Mathematics & Statistics (School of)
http://hdl.handle.net/10023/28
Sun, 23 Oct 2016 14:30:52 GMT
20161023T14:30:52Z
Mathematics & Statistics (School of)
http://researchrepository.standrews.ac.uk:80/bitstream/id/13/Mathematics and statistics.gif
http://hdl.handle.net/10023/28

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

Primitive groups, graph endomorphisms and synchronization
http://hdl.handle.net/10023/9648
Let Ω be a set of cardinality n, G be a permutation group on Ω and f:Ω→Ω be a map that is not a permutation. We say that G synchronizes f if the transformation semigroup ⟨G,f⟩ contains a constant map, and that G is a synchronizing group if G synchronizes every nonpermutation. A synchronizing group is necessarily primitive, but there are primitive groups that are not synchronizing. Every nonsynchronizing primitive group fails to synchronize at least one uniform transformation (that is, transformation whose kernel has parts of equal size), and it had previously been conjectured that this was essentially the only way in which a primitive group could fail to be synchronizing, in other words, that a primitive group synchronizes every nonuniform transformation. The first goal of this paper is to prove that this conjecture is false, by exhibiting primitive groups that fail to synchronize specific nonuniform transformations of ranks 5 and 6. As it has previously been shown that primitive groups synchronize every nonuniform transformation of rank at most 4, these examples are of the lowest possible rank. In addition, we produce graphs with primitive automorphism groups that have approximately √n nonsynchronizing ranks, thus refuting another conjecture on the number of nonsynchronizing ranks of a primitive group. The second goal of this paper is to extend the spectrum of ranks for which it is known that primitive groups synchronize every nonuniform transformation of that rank. It has previously been shown that a primitive group of degree nn synchronizes every nonuniform transformation of rank n−1 and n−2, and here this is extended to n−3 and n−4. In the process, we will obtain a purely graphtheoretical result showing that, with limited exceptions, in a vertexprimitive graph the union of neighbourhoods of a set of vertices A is bounded below by a function that is asymptotically √A. Determining the exact spectrum of ranks for which there exist nonuniform transformations not synchronized by some primitive group is just one of several natural, but possibly difficult, problems on automata, primitive groups, graphs and computational algebra arising from this work; these are outlined in the final section.
The third author has been partially supported by the Fundação para a Ciência e a Tecnologia through the project CEMATCIÊNCIAS UID/Multi/04621/2013.
Mon, 03 Oct 2016 00:00:00 GMT
http://hdl.handle.net/10023/9648
20161003T00:00:00Z
Araújo, João
Bentz, Wolfram
Cameron, Peter Jephson
Royle, Gordon
Schaefer, Artur
Let Ω be a set of cardinality n, G be a permutation group on Ω and f:Ω→Ω be a map that is not a permutation. We say that G synchronizes f if the transformation semigroup ⟨G,f⟩ contains a constant map, and that G is a synchronizing group if G synchronizes every nonpermutation. A synchronizing group is necessarily primitive, but there are primitive groups that are not synchronizing. Every nonsynchronizing primitive group fails to synchronize at least one uniform transformation (that is, transformation whose kernel has parts of equal size), and it had previously been conjectured that this was essentially the only way in which a primitive group could fail to be synchronizing, in other words, that a primitive group synchronizes every nonuniform transformation. The first goal of this paper is to prove that this conjecture is false, by exhibiting primitive groups that fail to synchronize specific nonuniform transformations of ranks 5 and 6. As it has previously been shown that primitive groups synchronize every nonuniform transformation of rank at most 4, these examples are of the lowest possible rank. In addition, we produce graphs with primitive automorphism groups that have approximately √n nonsynchronizing ranks, thus refuting another conjecture on the number of nonsynchronizing ranks of a primitive group. The second goal of this paper is to extend the spectrum of ranks for which it is known that primitive groups synchronize every nonuniform transformation of that rank. It has previously been shown that a primitive group of degree nn synchronizes every nonuniform transformation of rank n−1 and n−2, and here this is extended to n−3 and n−4. In the process, we will obtain a purely graphtheoretical result showing that, with limited exceptions, in a vertexprimitive graph the union of neighbourhoods of a set of vertices A is bounded below by a function that is asymptotically √A. Determining the exact spectrum of ranks for which there exist nonuniform transformations not synchronized by some primitive group is just one of several natural, but possibly difficult, problems on automata, primitive groups, graphs and computational algebra arising from this work; these are outlined in the final section.

Bernoulli convolutions and 1D dynamics
http://hdl.handle.net/10023/9629
We describe a family φλ of dynamical systems on the unit interval which preserve Bernoulli convolutions. We show that if there are parameter ranges for which these systems are piecewise convex, then the corresponding Bernoulli convolution will be absolutely continuous with bounded density. We study the systems φλ and give some numerical evidence to suggest values of λ for which φλ may be piecewise convex.
Thu, 08 Oct 2015 00:00:00 GMT
http://hdl.handle.net/10023/9629
20151008T00:00:00Z
Kempton, Thomas Michael William
Persson, Tomas
We describe a family φλ of dynamical systems on the unit interval which preserve Bernoulli convolutions. We show that if there are parameter ranges for which these systems are piecewise convex, then the corresponding Bernoulli convolution will be absolutely continuous with bounded density. We study the systems φλ and give some numerical evidence to suggest values of λ for which φλ may be piecewise convex.

Bayesian multispecies modelling of nonnegative continuous ecological data with a discrete mass at zero
http://hdl.handle.net/10023/9626
Thu, 01 Jan 2015 00:00:00 GMT
http://hdl.handle.net/10023/9626
20150101T00:00:00Z
Swallow, Ben

Dynamical patterns of coexisting strategies in a hybrid discretecontinuum spatial evolutionary game model
http://hdl.handle.net/10023/9625
We present a novel hybrid modelling framework that takes into account two aspects which have been largely neglected in previous models of spatial evolutionary games: random motion and chemotaxis. A stochastic individualbased model is used to describe the player dynamics,whereas the evolution of the chemoattractant is governed by a reactiondiffusion equation. The two models are coupled by deriving individual movement rules via the discretisation of a taxisdiffusion equation which describes the evolution of the local number of players. In this framework, individuals occupying the same position can engage in a twoplayer game, and are awarded a payoff, interms of reproductive fitness, according to their strategy. As an example, we let individuals play the HawkDove game. Numerical simulations illustrate how random motion and chemotactic response can bring about selfgenerated dynamical patterns that create favourable conditions for the coexistence of hawks and doves in situations in which the two strategies cannot coexist otherwise.In this sense, our work offers a new perspective of research on spatial evolutionary games, and provides a general formalism to study the dynamics of spatiallystructured populations in biological and social contexts where individual motion is likely to affect natural selection of behavioural traits.
Tue, 04 Oct 2016 00:00:00 GMT
http://hdl.handle.net/10023/9625
20161004T00:00:00Z
Burgess, Andrew
Schofield, Pieta
Hubbard, Steven
Chaplain, Mark Andrew Joseph
Lorenzi, Tommaso
We present a novel hybrid modelling framework that takes into account two aspects which have been largely neglected in previous models of spatial evolutionary games: random motion and chemotaxis. A stochastic individualbased model is used to describe the player dynamics,whereas the evolution of the chemoattractant is governed by a reactiondiffusion equation. The two models are coupled by deriving individual movement rules via the discretisation of a taxisdiffusion equation which describes the evolution of the local number of players. In this framework, individuals occupying the same position can engage in a twoplayer game, and are awarded a payoff, interms of reproductive fitness, according to their strategy. As an example, we let individuals play the HawkDove game. Numerical simulations illustrate how random motion and chemotactic response can bring about selfgenerated dynamical patterns that create favourable conditions for the coexistence of hawks and doves in situations in which the two strategies cannot coexist otherwise.In this sense, our work offers a new perspective of research on spatial evolutionary games, and provides a general formalism to study the dynamics of spatiallystructured populations in biological and social contexts where individual motion is likely to affect natural selection of behavioural traits.

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

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

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

Modelling observed decayless oscillations as resonantly enhanced KelvinHelmholtz vortices from transverse MHD waves and their seismological application
http://hdl.handle.net/10023/9577
In the highly structured solar corona, resonant absorption is an unavoidable mechanism of energy transfer from global transverse MHD waves to local azimuthal Alfvén waves. Due to its localised nature, a direct detection of this mechanism is extremely difficult. Yet, it is the leading theory explaining the observed fast damping of the global transverse waves. However, at odds with this theoretical prediction, recent observations indicate that in the low amplitude regime such transverse MHD waves can also appear decayless, a yet unsolved phenomenon. Recent numerical work has shown that KelvinHelmholtz instabilities (KHI) often accompany transverse MHD waves. In this work, we combine 3D MHD simulations and forward modelling to show that for currently achieved spatial resolution and observed small amplitudes, an apparent decayless oscillation is obtained. This effect results from the combination of periodic brightenings produced by the KHI and the coherent motion of the KHI vortices amplified by resonant absorption. Such effect is especially clear in emission lines forming at temperatures that capture the boundary dynamics rather than the core, and reflects the low damping character of the local azimuthal Alfvén waves resonantly coupled to the kink mode. Due to phase mixing, the detected period can vary depending on the emission line, with those sensitive to the boundary having shorter periods than those sensitive to the loop core. This allows to estimate the density contrast at the boundary.
Thu, 20 Oct 2016 00:00:00 GMT
http://hdl.handle.net/10023/9577
20161020T00:00:00Z
Antolin, Patrick
De Moortel, Ineke
Van Doorsselaere, Tom
Yokoyama, T
In the highly structured solar corona, resonant absorption is an unavoidable mechanism of energy transfer from global transverse MHD waves to local azimuthal Alfvén waves. Due to its localised nature, a direct detection of this mechanism is extremely difficult. Yet, it is the leading theory explaining the observed fast damping of the global transverse waves. However, at odds with this theoretical prediction, recent observations indicate that in the low amplitude regime such transverse MHD waves can also appear decayless, a yet unsolved phenomenon. Recent numerical work has shown that KelvinHelmholtz instabilities (KHI) often accompany transverse MHD waves. In this work, we combine 3D MHD simulations and forward modelling to show that for currently achieved spatial resolution and observed small amplitudes, an apparent decayless oscillation is obtained. This effect results from the combination of periodic brightenings produced by the KHI and the coherent motion of the KHI vortices amplified by resonant absorption. Such effect is especially clear in emission lines forming at temperatures that capture the boundary dynamics rather than the core, and reflects the low damping character of the local azimuthal Alfvén waves resonantly coupled to the kink mode. Due to phase mixing, the detected period can vary depending on the emission line, with those sensitive to the boundary having shorter periods than those sensitive to the loop core. This allows to estimate the density contrast at the boundary.

Effects of a scientific echo sounder on the behavior of shortfinned pilot whales (Globicephala macrorhynchus)
http://hdl.handle.net/10023/9555
Active echo sounding devices are often employed for commercial or scientific purposes in the foraging habitats of marine mammals. We conducted an experiment off Cape Hatteras, North Carolina, USA to assess whether the behavior of shortfinned pilot whales changed when exposed to an EK60 scientific echo sounder. We attached digital acoustic recording tags (DTAGs) to nine individuals, five of which were exposed. A hidden Markov model (HMM) to characterize diving states with and without exposure provided no evidence for a change in foraging behavior. However, Generalized Estimating Equations (GEE’s), to model changes in heading variance over the entire tag record, under all experimental conditions, showed a consistent increase in heading variance during exposure, over all values of depth and pitch. This suggests that, regardless of behavioral state, the whales changed their heading more frequently when the echo sounder was active. This response could represent increased vigilance in which whales maintained awareness of echo sounder location by increasing their heading variance, and provides the first quantitative analysis on reactions of cetaceans to a scientific echo sounder.
This work was supported by award RC2154 from the Strategic Environmental Research and Development Program and funding from the Naval Facilities Engineering Command Atlantic and NOAA Fisheries, Southeast Region.
Wed, 07 Sep 2016 00:00:00 GMT
http://hdl.handle.net/10023/9555
20160907T00:00:00Z
Quick, Nicola Jane
ScottHayward, Lindesay Alexandra Sarah
Sadykova, Dinara
Nowacek, Doug
Read, Andrew
Active echo sounding devices are often employed for commercial or scientific purposes in the foraging habitats of marine mammals. We conducted an experiment off Cape Hatteras, North Carolina, USA to assess whether the behavior of shortfinned pilot whales changed when exposed to an EK60 scientific echo sounder. We attached digital acoustic recording tags (DTAGs) to nine individuals, five of which were exposed. A hidden Markov model (HMM) to characterize diving states with and without exposure provided no evidence for a change in foraging behavior. However, Generalized Estimating Equations (GEE’s), to model changes in heading variance over the entire tag record, under all experimental conditions, showed a consistent increase in heading variance during exposure, over all values of depth and pitch. This suggests that, regardless of behavioral state, the whales changed their heading more frequently when the echo sounder was active. This response could represent increased vigilance in which whales maintained awareness of echo sounder location by increasing their heading variance, and provides the first quantitative analysis on reactions of cetaceans to a scientific echo sounder.

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

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

Modelling the sun's small scale global photospheric magnetic field
http://hdl.handle.net/10023/9511
We present a new model for the Sun's global photospheric magnetic field during a deep minimum of activity, in which no active regions emerge. The emergence and subsequent evolution of small scale magnetic features across the full solar surface is simulated, subject to the infuence of a global supergranular flow pattern. Visually, the resulting simulated magnetograms reproduce the typical structure and scale observed in quiet Sun magnetograms. Quantitatively, the simulation quickly reaches a steady state, resulting in a mean field and flux distribution that are in good agreement with those determined from observations. A potential coronal magnetic field is extrapolated from the simulated full Sun magnetograms, to consider the implications of such a quiet photospheric magnetic field on the corona and inner heliosphere. The bulk of the coronal magnetic field closes very low down, in short connections between smallscale features in the simulated magnetic network. Just 0.1% of the photospheric magnetic flux is found to be open at 2:5 Rsun, around 10 100 times less than that determined for typical HMI synoptic map observations. If such conditions were to exist on the Sun, this would lead to a significantly weaker interplanetary magnetic field than is presently observed, and hence a much higher cosmic ray flux at Earth.
Wed, 19 Oct 2016 00:00:00 GMT
http://hdl.handle.net/10023/9511
20161019T00:00:00Z
Meyer, Karen Alison
Mackay, Duncan Hendry
We present a new model for the Sun's global photospheric magnetic field during a deep minimum of activity, in which no active regions emerge. The emergence and subsequent evolution of small scale magnetic features across the full solar surface is simulated, subject to the infuence of a global supergranular flow pattern. Visually, the resulting simulated magnetograms reproduce the typical structure and scale observed in quiet Sun magnetograms. Quantitatively, the simulation quickly reaches a steady state, resulting in a mean field and flux distribution that are in good agreement with those determined from observations. A potential coronal magnetic field is extrapolated from the simulated full Sun magnetograms, to consider the implications of such a quiet photospheric magnetic field on the corona and inner heliosphere. The bulk of the coronal magnetic field closes very low down, in short connections between smallscale features in the simulated magnetic network. Just 0.1% of the photospheric magnetic flux is found to be open at 2:5 Rsun, around 10 100 times less than that determined for typical HMI synoptic map observations. If such conditions were to exist on the Sun, this would lead to a significantly weaker interplanetary magnetic field than is presently observed, and hence a much higher cosmic ray flux at Earth.

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

3D MHD modeling of twisted coronal loops
http://hdl.handle.net/10023/9475
We perform MHD modeling of a single bright coronal loop to include the interaction with a nonuniform magnetic field. The field is stressed by random footpoint rotation in the central region and its energy is dissipated into heating by growing currents through anomalous magnetic diffusivity that switches on in the corona above a current density threshold. We model an entire single magnetic flux tube, in the solar atmosphere extending from the highbeta chromosphere to the lowbetacorona through the steep transition region. The magnetic field expands from the chromosphere to the corona. The maximum resolution is ~30 km. We obtain an overall evolution typical of loop models and realistic loop emission in the EUV and Xray bands. The plasma confined in the fluxtube is heated to active region temperatures (~3 MK) after ~2/3 hr. Upflows from the chromosphere up to ~100 km/s fill the core of the fluxtube to densities above 109 cm3. More heating is released in the low corona than the high corona and is finely structured both in space and time.
Sat, 16 Jul 2016 00:00:00 GMT
http://hdl.handle.net/10023/9475
20160716T00:00:00Z
Reale, F.
Orlando, S.
Guarrasi, M.
Mignone, A.
Peres, G.
Hood, A. W.
Priest, E. R.
We perform MHD modeling of a single bright coronal loop to include the interaction with a nonuniform magnetic field. The field is stressed by random footpoint rotation in the central region and its energy is dissipated into heating by growing currents through anomalous magnetic diffusivity that switches on in the corona above a current density threshold. We model an entire single magnetic flux tube, in the solar atmosphere extending from the highbeta chromosphere to the lowbetacorona through the steep transition region. The magnetic field expands from the chromosphere to the corona. The maximum resolution is ~30 km. We obtain an overall evolution typical of loop models and realistic loop emission in the EUV and Xray bands. The plasma confined in the fluxtube is heated to active region temperatures (~3 MK) after ~2/3 hr. Upflows from the chromosphere up to ~100 km/s fill the core of the fluxtube to densities above 109 cm3. More heating is released in the low corona than the high corona and is finely structured both in space and time.

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

Sunspot rotation : II. Effects of varying the field strength and twist of an emerging flux tube
http://hdl.handle.net/10023/9442
Context. Observations of flux emergence indicate that rotational velocities may develop within sunspots. However, the dependence of this rotation on subphotospheric field strength and twist remains largely unknown. Aims. We investigate the effects of varying the initial field strength and twist of an emerging subphotospheric magnetic flux tube onthe rotation of the sunspots at the photosphere. Methods. We consider a simple model of a stratified domain with a subphotospheric interior layer and three overlying atmospheric layers. A twisted arched flux tube is inserted in the interior and is allowed to rise into the atmosphere. To achieve this, the MHD equations are solved using the Lagrangianremap code, Lare3d. We perform a parameter study by independently varying the subphotospheric magnetic field strength and twist. Results. Altering the initial magnetic field strength and twist of the flux tube significantly affects the tube’s evolution and the rotational motions that develop at the photosphere. The rotation angle, vorticity, and current show a direct dependence on the initial field strength. We find that an increase in field strength increases the angle through which the fieldlines rotate, the length of the fieldlines extending into the atmosphere, and the magnetic energy transported to the atmosphere. This also affects the amount of residual twist in the interior. The length of the fieldlines is crucial as we predict the twist per unit length equilibrates to a lower value on longer fieldlines. No such direct dependence is found when we modify the twist of the magnetic field owing to the complex effect this has on the tension force acting on the tube. However, there is still a clear ordering in quantities such as the rotation angle, helicity, and free energy with higher initial twist cases being related to sunspots that rotate more rapidly, transporting more helicity and magnetic energy to the atmosphere.
ZS acknowledges the financial support of the Carnegie Trust for Scotland. This work used the DIRAC 1, UKMHD Consortium machine at the University of St Andrews and the DiRAC Data Centric system at Durham University, operated by the Institute for Computational Cosmology on behalf of the STFC DiRAC HPC Facility (www.dirac.ac.uk). This equipment was funded by BIS National Einfrastructure capital grant ST/K00042X/1, STFC capital grant ST/H008519/1, and STFC DiRAC Operations grant ST/K003267/1 and Durham University. DiRAC is part of the National EInfrastructure.
Wed, 21 Sep 2016 00:00:00 GMT
http://hdl.handle.net/10023/9442
20160921T00:00:00Z
Sturrock, Zoe
Hood, Alan William
Context. Observations of flux emergence indicate that rotational velocities may develop within sunspots. However, the dependence of this rotation on subphotospheric field strength and twist remains largely unknown. Aims. We investigate the effects of varying the initial field strength and twist of an emerging subphotospheric magnetic flux tube onthe rotation of the sunspots at the photosphere. Methods. We consider a simple model of a stratified domain with a subphotospheric interior layer and three overlying atmospheric layers. A twisted arched flux tube is inserted in the interior and is allowed to rise into the atmosphere. To achieve this, the MHD equations are solved using the Lagrangianremap code, Lare3d. We perform a parameter study by independently varying the subphotospheric magnetic field strength and twist. Results. Altering the initial magnetic field strength and twist of the flux tube significantly affects the tube’s evolution and the rotational motions that develop at the photosphere. The rotation angle, vorticity, and current show a direct dependence on the initial field strength. We find that an increase in field strength increases the angle through which the fieldlines rotate, the length of the fieldlines extending into the atmosphere, and the magnetic energy transported to the atmosphere. This also affects the amount of residual twist in the interior. The length of the fieldlines is crucial as we predict the twist per unit length equilibrates to a lower value on longer fieldlines. No such direct dependence is found when we modify the twist of the magnetic field owing to the complex effect this has on the tension force acting on the tube. However, there is still a clear ordering in quantities such as the rotation angle, helicity, and free energy with higher initial twist cases being related to sunspots that rotate more rapidly, transporting more helicity and magnetic energy to the atmosphere.

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

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

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

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

Recurrence and transience for suspension flows
http://hdl.handle.net/10023/9416
We study the thermodynamic formalism for suspension flows over countable Markov shifts with roof functions not necessarily bounded away from zero. We establish conditions to ensure the existence and uniqueness of equilibrium measures for regular potentials. We define the notions of recurrence and transience of a potential in this setting. We define the renewal flow, which is a symbolic model for a class of flows with diverse recurrence features. We study the corresponding thermodynamic formalism, establishing conditions for the existence of equilibrium measures and phase transitions. Applications are given to suspension flows defined over interval maps having parabolic fixed points.
Funding: Proyecto Fondecyt 1110040 for funding visit to PUCChile and partial support from NSF grant DMS 1109587.
Thu, 01 Jan 2015 00:00:00 GMT
http://hdl.handle.net/10023/9416
20150101T00:00:00Z
Iommi, Godofredo
Jordan, Thomas
Todd, Michael John
We study the thermodynamic formalism for suspension flows over countable Markov shifts with roof functions not necessarily bounded away from zero. We establish conditions to ensure the existence and uniqueness of equilibrium measures for regular potentials. We define the notions of recurrence and transience of a potential in this setting. We define the renewal flow, which is a symbolic model for a class of flows with diverse recurrence features. We study the corresponding thermodynamic formalism, establishing conditions for the existence of equilibrium measures and phase transitions. Applications are given to suspension flows defined over interval maps having parabolic fixed points.

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

A note on the probability of generating alternating or symmetric groups
http://hdl.handle.net/10023/9348
We improve on recent estimates for the probability of generating the alternating and symmetric groups An and Sn. In particular, we find the sharp lower bound if the probability is given by a quadratic in n−1. This leads to improved bounds on the largest number h(An) such that a direct product of h(An) copies of An can be generated by two elements.
The research of the first author is supported by the Australian Research Council grant DP120100446.
Tue, 01 Sep 2015 00:00:00 GMT
http://hdl.handle.net/10023/9348
20150901T00:00:00Z
Morgan, Luke
RoneyDougal, Colva Mary
We improve on recent estimates for the probability of generating the alternating and symmetric groups An and Sn. In particular, we find the sharp lower bound if the probability is given by a quadratic in n−1. This leads to improved bounds on the largest number h(An) such that a direct product of h(An) copies of An can be generated by two elements.

