Applied Mathematics Research
http://hdl.handle.net/10023/96
Thu, 18 Jul 2019 21:34:33 GMT2019-07-18T21:34:33ZMaser radiation from collisionless shocks
http://hdl.handle.net/10023/17340
This paper describes a model of electron energization and cyclotron-maser emission applicable to astrophysical magnetized collisionless shocks. It is motivated by the work of Begelman, Ergun and Rees [Astrophys. J. 625 , 51 (2005)] who argued that the cyclotron-maser instability occurs in localized magnetized collisionless shocks such as those expected in blazar jets. We report on recent research carried out to investigate electron acceleration at collisionless shocks and maser radiation associated with the accelerated electrons. We describe how electrons accelerated by lower-hybrid,waves at collisionless shocks generate cyclotron-maser radiation when the accelerated electrons move into regions of stronger magnetic fields. The electrons are accelerated along the magnetic field and magnetically compressed leading to the formation of an electron velocity distribution having a horseshoe shape due to conservation of the electron magnetic moment. Under certain conditions the horseshoe electron velocity distribution function is unstable to the cyclotron-maser instability [Bingham and Cairns, Phys. Plasmas 7, 3089 (2000); Melrose, Rev. Mod. Plasma Phys. 1 , 5 (2017)].
Funding: UK Engineering and Physical Sciences Research Council (grant Nos. EP/N014472/1, EP/R004773/1 and EP/N013298/1) and the Science and Technologies Facilities Council of the United Kingdom. F.C. and L.O.S. acknowledge support from the European Research Council (InPairs ERC-2015-AdG 695088) and FCT Portugal (grant No. PD/BD/114307/2016).
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/10023/173402019-01-01T00:00:00ZSpeirs, D. C.Ronald, K.Phelps, A. D. R.Koepke, M. E.Cairns, Robert AlanRigby, A.Cruz, F.Trines, R. M. G. M.Bamford, R.Kellet, B. J.Albertazzi, B.Cross, J. E.Fraschetti, F.Graham, P.Kozlowski, P. M.Kuramitsu, Y.Miniati, F.Morita, T.Oliver, M.Reville, B.Sakawa, Y.Sarkar, S.Spindloe, C.Koenig, M.Silva, L. O.Lamb, D. Q.Tzeferacos, P.Lebedev, S.Gregori, G.Bingham, R.This paper describes a model of electron energization and cyclotron-maser emission applicable to astrophysical magnetized collisionless shocks. It is motivated by the work of Begelman, Ergun and Rees [Astrophys. J. 625 , 51 (2005)] who argued that the cyclotron-maser instability occurs in localized magnetized collisionless shocks such as those expected in blazar jets. We report on recent research carried out to investigate electron acceleration at collisionless shocks and maser radiation associated with the accelerated electrons. We describe how electrons accelerated by lower-hybrid,waves at collisionless shocks generate cyclotron-maser radiation when the accelerated electrons move into regions of stronger magnetic fields. The electrons are accelerated along the magnetic field and magnetically compressed leading to the formation of an electron velocity distribution having a horseshoe shape due to conservation of the electron magnetic moment. Under certain conditions the horseshoe electron velocity distribution function is unstable to the cyclotron-maser instability [Bingham and Cairns, Phys. Plasmas 7, 3089 (2000); Melrose, Rev. Mod. Plasma Phys. 1 , 5 (2017)].Measuring the electron temperatures of coronal mass ejections with future space-based multi-channel coronagraphs : a numerical test
http://hdl.handle.net/10023/17229
Context. The determination from coronagraphic observations of physical parameters of the plasma embedded in coronal mass ejections (CMEs) is of crucial importance for our understanding of the origin and evolution of these phenomena. Aims. The aim of this work is to perform the first ever numerical simulations of a CME as it will be observed by future two-channel (visible light VL and UV Ly-α) coronagraphs, such as the Metis instrument on-board ESA-Solar Orbiter mission, or any other future coronagraphs with the same spectral band-passes. These simulations are then used to test and optimize the plasma diagnostic techniques to be applied to future observations of CMEs. Methods. The CME diagnostic techniques are tested here by analyzing synthetic coronagraphic observations. First, a numerical three-dimensional (3D) magnetohydrodynamic (MHD) simulation of a CME is performed, and the plasma parameters in the simulation are used to generate synthetic visible light (VL) and ultraviolet (UV) coronagraphic two-dimensional (2D) images of the eruption (i.e., integrated along the line-of-sight). Second, synthetic data are analyzed with different assumptions (as will be done with real data), to infer the kinematic properties of the CME (such as the extension along the line-of-sight of the emitting region, the expansion speed, and the CME propagation direction), as well as physical parameters of the CME plasma (the plasma electron density and temperature). A comparison between input parameters from the simulation and output parameters from the synthetic data analysis is then performed. Results. The inversion of VL polarized data allows to successfully determine the CME speed and 3D propagation direction (with the polarization ratio technique), as well as to derive information on the extension along the line-of-sight of the emitting plasma, a crucial parameter needed to convert the plasma electron column densities into number densities. These parameters are used to analyze UV Ly-α images and to estimate the CME plasma temperature, also taking into account Doppler dimming effect. Output plasma temperatures are in general underestimated, both in the CME body and core regions. By neglecting the UV Ly-α radiative excitation of H atoms, reliable temperatures can be more easily derived in the CME core (within ∼60%). On the other hand, we show that a determination of temperatures (within ∼20−30%) in the CME body requires 2D maps of CME radial speeds and Doppler dimming coefficients to be derived.
Funding: This research has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (grant agreement No. 647214).
Thu, 01 Nov 2018 00:00:00 GMThttp://hdl.handle.net/10023/172292018-11-01T00:00:00ZBemporad, AlessandroPagano, PaoloGiordano, SilvioContext. The determination from coronagraphic observations of physical parameters of the plasma embedded in coronal mass ejections (CMEs) is of crucial importance for our understanding of the origin and evolution of these phenomena. Aims. The aim of this work is to perform the first ever numerical simulations of a CME as it will be observed by future two-channel (visible light VL and UV Ly-α) coronagraphs, such as the Metis instrument on-board ESA-Solar Orbiter mission, or any other future coronagraphs with the same spectral band-passes. These simulations are then used to test and optimize the plasma diagnostic techniques to be applied to future observations of CMEs. Methods. The CME diagnostic techniques are tested here by analyzing synthetic coronagraphic observations. First, a numerical three-dimensional (3D) magnetohydrodynamic (MHD) simulation of a CME is performed, and the plasma parameters in the simulation are used to generate synthetic visible light (VL) and ultraviolet (UV) coronagraphic two-dimensional (2D) images of the eruption (i.e., integrated along the line-of-sight). Second, synthetic data are analyzed with different assumptions (as will be done with real data), to infer the kinematic properties of the CME (such as the extension along the line-of-sight of the emitting region, the expansion speed, and the CME propagation direction), as well as physical parameters of the CME plasma (the plasma electron density and temperature). A comparison between input parameters from the simulation and output parameters from the synthetic data analysis is then performed. Results. The inversion of VL polarized data allows to successfully determine the CME speed and 3D propagation direction (with the polarization ratio technique), as well as to derive information on the extension along the line-of-sight of the emitting plasma, a crucial parameter needed to convert the plasma electron column densities into number densities. These parameters are used to analyze UV Ly-α images and to estimate the CME plasma temperature, also taking into account Doppler dimming effect. Output plasma temperatures are in general underestimated, both in the CME body and core regions. By neglecting the UV Ly-α radiative excitation of H atoms, reliable temperatures can be more easily derived in the CME core (within ∼60%). On the other hand, we show that a determination of temperatures (within ∼20−30%) in the CME body requires 2D maps of CME radial speeds and Doppler dimming coefficients to be derived.Computational approaches and analysis for a spatio-structural-temporal invasive carcinoma model
http://hdl.handle.net/10023/17200
Spatio-temporal models have long been used to describe biological systems of cancer, but it has not been until very recently that increased attention has been paid to structural dynamics of the interaction between cancer populations and the molecular mechanisms associated with local invasion. One system that is of particular interest is that of the urokinase plasminogen activator (uPA) wherein uPA binds uPA receptors on the cancer cell surface, allowing plasminogen to be cleaved into plasmin, which degrades the extracellular matrix and this way leads to enhanced cancer cell migration. In this paper, we develop a novel numerical approach and associated analysis for spatio-structuro-temporal modelling of the uPA system for up to two-spatial and two-structural dimensions. This is accompanied by analytical exploration of the numerical techniques used in simulating this system, with special consideration being given to the proof of stability within numerical regimes encapsulating a central differences approach to approximating numerical gradients. The stability analysis performed here reveals instabilities induced by the coupling of the structural binding and proliferative processes. The numerical results expound how the uPA system aids the tumour in invading the local stroma, whilst the inhibitor to this system may impede this behaviour and encourage a more sporadic pattern of invasion.
Sun, 01 Apr 2018 00:00:00 GMThttp://hdl.handle.net/10023/172002018-04-01T00:00:00ZHodgkinson, ArranChaplain, Mark Andrew JosephDomschke, PiaTrucu, DumitruSpatio-temporal models have long been used to describe biological systems of cancer, but it has not been until very recently that increased attention has been paid to structural dynamics of the interaction between cancer populations and the molecular mechanisms associated with local invasion. One system that is of particular interest is that of the urokinase plasminogen activator (uPA) wherein uPA binds uPA receptors on the cancer cell surface, allowing plasminogen to be cleaved into plasmin, which degrades the extracellular matrix and this way leads to enhanced cancer cell migration. In this paper, we develop a novel numerical approach and associated analysis for spatio-structuro-temporal modelling of the uPA system for up to two-spatial and two-structural dimensions. This is accompanied by analytical exploration of the numerical techniques used in simulating this system, with special consideration being given to the proof of stability within numerical regimes encapsulating a central differences approach to approximating numerical gradients. The stability analysis performed here reveals instabilities induced by the coupling of the structural binding and proliferative processes. The numerical results expound how the uPA system aids the tumour in invading the local stroma, whilst the inhibitor to this system may impede this behaviour and encourage a more sporadic pattern of invasion.Robustness of vortex populations in the two-dimensional inverse energy cascade
http://hdl.handle.net/10023/16825
We study how the properties of forcing and dissipation affect the scaling behaviour of the vortex population in the two-dimensional turbulent inverse energy cascade. When the flow is forced at scales intermediate between the domain and dissipation scales, the growth rates of the largest vortex area and the spectral peak length scale are robust to all simulation parameters. For white-in-time forcing the number density distribution of vortex areas follows the scaling theory predictions of Burgess & Scott (J. Fluid Mech., vol. 811, 2017, pp. 742–756) and shows little sensitivity either to the forcing bandwidth or to the nature of the small-scale dissipation: both narrowband and broadband forcing generate nearly identical vortex populations, as do Laplacian diffusion and hyperdiffusion. The greatest differences arise in comparing simulations with correlated forcing to those with white-in-time forcing: in flows with correlated forcing the intermediate range in the vortex number density steepens significantly past the predicted scale-invariant A-1 scaling. We also study the impact of the forcing Reynolds number Rej, a measure of the relative importance of nonlinear terms and dissipation at the forcing scale, on vortex formation and the scaling of the number density. As Rej decreases, the flow changes from one dominated by intense circular vortices surrounded by filaments to a less structured flow in which vortex formation becomes progressively more suppressed and the filamentary nature of the surrounding vorticity field is lost. However, even at very small Rej, and in the absence of intense coherent vortex formation, regions of anomalously high vorticity merge and grow in area as predicted by the scaling theory, generating a three-part number density similar to that found at higher Rej. At late enough stages the aggregation process results in the formation of long-lived circular vortices, demonstrating a strong tendency to vortex formation, and via a route distinct from the axisymmetrization of forcing extrema seen at higher Rej. Our results establish coherent vortices as a robust feature of the two-dimensional inverse energy cascade, and provide clues as to the dynamical mechanisms shaping their statistics.
Funding: Leverhulme Early Career Fellowship from the Leverhulme Trust, the Natural Environment Research Council grant NE/M014983/1 (B.H.B.).
Mon, 10 Sep 2018 00:00:00 GMThttp://hdl.handle.net/10023/168252018-09-10T00:00:00ZBurgess, Belle HelenScott, Richard KirknessWe study how the properties of forcing and dissipation affect the scaling behaviour of the vortex population in the two-dimensional turbulent inverse energy cascade. When the flow is forced at scales intermediate between the domain and dissipation scales, the growth rates of the largest vortex area and the spectral peak length scale are robust to all simulation parameters. For white-in-time forcing the number density distribution of vortex areas follows the scaling theory predictions of Burgess & Scott (J. Fluid Mech., vol. 811, 2017, pp. 742–756) and shows little sensitivity either to the forcing bandwidth or to the nature of the small-scale dissipation: both narrowband and broadband forcing generate nearly identical vortex populations, as do Laplacian diffusion and hyperdiffusion. The greatest differences arise in comparing simulations with correlated forcing to those with white-in-time forcing: in flows with correlated forcing the intermediate range in the vortex number density steepens significantly past the predicted scale-invariant A-1 scaling. We also study the impact of the forcing Reynolds number Rej, a measure of the relative importance of nonlinear terms and dissipation at the forcing scale, on vortex formation and the scaling of the number density. As Rej decreases, the flow changes from one dominated by intense circular vortices surrounded by filaments to a less structured flow in which vortex formation becomes progressively more suppressed and the filamentary nature of the surrounding vorticity field is lost. However, even at very small Rej, and in the absence of intense coherent vortex formation, regions of anomalously high vorticity merge and grow in area as predicted by the scaling theory, generating a three-part number density similar to that found at higher Rej. At late enough stages the aggregation process results in the formation of long-lived circular vortices, demonstrating a strong tendency to vortex formation, and via a route distinct from the axisymmetrization of forcing extrema seen at higher Rej. Our results establish coherent vortices as a robust feature of the two-dimensional inverse energy cascade, and provide clues as to the dynamical mechanisms shaping their statistics.The merger of geophysical vortices at finite Rossby and Froude number
http://hdl.handle.net/10023/16629
We investigate the merger of two co-rotating geophysical vortices at finite Rossby and Froude number. The initial conditions consist of two uniform potential vorticity vortices in near equilibrium and in a near 'balanced' state (i.e. with negligible emission of inertia-gravity wave radiation). We determine the critical merger distance between the two vortices. This distance is found to increase with the magnitude of the Rossby number: intense cyclones or intense anticyclones. Note that the Froude number is proportional to the Rossby number for the near equilibrium initial conditions considered. The critical merging distance also depends on the sign of the potential vorticity anomaly, which is positive for 'cyclones' and negative for 'anticyclones'. We show ageostrophic motions occurring at finite Rossby number tend to draw cyclones together but draw anticyclones apart. On the other hand, we show that anticyclones tend to deform more, in particular when subject to vertical shear (as when the vortices are vertically offset). These two effects compete. Overall, nearly aligned cyclones tend to merge from further apart than their anticyclonic counterparts, while vertically offset anticyclones merger from further apart than cyclones.
Partial support for this research has come from the UK Engineering and Physical Sciences Research Council (grant number EP/H001794/1).
Fri, 10 Aug 2018 00:00:00 GMThttp://hdl.handle.net/10023/166292018-08-10T00:00:00ZReinaud, Jean N.Dritschel, David G.We investigate the merger of two co-rotating geophysical vortices at finite Rossby and Froude number. The initial conditions consist of two uniform potential vorticity vortices in near equilibrium and in a near 'balanced' state (i.e. with negligible emission of inertia-gravity wave radiation). We determine the critical merger distance between the two vortices. This distance is found to increase with the magnitude of the Rossby number: intense cyclones or intense anticyclones. Note that the Froude number is proportional to the Rossby number for the near equilibrium initial conditions considered. The critical merging distance also depends on the sign of the potential vorticity anomaly, which is positive for 'cyclones' and negative for 'anticyclones'. We show ageostrophic motions occurring at finite Rossby number tend to draw cyclones together but draw anticyclones apart. On the other hand, we show that anticyclones tend to deform more, in particular when subject to vertical shear (as when the vortices are vertically offset). These two effects compete. Overall, nearly aligned cyclones tend to merge from further apart than their anticyclonic counterparts, while vertically offset anticyclones merger from further apart than cyclones.The interaction of two co-rotating quasi-geostrophic vortices in the vicinity of a surface buoyancy filament
http://hdl.handle.net/10023/16616
In this paper, we investigate the interaction between two like-signed quasi-geostrophic uniform potential vorticity internal vortices in the vicinity of a surface buoyancy anomaly filament in a three dimensional, stably stratified and rapidly rotating fluid. The surface buoyancy distribution locally modifies the pressure fields and generates a shear flow. We start the study by first considering the effects of a uniform linear horizontal shear on the binary vortex interaction. We confirm that a cooperative shear facilitates the merger of a pair of vortices while an adverse shear has the opposite effect. We next investigate the binary vortex interaction in thevicinity of the surface buoyancy filament explicitly. Here, not only the filament generates a shear flow, but it also responds dynamically to the forcing by the vortex pair. The filament destabilises and forms buoyancy billows at the surface. These billows interact with the internal vortices. In particular, a surface billow may pair with one of the internal vortices. In such cases, the like-signed internal vortex pair may separate if they are initially moderately distant from each other.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10023/166162018-01-01T00:00:00ZReinaud, Jean NoelIn this paper, we investigate the interaction between two like-signed quasi-geostrophic uniform potential vorticity internal vortices in the vicinity of a surface buoyancy anomaly filament in a three dimensional, stably stratified and rapidly rotating fluid. The surface buoyancy distribution locally modifies the pressure fields and generates a shear flow. We start the study by first considering the effects of a uniform linear horizontal shear on the binary vortex interaction. We confirm that a cooperative shear facilitates the merger of a pair of vortices while an adverse shear has the opposite effect. We next investigate the binary vortex interaction in thevicinity of the surface buoyancy filament explicitly. Here, not only the filament generates a shear flow, but it also responds dynamically to the forcing by the vortex pair. The filament destabilises and forms buoyancy billows at the surface. These billows interact with the internal vortices. In particular, a surface billow may pair with one of the internal vortices. In such cases, the like-signed internal vortex pair may separate if they are initially moderately distant from each other.Three-dimensional solutions of the magnetohydrostatic equations for rigidly rotating magnetospheres in cylindrical coordinates
http://hdl.handle.net/10023/16582
We present new analytical three-dimensional solutions of the magnetohydrostatic equations, which are applicable to the co-rotating frame of reference outside a rigidly rotating cylindrical body, and have potential applications to planetary magnetospheres and stellar coronae. We consider the case with centrifugal force only, and use a transformation method in which the governing equation for the "pseudo-potential" (from which the magnetic field can be calculated) becomes the Laplace partial differential equation. The new solutions extend the set of previously found solutions to those of a "fractional multipole" nature, and offer wider possibilities for modelling than before. We consider some special cases, and present example solutions.
Funding: Science and Technology Facilities Council under grants ST/K000950/1 and ST/N000609/1.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10023/165822018-01-01T00:00:00ZWilson, FionaNeukirch, ThomasWe present new analytical three-dimensional solutions of the magnetohydrostatic equations, which are applicable to the co-rotating frame of reference outside a rigidly rotating cylindrical body, and have potential applications to planetary magnetospheres and stellar coronae. We consider the case with centrifugal force only, and use a transformation method in which the governing equation for the "pseudo-potential" (from which the magnetic field can be calculated) becomes the Laplace partial differential equation. The new solutions extend the set of previously found solutions to those of a "fractional multipole" nature, and offer wider possibilities for modelling than before. We consider some special cases, and present example solutions.Statistics of ambiguous rotations
http://hdl.handle.net/10023/16511
The orientation of a rigid object can be described by a rotation that transforms it into a standard position. For a symmetrical object the rotation is known only up to multiplication by an element of the symmetry group. Such ambiguous rotations arise in biomechanics, crystallography and seismology. We develop methods for analyzing data of this form. A test of uniformity is given. Parametric models for ambiguous rotations are presented, tests of location are considered, and a regression model is proposed. An example involving orientations of diopside crystals (which have symmetry of order 2) is used throughout to illustrate how our methods can be applied.
Tue, 01 May 2018 00:00:00 GMThttp://hdl.handle.net/10023/165112018-05-01T00:00:00ZArnold, R.Jupp, P. E.Schaeben, H.The orientation of a rigid object can be described by a rotation that transforms it into a standard position. For a symmetrical object the rotation is known only up to multiplication by an element of the symmetry group. Such ambiguous rotations arise in biomechanics, crystallography and seismology. We develop methods for analyzing data of this form. A test of uniformity is given. Parametric models for ambiguous rotations are presented, tests of location are considered, and a regression model is proposed. An example involving orientations of diopside crystals (which have symmetry of order 2) is used throughout to illustrate how our methods can be applied.Uphill acceleration in a spatially modulated electrostatic field particle accelerator
http://hdl.handle.net/10023/16468
Spatially modulated electrostatic fields can be designed to efficiently accelerate particles by exploring the relations between the amplitude, the phase velocity, the shape of the potential and the initial velocity of the particle. The acceleration process occurs when the value of the velocity excursions of the particle surpass the phase velocity of the carrier, as a resonant mechanism. The ponderomotive approximation based on the Lagrangian average is usually applied in this kind of system in non accelerating regimes. The mean dynamics of the particle is well described by this approximation far from resonance. However, the approximation fails to predict some interesting features of the model near resonance, such as the uphill acceleration phenomenon. A canonical perturbation theory is more accurate in these conditions. In this work we compare the results from the Lagrangian average and from a canonical perturbation theory, focusing in regions where the results of these two approaches differ from each other.
