governed by the twodimensional NavierStokes (2DNS),
surface quasigeostrophic (SQG), alphaturbulence and magnetohydrodynamic (MHD)
equations. The main analytical focus is on the number of degrees of freedom
of a given system, defined as the least value $N$ such that all
$n$dimensional ($n$ ≥ $N$) volume elements along a given trajectory contract
during the course of evolution. By equating $N$ with the number of active
Fourierspace modes, that is the number of modes in the inertial range, and
assuming powerlaw spectra in the inertial range, the scaling of $N$ with the
Reynolds number $Re$ allows bounds to be put on the exponent of the spectrum.
This allows the recovery of analytic results that have until now only been
derived phenomenologically, such as the $k$[superscript(5/3)] energy spectrum in the
energy inertial range in SQG turbulence. Phenomenologically I study the modal
interactions that control the transfer of various conserved quantities. Among
other results I show that in MHD dynamo triads (those converting kinetic into
magnetic energy) are associated with a direct magnetic energy flux while
antidynamo triads (those converting magnetic into kinetic energy) are
associated with an inverse magnetic energy flux. As both dynamo and antidynamo
interacting triads are integral parts of the direct energy transfer, the
antidynamo inverse flux partially neutralises the dynamo direct flux, arguably
resulting in relatively weak direct energy transfer and giving rise to dynamo
saturation. These theoretical results are backed up by high resolution
numerical simulations, out of which have emerged some new results such as the
suggestion that for alpha turbulence the generalised enstrophy spectra are not
closely approximated by those that have been derived phenomenologically, and
new theories may be needed in order to explain them.
Fri, 29 Nov 2013 00:00:00 GMT
http://hdl.handle.net/10023/4291
20131129T00:00:00Z
Blackbourn, Luke A. K.
In this thesis I study a variety of twodimensional turbulent systems using a
mixed analytical, phenomenological and numerical approach. The systems under
consideration are governed by the twodimensional NavierStokes (2DNS),
surface quasigeostrophic (SQG), alphaturbulence and magnetohydrodynamic (MHD)
equations. The main analytical focus is on the number of degrees of freedom
of a given system, defined as the least value $N$ such that all
$n$dimensional ($n$ ≥ $N$) volume elements along a given trajectory contract
during the course of evolution. By equating $N$ with the number of active
Fourierspace modes, that is the number of modes in the inertial range, and
assuming powerlaw spectra in the inertial range, the scaling of $N$ with the
Reynolds number $Re$ allows bounds to be put on the exponent of the spectrum.
This allows the recovery of analytic results that have until now only been
derived phenomenologically, such as the $k$[superscript(5/3)] energy spectrum in the
energy inertial range in SQG turbulence. Phenomenologically I study the modal
interactions that control the transfer of various conserved quantities. Among
other results I show that in MHD dynamo triads (those converting kinetic into
magnetic energy) are associated with a direct magnetic energy flux while
antidynamo triads (those converting magnetic into kinetic energy) are
associated with an inverse magnetic energy flux. As both dynamo and antidynamo
interacting triads are integral parts of the direct energy transfer, the
antidynamo inverse flux partially neutralises the dynamo direct flux, arguably
resulting in relatively weak direct energy transfer and giving rise to dynamo
saturation. These theoretical results are backed up by high resolution
numerical simulations, out of which have emerged some new results such as the
suggestion that for alpha turbulence the generalised enstrophy spectra are not
closely approximated by those that have been derived phenomenologically, and
new theories may be needed in order to explain them.

Effect of gravitational stratification on the propagation of a CME
http://hdl.handle.net/10023/4244
Our aim is to study the role of gravitational stratification on the propagation of CMEs. In particular, we assess how it influences the speed and shape of CMEs and under what conditions the flux rope ejection becomes a CME or when it is quenched. We ran a set of MHD simulations that adopt an eruptive initial magnetic configuration that has already been shown to be suitable for a flux rope ejection. We varied the temperature of the backgroud corona and the intensity of the initial magnetic field to tune the gravitational stratification and the amount of ejected magnetic flux. We used an automatic technique to track the expansion and the propagation of the magnetic flux rope in the MHD simulations. From the analysis of the parameter space, we evaluate the role of gravitational stratification on the CME speed and expansion. Our study shows that gravitational stratification plays a significant role in determining whether the flux rope ejection will turn into a full CME or whether the magnetic flux rope will stop in the corona. The CME speed is affected by the background corona where it travels faster when the corona is colder and when the initial magnetic field is more intense. The fastest CME we reproduce in our parameter space travels at 850 km/s. Moreover, the background gravitational stratification plays a role in the side expansion of the CME, and we find that when the background temperature is higher, the resulting shape of the CME is flattened more. Our study shows that although the initiation mechanisms of the CME are purely magnetic, the background coronal plasma plays a key role in the CME propagation, and full MHD models should be applied when one focusses especially on the production of a CME from a flux rope ejection.
Mon, 02 Dec 2013 00:00:00 GMT
http://hdl.handle.net/10023/4244
20131202T00:00:00Z
Pagano, Paolo
Mackay, Duncan Hendry
Poedts, Stefaan
Our aim is to study the role of gravitational stratification on the propagation of CMEs. In particular, we assess how it influences the speed and shape of CMEs and under what conditions the flux rope ejection becomes a CME or when it is quenched. We ran a set of MHD simulations that adopt an eruptive initial magnetic configuration that has already been shown to be suitable for a flux rope ejection. We varied the temperature of the backgroud corona and the intensity of the initial magnetic field to tune the gravitational stratification and the amount of ejected magnetic flux. We used an automatic technique to track the expansion and the propagation of the magnetic flux rope in the MHD simulations. From the analysis of the parameter space, we evaluate the role of gravitational stratification on the CME speed and expansion. Our study shows that gravitational stratification plays a significant role in determining whether the flux rope ejection will turn into a full CME or whether the magnetic flux rope will stop in the corona. The CME speed is affected by the background corona where it travels faster when the corona is colder and when the initial magnetic field is more intense. The fastest CME we reproduce in our parameter space travels at 850 km/s. Moreover, the background gravitational stratification plays a role in the side expansion of the CME, and we find that when the background temperature is higher, the resulting shape of the CME is flattened more. Our study shows that although the initiation mechanisms of the CME are purely magnetic, the background coronal plasma plays a key role in the CME propagation, and full MHD models should be applied when one focusses especially on the production of a CME from a flux rope ejection.

Magnetohydrodynamics dynamical relaxation of coronal magnetic fields : IV. 3D tilted nulls
http://hdl.handle.net/10023/4084
In this paper we study current accumulations in 3D "tilted" nulls formed by a folding of the spine and fan. A nonzero component of current parallel to the fan is required such that the null's fan plane and spine are not perpendicular. Our aims are to provide valid magnetohydrostatic equilibria and to describe the current accumulations in various cases involving finite plasma pressure.To create our equilibrium current structures we use a full, nonresistive, magnetohydrodynamic (MHD) code so that no reconnection is allowed. A series of experiments are performed in which a perturbed 3D tilted null relaxes towards an equilibrium via real, viscous damping forces. Changes to the initial plasma pressure and to magnetic parameters are investigated systematically.An initially tilted fan is associated with a nonzero Lorentz force that drives the fan and spine to collapse towards each other, in a similar manner to the collapse of a 2D Xpoint. In the final equilibrium state for an initially radial null with only the current perpendicular to the spine, the current concentrates along the tilt axis of the fan and in a layer about the null point with a sharp peak at the null itself. The continued growth of this peak indicates that the system is in an asymptotic regime involving an infinite time singularity at the null. When the initial tilt disturbance (current perpendicular to the spine) is combined with a spiraltype disturbance (current parallel to the spine), the final current density concentrates in three regions: one on the fan along its tilt axis and two around the spine, above and below the fan. The increased area of current accumulation leads to a weakening of the singularity formed at the null. The 3D spinefan collapse with generic current studied here provides the ideal setup for nonsteady reconnection studies.
Thu, 12 Sep 2013 00:00:00 GMT
http://hdl.handle.net/10023/4084
20130912T00:00:00Z
FuentesFernandez, Jorge
Parnell, Clare E.
In this paper we study current accumulations in 3D "tilted" nulls formed by a folding of the spine and fan. A nonzero component of current parallel to the fan is required such that the null's fan plane and spine are not perpendicular. Our aims are to provide valid magnetohydrostatic equilibria and to describe the current accumulations in various cases involving finite plasma pressure.To create our equilibrium current structures we use a full, nonresistive, magnetohydrodynamic (MHD) code so that no reconnection is allowed. A series of experiments are performed in which a perturbed 3D tilted null relaxes towards an equilibrium via real, viscous damping forces. Changes to the initial plasma pressure and to magnetic parameters are investigated systematically.An initially tilted fan is associated with a nonzero Lorentz force that drives the fan and spine to collapse towards each other, in a similar manner to the collapse of a 2D Xpoint. In the final equilibrium state for an initially radial null with only the current perpendicular to the spine, the current concentrates along the tilt axis of the fan and in a layer about the null point with a sharp peak at the null itself. The continued growth of this peak indicates that the system is in an asymptotic regime involving an infinite time singularity at the null. When the initial tilt disturbance (current perpendicular to the spine) is combined with a spiraltype disturbance (current parallel to the spine), the final current density concentrates in three regions: one on the fan along its tilt axis and two around the spine, above and below the fan. The increased area of current accumulation leads to a weakening of the singularity formed at the null. The 3D spinefan collapse with generic current studied here provides the ideal setup for nonsteady reconnection studies.