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

Lengths of words in transformation semigroups generated by digraphs
http://hdl.handle.net/10023/9277
Given a simple digraph D on n vertices (with n≥2), there is a natural construction of a semigroup of transformations ⟨D⟩. For any edge (a, b) of D, let a→b be the idempotent of rank n−1 mapping a to b and fixing all vertices other than a; then, define ⟨D⟩ to be the semigroup generated by a→b for all (a,b)∈E(D). For α∈⟨D⟩, let ℓ(D,α) be the minimal length of a word in E(D) expressing α. It is well known that the semigroup Singn of all transformations of rank at most n−1 is generated by its idempotents of rank n−1. When D=Kn is the complete undirected graph, Howie and Iwahori, independently, obtained a formula to calculate ℓ(Kn,α), for any α∈⟨Kn⟩=Singn; however, no analogous nontrivial results are known when D≠Kn. In this paper, we characterise all simple digraphs D such that either ℓ(D,α) is equal to Howie–Iwahori’s formula for all α∈⟨D⟩, or ℓ(D,α)=n−fix(α) for all α∈⟨D⟩, or ℓ(D,α)=n−rk(α) for all α∈⟨D⟩. We also obtain bounds for ℓ(D,α) when D is an acyclic digraph or a strong tournament (the latter case corresponds to a smallest generating set of idempotents of rank n−1 of Singn). We finish the paper with a list of conjectures and open problems
The second and third authors were supported by the EPSRC grant EP/K033956/1.
Mon, 08 Aug 2016 00:00:00 GMT
http://hdl.handle.net/10023/9277
20160808T00:00:00Z
Cameron, P. J.
CastilloRamirez, A.
Gadouleau, M.
Mitchell, J. D.
Given a simple digraph D on n vertices (with n≥2), there is a natural construction of a semigroup of transformations ⟨D⟩. For any edge (a, b) of D, let a→b be the idempotent of rank n−1 mapping a to b and fixing all vertices other than a; then, define ⟨D⟩ to be the semigroup generated by a→b for all (a,b)∈E(D). For α∈⟨D⟩, let ℓ(D,α) be the minimal length of a word in E(D) expressing α. It is well known that the semigroup Singn of all transformations of rank at most n−1 is generated by its idempotents of rank n−1. When D=Kn is the complete undirected graph, Howie and Iwahori, independently, obtained a formula to calculate ℓ(Kn,α), for any α∈⟨Kn⟩=Singn; however, no analogous nontrivial results are known when D≠Kn. In this paper, we characterise all simple digraphs D such that either ℓ(D,α) is equal to Howie–Iwahori’s formula for all α∈⟨D⟩, or ℓ(D,α)=n−fix(α) for all α∈⟨D⟩, or ℓ(D,α)=n−rk(α) for all α∈⟨D⟩. We also obtain bounds for ℓ(D,α) when D is an acyclic digraph or a strong tournament (the latter case corresponds to a smallest generating set of idempotents of rank n−1 of Singn). We finish the paper with a list of conjectures and open problems

Idempotent rank in the endomorphism monoid of a nonuniform partition
http://hdl.handle.net/10023/9275
We calculate the rank and idempotent rank of the semigroup E(X,P) generated by the idempotents of the semigroup T(X,P), which consists of all transformations of the finite set X preserving a nonuniform partition P. We also classify and enumerate the idempotent generating sets of this minimal possible size. This extends results of the first two authors in the uniform case.
Mon, 01 Feb 2016 00:00:00 GMT
http://hdl.handle.net/10023/9275
20160201T00:00:00Z
Dolinka, Igor
East, James
Mitchell, James D.
We calculate the rank and idempotent rank of the semigroup E(X,P) generated by the idempotents of the semigroup T(X,P), which consists of all transformations of the finite set X preserving a nonuniform partition P. We also classify and enumerate the idempotent generating sets of this minimal possible size. This extends results of the first two authors in the uniform case.

Modeling the aggregated exposure and responses of bowhead whales Balaena mysticetus to multiple sources of anthropogenic underwater sound
http://hdl.handle.net/10023/9259
Potential responses of marine mammals to anthropogenic underwater sound are usually assessed by researchers and regulators on the basis of exposure to a single, relatively loud sound source. However, marine mammals typically receive sounds from multiple, dynamic sources. We developed a method to aggregate modeled sounds from multiple sources and estimate the sound levels received by individuals. To illustrate the method, we modeled the sound fields of 9 sources associated with oil development and estimated the sound received over 47 d by a population of 10 000 simulated bowhead whales Balaena mysticetus on their annual migration through the Alaskan Beaufort Sea. Empirical data were sufficient to parameterize simulations of the distribution of individual whales over time and their range of movement patterns. We ran 2 simulations to estimate the sound exposure history and distances traveled by bowhead whales: one in which they could change their movement paths (avert) in response to set levels of sound and one in which they could not avert. When animals could not avert, about 2% of the simulated population was exposed to root mean square (rms) sound pressure levels (SPL) ≥ 180 dB re 1 mu Pa, a level that regulators in the U.S. often associate with injury. When animals could avert from sound levels that regulators often associate with behavioral disturbance (rms SPL > 160 dB re 1 μPa), <1% of the simulated population was exposed to levels associated with injury. Nevertheless, many simulated bowhead whales received sound levels considerably above ambient throughout their migration. Our method enables estimates of the aggregated level of sound to which populations are exposed over extensive areas and time periods.
This work was supported in part by a contract between BP Exploration (Alaska) Inc. and the University of California, Santa Barbara (E.F.), and by the North Slope Borough.
Mon, 02 May 2016 00:00:00 GMT
http://hdl.handle.net/10023/9259
20160502T00:00:00Z
Ellison, William T.
Racca, Roberto
Clark, Christopher W.
Streever, Bill
Frankel, Adam S.
Fleishman, Erica
Angliss, Robyn
Berger, Joel
Ketten, Darlene
Guerra, Melania
Leu, Matthias
McKenna, Megan
Sformo, Todd
Southall, Brandon
Suydam, Robert
Thomas, Len
Potential responses of marine mammals to anthropogenic underwater sound are usually assessed by researchers and regulators on the basis of exposure to a single, relatively loud sound source. However, marine mammals typically receive sounds from multiple, dynamic sources. We developed a method to aggregate modeled sounds from multiple sources and estimate the sound levels received by individuals. To illustrate the method, we modeled the sound fields of 9 sources associated with oil development and estimated the sound received over 47 d by a population of 10 000 simulated bowhead whales Balaena mysticetus on their annual migration through the Alaskan Beaufort Sea. Empirical data were sufficient to parameterize simulations of the distribution of individual whales over time and their range of movement patterns. We ran 2 simulations to estimate the sound exposure history and distances traveled by bowhead whales: one in which they could change their movement paths (avert) in response to set levels of sound and one in which they could not avert. When animals could not avert, about 2% of the simulated population was exposed to root mean square (rms) sound pressure levels (SPL) ≥ 180 dB re 1 mu Pa, a level that regulators in the U.S. often associate with injury. When animals could avert from sound levels that regulators often associate with behavioral disturbance (rms SPL > 160 dB re 1 μPa), <1% of the simulated population was exposed to levels associated with injury. Nevertheless, many simulated bowhead whales received sound levels considerably above ambient throughout their migration. Our method enables estimates of the aggregated level of sound to which populations are exposed over extensive areas and time periods.

Ends of semigroups
http://hdl.handle.net/10023/9254
We define the notion of the partial order of ends of the Cayley graph of a semigroup. We prove that the structure of the ends of a semigroup is invariant under change of finite generating set and at the same time is inherited by subsemigroups and extensions of finite Rees index. We prove an analogue of Hopf's Theorem, stating that a group has 1, 2 or infinitely many ends, for left cancellative semigroups and that the cardinality of the set of ends is invariant in subsemigroups and extension of finite Green index in left cancellative semigroups.
Wed, 27 Jul 2016 00:00:00 GMT
http://hdl.handle.net/10023/9254
20160727T00:00:00Z
Craik, S.
Gray, R.
Kilibarda, V.
Mitchell, J. D.
Ruskuc, N.
We define the notion of the partial order of ends of the Cayley graph of a semigroup. We prove that the structure of the ends of a semigroup is invariant under change of finite generating set and at the same time is inherited by subsemigroups and extensions of finite Rees index. We prove an analogue of Hopf's Theorem, stating that a group has 1, 2 or infinitely many ends, for left cancellative semigroups and that the cardinality of the set of ends is invariant in subsemigroups and extension of finite Green index in left cancellative semigroups.

Dimension conservation for selfsimilar sets and fractal percolation
http://hdl.handle.net/10023/9253
We introduce a technique that uses projection properties of fractal percolation to establish dimension conservation results for sections of deterministic selfsimilar sets. For example, let K be a selfsimilar subset of R2 with Hausdorff dimension dimHK >1 such that the rotational components of the underlying similarities generate the full rotation group. Then for all ε >0, writing πθ for projection onto the line Lθ in direction θ, the Hausdorff dimensions of the sections satisfy dimH (K ∩ πθ1x)> dimHK  1  ε for a set of x ∈ Lθ of positive Lebesgue measure, for all directions θ except for those in a set of Hausdorff dimension 0. For a class of selfsimilar sets we obtain a similar conclusion for all directions, but with lower box dimension replacing Hausdorff dimensions of sections. We obtain similar inequalities for the dimensions of sections of Mandelbrot percolation sets.
Thu, 01 Jan 2015 00:00:00 GMT
http://hdl.handle.net/10023/9253
20150101T00:00:00Z
Falconer, Kenneth John
Jin, Xiong
We introduce a technique that uses projection properties of fractal percolation to establish dimension conservation results for sections of deterministic selfsimilar sets. For example, let K be a selfsimilar subset of R2 with Hausdorff dimension dimHK >1 such that the rotational components of the underlying similarities generate the full rotation group. Then for all ε >0, writing πθ for projection onto the line Lθ in direction θ, the Hausdorff dimensions of the sections satisfy dimH (K ∩ πθ1x)> dimHK  1  ε for a set of x ∈ Lθ of positive Lebesgue measure, for all directions θ except for those in a set of Hausdorff dimension 0. For a class of selfsimilar sets we obtain a similar conclusion for all directions, but with lower box dimension replacing Hausdorff dimensions of sections. We obtain similar inequalities for the dimensions of sections of Mandelbrot percolation sets.

Sixty years of fractal projections
http://hdl.handle.net/10023/9231
Sixty years ago, John Marstrand published a paper which, among other things, relates the Hausdorff dimension of a plane set to the dimensions of its orthogonal projections onto lines. For many years, the paper attracted very little attention. However, over the past 30 years, Marstrand’s projection theorems have become the prototype for many results in fractal geometry with numerous variants and applications and they continue to motivate leading research.
Fri, 31 Jul 2015 00:00:00 GMT
http://hdl.handle.net/10023/9231
20150731T00:00:00Z
Falconer, Kenneth John
Fraser, Jonathan Macdonald
Jin, Xiong
Sixty years ago, John Marstrand published a paper which, among other things, relates the Hausdorff dimension of a plane set to the dimensions of its orthogonal projections onto lines. For many years, the paper attracted very little attention. However, over the past 30 years, Marstrand’s projection theorems have become the prototype for many results in fractal geometry with numerous variants and applications and they continue to motivate leading research.

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

Hitting times and periodicity in random dynamics
http://hdl.handle.net/10023/9179
We prove quenched laws of hitting time statistics for random subshifts of finite type. In particular we prove a dichotomy between the law for periodic and for nonperiodic points. We show that this applies to random Gibbs measures.
Thu, 01 Oct 2015 00:00:00 GMT
http://hdl.handle.net/10023/9179
20151001T00:00:00Z
Todd, Michael John
Rousseau, Jerome
We prove quenched laws of hitting time statistics for random subshifts of finite type. In particular we prove a dichotomy between the law for periodic and for nonperiodic points. We show that this applies to random Gibbs measures.

Automorphism groups of countable algebraically closed graphs and endomorphisms of the random graph
http://hdl.handle.net/10023/9178
We establish links between countable algebraically closed graphs and the endomorphisms of the countable universal graph R. As a consequence we show that, for any countable graph Γ, there are uncountably many maximal subgroups of the endomorphism monoid of R isomorphic to the automorphism group of Γ. Further structural information about End R is established including that Aut Γ arises in uncountably many ways as a Schützenberger group. Similar results are proved for the countable universal directed graph and the countable universal bipartite graph.
Sun, 01 May 2016 00:00:00 GMT
http://hdl.handle.net/10023/9178
20160501T00:00:00Z
Dolinka, Igor
Gray, Robert Duncan
McPhee, Jillian Dawn
Mitchell, James David
Quick, Martyn
We establish links between countable algebraically closed graphs and the endomorphisms of the countable universal graph R. As a consequence we show that, for any countable graph Γ, there are uncountably many maximal subgroups of the endomorphism monoid of R isomorphic to the automorphism group of Γ. Further structural information about End R is established including that Aut Γ arises in uncountably many ways as a Schützenberger group. Similar results are proved for the countable universal directed graph and the countable universal bipartite graph.

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

Nestbuilding males trade off material collection costs with territory value
http://hdl.handle.net/10023/9164
Building a structurally robust nest is crucial for reproductive success in many birds. However, we know little about the criteria birds use to select material or where they go to collect it. Here we observed the material collection of male Cape Weavers (Ploceus capensis). Males typically selected long, strong material to build their nests and each male collected material from different locations. Males that built more nests nested in a different area of the colony and flew further to collect nest material than did males that built fewer nests. As these males that flew further to collect material had longer tails and wings and attracted more females to their territories than did males that flew shorter distances, they may have traded off the travel costs of collecting nest materials with benefits gained from holding a territory in a more 'desirable' part of the colony. Nest construction, then, appears to be a multidimensional task whereby birds take into account material's structural properties, material proximity to the nest site and territory quality. Males that do this effectively both attract more mates and provide structurally sound nests for their young.
This work was supported by the BBSRC (BB/I019502/1 to SDH and SLM) and Roslin Institute Strategic Grant funding from the BBSRC (SLM).
Mon, 25 Jan 2016 00:00:00 GMT
http://hdl.handle.net/10023/9164
20160125T00:00:00Z
Bailey, Ida E.
Morgan, Kate V.
Oschadleus, H. Dieter
DeRuiter, Stacy L.
Meddle, Simone L.
Healy, Susan D.
Building a structurally robust nest is crucial for reproductive success in many birds. However, we know little about the criteria birds use to select material or where they go to collect it. Here we observed the material collection of male Cape Weavers (Ploceus capensis). Males typically selected long, strong material to build their nests and each male collected material from different locations. Males that built more nests nested in a different area of the colony and flew further to collect nest material than did males that built fewer nests. As these males that flew further to collect material had longer tails and wings and attracted more females to their territories than did males that flew shorter distances, they may have traded off the travel costs of collecting nest materials with benefits gained from holding a territory in a more 'desirable' part of the colony. Nest construction, then, appears to be a multidimensional task whereby birds take into account material's structural properties, material proximity to the nest site and territory quality. Males that do this effectively both attract more mates and provide structurally sound nests for their young.

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

Flexible density surface estimation for spatially explicit capturerecapture surveys
http://hdl.handle.net/10023/9147
1. Existing spatially explicit capturerecapture (SECR) software does not have the ability to fit flexible nonparametric models of animal density. 2. We describe and implement in the R package secrgam, a flexible method for estimating density surfaces from SECR data, using regression splines. 3. Package secrgam is an extension of package secr to implement some models available in the generalised additive model package mvcv. It accommodates density models that are arbitrarily flexible functions of spatially and temporallyreferenced variables. This includes onedimensional and multidimensional smooths of covariates and smooths with interactions. The shape and smoothness of the fitted density surfaces is datadriven and can be determined using AIC or similar criteria. We illustrate use of the package by estimating the density surface from a simulated camera trap survey of leopards. 4. Package secrgam provides a flexible tool for species distribution modelling using SECR data.
Tue, 01 Jul 2014 00:00:00 GMT
http://hdl.handle.net/10023/9147
20140701T00:00:00Z
Borchers, David Louis
Kidney, Darren
1. Existing spatially explicit capturerecapture (SECR) software does not have the ability to fit flexible nonparametric models of animal density. 2. We describe and implement in the R package secrgam, a flexible method for estimating density surfaces from SECR data, using regression splines. 3. Package secrgam is an extension of package secr to implement some models available in the generalised additive model package mvcv. It accommodates density models that are arbitrarily flexible functions of spatially and temporallyreferenced variables. This includes onedimensional and multidimensional smooths of covariates and smooths with interactions. The shape and smoothness of the fitted density surfaces is datadriven and can be determined using AIC or similar criteria. We illustrate use of the package by estimating the density surface from a simulated camera trap survey of leopards. 4. Package secrgam provides a flexible tool for species distribution modelling using SECR data.

On regularity and the word problem for free idempotent generated semigroups
http://hdl.handle.net/10023/9145
Thu, 07 May 2015 00:00:00 GMT
http://hdl.handle.net/10023/9145
20150507T00:00:00Z
Dolinka, I.
Gray, R.
Ruskuc, Nikola

The infinite simple group V of Richard J. Thompson : presentations by permutations
http://hdl.handle.net/10023/9143
We show one can naturally describe elements of R. Thompson's infinite finitely presented simple group V, known by Thompson to have a presentation with four generators and fourteen relations, as products of permutations analogous to transpositions. This perspective provides an intuitive explanation towards the simplicity of V and also perhaps indicates a reason as to why it was one of the first discovered infinite finitely presented simple groups; it is (in some basic sense) a relative of the finite alternating groups. We find a natural infinite presentation for V as a group generated by these "transpositions," which presentation bears comparison with Dehornoy's infinite presentation, and which enables us to develop two small presentations for V: a humaninterpretable presentation with three generators and eight relations, and a Tietzederived presentation with two generators and seven relations.
Thu, 01 Jan 2015 00:00:00 GMT
http://hdl.handle.net/10023/9143
20150101T00:00:00Z
Quick, Martyn
Bleak, Collin Patrick
We show one can naturally describe elements of R. Thompson's infinite finitely presented simple group V, known by Thompson to have a presentation with four generators and fourteen relations, as products of permutations analogous to transpositions. This perspective provides an intuitive explanation towards the simplicity of V and also perhaps indicates a reason as to why it was one of the first discovered infinite finitely presented simple groups; it is (in some basic sense) a relative of the finite alternating groups. We find a natural infinite presentation for V as a group generated by these "transpositions," which presentation bears comparison with Dehornoy's infinite presentation, and which enables us to develop two small presentations for V: a humaninterpretable presentation with three generators and eight relations, and a Tietzederived presentation with two generators and seven relations.

The random continued fraction transformation
http://hdl.handle.net/10023/9142
We introduce a random dynamical system related to continued fraction expansions. It uses random combination of the Gauss map and the R\'enyi (or backwards) continued fraction map. We explore the continued fraction expansions that this system produces as well as the dynamical properties of the system.
Wed, 01 Jul 2015 00:00:00 GMT
http://hdl.handle.net/10023/9142
20150701T00:00:00Z
Kalle, Charlene
Kempton, Thomas Michael William
Verbitskiy, Evgeny
We introduce a random dynamical system related to continued fraction expansions. It uses random combination of the Gauss map and the R\'enyi (or backwards) continued fraction map. We explore the continued fraction expansions that this system produces as well as the dynamical properties of the system.

The scenery flow for selfaffine measures
http://hdl.handle.net/10023/9141
We describe the scaling scenery associated to Bernoulli measures supported on separated selfaffine sets under the condition that certain projections of the measure are absolutely continuous.
Fri, 01 May 2015 00:00:00 GMT
http://hdl.handle.net/10023/9141
20150501T00:00:00Z
Kempton, Thomas Michael William
We describe the scaling scenery associated to Bernoulli measures supported on separated selfaffine sets under the condition that certain projections of the measure are absolutely continuous.

Computing finite semigroups
http://hdl.handle.net/10023/9138
Using a variant of Schreier's Theorem, and the theory of Green's relations, we show how to reduce the computation of an arbitrary subsemigroup of a finite regular semigroup to that of certain associated subgroups. Examples of semigroups to which these results apply include many important classes: transformation semigroups, partial permutation semigroups and inverse semigroups, partition monoids, matrix semigroups, and subsemigroups of finite regular Rees matrix and $0$matrix semigroups over groups. For any subsemigroup of such a semigroup, it is possible to, among other things, efficiently compute its size and Green's relations, test membership, factorize elements over the generators, find the semigroup generated by the given subsemigroup and any collection of additional elements, calculate the partial order of the $\mathscr{D}$classes, test regularity, and determine the idempotents. This is achieved by representing the given subsemigroup without exhaustively enumerating its elements. It is also possible to compute the Green's classes of an element of such a subsemigroup without determining the global structure of the semigroup.
Wed, 07 Oct 2015 00:00:00 GMT
http://hdl.handle.net/10023/9138
20151007T00:00:00Z
East, J.
EgriNagy, A.
Mitchell, J. D.
Péresse, Y.
Using a variant of Schreier's Theorem, and the theory of Green's relations, we show how to reduce the computation of an arbitrary subsemigroup of a finite regular semigroup to that of certain associated subgroups. Examples of semigroups to which these results apply include many important classes: transformation semigroups, partial permutation semigroups and inverse semigroups, partition monoids, matrix semigroups, and subsemigroups of finite regular Rees matrix and $0$matrix semigroups over groups. For any subsemigroup of such a semigroup, it is possible to, among other things, efficiently compute its size and Green's relations, test membership, factorize elements over the generators, find the semigroup generated by the given subsemigroup and any collection of additional elements, calculate the partial order of the $\mathscr{D}$classes, test regularity, and determine the idempotents. This is achieved by representing the given subsemigroup without exhaustively enumerating its elements. It is also possible to compute the Green's classes of an element of such a subsemigroup without determining the global structure of the semigroup.

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

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

Embedding rightangled Artin groups into BrinThompson groups
http://hdl.handle.net/10023/9080
We prove that every finitelygenerated rightangled Artin group can be embedded into some BrinThompson group nV. It follows that many other groups can be embedded into some nV (e.g., any finite extension of any of Haglund and Wise's special groups), and that various decision problems involving subgroups of nV are unsolvable.
7 pages, no figures
Sat, 27 Feb 2016 00:00:00 GMT
http://hdl.handle.net/10023/9080
20160227T00:00:00Z
Belk, James
Bleak, Collin
Matucci, Francesco
We prove that every finitelygenerated rightangled Artin group can be embedded into some BrinThompson group nV. It follows that many other groups can be embedded into some nV (e.g., any finite extension of any of Haglund and Wise's special groups), and that various decision problems involving subgroups of nV are unsolvable.