Funding: UK Science and Engineering Research Council grant EP/N028694/1.
Thu, 01 Nov 2018 00:00:00 GMThttp://hdl.handle.net/10023/164682018-11-01T00:00:00ZAlmansa, IBurton, DavidCairns, Robert AlanMarini, SPeter, EduardoRizzato, FelipeRussman, FSpatially modulated electrostatic fields can be designed to efficiently accelerate particles by exploring the relations between the amplitude, the phase velocity, the shape of the potential and the initial velocity of the particle. The acceleration process occurs when the value of the velocity excursions of the particle surpass the phase velocity of the carrier, as a resonant mechanism. The ponderomotive approximation based on the Lagrangian average is usually applied in this kind of system in non accelerating regimes. The mean dynamics of the particle is well described by this approximation far from resonance. However, the approximation fails to predict some interesting features of the model near resonance, such as the uphill acceleration phenomenon. A canonical perturbation theory is more accurate in these conditions. In this work we compare the results from the Lagrangian average and from a canonical perturbation theory, focusing in regions where the results of these two approaches differ from each other.Broadening of the differential emission measure by multi-shelled and turbulent loops
http://hdl.handle.net/10023/16275
Context. Broad differential emission measure (DEM) distributions in the corona are a sign of multi-thermal plasma along the line-of-sight.Traditionally, this is interpreted as evidence of multi-stranded loops. Recently, however, it has been shown that multi-stranded loops are unlikely to exist in the solar corona, because of their instability to transverse perturbations. Aims. We aim to test if loop models subject to the Transverse Wave-Induced Kelvin-Helmholtz (TWIKH) instability result in broad DEMs, potentially explaining the observations. We took simulation snapshots and compute the numerical DEM. Moreover, we performed forward-modelling in the relevant AIA channels before reconstructing the DEM. Results. We find that turbulent loop models broaden their initial DEM, because of the turbulent mixing. The width of the DEM is determined by the initial temperature contrast with the exterior. Conclusions. We conclude that impulsively excited loop models have a rather narrow DEM, but that continuously driven models result in broad DEMs that are comparable to the observations.
Funding: UK Science and Technology Facilities Council (Consolidated Grant ST/K000950/1), the European Union Horizon 2020 research and innovation programme (grant agreement No. 647214) and STFC Ernest Rutherford Fellowship (grant agreement No. ST/R004285/1) (PA).
Sat, 01 Dec 2018 00:00:00 GMThttp://hdl.handle.net/10023/162752018-12-01T00:00:00ZVan Doorsselaere, TomAntolin, PatrickKarampelas, KostasContext. Broad differential emission measure (DEM) distributions in the corona are a sign of multi-thermal plasma along the line-of-sight.Traditionally, this is interpreted as evidence of multi-stranded loops. Recently, however, it has been shown that multi-stranded loops are unlikely to exist in the solar corona, because of their instability to transverse perturbations. Aims. We aim to test if loop models subject to the Transverse Wave-Induced Kelvin-Helmholtz (TWIKH) instability result in broad DEMs, potentially explaining the observations. We took simulation snapshots and compute the numerical DEM. Moreover, we performed forward-modelling in the relevant AIA channels before reconstructing the DEM. Results. We find that turbulent loop models broaden their initial DEM, because of the turbulent mixing. The width of the DEM is determined by the initial temperature contrast with the exterior. Conclusions. We conclude that impulsively excited loop models have a rather narrow DEM, but that continuously driven models result in broad DEMs that are comparable to the observations.Self-similar approach for rotating magnetohydrodynamic solar and astrophysical structures
http://hdl.handle.net/10023/15963
Rotating magnetic structures are common in astrophysics, from vortex tubes and tornadoes in the Sun all the way to jets in different astrophysical systems. The physics of these objects often combine inertial, magnetic, gas pressure, and gravitational terms. Also, they often show approximate symmetries that help simplify the otherwise rather intractable equations governing their morphology and evolution. Here we propose a general formulation of the equations assuming axisymmetry and a self-similar form for all variables: in spherical coordinates ( r , θ , φ ), the magnetic field and plasma velocity are taken to be of the form B = f(θ)/rn and v = g(θ)/rm, with corresponding expressions for the scalar variables like pressure and density. Solutions are obtained for potential, force-free, and non-force-free magnetic configurations. Potential field solutions can be found for all values of n . Nonpotential force-free solutions possess an azimuthal component Bφ and exist only for n ≥ 2; the resulting structures are twisted and have closed field lines but are not collimated around the system axis. In the non-force-free case, including gas pressure, the magnetic field lines acquire an additional curvature to compensate for an outward pointing pressure gradient force. We have also considered a pure rotation situation with no gravity, in the zero- β limit: the solution has cylindrical geometry and twisted magnetic field lines. The latter solutions can be helpful in producing a collimated magnetic field structure; but they exist only when n < 0 and m < 0: for applications they must be matched to an external system at a finite distance from the origin.
Support by the Spanish Ministry of Economy and Competitiveness through project AYA2014-55078-P is acknowledged. M.L. also acknowledges support from the International Space Science Institute (ISSI) to the Team 374 on “Solving the Prominence Paradox” led by Nicolas Labrosse.
Mon, 20 Aug 2018 00:00:00 GMThttp://hdl.handle.net/10023/159632018-08-20T00:00:00ZLuna, M.Priest, E.Moreno-Insertis, F.Rotating magnetic structures are common in astrophysics, from vortex tubes and tornadoes in the Sun all the way to jets in different astrophysical systems. The physics of these objects often combine inertial, magnetic, gas pressure, and gravitational terms. Also, they often show approximate symmetries that help simplify the otherwise rather intractable equations governing their morphology and evolution. Here we propose a general formulation of the equations assuming axisymmetry and a self-similar form for all variables: in spherical coordinates ( r , θ , φ ), the magnetic field and plasma velocity are taken to be of the form B = f(θ)/rn and v = g(θ)/rm, with corresponding expressions for the scalar variables like pressure and density. Solutions are obtained for potential, force-free, and non-force-free magnetic configurations. Potential field solutions can be found for all values of n . Nonpotential force-free solutions possess an azimuthal component Bφ and exist only for n ≥ 2; the resulting structures are twisted and have closed field lines but are not collimated around the system axis. In the non-force-free case, including gas pressure, the magnetic field lines acquire an additional curvature to compensate for an outward pointing pressure gradient force. We have also considered a pure rotation situation with no gravity, in the zero- β limit: the solution has cylindrical geometry and twisted magnetic field lines. The latter solutions can be helpful in producing a collimated magnetic field structure; but they exist only when n < 0 and m < 0: for applications they must be matched to an external system at a finite distance from the origin.Bimodal or quadrimodal? Statistical tests for the shape of fault patterns
http://hdl.handle.net/10023/15962
Natural fault patterns formed in response to a single tectonic event often display significant variation in their orientation distribution. The cause of this variation is the subject of some debate: it could be "noise" on underlying conjugate (or bimodal) fault patterns or it could be intrinsic "signal" from an underlying polymodal (e.g. quadrimodal) pattern. In this contribution, we present new statistical tests to assess the probability of a fault pattern having two (bimodal, or conjugate) or four (quadrimodal) underlying modes and orthorhombic symmetry. We use the eigenvalues of the second- and fourth-rank orientation tensors, derived from the direction cosines of the poles to the fault planes, as the basis for our tests. Using a combination of the existing fabric eigenvalue (or modified Flinn) plot and our new tests, we can discriminate reliably between bimodal (conjugate) and quadrimodal fault patterns. We validate our tests using synthetic fault orientation datasets constructed from multimodal Watson distributions and then assess six natural fault datasets from outcrops and earthquake focal plane solutions. We show that five out of six of these natural datasets are probably quadrimodal and orthorhombic. The tests have been implemented in the R language and a link is given to the authors' source code.
David Healy gratefully acknowledges receipt of NERC grant NE/N003063/1 and thanks the School of Geosciences at the University of Aberdeen for accommodating a period of research study leave, during which time this paper was written.
Wed, 22 Aug 2018 00:00:00 GMThttp://hdl.handle.net/10023/159622018-08-22T00:00:00ZHealy, DavidJupp, PeterNatural fault patterns formed in response to a single tectonic event often display significant variation in their orientation distribution. The cause of this variation is the subject of some debate: it could be "noise" on underlying conjugate (or bimodal) fault patterns or it could be intrinsic "signal" from an underlying polymodal (e.g. quadrimodal) pattern. In this contribution, we present new statistical tests to assess the probability of a fault pattern having two (bimodal, or conjugate) or four (quadrimodal) underlying modes and orthorhombic symmetry. We use the eigenvalues of the second- and fourth-rank orientation tensors, derived from the direction cosines of the poles to the fault planes, as the basis for our tests. Using a combination of the existing fabric eigenvalue (or modified Flinn) plot and our new tests, we can discriminate reliably between bimodal (conjugate) and quadrimodal fault patterns. We validate our tests using synthetic fault orientation datasets constructed from multimodal Watson distributions and then assess six natural fault datasets from outcrops and earthquake focal plane solutions. We show that five out of six of these natural datasets are probably quadrimodal and orthorhombic. The tests have been implemented in the R language and a link is given to the authors' source code.In situ generation of transverse magnetohydrodynamic waves from colliding flows in the solar corona
http://hdl.handle.net/10023/15178
Transverse magnetohydrodynamic (MHD) waves permeate the solar atmosphere and are a candidate for coronal heating. However, the origin of these waves is still unclear. In this Letter, we analyze coordinated observations from Hinode/Solar Optical Telescope (SOT) and Interface Region Imaging Spectrograph (IRIS) of a prominence/coronal rain loop-like structure at the limb of the Sun. Cool and dense downflows and upflows are observed along the structure. A collision between a downward and an upward flow with an estimated energy flux of 107–108 erg cm−2 s−1 is observed to generate oscillatory transverse perturbations of the strands with an estimated ≈40 km s−1 total amplitude, and a short-lived brightening event with the plasma temperature increasing to at least 105 K. We interpret this response as sausage and kink transverse MHD waves based on 2D MHD simulations of plasma flow collision. The lengths, density, and velocity differences between the colliding clumps and the strength of the magnetic field are major parameters defining the response to the collision. The presence of asymmetry between the clumps (angle of impact surface and/or offset of flowing axis) is crucial for generating a kink mode. Using the observed values, we successfully reproduce the observed transverse perturbations and brightening, and show adiabatic heating to coronal temperatures. The numerical modeling indicates that the plasma β in this loop-like structure is confined between 0.09 and 0.36. These results suggest that such collisions from counter-streaming flows can be a source of in situ transverse MHD waves, and that for cool and dense prominence conditions such waves could have significant amplitudes.
This research has received funding from the UK Science and Technology Facilities Council (Consolidated Grant ST/K000950/1) and the European Union Horizon 2020 Research and Innovation Programme (grant agreement No. 647214). V.M.N. acknowledges the support of the BK21 plus program through the National Research Foundation funded by the Ministry of Education of Korea.
Mon, 09 Jul 2018 00:00:00 GMThttp://hdl.handle.net/10023/151782018-07-09T00:00:00ZAntolin, PatrickPagano, PaoloDe Moortel, InekeNakariakov, Valery M.Transverse magnetohydrodynamic (MHD) waves permeate the solar atmosphere and are a candidate for coronal heating. However, the origin of these waves is still unclear. In this Letter, we analyze coordinated observations from Hinode/Solar Optical Telescope (SOT) and Interface Region Imaging Spectrograph (IRIS) of a prominence/coronal rain loop-like structure at the limb of the Sun. Cool and dense downflows and upflows are observed along the structure. A collision between a downward and an upward flow with an estimated energy flux of 107–108 erg cm−2 s−1 is observed to generate oscillatory transverse perturbations of the strands with an estimated ≈40 km s−1 total amplitude, and a short-lived brightening event with the plasma temperature increasing to at least 105 K. We interpret this response as sausage and kink transverse MHD waves based on 2D MHD simulations of plasma flow collision. The lengths, density, and velocity differences between the colliding clumps and the strength of the magnetic field are major parameters defining the response to the collision. The presence of asymmetry between the clumps (angle of impact surface and/or offset of flowing axis) is crucial for generating a kink mode. Using the observed values, we successfully reproduce the observed transverse perturbations and brightening, and show adiabatic heating to coronal temperatures. The numerical modeling indicates that the plasma β in this loop-like structure is confined between 0.09 and 0.36. These results suggest that such collisions from counter-streaming flows can be a source of in situ transverse MHD waves, and that for cool and dense prominence conditions such waves could have significant amplitudes.Constraining the pass-band of future space-based coronagraphs for observations of solar eruptions in the FeXIV 530.3 nm “green line”
http://hdl.handle.net/10023/14139
Observations of the solar corona in the FeXIV 530.3 nm “green line” have been very important in the past, and are planned for future coronagraphs on-board forthcoming space missions such as PROBA-3 and Aditya. For these instruments, a very important parameter to be optimized is the spectral width of the band-pass filter to be centred over the “green line”. Focusing on solar eruptions, motions occurring along the line of sight will Doppler shift the line profiles producing an emission that will partially fall out of the narrower pass-band, while broader pass-band will provide observations with reduced spectral purity. To address these issues, we performed numerical (MHD) simulation of CME emission in the “green line” and produced synthetic images assuming 4 different widths of the pass-band (Δλ = 20 Å, 10 Å, 5 Å, and 2 Å). It turns out that, as expected, during solar eruptions a significant fraction of “green line” emission will be lost using narrower filters; on the other hand these images will have a higher spectral purity and will contain emission coming from parcels of plasma expanding only along the plane of the sky. This will provide a better definition of single filamentary features and will help isolating single slices of plasma through the eruption, thus reducing the problem of superposition of different features along the line of sight and helping physical interpretation of limb events. For these reasons, we suggest to use narrower band passes (Δλ ≤ 2 Å) for the observations of solar eruptions with future coronagraphs.
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.
Sun, 01 Oct 2017 00:00:00 GMThttp://hdl.handle.net/10023/141392017-10-01T00:00:00ZBemporad, AlessandroPagano, PaoloGiordano, SilvioFineschi, SilvanoObservations of the solar corona in the FeXIV 530.3 nm “green line” have been very important in the past, and are planned for future coronagraphs on-board forthcoming space missions such as PROBA-3 and Aditya. For these instruments, a very important parameter to be optimized is the spectral width of the band-pass filter to be centred over the “green line”. Focusing on solar eruptions, motions occurring along the line of sight will Doppler shift the line profiles producing an emission that will partially fall out of the narrower pass-band, while broader pass-band will provide observations with reduced spectral purity. To address these issues, we performed numerical (MHD) simulation of CME emission in the “green line” and produced synthetic images assuming 4 different widths of the pass-band (Δλ = 20 Å, 10 Å, 5 Å, and 2 Å). It turns out that, as expected, during solar eruptions a significant fraction of “green line” emission will be lost using narrower filters; on the other hand these images will have a higher spectral purity and will contain emission coming from parcels of plasma expanding only along the plane of the sky. This will provide a better definition of single filamentary features and will help isolating single slices of plasma through the eruption, thus reducing the problem of superposition of different features along the line of sight and helping physical interpretation of limb events. For these reasons, we suggest to use narrower band passes (Δλ ≤ 2 Å) for the observations of solar eruptions with future coronagraphs.Impact of type II spicules in the corona : simulations and synthetic observables
http://hdl.handle.net/10023/13569
The role of type II spicules in the corona has been a much debated topic in recent years. This paper aims to shed light on the impact of type II spicules in the corona using novel 2.5D radiative MHD simulations including ion-neutral interaction effects with the Bifrost code. We find that the formation of simulated type II spicules, driven by the release of magnetic tension, impacts the corona in various manners. Associated with the formation of spicules, the corona exhibits 1) magneto-acoustic shocks and flows which supply mass to coronal loops, and 2) transversal magnetic waves and electric currents that propagate at Alfvén speeds. The transversal waves and electric currents, generated by the spicule's driver and lasting for many minutes, are dissipated and heat the associated loop. These complex interactions in the corona can be connected with blue shifted secondary components in coronal spectral lines (Red-Blue asymmetries) observed with Hinode/EIS and SOHO/SUMER, as well as the EUV counterpart of type II spicules and propagating coronal disturbances (PCDs) observed with the 171 Å and 193 Å SDO/AIA channels.
We gratefully acknowledge support by NASA grants, NNX16AG90G, NNH15ZDA001N, NNX17AD33G, and NNG09FA40C (IRIS), NSF grant AST1714955. This research has received funding from the UK Science and Technology Facilities Council (Consolidated Grant ST/K000950/1) and the European Union Horizon 2020 research and innovation programme (grant agreement No. 647214). This research was supported by the European Research Council under the European Union's Seventh Framework Programme (FP7/2007-2013) / ERC Grant agreement nr. 291058. We thankfully acknowledge the support of the Research Council of Norway through grant 230938/F50, through its Center of Excellence scheme, project number 262622, and through grants of computing time from the Programme for Supercomputing.
Tue, 19 Jun 2018 00:00:00 GMThttp://hdl.handle.net/10023/135692018-06-19T00:00:00ZMartínez-Sykora, JuanDe Pontieu, BartDe Moortel, InekeHansteen, ViggoCarlsson, MatsThe role of type II spicules in the corona has been a much debated topic in recent years. This paper aims to shed light on the impact of type II spicules in the corona using novel 2.5D radiative MHD simulations including ion-neutral interaction effects with the Bifrost code. We find that the formation of simulated type II spicules, driven by the release of magnetic tension, impacts the corona in various manners. Associated with the formation of spicules, the corona exhibits 1) magneto-acoustic shocks and flows which supply mass to coronal loops, and 2) transversal magnetic waves and electric currents that propagate at Alfvén speeds. The transversal waves and electric currents, generated by the spicule's driver and lasting for many minutes, are dissipated and heat the associated loop. These complex interactions in the corona can be connected with blue shifted secondary components in coronal spectral lines (Red-Blue asymmetries) observed with Hinode/EIS and SOHO/SUMER, as well as the EUV counterpart of type II spicules and propagating coronal disturbances (PCDs) observed with the 171 Å and 193 Å SDO/AIA channels.Transverse wave induced Kelvin-Helmholtz rolls in spicules
http://hdl.handle.net/10023/12880
In addition to their jet-like dynamic behaviour, spicules usually exhibit strong transverse speeds, multi-stranded structure and heating from chromospheric to transition region temperatures. In this work we first analyse Hinode & IRIS observations of spicules and find different behaviours in terms of their Doppler velocity evolution and collective motion of their sub-structure. Some have a Doppler shift sign change that is rather fixed along the spicule axis, and lack coherence in the oscillatory motion of strand-like structure, matching rotation models or long wavelength torsional Alfvén waves. Others exhibit a Doppler shift sign change at maximum displacement and coherent motion of their strands, suggesting a collective MHD wave. By comparing with an idealised 3D MHD simulation combined with radiative transfer modelling, we analyse the role of transverse MHD waves and associated instabilities in spicule-like features. We find that Transverse Wave Induced Kelvin-Helmholtz (TWIKH) rolls lead to coherence of strand-like structure in imaging and spectral maps, as seen in some observations. The rapid transverse dynamics and the density and temperature gradients at the spicule boundary lead to ring-shaped Mg II k and Ca II H source functions in the transverse cross-section, potentially allowing IRIS to capture the KHI dynamics. Twists and currents propagate along the spicule at Alfvénic speeds, and the temperature variations within TWIKH rolls produce sudden appearance/disappearance of strands seen in Doppler velocity and in Ca II H intensity. However, only a mild intensity increase in higher temperature lines is obtained, suggesting there is an additional heating mechanism at work in spicules.
This research has received funding from the UK Science and Technology Facilities Council (Consolidated Grant ST/K000950/1) and the European Union Horizon 2020 research and innovation programme (grant agreement No. 647214).