The structure of zonal jets in geostrophic turbulence
http://hdl.handle.net/10023/4064
The structure of zonal jets arising in forceddissipative, twodimensional turbulent flow on the βplane is investigated using highresolution, longtime numerical integrations, with particular emphasis on the latetime distribution of potential vorticity. The structure of the jets is found to depend in a simple way on a single nondimensional parameter, which may be conveniently expressed as the ratio LRh/Lg, where LRh = √U/β and Lg = (ε/β3)1/5 are two natural length scales arising in the problem; here U may be taken as the r.m.s. velocity, β is the background gradient of potential vorticity in the north–south direction, and ε is the rate of energy input by the forcing. It is shown that jet strength increases with LRh/Lg, with the limiting case of the potential vorticity staircase, comprising a monotonic, piecewiseconstant profile in the north–south direction, being approached for LRh/Lg ∼ 0(10). At lower values, eddies created by the forcing become sufficiently intense to continually disrupt the steepening of potential vorticity gradients in the jet cores, preventing strong jets from developing. Although detailed features such as the regularity of jet spacing and intensity are found to depend on the spectral distribution of the forcing, the approach of the staircase limit with increasing LRh/Lg is robust across a variety of different forcing types considered.
Thu, 01 Nov 2012 00:00:00 GMT
http://hdl.handle.net/10023/4064
20121101T00:00:00Z
Scott, Richard Kirkness
Dritschel, David Gerard
The structure of zonal jets arising in forceddissipative, twodimensional turbulent flow on the βplane is investigated using highresolution, longtime numerical integrations, with particular emphasis on the latetime distribution of potential vorticity. The structure of the jets is found to depend in a simple way on a single nondimensional parameter, which may be conveniently expressed as the ratio LRh/Lg, where LRh = √U/β and Lg = (ε/β3)1/5 are two natural length scales arising in the problem; here U may be taken as the r.m.s. velocity, β is the background gradient of potential vorticity in the north–south direction, and ε is the rate of energy input by the forcing. It is shown that jet strength increases with LRh/Lg, with the limiting case of the potential vorticity staircase, comprising a monotonic, piecewiseconstant profile in the north–south direction, being approached for LRh/Lg ∼ 0(10). At lower values, eddies created by the forcing become sufficiently intense to continually disrupt the steepening of potential vorticity gradients in the jet cores, preventing strong jets from developing. Although detailed features such as the regularity of jet spacing and intensity are found to depend on the spectral distribution of the forcing, the approach of the staircase limit with increasing LRh/Lg is robust across a variety of different forcing types considered.

Consequences of spontaneous reconnection at a twodimensional nonforcefree current layer
http://hdl.handle.net/10023/4007
Magnetic neutral points, where the magnitude of the magnetic field vanishes locally, are potential locations for energy conversion in the solar corona. The fact that the magnetic field is identically zero at these points suggests that for the study of current sheet formation and of any subsequent resistive dissipation phase, a finite beta plasma should be considered, rather than neglecting the plasma pressure as has often been the case in the past. The rapid dissipation of a finite current layer in nonforcefree equilibrium is investigated numerically, after the sudden onset of an anomalous resistivity. The aim of this study is to determine how the energy is redistributed during the initial diffusion phase, and what is the nature of the outward transmission of information and energy. The resistivity rapidly diffuses the current at the null point. The presence of a plasma pressure allows the vast majority of the free energy to be transferred into internal energy. Most of the converted energy is used in direct heating of the surrounding plasma, and only about 3% is converted into kinetic energy, causing a perturbation in the magnetic field and the plasma which propagates away from the null at the local fast magnetoacoustic speed. The propagating pulses show a complex structure due to the highly nonuniform initial state. It is shown that this perturbation carries no net current as it propagates away from the null. The fact that, under the assumptions taken in this paper, most of the magnetic energy released in the reconnection converts internal energy of the plasma, may be highly important for the chromospheric and coronal heating problem.
Wed, 01 Feb 2012 00:00:00 GMT
http://hdl.handle.net/10023/4007
20120201T00:00:00Z
Fuentes Fernandez, Jorge
Parnell, Clare Elizabeth
Hood, Alan William
Priest, Eric Ronald
Longcope, Dana
Magnetic neutral points, where the magnitude of the magnetic field vanishes locally, are potential locations for energy conversion in the solar corona. The fact that the magnetic field is identically zero at these points suggests that for the study of current sheet formation and of any subsequent resistive dissipation phase, a finite beta plasma should be considered, rather than neglecting the plasma pressure as has often been the case in the past. The rapid dissipation of a finite current layer in nonforcefree equilibrium is investigated numerically, after the sudden onset of an anomalous resistivity. The aim of this study is to determine how the energy is redistributed during the initial diffusion phase, and what is the nature of the outward transmission of information and energy. The resistivity rapidly diffuses the current at the null point. The presence of a plasma pressure allows the vast majority of the free energy to be transferred into internal energy. Most of the converted energy is used in direct heating of the surrounding plasma, and only about 3% is converted into kinetic energy, causing a perturbation in the magnetic field and the plasma which propagates away from the null at the local fast magnetoacoustic speed. The propagating pulses show a complex structure due to the highly nonuniform initial state. It is shown that this perturbation carries no net current as it propagates away from the null. The fact that, under the assumptions taken in this paper, most of the magnetic energy released in the reconnection converts internal energy of the plasma, may be highly important for the chromospheric and coronal heating problem.

Magnetohydrodynamics dynamical relaxation of coronal magnetic fields : III. 3D spiral nulls
http://hdl.handle.net/10023/3978
Context: The majority of studies on stressed 3D magnetic null points consider magnetic reconnection driven by an external perturbation, but the formation of a genuine current sheet equilibrium remains poorly understood. This problem has been considered more extensively in twodimensions, but lacks a generalization into 3D fields. Aims: 3D magnetic nulls are more complex than 2D nulls and the field can take a greater range of magnetic geometries local to the null. Here, we focus on one type and consider the dynamical nonresistive relaxation of 3D spiral nulls with initial spinealigned current. We aim to provide a valid magnetohydrostatic equilibrium, and describe the electric current accumulations in various cases, involving a finite plasma pressure. Methods: A full MHD code is used, with the resistivity set to zero so that reconnection is not allowed, to run a series of experiments in which a perturbed spiral 3D null point is allowed to relax towards an equilibrium, via real, viscous damping forces. Changes to the initial plasma pressure and other magnetic parameters are investigated systematically. Results: For the axisymmetric case, the evolution of the field and the plasma is such that it concentrates the current density in two coneshaped regions along the spine, thus concentrating the twist of the magnetic field around the spine, leaving a radial configuration in the fan plane. The plasma pressure redistributes in order to maintain the current density accumulations. However, it is found that changes in the initial plasma pressure do not modify the final state significantly. In the cases where the initial magnetic field is not axisymmetric, a infinitetime singularity of current perpendicular to the fan is found at the location of the null.
Fri, 01 Jun 2012 00:00:00 GMT
http://hdl.handle.net/10023/3978
20120601T00:00:00Z
FuentesFernandez, Jorge
Parnell, Clare E.
Context: The majority of studies on stressed 3D magnetic null points consider magnetic reconnection driven by an external perturbation, but the formation of a genuine current sheet equilibrium remains poorly understood. This problem has been considered more extensively in twodimensions, but lacks a generalization into 3D fields. Aims: 3D magnetic nulls are more complex than 2D nulls and the field can take a greater range of magnetic geometries local to the null. Here, we focus on one type and consider the dynamical nonresistive relaxation of 3D spiral nulls with initial spinealigned current. We aim to provide a valid magnetohydrostatic equilibrium, and describe the electric current accumulations in various cases, involving a finite plasma pressure. Methods: A full MHD code is used, with the resistivity set to zero so that reconnection is not allowed, to run a series of experiments in which a perturbed spiral 3D null point is allowed to relax towards an equilibrium, via real, viscous damping forces. Changes to the initial plasma pressure and other magnetic parameters are investigated systematically. Results: For the axisymmetric case, the evolution of the field and the plasma is such that it concentrates the current density in two coneshaped regions along the spine, thus concentrating the twist of the magnetic field around the spine, leaving a radial configuration in the fan plane. The plasma pressure redistributes in order to maintain the current density accumulations. However, it is found that changes in the initial plasma pressure do not modify the final state significantly. In the cases where the initial magnetic field is not axisymmetric, a infinitetime singularity of current perpendicular to the fan is found at the location of the null.

The onset of impulsive bursty reconnection at a twodimensional current layer
http://hdl.handle.net/10023/3977
The sudden reconnection of a nonforce free 2D current layer, embedded in a lowbeta plasma, triggered by the onset of an anomalous resistivity, is studied in detail. The resulting behaviour consists of two main phases. Firstly, a transient reconnection phase, in which the current in the layer is rapidly dispersed and some flux is reconnected. This dispersal of current launches a family of small amplitude magnetic and plasma perturbations, which propagate away from the null at the local fast and slow magnetosonic speeds. The vast majority of the magnetic energy released in this phase goes into internal energy of the plasma, and only a tiny amount is converted into kinetic energy. In the wake of the outwards propagating pulses, an imbalance of Lorentz and pressure forces creates a stagnation flow which drives a regime of impulsive bursty reconnection, in which fast reconnection is turned on and off in a turbulent manner as the current density exceeds and falls below a critical value. During this phase, the null current density is continuously built up above a certain critical level, then dissipated very rapidly, and built up again, in a stochastic manner. Interestingly, the magnetic energy converted during this quasisteady phase is greater than that converted during the initial transient reconnection phase. Again essentially all the energy converted during this phase goes directly to internal energy. These results are of potential importance for solar flares and coronal heating, and set a conceptually important reference for future 3D studies.
Wed, 09 May 2012 00:00:00 GMT
http://hdl.handle.net/10023/3977
20120509T00:00:00Z
FuentesFernández, J.
Parnell, Clare Elizabeth
Priest, Eric Ronald
The sudden reconnection of a nonforce free 2D current layer, embedded in a lowbeta plasma, triggered by the onset of an anomalous resistivity, is studied in detail. The resulting behaviour consists of two main phases. Firstly, a transient reconnection phase, in which the current in the layer is rapidly dispersed and some flux is reconnected. This dispersal of current launches a family of small amplitude magnetic and plasma perturbations, which propagate away from the null at the local fast and slow magnetosonic speeds. The vast majority of the magnetic energy released in this phase goes into internal energy of the plasma, and only a tiny amount is converted into kinetic energy. In the wake of the outwards propagating pulses, an imbalance of Lorentz and pressure forces creates a stagnation flow which drives a regime of impulsive bursty reconnection, in which fast reconnection is turned on and off in a turbulent manner as the current density exceeds and falls below a critical value. During this phase, the null current density is continuously built up above a certain critical level, then dissipated very rapidly, and built up again, in a stochastic manner. Interestingly, the magnetic energy converted during this quasisteady phase is greater than that converted during the initial transient reconnection phase. Again essentially all the energy converted during this phase goes directly to internal energy. These results are of potential importance for solar flares and coronal heating, and set a conceptually important reference for future 3D studies.