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

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

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

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

Universal sequences for the orderautomorphisms of the rationals
http://hdl.handle.net/10023/9024
In this paper, we consider the group Aut(Q,≤) of orderautomorphisms of the rational numbers, proving a result analogous to a theorem of Galvin's for the symmetric group. In an announcement, Khélif states that every countable subset of Aut(Q,≤) is contained in an Ngenerated subgroup of Aut(Q,≤) for some fixed N ∈ N. We show that the least such N is 2. Moreover, for every countable subset of Aut(Q,≤), we show that every element can be given as a prescribed product of two generators without using their inverses. More precisely, suppose that a and b freely generate the free semigroup {a,b}+ consisting of the nonempty words over a and b. Then we show that there exists a sequence of words w1, w2,... over {a,b} such that for every sequence f1, f2, ... ∈ Aut(Q,≤) there is a homomorphism φ : {a,b}+ → Aut(Q,≤) where (wi)φ=fi for every i. The main theorem in this paper provides an alternative proof of a result of Droste and Holland showing that the strong cofinality of Aut(Q,≤) is uncountable, or equivalently that Aut(Q,≤) has uncountable cofinality and Bergman's property.
Mon, 01 Aug 2016 00:00:00 GMT
http://hdl.handle.net/10023/9024
20160801T00:00:00Z
Hyde, J.
Jonusas, J.
Mitchell, J. D.
Peresse, Y. H.
In this paper, we consider the group Aut(Q,≤) of orderautomorphisms of the rational numbers, proving a result analogous to a theorem of Galvin's for the symmetric group. In an announcement, Khélif states that every countable subset of Aut(Q,≤) is contained in an Ngenerated subgroup of Aut(Q,≤) for some fixed N ∈ N. We show that the least such N is 2. Moreover, for every countable subset of Aut(Q,≤), we show that every element can be given as a prescribed product of two generators without using their inverses. More precisely, suppose that a and b freely generate the free semigroup {a,b}+ consisting of the nonempty words over a and b. Then we show that there exists a sequence of words w1, w2,... over {a,b} such that for every sequence f1, f2, ... ∈ Aut(Q,≤) there is a homomorphism φ : {a,b}+ → Aut(Q,≤) where (wi)φ=fi for every i. The main theorem in this paper provides an alternative proof of a result of Droste and Holland showing that the strong cofinality of Aut(Q,≤) is uncountable, or equivalently that Aut(Q,≤) has uncountable cofinality and Bergman's property.

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

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

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

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

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

A changepoint analysis of spatiotemporal point processes
http://hdl.handle.net/10023/8935
This work introduces a Bayesian approach to detecting multiple unknown changepoints over time in the inhomogeneous intensity of a spatiotemporal point process with spatial and temporal dependence within segments. We propose a new method for detecting changes by fitting a spatiotemporal logGaussian Cox process model using the computational efficiency and flexibility of integrated nested Laplace approximation, and by studying the posterior distribution of the potential changepoint positions. In this paper, the context of the problem and the research questions are introduced, then the methodology is presented and discussed in detail. A simulation study assesses the validity and properties of the proposed methods. Lastly, questions are addressed concerning potential unknown changepoints in the intensity of radioactive particles found on Sandside beach, Dounreay, Scotland.
As regards author Linda Altieri, the research work underlying this paper was partially funded by a FIRB 2012 grant (project no. RBFR12URQJ; title: Statistical modeling of environmental phenomena: pollution, meteorology, health and their interactions) for research projects by the Italian Ministry of Education, Universities and Research.
Thu, 01 Jan 2015 00:00:00 GMT
http://hdl.handle.net/10023/8935
20150101T00:00:00Z
Altieri, Linda
Scott, E. Marian
Cocchi, Daniela
Illian, Janine B.
This work introduces a Bayesian approach to detecting multiple unknown changepoints over time in the inhomogeneous intensity of a spatiotemporal point process with spatial and temporal dependence within segments. We propose a new method for detecting changes by fitting a spatiotemporal logGaussian Cox process model using the computational efficiency and flexibility of integrated nested Laplace approximation, and by studying the posterior distribution of the potential changepoint positions. In this paper, the context of the problem and the research questions are introduced, then the methodology is presented and discussed in detail. A simulation study assesses the validity and properties of the proposed methods. Lastly, questions are addressed concerning potential unknown changepoints in the intensity of radioactive particles found on Sandside beach, Dounreay, Scotland.

PReMiuM : an R package for profile regression mixture models using Dirichlet processes
http://hdl.handle.net/10023/8931
PReMiuM is a recently developed R package for Bayesian clustering using a Dirichlet process mixture model. This model is an alternative to regression models, nonparametrically linking a response vector to covariate data through cluster membership (Molitor, Papathomas, Jerrett, and Richardson 2010). The package allows binary, categorical, count and continuous response, as well as continuous and discrete covariates. Additionally, predictions may be made for the response, and missing values for the covariates are handled. Several samplers and label switching moves are implemented along with diagnostic tools to assess convergence. A number of R functions for postprocessing of the output are also provided. In addition to tting mixtures, it may additionally be of interest to determine which covariates actively drive the mixture components. This is implemented in the package as variable selection.
Fri, 20 Mar 2015 00:00:00 GMT
http://hdl.handle.net/10023/8931
20150320T00:00:00Z
Liverani, Silvia
Hastie, David
Azizi, Lamiae
Papathomas, Michail
Richardson, Sylvia
PReMiuM is a recently developed R package for Bayesian clustering using a Dirichlet process mixture model. This model is an alternative to regression models, nonparametrically linking a response vector to covariate data through cluster membership (Molitor, Papathomas, Jerrett, and Richardson 2010). The package allows binary, categorical, count and continuous response, as well as continuous and discrete covariates. Additionally, predictions may be made for the response, and missing values for the covariates are handled. Several samplers and label switching moves are implemented along with diagnostic tools to assess convergence. A number of R functions for postprocessing of the output are also provided. In addition to tting mixtures, it may additionally be of interest to determine which covariates actively drive the mixture components. This is implemented in the package as variable selection.

Aspects of order and congruence relations on regular semigroups
http://hdl.handle.net/10023/8926
On a regular semigroup S natural order relations have been defined
by Nambooripad and by Lallement. Different characterisations and
relationships between the Nambooripad order J, Lallement's order λ and
a certain relation k are considered in Chapter I. It is shown that on
a regular semigroup S the partial order J is left compatible if and
only if S is locally Runipotent. This condition in the case where S
is orthodox is equivalent to saying that E(S) is a left seminormal
band. It is also proved that λ is the least compatible partial order
contained in J and that k = λ if and only if k is compatible and k
if and only if J is compatible. A description of λ and J in the
semigroups T(X) and PT(X) is presented.
In Chapter II, it is proved that in an orthodox semigroup S the
band of idempotents E(S) is left quasinormal if and only if there
exists a local isomorphism from S onto an Runipotent semigroup. It is
shown that there exists a least Runipotent congruence on any orthodox
semigroup, generated by a certain left compatible equivalence R. This
equivalence is a congruence if and only if E(S) is a right semiregular
band.
The last Chapter is particularly concerned with the description of
Runipotent congruences on a regular semigroup S by means of their
kernels and traces. The lattice RC(S) of all Runipotent congruences
on a regular semigroup S is studied. A congruence≡ on the lattice
RC(S) is considered and the greatest and the least element of each
≡class are described.
Sat, 01 Jan 1983 00:00:00 GMT
http://hdl.handle.net/10023/8926
19830101T00:00:00Z
Gomes, Gracinda Maria dos Santos
On a regular semigroup S natural order relations have been defined
by Nambooripad and by Lallement. Different characterisations and
relationships between the Nambooripad order J, Lallement's order λ and
a certain relation k are considered in Chapter I. It is shown that on
a regular semigroup S the partial order J is left compatible if and
only if S is locally Runipotent. This condition in the case where S
is orthodox is equivalent to saying that E(S) is a left seminormal
band. It is also proved that λ is the least compatible partial order
contained in J and that k = λ if and only if k is compatible and k
if and only if J is compatible. A description of λ and J in the
semigroups T(X) and PT(X) is presented.
In Chapter II, it is proved that in an orthodox semigroup S the
band of idempotents E(S) is left quasinormal if and only if there
exists a local isomorphism from S onto an Runipotent semigroup. It is
shown that there exists a least Runipotent congruence on any orthodox
semigroup, generated by a certain left compatible equivalence R. This
equivalence is a congruence if and only if E(S) is a right semiregular
band.
The last Chapter is particularly concerned with the description of
Runipotent congruences on a regular semigroup S by means of their
kernels and traces. The lattice RC(S) of all Runipotent congruences
on a regular semigroup S is studied. A congruence≡ on the lattice
RC(S) is considered and the greatest and the least element of each
≡class are described.

SSALMON  the Solar Simulations for the Atacama Large Millimeter Observatory Network
http://hdl.handle.net/10023/8874
The Solar Simulations for the Atacama Large Millimeter Observatory Network (SSALMON) was initiated in 2014 in connection with two ALMA development studies. The Atacama Large Millimeter/submillimeter Array (ALMA) is a powerful new tool, which can also observe the Sun at high spatial, temporal, and spectral resolution. The international SSALMONetwork aims at coordinating the further development of solar observing modes for ALMA and at promoting scientific opportunities for solar physics with particular focus on numerical simulations, which can provide important constraints for the observing modes and can aid the interpretation of future observations. The radiation detected by ALMA originates mostly in the solar chromosphere – a complex and dynamic layer between the photosphere and corona, which plays an important role in the transport of energy and matter and the heating of the outer layers of the solar atmosphere. Potential targets include active regions, prominences, quiet Sun regions, flares. Here, we give a brief overview over the network and potential science cases for future solar observations with ALMA.
Thu, 01 Jan 2015 00:00:00 GMT
http://hdl.handle.net/10023/8874
20150101T00:00:00Z
Wedemeyer, S.
Bastian, T.
Brajša, R.
Barta, M.
Hudson, H.
Fleishman, G.
Loukitcheva, M.
Fleck, B.
Kontar, E.
De Pontieu, B.
Tiwari, S.
Kato, Y.
Soler, R.
Yagoubov, P.
Black, J.H.
Antolin, P.
Gunár, S.
Labrosse, N.
Benz, A.O.
Nindos, A.
Steffen, M.
Scullion, E.
Doyle, J.G.
Zaqarashvili, T.
Hanslmeier, A.
Nakariakov, V.M.
Heinzel, P.
Ayres, T.
Karlicky, M.
The Solar Simulations for the Atacama Large Millimeter Observatory Network (SSALMON) was initiated in 2014 in connection with two ALMA development studies. The Atacama Large Millimeter/submillimeter Array (ALMA) is a powerful new tool, which can also observe the Sun at high spatial, temporal, and spectral resolution. The international SSALMONetwork aims at coordinating the further development of solar observing modes for ALMA and at promoting scientific opportunities for solar physics with particular focus on numerical simulations, which can provide important constraints for the observing modes and can aid the interpretation of future observations. The radiation detected by ALMA originates mostly in the solar chromosphere – a complex and dynamic layer between the photosphere and corona, which plays an important role in the transport of energy and matter and the heating of the outer layers of the solar atmosphere. Potential targets include active regions, prominences, quiet Sun regions, flares. Here, we give a brief overview over the network and potential science cases for future solar observations with ALMA.

50Year Anniversary of Papers by Cormack, Jolly and Seber
http://hdl.handle.net/10023/8872
Sun, 01 May 2016 00:00:00 GMT
http://hdl.handle.net/10023/8872
20160501T00:00:00Z
Buckland, Stephen Terrence
Morgan, Byron J T

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

A conversation with Richard M. Cormack
http://hdl.handle.net/10023/8869
Richard Melville Cormack is one of the giants who developed the theory of markrecapture. Referring to his key paper in 1964, and the papers published backtoback in 1965 by George Jolly and George Seber, the `CormackJollySeber model' is central to the development of markrecapture methods for estimating survival. Richard was born on 12 March 1935. His father was Principal of Stow College of Engineering in Glasgow. From the age of 7, Richard attended Glasgow Academy, and later entered directly into the second year at Kings College, Cambridge, intending at the time to be a theoretical astronomer. He secured first class honours in Special Mathematics from London as an external student in 1954, and second class honours in Mathematics from Cambridge in 1955. After changing direction, he left Cambridge in 1956 with a Distinction in the Diploma in Mathematical Statistics. Richard's PhD, undertaken while a lecturer at Aberdeen, was completed in 1961. Richard's period at Aberdeen (195666) coincided with a golden era for statistics there, and his colleagues included D.J. Finney, Bill Brass, Peter Fisk, David M.G. Wishart, Michael Sampford, Robert Curnow, George Jolly and Andrew Rutherford (the last four being members of the ARC Unit of Statistics). In common with a number of these colleagues, he moved to Edinburgh in 1966, holding a Senior Lectureship there until 1972, when he became the first Professor of Statistics at St Andrews. Richard's groundbreaking contributions to markrecapture in the early 1960s continued when he addressed the issue of heterogeneity in capture probabilities, publishing a test for heterogeneity in Biometrics in 1966. Then in 1972, in another Biometrics paper, he showed the logic behind capturerecapture estimates, making the methods more accessible and understandable to the user community. In 1981, jointly with Philip North, Richard published important insights into markrecovery models. His work on loglinear models for markrecapture led to papers in Biometrika in 1984 (with Ron Sandland) and 1991 (with Peter Jupp), and in Biometrics in 1989, and additionally, to four book chapters. There was also a sequence of Biometrics capturerecapture papers in the 1990s: on modelling covariates (1990), on interval estimation (1992) and on variance estimation (1993). After retirement in 1994, his publications in markrecapture were mostly as coauthor in epidemiology studies. Richard also published on other diverse topics, often with scientists from other disciplines. His 1971 review of classification, read to the Research Committee of RSS and later appearing in JRSS A, is a classic, and while his 1988 exposition on statistical challenges in the environmental sciences (also in JRSS A) has had substantially less impact, it too showed his characteristic incisiveness. His contributions to a wide range of committees, working groups, visiting groups and scientific organisations (including council member for NERC and the Freshwater Biological Association) were substantial. He was elected a member of the ISI in 1962 and a Fellow of the Royal Society of Edinburgh in 1974. He held various offices within the Biometric Society, as Secretary of the British Region 197077, Regional President 199092 and President of the International Society 198081. He served on the Council and various committees of the Royal Statistical Society. Richard married Edith Whittaker on 1st September 1960, at King's College Chapel, Aberdeen. Edith is a plant ecologist, and a past chairperson of the Fife and Kinross Branch of the Scottish Wildlife Trust and of the Friends of St Andrews Botanic Garden: she was also a founding member of the Garden's Education Trust. Their son Andrew is a European Chartered Engineer working for the JANET network, while their daughter Anne is a Marketing Manager. Photography has been a passion of Richard's for many decades. He was lecturer and judge for 40 years for the Scottish Photographic Federation, and was placed on their roll of honour. He has held exhibitions in Dundee (Land of the Berbers), St Andrews (Growth and Form) and Aberdeen (Walking in the North), and has given many talks. Richard firmly established the University of St Andrews as a centre for statistical ecology, a strength that continues today.
Sun, 01 May 2016 00:00:00 GMT
http://hdl.handle.net/10023/8869
20160501T00:00:00Z
Buckland, Stephen Terrence
Richard Melville Cormack is one of the giants who developed the theory of markrecapture. Referring to his key paper in 1964, and the papers published backtoback in 1965 by George Jolly and George Seber, the `CormackJollySeber model' is central to the development of markrecapture methods for estimating survival. Richard was born on 12 March 1935. His father was Principal of Stow College of Engineering in Glasgow. From the age of 7, Richard attended Glasgow Academy, and later entered directly into the second year at Kings College, Cambridge, intending at the time to be a theoretical astronomer. He secured first class honours in Special Mathematics from London as an external student in 1954, and second class honours in Mathematics from Cambridge in 1955. After changing direction, he left Cambridge in 1956 with a Distinction in the Diploma in Mathematical Statistics. Richard's PhD, undertaken while a lecturer at Aberdeen, was completed in 1961. Richard's period at Aberdeen (195666) coincided with a golden era for statistics there, and his colleagues included D.J. Finney, Bill Brass, Peter Fisk, David M.G. Wishart, Michael Sampford, Robert Curnow, George Jolly and Andrew Rutherford (the last four being members of the ARC Unit of Statistics). In common with a number of these colleagues, he moved to Edinburgh in 1966, holding a Senior Lectureship there until 1972, when he became the first Professor of Statistics at St Andrews. Richard's groundbreaking contributions to markrecapture in the early 1960s continued when he addressed the issue of heterogeneity in capture probabilities, publishing a test for heterogeneity in Biometrics in 1966. Then in 1972, in another Biometrics paper, he showed the logic behind capturerecapture estimates, making the methods more accessible and understandable to the user community. In 1981, jointly with Philip North, Richard published important insights into markrecovery models. His work on loglinear models for markrecapture led to papers in Biometrika in 1984 (with Ron Sandland) and 1991 (with Peter Jupp), and in Biometrics in 1989, and additionally, to four book chapters. There was also a sequence of Biometrics capturerecapture papers in the 1990s: on modelling covariates (1990), on interval estimation (1992) and on variance estimation (1993). After retirement in 1994, his publications in markrecapture were mostly as coauthor in epidemiology studies. Richard also published on other diverse topics, often with scientists from other disciplines. His 1971 review of classification, read to the Research Committee of RSS and later appearing in JRSS A, is a classic, and while his 1988 exposition on statistical challenges in the environmental sciences (also in JRSS A) has had substantially less impact, it too showed his characteristic incisiveness. His contributions to a wide range of committees, working groups, visiting groups and scientific organisations (including council member for NERC and the Freshwater Biological Association) were substantial. He was elected a member of the ISI in 1962 and a Fellow of the Royal Society of Edinburgh in 1974. He held various offices within the Biometric Society, as Secretary of the British Region 197077, Regional President 199092 and President of the International Society 198081. He served on the Council and various committees of the Royal Statistical Society. Richard married Edith Whittaker on 1st September 1960, at King's College Chapel, Aberdeen. Edith is a plant ecologist, and a past chairperson of the Fife and Kinross Branch of the Scottish Wildlife Trust and of the Friends of St Andrews Botanic Garden: she was also a founding member of the Garden's Education Trust. Their son Andrew is a European Chartered Engineer working for the JANET network, while their daughter Anne is a Marketing Manager. Photography has been a passion of Richard's for many decades. He was lecturer and judge for 40 years for the Scottish Photographic Federation, and was placed on their roll of honour. He has held exhibitions in Dundee (Land of the Berbers), St Andrews (Growth and Form) and Aberdeen (Walking in the North), and has given many talks. Richard firmly established the University of St Andrews as a centre for statistical ecology, a strength that continues today.

Avoidance of wind farms by harbour seals is limited to pile driving activities
http://hdl.handle.net/10023/8856
1. As part of global efforts to reduce dependence on carbonbased energy sources there has been a rapid increase in the installation of renewable energy devices. The installation and operation of these devices can result in conflicts with wildlife. In the marine environment, mammals may avoid wind farms that are under construction or operating. Such avoidance may lead to more time spent travelling or displacement from key habitats. A paucity of data on atsea movements of marine mammals around wind farms limits our understanding of the nature of their potential impacts. 2. Here, we present the results of a telemetry study on harbour seals Phoca vitulina in The Wash, southeast England, an area where wind farms are being constructed using impact pile driving. We investigated whether seals avoid wind farms during operation, construction in its entirety, or during piling activity. The study was carried out using historical telemetry data collected prior to any wind farm development and telemetry data collected in 2012 during the construction of one wind farm and the operation of another. 3. Within an operational wind farm, there was a closetosignificant increase in seal usage compared to prior to wind farm development. However, the wind farm was at the edge of a large area of increased usage, so the presence of the wind farm was unlikely to be the cause. 4. There was no significant displacement during construction as a whole. However, during piling, seal usage (abundance) was significantly reduced up to 25 km from the piling activity; within 25 km of the centre of the wind farm, there was a 19 to 83% (95% confidence intervals) decrease in usage compared to during breaks in piling, equating to a mean estimated displacement of 440 individuals. This amounts to significant displacement starting from predicted received levels of between 166 and 178 dB re 1 μPa(p·p). Displacement was limited to piling activity; within 2 h of cessation of pile driving, seals were distributed as per the nonpiling scenario. 5. Synthesis and applications. Our spatial and temporal quantification of avoidance of wind farms by harbour seals is critical to reduce uncertainty and increase robustness in environmental impact assessments of future developments. Specifically, the results will allow policymakers to produce industry guidance on the likelihood of displacement of seals in response to pile driving; the relationship between sound levels and avoidance rates; and the duration of any avoidance, thus allowing far more accurate environmental assessments to be carried out during the consenting process. Further, our results can be used to inform mitigation strategies in terms of both the sound levels likely to cause displacement and what temporal patterns of piling would minimize the magnitude of the energetic impacts of displacement.
DJFR, GH, VMJ and BM were funded by the UK Department of Energy and Climate Change (DECC) as part of their Offshore Energy Strategic Environmental Assessment programme. DT and GH were also funded by NERC/Defra EBAO NE/J004243/1. ELJ was funded under Scottish Government grant MMSS001/01. This work was also supported by National Capability funding from the Natural Environment Research Council to SMRU (grant no. SMRU1001). Tags and their deployment in the Thames in 2006 and The Wash were funded by DECC. Tags and their deployment in the Thames in 2012 were commissioned by Zoological Society London, with funding from BBC Wildlife Fund and Sita Trust.
Mon, 23 May 2016 00:00:00 GMT
http://hdl.handle.net/10023/8856
20160523T00:00:00Z
Russell, Deborah Jill
Hastie, Gordon Drummond
Thompson, David
Janik, Vincent M.
Hammond, Philip Steven
ScottHayward, Lindesay Alexandra Sarah
Matthiopoulos, Jason
Jones, Esther Lane
McConnell, Bernie J
1. As part of global efforts to reduce dependence on carbonbased energy sources there has been a rapid increase in the installation of renewable energy devices. The installation and operation of these devices can result in conflicts with wildlife. In the marine environment, mammals may avoid wind farms that are under construction or operating. Such avoidance may lead to more time spent travelling or displacement from key habitats. A paucity of data on atsea movements of marine mammals around wind farms limits our understanding of the nature of their potential impacts. 2. Here, we present the results of a telemetry study on harbour seals Phoca vitulina in The Wash, southeast England, an area where wind farms are being constructed using impact pile driving. We investigated whether seals avoid wind farms during operation, construction in its entirety, or during piling activity. The study was carried out using historical telemetry data collected prior to any wind farm development and telemetry data collected in 2012 during the construction of one wind farm and the operation of another. 3. Within an operational wind farm, there was a closetosignificant increase in seal usage compared to prior to wind farm development. However, the wind farm was at the edge of a large area of increased usage, so the presence of the wind farm was unlikely to be the cause. 4. There was no significant displacement during construction as a whole. However, during piling, seal usage (abundance) was significantly reduced up to 25 km from the piling activity; within 25 km of the centre of the wind farm, there was a 19 to 83% (95% confidence intervals) decrease in usage compared to during breaks in piling, equating to a mean estimated displacement of 440 individuals. This amounts to significant displacement starting from predicted received levels of between 166 and 178 dB re 1 μPa(p·p). Displacement was limited to piling activity; within 2 h of cessation of pile driving, seals were distributed as per the nonpiling scenario. 5. Synthesis and applications. Our spatial and temporal quantification of avoidance of wind farms by harbour seals is critical to reduce uncertainty and increase robustness in environmental impact assessments of future developments. Specifically, the results will allow policymakers to produce industry guidance on the likelihood of displacement of seals in response to pile driving; the relationship between sound levels and avoidance rates; and the duration of any avoidance, thus allowing far more accurate environmental assessments to be carried out during the consenting process. Further, our results can be used to inform mitigation strategies in terms of both the sound levels likely to cause displacement and what temporal patterns of piling would minimize the magnitude of the energetic impacts of displacement.