Fri, 23 Mar 2018 00:00:00 GMThttp://hdl.handle.net/10023/128802018-03-23T00:00:00ZAntolin, PatrickSchmit, DonPereira, Tiago M. D.De Pontieu, BartDe Moortel, InekeIn addition to their jet-like dynamic behaviour, spicules usually exhibit strong transverse speeds, multi-stranded structure and heating from chromospheric to transition region temperatures. In this work we first analyse Hinode & IRIS observations of spicules and find different behaviours in terms of their Doppler velocity evolution and collective motion of their sub-structure. Some have a Doppler shift sign change that is rather fixed along the spicule axis, and lack coherence in the oscillatory motion of strand-like structure, matching rotation models or long wavelength torsional Alfvén waves. Others exhibit a Doppler shift sign change at maximum displacement and coherent motion of their strands, suggesting a collective MHD wave. By comparing with an idealised 3D MHD simulation combined with radiative transfer modelling, we analyse the role of transverse MHD waves and associated instabilities in spicule-like features. We find that Transverse Wave Induced Kelvin-Helmholtz (TWIKH) rolls lead to coherence of strand-like structure in imaging and spectral maps, as seen in some observations. The rapid transverse dynamics and the density and temperature gradients at the spicule boundary lead to ring-shaped Mg II k and Ca II H source functions in the transverse cross-section, potentially allowing IRIS to capture the KHI dynamics. Twists and currents propagate along the spicule at Alfvénic speeds, and the temperature variations within TWIKH rolls produce sudden appearance/disappearance of strands seen in Doppler velocity and in Ca II H intensity. However, only a mild intensity increase in higher temperature lines is obtained, suggesting there is an additional heating mechanism at work in spicules.Penalized nonparametric scalar-on-function regression via principal coordinates
http://hdl.handle.net/10023/12663
A number of classical approaches to nonparametric regression have recently been extended to the case of functional predictors. This article introduces a new method of this type, which extends intermediate-rank penalized smoothing to scalar-on-function regression. In the proposed method, which we call principal coordinate ridge regression, one regresses the response on leading principal coordinates defined by a relevant distance among the functional predictors, while applying a ridge penalty. Our publicly available implementation, based on generalized additive modeling software, allows for fast optimal tuning parameter selection and for extensions to multiple functional predictors, exponential family-valued responses, and mixed-effects models. In an application to signature verification data, principal coordinate ridge regression, with dynamic time warping distance used to define the principal coordinates, is shown to outperform a functional generalized linear model. Supplementary materials for this article are available online.
Philip Reiss, Pei-Shien Wu, and Wen-Yu Hua gratefully acknowledge the support of the U.S. National Institute of Mental Health (grant 1R01MH095836-01A1).
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10023/126632017-01-01T00:00:00ZReiss, Philip T.Miller, David L.Wu, Pei ShienHua, Wen YuA number of classical approaches to nonparametric regression have recently been extended to the case of functional predictors. This article introduces a new method of this type, which extends intermediate-rank penalized smoothing to scalar-on-function regression. In the proposed method, which we call principal coordinate ridge regression, one regresses the response on leading principal coordinates defined by a relevant distance among the functional predictors, while applying a ridge penalty. Our publicly available implementation, based on generalized additive modeling software, allows for fast optimal tuning parameter selection and for extensions to multiple functional predictors, exponential family-valued responses, and mixed-effects models. In an application to signature verification data, principal coordinate ridge regression, with dynamic time warping distance used to define the principal coordinates, is shown to outperform a functional generalized linear model. Supplementary materials for this article are available online.Combining radiation with hyperthermia : a multiscale model informed by in vitro experiments
http://hdl.handle.net/10023/12590
Combined radiotherapy and hyperthermia offer great potential for the successful treatment of radio-resistant tumours through thermo-radiosensitization. Tumour response heterogeneity, due to intrinsic, or micro-environmentally induced factors, may greatly influence treatment outcome, but is difficult to account for using traditional treatment planning approaches. Systems oncology simulation, using mathematical models designed to predict tumour growth and treatment response, provides a powerful tool for analysis and optimization of combined treatments. We present a framework that simulates such combination treatments on a cellular level. This multiscale hybrid cellular automaton simulates large cell populations (up to 107 cells) in vitro, while allowing individual cell-cycle progression, and treatment response by modelling radiation-induced mitotic cell death, and immediate cell kill in response to heating. Based on a calibration using a number of experimental growth, cell cycle and survival datasets for HCT116 cells, model predictions agreed well (R2 > 0.95) with experimental data within the range of (thermal and radiation) doses tested (0–40 CEM43, 0–5 Gy). The proposed framework offers flexibility for modelling multimodality treatment combinations in different scenarios. It may therefore provide an important step towards the modelling of personalized therapies using a virtual patient tumour.
Funding: Cancer Research UK. Research at The Institute of Cancer Research is supported by Cancer Research UK under Programme C33589/A19727. Peter Ziegenhein is supported by Cancer Research UK under Programme C33589/A19908.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10023/125902018-01-01T00:00:00ZBrüningk, SarahPowathil, GibinZiegenhein, PeterIjaz, JannatRivens, IanNill, S.Chaplain, Mark Andrew JosephOelfke, Uweter Haar, GailCombined radiotherapy and hyperthermia offer great potential for the successful treatment of radio-resistant tumours through thermo-radiosensitization. Tumour response heterogeneity, due to intrinsic, or micro-environmentally induced factors, may greatly influence treatment outcome, but is difficult to account for using traditional treatment planning approaches. Systems oncology simulation, using mathematical models designed to predict tumour growth and treatment response, provides a powerful tool for analysis and optimization of combined treatments. We present a framework that simulates such combination treatments on a cellular level. This multiscale hybrid cellular automaton simulates large cell populations (up to 107 cells) in vitro, while allowing individual cell-cycle progression, and treatment response by modelling radiation-induced mitotic cell death, and immediate cell kill in response to heating. Based on a calibration using a number of experimental growth, cell cycle and survival datasets for HCT116 cells, model predictions agreed well (R2 > 0.95) with experimental data within the range of (thermal and radiation) doses tested (0–40 CEM43, 0–5 Gy). The proposed framework offers flexibility for modelling multimodality treatment combinations in different scenarios. It may therefore provide an important step towards the modelling of personalized therapies using a virtual patient tumour.Special subgroups of regular semigroups
http://hdl.handle.net/10023/12231
Extending the notions of inverse transversal and associate subgroup, we consider a regular semigroup S with the property that there exists a subsemigroup T which contains, for each x∈S, a unique y such that both xy and yx are idempotent. Such a subsemigroup is necessarily a group which we call a special subgroup. Here we investigate regular semigroups with this property. In particular, we determine when the subset of perfect elements is a subsemigroup and describe its structure in naturally arising situations.
This work was partially supported by the Portuguese Foundation for Science and Technology through the grant UID/MAT/00297/2013 (CMA).
Tue, 03 Oct 2017 00:00:00 GMThttp://hdl.handle.net/10023/122312017-10-03T00:00:00ZBlyth, T. S.Almeida Santos, M. H.Extending the notions of inverse transversal and associate subgroup, we consider a regular semigroup S with the property that there exists a subsemigroup T which contains, for each x∈S, a unique y such that both xy and yx are idempotent. Such a subsemigroup is necessarily a group which we call a special subgroup. Here we investigate regular semigroups with this property. In particular, we determine when the subset of perfect elements is a subsemigroup and describe its structure in naturally arising situations.Regularity of Navier--Stokes flows with bounds for the pressure
http://hdl.handle.net/10023/12230
This study derives regularity criteria for solutions of the Navier–Stokes equations. Let Ω(t) := {x : |u(x, t)| > c ||u||Lr(R3) }, for some r ≥ 3 and constant c independent of t, with measure |Ω|. It is shown that if ||p + P||L3/2(Ω) becomes sufficiently small as |Ω| decreases, then||u||L(r+6)/3(R3) decays and regularity is secured. Here p is the physical pressure and P is a pressure moderator of relatively broad forms. The implications of the results are discussed and regularity criteria in terms of bounds for |p + P| within Ω are deduced.
This paper was presented at the Warwick EPSRC Symposium on PDEs in Fluid Mechanics, September 2016. Part of this research was carried out when CVT was visiting the University of Alberta, whose hospitality is gratefully acknowledged. XY was partially supported by NSERC Discovery grant RES0020476
Mon, 01 May 2017 00:00:00 GMThttp://hdl.handle.net/10023/122302017-05-01T00:00:00ZTran, Chuong V.Yu, XinweiThis study derives regularity criteria for solutions of the Navier–Stokes equations. Let Ω(t) := {x : |u(x, t)| > c ||u||Lr(R3) }, for some r ≥ 3 and constant c independent of t, with measure |Ω|. It is shown that if ||p + P||L3/2(Ω) becomes sufficiently small as |Ω| decreases, then||u||L(r+6)/3(R3) decays and regularity is secured. Here p is the physical pressure and P is a pressure moderator of relatively broad forms. The implications of the results are discussed and regularity criteria in terms of bounds for |p + P| within Ω are deduced.Above the noise : the search for periodicities in the inner heliosphere
http://hdl.handle.net/10023/12054
Remote sensing of coronal and heliospheric periodicities can provide vital insight into the local conditions and dynamics of the solar atmosphere. We seek to trace long (one hour or longer) periodic oscillatory signatures (previously identified above the limb in the corona by, e.g., Telloni et al., 2013, Astrophys. J., 767, 138) from their origin at the solar surface out into the heliosphere. To do this, we combine on-disk measurements taken by the Atmospheric Imaging Assembly (AIA) onboard the Solar Dynamics Observatory (SDO) and concurrent extreme ultra-violet (EUV) and coronagraph data from one of the Solar Terrestrial Relations Observatory (STEREO) spacecraft to study the evolution of two active regions in the vicinity of an equatorial coronal hole over several days in early 2011. Fourier and wavelet analysis of signals are performed. Applying white-noise-based confidence levels to the power spectra associated with detrended intensity time series yields detections of oscillatory signatures with periods from 6 − 13 hours in both AIA and STEREO data. As was found by Telloni et al. (2013), these signatures are aligned with local magnetic structures. However, typical spectral power densities all vary substantially as a function of period, indicating spectra dominated by red (rather than white) noise. Contrary to the white-noise-based results, applying global confidence levels based on a generic background noise model (allowing a combination of white noise, red noise, and transients following Auch`ere et al., 2016, Astrophys. J., 825, 110) without detrending the time series, uncovers only sporadic, spatially uncorrelated evidence of periodic signatures in either instrument. Automating this method to individual pixels in the STEREO/COR coronagraph field of view is non-trivial.
Wed, 01 Nov 2017 00:00:00 GMThttp://hdl.handle.net/10023/120542017-11-01T00:00:00ZThrelfall, James WilliamDe Moortel, InekeConlon, Thomas MichaelRemote sensing of coronal and heliospheric periodicities can provide vital insight into the local conditions and dynamics of the solar atmosphere. We seek to trace long (one hour or longer) periodic oscillatory signatures (previously identified above the limb in the corona by, e.g., Telloni et al., 2013, Astrophys. J., 767, 138) from their origin at the solar surface out into the heliosphere. To do this, we combine on-disk measurements taken by the Atmospheric Imaging Assembly (AIA) onboard the Solar Dynamics Observatory (SDO) and concurrent extreme ultra-violet (EUV) and coronagraph data from one of the Solar Terrestrial Relations Observatory (STEREO) spacecraft to study the evolution of two active regions in the vicinity of an equatorial coronal hole over several days in early 2011. Fourier and wavelet analysis of signals are performed. Applying white-noise-based confidence levels to the power spectra associated with detrended intensity time series yields detections of oscillatory signatures with periods from 6 − 13 hours in both AIA and STEREO data. As was found by Telloni et al. (2013), these signatures are aligned with local magnetic structures. However, typical spectral power densities all vary substantially as a function of period, indicating spectra dominated by red (rather than white) noise. Contrary to the white-noise-based results, applying global confidence levels based on a generic background noise model (allowing a combination of white noise, red noise, and transients following Auch`ere et al., 2016, Astrophys. J., 825, 110) without detrending the time series, uncovers only sporadic, spatially uncorrelated evidence of periodic signatures in either instrument. Automating this method to individual pixels in the STEREO/COR coronagraph field of view is non-trivial.Bifurcations and chaotic dynamics in a tumour-immune-virus system
http://hdl.handle.net/10023/11999
Despite mounting evidence that oncolytic viruses can be effective in treating cancer, understanding the details of the interactions between tumour cells, oncolytic viruses and immune cells that could lead to tumour control or tumour escape is still an open problem. Mathematical modelling of cancer oncolytic therapies has been used to investigate the biological mechanisms behind the observed temporal patterns of tumour growth. However, many models exhibit very complex dynamics, which renders them difficult to investigate. In this case, bifurcation diagrams could enable the visualisation of model dynamics by identifying (in the parameter space) the particular transition points between different behaviours. Here, we describe and investigate two simple mathematical models for oncolytic virus cancer therapy, with constant and immunity-dependent carrying capacity. While both models can exhibit complex dynamics, namely fixed points, periodic orbits and chaotic behaviours, only the model with immunity-dependent carrying capacity can exhibit them for biologically realistic situations, i.e., before the tumour grows too large and the experiment is terminated. Moreover, with the help of the bifurcation diagrams we uncover two unexpected behaviours in virus-tumour dynamics: (i) for short virus half-life, the tumour size seems to be too small to be detected, while for long virus half-life the tumour grows to larger sizes that can be detected; (ii) some model parameters have opposite effects on the transient and asymptotic dynamics of the tumour.
Wed, 07 Dec 2016 00:00:00 GMThttp://hdl.handle.net/10023/119992016-12-07T00:00:00ZEftimie, R.Macnamara, C. K.Dushoff, JonathanBramson, J. L.Earn, D. J. D.Despite mounting evidence that oncolytic viruses can be effective in treating cancer, understanding the details of the interactions between tumour cells, oncolytic viruses and immune cells that could lead to tumour control or tumour escape is still an open problem. Mathematical modelling of cancer oncolytic therapies has been used to investigate the biological mechanisms behind the observed temporal patterns of tumour growth. However, many models exhibit very complex dynamics, which renders them difficult to investigate. In this case, bifurcation diagrams could enable the visualisation of model dynamics by identifying (in the parameter space) the particular transition points between different behaviours. Here, we describe and investigate two simple mathematical models for oncolytic virus cancer therapy, with constant and immunity-dependent carrying capacity. While both models can exhibit complex dynamics, namely fixed points, periodic orbits and chaotic behaviours, only the model with immunity-dependent carrying capacity can exhibit them for biologically realistic situations, i.e., before the tumour grows too large and the experiment is terminated. Moreover, with the help of the bifurcation diagrams we uncover two unexpected behaviours in virus-tumour dynamics: (i) for short virus half-life, the tumour size seems to be too small to be detected, while for long virus half-life the tumour grows to larger sizes that can be detected; (ii) some model parameters have opposite effects on the transient and asymptotic dynamics of the tumour.Can substorm particle acceleration be applied to solar flares?
http://hdl.handle.net/10023/11912
Using test particle studies in the electromagnetic fields of three-dimensional magnetohydrodynamic (MHD) simulations of magnetic reconnection, we study the energization of charged particles in the context of the standard two-ribbon flare picture in analogy to the standard magnetospheric substorm paradigm. In particular, we investigate the effects of the collapsing field ("collapsing magnetic trap") below a reconnection site, which has been demonstrated to be the major acceleration mechanism that causes energetic particle acceleration and injections observed in Earth's magnetotail associated with substorms and other impulsive events. We contrast an initially force-free, high-shear field (low beta) with low and moderate shear, finite-pressure (high-beta) arcade structures, where beta represents the ratio between gas (plasma) and magnetic pressure. We demonstrate that the energization affects large numbers of particles, but the acceleration is modest in the presence of a significant shear field. Without incorporating loss mechanisms, the effect on particles at different energies is similar, akin to adiabatic heating, and thus is not a likely mechanism to generate a power-law tail onto a (heated or not heated) Maxwellian velocity distribution.
Fri, 20 Oct 2017 00:00:00 GMThttp://hdl.handle.net/10023/119122017-10-20T00:00:00ZBirn, JoachimBattaglia, MarinaFletcher, LyndsayHesse, MichaelNeukirch, ThomasUsing test particle studies in the electromagnetic fields of three-dimensional magnetohydrodynamic (MHD) simulations of magnetic reconnection, we study the energization of charged particles in the context of the standard two-ribbon flare picture in analogy to the standard magnetospheric substorm paradigm. In particular, we investigate the effects of the collapsing field ("collapsing magnetic trap") below a reconnection site, which has been demonstrated to be the major acceleration mechanism that causes energetic particle acceleration and injections observed in Earth's magnetotail associated with substorms and other impulsive events. We contrast an initially force-free, high-shear field (low beta) with low and moderate shear, finite-pressure (high-beta) arcade structures, where beta represents the ratio between gas (plasma) and magnetic pressure. We demonstrate that the energization affects large numbers of particles, but the acceleration is modest in the presence of a significant shear field. Without incorporating loss mechanisms, the effect on particles at different energies is similar, akin to adiabatic heating, and thus is not a likely mechanism to generate a power-law tail onto a (heated or not heated) Maxwellian velocity distribution.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 (force-free 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 GMThttp://hdl.handle.net/10023/118902018-01-01T00:00:00ZNeukirch, ThomasWilson, FionaAllanson, Oliver DouglasCurrent 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 (force-free 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 cloud-tracking 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 cloud-tops 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 GMThttp://hdl.handle.net/10023/118502017-04-16T00:00:00ZScott, R. K.Dunkerton, T. J.Zonal mean zonal velocity profiles from cloud-tracking 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 cloud-tops 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.Emergence of spatial patterns in a mathematical model for the co-culture dynamics of epithelial-like and mesenchymal-like 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 integro-differential model for the co-culture dynamics of epithelial-like and mesenchymal-like cells. Our model takes into account the effects of chemotaxis, adhesive interactions between epithelial-like 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 epithelial-like and mesenchymal-like cells can segregate when there is little competition for nutrients. Furthermore, our computational results provide a possible explanation for how the concerted action between epithelial-cell adhesion and mesenchymal-cell spreading can precipitate the formation of ring-like structures, which resemble the fibrous capsules frequently observed in hepatic tumours.
Wed, 01 Feb 2017 00:00:00 GMThttp://hdl.handle.net/10023/117752017-02-01T00:00:00ZDelitala, MarcelloLorenzi, TommasoAccumulating evidence indicates that the interaction between epithelial and mesenchymal cells plays a pivotal role in cancer development and metastasis formation. Here we propose an integro-differential model for the co-culture dynamics of epithelial-like and mesenchymal-like cells. Our model takes into account the effects of chemotaxis, adhesive interactions between epithelial-like 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 epithelial-like and mesenchymal-like cells can segregate when there is little competition for nutrients. Furthermore, our computational results provide a possible explanation for how the concerted action between epithelial-cell adhesion and mesenchymal-cell spreading can precipitate the formation of ring-like structures, which resemble the fibrous capsules frequently observed in hepatic tumours.Spatio-temporal 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 spatio-temporal models of synthetic gene regulatory networks e.g. n-gene repressilators and activator-repressor systems.
Wed, 01 Feb 2017 00:00:00 GMThttp://hdl.handle.net/10023/117742017-02-01T00:00:00ZMacnamara, 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 spatio-temporal models of synthetic gene regulatory networks e.g. n-gene repressilators and activator-repressor systems.Wave of chaos in a spatial eco-epidemiological system : generating realistic patterns of patchiness in rabbit-lynx dynamics
http://hdl.handle.net/10023/11666
In the present paper, we propose and analyse an eco-epidemiological 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 rabbit-lynx 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 eco-epidemiological 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 (RPG-2014-149).
Tue, 01 Nov 2016 00:00:00 GMThttp://hdl.handle.net/10023/116662016-11-01T00:00:00ZUpadhyay, RanjitRoy, ParimitaVenkataraman, C.Madzvamuse, AnotidaIn the present paper, we propose and analyse an eco-epidemiological 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 rabbit-lynx 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 eco-epidemiological 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 two-layer baroclinic flow
http://hdl.handle.net/10023/11637
The formation, evolution and co-existence of jets and vortices in turbulent planetary atmospheres is examined using a two-layer quasi-geostrophic β -channel shallow-water 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/anti-cyclonic pairs, called hetons, to the flow, though the qualitative flow evolution is evidently not sensitive to this or other small-scale 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 GMThttp://hdl.handle.net/10023/116372017-04-01T00:00:00ZJougla, ThibaultDritschel, David GerardThe formation, evolution and co-existence of jets and vortices in turbulent planetary atmospheres is examined using a two-layer quasi-geostrophic β -channel shallow-water 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/anti-cyclonic pairs, called hetons, to the flow, though the qualitative flow evolution is evidently not sensitive to this or other small-scale 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 Vlasov-Maxwell equilibria for asymmetric current sheets
http://hdl.handle.net/10023/11626
The NASA Magnetospheric Multiscale mission has made in-situ diffusion region and kinetic-scale 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 particle-in-cell simulations. Many particle-in-cell simulations of asymmetric collisionless reconnection start from an asymmetric Harris-type 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 Vlasov-Maxwell system that are self-consistent with one-dimensional asymmetric current sheets, with an asymmetric Harris-type magnetic field profile, plus a constant non-zero 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 (Rad-Sat) (O.A.)