Magnetohydodynamics dynamical relaxation of coronal magnetic fields : II. 2D Magnetic XPoints
http://hdl.handle.net/10023/3976
Context. Magnetic neutral points are potential locations for energy conversion in the solar corona. 2D Xpoints have been widely studied in the past, but only a few of those studies have taken finite plasma beta effects into consideration, and none of them look at the dynamical evolution of the system. At the moment there exists no description of the formation of a nonforcefree equilibrium around a twodimensional Xpoint. Aims. Our aim is to provide a valid magnetohydrostatic equilibrium from the collapse of a 2D Xpoint in the presence of a finite plasma pressure, in which the current density is not simply concentrated in an infinitesimally thin, onedimensional current sheet, as found in forcefree solutions. In particular, we wish to determine if a finite pressure current sheet will still involve a singular current, and if so, what is the nature of the singularity. Methods. We use a full MHD code, with the resistivity set to zero, so that reconnection is not allowed, to run a series of experiments in which an Xpoint is perturbed and then is allowed to relax towards an equilibrium, via real, viscous damping forces. Changes to the magnitude of the perturbation and the initial plasma pressure are investigated systematically. Results. The final state found in our experiments is a “quasistatic” equilibrium where the viscous relaxation has completely ended, but the peak current density at the null increases very slowly following an asymptotic regime towards an infinite time singularity. Using a high grid resolution allows us to resolve the current structures in this state both in width and length. In comparison with the well known pressureless studies, the system does not evolve towards a thin current sheet, but concentrates the current at the null and the separatrices. The growth rate of the singularity is found to be tD, with 0 < D < 1. This rate depends directly on the initial plasma pressure, and decreases as the pressure is increased. At the end of our study, we present an analytical description of the system in a quasistatic nonsingular equilibrium at a given time, in which a finite thick current layer has formed at the null. The dynamical evolution of the system and the dependence of the final state on the initial plasma and magnetic quantities is discussed, as are the energetic consequences.
Thu, 01 Dec 2011 00:00:00 GMT
http://hdl.handle.net/10023/3976
20111201T00:00:00Z
FuentesFernández, Jorge
Parnell, Clare Elizabeth
Hood, Alan William
Context. Magnetic neutral points are potential locations for energy conversion in the solar corona. 2D Xpoints have been widely studied in the past, but only a few of those studies have taken finite plasma beta effects into consideration, and none of them look at the dynamical evolution of the system. At the moment there exists no description of the formation of a nonforcefree equilibrium around a twodimensional Xpoint. Aims. Our aim is to provide a valid magnetohydrostatic equilibrium from the collapse of a 2D Xpoint in the presence of a finite plasma pressure, in which the current density is not simply concentrated in an infinitesimally thin, onedimensional current sheet, as found in forcefree solutions. In particular, we wish to determine if a finite pressure current sheet will still involve a singular current, and if so, what is the nature of the singularity. Methods. We use a full MHD code, with the resistivity set to zero, so that reconnection is not allowed, to run a series of experiments in which an Xpoint is perturbed and then is allowed to relax towards an equilibrium, via real, viscous damping forces. Changes to the magnitude of the perturbation and the initial plasma pressure are investigated systematically. Results. The final state found in our experiments is a “quasistatic” equilibrium where the viscous relaxation has completely ended, but the peak current density at the null increases very slowly following an asymptotic regime towards an infinite time singularity. Using a high grid resolution allows us to resolve the current structures in this state both in width and length. In comparison with the well known pressureless studies, the system does not evolve towards a thin current sheet, but concentrates the current at the null and the separatrices. The growth rate of the singularity is found to be tD, with 0 < D < 1. This rate depends directly on the initial plasma pressure, and decreases as the pressure is increased. At the end of our study, we present an analytical description of the system in a quasistatic nonsingular equilibrium at a given time, in which a finite thick current layer has formed at the null. The dynamical evolution of the system and the dependence of the final state on the initial plasma and magnetic quantities is discussed, as are the energetic consequences.

Magnetohydrodynamic simulations of the ejection of a magnetic flux rope
http://hdl.handle.net/10023/3855
Context. Coronal mass ejections (CME’s) are one of the most violent phenomena found on the Sun. One model to explain their occurrence is the flux rope ejection model. In this model, magnetic flux ropes form slowly over time periods of days to weeks. They then lose equilibrium and are ejected from the solar corona over a few hours. The contrasting time scales of formation and ejection pose a serious problem for numerical simulations. Aims. We simulate the whole life span of a flux rope from slow formation to rapid ejection and investigate whether magnetic flux ropes formed from a continuous magnetic field distribution, during a quasistatic evolution, can erupt to produce a CME. Methods. To model the full life span of magnetic flux ropes we couple two models. The global nonlinear forcefree field (GNLFFF) evolution model is used to follow the quasistatic formation of a flux rope. The MHD code ARMVAC is used to simulate the production of a CME through the loss of equilibrium and ejection of this flux rope. Results. We show that the two distinct models may be successfully coupled and that the flux rope is ejected out of our simulation box, where the outer boundary is placed at 2.5 R⊙. The plasma expelled during the flux rope ejection travels outward at a speed of 100 km s1, which is consistent with the observed speed of CMEs in the low corona. Conclusions. Our work shows that flux ropes formed in the GNLFFF can lead to the ejection of a mass loaded magnetic flux rope in full MHD simulations. Coupling the two distinct models opens up a new avenue of research to investigate phenomena where different phases of their evolution occur on drastically different time scales.
Sat, 01 Jun 2013 00:00:00 GMT
http://hdl.handle.net/10023/3855
20130601T00:00:00Z
Pagano, Paolo
Mackay, Duncan Hendry
Poedts, Stefaan
Context. Coronal mass ejections (CME’s) are one of the most violent phenomena found on the Sun. One model to explain their occurrence is the flux rope ejection model. In this model, magnetic flux ropes form slowly over time periods of days to weeks. They then lose equilibrium and are ejected from the solar corona over a few hours. The contrasting time scales of formation and ejection pose a serious problem for numerical simulations. Aims. We simulate the whole life span of a flux rope from slow formation to rapid ejection and investigate whether magnetic flux ropes formed from a continuous magnetic field distribution, during a quasistatic evolution, can erupt to produce a CME. Methods. To model the full life span of magnetic flux ropes we couple two models. The global nonlinear forcefree field (GNLFFF) evolution model is used to follow the quasistatic formation of a flux rope. The MHD code ARMVAC is used to simulate the production of a CME through the loss of equilibrium and ejection of this flux rope. Results. We show that the two distinct models may be successfully coupled and that the flux rope is ejected out of our simulation box, where the outer boundary is placed at 2.5 R⊙. The plasma expelled during the flux rope ejection travels outward at a speed of 100 km s1, which is consistent with the observed speed of CMEs in the low corona. Conclusions. Our work shows that flux ropes formed in the GNLFFF can lead to the ejection of a mass loaded magnetic flux rope in full MHD simulations. Coupling the two distinct models opens up a new avenue of research to investigate phenomena where different phases of their evolution occur on drastically different time scales.