An efficient acoustic density estimation method with human detectors applied to gibbons in Cambodia
http://hdl.handle.net/10023/8842
Some animal species are hard to see but easy to hear. Standard visual methods for estimating population density for such species are often ineffective or inefficient, but methods based on passive acoustics show more promise. We develop spatially explicit capturerecapture (SECR) methods for territorial vocalising species, in which humans act as an acoustic detector array. We use SECR and estimated bearing data from a singleoccasion acoustic survey of a gibbon population in northeastern Cambodia to estimate the density of calling groups. The properties of the estimator are assessed using a simulation study, in which a variety of survey designs are also investigated. We then present a new form of the SECR likelihood for multioccasion data which accounts for the stochastic availability of animals. In the context of gibbon surveys this allows modelbased estimation of the proportion of groups that produce territorial vocalisations on a given day, thereby enabling the density of groups, instead of the density of calling groups, to be estimated. We illustrate the performance of this new estimator by simulation. We show that it is possible to estimate density reliably from human acoustic detections of visually cryptic species using SECR methods. For gibbon surveys we also show that incorporating observers' estimates of bearings to detected groups substantially improves estimator performance. Using the new form of the SECR likelihood we demonstrate that estimates of availability, in addition to population density and detection function parameters, can be obtained from multioccasion data, and that the detection function parameters are not confounded with the availability parameter. This acoustic SECR method provides a means of obtaining reliable density estimates for territorial vocalising species. It is also efficient in terms of data requirements since it only requires routine survey data. We anticipate that the lowtech field requirements will make this method an attractive option in many situations where populations can be surveyed acoustically by humans.
D. Kidney was supported by an Engineering and Physical Sciences Research Council (EPSRC) Doctoral Training Grant studentship (EPSRC grant EP/P505097/1). B. Stevenson was supported by a studentship jointly funded by the University of St Andrews and EPSRC, through the National Centre for Statistical Ecology (EPSRC grant EP/I000917/1).
Thu, 19 May 2016 00:00:00 GMT
http://hdl.handle.net/10023/8842
20160519T00:00:00Z
Kidney, Darren
Rawson, Benjamin M.
Borchers, David Louis
Stevenson, Ben
Marques, Tiago A.
Thomas, Len
Some animal species are hard to see but easy to hear. Standard visual methods for estimating population density for such species are often ineffective or inefficient, but methods based on passive acoustics show more promise. We develop spatially explicit capturerecapture (SECR) methods for territorial vocalising species, in which humans act as an acoustic detector array. We use SECR and estimated bearing data from a singleoccasion acoustic survey of a gibbon population in northeastern Cambodia to estimate the density of calling groups. The properties of the estimator are assessed using a simulation study, in which a variety of survey designs are also investigated. We then present a new form of the SECR likelihood for multioccasion data which accounts for the stochastic availability of animals. In the context of gibbon surveys this allows modelbased estimation of the proportion of groups that produce territorial vocalisations on a given day, thereby enabling the density of groups, instead of the density of calling groups, to be estimated. We illustrate the performance of this new estimator by simulation. We show that it is possible to estimate density reliably from human acoustic detections of visually cryptic species using SECR methods. For gibbon surveys we also show that incorporating observers' estimates of bearings to detected groups substantially improves estimator performance. Using the new form of the SECR likelihood we demonstrate that estimates of availability, in addition to population density and detection function parameters, can be obtained from multioccasion data, and that the detection function parameters are not confounded with the availability parameter. This acoustic SECR method provides a means of obtaining reliable density estimates for territorial vocalising species. It is also efficient in terms of data requirements since it only requires routine survey data. We anticipate that the lowtech field requirements will make this method an attractive option in many situations where populations can be surveyed acoustically by humans.

Neonicotinoids target distinct nicotinic acetylcholine receptors and neurons, leading to differential risks to bumblebees
http://hdl.handle.net/10023/8793
There is growing concern over the risk to bee populations from neonicotinoid insecticides and the longterm consequences of reduced numbers of insect pollinators to essential ecosystem services and food security. Our knowledge of the risk of neonicotinoids to bees is based on studies of imidacloprid and thiamethoxam and these findings are extrapolated to clothianidin based on its higher potency at nicotinic acetylcholine receptors. This study addresses the specificity and consequences of all three neonicotinoids to determine their relative risk to bumblebees at fieldrelevant levels (2.5 ppb). We find compoundspecific effects at all levels (individual cells, bees and whole colonies in semifield conditions). Imidacloprid and clothianidin display distinct, overlapping, abilities to stimulate Kenyon cells, indicating the potential to differentially influence bumblebee behavior. Bee immobility was induced only by imidacloprid, and an increased vulnerability to clothianidin toxicity only occurred following chronic exposure to clothianidin or thiamethoxam. At the whole colony level, only thiamethoxam altered the sex ratio (more males present) and only clothianidin increased queen production. Finally, both imidacloprid and thiamethoxam caused deficits in colony strength, while no detrimental effects of clothianidin were observed. Given these findings, neonicotinoid risk needs to be considered independently for each compound and target species.
This research was funded jointly by BBSRC, DEFRA, NERC, the Scottish Government and The Wellcome Trust, under the Insect Pollinators Initiative (UK) grant BB/1000313/1(CNC).
Thu, 28 Apr 2016 00:00:00 GMT
http://hdl.handle.net/10023/8793
20160428T00:00:00Z
Moffat, Christopher
Buckland, Stephen T.
Samson, Andrew J.
McArthur, Robin
Chamosa Pino, Victor
Bollan, Karen A.
Huang, Jeffrey T. J.
Connolly, Christopher N.
There is growing concern over the risk to bee populations from neonicotinoid insecticides and the longterm consequences of reduced numbers of insect pollinators to essential ecosystem services and food security. Our knowledge of the risk of neonicotinoids to bees is based on studies of imidacloprid and thiamethoxam and these findings are extrapolated to clothianidin based on its higher potency at nicotinic acetylcholine receptors. This study addresses the specificity and consequences of all three neonicotinoids to determine their relative risk to bumblebees at fieldrelevant levels (2.5 ppb). We find compoundspecific effects at all levels (individual cells, bees and whole colonies in semifield conditions). Imidacloprid and clothianidin display distinct, overlapping, abilities to stimulate Kenyon cells, indicating the potential to differentially influence bumblebee behavior. Bee immobility was induced only by imidacloprid, and an increased vulnerability to clothianidin toxicity only occurred following chronic exposure to clothianidin or thiamethoxam. At the whole colony level, only thiamethoxam altered the sex ratio (more males present) and only clothianidin increased queen production. Finally, both imidacloprid and thiamethoxam caused deficits in colony strength, while no detrimental effects of clothianidin were observed. Given these findings, neonicotinoid risk needs to be considered independently for each compound and target species.

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

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

Embeddings into Thompson's group V and coCF groups
http://hdl.handle.net/10023/8747
Lehnert and Schweitzer show in [21] that R. Thompson's group V is a cocontextfree (coCF ) group, thus implying that all of its finitely generated subgroups are also coCF groups. Also, Lehnert shows in his thesis that V embeds inside the coCF group QAut(T2;c), which is a group of particular bijections on the vertices of an infinite binary 2edgecolored tree, and he conjectures that QAut(T2;c) is a universal coCF group. We show that QAut(T2;c) embeds into V , and thus obtain a new form for Lehnert's conjecture. Following up on these ideas, we begin work to build a representation theory into R. Thompson's group V . In particular we classify precisely which BaumslagSolitar groups embed into V .
Thu, 28 Apr 2016 00:00:00 GMT
http://hdl.handle.net/10023/8747
20160428T00:00:00Z
Bleak, Collin
Matucci, Francesco
Neunhöffer, Max
Lehnert and Schweitzer show in [21] that R. Thompson's group V is a cocontextfree (coCF ) group, thus implying that all of its finitely generated subgroups are also coCF groups. Also, Lehnert shows in his thesis that V embeds inside the coCF group QAut(T2;c), which is a group of particular bijections on the vertices of an infinite binary 2edgecolored tree, and he conjectures that QAut(T2;c) is a universal coCF group. We show that QAut(T2;c) embeds into V , and thus obtain a new form for Lehnert's conjecture. Following up on these ideas, we begin work to build a representation theory into R. Thompson's group V . In particular we classify precisely which BaumslagSolitar groups embed into V .

Gauging allowable harm limits to cumulative, sublethal effects of human activities on wildlife : a casestudy approach using two whale populations
http://hdl.handle.net/10023/8716
As sublethal human pressures on marine wildlife and their habitats increase and interact in complex ways, there is a pressing need for methods to quantify cumulative impacts of these stressors on populations, and policy decisions about allowable harm limits. Few studies quantify population consequences of individual stressors, and fewer quantify synergistic effects. Incorporating all sources of uncertainty can cause predictions to span the range from negligible to catastrophic. Two places were identified to bound this problem through energetic mechanisms that reduce prey available to individuals. First, the US Marine Mammal Protection Act's Potential Biological Removal (PBR) equation was used as a placeholder allowable harm limit to represent the number of animals that can be removed annually without depleting a population below agreedupon management targets. That rephrased the research question from, “How big could cumulative impacts be?” to “How big would cumulative impacts have to be to exceed an agreedupon threshold?” Secondly, two datarich case studies, namely Gulf of Maine humpback and northeast Pacific resident killer whales, were used as examples to parameterize the weakest link, namely between prey availability and demography. Given no additional information, the model predicted that human activities need only reduce prey available to the killer whale population by ~10% to cause a populationlevel take, through reduced fecundity and/or survival, equivalent to PBR. By contrast, in the humpback population, reduction in prey availability of ~50% was needed to cause a similar, PBRsized effect. The paper describes an approach – results are merely illustrative. The two case studies differ in prey specialization, life history, and, no doubt, proximity to carrying capacity. This method of inverting the problem refocuses discussions around what the level of prey depletion – via competition with commercial fisheries, displacement from feeding areas through noisegenerating activities, or acoustic masking of signals used to detect prey – would have to occur to exceed allowable harm limits set for lethal takes in fisheries or other, more easily quantifiable, human activities.
Rob Williams was supported by a Marie Curie International Incoming Fellowship within the 7th European Community Framework Programme (Project CONCEAL, FP7, PIIFGA2009253407).
Mon, 01 Aug 2016 00:00:00 GMT
http://hdl.handle.net/10023/8716
20160801T00:00:00Z
Williams, Rob
Thomas, Len
Ashe, Erin
Clark, Christopher W.
Hammond, Philip S.
As sublethal human pressures on marine wildlife and their habitats increase and interact in complex ways, there is a pressing need for methods to quantify cumulative impacts of these stressors on populations, and policy decisions about allowable harm limits. Few studies quantify population consequences of individual stressors, and fewer quantify synergistic effects. Incorporating all sources of uncertainty can cause predictions to span the range from negligible to catastrophic. Two places were identified to bound this problem through energetic mechanisms that reduce prey available to individuals. First, the US Marine Mammal Protection Act's Potential Biological Removal (PBR) equation was used as a placeholder allowable harm limit to represent the number of animals that can be removed annually without depleting a population below agreedupon management targets. That rephrased the research question from, “How big could cumulative impacts be?” to “How big would cumulative impacts have to be to exceed an agreedupon threshold?” Secondly, two datarich case studies, namely Gulf of Maine humpback and northeast Pacific resident killer whales, were used as examples to parameterize the weakest link, namely between prey availability and demography. Given no additional information, the model predicted that human activities need only reduce prey available to the killer whale population by ~10% to cause a populationlevel take, through reduced fecundity and/or survival, equivalent to PBR. By contrast, in the humpback population, reduction in prey availability of ~50% was needed to cause a similar, PBRsized effect. The paper describes an approach – results are merely illustrative. The two case studies differ in prey specialization, life history, and, no doubt, proximity to carrying capacity. This method of inverting the problem refocuses discussions around what the level of prey depletion – via competition with commercial fisheries, displacement from feeding areas through noisegenerating activities, or acoustic masking of signals used to detect prey – would have to occur to exceed allowable harm limits set for lethal takes in fisheries or other, more easily quantifiable, human activities.

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

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

Capturerecapture abundance estimation using a semicomplete data likelihood approach
http://hdl.handle.net/10023/8690
Capturerecapture data are often collected when abundance estimation is of interest. In the presence of unobserved individual heterogeneity, specified on a continuous scale for the capture probabilities, the likelihood is not generally available in closed form, but expressible only as an analytically intractable integral. Modelfitting algorithms to estimate abundance most notably include a numerical approximation for the likelihood or use of a Bayesian data augmentation technique considering the complete data likelihood. We consider a Bayesian hybrid approach, defining a "semicomplete" data likelihood, composed of the product of a complete data likelihood component for individuals seen at least once within the study and a marginal data likelihood component for the individuals not seen within the study, approximated using numerical integration. This approach combines the advantages of the two different approaches, with the semicomplete likelihood component specified as a single integral (over the dimension of the individual heterogeneity component). In addition, the models can be fitted within BUGS/JAGS (commonly used for the Bayesian complete data likelihood approach) but with significantly improved computational efficiency compared to the commonly used superpopulation data augmentation approaches (between about 10 and 77 times more efficient in the two examples we consider). The semicomplete likelihood approach is flexible and applicable to a range of models, including spatially explicit capturerecapture models. The modelfitting approach is applied to two different datasets corresponding to the closed population model Mh for snowshoe hare data and a spatially explicit capturerecapture model applied to gibbon data.
Tue, 01 Mar 2016 00:00:00 GMT
http://hdl.handle.net/10023/8690
20160301T00:00:00Z
King, Ruth
T. McClintock, Brett
Kidney, Darren
Borchers, David
Capturerecapture data are often collected when abundance estimation is of interest. In the presence of unobserved individual heterogeneity, specified on a continuous scale for the capture probabilities, the likelihood is not generally available in closed form, but expressible only as an analytically intractable integral. Modelfitting algorithms to estimate abundance most notably include a numerical approximation for the likelihood or use of a Bayesian data augmentation technique considering the complete data likelihood. We consider a Bayesian hybrid approach, defining a "semicomplete" data likelihood, composed of the product of a complete data likelihood component for individuals seen at least once within the study and a marginal data likelihood component for the individuals not seen within the study, approximated using numerical integration. This approach combines the advantages of the two different approaches, with the semicomplete likelihood component specified as a single integral (over the dimension of the individual heterogeneity component). In addition, the models can be fitted within BUGS/JAGS (commonly used for the Bayesian complete data likelihood approach) but with significantly improved computational efficiency compared to the commonly used superpopulation data augmentation approaches (between about 10 and 77 times more efficient in the two examples we consider). The semicomplete likelihood approach is flexible and applicable to a range of models, including spatially explicit capturerecapture models. The modelfitting approach is applied to two different datasets corresponding to the closed population model Mh for snowshoe hare data and a spatially explicit capturerecapture model applied to gibbon data.

Consistency in eyewitness reports of aquatic "monsters"
http://hdl.handle.net/10023/8676
Little work has been undertaken on the consistency/repeatabilityof reports of natural historical anomalies. Such information is usefulin understanding the reporting process associated with such accountsand distinguishing any underlying biological signal. Here we used intraclasscorrelation as a measure of consistency in descriptions of a variety of quantitative features from a large collection of firsthand accounts of apparentlyunknown aquatic animals (hereafter “monsters”) in each of two differentcases. In the first case, same observer, same encounter (sose), the correlationwas estimated from two different accounts of the same event from thesame witness. In the second case, the correlation was between two differentobservers of the same event (dose). Overall, levels of consistency weresurprisingly high, with length of monster, distance of monster to the witness,and duration of encounter varying between 0.63 and 1. Interestingly,there was no evidence that sose accounts generally had higher consistencythan dose accounts.
Tue, 15 Mar 2016 00:00:00 GMT
http://hdl.handle.net/10023/8676
20160315T00:00:00Z
Paxton, Charles George Mackay
Shine, Adrian J.
Little work has been undertaken on the consistency/repeatabilityof reports of natural historical anomalies. Such information is usefulin understanding the reporting process associated with such accountsand distinguishing any underlying biological signal. Here we used intraclasscorrelation as a measure of consistency in descriptions of a variety of quantitative features from a large collection of firsthand accounts of apparentlyunknown aquatic animals (hereafter “monsters”) in each of two differentcases. In the first case, same observer, same encounter (sose), the correlationwas estimated from two different accounts of the same event from thesame witness. In the second case, the correlation was between two differentobservers of the same event (dose). Overall, levels of consistency weresurprisingly high, with length of monster, distance of monster to the witness,and duration of encounter varying between 0.63 and 1. Interestingly,there was no evidence that sose accounts generally had higher consistencythan dose accounts.

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

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

Graph automatic semigroups
http://hdl.handle.net/10023/8645
In this thesis we examine properties and constructions of graph automatic semigroups, a generalisation of both automatic semigroups and finitely generated FApresentable semigroups.
We consider the properties of graph automatic semigroups, showing that they are independent of the choice of generating set, have decidable word problem, and that if we have a graph automatic structure for a semigroup then we can find one with uniqueness.
Semigroup constructions and their effect on graph automaticity are considered. We show that finitely generated direct products, free products, finitely generated Rees matrix semigroup constructions, zero unions, and ordinal sums all preserve unary graph automaticity, and examine when the converse also holds. We also demonstrate situations where semidirect products, BruckReilly extensions, and semilattice constructions preserve graph automaticity, and consider the conditions we may impose on such constructions in order to ensure that graph automaticity is preserved.
Unary graph automatic semigroups, that is semigroups which have graph automatic structures over a single letter alphabet, are also examined. We consider the form of an automaton recognising multiplication by generators in such a semigroup, and use this to demonstrate various properties of unary graph automatic semigroups. We show that infinite periodic semigroups are not unary graph automatic, and show that we may always find a uniform set of normal forms for a unary graph automatic semigroup. We also determine some necessary conditions for a semigroup to be unary graph automatic, and use this to provide examples of semigroups which are not unary graph automatic.
Finally we consider semigroup constructions for unary graph automatic semigroups. We show that the free product of two semigroups is unary graph automatic if and only if both semigroups are trivial; that direct products do not always preserve unary graph automaticity; and that BruckReilly extensions are never unary graph automatic.
Fri, 24 Jun 2016 00:00:00 GMT
http://hdl.handle.net/10023/8645
20160624T00:00:00Z
Carey, Rachael Marie
In this thesis we examine properties and constructions of graph automatic semigroups, a generalisation of both automatic semigroups and finitely generated FApresentable semigroups.
We consider the properties of graph automatic semigroups, showing that they are independent of the choice of generating set, have decidable word problem, and that if we have a graph automatic structure for a semigroup then we can find one with uniqueness.
Semigroup constructions and their effect on graph automaticity are considered. We show that finitely generated direct products, free products, finitely generated Rees matrix semigroup constructions, zero unions, and ordinal sums all preserve unary graph automaticity, and examine when the converse also holds. We also demonstrate situations where semidirect products, BruckReilly extensions, and semilattice constructions preserve graph automaticity, and consider the conditions we may impose on such constructions in order to ensure that graph automaticity is preserved.
Unary graph automatic semigroups, that is semigroups which have graph automatic structures over a single letter alphabet, are also examined. We consider the form of an automaton recognising multiplication by generators in such a semigroup, and use this to demonstrate various properties of unary graph automatic semigroups. We show that infinite periodic semigroups are not unary graph automatic, and show that we may always find a uniform set of normal forms for a unary graph automatic semigroup. We also determine some necessary conditions for a semigroup to be unary graph automatic, and use this to provide examples of semigroups which are not unary graph automatic.
Finally we consider semigroup constructions for unary graph automatic semigroups. We show that the free product of two semigroups is unary graph automatic if and only if both semigroups are trivial; that direct products do not always preserve unary graph automaticity; and that BruckReilly extensions are never unary graph automatic.

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

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

Randomizationbased models for multitiered experiments : I. a chain of randomizations
http://hdl.handle.net/10023/8636
We derive randomizationbased models for experiments with a chain of randomizations. Estimation theory for these models leads to formulae for the estimators of treatment effects, their standard errors, and expected mean squares in the analysis of variance. We discuss the practicalities in fitting these models and outline the difficulties that can occur, many of which do not arise in twotiered experiments.
Wed, 01 Jun 2016 00:00:00 GMT
http://hdl.handle.net/10023/8636
20160601T00:00:00Z
Bailey, Rosemary Anne
Brien, C. J.
We derive randomizationbased models for experiments with a chain of randomizations. Estimation theory for these models leads to formulae for the estimators of treatment effects, their standard errors, and expected mean squares in the analysis of variance. We discuss the practicalities in fitting these models and outline the difficulties that can occur, many of which do not arise in twotiered experiments.

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

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

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

Tracking marine mammals in 3D using electronic tag data
http://hdl.handle.net/10023/8591
1. Information about atdepth behaviour of marine mammals is fundamental yet very hard to obtain from direct visual observation. Animalborne multisensor electronic tags provide a unique window of observation into such behaviours. 2. Electronic tag sensors allow the estimation of the animal's 3dimensional (3D) orientation, depth and speed. Using tag flow noise level to provide an estimate of animal speed, we extend existing approaches of 3D track reconstruction by allowing the direction of movement to differ from that of the animal's longitudinal axis. 3. Data are processed by a hierarchical Bayesian model that allows processing of multisource data, accounting for measurement errors and testing hypotheses about animal movement by comparing models. 4. We illustrate the approach by reconstructing the 3D track of a 52min deep dive of a Blainville's beaked whale Mesoplodon densirostris adult male fit with a digital tag (DTAG) in the Bahamas. At depth, the whale alternated regular movements at large speed (>1·5 m s1) and more complex movements at lower speed (<1·5 m s1) with diﬀerences between movement and longitudinal axis directions of up to 28°. The reconstructed 3D track agrees closely with independent acousticbased localizations. 5. The approach is potentially applicable to study the underwater behaviour (e.g. response to anthropogenic disturbances) of a wide variety of species of marine mammals ﬁtted with triaxial magnetometer and accelerometer tags.
Date of Acceptance: 05/03/2015
Tue, 01 Sep 2015 00:00:00 GMT
http://hdl.handle.net/10023/8591
20150901T00:00:00Z
Laplanche, C.
Marques, T.A.
Thomas, L.
1. Information about atdepth behaviour of marine mammals is fundamental yet very hard to obtain from direct visual observation. Animalborne multisensor electronic tags provide a unique window of observation into such behaviours. 2. Electronic tag sensors allow the estimation of the animal's 3dimensional (3D) orientation, depth and speed. Using tag flow noise level to provide an estimate of animal speed, we extend existing approaches of 3D track reconstruction by allowing the direction of movement to differ from that of the animal's longitudinal axis. 3. Data are processed by a hierarchical Bayesian model that allows processing of multisource data, accounting for measurement errors and testing hypotheses about animal movement by comparing models. 4. We illustrate the approach by reconstructing the 3D track of a 52min deep dive of a Blainville's beaked whale Mesoplodon densirostris adult male fit with a digital tag (DTAG) in the Bahamas. At depth, the whale alternated regular movements at large speed (>1·5 m s1) and more complex movements at lower speed (<1·5 m s1) with diﬀerences between movement and longitudinal axis directions of up to 28°. The reconstructed 3D track agrees closely with independent acousticbased localizations. 5. The approach is potentially applicable to study the underwater behaviour (e.g. response to anthropogenic disturbances) of a wide variety of species of marine mammals ﬁtted with triaxial magnetometer and accelerometer tags.