Sat, 16 Sep 2017 00:00:00 GMThttp://hdl.handle.net/10023/116262017-09-16T00:00:00ZAllanson, O.Wilson, F.Neukirch, T.Liu, Yi-HsinHodgson, J. D. B.The NASA Magnetospheric Multiscale mission has made in-situ diffusion region and kinetic-scale 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 particle-in-cell simulations. Many particle-in-cell simulations of asymmetric collisionless reconnection start from an asymmetric Harris-type 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 Vlasov-Maxwell system that are self-consistent with one-dimensional asymmetric current sheets, with an asymmetric Harris-type magnetic field profile, plus a constant non-zero 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 reaction-diffusion 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 GMThttp://hdl.handle.net/10023/116182017-01-01T00:00:00ZVenkataraman, ChandrasekharSekimura, ToshioDespite 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 reaction-diffusion 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.Force-free collisionless current sheet models with non-uniform temperature and density profiles
http://hdl.handle.net/10023/11614
We present a class of one-dimensional, strictly neutral, Vlasov-Maxwell equilibrium distribution functions for force-free current sheets, with magnetic fields defined in terms of Jacobian elliptic functions, extending the results of Abraham-Shrauner48 to allow for non-uniform density and temperature pro les. To achieve this, we use an approach previously applied to the force-free 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 force-free 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 (Rad-Sat) (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 GMThttp://hdl.handle.net/10023/116142017-08-17T00:00:00ZWilson, FionaNeukirch, ThomasAllanson, Oliver DouglasWe present a class of one-dimensional, strictly neutral, Vlasov-Maxwell equilibrium distribution functions for force-free current sheets, with magnetic fields defined in terms of Jacobian elliptic functions, extending the results of Abraham-Shrauner48 to allow for non-uniform density and temperature pro les. To achieve this, we use an approach previously applied to the force-free 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 force-free 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 GMThttp://hdl.handle.net/10023/115432017-08-22T00:00:00ZO'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 Mars-like 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 0.5-2 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 GMThttp://hdl.handle.net/10023/115412017-05-01T00:00:00ZSeviour, WilliamWaugh, DarrynScott, Richard KirknessThe 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 Mars-like 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 0.5-2 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.Pressure moderation and effective pressure in Navier-Stokes flows
http://hdl.handle.net/10023/11499
We study the Cauchy problem of the Navier–Stokes equations by both semi-analytic 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 ||u||Lq , 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 ||u||Lq , 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 GMThttp://hdl.handle.net/10023/114992016-08-17T00:00:00ZTran, Chuong VanYu, XinweiWe study the Cauchy problem of the Navier–Stokes equations by both semi-analytic 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 ||u||Lq , 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 ||u||Lq , 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 Kelvin-Helmholtz 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 Kelvin-Helmholtz instability (KHI) in transversely oscillating coronal loops. Methods. We modelled a fundamental standing kink mode in a straight, density-enhanced 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 non-zero 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).
Thu, 16 Nov 2017 00:00:00 GMThttp://hdl.handle.net/10023/114442017-11-16T00:00:00ZHowson, T. A.De Moortel, I.Antolin, P.Aims. We quantify the effects of twisted magnetic fields on the development of the magnetic Kelvin-Helmholtz instability (KHI) in transversely oscillating coronal loops. Methods. We modelled a fundamental standing kink mode in a straight, density-enhanced 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 non-zero 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.N-body 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 N-body and N-vortex 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 GMThttp://hdl.handle.net/10023/114262016-08-01T00:00:00ZBoatto, StefanellaDritschel, David GerardSchaefer, Rodrigo GA major challenge for our understanding of the mathematical basis of particle dynamics is the formulation of N-body and N-vortex 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 between a surface quasi-geostrophic 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 co-operative 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 GMThttp://hdl.handle.net/10023/114042017-08-01T00:00:00ZReinaud, Jean NoelDritschel, David GerardCarton, XavierThis 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 co-operative 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.Evolutionary dynamics of phenotype-structured populations : from individual-level mechanisms to population-level 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 proof-of-concept mathematical models. Here, we present a stochastic agent-based model and a related deterministic integrodifferential equation model for the evolution of a phenotype-structured population composed of asexually-reproducing 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 [ANR-13-BS01-0004] and the “ANR JC” project Modevol [ANR-13-JS01-0009]. 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 [ANR-11-LABX-0056-LMH]. LD was also supported in part by Université Sorbonne Paris Cité “Investissements d’Avenir”[ANR-11-IDEX-0005].
Mon, 01 Aug 2016 00:00:00 GMThttp://hdl.handle.net/10023/113282016-08-01T00:00:00ZChisholm, Rebecca H.Lorenzi, TommasoDesvillettes, LaurentHughes, 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 proof-of-concept mathematical models. Here, we present a stochastic agent-based model and a related deterministic integrodifferential equation model for the evolution of a phenotype-structured population composed of asexually-reproducing 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 small-scale 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 fine-scale 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 fast-particle 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 GMThttp://hdl.handle.net/10023/113202017-07-14T00:00:00ZPriest, EricThis 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 small-scale 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 fine-scale 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 fast-particle 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 gene-sites 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 Hopf-bifurcation. 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 gene-site and a protein production site in order to achieve oscillations. We first present a model of a well-known GRN, the Hes1 system, and then extend the approach to examine spatio-temporal models of synthetic GRNs e.g. n-gene repressilator and activator-repressor 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 GMThttp://hdl.handle.net/10023/112582016-10-21T00:00:00ZMacnamara, Cicely KrystynaChaplain, Mark Andrew JosephGene 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 gene-sites 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 Hopf-bifurcation. 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 gene-site and a protein production site in order to achieve oscillations. We first present a model of a well-known GRN, the Hes1 system, and then extend the approach to examine spatio-temporal models of synthetic GRNs e.g. n-gene repressilator and activator-repressor 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 geo-positioning 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 smoking-related 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 person-centred 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 2-week logging phase where pre-quit patients log all of their smoking and craving events; and (2) a post-quit 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 follow-up 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 GMThttp://hdl.handle.net/10023/112052017-07-14T00:00:00ZSchick, Robert S.Kelsey, Thomas W.Marston, JohnSampson, KayHumphris, Gerald M.Background: Approximately 11,000 people die in Scotland each year as a result of smoking-related 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 person-centred 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 2-week logging phase where pre-quit patients log all of their smoking and craving events; and (2) a post-quit 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 follow-up 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.The characteristics of billows generated by internal solitary waves
http://hdl.handle.net/10023/11156
The spatial and temporal development of shear-induced 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 contour-advective semi-Lagrangian 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 wave-induced 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 long-wave counterparts for a given stratification.
Wed, 01 Feb 2017 00:00:00 GMThttp://hdl.handle.net/10023/111562017-02-01T00:00:00ZCarr, MagdaFranklin, JamesKing, Stuart EdwardDavies, PeterGrue, JohnDritschel, David GerardThe spatial and temporal development of shear-induced 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 contour-advective semi-Lagrangian 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 wave-induced 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 long-wave counterparts for a given stratification.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 semi-geostrophic 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 large-scale semi-geostrophic (GLSG) models contains the L 1-model introduced by Simon (J. Fluid. Mech., vol. 132, pp. 431-444) 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 1-member 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).
Mon, 10 Jul 2017 00:00:00 GMThttp://hdl.handle.net/10023/111002017-07-10T00:00:00ZDritschel, David GerardGottwald, GeorgOliver, MarcelWe present an extensive numerical comparison of a family of balance models appropriate to the semi-geostrophic 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 large-scale semi-geostrophic (GLSG) models contains the L 1-model introduced by Simon (J. Fluid. Mech., vol. 132, pp. 431-444) 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 1-member 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.Scaling theory for vortices in the two-dimensional inverse energy cascade
http://hdl.handle.net/10023/11014
We propose a new similarity theory for the two-dimensional 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 three-part, time-evolving vortex number density distribution, n(A) ∼ tαiA−ri, i ∈ 1,2,3. Just above the forcing scale (i =1) there is a forcing-equilibrated scaling range in which the number of vortices at fixed A is constant and vortex ‘self-energy’ Evcm = (2D)−1∫ωv2A2n(A) dA is conserved in A-space 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 scale-invariant 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 vortex-containing 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 point-like; in this range we predict n(A) ∼ tr3−1A−r3. Allowing for time-varying ωv2 results in a small but significant correction to these temporal dependences. High-resolution 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 GMThttp://hdl.handle.net/10023/110142017-01-01T00:00:00ZBurgess, B. H.Scott, R. K.We propose a new similarity theory for the two-dimensional 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 three-part, time-evolving vortex number density distribution, n(A) ∼ tαiA−ri, i ∈ 1,2,3. Just above the forcing scale (i =1) there is a forcing-equilibrated scaling range in which the number of vortices at fixed A is constant and vortex ‘self-energy’ Evcm = (2D)−1∫ωv2A2n(A) dA is conserved in A-space 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 scale-invariant 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 vortex-containing 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 point-like; in this range we predict n(A) ∼ tr3−1A−r3. Allowing for time-varying ωv2 results in a small but significant correction to these temporal dependences. High-resolution 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.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 non-thermal particle populations in solar flares. CMTs occur if an initially stretched magnetic field structure relaxes rapidly into a lower-energy configuration, which is believed to happen as a by-product 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 GMThttp://hdl.handle.net/10023/108962016-01-01T00:00:00ZBorissov, AlexeiNeukirch, ThomasThrelfall, James WilliamCollapsing magnetic traps (CMTs) are one proposed mechanism for generating non-thermal particle populations in solar flares. CMTs occur if an initially stretched magnetic field structure relaxes rapidly into a lower-energy configuration, which is believed to happen as a by-product 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 opposite-polarity 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 GMThttp://hdl.handle.net/10023/108932017-05-04T00:00:00ZChen, JieSu, JiangtaoDeng, YuanyongPriest, 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 opposite-polarity fragment between them.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 two-ribbon flares. Flare ribbons and loops spread along the PIL at a speed ranging from a few to a hundred km s-1. 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 AGS-1460059.
Mon, 20 Mar 2017 00:00:00 GMThttp://hdl.handle.net/10023/106862017-03-20T00:00:00ZQiu, JiongLongcope, 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 two-ribbon flares. Flare ribbons and loops spread along the PIL at a speed ranging from a few to a hundred km s-1. 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.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 population-level 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 well-surveyed 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 deep-sea 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 N62470-13-2-8008), NASA (NNX08AK73G) and NOAA/NMFS (EE-133F-14-SE-3558).
Thu, 01 Jun 2017 00:00:00 GMThttp://hdl.handle.net/10023/106822017-06-01T00:00:00ZMannocci, LauraRoberts, 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 population-level 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 well-surveyed 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 deep-sea 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 radiation-induced 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 low-doses of radiotherapy, doing more damage than that due to direct radiation. The survival curves derived from our computational simulations showed an area of hyper-radiosensitivity at low-doses 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 DG-CNECT Contract 318202.
Thu, 21 Jul 2016 00:00:00 GMThttp://hdl.handle.net/10023/106152016-07-21T00:00:00ZPowathil, GibinMunro, Alastair JohnChaplain, Mark Andrew JosephSwat, MaciejRadiotherapy 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 radiation-induced 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 low-doses of radiotherapy, doing more damage than that due to direct radiation. The survival curves derived from our computational simulations showed an area of hyper-radiosensitivity at low-doses that are not obtained using a traditional radiobiological model.Particle acceleration due to coronal non-null magnetic reconnection
http://hdl.handle.net/10023/10551
Various topological features, for example magnetic null-points 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 non-topological 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 gyro-averaged 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 time-dependent acceleration and impact sites for each particle species and compare our findings to those recovered by topologically based studies of three-dimensional (3D) reconnection and particle acceleration. We also broadly compare aspects of our findings to general observational features typically seen during two-ribbon flare events.
Wed, 01 Mar 2017 00:00:00 GMThttp://hdl.handle.net/10023/105512017-03-01T00:00:00ZThrelfall, James WilliamNeukirch, ThomasParnell, Clare ElizabethVarious topological features, for example magnetic null-points 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 non-topological 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 gyro-averaged 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 time-dependent acceleration and impact sites for each particle species and compare our findings to those recovered by topologically based studies of three-dimensional (3D) reconnection and particle acceleration. We also broadly compare aspects of our findings to general observational features typically seen during two-ribbon flare events.Blockage of saline intrusions in restricted, two-layer exchange flows across a submerged sill obstruction
http://hdl.handle.net/10023/10543
Results are presented from a series of large-scale experiments investigating the internal and near-bed dynamics of bi-directional stratified flows with a net-barotropic component across a submerged, trapezoidal, sill obstruction. High-resolution velocity and density profiles are obtained in the vicinity of the obstruction to observe internal-flow 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 two-layer exchange flows is measured using micro-conductivity probes at several sill locations. These measurements are designed to aid qualitative and quantitative interpretation of the internal-flow 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, net-barotropic, flow conditions in the upper freshwater layer. This interfacial mixing is quantified by considering both the isopycnal separation of vertically-sorted 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 two-layer 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 internal-flow 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, 01 Feb 2018 00:00:00 GMThttp://hdl.handle.net/10023/105432018-02-01T00:00:00ZCuthbertson, AlanLaanearu, JanekCarr, MagdaSommeria, JoelViboud, SamuelResults are presented from a series of large-scale experiments investigating the internal and near-bed dynamics of bi-directional stratified flows with a net-barotropic component across a submerged, trapezoidal, sill obstruction. High-resolution velocity and density profiles are obtained in the vicinity of the obstruction to observe internal-flow 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 two-layer exchange flows is measured using micro-conductivity probes at several sill locations. These measurements are designed to aid qualitative and quantitative interpretation of the internal-flow 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, net-barotropic, flow conditions in the upper freshwater layer. This interfacial mixing is quantified by considering both the isopycnal separation of vertically-sorted 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 two-layer 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 internal-flow 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.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 extreme-ultraviolet 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 tether-cutting 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 3D-type in the early phase, as manifested in a strong-to-weak shear transition in flare loops, and becomes more 2D-like in the later phase, as shown by the apparent rising motion of an arcade of flare loops.
Tue, 31 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10023/104862017-01-31T00:00:00ZLi, 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 extreme-ultraviolet 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 tether-cutting 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 3D-type in the early phase, as manifested in a strong-to-weak shear transition in flare loops, and becomes more 2D-like in the later phase, as shown by the apparent rising motion of an arcade of flare loops.Geostrophic tripolar vortices in a two-layer fluid : linear stability and nonlinear evolution of equilibria
http://hdl.handle.net/10023/10411
We investgate equilibrium solutions for tripolar vortices in a two-layer quasi-geostrophic flow. Two of the vortices are like-signed and lie in one layer. An opposite-signed vortex lies in the other layer. The families of equilibria can be spanned by the distance (called separation) between the two like-signed vortices. Two equilibrium configurations are possible when the opposite-signed 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 co-exist 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 like-signed 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 GMThttp://hdl.handle.net/10023/104112017-03-01T00:00:00ZReinaud, Jean NoelSokolovskiy, MikhailCarton, XavierWe investgate equilibrium solutions for tripolar vortices in a two-layer quasi-geostrophic flow. Two of the vortices are like-signed and lie in one layer. An opposite-signed vortex lies in the other layer. The families of equilibria can be spanned by the distance (called separation) between the two like-signed vortices. Two equilibrium configurations are possible when the opposite-signed 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 co-exist 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 like-signed 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 non-symmetrical 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 GMThttp://hdl.handle.net/10023/103702016-06-01T00:00:00ZJupp, P.E.Regoli, G.Azzalini, A.A standard method of obtaining non-symmetrical 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 Navier-Stokes 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 Navier-Stokes 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 Navier-Stokes equations, Applied Mathematics Letters 22 (2009) 1438–1443].
XY is partially supported by a grant from NSERC.
Mon, 01 Aug 2016 00:00:00 GMThttp://hdl.handle.net/10023/103192016-08-01T00:00:00ZTran, Chuong VanYu, XinweiIn this article we prove a logarithmic improvement of regularity criteria in the multiplier spaces for the Cauchy problem of the incompressible Navier-Stokes 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 Navier-Stokes 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 GMThttp://hdl.handle.net/10023/103052017-03-10T00:00:00ZHodgson, Jonathan David BrockieNeukirch, ThomasWe 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.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 multi-wavelength observations from the Solar Dynamics Observatory (SDO) and the Hinode Extreme-ultraviolet Imaging Spectrometer. The Hα observations were conducted on 2012 February 11 with the Hydrogen-Alpha 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 free-fall 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 GMThttp://hdl.handle.net/10023/102912015-05-12T00:00:00ZChristian, Damian J.Jess, David B.Antolin, PatrickMathioudakis, MihalisWe have obtained Hα high spatial and time resolution observations of the upper solar chromosphere and supplemented these with multi-wavelength observations from the Solar Dynamics Observatory (SDO) and the Hinode Extreme-ultraviolet Imaging Spectrometer. The Hα observations were conducted on 2012 February 11 with the Hydrogen-Alpha 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 free-fall 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.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 short-lived 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 free-fall 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 small-scale heating events in sunspots in the TR.
Fri, 27 Jun 2014 00:00:00 GMThttp://hdl.handle.net/10023/102822014-06-27T00:00:00ZKleint, L.Antolin, P.Tian, H.Judge, P.Testa, P.De Pontieu, B.Martínez-Sykora, 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 short-lived 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 free-fall 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 small-scale 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 three-dimensional magnetohydrodynamic model of a plasmacylinder. Effects of the line-of-sight angle and instrumental resolutionon perturbations of the GS intensity are analyzed for two models: a basemodel with strong Razin suppression and a low-density model in which theRazin effect was unimportant. Our finding contradicts previouspredictions made with simpler models: an in-phase variation of intensitybetween low (f <fpeak) and high (f > fpeak) frequencies is found for the low-density model and ananti-phase 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 GMThttp://hdl.handle.net/10023/102802014-03-28T00:00:00ZReznikova, 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 three-dimensional magnetohydrodynamic model of a plasmacylinder. Effects of the line-of-sight angle and instrumental resolutionon perturbations of the GS intensity are analyzed for two models: a basemodel with strong Razin suppression and a low-density model in which theRazin effect was unimportant. Our finding contradicts previouspredictions made with simpler models: an in-phase variation of intensitybetween low (f <fpeak) and high (f > fpeak) frequencies is found for the low-density model and ananti-phase 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.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 quasi-geostrophic 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 quasi-geostrophic 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 higher-order 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, quasi-geostrophic order. Unlike the quasi-geostrophic 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 leading-order quasi-geostrophic 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 GMThttp://hdl.handle.net/10023/102272016-09-01T00:00:00ZMckiver, 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 quasi-geostrophic 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 quasi-geostrophic 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 higher-order 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, quasi-geostrophic order. Unlike the quasi-geostrophic 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 leading-order quasi-geostrophic 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.Spectral non-locality, absolute equilibria and Kraichnan-Leith-Batchelor phenomenology in two-dimensional turbulent energy cascades
http://hdl.handle.net/10023/10062
We study the degree to which Kraichnan-Leith-Batchelor (KLB) phenomenology describes two-dimensional 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)= k-α θ over bar (k) in Fourier space. These models differ in spectral non-locality, and include surface quasigeostrophic flow (alpha = 1), regular two-dimensional flow (α = 2) and rotating shallow flow (α = 3), which is the isotropic limit of a mantle convection model. We re-examine 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 α-dependent eddy-damped quasinormal Markovian (EDQNM) closure, we seek self-similar inertial range solutions and study their characteristics. Our present focus is not on coherent structures, which the EDQNM filters out, but on any self-similar 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. Non-local triads contribute increasingly to the energy flux as α increases. More importantly, the energy cascade is downscale in the self-similar 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 self-similar for α <4. However, downscale energy flux in the EDQNM self-similar 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 GMThttp://hdl.handle.net/10023/100622013-06-01T00:00:00ZBurgess, B. H.Shepherd, T. G.We study the degree to which Kraichnan-Leith-Batchelor (KLB) phenomenology describes two-dimensional 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)= k-α θ over bar (k) in Fourier space. These models differ in spectral non-locality, and include surface quasigeostrophic flow (alpha = 1), regular two-dimensional flow (α = 2) and rotating shallow flow (α = 3), which is the isotropic limit of a mantle convection model. We re-examine 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 α-dependent eddy-damped quasinormal Markovian (EDQNM) closure, we seek self-similar inertial range solutions and study their characteristics. Our present focus is not on coherent structures, which the EDQNM filters out, but on any self-similar 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. Non-local triads contribute increasingly to the energy flux as α increases. More importantly, the energy cascade is downscale in the self-similar 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 self-similar for α <4. However, downscale energy flux in the EDQNM self-similar 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 Prodi-Serrin-Ladyzhenskaya type regularity criteria for the Navier-Stokes equations
http://hdl.handle.net/10023/10048
In this article we prove new regularity criteria of the Prodi-Serrin-Ladyzhenskaya type for the Cauchy problem of the three-dimensional Navier-Stokes 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 ||u||L3 and ||u||H1/2.