Inhomogeneous magnetic fields in the solar atmosphere
http://hdl.handle.net/10023/3830
The magnetic field in the solar atmosphere is highly inhomogeneous. In the photosphere, the field is concentrated into intense flux tubes and the coronal magnetic field consists of many loops and regions of open field. This thesis investigates some of the basic properties of inhomogeneous solar magnetic fields.
First of all, the equilibrium properties of untwisted flux tubes, confined by a spatially varying external pressure distribution, are investigated. The behaviour of thick flux tubes, including the effects of a transverse field component and a variation in the field across the tube, is compared with slender flux tube theory. It is shown that slender tube theory is accurate for tubes which are approximately slender, but that completely misleading results can be obtained by applying slender tube theory if the pressure distribution is not slowly varying.
Twisted flux tubes are then studied, with the aim of finding how twisting affects a tube confined by an inhomogeneous pressure distribution. It is shown that, in general, a tube expands as it is twisted; this is illustrated both by extensions to slender tube theory and by some exact analytical solutions. A family of linear solutions is used to model the evolution of a finite tube confined by a falling external pressure. It is shown that, if the confining pressure falls too low, the tube may burst, with some dynamic process ensuing.
The equilibrium properties of a flux tube with a curved axis are then investigated, with the main aim of modelling coronal loops. Previous theory for the equilibrium of a curved slender flux tube in a gravitationally stratified atmosphere, with a balance between magnetic buoyancy and tension forces, is extended to take into account an external field and the effects of twist. Increasing the magnitude of the external field tends to lower the summit height of the tube. It is found that nonequilibrium sets in if the footpoints are separated more than a certain critical width, which does not depend on the magnitude of the external field. It is found that two possible equilibrium heights can exist for a twisted tube; however, if the tube is twisted too far, or if the footpoints are moved apart, nonequilibrium can set in. The critical width at which nonequilibrium occurs is lower for a twisted tube than for an untwisted one. This is suggested as an explanation for the rise of a filament prior to a two ribbon flare, and as a mechanism for coronal transients.
An alternative description of the coronal magnetic field is given, using a perturbation expansion for an almost potential field, with small pressure gradients. The field is assumed to be linetied at the photospheric base.
Then the equilibrium properties of the global magnetic field of a star are investigated. A linear and nonlinear family of solutions to the magnetostatic equilibrium equation are found. The linear solutions are used to investigate the twisting up of forcefree dipolar and quadrupolar fields, including in a simple manner the effects of a stellar wind. In both cases, it was found that the field becomes physically unreasonable if it is twisted too far, with field lines detached from the star being formed, which would be pulled out by the stellar wind. Thus, if the field is twisted more than a critical amount, nonequilibrium sets in and some catastrophic behaviour takes place. This is suggested as a possible mechanism for stellar flares. Similar results are found in a study of the effects of increasing the pressure gradients at the stellar surface of a magnetostatic dipolelike field. The linear solutions are also used to study the equilibrium of a finite magnetosphere, and multiple equilibria are found.
Finally, one aspect of the propagation of waves in an inhomogeneous magnetic field is studied, with particular reference to the problem of heating the solar corona. The mechanism of phasemixing, which provides a means of dissipating shear Alfven waves that propagate in an inhomogeneous magnetic field, is investigated. The onset of KelvinHelmholtz instability, which could disrupt the wave and thus enhance the dissipation, is studied. First, the dispersion relation of the instability is calculated for the case of fully developed phasemixing. Then, the onset of the instability is investigated, to find out whether the instability can grow before the phasemixing is fully developed. It is found that instability can set in after only a very few wave periods. It is suggested that the instability triggers off a turbulent cascade which dissipates the wave energy. The heating rates that could be produced by such a process are calculated, and are found to be more than adequate for coronal heating.
Sun, 01 Jan 1984 00:00:00 GMT
http://hdl.handle.net/10023/3830
19840101T00:00:00Z
Browning, Philippa
The magnetic field in the solar atmosphere is highly inhomogeneous. In the photosphere, the field is concentrated into intense flux tubes and the coronal magnetic field consists of many loops and regions of open field. This thesis investigates some of the basic properties of inhomogeneous solar magnetic fields.
First of all, the equilibrium properties of untwisted flux tubes, confined by a spatially varying external pressure distribution, are investigated. The behaviour of thick flux tubes, including the effects of a transverse field component and a variation in the field across the tube, is compared with slender flux tube theory. It is shown that slender tube theory is accurate for tubes which are approximately slender, but that completely misleading results can be obtained by applying slender tube theory if the pressure distribution is not slowly varying.
Twisted flux tubes are then studied, with the aim of finding how twisting affects a tube confined by an inhomogeneous pressure distribution. It is shown that, in general, a tube expands as it is twisted; this is illustrated both by extensions to slender tube theory and by some exact analytical solutions. A family of linear solutions is used to model the evolution of a finite tube confined by a falling external pressure. It is shown that, if the confining pressure falls too low, the tube may burst, with some dynamic process ensuing.
The equilibrium properties of a flux tube with a curved axis are then investigated, with the main aim of modelling coronal loops. Previous theory for the equilibrium of a curved slender flux tube in a gravitationally stratified atmosphere, with a balance between magnetic buoyancy and tension forces, is extended to take into account an external field and the effects of twist. Increasing the magnitude of the external field tends to lower the summit height of the tube. It is found that nonequilibrium sets in if the footpoints are separated more than a certain critical width, which does not depend on the magnitude of the external field. It is found that two possible equilibrium heights can exist for a twisted tube; however, if the tube is twisted too far, or if the footpoints are moved apart, nonequilibrium can set in. The critical width at which nonequilibrium occurs is lower for a twisted tube than for an untwisted one. This is suggested as an explanation for the rise of a filament prior to a two ribbon flare, and as a mechanism for coronal transients.
An alternative description of the coronal magnetic field is given, using a perturbation expansion for an almost potential field, with small pressure gradients. The field is assumed to be linetied at the photospheric base.
Then the equilibrium properties of the global magnetic field of a star are investigated. A linear and nonlinear family of solutions to the magnetostatic equilibrium equation are found. The linear solutions are used to investigate the twisting up of forcefree dipolar and quadrupolar fields, including in a simple manner the effects of a stellar wind. In both cases, it was found that the field becomes physically unreasonable if it is twisted too far, with field lines detached from the star being formed, which would be pulled out by the stellar wind. Thus, if the field is twisted more than a critical amount, nonequilibrium sets in and some catastrophic behaviour takes place. This is suggested as a possible mechanism for stellar flares. Similar results are found in a study of the effects of increasing the pressure gradients at the stellar surface of a magnetostatic dipolelike field. The linear solutions are also used to study the equilibrium of a finite magnetosphere, and multiple equilibria are found.
Finally, one aspect of the propagation of waves in an inhomogeneous magnetic field is studied, with particular reference to the problem of heating the solar corona. The mechanism of phasemixing, which provides a means of dissipating shear Alfven waves that propagate in an inhomogeneous magnetic field, is investigated. The onset of KelvinHelmholtz instability, which could disrupt the wave and thus enhance the dissipation, is studied. First, the dispersion relation of the instability is calculated for the case of fully developed phasemixing. Then, the onset of the instability is investigated, to find out whether the instability can grow before the phasemixing is fully developed. It is found that instability can set in after only a very few wave periods. It is suggested that the instability triggers off a turbulent cascade which dissipates the wave energy. The heating rates that could be produced by such a process are calculated, and are found to be more than adequate for coronal heating.

The structure, stability and interaction of geophysical vortices
http://hdl.handle.net/10023/3729
This thesis examines the structure, stability and interaction of geophysical vortices. We do so by restricting our attention to relative vortex equilibria, or states which appear stationary in a corotating frame of reference. We approach the problem from three different perspectives, namely by first studying the singlevortex, quasigeostrophic shallowwater problem, next by generalising it to an (asymmetric) twovortex problem, and finally by revisiting the singlevortex problem, making use of the more realistic, although more complicated, shallowwater model.
We find that in all of the systems studied, small vortices (compared to the Rossby deformation length) are more likely to be unstable than large ones. For the singlevortex problem, this means that large vortices can sustain much greater deformations before destabilising than small vortices, and for the twovortex problem this means that vortices are able to come closer together before destabilising. Additionally, we find that for large vortices, the degree of asymmetry of a vortex pair does not affect its stability, although it does affect the underlying steady state into which an unstable state transitions. Lastly, by carefully defining the "equivalence" between cyclones and anticyclones which appear in the shallowwater system, we find that cyclones are more stable than anticyclones. This is contrary to what is generally reported in the literature.
Fri, 28 Jun 2013 00:00:00 GMT
http://hdl.handle.net/10023/3729
20130628T00:00:00Z
Płotka, Hanna
This thesis examines the structure, stability and interaction of geophysical vortices. We do so by restricting our attention to relative vortex equilibria, or states which appear stationary in a corotating frame of reference. We approach the problem from three different perspectives, namely by first studying the singlevortex, quasigeostrophic shallowwater problem, next by generalising it to an (asymmetric) twovortex problem, and finally by revisiting the singlevortex problem, making use of the more realistic, although more complicated, shallowwater model.
We find that in all of the systems studied, small vortices (compared to the Rossby deformation length) are more likely to be unstable than large ones. For the singlevortex problem, this means that large vortices can sustain much greater deformations before destabilising than small vortices, and for the twovortex problem this means that vortices are able to come closer together before destabilising. Additionally, we find that for large vortices, the degree of asymmetry of a vortex pair does not affect its stability, although it does affect the underlying steady state into which an unstable state transitions. Lastly, by carefully defining the "equivalence" between cyclones and anticyclones which appear in the shallowwater system, we find that cyclones are more stable than anticyclones. This is contrary to what is generally reported in the literature.

Twodimensional magnetohydrodynamic turbulence in the small magnetic Prandtl number limit
http://hdl.handle.net/10023/3698
In this paper we introduce a new method for computations of twodimensional magnetohydrodynamic (MHD) turbulence at low magnetic Prandtl number $\Pra=\nu/\eta$. When $\Pra \ll 1$, the magnetic field dissipates at a scale much larger than the velocity field. The method we utilise is a novel hybrid contourspectral method, the ``Combined Lagrangian Advection Method'', formally to integrate the equations with zero viscous dissipation. The method is compared with a standard pseudospectral method for decreasing $\Pra$ for the problem of decaying twodimensional MHD turbulence. The method is shown to agree well for a wide range of imposed magnetic field strengths. Examples of problems for which such a method may prove invaluable are also given.
Sun, 01 Jul 2012 00:00:00 GMT
http://hdl.handle.net/10023/3698
20120701T00:00:00Z
Dritschel, David Gerard
Tobias, Steve
In this paper we introduce a new method for computations of twodimensional magnetohydrodynamic (MHD) turbulence at low magnetic Prandtl number $\Pra=\nu/\eta$. When $\Pra \ll 1$, the magnetic field dissipates at a scale much larger than the velocity field. The method we utilise is a novel hybrid contourspectral method, the ``Combined Lagrangian Advection Method'', formally to integrate the equations with zero viscous dissipation. The method is compared with a standard pseudospectral method for decreasing $\Pra$ for the problem of decaying twodimensional MHD turbulence. The method is shown to agree well for a wide range of imposed magnetic field strengths. Examples of problems for which such a method may prove invaluable are also given.