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

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

Constructing flagtransitive, pointimprimitive designs
http://hdl.handle.net/10023/8546
We give a construction of a family of designs with a specified pointpartition and determine the subgroup of automorphisms leaving invariant the pointpartition. We give necessary and sufficient conditions for a design in the family to possess a flagtransitive group of automorphisms preserving the specified pointpartition. We give examples of flagtransitive designs in the family, including a new symmetric 2(1408,336,80) design with automorphism group 2^12:((3⋅M22):2) and a construction of one of the families of the symplectic designs (the designs S^−(n) ) exhibiting a flagtransitive, pointimprimitive automorphism group.
Wed, 04 May 2016 00:00:00 GMT
http://hdl.handle.net/10023/8546
20160504T00:00:00Z
Cameron, Peter Jephson
Praeger, Cheryl E.
We give a construction of a family of designs with a specified pointpartition and determine the subgroup of automorphisms leaving invariant the pointpartition. We give necessary and sufficient conditions for a design in the family to possess a flagtransitive group of automorphisms preserving the specified pointpartition. We give examples of flagtransitive designs in the family, including a new symmetric 2(1408,336,80) design with automorphism group 2^12:((3⋅M22):2) and a construction of one of the families of the symplectic designs (the designs S^−(n) ) exhibiting a flagtransitive, pointimprimitive automorphism group.

Permutation groups and transformation semigroups : results and problems
http://hdl.handle.net/10023/8532
J.M. Howie, the influential St Andrews semigroupist, claimed that we value an area of pure mathematics to the extent that (a) it gives rise to arguments that are deep and elegant, and (b) it has interesting interconnections with other parts of pure mathematics. This paper surveys some recent results on the transformation semigroup generated by a permutation group G and a single nonpermutation a. Our particular concern is the influence that properties of G (related to homogeneity, transitivity and primitivity) have on the structure of the semigroup. In the first part of the paper, we consider properties of S=<G,a> such as regularity and generation. The second is a brief report on the synchronization project, which aims to decide in what circumstances S contains an element of rank 1. The paper closes with a list of open problems on permutation groups and linear groups, and some comments about the impact on semigroups are provided. These two research directions outlined above lead to very interesting and challenging problems on primitive permutation groups whose solutions require combining results from several different areas of mathematics, certainly fulfilling both of Howie's elegance and value tests in a new and fascinating way.
Thu, 01 Oct 2015 00:00:00 GMT
http://hdl.handle.net/10023/8532
20151001T00:00:00Z
Araujo, Joao
Cameron, Peter Jephson
J.M. Howie, the influential St Andrews semigroupist, claimed that we value an area of pure mathematics to the extent that (a) it gives rise to arguments that are deep and elegant, and (b) it has interesting interconnections with other parts of pure mathematics. This paper surveys some recent results on the transformation semigroup generated by a permutation group G and a single nonpermutation a. Our particular concern is the influence that properties of G (related to homogeneity, transitivity and primitivity) have on the structure of the semigroup. In the first part of the paper, we consider properties of S=<G,a> such as regularity and generation. The second is a brief report on the synchronization project, which aims to decide in what circumstances S contains an element of rank 1. The paper closes with a list of open problems on permutation groups and linear groups, and some comments about the impact on semigroups are provided. These two research directions outlined above lead to very interesting and challenging problems on primitive permutation groups whose solutions require combining results from several different areas of mathematics, certainly fulfilling both of Howie's elegance and value tests in a new and fascinating way.

Guessing games on trianglefree graphs
http://hdl.handle.net/10023/8518
The guessing game introduced by Riis is a variant of the "guessing your own hats" game and can be played on any simple directed graph G on n vertices. For each digraph G, it is proved that there exists a unique guessing number gn(G) associated to the guessing game played on G. When we consider the directed edge to be bidirected, in other words, the graph G is undirected, Christofides and Markström introduced a method to bound the value of the guessing number from below using the fractional clique cover number kappa_f(G). In particular they showed gn(G) >= V(G)  kappa_f(G). Moreover, it is pointed out that equality holds in this bound if the underlying undirected graph G falls into one of the following categories: perfect graphs, cycle graphs or their complement. In this paper, we show that there are trianglefree graphs that have guessing numbers which do not meet the fractional clique cover bound. In particular, the famous trianglefree HigmanSims graph has guessing number at least 77 and at most 78, while the bound given by fractional clique cover is 50.
Fri, 01 Jan 2016 00:00:00 GMT
http://hdl.handle.net/10023/8518
20160101T00:00:00Z
Cameron, Peter Jephson
Dang, Anh
Riis, Soren
The guessing game introduced by Riis is a variant of the "guessing your own hats" game and can be played on any simple directed graph G on n vertices. For each digraph G, it is proved that there exists a unique guessing number gn(G) associated to the guessing game played on G. When we consider the directed edge to be bidirected, in other words, the graph G is undirected, Christofides and Markström introduced a method to bound the value of the guessing number from below using the fractional clique cover number kappa_f(G). In particular they showed gn(G) >= V(G)  kappa_f(G). Moreover, it is pointed out that equality holds in this bound if the underlying undirected graph G falls into one of the following categories: perfect graphs, cycle graphs or their complement. In this paper, we show that there are trianglefree graphs that have guessing numbers which do not meet the fractional clique cover bound. In particular, the famous trianglefree HigmanSims graph has guessing number at least 77 and at most 78, while the bound given by fractional clique cover is 50.

Some undecidability results for asynchronous transducers and the BrinThompson group 2V
http://hdl.handle.net/10023/8508
Using a result of Kari and Ollinger, we prove that the torsion problem for elements of the BrinThompson group 2V is undecidable. As a result, we show that there does not exist an algorithm to determine whether an element of the rational group R of Grigorchuk, Nekrashevich, and Sushchanskii has finite order. A modification of the construction gives other undecidability results about the dynamics of the action of elements of 2V on Cantor Space. Arzhantseva, Lafont, and Minasyanin prove in 2012 that there exists a finitely presented group with solvable word problem and unsolvable torsion problem. To our knowledge, 2V furnishes the first concrete example of such a group, and gives an example of a direct undecidability result in the extended family of R. Thompson type groups.
Tue, 29 Mar 2016 00:00:00 GMT
http://hdl.handle.net/10023/8508
20160329T00:00:00Z
Belk, James
Bleak, Collin
Using a result of Kari and Ollinger, we prove that the torsion problem for elements of the BrinThompson group 2V is undecidable. As a result, we show that there does not exist an algorithm to determine whether an element of the rational group R of Grigorchuk, Nekrashevich, and Sushchanskii has finite order. A modification of the construction gives other undecidability results about the dynamics of the action of elements of 2V on Cantor Space. Arzhantseva, Lafont, and Minasyanin prove in 2012 that there exists a finitely presented group with solvable word problem and unsolvable torsion problem. To our knowledge, 2V furnishes the first concrete example of such a group, and gives an example of a direct undecidability result in the extended family of R. Thompson type groups.

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

Distance sampling with a random scale detection function
http://hdl.handle.net/10023/8454
Distance sampling was developed to estimate wildlife abundance from observational surveys with uncertain detection in the search area. We present novel analysis methods for estimating detection probabilities that make use of random effects models to allow for unmodeled heterogeneity in detection. The scale parameter of the halfnormal detection function is modeled by means of an intercept plus an error term varying with detections, normally distributed with zero mean and unknown variance. In contrast to conventional distance sampling methods, our approach can deal with longtailed detection functions without truncation. Compared to a fixed effect covariate approach, we think of the random effect as a covariate with unknown values and integrate over the random effect. We expand the random scale to a mixed scale model by adding fixed effect covariates. We analyzed simulated data with large sample sizes to demonstrate that the code performs correctly for random and mixed effect models. We also generated replicate simulations with more practical sample sizes ((Formula presented.)) and compared the random scale halfnormal with the hazard rate detection function. As expected each estimation model was best for different simulation models. We illustrate the mixed effect modeling approach using harbor porpoise vessel survey data where the mixed effect model provided an improved model fit in comparison to a fixed effect model with the same covariates. We propose that a random or mixed effect model of the detection function scale be adopted as one of the standard approaches for fitting detection functions in distance sampling.
Cornelia Oedekoven was supported by a studentship jointly funded by the University of St Andrews and EPSRC, through the National Centre for Statistical Ecology (EPSRC Grant EP/C522702/1). Hans Skaug thanks the Center for Stock Assessment Research for facilitating his visit to University of California, Santa Cruz.
Tue, 01 Dec 2015 00:00:00 GMT
http://hdl.handle.net/10023/8454
20151201T00:00:00Z
Oedekoven, C.S.
Laake, J.L.
Skaug, H.J.
Distance sampling was developed to estimate wildlife abundance from observational surveys with uncertain detection in the search area. We present novel analysis methods for estimating detection probabilities that make use of random effects models to allow for unmodeled heterogeneity in detection. The scale parameter of the halfnormal detection function is modeled by means of an intercept plus an error term varying with detections, normally distributed with zero mean and unknown variance. In contrast to conventional distance sampling methods, our approach can deal with longtailed detection functions without truncation. Compared to a fixed effect covariate approach, we think of the random effect as a covariate with unknown values and integrate over the random effect. We expand the random scale to a mixed scale model by adding fixed effect covariates. We analyzed simulated data with large sample sizes to demonstrate that the code performs correctly for random and mixed effect models. We also generated replicate simulations with more practical sample sizes ((Formula presented.)) and compared the random scale halfnormal with the hazard rate detection function. As expected each estimation model was best for different simulation models. We illustrate the mixed effect modeling approach using harbor porpoise vessel survey data where the mixed effect model provided an improved model fit in comparison to a fixed effect model with the same covariates. We propose that a random or mixed effect model of the detection function scale be adopted as one of the standard approaches for fitting detection functions in distance sampling.

Weak collisionless shocks in laserplasmas
http://hdl.handle.net/10023/8442
We obtain a theory describing laminar shocklike structures in a collisionless plasma and examine the parameter limits, in terms of the ion sound Mach number and the electron/ion temperature ratio, within which these structures exist. The essential feature is the inclusion of finite ion temperature with the result that some ions are reflected from a potential ramp. This destroys the symmetry between upstream and downstream regions that would otherwise give the wellknown ion solitary wave solution. We have shown earlier (Cairns et al 2014 Phys. Plasmas 21 022112) that such structures may be relevant to problems such as the existence of strong, localized electric fields observed in laser compressed pellets and laser acceleration of ions. Here we present results on the way in which these structures may produce species separation in fusion targets and suggest that it may be possible to use shock ion acceleration for fast ignition.
Wed, 01 Apr 2015 00:00:00 GMT
http://hdl.handle.net/10023/8442
20150401T00:00:00Z
Cairns, R. A.
Bingham, R.
Trines, R. G. M.
Norreys, P.
We obtain a theory describing laminar shocklike structures in a collisionless plasma and examine the parameter limits, in terms of the ion sound Mach number and the electron/ion temperature ratio, within which these structures exist. The essential feature is the inclusion of finite ion temperature with the result that some ions are reflected from a potential ramp. This destroys the symmetry between upstream and downstream regions that would otherwise give the wellknown ion solitary wave solution. We have shown earlier (Cairns et al 2014 Phys. Plasmas 21 022112) that such structures may be relevant to problems such as the existence of strong, localized electric fields observed in laser compressed pellets and laser acceleration of ions. Here we present results on the way in which these structures may produce species separation in fusion targets and suggest that it may be possible to use shock ion acceleration for fast ignition.

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

Wild attractors and thermodynamic formalism
http://hdl.handle.net/10023/8394
Fibonacci unimodal maps can have a wild Cantor attractor, and hence be Lebesgue dissipative, depending on the order of the critical point. We present a oneparameter family ƒλ of countably piecewise linear unimodal Fibonacci maps in order to study the thermodynamic formalism of dynamics where dissipativity of Lebesgue (and conformal) measure is responsible for phase transitions. We show that for the potential φt = t log ƒλ', there is a unique phase transition at some t1 ≤ 1, and the pressure P(φt ) is analytic (with unique equilibrium state) elsewhere. The pressure is majorised by a nonanalytic C∞ curve (with all derivatives equal to 0 at t1 < 1) at the emergence of a wild attractor, whereas the phase transition at t1 = 1 can be of any finite order for those λ for which ƒλ is Lebesgue conservative. We also obtain results on the existence of conformal measures and equilibrium states, as well as the hyperbolic dimension and the dimension of the basin of ω(c).
MT was partially supported by NSF Grants DMS 0606343 and DMS 0908093.
Tue, 01 Sep 2015 00:00:00 GMT
http://hdl.handle.net/10023/8394
20150901T00:00:00Z
Bruin, Henk
Todd, Michael John
Fibonacci unimodal maps can have a wild Cantor attractor, and hence be Lebesgue dissipative, depending on the order of the critical point. We present a oneparameter family ƒλ of countably piecewise linear unimodal Fibonacci maps in order to study the thermodynamic formalism of dynamics where dissipativity of Lebesgue (and conformal) measure is responsible for phase transitions. We show that for the potential φt = t log ƒλ', there is a unique phase transition at some t1 ≤ 1, and the pressure P(φt ) is analytic (with unique equilibrium state) elsewhere. The pressure is majorised by a nonanalytic C∞ curve (with all derivatives equal to 0 at t1 < 1) at the emergence of a wild attractor, whereas the phase transition at t1 = 1 can be of any finite order for those λ for which ƒλ is Lebesgue conservative. We also obtain results on the existence of conformal measures and equilibrium states, as well as the hyperbolic dimension and the dimension of the basin of ω(c).

Particleincell simulations of collisionless magnetic reconnection with a nonuniform guide field
http://hdl.handle.net/10023/8386
Results are presented of a first study of collisionless magnetic reconnection starting from a recently found exact nonlinear forcefree VlasovMaxwell equilibrium. The initial state has a Harris sheet magnetic field profile in one direction and a nonuniform guide field in a second direction, resulting in a spatially constant magnetic field strength as well as a constant initial plasma density and plasma pressure. It is found that the reconnection process initially resembles guide field reconnection, but that a gradual transition to antiparallel reconnection happens as the system evolves. The time evolution of a number of plasma parameters is investigated, and the results are compared with simulations starting from a Harris sheet equilibrium and a Harris sheet plus constant guide field equilibrium.
Wed, 02 Mar 2016 00:00:00 GMT
http://hdl.handle.net/10023/8386
20160302T00:00:00Z
Wilson, Fiona
Neukirch, Thomas
Hesse, Michael
Harrison, Michael G.
Stark, Craig R.
Results are presented of a first study of collisionless magnetic reconnection starting from a recently found exact nonlinear forcefree VlasovMaxwell equilibrium. The initial state has a Harris sheet magnetic field profile in one direction and a nonuniform guide field in a second direction, resulting in a spatially constant magnetic field strength as well as a constant initial plasma density and plasma pressure. It is found that the reconnection process initially resembles guide field reconnection, but that a gradual transition to antiparallel reconnection happens as the system evolves. The time evolution of a number of plasma parameters is investigated, and the results are compared with simulations starting from a Harris sheet equilibrium and a Harris sheet plus constant guide field equilibrium.

Description and seasonal detection of two potential whale calls recorded in the Indian Ocean
http://hdl.handle.net/10023/8382
Unidentified acoustic signals are recorded by hydrophones placed in the world's oceans. Some of these sounds are suspected to originate from marine mammals. In this study, two acoustic signals recorded by two arrays at Diego Garcia in the northern Indian Ocean are described. Data were available between January 2002 and December 2003. Signals were detected manually using longterm spectral average plots. Time and frequency measurements were taken from a sample of both signals. The first unidentified signal [Diego Garcia Downsweep (DGD)] consisted of two main components. The mean frequency range of the entire signal was 19.345.0 Hz, with a mean duration of 36.5 s (n = 22). Detections of DGD at the northern array peaked in the austral summer, though detections at the southern array peaked during winter and spring. The second unidentified signal [Diego Garcia Croak (DGC)] consisted of one component with a mean frequency range of 16.949.6 Hz. The mean duration of the signal was 13.1 s (n = 10). Detections of DGC did not follow a clear seasonal pattern. These signals followed characteristics of biological sources, suggesting that they could be whale calls. Fin whale calls and possible blue whales Dcalls were also identified in the data.
Tue, 01 Sep 2015 00:00:00 GMT
http://hdl.handle.net/10023/8382
20150901T00:00:00Z
Sousa, Andreia G
Harris, Danielle
Unidentified acoustic signals are recorded by hydrophones placed in the world's oceans. Some of these sounds are suspected to originate from marine mammals. In this study, two acoustic signals recorded by two arrays at Diego Garcia in the northern Indian Ocean are described. Data were available between January 2002 and December 2003. Signals were detected manually using longterm spectral average plots. Time and frequency measurements were taken from a sample of both signals. The first unidentified signal [Diego Garcia Downsweep (DGD)] consisted of two main components. The mean frequency range of the entire signal was 19.345.0 Hz, with a mean duration of 36.5 s (n = 22). Detections of DGD at the northern array peaked in the austral summer, though detections at the southern array peaked during winter and spring. The second unidentified signal [Diego Garcia Croak (DGC)] consisted of one component with a mean frequency range of 16.949.6 Hz. The mean duration of the signal was 13.1 s (n = 10). Detections of DGC did not follow a clear seasonal pattern. These signals followed characteristics of biological sources, suggesting that they could be whale calls. Fin whale calls and possible blue whales Dcalls were also identified in the data.

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

Exploring dependence between categorical variables : benefits and limitations of using variable selection within Bayesian clustering in relation to loglinear modelling with interaction terms
http://hdl.handle.net/10023/8356
This manuscript is concerned with relating two approaches that can be used to explore complex dependence structures between categorical variables, namely Bayesian partitioning of the covariate space incorporating a variable selection procedure that highlights the covariates that drive the clustering, and loglinear modelling with interaction terms. We derive theoretical results on this relation and discuss if they can be employed to assist loglinear model determination, demonstrating advantages and limitations with simulated and real data sets. The main advantage concerns sparse contingency tables. Inferences from clustering can potentially reduce the number of covariates considered and, subsequently, the number of competing loglinear models, making the exploration of the model space feasible. Variable selection within clustering can inform on marginal independence in general, thus allowing for a more efficient exploration of the loglinear model space. However, we show that the clustering structure is not informative on the existence of interactions in a consistent manner. This work is of interest to those who utilize loglinear models, as well as practitioners such as epidemiologists that use clustering models to reduce the dimensionality in the data and to reveal interesting patterns on how covariates combine.
This work was supported by MRC grant G1002319.
Wed, 01 Jun 2016 00:00:00 GMT
http://hdl.handle.net/10023/8356
20160601T00:00:00Z
Papathomas, Michail
Richardson, Sylvia
This manuscript is concerned with relating two approaches that can be used to explore complex dependence structures between categorical variables, namely Bayesian partitioning of the covariate space incorporating a variable selection procedure that highlights the covariates that drive the clustering, and loglinear modelling with interaction terms. We derive theoretical results on this relation and discuss if they can be employed to assist loglinear model determination, demonstrating advantages and limitations with simulated and real data sets. The main advantage concerns sparse contingency tables. Inferences from clustering can potentially reduce the number of covariates considered and, subsequently, the number of competing loglinear models, making the exploration of the model space feasible. Variable selection within clustering can inform on marginal independence in general, thus allowing for a more efficient exploration of the loglinear model space. However, we show that the clustering structure is not informative on the existence of interactions in a consistent manner. This work is of interest to those who utilize loglinear models, as well as practitioners such as epidemiologists that use clustering models to reduce the dimensionality in the data and to reveal interesting patterns on how covariates combine.

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

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

Bayesian sequential tests of the initial size of a linear pure death process
http://hdl.handle.net/10023/8286
We provide a recursive algorithm for determining the sampling plans of invariant Bayesian sequential tests of the initial size of a linear pure death process of unknown rate. These tests compare favourably with the corresponding truncated sequential probability ratio tests.
Fri, 01 May 2015 00:00:00 GMT
http://hdl.handle.net/10023/8286
20150501T00:00:00Z
Goudie, I.B.J.
We provide a recursive algorithm for determining the sampling plans of invariant Bayesian sequential tests of the initial size of a linear pure death process of unknown rate. These tests compare favourably with the corresponding truncated sequential probability ratio tests.

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

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

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

A singlestation method for the detection, classification and location of fin whale calls using oceanbottom seismic stations
http://hdl.handle.net/10023/8064
Passive seismic monitoring in the oceans uses longterm deployments of Ocean Bottom Seismometers (OBSs). An OBS usually records the three components of ground motion and pressure, typically at 100Hz. This makes the OBS an ideal tool to investigate fin and blue whales that vocalize at frequencies below 45Hz. Previous applications of OBS data to locate whale calls have relied on single channel analyses that disregard the information that is conveyed by the horizontal seismic channels. Recently, Harris, Matias, Thomas, Harwood, and Geissler [J. Acoust. Soc. Am. 134, 35223535 (2013)] presented a method that used all four channels recorded by one OBS to derive the range and azimuth of fin whale calls. In this work, the detection, classification, and ranging of calls using this fourchannel method were further investigated, focusing on methods to increase the accuracy of range estimates to direct path arrivals. Corrections to account for the influences of the sound speed in the water layer and the velocity structure in the top strata of the seabed were considered. The single station method discussed here is best implemented when OBSs have been deployed in deep water on top of seabed strata with low Pwave velocity. These conditions maximize the ability to detect and estimate ranges to fin whale calls.
Wed, 01 Jul 2015 00:00:00 GMT
http://hdl.handle.net/10023/8064
20150701T00:00:00Z
Matias, L.
Harris, D.
Passive seismic monitoring in the oceans uses longterm deployments of Ocean Bottom Seismometers (OBSs). An OBS usually records the three components of ground motion and pressure, typically at 100Hz. This makes the OBS an ideal tool to investigate fin and blue whales that vocalize at frequencies below 45Hz. Previous applications of OBS data to locate whale calls have relied on single channel analyses that disregard the information that is conveyed by the horizontal seismic channels. Recently, Harris, Matias, Thomas, Harwood, and Geissler [J. Acoust. Soc. Am. 134, 35223535 (2013)] presented a method that used all four channels recorded by one OBS to derive the range and azimuth of fin whale calls. In this work, the detection, classification, and ranging of calls using this fourchannel method were further investigated, focusing on methods to increase the accuracy of range estimates to direct path arrivals. Corrections to account for the influences of the sound speed in the water layer and the velocity structure in the top strata of the seabed were considered. The single station method discussed here is best implemented when OBSs have been deployed in deep water on top of seabed strata with low Pwave velocity. These conditions maximize the ability to detect and estimate ranges to fin whale calls.