X.Y. is partially supported by the Discovery Grant No. RES0020476 from NSERC.
Wed, 18 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10023/100482017-01-18T00:00:00ZTran, Chuong VanYu, XinweiIn this article we prove new regularity criteria of the Prodi-Serrin-Ladyzhenskaya type for the Cauchy problem of the three-dimensional Navier-Stokes 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 ||u||L3 and ||u||H1/2.Toward a PV-based algorithm for the dynamical core of hydrostatic global models
http://hdl.handle.net/10023/9957
The diabatic contour-advective semi-Lagrangian (DCASL) algorithms previously constructed for the shallow-water and multilayer Boussinesq primitive equations are extended to multilayer non-Boussinesq equations on the sphere using a hybrid terrain-following-isentropic (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 semi-implicit time-stepping scheme to reduce computational cost. The prognostic variables are an approximation to the Rossby-Ertel 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 semi-Lagrangian solution for Q and another with an Eulerian grid-based 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 GMThttp://hdl.handle.net/10023/99572016-06-01T00:00:00ZMohebalhojeh, Ali R.Joghataei, MohammadDritschel, David G.The diabatic contour-advective semi-Lagrangian (DCASL) algorithms previously constructed for the shallow-water and multilayer Boussinesq primitive equations are extended to multilayer non-Boussinesq equations on the sphere using a hybrid terrain-following-isentropic (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 semi-implicit time-stepping scheme to reduce computational cost. The prognostic variables are an approximation to the Rossby-Ertel 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 semi-Lagrangian solution for Q and another with an Eulerian grid-based 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.A comparison of global magnetic field skeletons and active-region 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 open-field 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 active-region 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 potential-field 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 GMThttp://hdl.handle.net/10023/98752016-01-01T00:00:00ZEdwards, 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 open-field 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 active-region 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 potential-field 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.Models of interacting pairs of thin, quasi-geostrophic vortices: steady-state solutions and nonlinear stability
http://hdl.handle.net/10023/9744
We study pairwise interactions of elliptical quasi-geostrophic 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 non-zero 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 non-elliptical 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 quasi-geostrophic (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 shorter-range interactions.
This work was supported by the Office of Naval Research under Grant N00014-11- 1-0087; 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 GMThttp://hdl.handle.net/10023/97442016-01-01T00:00:00ZBersanelli, MatteoDritschel, David G.Lancellotti, CarloPoje, Andrew C.We study pairwise interactions of elliptical quasi-geostrophic 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 non-zero 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 non-elliptical 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 quasi-geostrophic (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 shorter-range interactions.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 high-resolution 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 footpoint-driven 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 Multi-channel Polarimeter) Doppler shift observations of large, off-limb, trans-equatorial loops shows that Fourier power at the apex appears to be higher in the high-frequency part of the spectrum than expected from theoretical models. This excess high-frequency FFT power could be tentative evidence for the onset of a cascade of the low-to-mid frequency waves into (Alfvenic) turbulence.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10023/96842016-01-01T00:00:00ZDe Moortel, InekePascoe, David JamesWright, Andrew NicholasHood, Alan WilliamAs 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 high-resolution 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 footpoint-driven 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 Multi-channel Polarimeter) Doppler shift observations of large, off-limb, trans-equatorial loops shows that Fourier power at the apex appears to be higher in the high-frequency part of the spectrum than expected from theoretical models. This excess high-frequency FFT power could be tentative evidence for the onset of a cascade of the low-to-mid frequency waves into (Alfvenic) turbulence.The usage of a three-compartment model to investigate the metabolic differences between hepatic reductase null and wild-type 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 three-compartment 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 two-compartment model using experimental data from studies using wild-type 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. IAP-VI/10.
Mon, 05 Oct 2015 00:00:00 GMThttp://hdl.handle.net/10023/96112015-10-05T00:00:00ZHill, LydiaChaplain, Mark Andrew JosephWolf, RolandKapelyukh, YuryThe 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 three-compartment 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 two-compartment model using experimental data from studies using wild-type 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/s-1. That signal has a clear signature in the slit-jaw 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 jet-like features in the IRIS Si IV slit-jaw 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 GMThttp://hdl.handle.net/10023/96002016-09-01T00:00:00ZBryans, PaulMcIntosh, Scott W.De Moortel, InekeDe Pontieu, BartThe 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/s-1. That signal has a clear signature in the slit-jaw 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 jet-like features in the IRIS Si IV slit-jaw 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 quasi-geostrophic 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 long-lived. 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 three-dimensional quasi-geostrophic, 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 same-depth 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 meta-stable 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, finite-core vortices.
Sun, 01 May 2016 00:00:00 GMThttp://hdl.handle.net/10023/95932016-05-01T00:00:00ZReinaud, Jean NoelCarton, XavierWe investigate numerically the nonlinear interactions between hetons. Hetons are baroclinic structures consisting of two vortices of opposite sign lying at different depths. Hetons are long-lived. 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 three-dimensional quasi-geostrophic, 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 same-depth 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 meta-stable 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, finite-core vortices.Neutral and non-neutral collisionless plasma equilibria for twisted flux tubes : the Gold-Hoyle model in a background field
http://hdl.handle.net/10023/9539
We calculate exact one-dimensional collisionless plasma equilibria for a continuum of flux tube models, for which the total magnetic field is made up of the `force-free' Gold-Hoyle magnetic flux tube embedded in a uniform and anti-parallel 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 force-free, but by reducing its magnitude the departure from force-free 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 non-neutral 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 GMThttp://hdl.handle.net/10023/95392016-09-01T00:00:00ZAllanson, Oliver DouglasWilson, FionaNeukirch, ThomasWe calculate exact one-dimensional collisionless plasma equilibria for a continuum of flux tube models, for which the total magnetic field is made up of the `force-free' Gold-Hoyle magnetic flux tube embedded in a uniform and anti-parallel 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 force-free, but by reducing its magnitude the departure from force-free 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 non-neutral 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.Three-dimensional forced-damped dynamical systems with rich dynamics : bifurcations, chaos and unbounded solutions
http://hdl.handle.net/10023/9468
We consider certain autonomous three-dimensional dynamical systems that can arise in mechanical and fluid-dynamical contexts. Extending a previous study in Craik and Okamoto (2002), to include linear forcing and damping, we find that the four-leaf structure discovered in that paper, and unbounded orbits, persist, but may now be accompanied by three distinct period-doubling 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 Grant-in-Aid for JSPS Fellow No. 24·5312. H.O. is partially supported by JSPS KAKENHI 24244007.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10023/94682015-01-01T00:00:00ZMiyaji, TomoyukiOkamoto, HisashiCraik, Alexander Duncan DavidsonWe consider certain autonomous three-dimensional dynamical systems that can arise in mechanical and fluid-dynamical contexts. Extending a previous study in Craik and Okamoto (2002), to include linear forcing and damping, we find that the four-leaf structure discovered in that paper, and unbounded orbits, persist, but may now be accompanied by three distinct period-doubling 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.Study of the three-dimensional 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 three-dimensional (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 force-free field approximation using SOHO/MDI magnetograms, aiming toward a first-order identification of extrapolated magnetic field lines corresponding to the reconstructed loops. In all cases, the best-fit extrapolated lines exhibit left-handed twist (α<0), in agreement with the dominant twist of the region.
Mon, 01 Oct 2012 00:00:00 GMThttp://hdl.handle.net/10023/94262012-10-01T00:00:00ZSyntelis, 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 three-dimensional (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 force-free field approximation using SOHO/MDI magnetograms, aiming toward a first-order identification of extrapolated magnetic field lines corresponding to the reconstructed loops. In all cases, the best-fit extrapolated lines exhibit left-handed twist (α<0), in agreement with the dominant twist of the region.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 non-potential 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 pre-eruptive 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 GMThttp://hdl.handle.net/10023/93202016-08-01T00:00:00ZPriest, Eric RonaldLongcope, D WJanvier, MDuring eruptive solar flares and coronal mass ejections, a non-potential 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 pre-eruptive 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.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 GMThttp://hdl.handle.net/10023/91662016-01-01T00:00:00ZFalconer, Isobel JessieLittlejohn, AllisonMcGill, LouBeetham, HelenOpen 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 OERSolar cycle variation of magnetic flux ropes in a quasi-static 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 11-year cycle, yet is poorly understood. As an alternative to traditional current-free "potential field" extrapolations, we investigate a model for the global coronal magnetic field which is non-potential and time-dependent, following the build-up and transport of magnetic helicity due to flux emergence and large-scale 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 model-in particular the flux ropes-varies 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, non-potential, magnetic structure at all latitudes.
Sat, 01 May 2010 00:00:00 GMThttp://hdl.handle.net/10023/90372010-05-01T00:00:00ZYeates, 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 11-year cycle, yet is poorly understood. As an alternative to traditional current-free "potential field" extrapolations, we investigate a model for the global coronal magnetic field which is non-potential and time-dependent, following the build-up and transport of magnetic helicity due to flux emergence and large-scale 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 model-in particular the flux ropes-varies 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, non-potential, magnetic structure at all latitudes.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 oppositely-signed 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 stagnation-flow, 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 impulsive-bursty reconnection that follows on after the initial fast-reconnection 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.
Tue, 01 Dec 2015 00:00:00 GMThttp://hdl.handle.net/10023/89602015-12-01T00:00:00ZE. H. Stevenson, JulieE. Parnell, ClareSudden 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 oppositely-signed 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 stagnation-flow, 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 impulsive-bursty reconnection that follows on after the initial fast-reconnection 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 topologically-distinct flux domains, are prime locations in three-dimensional 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. Three-dimensional, 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 opposite-polarity null points. The resulting reconnection occurs in two phases. The first is short involving rapid-reconnection 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 impulsive-bursty 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 GMThttp://hdl.handle.net/10023/89592016-01-27T00:00:00ZE. H. Stevenson, JulieE. Parnell, ClareMagnetic separators, which lie on the boundary between four topologically-distinct flux domains, are prime locations in three-dimensional 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. Three-dimensional, 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 opposite-polarity null points. The resulting reconnection occurs in two phases. The first is short involving rapid-reconnection 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 impulsive-bursty 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 co-ordinating 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 GMThttp://hdl.handle.net/10023/88742015-12-01T00:00:00ZWedemeyer, 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 co-ordinating 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.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, open-field regions and the quiet Sun. We find that the heating of active regions and open-field 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 open-field 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, 28 May 2015 00:00:00 GMThttp://hdl.handle.net/10023/86422015-05-28T00:00:00ZParnell, Clare E.Stevenson, Julie E.H.Threlfall, JamesEdwards, Sarah J.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, open-field regions and the quiet Sun. We find that the heating of active regions and open-field 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 open-field 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 Navier-Stokes flows : nonlinear depletion in NS flows
http://hdl.handle.net/10023/8620
The dynamics of the velocity norms ||u||Lq for q ≥ 3, in Navier-Stokes 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 ||u||Lq. We explore the possibility of non-singular growth of ||u||Lq.
Fri, 17 Apr 2015 00:00:00 GMThttp://hdl.handle.net/10023/86202015-04-17T00:00:00ZTran, Chuong VanYu, XinweiThe dynamics of the velocity norms ||u||Lq for q ≥ 3, in Navier-Stokes 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 ||u||Lq. We explore the possibility of non-singular growth of ||u||Lq.Memory versus effector immune responses in oncolytic virotherapies
http://hdl.handle.net/10023/8604
The main priority when designing cancer immuno-therapies 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 long-term 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 GMThttp://hdl.handle.net/10023/86042015-07-21T00:00:00ZMacnamara, Cicely KrystynaEftimie, RalucaThe main priority when designing cancer immuno-therapies 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 long-term 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.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 (RPG-2014-149). K.B. was partially supported by the Embirikion Foundation Grant (2011-2014) – Greece.
Tue, 15 Sep 2015 00:00:00 GMThttp://hdl.handle.net/10023/85822015-09-15T00:00:00ZBlazakis, Konstantinos N.Madzvamuse, AnotidaReyes-Aldasoro, Constantino CarlosStyles, VanessaVenkataraman, ChandrasekharCell 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 short-wavelength 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 short-wavelength (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 wave-electron 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 GMThttp://hdl.handle.net/10023/85812015-09-15T00:00:00ZBingham, R.Shukla, P. K.Eliasson, B.Cairns, A.Cairns, R AlanThe 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 short-wavelength (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 wave-electron interactions.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 GMThttp://hdl.handle.net/10023/84232010-06-01T00:00:00ZMacnamara, Cicely KrystynaRoberts, BernardAims: 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.Particle-in-cell simulations of collisionless magnetic reconnection with a non-uniform 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 force-free Vlasov-Maxwell equilibrium. The initial state has a Harris sheet magnetic field profile in one direction and a non-uniform 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 anti-parallel 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 GMThttp://hdl.handle.net/10023/83862016-03-01T00:00:00ZWilson, FionaNeukirch, ThomasHesse, MichaelHarrison, Michael G.Stark, Craig R.Results are presented of a first study of collisionless magnetic reconnection starting from a recently found exact nonlinear force-free Vlasov-Maxwell equilibrium. The initial state has a Harris sheet magnetic field profile in one direction and a non-uniform 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 anti-parallel 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.Head on collisions between two quasi-geostrophic hetons in a continuously stratified fluid
http://hdl.handle.net/10023/8219
We examine the interactions between two three-dimensional quasi-geostrophic 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 like-signed poles of the hetons. When they lie at the same depth, we refer to the configuration as symmetric; the anti-symmetric configuration corresponds to opposite-signed 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, anti-symmetric hetons recombine and escape perpendicularly as same-depth 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 width-to-height 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 re-configure 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 GMThttp://hdl.handle.net/10023/82192015-09-01T00:00:00ZReinaud, Jean NoelCarton, XavierWe examine the interactions between two three-dimensional quasi-geostrophic 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 like-signed poles of the hetons. When they lie at the same depth, we refer to the configuration as symmetric; the anti-symmetric configuration corresponds to opposite-signed 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, anti-symmetric hetons recombine and escape perpendicularly as same-depth 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 width-to-height 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 re-configure 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 non-flaring solar active region model
http://hdl.handle.net/10023/8203
The aim of this work is to investigate and characterise particle behaviour in a (observationally-driven) 3D MHD model of the solar atmosphere above a slowly evolving, non-flaring active region. We use a relativistic guiding-centre particle code to investigate particle acceleration in a single snapshot of the 3D MHD simulation. Despite the lack of flare-like behaviour in the active region, direct acceleration of electrons and protons to non-thermal energies (≲ 42 MeV) was found, yielding spectra with high-energy 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 non-flaring active region heating and reconnection.
Tue, 01 Mar 2016 00:00:00 GMThttp://hdl.handle.net/10023/82032016-03-01T00:00:00ZThrelfall, J.-A. Bourdin, Ph.Neukirch, T.E. Parnell, C.The aim of this work is to investigate and characterise particle behaviour in a (observationally-driven) 3D MHD model of the solar atmosphere above a slowly evolving, non-flaring active region. We use a relativistic guiding-centre particle code to investigate particle acceleration in a single snapshot of the 3D MHD simulation. Despite the lack of flare-like behaviour in the active region, direct acceleration of electrons and protons to non-thermal energies (≲ 42 MeV) was found, yielding spectra with high-energy 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 non-flaring 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⊙ M-dwarf star GJ 182.
Thu, 11 Feb 2016 00:00:00 GMThttp://hdl.handle.net/10023/80672016-02-11T00:00:00ZMacTaggart, DavidGregory, ScottNeukirch, ThomasDonati, Jean-FrancoisWe 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⊙ M-dwarf 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 guiding-centre test-particle 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 (time-dependent) 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 GMThttp://hdl.handle.net/10023/80012016-01-01T00:00:00ZThrelfall, 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 guiding-centre test-particle 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 (time-dependent) 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 two-dimensional reaction-diffusion 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 anterior-posterior 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 reaction-diffusion system model, in which an one-dimensional surface reaction-diffusion system, posed on the proximal vein, generates the morphogen concentrations that act as non-homogeneous Dirichlet (i.e., fixed) boundary conditions for the two-dimensional reaction-diffusion model posed in the wing cells. The two-stage 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 anterior-posterior 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 proximal-distal 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 (RPG-2014-149). 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 Sklodowska-Curie grant agreement No 642866. AM was partially supported by a grant from the Simons Foundation.
Wed, 04 Nov 2015 00:00:00 GMThttp://hdl.handle.net/10023/79042015-11-04T00:00:00ZSekimura, ToshioVenkataraman, ChandrasekharMadzvamuse, AnotidaUnsolved 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 two-dimensional reaction-diffusion 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 anterior-posterior 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 reaction-diffusion system model, in which an one-dimensional surface reaction-diffusion system, posed on the proximal vein, generates the morphogen concentrations that act as non-homogeneous Dirichlet (i.e., fixed) boundary conditions for the two-dimensional reaction-diffusion model posed in the wing cells. The two-stage 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 anterior-posterior 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 proximal-distal direction of the wing cell.Magneto-static 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 non-negligible plasma beta. We use high-resolution photospheric magnetic field measurements from SUNRISE/IMaX as boundary condition for a magneto-static 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 force-free (the Lorentz-force 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 self-consistently into account and compensate the non-vanishing Lorentz-force. Above a certain height (about 2 Mm) the non-magnetic forces become very weak and consequently the magnetic field becomes almost force-free. Here we apply a linear approach, where the electric current density consists of a superposition of a field-line 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 non-linear 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 GMThttp://hdl.handle.net/10023/78872015-12-01T00:00:00ZWiegelmann, ThomasNeukirch, ThomasNickeler, DieterSolanki, SamiMartinez Pillet, ValentinBorrero, Juan ManuleOur aim is to model the 3D magnetic field structure of the upper solar atmosphere, including regions of non-negligible plasma beta. We use high-resolution photospheric magnetic field measurements from SUNRISE/IMaX as boundary condition for a magneto-static 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 force-free (the Lorentz-force 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 self-consistently into account and compensate the non-vanishing Lorentz-force. Above a certain height (about 2 Mm) the non-magnetic forces become very weak and consequently the magnetic field becomes almost force-free. Here we apply a linear approach, where the electric current density consists of a superposition of a field-line 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 non-linear model.The appearance, motion, and disappearance of three-dimensional 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 co-located with a flow stagnation point, the introduction of asymmetry typically leads to non-ideal flows across the null point. To understand this behavior, we present exact expressions for the motion of three-dimensional 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 non-ideal 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 null-null pair or the reverse, the instantaneous velocity of separation or convergence of the null-null 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 null-null pairs are connected by a separator. Furthermore, except under special circumstances, there will not exist a straight line separator connecting a bifurcating null-null 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 non-ideal 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 AGS-1156076 and AGS-1358342 to SAO. C.E.P. acknowledges support from the St Andrews 2013 STFC Consolidated grant.
Fri, 30 Oct 2015 00:00:00 GMThttp://hdl.handle.net/10023/78682015-10-30T00:00:00ZA. Murphy, NicholasParnell, Clare ElizabethHaynes, Andrew LewisWhile theoretical models and simulations of magnetic reconnection often assume symmetry such that the magnetic null point when present is co-located with a flow stagnation point, the introduction of asymmetry typically leads to non-ideal flows across the null point. To understand this behavior, we present exact expressions for the motion of three-dimensional 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 non-ideal 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 null-null pair or the reverse, the instantaneous velocity of separation or convergence of the null-null 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 null-null pairs are connected by a separator. Furthermore, except under special circumstances, there will not exist a straight line separator connecting a bifurcating null-null 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 non-ideal behavior elsewhere along the field line.Near-threshold electron injection in the laser-plasma wakefield accelerator leading to femtosecond bunches
http://hdl.handle.net/10023/7750
The laser-plasma wakefield accelerator is a compact source of high brightness, ultra-short duration electron bunches. Self-injection occurs when electrons from the background plasma gain sufficient momentum at the back of the bubble-shaped accelerating structure to experience sustained acceleration. The shortest duration and highest brightness electron bunches result from self-injection close to the threshold for injection. Here we show that in this case injection is due to the localized charge density build-up 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 ultra-short 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 Laserlab-Europe (no. 284464), and the EUCARD-2 project (no. 312453).
Thu, 17 Sep 2015 00:00:00 GMThttp://hdl.handle.net/10023/77502015-09-17T00:00:00ZIslam, 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 AlanRaj, G.Jaroszynski, D.A.The laser-plasma wakefield accelerator is a compact source of high brightness, ultra-short duration electron bunches. Self-injection occurs when electrons from the background plasma gain sufficient momentum at the back of the bubble-shaped accelerating structure to experience sustained acceleration. The shortest duration and highest brightness electron bunches result from self-injection close to the threshold for injection. Here we show that in this case injection is due to the localized charge density build-up 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 ultra-short 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.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) magneto-acoustic waves and/or as quasi-periodic upflows remains unresolved. We used forward-modelling to construct observational signatures associated with a simple slow magneto-acoustic 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) line-of-sight 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 model-dependent.