On energetics and inertialrange scaling laws of twodimensional magnetohydrodynamic turbulence
http://hdl.handle.net/10023/3668
We study twodimensional magnetohydrodynamic turbulence, with an emphasis on its energetics and inertial range scaling laws. A detailed spectral analysis shows that dynamo triads (those converting kinetic into magnetic energy) are associated with a direct magnetic energy flux while antidynamo triads (those converting magnetic into kinetic energy) are associated with an inverse magnetic energy flux. As both dynamo and antidynamo interacting triads are integral parts of the direct energy transfer, the antidynamo inverse flux partially neutralizes the dynamo direct flux, arguably resulting in relatively weak direct energy transfer and giving rise to dynamo saturation. This result is consistent with a qualitative prediction of energy transfer reduction owing to Alfv\'en wave effects by the IroshnikovKraichnan theory (which was originally formulated for magnetohydrodynamic turbulence in three dimensions). We numerically confirm the correlation between dynamo action and direct magnetic energy flux and investigate the applicability of quantitative aspects of the IroshnikovKraichnan theory to the present case, particularly its predictions of energy equipartition and $k^{3/2}$ spectra in the energy inertial range. It is found that for turbulence satisfying the Kraichnan condition of magnetic energy at large scales exceeding total energy in the inertial range, the kinetic energy spectrum, which is significantly shallower than $k^{3/2}$, is shallower than its magnetic counterpart. This result suggests no energy equipartition. The total energy spectrum appears to depend on the energy composition of the turbulence but is clearly shallower than $k^{3/2}$ for $r\approx2$, even at moderate resolutions. Here $r\approx2$ is the magnetictokinetic energy ratio during the stage when the turbulence can be considered fully developed. The implication of the present findings is discussed in conjunction with further numerical results on the dependence of the energy dissipation rate on resolution.
L. Blackbourn was supported by an EPSRC postgraduate studentship.
Sun, 01 Jul 2012 00:00:00 GMT
http://hdl.handle.net/10023/3668
20120701T00:00:00Z
Blackbourn, Luke Austen Kazimierz
Tran, Chuong Van
We study twodimensional magnetohydrodynamic turbulence, with an emphasis on its energetics and inertial range scaling laws. A detailed spectral analysis shows that dynamo triads (those converting kinetic into magnetic energy) are associated with a direct magnetic energy flux while antidynamo triads (those converting magnetic into kinetic energy) are associated with an inverse magnetic energy flux. As both dynamo and antidynamo interacting triads are integral parts of the direct energy transfer, the antidynamo inverse flux partially neutralizes the dynamo direct flux, arguably resulting in relatively weak direct energy transfer and giving rise to dynamo saturation. This result is consistent with a qualitative prediction of energy transfer reduction owing to Alfv\'en wave effects by the IroshnikovKraichnan theory (which was originally formulated for magnetohydrodynamic turbulence in three dimensions). We numerically confirm the correlation between dynamo action and direct magnetic energy flux and investigate the applicability of quantitative aspects of the IroshnikovKraichnan theory to the present case, particularly its predictions of energy equipartition and $k^{3/2}$ spectra in the energy inertial range. It is found that for turbulence satisfying the Kraichnan condition of magnetic energy at large scales exceeding total energy in the inertial range, the kinetic energy spectrum, which is significantly shallower than $k^{3/2}$, is shallower than its magnetic counterpart. This result suggests no energy equipartition. The total energy spectrum appears to depend on the energy composition of the turbulence but is clearly shallower than $k^{3/2}$ for $r\approx2$, even at moderate resolutions. Here $r\approx2$ is the magnetictokinetic energy ratio during the stage when the turbulence can be considered fully developed. The implication of the present findings is discussed in conjunction with further numerical results on the dependence of the energy dissipation rate on resolution.

Equilibrium and stability properties of collisionless current sheet models
http://hdl.handle.net/10023/3548
The work in this thesis focuses primarily on equilibrium and stability properties of collisionless current sheet models, in particular of the forcefree Harris sheet model.
A detailed investigation is carried out into the properties of the distribution function found by Harrison and Neukirch (Physical Review Letters 102, 135003, 2009) for the forcefree Harris sheet, which is so far the only known nonlinear forcefree VlasovMaxwell equilibrium. Exact conditions on the parameters of the distribution function are found, which show when it can be single or multipeaked in two of the velocity space directions. This is important because it may have implications for the stability of the equilibrium.
One major aim of this thesis is to find new forcefree equilibrium distribution functions. By using a new method which is different from that of Harrison and Neukirch, it is possible to find a complete family of distribution functions for the forcefree Harris sheet, which includes the Harrison and Neukirch distribution function (Physical Review Letters 102, 135003, 2009). Each member of this family has a different dependence on the particle energy, although the dependence on the canonical momenta remains the same. Three detailed analytical examples are presented. Other possibilities for finding further collisionless forcefree equilibrium distribution functions have been explored, but were unsuccessful.
The first linear stability analysis of the Harrison and Neukirch equilibrium distribution function is then carried out, concentrating on macroscopic instabilities, and considering twodimensional perturbations only. The analysis is based on the technique of integration over unperturbed orbits. Similarly to the Harris sheet case (Nuovo Cimento, 23:115, 1962), this is only possible by using approximations to the exact orbits, which are unknown. Furthermore, the approximations for the Harris sheet case cannot be used for the forcefree Harris sheet, and so new techniques have to be developed in order to make analytical progress. Full analytical expressions for the perturbed current density are derived but, for the sake of simplicity, only the long wavelength limit is investigated. The dependence of the stability on various equilibrium parameters is investigated.
Fri, 28 Jun 2013 00:00:00 GMT
http://hdl.handle.net/10023/3548
20130628T00:00:00Z
Wilson, Fiona
The work in this thesis focuses primarily on equilibrium and stability properties of collisionless current sheet models, in particular of the forcefree Harris sheet model.
A detailed investigation is carried out into the properties of the distribution function found by Harrison and Neukirch (Physical Review Letters 102, 135003, 2009) for the forcefree Harris sheet, which is so far the only known nonlinear forcefree VlasovMaxwell equilibrium. Exact conditions on the parameters of the distribution function are found, which show when it can be single or multipeaked in two of the velocity space directions. This is important because it may have implications for the stability of the equilibrium.
One major aim of this thesis is to find new forcefree equilibrium distribution functions. By using a new method which is different from that of Harrison and Neukirch, it is possible to find a complete family of distribution functions for the forcefree Harris sheet, which includes the Harrison and Neukirch distribution function (Physical Review Letters 102, 135003, 2009). Each member of this family has a different dependence on the particle energy, although the dependence on the canonical momenta remains the same. Three detailed analytical examples are presented. Other possibilities for finding further collisionless forcefree equilibrium distribution functions have been explored, but were unsuccessful.
The first linear stability analysis of the Harrison and Neukirch equilibrium distribution function is then carried out, concentrating on macroscopic instabilities, and considering twodimensional perturbations only. The analysis is based on the technique of integration over unperturbed orbits. Similarly to the Harris sheet case (Nuovo Cimento, 23:115, 1962), this is only possible by using approximations to the exact orbits, which are unknown. Furthermore, the approximations for the Harris sheet case cannot be used for the forcefree Harris sheet, and so new techniques have to be developed in order to make analytical progress. Full analytical expressions for the perturbed current density are derived but, for the sake of simplicity, only the long wavelength limit is investigated. The dependence of the stability on various equilibrium parameters is investigated.

Twodimensional magnetohydrodynamic turbulence in the limits of infinite and vanishing magnetic Prandtl number
http://hdl.handle.net/10023/3539
We study both theoretically and numerically twodimensional magnetohydrodynamic turbulence at infinite and zero magnetic Prandtl number $Pm$ (and the limits thereof), with an emphasis on solution regularity. For $Pm=0$, both $\norm{\omega}^2$ and $\norm{j}^2$, where $\omega$ and $j$ are, respectively, the vorticity and current, are uniformly bounded. Furthermore, $\norm{\nabla j}^2$ is integrable over $[0,\infty)$. The uniform boundedness of $\norm{\omega}^2$ implies that in the presence of vanishingly small viscosity $\nu$ (i.e. in the limit $Pm\to0$), the kinetic energy dissipation rate $\nu\norm{\omega}^2$ vanishes for all times $t$, including $t=\infty$. Furthermore, for sufficiently small $Pm$, this rate decreases linearly with $Pm$. This linear behaviour of $\nu\norm{\omega}^2$ is investigated and confirmed by highresolution simulations with $Pm$ in the range $[1/64,1]$. Several criteria for solution regularity are established and numerically tested. As $Pm$ is decreased from unity, the ratio $\norm{\omega}_\infty/\norm{\omega}$ is observed to increase relatively slowly. This, together with the integrability of $\norm{\nabla j}^2$, suggests global regularity for $Pm=0$. When $Pm=\infty$, global regularity is secured when either $\norm{\nabla\u}_\infty/\norm{\omega}$, where $\u$ is the fluid velocity, or $\norm{j}_\infty/\norm{j}$ is bounded. The former is plausible given the presence of viscous effects for this case. Numerical results over the range $Pm\in[1,64]$ show that $\norm{\nabla\u}_\infty/\norm{\omega}$ varies slightly (with similar behaviour for $\norm{j}_\infty/\norm{j}$), thereby lending strong support for the possibility $\norm{\nabla\u}_\infty/\norm{\omega}<\infty$ in the limit $Pm\to\infty$. The peak of the magnetic energy dissipation rate $\mu\norm{j}^2$ is observed to decrease rapidly as $Pm$ is increased. This result suggests the possibility $\norm{j}^2<\infty$ in the limit $Pm\to\infty$. We discuss further evidence for the boundedness of the ratios $\norm{\omega}_\infty/\norm{\omega}$, $\norm{\nabla\u}_\infty/\norm{\omega}$ and $\norm{j}_\infty/\norm{j}$ in conjunction with observation on the density of filamentary structures in the vorticity, velocity gradient and current fields.
LAKB was supported by an EPSRC postgraduate studentship.
Sat, 01 Jun 2013 00:00:00 GMT
http://hdl.handle.net/10023/3539
20130601T00:00:00Z
Tran, Chuong Van
Yu, Xinwei
Blackbourn, Luke Austen Kazimierz
We study both theoretically and numerically twodimensional magnetohydrodynamic turbulence at infinite and zero magnetic Prandtl number $Pm$ (and the limits thereof), with an emphasis on solution regularity. For $Pm=0$, both $\norm{\omega}^2$ and $\norm{j}^2$, where $\omega$ and $j$ are, respectively, the vorticity and current, are uniformly bounded. Furthermore, $\norm{\nabla j}^2$ is integrable over $[0,\infty)$. The uniform boundedness of $\norm{\omega}^2$ implies that in the presence of vanishingly small viscosity $\nu$ (i.e. in the limit $Pm\to0$), the kinetic energy dissipation rate $\nu\norm{\omega}^2$ vanishes for all times $t$, including $t=\infty$. Furthermore, for sufficiently small $Pm$, this rate decreases linearly with $Pm$. This linear behaviour of $\nu\norm{\omega}^2$ is investigated and confirmed by highresolution simulations with $Pm$ in the range $[1/64,1]$. Several criteria for solution regularity are established and numerically tested. As $Pm$ is decreased from unity, the ratio $\norm{\omega}_\infty/\norm{\omega}$ is observed to increase relatively slowly. This, together with the integrability of $\norm{\nabla j}^2$, suggests global regularity for $Pm=0$. When $Pm=\infty$, global regularity is secured when either $\norm{\nabla\u}_\infty/\norm{\omega}$, where $\u$ is the fluid velocity, or $\norm{j}_\infty/\norm{j}$ is bounded. The former is plausible given the presence of viscous effects for this case. Numerical results over the range $Pm\in[1,64]$ show that $\norm{\nabla\u}_\infty/\norm{\omega}$ varies slightly (with similar behaviour for $\norm{j}_\infty/\norm{j}$), thereby lending strong support for the possibility $\norm{\nabla\u}_\infty/\norm{\omega}<\infty$ in the limit $Pm\to\infty$. The peak of the magnetic energy dissipation rate $\mu\norm{j}^2$ is observed to decrease rapidly as $Pm$ is increased. This result suggests the possibility $\norm{j}^2<\infty$ in the limit $Pm\to\infty$. We discuss further evidence for the boundedness of the ratios $\norm{\omega}_\infty/\norm{\omega}$, $\norm{\nabla\u}_\infty/\norm{\omega}$ and $\norm{j}_\infty/\norm{j}$ in conjunction with observation on the density of filamentary structures in the vorticity, velocity gradient and current fields.