An MHD avalanche in a multithreaded coronal loop
http://hdl.handle.net/10023/8061
For the first time, we demonstrate how an MHD avalanche might occur in a multithreaded coronal loop. Considering 23 nonpotential magnetic threads within a loop, we use 3D MHD simulations to show that only one thread needs to be unstable in order to start an avalanche even when the others are below marginal stability. This has significant implications for coronal heating in that it provides for energy dissipation with a trigger mechanism. The instability of the unstable thread follows the evolution determined in many earlier investigations. However, once one stable thread is disrupted, it coalesces with a neighbouring thread and this process disrupts other nearby threads. Coalescence with these disrupted threads then occurs leading to the disruption of yet more threads as the avalanche develops. Magnetic energy is released in discrete bursts as the surrounding stable threads are disrupted. The volume integrated heating, as a function of time, shows short spikes suggesting that the temporal form of the heating is more like that of \textit{nanoflares} than of constant heating.
We acknowledge the financial support of STFC through the Consolidated grants to the University of St Andrews and the University of Manchester.
Mon, 18 Jan 2016 00:00:00 GMT
http://hdl.handle.net/10023/8061
20160118T00:00:00Z
Hood, Alan William
Cargill, Peter
Browning, Philippa
Tam, Kuan
For the first time, we demonstrate how an MHD avalanche might occur in a multithreaded coronal loop. Considering 23 nonpotential magnetic threads within a loop, we use 3D MHD simulations to show that only one thread needs to be unstable in order to start an avalanche even when the others are below marginal stability. This has significant implications for coronal heating in that it provides for energy dissipation with a trigger mechanism. The instability of the unstable thread follows the evolution determined in many earlier investigations. However, once one stable thread is disrupted, it coalesces with a neighbouring thread and this process disrupts other nearby threads. Coalescence with these disrupted threads then occurs leading to the disruption of yet more threads as the avalanche develops. Magnetic energy is released in discrete bursts as the surrounding stable threads are disrupted. The volume integrated heating, as a function of time, shows short spikes suggesting that the temporal form of the heating is more like that of \textit{nanoflares} than of constant heating.

Using species proportions to quantify turnover in biodiversity
http://hdl.handle.net/10023/8033
Quantifying species turnover is an important aspect of biodiversity monitoring. Turnover measures are usually based on species presence/absence data, reflecting the rate at which species are replaced. However, measures that reflect the rate at which individuals of a species are replaced by individuals of another species are far more sensitive to change. In this paper, we propose families of turnover measures that reflect changes in species proportions. We study the properties of our measures, and use simulation to assess their success in detecting turnover. Using data on the British farmland bird community from the breeding bird survey, we evaluate our measures to quantify temporal turnover and how it varies across the British mainland.
We are very grateful to all the volunteers who have contributed to the BBS. Yuan was funded by EPSRC/NERC grant EP/1000917/1. Harrison was funded by the Scottish Government’s Centre of Expertise ClimateXChange (www.climatexchange.org.uk).
Wed, 01 Jun 2016 00:00:00 GMT
http://hdl.handle.net/10023/8033
20160601T00:00:00Z
Yuan, Yuan
Buckland, Stephen Terrence
Harrison, Phil
Foss, Sergey
Johnston, Alison
Quantifying species turnover is an important aspect of biodiversity monitoring. Turnover measures are usually based on species presence/absence data, reflecting the rate at which species are replaced. However, measures that reflect the rate at which individuals of a species are replaced by individuals of another species are far more sensitive to change. In this paper, we propose families of turnover measures that reflect changes in species proportions. We study the properties of our measures, and use simulation to assess their success in detecting turnover. Using data on the British farmland bird community from the breeding bird survey, we evaluate our measures to quantify temporal turnover and how it varies across the British mainland.

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

Efficient abstracting of dive profiles using a brokenstick model
http://hdl.handle.net/10023/7972
For diving animals, animalborne sensors are used to collect timedepth information for studying behaviour, ranging patterns and foraging ecology. Often, this information needs to be compressed for storage or transmission. Widely used devices called conductivitytemperaturedepth satellite relay data loggers (CTDSRDLs) sample time and depth at high resolution during a dive and then abstract the timedepth trajectory using a brokenstick model (BSM). This approximation method can summarize efficiently the curvilinear shape of a dive, using a piecewise linear shape with a small, fixed number of vertices, or break points. We present the process of abstracting dives using the BSM and quantify its performance, by measuring the uncertainty associated with the profiles it produces. We develop a method for obtaining a confidence zone and an index for the goodnessoffit (dive zone index, DZI) for abstracted dive profiles. We validate our results with a case study using dives from elephant seals (Mirounga spp.). We use generalized additive models (GAMs) to determine whether the DZI can be used as a proxy for an absolute measure of fit and investigate the relationship between the DZI and the dive shape. We found a strong correlation between the residual sum of squares (RSS) for the difference between the detailed and abstracted profiles, and the DZI and maximum residual (R4), for dives resulting from CTDSRDLs (69% deviance explained). On its own, the DZI explained a lower percentage of deviance which was variable for abstracted dives with different numbers of break points. We also found evidence for systematic differences in the DZI for different dive shapes (65% deviance explained). Although the proportional loss of information in the abstraction of timedepth dive profiles by BSM is high, what remains is sufficient to infer goodnessoffit of the abstracted profile by reversing the abstraction process. Our results suggest that together the DZI and R4 can be used as a proxy for the RSS, and we present the method for obtaining these metrics for BSMabstracted profiles.
This work was supported by SMRU Ltd (now SMRU Marine) in the form of a PhD fellowship (T.P.). Completion of the manuscript was supported by a National Research Foundation Scarce Skills Postdoctoral Fellowship at the University of Cape Town, South Africa (T.P.). The CTDSRDL data presented in this manuscript were collected as part of a project funded by the Natural Environment Research Council (NERC) grants NE/E018289/1 and NER/D/S/2002/00426.
Sun, 01 Mar 2015 00:00:00 GMT
http://hdl.handle.net/10023/7972
20150301T00:00:00Z
Photopoulou, T.
Lovell, Philip
Fedak, M.A.
Thomas, L.
Matthiopoulos, J.
For diving animals, animalborne sensors are used to collect timedepth information for studying behaviour, ranging patterns and foraging ecology. Often, this information needs to be compressed for storage or transmission. Widely used devices called conductivitytemperaturedepth satellite relay data loggers (CTDSRDLs) sample time and depth at high resolution during a dive and then abstract the timedepth trajectory using a brokenstick model (BSM). This approximation method can summarize efficiently the curvilinear shape of a dive, using a piecewise linear shape with a small, fixed number of vertices, or break points. We present the process of abstracting dives using the BSM and quantify its performance, by measuring the uncertainty associated with the profiles it produces. We develop a method for obtaining a confidence zone and an index for the goodnessoffit (dive zone index, DZI) for abstracted dive profiles. We validate our results with a case study using dives from elephant seals (Mirounga spp.). We use generalized additive models (GAMs) to determine whether the DZI can be used as a proxy for an absolute measure of fit and investigate the relationship between the DZI and the dive shape. We found a strong correlation between the residual sum of squares (RSS) for the difference between the detailed and abstracted profiles, and the DZI and maximum residual (R4), for dives resulting from CTDSRDLs (69% deviance explained). On its own, the DZI explained a lower percentage of deviance which was variable for abstracted dives with different numbers of break points. We also found evidence for systematic differences in the DZI for different dive shapes (65% deviance explained). Although the proportional loss of information in the abstraction of timedepth dive profiles by BSM is high, what remains is sufficient to infer goodnessoffit of the abstracted profile by reversing the abstraction process. Our results suggest that together the DZI and R4 can be used as a proxy for the RSS, and we present the method for obtaining these metrics for BSMabstracted profiles.

Well quasiorder in combinatorics : embeddings and homomorphisms
http://hdl.handle.net/10023/7963
The notion of well quasiorder (wqo) from the theory of ordered sets often arises naturally in contexts where one deals with infinite collections of structures which can somehow be compared, and it then represents a useful discriminator between ‘tame’ and ‘wild’ such classes. In this article we survey such situations within combinatorics, and attempt to identify promising directions for further research. We argue that these are intimately linked with a more systematic and detailed study of homomorphisms in combinatorics.
Wed, 01 Jul 2015 00:00:00 GMT
http://hdl.handle.net/10023/7963
20150701T00:00:00Z
Huczynska, Sophie
Ruskuc, Nik
The notion of well quasiorder (wqo) from the theory of ordered sets often arises naturally in contexts where one deals with infinite collections of structures which can somehow be compared, and it then represents a useful discriminator between ‘tame’ and ‘wild’ such classes. In this article we survey such situations within combinatorics, and attempt to identify promising directions for further research. We argue that these are intimately linked with a more systematic and detailed study of homomorphisms in combinatorics.

Expert elicitation of seasonal abundance of North Atlantic right whales Eubalaena glacialis in the midAtlantic
http://hdl.handle.net/10023/7921
North Atlantic right whales (Eubalaena glacialis; henceforth right whales) are among the most endangered large whales. Although protected since 1935, their abundance has remained low. Right whales occupy the Atlantic Ocean from southern Greenland and the Gulf of St. Lawrence south to Florida. The highly industrialized midAtlantic region is part of the species’ migratory corridor. Gaps in knowledge of the species’ movements through the midAtlantic limit informed management of stressors to the species. To contribute to filling of these gaps, we elicited estimates of the relative abundance of adult right whales in the midAtlantic during four months, representing each season, from ten experts. We elicited the minimum, maximum, and mode as the number of individuals in a hypothetical population of 100 right whales, and confidence estimates as percentages. For each monthsex combination, we merged the ten experts’ answers into one distribution. The estimated modes of relative abundances of both sexes were highest in January and April (females, 29 and 59; males, 22 and 23) and lowest in July and October (females, five and nine; males, three and five). In some cases, our elicitation results were consistent with the results of studies based on sightings data. However, these studies generally did not adjust for sampling effort, which was low and likely variable. Our results supplement the results of these studies and will increase the accuracy of priors in complementary Bayesian models of right whale abundances and movements through the midAtlantic.
This work was supported in part by US Office of Naval Research (ONR) grants to E.F.: N000140910896 at University of California, Santa Barbara and N000141210274 at University of California, Davis. This work was also supported by ONR grant N000141210286 to the University of St Andrews. In addition, we gratefully acknowledge funding for this work from The Marine Alliance for Science and Technology for Scotland (MASTS). MASTS is funded by the Scottish Funding Council (grant reference HR09011) and contributing institutions.
Wed, 04 Nov 2015 00:00:00 GMT
http://hdl.handle.net/10023/7921
20151104T00:00:00Z
Oedekoven, Cornelia Sabrina
Fleishman, Erica
Hamilton, Philip
Clark, James S.
Schick, Robert Schilling
North Atlantic right whales (Eubalaena glacialis; henceforth right whales) are among the most endangered large whales. Although protected since 1935, their abundance has remained low. Right whales occupy the Atlantic Ocean from southern Greenland and the Gulf of St. Lawrence south to Florida. The highly industrialized midAtlantic region is part of the species’ migratory corridor. Gaps in knowledge of the species’ movements through the midAtlantic limit informed management of stressors to the species. To contribute to filling of these gaps, we elicited estimates of the relative abundance of adult right whales in the midAtlantic during four months, representing each season, from ten experts. We elicited the minimum, maximum, and mode as the number of individuals in a hypothetical population of 100 right whales, and confidence estimates as percentages. For each monthsex combination, we merged the ten experts’ answers into one distribution. The estimated modes of relative abundances of both sexes were highest in January and April (females, 29 and 59; males, 22 and 23) and lowest in July and October (females, five and nine; males, three and five). In some cases, our elicitation results were consistent with the results of studies based on sightings data. However, these studies generally did not adjust for sampling effort, which was low and likely variable. Our results supplement the results of these studies and will increase the accuracy of priors in complementary Bayesian models of right whale abundances and movements through the midAtlantic.

Coprime invariable generation and minimalexponent groups
http://hdl.handle.net/10023/7910
A finite group G is coprimely invariably generated if there exists a set of generators {g1,. .,gu} of G with the property that the orders g1,. .,gu are pairwise coprime and that for all x1,. .,xu∈G the set {g1x1,. .,guxu} generates G.We show that if G is coprimely invariably generated, then G can be generated with three elements, or two if G is soluble, and that G has zero presentation rank. As a corollary, we show that if G is any finite group such that no proper subgroup has the same exponent as G, then G has zero presentation rank. Furthermore, we show that every finite simple group is coprimely invariably generated by two elements, except for O8+(2) which requires three elements.Along the way, we show that for each finite simple group S, and for each partition π1,. .,πu of the primes dividing S, the product of the number kπi(S) of conjugacy classes of πielements satisfies. ∏i=1ukπi(S)≤S2OutS.
Colva RoneyDougal acknowledges the support of EPSRC grant EP/I03582X/1.
Sat, 01 Aug 2015 00:00:00 GMT
http://hdl.handle.net/10023/7910
20150801T00:00:00Z
Detomi, Eloisa
Lucchini, Andrea
RoneyDougal, C.M.
A finite group G is coprimely invariably generated if there exists a set of generators {g1,. .,gu} of G with the property that the orders g1,. .,gu are pairwise coprime and that for all x1,. .,xu∈G the set {g1x1,. .,guxu} generates G.We show that if G is coprimely invariably generated, then G can be generated with three elements, or two if G is soluble, and that G has zero presentation rank. As a corollary, we show that if G is any finite group such that no proper subgroup has the same exponent as G, then G has zero presentation rank. Furthermore, we show that every finite simple group is coprimely invariably generated by two elements, except for O8+(2) which requires three elements.Along the way, we show that for each finite simple group S, and for each partition π1,. .,πu of the primes dividing S, the product of the number kπi(S) of conjugacy classes of πielements satisfies. ∏i=1ukπi(S)≤S2OutS.

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

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

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

Dimension and measure theory of selfsimilar structures with no separation condition
http://hdl.handle.net/10023/7854
We introduce methods to cope with selfsimilar sets when we do not assume any separation condition. For a selfsimilar set K ⊆ ℝᵈ we establish a similarity dimensionlike formula for Hausdorff dimension regardless of any separation condition. By the application of this result we deduce that the Hausdorff measure and Hausdorff content of K are equal, which implies that K is Ahlfors regular if and only if Hᵗ (K) > 0 where t = dim[sub]H K. We further show that if t = dim[sub]H K < 1 then Hᵗ (K) > 0 is also equivalent to the weak separation property. Regarding Hausdorff dimension, we give a dimension approximation method that provides a tool to generalise results on nonoverlapping selfsimilar sets to overlapping selfsimilar sets.
We investigate how the Hausdorff dimension and measure of a selfsimilar set
K ⊆ ℝᵈ behave under linear mappings. This depends on the nature of the group T generated by the orthogonal parts of the defining maps of K. We show that if T is finite then every linear image of K is a graph directed attractor and there exists at least one projection of K such that the dimension drops under projection. In general, with no restrictions on T we establish that Hᵗ (L ∘ O(K)) = Hᵗ (L(K)) for every element O of the closure of T , where L is a linear map and t = dim[sub]H K. We also prove that for disjoint subsets A and B of K we have that Hᵗ (L(A) ∩ L(B)) = 0. Hochman and Shmerkin showed that if T is dense in SO(d; ℝ) and the strong separation condition is satisfied then dim[sub]H (g(K)) = min {dim[sub]H K; l} for every continuously differentiable map g of rank l. We deduce the same result without any separation condition and we generalize a result of Eroğlu by obtaining that Hᵗ (g(K)) = 0.
We show that for the attractor (K1, … ,Kq) of a graph directed iterated function system, for each 1 ≤ j ≤ q and ε > 0 there exists a selfsimilar set K ⊆ Kj that satisfies the strong separation condition and dim[sub]H Kj  ε < dim[sub]H K. We show that we can further assume convenient conditions on the orthogonal parts and similarity ratios of the defining similarities of K. Using this property we obtain results on a range of topics including on dimensions of projections, intersections, distance sets and sums and products of sets.
We study the situations where the Hausdorff measure and Hausdorff content of a set are equal in the critical dimension. Our main result here shows that this equality holds for any subset of a set corresponding to a nontrivial cylinder of an irreducible subshift of finite type, and thus also for any selfsimilar or graph directed selfsimilar set, regardless of separation conditions. The main tool in the proof is an exhaustion lemma for Hausdorff measure based on the Vitali's Covering Theorem. We also give several examples showing that one cannot hope for the equality to hold in general if one moves in a number of the natural directions away from `selfsimilar'. Finally we consider an analogous version of the problem for packing measure. In this case we need the strong separation condition and can only prove that the packing measure and δapproximate packing premeasure coincide for sufficiently small δ > 0.
Mon, 30 Nov 2015 00:00:00 GMT
http://hdl.handle.net/10023/7854
20151130T00:00:00Z
Farkas, Ábel
We introduce methods to cope with selfsimilar sets when we do not assume any separation condition. For a selfsimilar set K ⊆ ℝᵈ we establish a similarity dimensionlike formula for Hausdorff dimension regardless of any separation condition. By the application of this result we deduce that the Hausdorff measure and Hausdorff content of K are equal, which implies that K is Ahlfors regular if and only if Hᵗ (K) > 0 where t = dim[sub]H K. We further show that if t = dim[sub]H K < 1 then Hᵗ (K) > 0 is also equivalent to the weak separation property. Regarding Hausdorff dimension, we give a dimension approximation method that provides a tool to generalise results on nonoverlapping selfsimilar sets to overlapping selfsimilar sets.
We investigate how the Hausdorff dimension and measure of a selfsimilar set
K ⊆ ℝᵈ behave under linear mappings. This depends on the nature of the group T generated by the orthogonal parts of the defining maps of K. We show that if T is finite then every linear image of K is a graph directed attractor and there exists at least one projection of K such that the dimension drops under projection. In general, with no restrictions on T we establish that Hᵗ (L ∘ O(K)) = Hᵗ (L(K)) for every element O of the closure of T , where L is a linear map and t = dim[sub]H K. We also prove that for disjoint subsets A and B of K we have that Hᵗ (L(A) ∩ L(B)) = 0. Hochman and Shmerkin showed that if T is dense in SO(d; ℝ) and the strong separation condition is satisfied then dim[sub]H (g(K)) = min {dim[sub]H K; l} for every continuously differentiable map g of rank l. We deduce the same result without any separation condition and we generalize a result of Eroğlu by obtaining that Hᵗ (g(K)) = 0.
We show that for the attractor (K1, … ,Kq) of a graph directed iterated function system, for each 1 ≤ j ≤ q and ε > 0 there exists a selfsimilar set K ⊆ Kj that satisfies the strong separation condition and dim[sub]H Kj  ε < dim[sub]H K. We show that we can further assume convenient conditions on the orthogonal parts and similarity ratios of the defining similarities of K. Using this property we obtain results on a range of topics including on dimensions of projections, intersections, distance sets and sums and products of sets.
We study the situations where the Hausdorff measure and Hausdorff content of a set are equal in the critical dimension. Our main result here shows that this equality holds for any subset of a set corresponding to a nontrivial cylinder of an irreducible subshift of finite type, and thus also for any selfsimilar or graph directed selfsimilar set, regardless of separation conditions. The main tool in the proof is an exhaustion lemma for Hausdorff measure based on the Vitali's Covering Theorem. We also give several examples showing that one cannot hope for the equality to hold in general if one moves in a number of the natural directions away from `selfsimilar'. Finally we consider an analogous version of the problem for packing measure. In this case we need the strong separation condition and can only prove that the packing measure and δapproximate packing premeasure coincide for sufficiently small δ > 0.

Acoustic sequences in nonhuman animals : a tutorial review and prospectus
http://hdl.handle.net/10023/7848
Animal acoustic communication often takes the form of complex sequences, made up of multiple distinct acoustic units. Apart from the wellknown example of birdsong, other animals such as insects, amphibians,and mammals (including bats, rodents, primates, and cetaceans) also generate complex acoustic sequences. Occasionally, such as with birdsong, the adaptive role of these sequences seems clear (e.g. mate attraction and territorial defence). More often however, researchers have only begun to characterise – let alone understand – the significance and meaning of acoustic sequences. Hypotheses abound, but there is little agreement as to how sequences should be defined and analysed. Our review aims to outline suitable methods for testing these hypotheses, and to describe the major limitations to our current and nearfuture knowledge on questions of acoustic sequences. This review and prospectus is the result of a collaborative effort between 43 scientists from the fields of animal behaviour, ecology and evolution, signal processing, machine learning,quantitative linguistics, and information theory, who gathered for a 2013 workshop entitled, ‘Analysing vocal sequences in animals’. Our goal is to present not just a review of the state of the art, but to propose a methodological framework that summarises what we suggest are the best practices for research in this field,across taxa and across disciplines. We also provide a tutorialstyle introduction to some of the most promising algorithmic approaches for analysing sequences. We divide our review into three sections: identifying the distinct units of an acoustic sequence, describing the different ways that information can be contained within a sequence, and analysing the structure of that sequence. Each of these sections is further subdivided to address the key questions and approaches in that area. We propose a uniform, systematic, and comprehensive approach to studying sequences, with the goal of clarifying research terms used in different fields, and facilitating collaboration and comparative studies. Allowing greater interdisciplinary collaboration will facilitate the investigation of many important questions in the evolution of communication and sociality.
Mon, 01 Feb 2016 00:00:00 GMT
http://hdl.handle.net/10023/7848
20160201T00:00:00Z
Kershenbaum, Arik
Blumstein, Dan
Roch, Marie
Akçay, Çaglar
Backus, Gregory
Bee, Mark A.
Bohn, Kirsten
Cao, Yan
Carter, Gerald
Cäsar, Cristiane
Coen, Michael
De Ruiter, Stacy Lynn
Doyle, Laurance
Edelman, Shimon
FerreriCancho, Ramon
Freeberg, Todd M.
Garland, Ellen Clare
Gustison, Morgan
Harley, Heidi E.
Huetz, Chloé
Hughes, Melissa
Bruno, Julia Hyland
Ilany, Amiyaal
Jin, Dezhe Z.
Johnson, Michael
Ju, Chenghui
Karnowski, Jeremy
Lohr, Bernard
Manser, Marta
McCowan, Brenda
Mercado III, Eduardo
Narins, Peter M.
Piel, Alex
Rice, Megan
Salmi, Roberta
Sasahara, Kazutoshi
Sayigh, Laela
Shiu, Yu
Taylor, Charles
Vallejo, Edgar E.
Waller, Sara
ZamoraGutierrez, Veronica
Animal acoustic communication often takes the form of complex sequences, made up of multiple distinct acoustic units. Apart from the wellknown example of birdsong, other animals such as insects, amphibians,and mammals (including bats, rodents, primates, and cetaceans) also generate complex acoustic sequences. Occasionally, such as with birdsong, the adaptive role of these sequences seems clear (e.g. mate attraction and territorial defence). More often however, researchers have only begun to characterise – let alone understand – the significance and meaning of acoustic sequences. Hypotheses abound, but there is little agreement as to how sequences should be defined and analysed. Our review aims to outline suitable methods for testing these hypotheses, and to describe the major limitations to our current and nearfuture knowledge on questions of acoustic sequences. This review and prospectus is the result of a collaborative effort between 43 scientists from the fields of animal behaviour, ecology and evolution, signal processing, machine learning,quantitative linguistics, and information theory, who gathered for a 2013 workshop entitled, ‘Analysing vocal sequences in animals’. Our goal is to present not just a review of the state of the art, but to propose a methodological framework that summarises what we suggest are the best practices for research in this field,across taxa and across disciplines. We also provide a tutorialstyle introduction to some of the most promising algorithmic approaches for analysing sequences. We divide our review into three sections: identifying the distinct units of an acoustic sequence, describing the different ways that information can be contained within a sequence, and analysing the structure of that sequence. Each of these sections is further subdivided to address the key questions and approaches in that area. We propose a uniform, systematic, and comprehensive approach to studying sequences, with the goal of clarifying research terms used in different fields, and facilitating collaboration and comparative studies. Allowing greater interdisciplinary collaboration will facilitate the investigation of many important questions in the evolution of communication and sociality.