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 (FP7/2007-2013) 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 GOA-2015-014 (KU Leuven). TVD acknowledges the funding from the FP7 ERG grant with number 276808.
Sun, 01 Feb 2015 00:00:00 GMThttp://hdl.handle.net/10023/77222015-02-01T00:00:00ZDe Moortel, I.Antolin, PatrickVan 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) magneto-acoustic waves and/or as quasi-periodic upflows remains unresolved. We used forward-modelling to construct observational signatures associated with a simple slow magneto-acoustic 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) line-of-sight 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 model-dependent.Systems oncology : towards patient-specific 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 sub-optimal 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 patient-specific multi-modality treatment protocols that may increase patients quality of life.
Sun, 01 Feb 2015 00:00:00 GMThttp://hdl.handle.net/10023/77132015-02-01T00:00:00ZPowathil, Gibin G.Swat, MaciejChaplain, 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 sub-optimal 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 patient-specific multi-modality treatment protocols that may increase patients quality of life.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 kinetochore-microtubule 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 GMThttp://hdl.handle.net/10023/77112014-07-01T00:00:00ZMatzavinos, AnastasiosRoitershtein, AlexanderShtylla, BlertaVoller, ZacharyLiu, SijiaChaplain, 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 kinetochore-microtubule 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.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 spatio-temporal 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 spatio-temporal 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 steady-state 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 spatio-temporal and spatially-homogeneous models.
Thu, 01 Oct 2015 00:00:00 GMThttp://hdl.handle.net/10023/77092015-10-01T00:00:00ZSturrock, 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 spatio-temporal 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 spatio-temporal 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 steady-state 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 spatio-temporal and spatially-homogeneous models.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 non-relativistic 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 non-relativistic guiding centre equations for comparison. Results. For mildly relativistic energies the relativistic and non-relativistic 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 non-relativistic calculations, and the mirror points of the relativistic orbits are systematically higher than for the corresponding non-relativistic 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 non-relativistic 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 GMThttp://hdl.handle.net/10023/76032014-07-01T00:00:00ZEradat 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 non-relativistic 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 non-relativistic guiding centre equations for comparison. Results. For mildly relativistic energies the relativistic and non-relativistic 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 non-relativistic calculations, and the mirror points of the relativistic orbits are systematically higher than for the corresponding non-relativistic 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 non-relativistic particle dynamics.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 spatio-temporal inter- actions between the protein and its mRNA in a 1-dimensional 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, NF-κB 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 GMThttp://hdl.handle.net/10023/75642015-06-15T00:00:00ZChaplain, MarkPtashnyk, MariyaSturrock, MarcGene 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 spatio-temporal inter- actions between the protein and its mRNA in a 1-dimensional 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, NF-κB 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.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 Grad-Shafranov 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 GMThttp://hdl.handle.net/10023/74842015-01-01T00:00:00ZHodgson, Jonathan David BrockieNeukirch, ThomasWe present an improved formalism for translationally invariant magnetohydrodynamic equilibria with anisotropic pressure and currents with a field aligned component. The derivation of a Grad-Shafranov 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.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 inertia-gravity 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 ≡ |ζ|max/f, and a small Froude number, Fr ≡ |.h|max/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 freely-evolving turbulence. We examine a wide variety of turbulent flows, at a mature and complex stage of their evolution, making use of the fully non-hydrostatic 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, PV-based 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 quasi-geostrophic 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 quasi-geostrophic 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 GMThttp://hdl.handle.net/10023/72012015-07-21T00:00:00ZDritschel, David GerardMcKiver, William JosephThe 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 inertia-gravity 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 ≡ |ζ|max/f, and a small Froude number, Fr ≡ |.h|max/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 freely-evolving turbulence. We examine a wide variety of turbulent flows, at a mature and complex stage of their evolution, making use of the fully non-hydrostatic 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, PV-based 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 quasi-geostrophic 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 quasi-geostrophic 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 Multi-channel Polarimeter and the Atmospheric Imaging Assembly on board the Solar Dynamics Observatory to study the characteristic properties of (propagating) Alfvenic motions and quasi-periodic 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 KZZD-EW-01-4. 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/ 2007-2013) 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 GMThttp://hdl.handle.net/10023/71902015-06-20T00:00:00ZLiu, JiajiaMcIntosh, Scott W.De Moortel, InekeWang, YumingWe combine observations of the Coronal Multi-channel Polarimeter and the Atmospheric Imaging Assembly on board the Solar Dynamics Observatory to study the characteristic properties of (propagating) Alfvenic motions and quasi-periodic 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 three-dimensional (3D) reconstruction of the location of coronal mass ejections (CMEs) obtained with the so-called 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 line-of-sight 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 R-circle 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 halo-CMEs 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 GMThttp://hdl.handle.net/10023/71782015-04-06T00:00:00ZBemporad, A.Pagano, P.Aims. The aim of this work is to quantify the uncertainties in the three-dimensional (3D) reconstruction of the location of coronal mass ejections (CMEs) obtained with the so-called 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 line-of-sight 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 R-circle 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 halo-CMEs for space weather prediction purposes.Non-LTE modelling of prominence fine structures using hydrogen Lyman-line profiles
http://hdl.handle.net/10023/7177
Aims. We perform a detailed statistical analysis of the spectral Lyman-line observations of the quiescent prominence observed on May 18, 2005. Methods. We used a profile-to-profile comparison of the synthetic Lyman spectra obtained by 2D single-thread prominence fine-structure model as a starting point for a full statistical analysis of the observed Lyman spectra. We employed 2D multi-thread fine-structure models with random positions and line-of-sight velocities of each thread to obtain a statistically significant set of synthetic Lyman-line profiles. We used for the first time multi-thread models composed of non-identical threads and viewed at line-of-sight 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 GMThttp://hdl.handle.net/10023/71772015-05-08T00:00:00ZSchwartz, P.Gunar, S.Curdt, W.Aims. We perform a detailed statistical analysis of the spectral Lyman-line observations of the quiescent prominence observed on May 18, 2005. Methods. We used a profile-to-profile comparison of the synthetic Lyman spectra obtained by 2D single-thread prominence fine-structure model as a starting point for a full statistical analysis of the observed Lyman spectra. We employed 2D multi-thread fine-structure models with random positions and line-of-sight velocities of each thread to obtain a statistically significant set of synthetic Lyman-line profiles. We used for the first time multi-thread models composed of non-identical threads and viewed at line-of-sight 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.Ellipsoidal vortices in rotating stratified fluids : beyond the quasi-geostrophic approximation
http://hdl.handle.net/10023/6889
We examine the basic properties and stability of isolated vortices having uniform potential vorticity (PV) in a non-hydrostatic rotating stratified fluid, under the Boussinesq approximation. For simplicity, we consider a uniform background rotation and a linear basic-state 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 ‘quasi-geostrophic’ (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 near-circular cross-section, 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 GMThttp://hdl.handle.net/10023/68892015-01-01T00:00:00ZTsang, Yue-KinDritschel, David G.We examine the basic properties and stability of isolated vortices having uniform potential vorticity (PV) in a non-hydrostatic rotating stratified fluid, under the Boussinesq approximation. For simplicity, we consider a uniform background rotation and a linear basic-state 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 ‘quasi-geostrophic’ (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 near-circular cross-section, 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.Experiments on the structure and stability of mode-2 internal solitary-like waves propagating on an offset pycnocline
http://hdl.handle.net/10023/6519
The structure and stability of mode-2 internal solitary-like waves is investigated experimentally. A rank-ordered train of mode-2 internal solitary waves is generated using a lock release configuration. The pycnocline is centred either on the mid-depth 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 K-H-like 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 mode-1 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 GMThttp://hdl.handle.net/10023/65192015-01-01T00:00:00ZCarr, MagdaDavies, PeterHoebers, RuudThe structure and stability of mode-2 internal solitary-like waves is investigated experimentally. A rank-ordered train of mode-2 internal solitary waves is generated using a lock release configuration. The pycnocline is centred either on the mid-depth 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 K-H-like 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 mode-1 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)].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 non-zero, a compensating uniform vorticity field is required to satisfy the Gauss condition (that the integral of the Laplace-Beltrami operator must vanish). On variable Gaussian curvature surfaces, this results in self-induced 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 GMThttp://hdl.handle.net/10023/62972015-02-25T00:00:00ZDritschel, David GerardBoatto, SWe 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 non-zero, a compensating uniform vorticity field is required to satisfy the Gauss condition (that the integral of the Laplace-Beltrami operator must vanish). On variable Gaussian curvature surfaces, this results in self-induced 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].Simply-connected vortex-patch shallow-water quasi-equilibria
http://hdl.handle.net/10023/6179
We examine the form, properties, stability and evolution of simply-connected vortex-patch relative quasi-equilibria in the single-layer ƒ-plane shallow-water 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 quasi-equilibria. 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 quasi-equilibria 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 large-γ, large-Ro states, (b) filamentation for small-γ states and (c) vortex splitting, asymmetric for intermediate-γ and symmetric for large-γ states.
This work is supported by a UK Natural Environment Research Council studentship
Wed, 05 Mar 2014 00:00:00 GMThttp://hdl.handle.net/10023/61792014-03-05T00:00:00ZPlotka, HannaDritschel, David GerardWe examine the form, properties, stability and evolution of simply-connected vortex-patch relative quasi-equilibria in the single-layer ƒ-plane shallow-water 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 quasi-equilibria. 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 quasi-equilibria 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 large-γ, large-Ro states, (b) filamentation for small-γ states and (c) vortex splitting, asymmetric for intermediate-γ and symmetric for large-γ states.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, volume-calculation nonlinear force-free (NLFF) method applied to finite coronal magnetic structures and a surface-calculation NLFF derivation that relies on a single photospheric or chromospheric vector magnetogram. Both methods were applied to two different data sets, namely synthetic active-region cases obtained by three-dimensional magneto-hydrodynamic (MHD) simulations and observed active-region cases, which include both eruptive and noneruptive magnetic structures. Results. The derived energy-helicity 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 energy-helicity 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° PIRG07-GA-2010-268245. 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 GMThttp://hdl.handle.net/10023/58722014-10-01T00:00:00ZTziotziou, 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, volume-calculation nonlinear force-free (NLFF) method applied to finite coronal magnetic structures and a surface-calculation NLFF derivation that relies on a single photospheric or chromospheric vector magnetogram. Both methods were applied to two different data sets, namely synthetic active-region cases obtained by three-dimensional magneto-hydrodynamic (MHD) simulations and observed active-region cases, which include both eruptive and noneruptive magnetic structures. Results. The derived energy-helicity 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 energy-helicity diagram of solar magnetic structures as adequately validated and envision a significant role of the uncovered scaling in future studies of solar magnetism.Backward wave cyclotron-maser emission in the auroral magnetosphere
http://hdl.handle.net/10023/5802
In this Letter, we present theory and particle-in-cell 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 down-going electron horseshoe distribution is due to a backward wave cyclotron-maser 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 GMThttp://hdl.handle.net/10023/58022014-10-07T00:00:00ZSpeirs, 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 particle-in-cell 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 down-going electron horseshoe distribution is due to a backward wave cyclotron-maser 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 three-dimensional equivalent to two-dimensional 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 non-resistive 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 infinite-time 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 GMThttp://hdl.handle.net/10023/57852015-01-01T00:00:00ZStevenson, Julie Elizabeth HelenParnell, Clare ElizabethPriest, Eric RonaldHaynes, Andrew LewisSeparators, which are in many ways the three-dimensional equivalent to two-dimensional 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 non-resistive 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 infinite-time 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 guiding-centre particle code in a time-dependent 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 GMThttp://hdl.handle.net/10023/57822015-02-01T00:00:00ZThrelfall, J.Neukirch, T.Parnell, Clare ElizabethEradat 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 guiding-centre particle code in a time-dependent 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.Ultraviolet and extreme-ultraviolet 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 two-phase 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 X-ray 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 steady-state 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 GMThttp://hdl.handle.net/10023/54992013-09-01T00:00:00ZQiu, 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 two-phase 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 X-ray 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 steady-state 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.Inertial-range dynamics and scaling laws of two-dimensional magnetic turbulence in the weak-field regime
http://hdl.handle.net/10023/5358
We study inertial-range dynamics and scaling laws in unforced two-dimensional magnetohydrodynamic turbulence in the regime of moderately small and small initial magnetic-to-kinetic 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 three-dimensional context). This conversion is an inertial-range phenomenon and, upon becoming quasi-saturated, 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 inertial-range 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 $\alpha\gtrsim-1$, 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 anti-dynamo excitation. This gives rise to a total energy spectrum poorly obeying a power-law 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 GMThttp://hdl.handle.net/10023/53582014-08-21T00:00:00ZBlackbourn, Luke Austen KazimierzTran, Chuong VanWe study inertial-range dynamics and scaling laws in unforced two-dimensional magnetohydrodynamic turbulence in the regime of moderately small and small initial magnetic-to-kinetic 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 three-dimensional context). This conversion is an inertial-range phenomenon and, upon becoming quasi-saturated, 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 inertial-range 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 $\alpha\gtrsim-1$, 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 anti-dynamo excitation. This gives rise to a total energy spectrum poorly obeying a power-law scaling.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 high-energy 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 highest-energy 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 non-relativistic 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 GMThttp://hdl.handle.net/10023/52752014-03-01T00:00:00ZEradat Oskoui, SolmazNeukirch, ThomasGrady, Keith JamesContext. Collapsing magnetic traps (CMTs) have been suggested as one possible mechanism responsible for the acceleration of high-energy 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 highest-energy 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 non-relativistic 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.Vortical control of forced two-dimensional turbulence
http://hdl.handle.net/10023/5236
A new numerical technique for the simulation of forced two-dimensional 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 Kraichnan-Batchelor scaling laws at higher Reynolds number than previously accessible with classical pseudo-spectral methods, making use of large simulation ensembles to allow a detailed consideration of the inverse cascade in a quasi-steady state. Our results support the recent finding of Scott [R. Scott, “Nonrobustness of the two-dimensional turbulent inverse cascade,” Phys. Rev. E75, 046301 (Year: 2007)10.1103/PhysRevE.75.046301], namely that when a direct enstrophy cascading range is well-represented 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. PIEF-GA-2008-221003.
Mon, 14 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10023/52362013-01-14T00:00:00ZFontane, Jerome Jacob LouisDritschel, David GerardScott, Richard KirknessA new numerical technique for the simulation of forced two-dimensional 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 Kraichnan-Batchelor scaling laws at higher Reynolds number than previously accessible with classical pseudo-spectral methods, making use of large simulation ensembles to allow a detailed consideration of the inverse cascade in a quasi-steady state. Our results support the recent finding of Scott [R. Scott, “Nonrobustness of the two-dimensional turbulent inverse cascade,” Phys. Rev. E75, 046301 (Year: 2007)10.1103/PhysRevE.75.046301], namely that when a direct enstrophy cascading range is well-represented 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 long-term, chaotic dynamics
http://hdl.handle.net/10023/5233
In this paper, we address the long-term 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 (grid-adaptive) computations, and comment on the challenge associated with resolving chaotic island formation and interaction. We will use shock-capturing, conservative, grid-adaptive 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 shock-capturing, high order finite differences, and particle in cell-like 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 FP7/2007-2013 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 VSC-Flemish Supercomputer Center, funded by the Hercules Foundation and the Flemish Government-Department 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 e-Infrastructure Cooperation.
Fri, 13 Sep 2013 00:00:00 GMThttp://hdl.handle.net/10023/52332013-09-13T00:00:00ZKeppens, R.Porth, O.Galsgaard, K.Frederiksen, J.T.Restante, A.L.Lapenta, G.Parnell, C.In this paper, we address the long-term 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 (grid-adaptive) computations, and comment on the challenge associated with resolving chaotic island formation and interaction. We will use shock-capturing, conservative, grid-adaptive 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 shock-capturing, high order finite differences, and particle in cell-like 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 no-slip case in this limit. We study the same problem, for both no-slip 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 no-slip 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 GMThttp://hdl.handle.net/10023/52322013-09-23T00:00:00ZSutherland, 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 no-slip case in this limit. We study the same problem, for both no-slip 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 no-slip 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.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 X-mode with efficiencies similar to 1-2% [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, [3-5] whilst 2D and 3D simulations are also being conducted to predict the experimental radiation power and mode, [6-9]. 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 cut-off TE01 mode, comparable with X-mode 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 GMThttp://hdl.handle.net/10023/51852014-05-07T00:00:00ZMcConville, 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 X-mode with efficiencies similar to 1-2% [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, [3-5] whilst 2D and 3D simulations are also being conducted to predict the experimental radiation power and mode, [6-9]. 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 cut-off TE01 mode, comparable with X-mode 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 X-mode. 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 GMThttp://hdl.handle.net/10023/51842014-01-01T00:00:00ZGillespie, 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 X-mode. 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 well-defined 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 backward-wave 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 GMThttp://hdl.handle.net/10023/51832014-05-07T00:00:00ZSpeirs, 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 well-defined 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 backward-wave 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 GMThttp://hdl.handle.net/10023/51802014-02-01T00:00:00ZCairns, 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 counter-propagating 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 pre-pulse produced.
Authors KH, RT, DCS, RAC, RB were supported by EPSRC grant EP/G04239X/1.
Tue, 01 Oct 2013 00:00:00 GMThttp://hdl.handle.net/10023/51732013-10-01T00:00:00ZHumphrey, 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 counter-propagating 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 pre-pulse produced.Quasi-geostrophic shallow-water doubly-connected vortex equilibria and their stability
http://hdl.handle.net/10023/5172
We examine the form, properties, stability and evolution of doubly-connected (two-vortex) relative equilibria in the single-layer ƒ-plane quasi-geostrophic shallow-water 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 near-equilibrium 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 large-γ 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 GMThttp://hdl.handle.net/10023/51722013-05-01T00:00:00ZPlotka, HannaDritschel, David GerardWe examine the form, properties, stability and evolution of doubly-connected (two-vortex) relative equilibria in the single-layer ƒ-plane quasi-geostrophic shallow-water 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 near-equilibrium 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 large-γ 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.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 'linear-conformist'. 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 non-linear 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.
Fri, 20 Jun 2014 00:00:00 GMThttp://hdl.handle.net/10023/50242014-06-20T00:00:00ZClaidière, 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 'linear-conformist'. 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 non-linear 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.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 ASPERA-4 experiment onboard the Venus Express spacecraft, and which constitute the first extensive in-situ 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 dawn-dusk asymmetry was consistent with a nightward transport of ions while the noon-midnight 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 GMThttp://hdl.handle.net/10023/47952012-12-01T00:00:00ZWood, 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.McKenna-Lawlor, 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 ASPERA-4 experiment onboard the Venus Express spacecraft, and which constitute the first extensive in-situ 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 dawn-dusk asymmetry was consistent with a nightward transport of ions while the noon-midnight observations indicated that the flow was highly variable but could contribute to the maintenance of the nightside ionosphere.Shallow-water vortex equilibria and their stability
http://hdl.handle.net/10023/4762
We first describe the equilibrium form and stability of steadily-rotating simply-connected vortex patches in the single-layer quasi-geostrophic model of geophysical fluid dynamics. This model, valid for rotating shallow-water 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 gravity-wave speed, g is gravity (or "reduced" gravity in a two-layer 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 shallow-water model to generate what we call "quasi-equilibria". 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 quasi-geostrophic equilibria to obtain shallow-water quasi-equilibria at finite Rossby number. We show a few examples of these states in this paper.
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/10023/47622011-01-01T00:00:00ZPłotka, H.Dritschel, D.G.We first describe the equilibrium form and stability of steadily-rotating simply-connected vortex patches in the single-layer quasi-geostrophic model of geophysical fluid dynamics. This model, valid for rotating shallow-water 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 gravity-wave speed, g is gravity (or "reduced" gravity in a two-layer 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 shallow-water model to generate what we call "quasi-equilibria". 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 quasi-geostrophic equilibria to obtain shallow-water quasi-equilibria at finite Rossby number. We show a few examples of these states in this paper.Potential Evidence for the Onset of Alfvénic Turbulence in Trans-equatorial Coronal Loops
http://hdl.handle.net/10023/4740
This study investigates Coronal Multi-channel Polarimeter Doppler-shift observations of a large, off-limb, trans-equatorial loop system observed on 2012 April 10-11. Doppler-shift 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 north-south 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 high-frequency part of the spectrum than expected from theoretical models. We suggest this excess high-frequency power could be tentative evidence for the onset of a cascade of the low-to-mid frequency waves into (Alfvénic) turbulence.