Note on solution regularity of the generalized magnetohydrodynamic equations with partial dissipation
http://hdl.handle.net/10023/3538
In this brief note we study the ndimensional magnetohydrodynamic equations with hyperviscosity and zero resistivity. We prove global regularity of solutions when the hyperviscosity is sufficiently strong.
Mon, 01 Jul 2013 00:00:00 GMT
http://hdl.handle.net/10023/3538
20130701T00:00:00Z
Tran, Chuong Van
Yu, Xinwei
Zhai, Zhichun
In this brief note we study the ndimensional magnetohydrodynamic equations with hyperviscosity and zero resistivity. We prove global regularity of solutions when the hyperviscosity is sufficiently strong.

Solar magnetic carpet III : coronal modelling of synthetic magnetograms
http://hdl.handle.net/10023/3536
Sun, 01 Sep 2013 00:00:00 GMT
http://hdl.handle.net/10023/3536
20130901T00:00:00Z
Meyer, Karen Alison
Mackay, Duncan Hendry
van Ballegooijen, Aad
Parnell, Clare Elizabeth

On global regularity of 2D generalized magnetohydrodynamic equations
http://hdl.handle.net/10023/3401
In this article we study the global regularity of 2D generalized magnetohydrodynamic equations (2D GMHD), in which the dissipation terms are –ν(–Δ)αu and –κ(–Δ)βb. We show that smooth solutions are global in the following three cases: α≥1/2, β≥1; 0≤α≤1/2, 2α+β>2; α≥2, β=0. We also show that in the inviscid case ν=0, if β>1, then smooth solutions are global as long as the direction of the magnetic field remains smooth enough.
Wed, 15 May 2013 00:00:00 GMT
http://hdl.handle.net/10023/3401
20130515T00:00:00Z
Tran, Chuong Van
Yu, Xinwei
Zhai, Zhichun
In this article we study the global regularity of 2D generalized magnetohydrodynamic equations (2D GMHD), in which the dissipation terms are –ν(–Δ)αu and –κ(–Δ)βb. We show that smooth solutions are global in the following three cases: α≥1/2, β≥1; 0≤α≤1/2, 2α+β>2; α≥2, β=0. We also show that in the inviscid case ν=0, if β>1, then smooth solutions are global as long as the direction of the magnetic field remains smooth enough.

Sharp global nonlinear stability for a fluid overlying a highly porous material
http://hdl.handle.net/10023/3399
The stability of convection in a twolayer system in which a layer of fluid with a temperaturedependent viscosity overlies and saturates a highly porous material is studied. Owing to the difficulties associated with incorporating the nonlinear advection term in the NavierStokes equations into a stability analysis, previous literature on fluid/porous thermal convection has modelled the fluid using the linear Stokes equations. This paper derives global stability for the full nonlinear system, by utilizing a model proposed by Ladyzhenskaya. The nonlinear stability boundaries are shown to be sharp when compared with the linear instability thresholds.
Fri, 08 Jan 2010 00:00:00 GMT
http://hdl.handle.net/10023/3399
20100108T00:00:00Z
Hill, Antony A.
Carr, Magda
The stability of convection in a twolayer system in which a layer of fluid with a temperaturedependent viscosity overlies and saturates a highly porous material is studied. Owing to the difficulties associated with incorporating the nonlinear advection term in the NavierStokes equations into a stability analysis, previous literature on fluid/porous thermal convection has modelled the fluid using the linear Stokes equations. This paper derives global stability for the full nonlinear system, by utilizing a model proposed by Ladyzhenskaya. The nonlinear stability boundaries are shown to be sharp when compared with the linear instability thresholds.

Nonlinear stability of the onedomain approach to modelling convection in superposed fluid and porous layers
http://hdl.handle.net/10023/3398
Studies of the nonlinear stability of fluid/porous systems have been developed very recently. A twodomain modelling approach has been adopted in previous works, but was restricted to specific configurations. The extension to the more general case of a Navier–Stokes modelled fluid over a porous material was not achieved for the twodomain approach owing to the difficulties associated with handling the interfacial boundary conditions. This paper addresses this issue by adopting a onedomain approach, where the governing equations for both regions are combined into a unique set of equations that are valid for the entire domain. It is shown that the nonlinear stability bound, in the onedomain approach, is very sharp and hence excludes the possibility of subcritical instabilities. Moreover, the onedomain approach is compared with an equivalent twodomain approach, and excellent agreement is found between the two.
Wed, 01 Sep 2010 00:00:00 GMT
http://hdl.handle.net/10023/3398
20100901T00:00:00Z
Hill, A A
Carr, Magda
Studies of the nonlinear stability of fluid/porous systems have been developed very recently. A twodomain modelling approach has been adopted in previous works, but was restricted to specific configurations. The extension to the more general case of a Navier–Stokes modelled fluid over a porous material was not achieved for the twodomain approach owing to the difficulties associated with handling the interfacial boundary conditions. This paper addresses this issue by adopting a onedomain approach, where the governing equations for both regions are combined into a unique set of equations that are valid for the entire domain. It is shown that the nonlinear stability bound, in the onedomain approach, is very sharp and hence excludes the possibility of subcritical instabilities. Moreover, the onedomain approach is compared with an equivalent twodomain approach, and excellent agreement is found between the two.

Instability in internal solitary waves with trapped cores
http://hdl.handle.net/10023/3397
A numerical method that employs a combination of contour advection and pseudospectral techniques is used to investigate instability in internal solitary waves with trapped cores. A threelayer configuration for the background stratification in which the top two layers are linearly stratified and the lower layer is homogeneous is considered throughout. The strength of the stratification in the very top layer is chosen to be sufficient so that waves of depression with trapped cores can be generated. The flow is assumed to satisfy the DubrielJacotinLong equation both inside and outside of the core region. The BruntVaisala frequency is modelled such that it varies from a constant value outside of the core to zero inside the core over a sharp but continuous transition length. This results in a stagnant core in which the vorticity is zero and the density is homogeneous and approximately equal to that at the core boundary. The time dependent simulations show that instability occurs on the boundary of the core. The instability takes the form of KelvinHelmholtz billows. If the instability in the vorticity field is energetic enough, disturbance in the buoyancy field is also seen and fluid exchange takes place across the core boundary. Occurrence of the KelvinHelmholtz billows is attributed to the sharp change in the vorticity field at the boundary between the core and the pycnocline. The numerical scheme is not limited by small Richardson number unlike the other alternatives currently available in the literature which appear to be.
Sun, 01 Jan 2012 00:00:00 GMT
http://hdl.handle.net/10023/3397
20120101T00:00:00Z
Carr, Magda
King, Stuart Edward
Dritschel, David Gerard
A numerical method that employs a combination of contour advection and pseudospectral techniques is used to investigate instability in internal solitary waves with trapped cores. A threelayer configuration for the background stratification in which the top two layers are linearly stratified and the lower layer is homogeneous is considered throughout. The strength of the stratification in the very top layer is chosen to be sufficient so that waves of depression with trapped cores can be generated. The flow is assumed to satisfy the DubrielJacotinLong equation both inside and outside of the core region. The BruntVaisala frequency is modelled such that it varies from a constant value outside of the core to zero inside the core over a sharp but continuous transition length. This results in a stagnant core in which the vorticity is zero and the density is homogeneous and approximately equal to that at the core boundary. The time dependent simulations show that instability occurs on the boundary of the core. The instability takes the form of KelvinHelmholtz billows. If the instability in the vorticity field is energetic enough, disturbance in the buoyancy field is also seen and fluid exchange takes place across the core boundary. Occurrence of the KelvinHelmholtz billows is attributed to the sharp change in the vorticity field at the boundary between the core and the pycnocline. The numerical scheme is not limited by small Richardson number unlike the other alternatives currently available in the literature which appear to be.