Dose response severity functions for acoustic disturbance in cetaceans using recurrent event survival analysis
http://hdl.handle.net/10023/7845
Behavioral response studies (BRSs) aim to enhance our understanding of the behavior changes made by animals in response to specific exposure levels of different stimuli, often presented in an increasing dosage. Here, we focus on BRSs that aim to understand behavioral responses of freeranging whales and dolphins to manmade acoustic signals (although the methods are applicable more generally). One desired outcome of these studies is doseresponse functions relevant to different species, signals and contexts. We adapted and applied recurrent event survival analysis (Cox proportional hazard models) to data from the 3S BRS project, where multiple behavioral responses of different severities had been observed per experimental exposure and per individual based upon expert scoring. We included species, signal type, exposure number and behavioral state prior to exposure as potential covariates. The best model included all main effect terms, with the exception of exposure number, as well as two interaction terms. The interactions between signal and behavioral state, and between species and behavioral state highlighted that the sensitivity of animals to different signal types (a 6–7 kHz upsweep sonar signal [MFAS] or a 1–2 kHz upsweep sonar signal [LFAS]) depended on their behavioral state (feeding or nonfeeding), and this differed across species. Of the three species included in this analysis (sperm whale [Physeter macrocephalus], killer whale [Orcinus orca] and longfinned pilot whale [Globicephala melas]), killer whales were consistently the most likely to exhibit behavioral responses to naval sonar exposure. We conclude that recurrent event survival analysis provides an effective framework for fitting doseresponse severity functions to data from behavioral response studies. It can provide outputs that can help government and industry to evaluate the potential impacts of anthropogenic sound production in the ocean.
Fri, 20 Nov 2015 00:00:00 GMT
http://hdl.handle.net/10023/7845
20151120T00:00:00Z
Harris, Catriona M
Sadykova, Dinara
De Ruiter, Stacy Lynn
Tyack, Peter Lloyd
Miller, Patrick
Kvadsheim, Petter
Lam, FransPeter
Thomas, Len
Behavioral response studies (BRSs) aim to enhance our understanding of the behavior changes made by animals in response to specific exposure levels of different stimuli, often presented in an increasing dosage. Here, we focus on BRSs that aim to understand behavioral responses of freeranging whales and dolphins to manmade acoustic signals (although the methods are applicable more generally). One desired outcome of these studies is doseresponse functions relevant to different species, signals and contexts. We adapted and applied recurrent event survival analysis (Cox proportional hazard models) to data from the 3S BRS project, where multiple behavioral responses of different severities had been observed per experimental exposure and per individual based upon expert scoring. We included species, signal type, exposure number and behavioral state prior to exposure as potential covariates. The best model included all main effect terms, with the exception of exposure number, as well as two interaction terms. The interactions between signal and behavioral state, and between species and behavioral state highlighted that the sensitivity of animals to different signal types (a 6–7 kHz upsweep sonar signal [MFAS] or a 1–2 kHz upsweep sonar signal [LFAS]) depended on their behavioral state (feeding or nonfeeding), and this differed across species. Of the three species included in this analysis (sperm whale [Physeter macrocephalus], killer whale [Orcinus orca] and longfinned pilot whale [Globicephala melas]), killer whales were consistently the most likely to exhibit behavioral responses to naval sonar exposure. We conclude that recurrent event survival analysis provides an effective framework for fitting doseresponse severity functions to data from behavioral response studies. It can provide outputs that can help government and industry to evaluate the potential impacts of anthropogenic sound production in the ocean.

Speed of convergence for laws of rare events and escape rates
http://hdl.handle.net/10023/7837
We obtain error terms on the rate of convergence to Extreme Value Laws, and to the asymptotic Hitting Time Statistics, for a general class of weakly dependent stochastic processes. The dependence of the error terms on the ‘time’ and ‘length’ scales is very explicit. Specialising to data derived from a class of dynamical systems we find even more detailed error terms, one application of which is to consider escape rates through small holes in these systems.
MT was partially supported by NSF grant DMS 1109587. All authors are supported by FCT (Portugal) projects PTDC/MAT/099493/2008 and PTDC/MAT/120346/2010, which are financed by national and European structural funds through the programs FEDER and COMPETE. All three authors were also supported by CMUP, which is financed by FCT (Portugal) through the programs POCTI and POSI, with national and European structural funds, under the project PEstC/MAT/UI0144/2013.
Wed, 01 Apr 2015 00:00:00 GMT
http://hdl.handle.net/10023/7837
20150401T00:00:00Z
Freitas, Ana
Freitas, Jorge
Todd, Michael John
We obtain error terms on the rate of convergence to Extreme Value Laws, and to the asymptotic Hitting Time Statistics, for a general class of weakly dependent stochastic processes. The dependence of the error terms on the ‘time’ and ‘length’ scales is very explicit. Specialising to data derived from a class of dynamical systems we find even more detailed error terms, one application of which is to consider escape rates through small holes in these systems.

A general framework for animal density estimation from acoustic detections across a fixed microphone array
http://hdl.handle.net/10023/7786
Acoustic monitoring can be an efficient, cheap, noninvasive alternative to physical trapping of individuals. Spatially explicit capturerecapture (SECR) methods have been proposed to estimate calling animal abundance and density from data collected by a fixed array of microphones. However, these methods make some assumptions that are unlikely to hold in many situations, and the consequences of violating these are yet to be investigated. We generalize existing acoustic SECR methodology, enabling these methods to be used in a much wider variety of situations. We incorporate timeofarrival (TOA) data collected by the microphone array, increasing the precision of calling animal density estimates. We use our method to estimate calling male density of the Cape Peninsula Moss Frog Arthroleptella lightfooti. Our method gives rise to an estimator of calling animal density that has negligible bias, and 95% confidence intervals with appropriate coverage. We show that using TOA information can substantially improve estimate precision. Our analysis of the A. lightfooti data provides the first statistically rigorous estimate of calling male density for an anuran population using a microphone array. This method fills a methodological gap in the monitoring of frog populations and is applicable to acoustic monitoring of other species that call or vocalize.
Funding for the frog survey was received from the National Geographic Society/Waitt Grants Program (No. W18411). The EPSRC and NERC helped to fund this research through a PhD grant (No. EP/I000917/1).
Thu, 01 Jan 2015 00:00:00 GMT
http://hdl.handle.net/10023/7786
20150101T00:00:00Z
Stevenson, B.C.
Borchers, D.L.
Altwegg, R.
Swift, R.J.
Gillespie, D.M.
Measey, G.J.
Acoustic monitoring can be an efficient, cheap, noninvasive alternative to physical trapping of individuals. Spatially explicit capturerecapture (SECR) methods have been proposed to estimate calling animal abundance and density from data collected by a fixed array of microphones. However, these methods make some assumptions that are unlikely to hold in many situations, and the consequences of violating these are yet to be investigated. We generalize existing acoustic SECR methodology, enabling these methods to be used in a much wider variety of situations. We incorporate timeofarrival (TOA) data collected by the microphone array, increasing the precision of calling animal density estimates. We use our method to estimate calling male density of the Cape Peninsula Moss Frog Arthroleptella lightfooti. Our method gives rise to an estimator of calling animal density that has negligible bias, and 95% confidence intervals with appropriate coverage. We show that using TOA information can substantially improve estimate precision. Our analysis of the A. lightfooti data provides the first statistically rigorous estimate of calling male density for an anuran population using a microphone array. This method fills a methodological gap in the monitoring of frog populations and is applicable to acoustic monitoring of other species that call or vocalize.

Passive acoustic monitoring of beaked whale densities in the Gulf of Mexico
http://hdl.handle.net/10023/7779
Beaked whales are deep diving elusive animals, difficult to census with conventional visual surveys. Methods are presented for the density estimation of beaked whales, using passive acoustic monitoring data collected at sites in the Gulf of Mexico (GOM) from the period during and following the Deepwater Horizon oil spill (2010–2013). Beaked whale species detected include: Gervais’ (Mesoplodon europaeus), Cuvier’s (Ziphius cavirostris), Blainville’s (Mesoplodon densirostris) and an unknown species of Mesoplodon sp. (designated as Beaked Whale Gulf — BWG). For Gervais’ and Cuvier’s beaked whales, we estimated weekly animal density using two methods, one based on the number of echolocation clicks, and another based on the detection of animal groups during 5 min timebins. Density estimates derived from these two methods were in good general agreement. At two sites in the western GOM, Gervais’ beaked whales were present throughout the monitoring period, but Cuvier’s beaked whales were present only seasonally, with periods of low density during the summer and higher density in the winter. At an eastern GOM site, both Gervais’ and Cuvier’s beaked whales had a high density throughout the monitoring period.
Funding to support the tag data was also received from the MASTS pooling initiative (The Marine Alliance for Science and Technology for Scotland) funded by the Scottish Funding Council (grant reference HR09011) and contributing institutions.
Thu, 12 Nov 2015 00:00:00 GMT
http://hdl.handle.net/10023/7779
20151112T00:00:00Z
Hildebrand, John
BaumannPickering, Simone
Frasier, Kaitlin
Trickey, Jennifer
Merkens, Karlina
Wiggins, Sean
McDonald, Mark
Garrison, Lance
Harris, Danielle
Marques, Tiago A.
Thomas, Len
Beaked whales are deep diving elusive animals, difficult to census with conventional visual surveys. Methods are presented for the density estimation of beaked whales, using passive acoustic monitoring data collected at sites in the Gulf of Mexico (GOM) from the period during and following the Deepwater Horizon oil spill (2010–2013). Beaked whale species detected include: Gervais’ (Mesoplodon europaeus), Cuvier’s (Ziphius cavirostris), Blainville’s (Mesoplodon densirostris) and an unknown species of Mesoplodon sp. (designated as Beaked Whale Gulf — BWG). For Gervais’ and Cuvier’s beaked whales, we estimated weekly animal density using two methods, one based on the number of echolocation clicks, and another based on the detection of animal groups during 5 min timebins. Density estimates derived from these two methods were in good general agreement. At two sites in the western GOM, Gervais’ beaked whales were present throughout the monitoring period, but Cuvier’s beaked whales were present only seasonally, with periods of low density during the summer and higher density in the winter. At an eastern GOM site, both Gervais’ and Cuvier’s beaked whales had a high density throughout the monitoring period.

On simultaneous local dimension functions of subsets of Rd
http://hdl.handle.net/10023/7778
For a subset E ⊑ Rd and x ∈ Rd, the local Hausdorff dimension function of E at x and the local packing dimension function of E at x are defined by (Formula presented.) where dimH and dimP denote the Hausdorff dimension and the packing dimension, respectively. In this note we give a short and simple proof showing that for any pair of continuous functions f,g: Rd → [0, d] with f ≤ g, it is possible to choose a set E that simultaneously has f as its local Hausdorff dimension function and g as its local packing dimension function.
Date of Acceptance: 04/05/2015
Wed, 30 Sep 2015 00:00:00 GMT
http://hdl.handle.net/10023/7778
20150930T00:00:00Z
Olsen, Lars Ole Ronnow
For a subset E ⊑ Rd and x ∈ Rd, the local Hausdorff dimension function of E at x and the local packing dimension function of E at x are defined by (Formula presented.) where dimH and dimP denote the Hausdorff dimension and the packing dimension, respectively. In this note we give a short and simple proof showing that for any pair of continuous functions f,g: Rd → [0, d] with f ≤ g, it is possible to choose a set E that simultaneously has f as its local Hausdorff dimension function and g as its local packing dimension function.

Occurrence, distribution and abundance of cetaceans in Onslow Bay, North Carolina, USA
http://hdl.handle.net/10023/7772
In this paper the occurrence, distribution and abundance of cetaceans in offshore waters of Onslow Bay, North Carolina, USA is described. Between June 2007 and June 2010 monthly aerial and shipboard linetransect surveys were conducted along ten 74km transects placed perpendicular to the shelf break. In total 42,676km of aerial trackline (218 sightings) and 5,209km of vessel trackline (100 sightings) were observed. Seven species of cetaceans were observed, but the fauna was dominated strongly by common bottlenose and Atlantic spotted dolphins. Both species were present yearround in the study area. Using photoidentification techniques, five bottlenose dolphins and one spotted dolphin were resighted during the threeyear period. In general, the abundance of cetaceans in Onslow Bay was low and too few sightings were made to estimate monthly abundances for species other than bottlenose and spotted dolphins. Maximum monthly abundances of bottlenose and spotted dolphins were 4,100 (95% CI: 1,300–9,400) in May 2010 and 6,000 (95% CI: 2,500–17,400) in March 2009, respectively. Bottlenose dolphins were found throughout the study area, although they were encountered most frequently just off the shelf break. In contrast, spotted dolphins exhibited a strong preference for waters over the continental shelf and were not encountered beyond the shelf break.
Wed, 01 Jan 2014 00:00:00 GMT
http://hdl.handle.net/10023/7772
20140101T00:00:00Z
Read, Andrew, J.
Barco, S.
Bell, J.
Borchers, David Louis
Burt, M Louise
Cummings, E.W.
Dunn, J.
Fougeres, J.
Hazen, L.
WilliamsHodge, L.E.
Laura, AM.
McAlarney, R.J.
Nilsson, P.
Pabst, D.A.
Paxton, Charles G. M.
Schneider, S.Z.
Urian, Kim
Waples, D.M.
McLellan, W.A.
In this paper the occurrence, distribution and abundance of cetaceans in offshore waters of Onslow Bay, North Carolina, USA is described. Between June 2007 and June 2010 monthly aerial and shipboard linetransect surveys were conducted along ten 74km transects placed perpendicular to the shelf break. In total 42,676km of aerial trackline (218 sightings) and 5,209km of vessel trackline (100 sightings) were observed. Seven species of cetaceans were observed, but the fauna was dominated strongly by common bottlenose and Atlantic spotted dolphins. Both species were present yearround in the study area. Using photoidentification techniques, five bottlenose dolphins and one spotted dolphin were resighted during the threeyear period. In general, the abundance of cetaceans in Onslow Bay was low and too few sightings were made to estimate monthly abundances for species other than bottlenose and spotted dolphins. Maximum monthly abundances of bottlenose and spotted dolphins were 4,100 (95% CI: 1,300–9,400) in May 2010 and 6,000 (95% CI: 2,500–17,400) in March 2009, respectively. Bottlenose dolphins were found throughout the study area, although they were encountered most frequently just off the shelf break. In contrast, spotted dolphins exhibited a strong preference for waters over the continental shelf and were not encountered beyond the shelf break.

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

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

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

Status and future of research on the behavioural responses of marine mammals to U.S. Navy sonar
http://hdl.handle.net/10023/7741
A review of the status and future of research into behavioral responses of marine mammals to naval sonar exposure was undertaken to evaluate the return on investment of current US Navy funded programs, identify the data needs and the contributions of current research programs to meeting data needs, and determine the ability to meet outstanding data needs given the current state of technology. As part of this review, a workshop was held from 2122 April 2015 in Monterey, California. Workshop attendees were key representatives of Navyfunded behavioral response studies, as well as three external reviewers who were selected because of their expertise in animal behavior and behavioral responses to anthropogenic stimuli in the aquatic and terrestrial environments. Prior to the workshop, a questionnaire was circulated to canvass the opinions of members of the scientific community (primarily workshop attendees exclusive of external reviewers) on each of the research approaches taken to address this topic. The workshop was then structured around the questionnaire and responses received, via a series of discussion sessions. Afterwards, each research approach was evaluated independently by the external reviewers. This report presents a synthesis of the evaluations and recommendations of the external reviewers on current and future behavioral response research relevant to naval sonar. All reviewers agreed that excellent progress has been made on this topic and that each of the research approaches has contributed to our understanding of cetacean responses to naval sonar. The report includes specific comments and recommendations of the reviewers relevant to each approach, but also includes suggestions for priority species and a comprehensive list of recommendations for the future of BRS research in general (Tables 1 and 2). In summary it was recommended that BRS research be continued and extended to increase sample sizes and experimental replication, and temporal duration and spatial scale including more research in areas where the animals are presumably more naïve than on the naval ranges. It was noted that future investigations would benefit from combining experimentation and observation to enable linkage of shortterm behavioral response to longterm fitness consequences of repeated exposure. Beaked whales were the species group ranked highest in terms of research priority. The importance of baseline studies and longerterm monitoring of animals before and after exposure is emphasized throughout.
Thu, 01 Jan 2015 00:00:00 GMT
http://hdl.handle.net/10023/7741
20150101T00:00:00Z
Harris, Catriona M
Thomas, Len
A review of the status and future of research into behavioral responses of marine mammals to naval sonar exposure was undertaken to evaluate the return on investment of current US Navy funded programs, identify the data needs and the contributions of current research programs to meeting data needs, and determine the ability to meet outstanding data needs given the current state of technology. As part of this review, a workshop was held from 2122 April 2015 in Monterey, California. Workshop attendees were key representatives of Navyfunded behavioral response studies, as well as three external reviewers who were selected because of their expertise in animal behavior and behavioral responses to anthropogenic stimuli in the aquatic and terrestrial environments. Prior to the workshop, a questionnaire was circulated to canvass the opinions of members of the scientific community (primarily workshop attendees exclusive of external reviewers) on each of the research approaches taken to address this topic. The workshop was then structured around the questionnaire and responses received, via a series of discussion sessions. Afterwards, each research approach was evaluated independently by the external reviewers. This report presents a synthesis of the evaluations and recommendations of the external reviewers on current and future behavioral response research relevant to naval sonar. All reviewers agreed that excellent progress has been made on this topic and that each of the research approaches has contributed to our understanding of cetacean responses to naval sonar. The report includes specific comments and recommendations of the reviewers relevant to each approach, but also includes suggestions for priority species and a comprehensive list of recommendations for the future of BRS research in general (Tables 1 and 2). In summary it was recommended that BRS research be continued and extended to increase sample sizes and experimental replication, and temporal duration and spatial scale including more research in areas where the animals are presumably more naïve than on the naval ranges. It was noted that future investigations would benefit from combining experimentation and observation to enable linkage of shortterm behavioral response to longterm fitness consequences of repeated exposure. Beaked whales were the species group ranked highest in terms of research priority. The importance of baseline studies and longerterm monitoring of animals before and after exposure is emphasized throughout.

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

A description of LATTE outputs
http://hdl.handle.net/10023/7720
Fri, 30 Oct 2015 00:00:00 GMT
http://hdl.handle.net/10023/7720
20151030T00:00:00Z
Marques, Tiago A.
Thomas, Len

Digit frequencies and Bernoulli convolutions
http://hdl.handle.net/10023/7719
It is well known that when β is a Pisot number, the corresponding Bernoulli convolution ν(β) has Hausdorff dimension less than 1, i.e. that there exists a set A(β) with (ν(β))(A(β))=1 and dim_H(A(β))<1. We show explicitly how to construct for each Pisot number β such a set A(β).
This work was supported partly by the Dutch Organisation for Scientific Research (NWO) grant number 613.001.022 and partly by the Engineering and Physical Sciences Research Council grant number EP/K029061/1.
Fri, 27 Jun 2014 00:00:00 GMT
http://hdl.handle.net/10023/7719
20140627T00:00:00Z
Kempton, Thomas Michael William
It is well known that when β is a Pisot number, the corresponding Bernoulli convolution ν(β) has Hausdorff dimension less than 1, i.e. that there exists a set A(β) with (ν(β))(A(β))=1 and dim_H(A(β))<1. We show explicitly how to construct for each Pisot number β such a set A(β).

Selfaffine sets with positive Lebesgue measure
http://hdl.handle.net/10023/7718
Using techniques introduced by C. Gunturk, we prove that the attractors of a family of overlapping selfaffine iterated function systems contain a neighbourhood of zero for all parameters in a certain range. This corresponds to giving conditions under which a single sequence may serve as a ‘simultaneous βexpansion’ of different numbers in different bases.
Fri, 27 Jun 2014 00:00:00 GMT
http://hdl.handle.net/10023/7718
20140627T00:00:00Z
Dajani, Karma
Jiang, Kan
Kempton, Thomas Michael William
Using techniques introduced by C. Gunturk, we prove that the attractors of a family of overlapping selfaffine iterated function systems contain a neighbourhood of zero for all parameters in a certain range. This corresponds to giving conditions under which a single sequence may serve as a ‘simultaneous βexpansion’ of different numbers in different bases.

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

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

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

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

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

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

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

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

A spatially explicit capturerecapture estimator for singlecatch traps
http://hdl.handle.net/10023/7680
1. Singlecatch traps are frequently used in livetrapping studies of small mammals. Thus far a likelihood for singlecatch traps has proven elusive and usually the likelihood for multicatch traps is used for spatially explicit capturerecapture (SECR) analyses of such data. Previous work found the multicatch likelihood to provide a robust estimator of average density. 2. We build on a recently developed continuoustime model for SECR to derive a likelihood for singlecatch traps. We use this to develop an estimator based on observed capture times and compare its performance by simulation to that of the multicatch estimator for various scenarios with nonconstant density surfaces. 3. While the multicatch estimator is found to be a surprisingly robust estimator of average density, its performance deteriorates with high trap saturation and increasing density gradients. Moreover, it is found to be a poor estimator of the height (but not range) of the detection function. By contrast, the single catch estimators of density, distribution and detection function parameters are found to be unbiased or nearly unbiased in all scenarios considered. This gain comes at the cost of higher variance, so that despite the lower bias of the singlecatch estimator of the density surface over space, its root mean squared error is similar to that of the multicatch estimator. 4. If there is no interest in interpreting the detection function parameters themselves, and if density is expected to be fairly constantover the survey region, then the multicatch estimator performs well with singlecatch traps. However if accurate estimation of the detection function is of interest, or if density is expected to vary substantially in space, then there is merit in using the singlecatch estimator when trap saturation is above about 60%. The estimator’s performance is improved if care is taken to place traps so as to span the range of variables that affect animal distribution. As a singlecatch likelihood with unknown capture times remains intractable for now, researchers using singlecatch traps should aim to incorporate timing devices with their traps.
This work was partfunded by EPSRC grant EP/I000917/1.
Sun, 01 Nov 2015 00:00:00 GMT
http://hdl.handle.net/10023/7680
20151101T00:00:00Z
Distiller, Greg
Borchers, David Louis
1. Singlecatch traps are frequently used in livetrapping studies of small mammals. Thus far a likelihood for singlecatch traps has proven elusive and usually the likelihood for multicatch traps is used for spatially explicit capturerecapture (SECR) analyses of such data. Previous work found the multicatch likelihood to provide a robust estimator of average density. 2. We build on a recently developed continuoustime model for SECR to derive a likelihood for singlecatch traps. We use this to develop an estimator based on observed capture times and compare its performance by simulation to that of the multicatch estimator for various scenarios with nonconstant density surfaces. 3. While the multicatch estimator is found to be a surprisingly robust estimator of average density, its performance deteriorates with high trap saturation and increasing density gradients. Moreover, it is found to be a poor estimator of the height (but not range) of the detection function. By contrast, the single catch estimators of density, distribution and detection function parameters are found to be unbiased or nearly unbiased in all scenarios considered. This gain comes at the cost of higher variance, so that despite the lower bias of the singlecatch estimator of the density surface over space, its root mean squared error is similar to that of the multicatch estimator. 4. If there is no interest in interpreting the detection function parameters themselves, and if density is expected to be fairly constantover the survey region, then the multicatch estimator performs well with singlecatch traps. However if accurate estimation of the detection function is of interest, or if density is expected to vary substantially in space, then there is merit in using the singlecatch estimator when trap saturation is above about 60%. The estimator’s performance is improved if care is taken to place traps so as to span the range of variables that affect animal distribution. As a singlecatch likelihood with unknown capture times remains intractable for now, researchers using singlecatch traps should aim to incorporate timing devices with their traps.