Mon, 10 Feb 2014 00:00:00 GMThttp://hdl.handle.net/10023/47402014-02-10T00:00:00ZDe Moortel, InekeMcIntosh, ScottThrelfall, James WilliamBethge, ChristianLiu, JThis study investigates Coronal Multi-channel Polarimeter Doppler-shift observations of a large, off-limb, trans-equatorial loop system observed on 2012 April 10-11. Doppler-shift 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 north-south 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 high-frequency part of the spectrum than expected from theoretical models. We suggest this excess high-frequency power could be tentative evidence for the onset of a cascade of the low-to-mid frequency waves into (Alfvénic) turbulence.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 laboratory-based 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 X-mode 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 cold-plasma 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 particle-in-cell 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 GMThttp://hdl.handle.net/10023/44942013-01-01T00:00:00ZSpeirs, DavidCairns, R AlanKellett, BarryVorgul, IrenaMcConville, SandraCross, AdrianPhelps, AlanRonald, KevinBingham, RobertThis 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 laboratory-based 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 X-mode 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 cold-plasma 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 particle-in-cell 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.Alfven wave phase-mixing 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 non-uniform 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 non-uniform plasma it is found that the spatially-integrated 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 GMThttp://hdl.handle.net/10023/43722011-01-01T00:00:00ZThrelfall, 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 non-uniform 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 non-uniform plasma it is found that the spatially-integrated 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 X-points 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 non-magnetohydrodynamic (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 X-points and the nature of the resulting reconnection. Methods: A Lagrangian remap shock-capturing 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 null-point finding algorithm was also used to locate and track the evolution of the multiple null-points 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 wave-null interaction. In particular, the initial fast-wave pulse now consists of whistler and ion-cyclotron 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 GMThttp://hdl.handle.net/10023/43682012-07-01T00:00:00ZThrelfall, James WilliamParnell, Clare ElizabethDe Moortel, InekeMcClements, KenArber, 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 non-magnetohydrodynamic (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 X-points and the nature of the resulting reconnection. Methods: A Lagrangian remap shock-capturing 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 null-point finding algorithm was also used to locate and track the evolution of the multiple null-points 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 wave-null interaction. In particular, the initial fast-wave pulse now consists of whistler and ion-cyclotron 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.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, P-1/2P(2), between the period P-1 of the fundamental mode and twice the period P-2 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 slab-like structures.
A75 article number
Tue, 01 Feb 2011 00:00:00 GMThttp://hdl.handle.net/10023/43662011-02-01T00:00:00ZMacnamara, 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, P-1/2P(2), between the period P-1 of the fundamental mode and twice the period P-2 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 slab-like structures.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 GMThttp://hdl.handle.net/10023/43352011-02-01T00:00:00ZCairns, R AlanVorgul, I.Bingham, RobertRonald, 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 dipole-type stars and planets. We have established a laboratory-based 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 X-mode 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 GMThttp://hdl.handle.net/10023/43342011-05-01T00:00:00ZVorgul, I.Kellett, B. J.Cairns, R AlanBingham, RobertRonald, 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 dipole-type stars and planets. We have established a laboratory-based 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 X-mode 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 one-dimensional Burgers flows
http://hdl.handle.net/10023/4333
Traveling-wave 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 so-called 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 GMThttp://hdl.handle.net/10023/43332010-03-01T00:00:00ZTran, Chuong VanDritschel, David GerardTraveling-wave 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 so-called 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 wave-induced flow over a fixed bottom boundary beneath an internal solitary wave of elevation propagating in an unsheared, two-layer, 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 wave-induced 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 GMThttp://hdl.handle.net/10023/43312010-02-01T00:00:00ZCarr, MagdaDavies, P AThe wave-induced flow over a fixed bottom boundary beneath an internal solitary wave of elevation propagating in an unsheared, two-layer, 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 wave-induced 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.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 non-zero 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, non-resistive, 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 non-zero Lorentz force that drives the fan and spine to collapse towards each other, in a similar manner to the collapse of a 2D X-point. 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 spiral-type 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 spine-fan collapse with generic current studied here provides the ideal setup for non-steady reconnection studies.
Thu, 12 Sep 2013 00:00:00 GMThttp://hdl.handle.net/10023/40842013-09-12T00:00:00ZFuentes-Fernandez, JorgeParnell, Clare E.In this paper we study current accumulations in 3D "tilted" nulls formed by a folding of the spine and fan. A non-zero 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, non-resistive, 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 non-zero Lorentz force that drives the fan and spine to collapse towards each other, in a similar manner to the collapse of a 2D X-point. 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 spiral-type 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 spine-fan collapse with generic current studied here provides the ideal setup for non-steady reconnection studies.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 two-dimensions, 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 non-resistive relaxation of 3D spiral nulls with initial spine-aligned 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 axi-symmetric case, the evolution of the field and the plasma is such that it concentrates the current density in two cone-shaped 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 axi-symmetric, a infinite-time singularity of current perpendicular to the fan is found at the location of the null.
Fri, 01 Jun 2012 00:00:00 GMThttp://hdl.handle.net/10023/39782012-06-01T00:00:00ZFuentes-Fernandez, JorgeParnell, 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 two-dimensions, 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 non-resistive relaxation of 3D spiral nulls with initial spine-aligned 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 axi-symmetric case, the evolution of the field and the plasma is such that it concentrates the current density in two cone-shaped 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 axi-symmetric, a infinite-time singularity of current perpendicular to the fan is found at the location of the null.The onset of impulsive bursty reconnection at a two-dimensional current layer
http://hdl.handle.net/10023/3977
The sudden reconnection of a non-force free 2D current layer, embedded in a low-beta 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 quasi-steady 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 GMThttp://hdl.handle.net/10023/39772012-05-09T00:00:00ZFuentes-Fernández, J.Parnell, Clare ElizabethPriest, Eric RonaldThe sudden reconnection of a non-force free 2D current layer, embedded in a low-beta 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 quasi-steady 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.Two-dimensional 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 two-dimensional 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 contour--spectral method, the ``Combined Lagrangian Advection Method'', formally to integrate the equations with zero viscous dissipation. The method is compared with a standard pseudo-spectral method for decreasing $\Pra$ for the problem of decaying two-dimensional 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 GMThttp://hdl.handle.net/10023/36982012-07-01T00:00:00ZDritschel, David GerardTobias, SteveIn this paper we introduce a new method for computations of two-dimensional 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 contour--spectral method, the ``Combined Lagrangian Advection Method'', formally to integrate the equations with zero viscous dissipation. The method is compared with a standard pseudo-spectral method for decreasing $\Pra$ for the problem of decaying two-dimensional 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 inertial-range scaling laws of two-dimensional magnetohydrodynamic turbulence
http://hdl.handle.net/10023/3668
We study two-dimensional 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 anti-dynamo triads (those converting magnetic into kinetic energy) are associated with an inverse magnetic energy flux. As both dynamo and anti-dynamo interacting triads are integral parts of the direct energy transfer, the anti-dynamo 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 Iroshnikov--Kraichnan 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 Iroshnikov--Kraichnan 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 magnetic-to-kinetic 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 post-graduate studentship.
Sun, 01 Jul 2012 00:00:00 GMThttp://hdl.handle.net/10023/36682012-07-01T00:00:00ZBlackbourn, Luke Austen KazimierzTran, Chuong VanWe study two-dimensional 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 anti-dynamo triads (those converting magnetic into kinetic energy) are associated with an inverse magnetic energy flux. As both dynamo and anti-dynamo interacting triads are integral parts of the direct energy transfer, the anti-dynamo 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 Iroshnikov--Kraichnan 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 Iroshnikov--Kraichnan 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 magnetic-to-kinetic 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.Two-dimensional magnetohydrodynamic turbulence in the limits of infinite and vanishing magnetic Prandtl number
http://hdl.handle.net/10023/3539
We study both theoretically and numerically two-dimensional 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 high-resolution 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 post-graduate studentship.
Sat, 01 Jun 2013 00:00:00 GMThttp://hdl.handle.net/10023/35392013-06-01T00:00:00ZTran, Chuong VanYu, XinweiBlackbourn, Luke Austen KazimierzWe study both theoretically and numerically two-dimensional 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 high-resolution 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.Sharp global nonlinear stability for a fluid overlying a highly porous material
http://hdl.handle.net/10023/3399
The stability of convection in a two-layer system in which a layer of fluid with a temperature-dependent viscosity overlies and saturates a highly porous material is studied. Owing to the difficulties associated with incorporating the nonlinear advection term in the Navier-Stokes 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 GMThttp://hdl.handle.net/10023/33992010-01-08T00:00:00ZHill, Antony A.Carr, MagdaThe stability of convection in a two-layer system in which a layer of fluid with a temperature-dependent viscosity overlies and saturates a highly porous material is studied. Owing to the difficulties associated with incorporating the nonlinear advection term in the Navier-Stokes 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.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 pseudo-spectral techniques is used to investigate instability in internal solitary waves with trapped cores. A three-layer 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 Dubriel-Jacotin-Long equation both inside and outside of the core region. The Brunt-Vaisala 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 Kelvin-Helmholtz 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 Kelvin-Helmholtz 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 GMThttp://hdl.handle.net/10023/33972012-01-01T00:00:00ZCarr, MagdaKing, Stuart EdwardDritschel, David GerardA numerical method that employs a combination of contour advection and pseudo-spectral techniques is used to investigate instability in internal solitary waves with trapped cores. A three-layer 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 Dubriel-Jacotin-Long equation both inside and outside of the core region. The Brunt-Vaisala 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 Kelvin-Helmholtz 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 Kelvin-Helmholtz 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.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 GMThttp://hdl.handle.net/10023/33052012-12-01T00:00:00ZKing, RuthIllian, Janine BaerbelKing, Stuart EdwardNightingale, Glenna FaithHendrichsen, DitteWe 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.Collisionless distribution function for the relativistic force-free Harris sheet
http://hdl.handle.net/10023/3154
A self-consistent collisionless distribution function for the relativistic analogue of the force-free Harris sheet is presented. This distribution function is the relativistic generalization of the distribution function for the non-relativistic collisionless force-free Harris sheet recently found by Harrison and Neukirch [Phys. Rev. Lett. 102, 135003 (2009)], as it has the same dependence on the particle energy and canonical momenta. We present a detailed calculation which shows that the proposed distribution function generates the required current density profile (and thus magnetic field profile) in a frame of reference in which the electric potential vanishes identically. The connection between the parameters of the distribution function and the macroscopic parameters such as the current sheet thickness is discussed. (C) 2012 American Institute of Physics. [doi: 10.1063/1.3677268]
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/10023/31542012-01-01T00:00:00ZStark, C. R.Neukirch, T.A self-consistent collisionless distribution function for the relativistic analogue of the force-free Harris sheet is presented. This distribution function is the relativistic generalization of the distribution function for the non-relativistic collisionless force-free Harris sheet recently found by Harrison and Neukirch [Phys. Rev. Lett. 102, 135003 (2009)], as it has the same dependence on the particle energy and canonical momenta. We present a detailed calculation which shows that the proposed distribution function generates the required current density profile (and thus magnetic field profile) in a frame of reference in which the electric potential vanishes identically. The connection between the parameters of the distribution function and the macroscopic parameters such as the current sheet thickness is discussed. (C) 2012 American Institute of Physics. [doi: 10.1063/1.3677268]Numerical simulation of shear-induced instabilities in internal solitary waves
http://hdl.handle.net/10023/3054
A numerical method that employs a combination of contour advection and pseudo-spectral techniques is used to simulate shear-induced instabilities in an internal solitary wave (ISW). A three-layer configuration for the background stratification, in which a linearly stratified intermediate layer is sandwiched between two homogeneous ones, is considered throughout. The flow is assumed to satisfy the inviscid, incompressible, Oberbeck–Boussinesq equations in two dimensions. Simulations are initialized by fully nonlinear, steady-state, ISWs. The results of the simulations show that the instability takes place in the pycnocline and manifests itself as Kelvin–Helmholtz billows. The billows form near the trough of the wave, subsequently grow and disturb the tail. Both the critical Richardson number (Ric) and the critical amplitude required for instability are found to be functions of the ratio of the undisturbed layer thicknesses. It is shown, therefore, that the constant, critical bound for instability in ISWs given in Barad & Fringer (J. Fluid Mech., vol. 644, 2010, pp. 61–95), namely Ric = 0.1 ± 0.01 , is not a sufficient condition for instability. It is also shown that the critical value of Lx/λ required for instability, where Lx is the length of the region in a wave in which Ri < 1/4 and λ is the half-width of the wave, is sensitive to the ratio of the layer thicknesses. Similarly, a linear stability analysis reveals that δiTw (where δi is the growth rate of the instability averaged over Tw, the period in which parcels of fluid are subjected to Ri < 1/4) is very sensitive to the transition between the undisturbed pycnocline and the homogeneous layers, and the amplitude of the wave. Therefore, the alternative tests for instability presented in Fructus et al. (J. Fluid Mech., vol. 620, 2009, pp. 1–29) and Barad & Fringer (J. Fluid Mech., vol. 644, 2010, pp. 61–95), respectively, namely Lx/λ ≥ 0.86 and δiTw > 5 , are shown to be valid only for a limited parameter range.
This work was supported by the UK Engineering and Physical Sciences Research Council [grant number EP/F030622/1]
Sun, 25 Sep 2011 00:00:00 GMThttp://hdl.handle.net/10023/30542011-09-25T00:00:00ZCarr, MagdaKing, Stuart EdwardDritschel, David GerardA numerical method that employs a combination of contour advection and pseudo-spectral techniques is used to simulate shear-induced instabilities in an internal solitary wave (ISW). A three-layer configuration for the background stratification, in which a linearly stratified intermediate layer is sandwiched between two homogeneous ones, is considered throughout. The flow is assumed to satisfy the inviscid, incompressible, Oberbeck–Boussinesq equations in two dimensions. Simulations are initialized by fully nonlinear, steady-state, ISWs. The results of the simulations show that the instability takes place in the pycnocline and manifests itself as Kelvin–Helmholtz billows. The billows form near the trough of the wave, subsequently grow and disturb the tail. Both the critical Richardson number (Ric) and the critical amplitude required for instability are found to be functions of the ratio of the undisturbed layer thicknesses. It is shown, therefore, that the constant, critical bound for instability in ISWs given in Barad & Fringer (J. Fluid Mech., vol. 644, 2010, pp. 61–95), namely Ric = 0.1 ± 0.01 , is not a sufficient condition for instability. It is also shown that the critical value of Lx/λ required for instability, where Lx is the length of the region in a wave in which Ri < 1/4 and λ is the half-width of the wave, is sensitive to the ratio of the layer thicknesses. Similarly, a linear stability analysis reveals that δiTw (where δi is the growth rate of the instability averaged over Tw, the period in which parcels of fluid are subjected to Ri < 1/4) is very sensitive to the transition between the undisturbed pycnocline and the homogeneous layers, and the amplitude of the wave. Therefore, the alternative tests for instability presented in Fructus et al. (J. Fluid Mech., vol. 620, 2009, pp. 1–29) and Barad & Fringer (J. Fluid Mech., vol. 644, 2010, pp. 61–95), respectively, namely Lx/λ ≥ 0.86 and δiTw > 5 , are shown to be valid only for a limited parameter range.Behind and beyond a theorem on groups related to trivalent graphs
http://hdl.handle.net/10023/2462
In 2006 we completed the proof of a five-part conjecture that was made in 1977 about a family of groups related to trivalent graphs. This family covers all 2-generator, 2-relator groups where one relator specifies that a generator is an involution and the other relator has three syllables. Our proof relies upon detailed but general computations in the groups under question. The proof is theoretical, but based upon explicit proofs produced by machine for individual cases. Here we explain how we derived the general proofs from specific cases. The conjecture essentially addressed only the finite groups in the family. Here we extend the results to infinite groups, effectively determining when members of this family of finitely presented groups are simply isomorphic to a specific quotient.
Mon, 01 Dec 2008 00:00:00 GMThttp://hdl.handle.net/10023/24622008-12-01T00:00:00ZHavas, GeorgeRobertson, Edmund F.Sutherland, Dale C.In 2006 we completed the proof of a five-part conjecture that was made in 1977 about a family of groups related to trivalent graphs. This family covers all 2-generator, 2-relator groups where one relator specifies that a generator is an involution and the other relator has three syllables. Our proof relies upon detailed but general computations in the groups under question. The proof is theoretical, but based upon explicit proofs produced by machine for individual cases. Here we explain how we derived the general proofs from specific cases. The conjecture essentially addressed only the finite groups in the family. Here we extend the results to infinite groups, effectively determining when members of this family of finitely presented groups are simply isomorphic to a specific quotient.Lower-hybrid waves generated by anomalous Doppler resonance in auroral plasmas
http://hdl.handle.net/10023/2457
This paper describes sonic aspects of lower-hybrid wave activity in space plasmas. Lower-hybrid waves are particularly important since they can transfer energy efficiently between electrons and ions in a collisionless magnetized plasma. We consider the 'fan' or anomalous Doppler resonance instability driven by energetic electron tails and show that it is responsible for the generation of lower-hybrid waves. We also demonstrate that observations of their intensity are sufficient to drive the modulational instability.
Sun, 01 Aug 2010 00:00:00 GMThttp://hdl.handle.net/10023/24572010-08-01T00:00:00ZBingham, RobertCairns, R AlanVorgul, I.Shapiro, V. D.This paper describes sonic aspects of lower-hybrid wave activity in space plasmas. Lower-hybrid waves are particularly important since they can transfer energy efficiently between electrons and ions in a collisionless magnetized plasma. We consider the 'fan' or anomalous Doppler resonance instability driven by energetic electron tails and show that it is responsible for the generation of lower-hybrid waves. We also demonstrate that observations of their intensity are sufficient to drive the modulational instability.Falling towards forgetfulness : synaptic decay prevents spontaneous recovery of memory
http://hdl.handle.net/10023/2455
Long after a new language has been learned and forgotten, relearning a few words seems to trigger the recall of other words. This "free-lunch learning'' (FLL) effect has been demonstrated both in humans and in neural network models. Specifically, previous work proved that linear networks that learn a set of associations, then partially forget them all, and finally relearn some of the associations, show improved performance on the remaining (i.e., nonrelearned) associations. Here, we prove that relearning forgotten associations decreases performance on nonrelearned associations; an effect we call negative free-lunch learning. The difference between free-lunch learning and the negative free-lunch learning presented here is due to the particular method used to induce forgetting. Specifically, if forgetting is induced by isotropic drifting of weight vectors (i.e., by adding isotropic noise), then free-lunch learning is observed. However, as proved here, if forgetting is induced by weight values that simply decay or fall towards zero, then negative free-lunch learning is observed. From a biological perspective, and assuming that nervous systems are analogous to the networks used here, this suggests that evolution may have selected physiological mechanisms that involve forgetting using a form of synaptic drift rather than synaptic decay, because synaptic drift, but not synaptic decay, yields free-lunch learning.
No funding was received for this work.
Fri, 22 Aug 2008 00:00:00 GMThttp://hdl.handle.net/10023/24552008-08-22T00:00:00ZStone, James V.Jupp, Peter EdmundLong after a new language has been learned and forgotten, relearning a few words seems to trigger the recall of other words. This "free-lunch learning'' (FLL) effect has been demonstrated both in humans and in neural network models. Specifically, previous work proved that linear networks that learn a set of associations, then partially forget them all, and finally relearn some of the associations, show improved performance on the remaining (i.e., nonrelearned) associations. Here, we prove that relearning forgotten associations decreases performance on nonrelearned associations; an effect we call negative free-lunch learning. The difference between free-lunch learning and the negative free-lunch learning presented here is due to the particular method used to induce forgetting. Specifically, if forgetting is induced by isotropic drifting of weight vectors (i.e., by adding isotropic noise), then free-lunch learning is observed. However, as proved here, if forgetting is induced by weight values that simply decay or fall towards zero, then negative free-lunch learning is observed. From a biological perspective, and assuming that nervous systems are analogous to the networks used here, this suggests that evolution may have selected physiological mechanisms that involve forgetting using a form of synaptic drift rather than synaptic decay, because synaptic drift, but not synaptic decay, yields free-lunch learning.On the relationship between equilibrium bifurcations and ideal MHD instabilities for line-tied coronal loops
http://hdl.handle.net/10023/2268
For axisymmetric models for coronal loops the relationship between the bifurcation points of magnetohydrodynamic (MHD) equilibrium sequences and the points of linear ideal MHD instability is investigated, imposing line-tied boundary conditions. Using a well-studied example based on the Gold -aEuro parts per thousand Hoyle equilibrium, it is demonstrated that if the equilibrium sequence is calculated using the Grad -aEuro parts per thousand Shafranov equation, the instability corresponds to the second bifurcation point and not the first bifurcation point, because the equilibrium boundary conditions allow for modes which are excluded from the linear ideal stability analysis. This is shown by calculating the bifurcating equilibrium branches and comparing the spatial structure of the solutions close to the bifurcation point with the spatial structure of the unstable mode. If the equilibrium sequence is calculated using Euler potentials, the first bifurcation point of the Grad -aEuro parts per thousand Shafranov case is not found, and the first bifurcation point of the Euler potential description coincides with the ideal instability threshold. An explanation of this results in terms of linear bifurcation theory is given and the implications for the use of MHD equilibrium bifurcations to explain eruptive phenomena is briefly discussed.