Shear induced breaking of large internal solitary waves
http://hdl.handle.net/10023/3396
The stability properties of 24 experimentally generated internal solitary waves (ISWs) of extremely large amplitude, all with minimum Richardson number less than 1/4, are investigated. The study is supplemented by fully nonlinear calculations in a threelayer fluid. The waves move along a linearly stratified pycnocline (depth h2) sandwiched between a thin upper layer (depth h1) and a deep lower layer (depth h3), both homogeneous. In particular, the waveinduced velocity profile through the pycnocline is measured by particle image velocimetry (PIV) and obtained in computation. Breaking ISWs were found to have amplitudes (a1) in the range a1>2.24 √h1h2(1+h2/h1), while stable waves were on or below this limit. Breaking ISWs were investigated for 0.27 < h2/h1 < 1 and 4.14 < h3/(h1 + h2) < 7.14 and stable waves for 0.36 < h2/h1 < 3.67 and 3.22 < h3/(h1 + h2) < 7.25. Kelvin–Helmholtzlike billows were observed in the breaking cases. They had a length of 7.9h2 and a propagation speed 0.09 times the wave speed. These measured values compared well with predicted values from a stability analysis, assuming steady shear flow with U(z) and ρ(z) taken at the wave maximum (U(z) horizontal velocity profile, ρ(z) density along the vertical z). Only unstable modes in waves of sufficient strength have the chance to grow sufficiently fast to develop breaking: the waves that broke had an estimated growth (of unstable modes) more than 3.3–3.7 times than in the strongest stable case. Evaluation of the minimum Richardson number (Rimin, in the pycnocline), the horizontal length of a pocket of possible instability, with waveinduced Ri < 14, (Lx) and the wavelength (λ), showed that all measurements fall within the range Rimin = −0.23Lx/λ + 0.298 ± 0.016 in the (Lx/λ, Rimin)plane. Breaking ISWs were found for Lx/λ > 0.86 and stable waves for Lx/λ < 0.86. The results show a sort of thresholdlike behaviour in terms of Lx/λ. The results demonstrate that the breaking threshold of Lx/λ = 0.86 was sharper than one based on a minimum Richardson number and reveal that the Richardson number was found to become almost antisymmetric across relatively thick pycnoclines, with the minimum occurring towards the top part of the pycnocline
Sun, 01 Feb 2009 00:00:00 GMT
http://hdl.handle.net/10023/3396
20090201T00:00:00Z
Fructus, D
Carr, Magda
Grue, J
Jensen, A
Davies, P A
The stability properties of 24 experimentally generated internal solitary waves (ISWs) of extremely large amplitude, all with minimum Richardson number less than 1/4, are investigated. The study is supplemented by fully nonlinear calculations in a threelayer fluid. The waves move along a linearly stratified pycnocline (depth h2) sandwiched between a thin upper layer (depth h1) and a deep lower layer (depth h3), both homogeneous. In particular, the waveinduced velocity profile through the pycnocline is measured by particle image velocimetry (PIV) and obtained in computation. Breaking ISWs were found to have amplitudes (a1) in the range a1>2.24 √h1h2(1+h2/h1), while stable waves were on or below this limit. Breaking ISWs were investigated for 0.27 < h2/h1 < 1 and 4.14 < h3/(h1 + h2) < 7.14 and stable waves for 0.36 < h2/h1 < 3.67 and 3.22 < h3/(h1 + h2) < 7.25. Kelvin–Helmholtzlike billows were observed in the breaking cases. They had a length of 7.9h2 and a propagation speed 0.09 times the wave speed. These measured values compared well with predicted values from a stability analysis, assuming steady shear flow with U(z) and ρ(z) taken at the wave maximum (U(z) horizontal velocity profile, ρ(z) density along the vertical z). Only unstable modes in waves of sufficient strength have the chance to grow sufficiently fast to develop breaking: the waves that broke had an estimated growth (of unstable modes) more than 3.3–3.7 times than in the strongest stable case. Evaluation of the minimum Richardson number (Rimin, in the pycnocline), the horizontal length of a pocket of possible instability, with waveinduced Ri < 14, (Lx) and the wavelength (λ), showed that all measurements fall within the range Rimin = −0.23Lx/λ + 0.298 ± 0.016 in the (Lx/λ, Rimin)plane. Breaking ISWs were found for Lx/λ > 0.86 and stable waves for Lx/λ < 0.86. The results show a sort of thresholdlike behaviour in terms of Lx/λ. The results demonstrate that the breaking threshold of Lx/λ = 0.86 was sharper than one based on a minimum Richardson number and reveal that the Richardson number was found to become almost antisymmetric across relatively thick pycnoclines, with the minimum occurring towards the top part of the pycnocline

Convectively induced shear instability in large amplitude internal solitary waves
http://hdl.handle.net/10023/3395
Laboratory study has been carried out to investigate the instability of an internal solitary wave of depression in a shallow stratified fluid system. The experimental campaign has been supported by theoretical computations and has focused on a two layered stratification consisting of a homogeneous dense layer below a linearly stratified top layer. The initial background stratification has been varied and it is found that the onset and intensity of breaking are affected dramatically by changes in the background stratification. Manifestations of a combination of shear and convective instability are seen on the leading face of the wave. It is shown that there is an interplay between the two instability types and convective instability induces shear by enhancing isopycnal compression. Variation in the upper boundary condition is also found to have an effect on stability. In particular, the implications for convective instability are shown to be profound and a dramatic increase in wave amplitude is seen for a fixed (as opposed to free) upper boundary condition.
Partially funded by grant no. GR/S27368/01 from EPSRC
Mon, 01 Dec 2008 00:00:00 GMT
http://hdl.handle.net/10023/3395
20081201T00:00:00Z
Carr, Magda
Fructus, D
Grue, J
Jensen, A
Davies, P A
Laboratory study has been carried out to investigate the instability of an internal solitary wave of depression in a shallow stratified fluid system. The experimental campaign has been supported by theoretical computations and has focused on a two layered stratification consisting of a homogeneous dense layer below a linearly stratified top layer. The initial background stratification has been varied and it is found that the onset and intensity of breaking are affected dramatically by changes in the background stratification. Manifestations of a combination of shear and convective instability are seen on the leading face of the wave. It is shown that there is an interplay between the two instability types and convective instability induces shear by enhancing isopycnal compression. Variation in the upper boundary condition is also found to have an effect on stability. In particular, the implications for convective instability are shown to be profound and a dramatic increase in wave amplitude is seen for a fixed (as opposed to free) upper boundary condition.

Number of degrees of freedom and energy spectrum of surface quasigeostrophic turbulence
http://hdl.handle.net/10023/3377
We study both theoretically and numerically surface quasigeostrophic turbulence regularized by the usual molecular viscosity, with an emphasis on a number of classical predictions. It is found that the system's number of degrees of freedom N, which is defined in terms of local Lyapunov exponents, scales as Re3/2, where R e is the Reynolds number expressible in terms of the viscosity, energy dissipation rate and system's integral scale. For general powerlaw energy spectra k(alpha), a comparison of N with the number of dynamically active Fourier modes, i.e. the modes within the energy inertial range, yields alpha = 5/3. This comparison further renders the scaling Re1/2 for the exponential dissipation rate at the dissipation wavenumber. These results have been predicted on the basis of Kolmogorov's theory. Our approach thus recovers these classical predictions and is an analytic alternative to the traditional phenomenological method. The implications of the present findings are discussed in conjunction with related results in the literature. Support for the analytic results is provided through a series of direct numerical simulations.
L.A.K.B. was supported by an EPSRC postgraduate studentship.
Sat, 01 Oct 2011 00:00:00 GMT
http://hdl.handle.net/10023/3377
20111001T00:00:00Z
Tran, Chuong Van
Blackbourn, Luke Austen Kazimierz
Scott, Richard Kirkness
We study both theoretically and numerically surface quasigeostrophic turbulence regularized by the usual molecular viscosity, with an emphasis on a number of classical predictions. It is found that the system's number of degrees of freedom N, which is defined in terms of local Lyapunov exponents, scales as Re3/2, where R e is the Reynolds number expressible in terms of the viscosity, energy dissipation rate and system's integral scale. For general powerlaw energy spectra k(alpha), a comparison of N with the number of dynamically active Fourier modes, i.e. the modes within the energy inertial range, yields alpha = 5/3. This comparison further renders the scaling Re1/2 for the exponential dissipation rate at the dissipation wavenumber. These results have been predicted on the basis of Kolmogorov's theory. Our approach thus recovers these classical predictions and is an analytic alternative to the traditional phenomenological method. The implications of the present findings are discussed in conjunction with related results in the literature. Support for the analytic results is provided through a series of direct numerical simulations.

Coronal heating by the partial relaxation of twisted loops
http://hdl.handle.net/10023/3373
Context: Relaxation theory offers a straightforward method for estimating the energy that is released when a magnetic field becomes unstable, as a result of continual convective driving. Aims: We present new results obtained from nonlinear magnetohydrodynamic (MHD) simulations of idealised coronal loops. The purpose of this work is to determine whether or not the simulation results agree with Taylor relaxation, which will require a modified version of relaxation theory applicable to unbounded field configurations. Methods: A threedimensional (3D) MHD Lagrangianremap code is used to simulate the evolution of a linetied cylindrical coronal loop model. This model comprises three concentric layers surrounded by a potential envelope; hence, being twisted locally, each loop configuration is distinguished by a piecewiseconstant current profile. Initially, all configurations carry zeronetcurrent fields and are in ideally unstable equilibrium. The simulation results are compared with the predictions of helicity conserving relaxation theory. Results: For all simulations, the change in helicity is no more than 2% of the initial value; also, the numerical helicities match the analyticallydetermined values. Magnetic energy dissipation predominantly occurs via shock heating associated with magnetic reconnection in distributed current sheets. The energy release and final field profiles produced by the numerical simulations are in agreement with the predictions given by a new model of partial relaxation theory: the relaxed field is close to a linear force free state; however, the extent of the relaxation region is limited, while the loop undergoes some radial expansion. Conclusions: The results presented here support the use of partial relaxation theory, specifically, when calculating the heatingevent distributions produced by ensembles of kinkunstable loops.
Fri, 01 Feb 2013 00:00:00 GMT
http://hdl.handle.net/10023/3373
20130201T00:00:00Z
Bareford, Michael
Hood, Alan
Browning, Philippa
Context: Relaxation theory offers a straightforward method for estimating the energy that is released when a magnetic field becomes unstable, as a result of continual convective driving. Aims: We present new results obtained from nonlinear magnetohydrodynamic (MHD) simulations of idealised coronal loops. The purpose of this work is to determine whether or not the simulation results agree with Taylor relaxation, which will require a modified version of relaxation theory applicable to unbounded field configurations. Methods: A threedimensional (3D) MHD Lagrangianremap code is used to simulate the evolution of a linetied cylindrical coronal loop model. This model comprises three concentric layers surrounded by a potential envelope; hence, being twisted locally, each loop configuration is distinguished by a piecewiseconstant current profile. Initially, all configurations carry zeronetcurrent fields and are in ideally unstable equilibrium. The simulation results are compared with the predictions of helicity conserving relaxation theory. Results: For all simulations, the change in helicity is no more than 2% of the initial value; also, the numerical helicities match the analyticallydetermined values. Magnetic energy dissipation predominantly occurs via shock heating associated with magnetic reconnection in distributed current sheets. The energy release and final field profiles produced by the numerical simulations are in agreement with the predictions given by a new model of partial relaxation theory: the relaxed field is close to a linear force free state; however, the extent of the relaxation region is limited, while the loop undergoes some radial expansion. Conclusions: The results presented here support the use of partial relaxation theory, specifically, when calculating the heatingevent distributions produced by ensembles of kinkunstable loops.