Fri, 01 Jan 2010 00:00:00 GMThttp://hdl.handle.net/10023/22682010-01-01T00:00:00ZNeukirch, T.Romeou, Z.For axisymmetric models for coronal loops the relationship between the bifurcation points of magnetohydrodynamic (MHD) equilibrium sequences and the points of linear ideal MHD instability is investigated, imposing line-tied boundary conditions. Using a well-studied example based on the Gold -aEuro parts per thousand Hoyle equilibrium, it is demonstrated that if the equilibrium sequence is calculated using the Grad -aEuro parts per thousand Shafranov equation, the instability corresponds to the second bifurcation point and not the first bifurcation point, because the equilibrium boundary conditions allow for modes which are excluded from the linear ideal stability analysis. This is shown by calculating the bifurcating equilibrium branches and comparing the spatial structure of the solutions close to the bifurcation point with the spatial structure of the unstable mode. If the equilibrium sequence is calculated using Euler potentials, the first bifurcation point of the Grad -aEuro parts per thousand Shafranov case is not found, and the first bifurcation point of the Euler potential description coincides with the ideal instability threshold. An explanation of this results in terms of linear bifurcation theory is given and the implications for the use of MHD equilibrium bifurcations to explain eruptive phenomena is briefly discussed.Automatic presentations and semigroup constructions
http://hdl.handle.net/10023/2148
An automatic presentation for a relational structure is, informally, an abstract representation of the elements of that structure by means of a regular language such that the relations can all be recognized by finite automata. A structure admitting an automatic presentation is said to be FA-presentable. This paper studies the interaction of automatic presentations and certain semigroup constructions, namely: direct products, free products, finite Rees index extensions and subsemigroups, strong semilattices of semigroups, Rees matrix semigroups, Bruck-Reilly extensions, zero-direct unions, semidirect products, wreath products, ideals, and quotient semigroups. For each case, the closure of the class of FA-presentable semigroups under that construction is considered, as is the question of whether the FA-presentability of the semigroup obtained from such a construction implies the FA-presentability of the original semigroup[s]. Classifications are also given of the FA-presentable finitely generated Clifford semigroups, completely simple semigroups, and completely 0-simple semigroups.
Sun, 01 Aug 2010 00:00:00 GMThttp://hdl.handle.net/10023/21482010-08-01T00:00:00ZCain, Alan J.Oliver, GrahamRuskuc, NikThomas, Richard M.An automatic presentation for a relational structure is, informally, an abstract representation of the elements of that structure by means of a regular language such that the relations can all be recognized by finite automata. A structure admitting an automatic presentation is said to be FA-presentable. This paper studies the interaction of automatic presentations and certain semigroup constructions, namely: direct products, free products, finite Rees index extensions and subsemigroups, strong semilattices of semigroups, Rees matrix semigroups, Bruck-Reilly extensions, zero-direct unions, semidirect products, wreath products, ideals, and quotient semigroups. For each case, the closure of the class of FA-presentable semigroups under that construction is considered, as is the question of whether the FA-presentability of the semigroup obtained from such a construction implies the FA-presentability of the original semigroup[s]. Classifications are also given of the FA-presentable finitely generated Clifford semigroups, completely simple semigroups, and completely 0-simple semigroups.Cancellative and Malcev presentations for finite Rees index subsemigroups and extensions
http://hdl.handle.net/10023/2138
It is known that, for semigroups, the property of admitting a finite presentation is preserved on passing to subsemigroups and extensions of finite Rees index. The present paper shows that the same holds true for Malcev, cancellative, left-cancellative and right-cancellative presentations. (A Malcev (respectively, cancellative, left-cancellative, right-cancellative) presentation is a presentation of a special type that can be used to define any group-embeddable (respectively, cancellative, left-cancellative, right-cancellative) semigroup.).
Fri, 01 Feb 2008 00:00:00 GMThttp://hdl.handle.net/10023/21382008-02-01T00:00:00ZCain, Alan JamesRobertson, Edmund FrederickRuskuc, NikIt is known that, for semigroups, the property of admitting a finite presentation is preserved on passing to subsemigroups and extensions of finite Rees index. The present paper shows that the same holds true for Malcev, cancellative, left-cancellative and right-cancellative presentations. (A Malcev (respectively, cancellative, left-cancellative, right-cancellative) presentation is a presentation of a special type that can be used to define any group-embeddable (respectively, cancellative, left-cancellative, right-cancellative) semigroup.).Quasi-geostrophic vortices in compressible atmospheres
http://hdl.handle.net/10023/1562
This paper considers the effect of an exponential variation in the background density field (as exists in compressible atmospheres) on the structure and dynamics of the quasi-geostrophic system, and compares the results with the corresponding Boussinesq limit in which background density variations are assumed small. The behaviour of the compressible system is understood via a closed-form analytic expression for the Green's function of the inversion operator relating potential vorticity and streamfunction. This expression makes explicit the anisotropy of the Green's function, inherited from the density profile, which has a slow, algebraic decay directly above the source and an exponential decay in all other directions. An immediate consequence for finite-volume vortices is a differential rotation of upper and lower levels that results in counterintuitive behaviour during the nonlinear evolution of ellipsoidal vortices, in which vortex destruction is confined to the lower vortex and wave activity is seen to propagate downwards. This is in contrast to the Boussinesq limit, which exhibits symmetric destruction of the upper and lower vortex, and in contrast to naive expectations based on a consideration of the mass distribution alone, which would lead to greater destruction of the upper vortex. Finally, the presence of a horizontal lower boundary introduces a strong barotropic component that is absent in the unbounded case (the presence of an upper boundary has almost no effect). The lower boundary also alters the differential rotation in the lower vortex with important consequences for the nonlinear evolution: for very small separation between the lower boundary and the vortex, the differential rotation is reversed leading to strong deformations of the middle vortex; for a critical separation, the vortex is stabilized by the reduction of the differential rotation, and remains coherent over remarkably long times.
Tue, 10 May 2005 00:00:00 GMThttp://hdl.handle.net/10023/15622005-05-10T00:00:00ZScott, Richard KirknessDritschel, David GerardThis paper considers the effect of an exponential variation in the background density field (as exists in compressible atmospheres) on the structure and dynamics of the quasi-geostrophic system, and compares the results with the corresponding Boussinesq limit in which background density variations are assumed small. The behaviour of the compressible system is understood via a closed-form analytic expression for the Green's function of the inversion operator relating potential vorticity and streamfunction. This expression makes explicit the anisotropy of the Green's function, inherited from the density profile, which has a slow, algebraic decay directly above the source and an exponential decay in all other directions. An immediate consequence for finite-volume vortices is a differential rotation of upper and lower levels that results in counterintuitive behaviour during the nonlinear evolution of ellipsoidal vortices, in which vortex destruction is confined to the lower vortex and wave activity is seen to propagate downwards. This is in contrast to the Boussinesq limit, which exhibits symmetric destruction of the upper and lower vortex, and in contrast to naive expectations based on a consideration of the mass distribution alone, which would lead to greater destruction of the upper vortex. Finally, the presence of a horizontal lower boundary introduces a strong barotropic component that is absent in the unbounded case (the presence of an upper boundary has almost no effect). The lower boundary also alters the differential rotation in the lower vortex with important consequences for the nonlinear evolution: for very small separation between the lower boundary and the vortex, the differential rotation is reversed leading to strong deformations of the middle vortex; for a critical separation, the vortex is stabilized by the reduction of the differential rotation, and remains coherent over remarkably long times.Subsemigroups of virtually free groups : finite Malcev presentations and testing for freeness
http://hdl.handle.net/10023/1561
This paper shows that, given a finite subset X of a finitely generated virtually free group F, the freeness of the subsemigroup of F generated by X can be tested algorithmically. (A group is virtually free if it contains a free subgroup of finite index.) It is then shown that every finitely generated subsemigroup, of F has a finite Malcev presentation (a type of semigroup presentation which can be used to define any semigroup that embeds in a group), and that such a presentation can be effectively found from any finite generating set.
Sat, 01 Jul 2006 00:00:00 GMThttp://hdl.handle.net/10023/15612006-07-01T00:00:00ZCain, AJRobertson, Edmund FrederickRuskuc, NikolaThis paper shows that, given a finite subset X of a finitely generated virtually free group F, the freeness of the subsemigroup of F generated by X can be tested algorithmically. (A group is virtually free if it contains a free subgroup of finite index.) It is then shown that every finitely generated subsemigroup, of F has a finite Malcev presentation (a type of semigroup presentation which can be used to define any semigroup that embeds in a group), and that such a presentation can be effectively found from any finite generating set.The shape of vortices in quasi-geostrophic turbulence
http://hdl.handle.net/10023/1557
The present work discusses the most commonly occurring shape of the coherent vortical structures in rapidly rotating stably stratified turbulence, under the quasi-geostrophic approximation. In decaying turbulence, these vortices-coherent regions of the materially-invariant potential vorticity-dominate the flow evolution, and indeed the flow evolution is governed by their interactions. An analysis of several exceptionally high-resolution simulations of quasi-geostrophic turbulence is performed. The results indicate that the population of vortices exhibits a mean height-to-width aspect ratio less than unity, in fact close to 0.8. This finding is justified here by a simple model, in which vortices are taken to be ellipsoids of uniform potential vorticity. The model focuses on steady ellipsoids within a uniform background strain flow. This background flow approximates the effects of surrounding vortices in a turbulent flow on a given vortex. It is argued that the vortices which are able to withstand the highest levels of strain are those most likely to be found in the actual turbulent flow. Our calculations confirm that the optimal height-to-width aspect ratio is close to 0.8 for a wide range of background straining flows.
Partially supported by the UK EPSRC (Grant GR/N11711)
Fri, 10 Jan 2003 00:00:00 GMThttp://hdl.handle.net/10023/15572003-01-10T00:00:00ZReinaud, Jean NoelDritschel, David GerardKoudella, CRThe present work discusses the most commonly occurring shape of the coherent vortical structures in rapidly rotating stably stratified turbulence, under the quasi-geostrophic approximation. In decaying turbulence, these vortices-coherent regions of the materially-invariant potential vorticity-dominate the flow evolution, and indeed the flow evolution is governed by their interactions. An analysis of several exceptionally high-resolution simulations of quasi-geostrophic turbulence is performed. The results indicate that the population of vortices exhibits a mean height-to-width aspect ratio less than unity, in fact close to 0.8. This finding is justified here by a simple model, in which vortices are taken to be ellipsoids of uniform potential vorticity. The model focuses on steady ellipsoids within a uniform background strain flow. This background flow approximates the effects of surrounding vortices in a turbulent flow on a given vortex. It is argued that the vortices which are able to withstand the highest levels of strain are those most likely to be found in the actual turbulent flow. Our calculations confirm that the optimal height-to-width aspect ratio is close to 0.8 for a wide range of background straining flows.The persistence of balance in geophysical flows
http://hdl.handle.net/10023/1496
Rotating stably stratified geophysical flows can exhibit a near 'balanced' evolution controlled by the conservative advection of a single scalar quantity, the potential vorticity (PV). This occurs frequently in the Earth's atmosphere and oceans where motions tend to be weak compared with the background planetary rotation and where stratification greatly inhibits vertical motion. Under these circumstances, both high-frequency acoustic waves and lower-frequency inertia-gravity waves (IGWs) contribute little to the flow evolution compared with the even-lower-frequency advection of PV. Moreover, this 'slow' PV-controlled balanced evolution appears unable to excite these higher-frequency waves in any significant way-i.e. balance persists. The present work pushes the limits of balance by systematically exploring the evolution of a range of highly nonlinear flows in which motions are comparable with the background rotation. These flows do not possess a frequency separation between PV advection and IGWs. Nonetheless, the flows exhibit a remarkable persistence of balance. Even when flows are not initialized to minimize the amount of IGWs initially present, and indeed even when flows are deliberately seeded with significant IGW amplitudes, the flow evolution-over many inertial periods (days)-remains strongly controlled by PV advection.
This paper introduces a novel, powerful way to understand the why geophysical flows are largely under the control of a single scalar field, the potential vorticity, a materially conserved dynamical tracer in the absence of viscous and diabatic effects.
Wed, 10 Jan 2007 00:00:00 GMThttp://hdl.handle.net/10023/14962007-01-10T00:00:00ZDritschel, David GerardViudez, ARotating stably stratified geophysical flows can exhibit a near 'balanced' evolution controlled by the conservative advection of a single scalar quantity, the potential vorticity (PV). This occurs frequently in the Earth's atmosphere and oceans where motions tend to be weak compared with the background planetary rotation and where stratification greatly inhibits vertical motion. Under these circumstances, both high-frequency acoustic waves and lower-frequency inertia-gravity waves (IGWs) contribute little to the flow evolution compared with the even-lower-frequency advection of PV. Moreover, this 'slow' PV-controlled balanced evolution appears unable to excite these higher-frequency waves in any significant way-i.e. balance persists. The present work pushes the limits of balance by systematically exploring the evolution of a range of highly nonlinear flows in which motions are comparable with the background rotation. These flows do not possess a frequency separation between PV advection and IGWs. Nonetheless, the flows exhibit a remarkable persistence of balance. Even when flows are not initialized to minimize the amount of IGWs initially present, and indeed even when flows are deliberately seeded with significant IGW amplitudes, the flow evolution-over many inertial periods (days)-remains strongly controlled by PV advection.Bending and twisting instabilities of columnar elliptical vortices in a rotating strongly stratified fluid
http://hdl.handle.net/10023/1495
In this paper, we investigate the three-dimensional stability of the Moore-Saffman elliptical vortex in a rotating stratified fluid. By means of an asymptotic analysis for long vertical wavelength perturbations and small Froude number, we study the effects of Rossby number, external strain, and ellipticity of the vortex on the stability of azimuthal modes m = 1 (corresponding to a bending instability) and m = 2 (corresponding to a twisting instability). In the case of a quasi-geostrophic fluid (small Rossby number), the asymptotic results are in striking agreement with previous numerical stability analyses even for vertical wavelengths of order one. For arbitrary Rossby number, the key finding is that the Rossby number has no effect on the domains of long-wavelength instability of these two modes: the two-dimensional or three-dimensional nature of the instabilities is controlled only by the background strain rate gamma and by the rotation rate Omega of the principal axes of the elliptical vortex relative to the rotating frame of reference. For the m = 1 mode, it is shown that when Omega < -gamma, the vortex is stable to any long-wavelength disturbances, when -gamma < Omega less than or similar to 0, two-dimensional perturbations are most unstable, when 0 less than or similar to Omega < gamma, long-wavelength three-dimensional disturbances are the most unstable, and finally when gamma < Omega, short-wavelength three-dimensional perturbations are the most unstable. Similarly, the m = 2 instability is two-dimensional or three-dimensional depending only on gamma and Omega, independent of the Rossby number. This means that if a long-wavelength three-dimensional instability exists for a given elliptical vortex in a quasi-geostrophic fluid, a similar instability should be observed for any other Rossby number, in particular for infinite Rossby number (strongly stratified fluids). This implies that the planetary rotation plays a minor role in the nature of the instabilities observed in rotating strongly stratified fluids. The present results for the azimuthal mode m = 1 suggest that the vortex-bending instabilities observed previously in quasi-geostrophic fluids (tall-column instability) and in strongly stratified fluids (zigzag instability) are fundamentally related.
This is a comprehensive analysis of the linear stability of columnar elliptical vortices subject to two-dimensional strain in a rotating, stratified fluid. It is the culmination of two lines of research, one started by Dritschel involving the tall-column instability, and another started by Billant and Chomaz involving the zigzag instability. Our joint work unifies these instabilities, and shows that they exist over a vast parameter space. This work represents over 7 years of collaborative effort.
Fri, 25 Aug 2006 00:00:00 GMThttp://hdl.handle.net/10023/14952006-08-25T00:00:00ZBillant, PaulDritschel, David GerardChomaz, Jean-MarcIn this paper, we investigate the three-dimensional stability of the Moore-Saffman elliptical vortex in a rotating stratified fluid. By means of an asymptotic analysis for long vertical wavelength perturbations and small Froude number, we study the effects of Rossby number, external strain, and ellipticity of the vortex on the stability of azimuthal modes m = 1 (corresponding to a bending instability) and m = 2 (corresponding to a twisting instability). In the case of a quasi-geostrophic fluid (small Rossby number), the asymptotic results are in striking agreement with previous numerical stability analyses even for vertical wavelengths of order one. For arbitrary Rossby number, the key finding is that the Rossby number has no effect on the domains of long-wavelength instability of these two modes: the two-dimensional or three-dimensional nature of the instabilities is controlled only by the background strain rate gamma and by the rotation rate Omega of the principal axes of the elliptical vortex relative to the rotating frame of reference. For the m = 1 mode, it is shown that when Omega < -gamma, the vortex is stable to any long-wavelength disturbances, when -gamma < Omega less than or similar to 0, two-dimensional perturbations are most unstable, when 0 less than or similar to Omega < gamma, long-wavelength three-dimensional disturbances are the most unstable, and finally when gamma < Omega, short-wavelength three-dimensional perturbations are the most unstable. Similarly, the m = 2 instability is two-dimensional or three-dimensional depending only on gamma and Omega, independent of the Rossby number. This means that if a long-wavelength three-dimensional instability exists for a given elliptical vortex in a quasi-geostrophic fluid, a similar instability should be observed for any other Rossby number, in particular for infinite Rossby number (strongly stratified fluids). This implies that the planetary rotation plays a minor role in the nature of the instabilities observed in rotating strongly stratified fluids. The present results for the azimuthal mode m = 1 suggest that the vortex-bending instabilities observed previously in quasi-geostrophic fluids (tall-column instability) and in strongly stratified fluids (zigzag instability) are fundamentally related.A balanced approach to modelling rotating stably stratified geophysical flows
http://hdl.handle.net/10023/1493
We describe a new approach to modelling three-dimensional rotating stratified flows under the Boussinesq approximation. This approach is based on the explicit conservation of potential vorticity, and exploits the underlying leading-order geostrophic and hydrostratic balances inherent in these equations in the limit of small Froude and Rossby numbers. These balances are not imposed, but instead are used to motivate the use of a pair of new variables expressing the departure from geostrophic and hydrostratic balance. These new variables are the ageostrophic horizontal vorticity components, i.e. the vorticity not directly associated with the displacement of isopycnal surfaces. The use of potential vorticity and ageostrophic horizontal vorticity, rather than the usual primitive variables of velocity and density, reveals a deep mathematical structure and appears to have advantages numerically. This change of variables results in a diagnostic equation, of Monge-Amp re type, for one component of a vector potential phi, and two Poisson equations for the other two components. The curl of phi gives the velocity field while the divergence of phi is proportional to the displacement of isopycnal surfaces. This diagnostic equation makes transparent the conditions for both static and inertial stability, and may change form from (spatially) elliptic to (spatially) hyperbolic even when the flow is statically and inertially stable. A numerical method based on these new variables is developed and used to examine the instability of a horizontal elliptical shear zone (modelling a jet streak). The basic-state flow is in exact geostrophic and hydrostratic balance. Given a small perturbation however, the shear zone destabilizes by rolling up into a street of vortices and radiating inertia-gravity waves.
This work was the first to show how one can rewrite the equations for a rotating stratified fluid in a way which makes potential vorticity conservation explicit. Potential vorticity is linked closely to balance, a state void of high-frequency gravity waves. The mathematical transformation reveals a deep underlying mathematical structure, including explicit conditions for inertial and static stability as well as a new double Monge-Ampere equation. This work forms the cornerstone of much subsequent research into the fundamental nature of rotating stratified fluids.
Sun, 10 Aug 2003 00:00:00 GMThttp://hdl.handle.net/10023/14932003-08-10T00:00:00ZDritschel, David GerardViúdez, AlvaroWe describe a new approach to modelling three-dimensional rotating stratified flows under the Boussinesq approximation. This approach is based on the explicit conservation of potential vorticity, and exploits the underlying leading-order geostrophic and hydrostratic balances inherent in these equations in the limit of small Froude and Rossby numbers. These balances are not imposed, but instead are used to motivate the use of a pair of new variables expressing the departure from geostrophic and hydrostratic balance. These new variables are the ageostrophic horizontal vorticity components, i.e. the vorticity not directly associated with the displacement of isopycnal surfaces. The use of potential vorticity and ageostrophic horizontal vorticity, rather than the usual primitive variables of velocity and density, reveals a deep mathematical structure and appears to have advantages numerically. This change of variables results in a diagnostic equation, of Monge-Amp re type, for one component of a vector potential phi, and two Poisson equations for the other two components. The curl of phi gives the velocity field while the divergence of phi is proportional to the displacement of isopycnal surfaces. This diagnostic equation makes transparent the conditions for both static and inertial stability, and may change form from (spatially) elliptic to (spatially) hyperbolic even when the flow is statically and inertially stable. A numerical method based on these new variables is developed and used to examine the instability of a horizontal elliptical shear zone (modelling a jet streak). The basic-state flow is in exact geostrophic and hydrostratic balance. Given a small perturbation however, the shear zone destabilizes by rolling up into a street of vortices and radiating inertia-gravity waves.