Damping of kink waves by mode coupling : I. Analytical treatment
http://hdl.handle.net/10023/3340
Aims. To investigate the spatial damping of propagating kink waves in an inhomogeneous plasma. In the limit of a thin tube surrounded by a thin transition layer, an analytical formulation for kink waves driven in from the bottom boundary of the corona is presented. Methods. The spatial form for the damping of the kink mode was investigated using various analytical approximations. When the density ratio between the internal density and the external density is not too large, a simple di.erentialintegral equation was used. Approximate analytical solutions to this equation are presented. Results. For the first time, the form of the spatial damping of the kink mode is shown analytically to be Gaussian in nature near the driven boundary. For several wavelengths, the amplitude of the kink mode is proportional to (1 + exp(z2 /L2 g))/2, where L2g = 16/ǫκ2 k2 . Although the actual value of 16 in Lg depends on the particular form of the driver, this form is very general and its dependence on the other parameters does not change. For large distances, the damping profile appears to be roughly linear exponential decay. This is shown analytically by a series expansion when the inhomogeneous layer width is small enough.
Fri, 01 Mar 2013 00:00:00 GMT
http://hdl.handle.net/10023/3340
20130301T00:00:00Z
Hood, Alan William
Ruderman, Michael
Pascoe, David James
De Moortel, Ineke
Terradas, Jaume
Wright, Andrew Nicholas
Aims. To investigate the spatial damping of propagating kink waves in an inhomogeneous plasma. In the limit of a thin tube surrounded by a thin transition layer, an analytical formulation for kink waves driven in from the bottom boundary of the corona is presented. Methods. The spatial form for the damping of the kink mode was investigated using various analytical approximations. When the density ratio between the internal density and the external density is not too large, a simple di.erentialintegral equation was used. Approximate analytical solutions to this equation are presented. Results. For the first time, the form of the spatial damping of the kink mode is shown analytically to be Gaussian in nature near the driven boundary. For several wavelengths, the amplitude of the kink mode is proportional to (1 + exp(z2 /L2 g))/2, where L2g = 16/ǫκ2 k2 . Although the actual value of 16 in Lg depends on the particular form of the driver, this form is very general and its dependence on the other parameters does not change. For large distances, the damping profile appears to be roughly linear exponential decay. This is shown analytically by a series expansion when the inhomogeneous layer width is small enough.

The influence of a fluidporous interface on solar pond stability
http://hdl.handle.net/10023/3338
The linear instability of the gradient zone of a solar pond containing a fluidporous interface is investigated. It is found that the gradient zone can retain the same stability for lower values of the solute Rayleigh number with the introduction of a porous material compared with a purely fluid layer, whilst maintaining the same lower convective zone temperature. Interestingly, it is also shown that for certain parameter values the penetration of a porous medium into the gradient zone can cause the temperature of the lower convective zone to rise. However, for certain parameter ranges, when the fluidporous interface is towards the top of the gradient zone, the solar pond can become highly unstable.
Fri, 01 Feb 2013 00:00:00 GMT
http://hdl.handle.net/10023/3338
20130201T00:00:00Z
Hill, A. A
Carr, Magda
The linear instability of the gradient zone of a solar pond containing a fluidporous interface is investigated. It is found that the gradient zone can retain the same stability for lower values of the solute Rayleigh number with the introduction of a porous material compared with a purely fluid layer, whilst maintaining the same lower convective zone temperature. Interestingly, it is also shown that for certain parameter values the penetration of a porous medium into the gradient zone can cause the temperature of the lower convective zone to rise. However, for certain parameter ranges, when the fluidporous interface is towards the top of the gradient zone, the solar pond can become highly unstable.

A Bayesian approach to fitting Gibbs processes with temporal random effects
http://hdl.handle.net/10023/3305
We consider spatial point pattern data that have been observed repeatedly over a period of time in an inhomogeneous environment. Each spatial point pattern can be regarded as a “snapshot” of the underlying point process at a series of times. Thus, the number of points and corresponding locations of points differ for each snapshot. Each snapshot can be analyzed independently, but in many cases there may be little information in the data relating to model parameters, particularly parameters relating to the interaction between points. Thus, we develop an integrated approach, simultaneously analyzing all snapshots within a single robust and consistent analysis. We assume that sufficient time has passed between observation dates so that the spatial point patterns can be regarded as independent replicates, given spatial covariates. We develop a joint mixed effects Gibbs point process model for the replicates of spatial point patterns by considering environmental covariates in the analysis as fixed effects, to model the heterogeneous environment, with a random effects (or hierarchical) component to account for the different observation days for the intensity function. We demonstrate how the model can be fitted within a Bayesian framework using an auxiliary variable approach to deal with the issue of the random effects component. We apply the methods to a data set of musk oxen herds and demonstrate the increased precision of the parameter estimates when considering all available data within a single integrated analysis.
This work is partially supported by Research Councils UK
Sat, 01 Dec 2012 00:00:00 GMT
http://hdl.handle.net/10023/3305
20121201T00:00:00Z
King, Ruth
Illian, Janine Baerbel
King, Stuart Edward
Nightingale, Glenna Faith
Hendrichsen, Ditte
We consider spatial point pattern data that have been observed repeatedly over a period of time in an inhomogeneous environment. Each spatial point pattern can be regarded as a “snapshot” of the underlying point process at a series of times. Thus, the number of points and corresponding locations of points differ for each snapshot. Each snapshot can be analyzed independently, but in many cases there may be little information in the data relating to model parameters, particularly parameters relating to the interaction between points. Thus, we develop an integrated approach, simultaneously analyzing all snapshots within a single robust and consistent analysis. We assume that sufficient time has passed between observation dates so that the spatial point patterns can be regarded as independent replicates, given spatial covariates. We develop a joint mixed effects Gibbs point process model for the replicates of spatial point patterns by considering environmental covariates in the analysis as fixed effects, to model the heterogeneous environment, with a random effects (or hierarchical) component to account for the different observation days for the intensity function. We demonstrate how the model can be fitted within a Bayesian framework using an auxiliary variable approach to deal with the issue of the random effects component. We apply the methods to a data set of musk oxen herds and demonstrate the increased precision of the parameter estimates when considering all available data within a single integrated analysis.

Finite and infinite ergodic theory for linear and conformal dynamical systems
http://hdl.handle.net/10023/3220
The first main topic of this thesis is the thorough analysis of two families of piecewise linear
maps on the unit interval, the αLüroth and αFarey maps. Here, α denotes a countably infinite
partition of the unit interval whose atoms only accumulate at the origin. The basic properties
of these maps will be developed, including that each αLüroth map (denoted Lα) gives rise to a
series expansion of real numbers in [0,1], a certain type of Generalised Lüroth Series. The first
example of such an expansion was given by Lüroth. The map Lα is the jump transformation
of the corresponding αFarey map Fα. The maps Lα and Fα share the same relationship as the
classical Farey and Gauss maps which give rise to the continued fraction expansion of a real
number. We also consider the topological properties of Fα and some Diophantinetype sets of
numbers expressed in terms of the αLüroth expansion.
Next we investigate certain ergodictheoretic properties of the maps Lα and Fα. It will turn
out that the Lebesgue measure λ is invariant for every map Lα and that there exists a unique
Lebesgueabsolutely continuous invariant measure for Fα. We will give a precise expression for
the density of this measure. Our main result is that both Lα and Fα are exact, and thus ergodic.
The interest in the invariant measure for Fα lies in the fact that under a particular condition on
the underlying partition α, the invariant measure associated to the map Fα is infinite.
Then we proceed to introduce and examine the sequence of αsumlevel sets arising from
the αLüroth map, for an arbitrary given partition α. These sets can be written dynamically in
terms of Fα. The main result concerning the αsumlevel sets is to establish weak and strong
renewal laws. Note that for the Farey map and the Gauss map, the analogue of this result has
been obtained by Kesseböhmer and Stratmann. There the results were derived by using advanced
infinite ergodic theory, rather than the strong renewal theorems employed here. This underlines
the fact that one of the main ingredients of infinite ergodic theory is provided by some delicate
estimates in renewal theory.
Our final main result concerning the αLüroth and αFarey systems is to provide a fractalgeometric
description of the Lyapunov spectra associated with each of the maps Lα and Fα.
The Lyapunov spectra for the Farey map and the Gauss map have been investigated in detail by
Kesseböhmer and Stratmann. The Farey map and the Gauss map are nonlinear, whereas the
systems we consider are always piecewise linear. However, since our analysis is based on a large
family of different partitions of U , the class of maps which we consider in this paper allows us
to detect a variety of interesting new phenomena, including that of phase transitions.
Finally, we come to the conformal systems of the title. These are the limit sets of discrete
subgroups of the group of isometries of the hyperbolic plane. For these socalled Fuchsian
groups, our first main result is to establish the Hausdorff dimension of some Diophantinetype
sets contained in the limit set that are similar to those considered for the maps Lα. These sets
are then used in our second main result to analyse the more geometrically defined strictJarník
limit set of a Fuchsian group. Finally, we obtain a “weak multifractal spectrum” for the Patterson
measure associated to the Fuchsian group.
Wed, 30 Nov 2011 00:00:00 GMT
http://hdl.handle.net/10023/3220
20111130T00:00:00Z
Munday, Sara
The first main topic of this thesis is the thorough analysis of two families of piecewise linear
maps on the unit interval, the αLüroth and αFarey maps. Here, α denotes a countably infinite
partition of the unit interval whose atoms only accumulate at th