Homomorphic image orders on combinatorial structures
http://hdl.handle.net/10023/7679
Combinatorial structures have been considered under various orders, including substructure order and homomorphism order. In this paper, we investigate the homomorphic image order, corresponding to the existence of a surjective homomorphism between two structures. We distinguish between strong and induced forms of the order and explore how they behave in the context of different common combinatorial structures. We focus on three aspects: antichains and partial wellorder, the joint preimage property and the dual amalgamation property. The two latter properties are natural analogues of the wellknown joint embedding property and amalgamation property, and are investigated here for the first time.
Wed, 01 Jul 2015 00:00:00 GMT
http://hdl.handle.net/10023/7679
20150701T00:00:00Z
Huczynska, Sophie
Ruskuc, Nik
Combinatorial structures have been considered under various orders, including substructure order and homomorphism order. In this paper, we investigate the homomorphic image order, corresponding to the existence of a surjective homomorphism between two structures. We distinguish between strong and induced forms of the order and explore how they behave in the context of different common combinatorial structures. We focus on three aspects: antichains and partial wellorder, the joint preimage property and the dual amalgamation property. The two latter properties are natural analogues of the wellknown joint embedding property and amalgamation property, and are investigated here for the first time.

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

A Höldertype inequality on a regular rooted tree
http://hdl.handle.net/10023/7658
We establish an inequality which involves a nonnegative function defined on the vertices of a finite mary regular rooted tree. The inequality may be thought of as relating an interaction energy defined on the free vertices of the tree summed over automorphisms of the tree, to a product of sums of powers of the function over vertices at certain levels of the tree. Conjugate powers arise naturally in the inequality, indeed, Hölder's inequality is a key tool in the proof which uses induction on subgroups of the automorphism group of the tree.
Sun, 15 Mar 2015 00:00:00 GMT
http://hdl.handle.net/10023/7658
20150315T00:00:00Z
Falconer, Kenneth John
We establish an inequality which involves a nonnegative function defined on the vertices of a finite mary regular rooted tree. The inequality may be thought of as relating an interaction energy defined on the free vertices of the tree summed over automorphisms of the tree, to a product of sums of powers of the function over vertices at certain levels of the tree. Conjugate powers arise naturally in the inequality, indeed, Hölder's inequality is a key tool in the proof which uses induction on subgroups of the automorphism group of the tree.

The modelling and assessment of whalewatching impacts
http://hdl.handle.net/10023/7642
In recent years there has been significant interest in modelling cumulative effects and the population consequences of individual changes in cetacean behaviour and physiology due to disturbance. One potential source of disturbance that has garnered particular interest is whalewatching. Though perceived as 'green' or ecofriendly tourism, there is evidence that whalewatching can result in statistically significant and biologically meaningful changes in cetacean behaviour, raising the question whether whalewatching is in fact a long term sustainable activity. However, an assessment of the impacts of whalewatching on cetaceans requires an understanding of the potential behavioural and physiological effects, data to effectively address the question and suitable modelling techniques. Here, we review the current state of knowledge on the viability of longterm whalewatching, as well as logistical limitations and potential opportunities. We conclude that an integrated, coordinated approach will be needed to further understanding of the possible effects of whalewatching on cetaceans.
Thu, 01 Oct 2015 00:00:00 GMT
http://hdl.handle.net/10023/7642
20151001T00:00:00Z
New, Leslie Frances
Hall, Ailsa Jane
Harcourt, R.
Kaufman, G.
Parsons, E.C.M.
Pearson, H.C.
Cosentino, A.M.
Schick, Robert Schilling
In recent years there has been significant interest in modelling cumulative effects and the population consequences of individual changes in cetacean behaviour and physiology due to disturbance. One potential source of disturbance that has garnered particular interest is whalewatching. Though perceived as 'green' or ecofriendly tourism, there is evidence that whalewatching can result in statistically significant and biologically meaningful changes in cetacean behaviour, raising the question whether whalewatching is in fact a long term sustainable activity. However, an assessment of the impacts of whalewatching on cetaceans requires an understanding of the potential behavioural and physiological effects, data to effectively address the question and suitable modelling techniques. Here, we review the current state of knowledge on the viability of longterm whalewatching, as well as logistical limitations and potential opportunities. We conclude that an integrated, coordinated approach will be needed to further understanding of the possible effects of whalewatching on cetaceans.

Impacts of anthropogenic noise on marine life : publication patterns, new discoveries, and future directions in research and management
http://hdl.handle.net/10023/7640
Anthropogenic underwater noise is now recognized as a worldwide problem, and recent studies have shown a broad range of negative effects in a variety of taxa. Underwater noise from shipping is increasingly recognized as a significant and pervasive pollutant with the potential to impact marine ecosystems on a global scale. We reviewed six regional case studies as examples of recent research and management activities relating to ocean noise in a variety of taxonomic groups, locations, and approaches. However, as no six projects could ever cover all taxa, sites and noise sources, a brief bibliometric analysis places these case studies into the broader historical and topical context of the peerreviewed ocean noise literature as a whole. The case studies highlighted emerging knowledge of impacts, including the ways that noninjurious effects can still accumulate at the population level, and detailed approaches to guide ocean noise management. They build a compelling case that a number of anthropogenic noise types can affect a variety of marine taxa. Meanwhile, the bibliometric analyses revealed an increasing diversity of ocean noise topics covered and journal outlets since the 1940s. This could be seen in terms of both the expansion of the literature from more physical interests to ecological impacts of noise, management and policy, and consideration of a widening range of taxa. However, if our scientific knowledge base is ever to get ahead of the curve of rapid industrialization of the ocean, we are going to have to identify naïve populations and relatively pristine seas, and construct mechanistic models, so that we can predict impacts before they occur, and guide effective mitigation for the most vulnerable populations.
Funding for R. Bruintjes, J. Purser, A. N. Radford, S. D, Simpson and M. A. Wale was provided by the UK Department for Environment Food and Rural Affairs (Defra). N.D. Merchant received travel funding from Ocean Networks Canada. RW was supported by a Marie Curie International Incoming Fellowship within the 7th European Community Framework Programme (Project CONCEAL, FP7, PIIFGA2009253407), and received travel funding to attend IMCC3 from the Society for Conservation Biology (SCB) Marine Section and the International Whaling Commission’s Climate Change steering group (with thanks to Mark Simmonds). A.J. Wright also received travel funding to attend IMCC3 from the SCB Marine Section. Date of Acceptance: 28/05/2015
Thu, 01 Oct 2015 00:00:00 GMT
http://hdl.handle.net/10023/7640
20151001T00:00:00Z
Williams, Robert
Wright, Andrew J
Ashe, Erin
Blight, LK
Bruintjes, R
Canessa, R
Clark, CW
CullisSuzuki, S
Dakin, DT
Erbe, C
Hammond, Philip Steven
Merchant, MD
O'Hara, PD
Purser, J
Radford, AN
Simpson, SD
Thomas, Len
Wale, MA
Anthropogenic underwater noise is now recognized as a worldwide problem, and recent studies have shown a broad range of negative effects in a variety of taxa. Underwater noise from shipping is increasingly recognized as a significant and pervasive pollutant with the potential to impact marine ecosystems on a global scale. We reviewed six regional case studies as examples of recent research and management activities relating to ocean noise in a variety of taxonomic groups, locations, and approaches. However, as no six projects could ever cover all taxa, sites and noise sources, a brief bibliometric analysis places these case studies into the broader historical and topical context of the peerreviewed ocean noise literature as a whole. The case studies highlighted emerging knowledge of impacts, including the ways that noninjurious effects can still accumulate at the population level, and detailed approaches to guide ocean noise management. They build a compelling case that a number of anthropogenic noise types can affect a variety of marine taxa. Meanwhile, the bibliometric analyses revealed an increasing diversity of ocean noise topics covered and journal outlets since the 1940s. This could be seen in terms of both the expansion of the literature from more physical interests to ecological impacts of noise, management and policy, and consideration of a widening range of taxa. However, if our scientific knowledge base is ever to get ahead of the curve of rapid industrialization of the ocean, we are going to have to identify naïve populations and relatively pristine seas, and construct mechanistic models, so that we can predict impacts before they occur, and guide effective mitigation for the most vulnerable populations.

On generators, relations and Dsimplicity of direct products, Byleen extensions, and other semigroup constructions
http://hdl.handle.net/10023/7629
In this thesis we study two different topics, both in the context of semigroup constructions. The first is the investigation of an embedding problem, specifically the problem of whether it is possible to embed any given finitely presentable semigroup into a Dsimple finitely presentable semigroup. We consider some wellknown semigroup constructions, investigating their properties to determine whether they might prove useful for finding a solution to our problem. We carry out a more detailed study into a more complicated semigroup construction, the Byleen extension, which has been used to solve several other embedding problems. We prove several results regarding the structure of this extension, finding necessary and sufficient conditions for an extension to be Dsimple and a very strong necessary condition for an extension to be finitely presentable.
The second topic covered in this thesis is relative rank, specifically the sequence obtained by taking the rank of incremental direct powers of a given semigroup modulo the diagonal subsemigroup. We investigate the relative rank sequences of infinite Cartesian products of groups and of semigroups. We characterise all semigroups for which the relative rank sequence of an infinite Cartesian product is finite, and show that if the sequence is finite then it is bounded above by a logarithmic function. We will find sufficient conditions for the relative rank sequence of an infinite Cartesian product to be logarithmic, and sufficient conditions for it to be constant. Chapter 4 ends with the introduction of a new topic, relative presentability, which follows naturally from the topic of relative rank.
Mon, 30 Nov 2015 00:00:00 GMT
http://hdl.handle.net/10023/7629
20151130T00:00:00Z
Baynes, Samuel
In this thesis we study two different topics, both in the context of semigroup constructions. The first is the investigation of an embedding problem, specifically the problem of whether it is possible to embed any given finitely presentable semigroup into a Dsimple finitely presentable semigroup. We consider some wellknown semigroup constructions, investigating their properties to determine whether they might prove useful for finding a solution to our problem. We carry out a more detailed study into a more complicated semigroup construction, the Byleen extension, which has been used to solve several other embedding problems. We prove several results regarding the structure of this extension, finding necessary and sufficient conditions for an extension to be Dsimple and a very strong necessary condition for an extension to be finitely presentable.
The second topic covered in this thesis is relative rank, specifically the sequence obtained by taking the rank of incremental direct powers of a given semigroup modulo the diagonal subsemigroup. We investigate the relative rank sequences of infinite Cartesian products of groups and of semigroups. We characterise all semigroups for which the relative rank sequence of an infinite Cartesian product is finite, and show that if the sequence is finite then it is bounded above by a logarithmic function. We will find sufficient conditions for the relative rank sequence of an infinite Cartesian product to be logarithmic, and sufficient conditions for it to be constant. Chapter 4 ends with the introduction of a new topic, relative presentability, which follows naturally from the topic of relative rank.

Genetic censusing identifies an unexpectedly sizeable population of an endangered large mammal in a fragmented forest landscape
http://hdl.handle.net/10023/7614
Background: As habitat degradation and fragmentation continue to impact wildlife populations around the world, it is critical to understand the behavioral flexibility of species in these environments. In Uganda, the mostly unprotected forest fragment landscape between the Budongo and Bugoma Forests is a potential corridor for chimpanzees, yet little is known about the status of chimpanzee populations in these fragments. Results: From 2011 through 2013, we noninvasively collected 865 chimpanzee fecal samples across 633 km2 and successfully genotyped 662 (77%) at up to 14 microsatellite loci. These genotypes corresponded to 182 chimpanzees, with a mean of 3.5 captures per individual. We obtained population size estimates of 256 (95% confidence interval 246321) and 319 (288357) chimpanzees using capturewithreplacement and spatially explicit capturerecapture models, respectively. The spatial clustering of associated genotypes suggests the presence of at least nine communities containing a minimum of 833 individuals each. Putative community distributions defined by the locations of associated genotypes correspond well with the distribution of 14 Ychromosome haplotypes. Conclusions: These census figures are more than three times greater than a previous estimate based on an extrapolation from smallscale nest count surveys that tend to underestimate population size. The distribution of genotype clusters and Ychromosome haplotypes together indicate the presence of numerous male philopatric chimpanzee communities throughout the corridor habitat. Our findings demonstrate that, despite extensive habitat loss and fragmentation, chimpanzees remain widely distributed and exhibit distinct community home ranges. Our results further imply that elusive and rare species may adapt to degraded habitats more successfully than previously believed. Their longterm persistence is unlikely, however, if protection is not afforded to them and habitat loss continues unabated.
This study was funded by the American Society of Primatologists, the German Academic Exchange Service (DAAD), the Max Planck Society, the University of Southern California Jane Goodall Research Center and Dornsife College of Letters, Arts, and Sciences, the Nacey Maggioncalda Foundation, and Primate Conservation, Inc.
Tue, 25 Aug 2015 00:00:00 GMT
http://hdl.handle.net/10023/7614
20150825T00:00:00Z
McCarthy, M.S.
Lester, J.D.
Howe, Eric John
Arandjelovic, M.
Stanford, C.B.
Vigilant, L.
Background: As habitat degradation and fragmentation continue to impact wildlife populations around the world, it is critical to understand the behavioral flexibility of species in these environments. In Uganda, the mostly unprotected forest fragment landscape between the Budongo and Bugoma Forests is a potential corridor for chimpanzees, yet little is known about the status of chimpanzee populations in these fragments. Results: From 2011 through 2013, we noninvasively collected 865 chimpanzee fecal samples across 633 km2 and successfully genotyped 662 (77%) at up to 14 microsatellite loci. These genotypes corresponded to 182 chimpanzees, with a mean of 3.5 captures per individual. We obtained population size estimates of 256 (95% confidence interval 246321) and 319 (288357) chimpanzees using capturewithreplacement and spatially explicit capturerecapture models, respectively. The spatial clustering of associated genotypes suggests the presence of at least nine communities containing a minimum of 833 individuals each. Putative community distributions defined by the locations of associated genotypes correspond well with the distribution of 14 Ychromosome haplotypes. Conclusions: These census figures are more than three times greater than a previous estimate based on an extrapolation from smallscale nest count surveys that tend to underestimate population size. The distribution of genotype clusters and Ychromosome haplotypes together indicate the presence of numerous male philopatric chimpanzee communities throughout the corridor habitat. Our findings demonstrate that, despite extensive habitat loss and fragmentation, chimpanzees remain widely distributed and exhibit distinct community home ranges. Our results further imply that elusive and rare species may adapt to degraded habitats more successfully than previously believed. Their longterm persistence is unlikely, however, if protection is not afforded to them and habitat loss continues unabated.

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

Pairwise interaction point processes for modelling bivariate spatial point patterns in the presence of interaction uncertainty
http://hdl.handle.net/10023/7583
Current ecological research seeks to understand the mechanisms that sustain biodiversity and allow a large number of species to coexist. Coexistence concerns interindividual interactions. Consequently, there is an interest in identifying and quantifying interactions within and between species as reflected in the spatial pattern formed by the individuals. This study analyses the spatial pattern formed by the locations of plants in a community with high biodiversity from Western Australia. We fit a pairwise interaction Gibbs marked point process to the data using a Bayesian approach and quantify the inhibitory interactions within and between the two species. We quantitatively discriminate between competing models corresponding to different interspecific and intraspecific interactions via posterior model probabilities. The analysis provides evidence that the intraspecific interactions for the two species of the genus Banksia are generally similar to those between the two species providing some evidence for mechanisms that sustain biodiversity.
Tue, 01 Sep 2015 00:00:00 GMT
http://hdl.handle.net/10023/7583
20150901T00:00:00Z
Nightingale, Glenna Faith
Illian, Janine Baerbel
King, Ruth
Current ecological research seeks to understand the mechanisms that sustain biodiversity and allow a large number of species to coexist. Coexistence concerns interindividual interactions. Consequently, there is an interest in identifying and quantifying interactions within and between species as reflected in the spatial pattern formed by the individuals. This study analyses the spatial pattern formed by the locations of plants in a community with high biodiversity from Western Australia. We fit a pairwise interaction Gibbs marked point process to the data using a Bayesian approach and quantify the inhibitory interactions within and between the two species. We quantitatively discriminate between competing models corresponding to different interspecific and intraspecific interactions via posterior model probabilities. The analysis provides evidence that the intraspecific interactions for the two species of the genus Banksia are generally similar to those between the two species providing some evidence for mechanisms that sustain biodiversity.

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

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

Procedure description : using AUTEC’s hydrophones surrounding a DTAGed whale to obtain localizations
http://hdl.handle.net/10023/7523
Thu, 01 Jan 2015 00:00:00 GMT
http://hdl.handle.net/10023/7523
20150101T00:00:00Z
Marques, Tiago A.
Shaeffer, Jessica
Moretti, David
Thomas, Len

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

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

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

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

On the theory of translationally invariant magnetohydrodynamic equilibria with anisotropic pressure and magnetic shear
http://hdl.handle.net/10023/7484
We present an improved formalism for translationally invariant magnetohydrodynamic equilibria with anisotropic pressure and currents with a field aligned component. The derivation of a GradShafranov type equation is given along with a constraint which links the shear field to the parallel pressure. The difficulties of the formalism are discussed and various methods of circumventing these difficulties are given. A simple example is then used to highlight the methods and difficulties involved.
Funding: STFC Doctoral Training Grant ST/K502327/1 (Jonathan Hodgson) and STFC Consolidated Grant ST/K000950/1 (Thomas Neukirch)
Wed, 02 Sep 2015 00:00:00 GMT
http://hdl.handle.net/10023/7484
20150902T00:00:00Z
Hodgson, Jonathan David Brockie
Neukirch, Thomas
We present an improved formalism for translationally invariant magnetohydrodynamic equilibria with anisotropic pressure and currents with a field aligned component. The derivation of a GradShafranov type equation is given along with a constraint which links the shear field to the parallel pressure. The difficulties of the formalism are discussed and various methods of circumventing these difficulties are given. A simple example is then used to highlight the methods and difficulties involved.

Higher moments for random multiplicative measures
http://hdl.handle.net/10023/7474
We obtain a condition for the Lqconvergence of martingales generated by random multiplicative cascade measures for q>1 without any selfsimilarity requirements on the cascades.
Sat, 01 Aug 2015 00:00:00 GMT
http://hdl.handle.net/10023/7474
20150801T00:00:00Z
Falconer, Kenneth John
We obtain a condition for the Lqconvergence of martingales generated by random multiplicative cascade measures for q>1 without any selfsimilarity requirements on the cascades.

Circular designs balanced for neighbours at distances one and two
http://hdl.handle.net/10023/7454
We define three types of neighbourbalanced designs for experiments where the units are arranged in a circle or single line in space or time. The designs are balanced with respect to neighbours at distance one and at distance two. The variants come from allowing or forbidding selfneighbours, and from considering neighbours to be directed or undirected. For two of the variants, we give a method of constructing a design for all values of the number of treatments, except for some small values where it is impossible. In the third case, we give a partial solution that covers all sizes likely to be used in practice.
Mon, 01 Dec 2014 00:00:00 GMT
http://hdl.handle.net/10023/7454
20141201T00:00:00Z
Aldred, R. E. L.
Bailey, R. A.
Mckay, Brendan D.
Wanless, Ian M.
We define three types of neighbourbalanced designs for experiments where the units are arranged in a circle or single line in space or time. The designs are balanced with respect to neighbours at distance one and at distance two. The variants come from allowing or forbidding selfneighbours, and from considering neighbours to be directed or undirected. For two of the variants, we give a method of constructing a design for all values of the number of treatments, except for some small values where it is impossible. In the third case, we give a partial solution that covers all sizes likely to be used in practice.

Modelbased distance sampling
http://hdl.handle.net/10023/7410
Conventional distance sampling adopts a mixed approach, using modelbased methods for the detection process, and designbased methods to estimate animal abundance in the study region, given estimated probabilities of detection. In recent years, there has been increasing interest in fully modelbased methods. Modelbased methods are less robust for estimating animal abundance than conventional methods, but offer several advantages: they allow the analyst to explore how animal density varies by habitat or topography; abundance can be estimated for any subregion of interest; they provide tools for analysing data from designed distance sampling experiments, to assess treatment effects. We develop a common framework for modelbased distance sampling, and show how the various modelbased methods that have been proposed fit within this framework.
CSO was partfunded by EPSRC/NERC Grant EP/1000917/1.
Tue, 01 Mar 2016 00:00:00 GMT
http://hdl.handle.net/10023/7410
20160301T00:00:00Z
Buckland, Stephen Terrence
Oedekoven, Cornelia Sabrina
Borchers, David Louis
Conventional distance sampling adopts a mixed approach, using modelbased methods for the detection process, and designbased methods to estimate animal abundance in the study region, given estimated probabilities of detection. In recent years, there has been increasing interest in fully modelbased methods. Modelbased methods are less robust for estimating animal abundance than conventional methods, but offer several advantages: they allow the analyst to explore how animal density varies by habitat or topography; abundance can be estimated for any subregion of interest; they provide tools for analysing data from designed distance sampling experiments, to assess treatment effects. We develop a common framework for modelbased distance sampling, and show how the various modelbased methods that have been proposed fit within this framework.

The statistical analysis of point events associated with a fixed point
http://hdl.handle.net/10023/7294
This work concerns the analysis of point events which are distributed on a planar region and are thought to be related to a fixed point. Data examples are considered from Epidemiology, where morbidity events are thought to be related to a pollution source, and Ecology and Geology where events associated with a central point are to be modelled. We have developed a variety of Heterogeneous Poisson Process (HEPP) models for the above examples. In particular, I have developed interaction and 8dependence models for angularlinear correlation, with their ML estimation and associated score/W aId tests. In the Epidemiological case we have developed casecontrol models and tests. The possibility of secondorder effects being important has also led to the development of Bayesian Spatial Prior (BSP) models. In addition, we have developed a new deviance residual for HEPP models and explored the use of GLIM for modelling purposes. A variety of results were found in data analysis. In some cases HEPP models provide adequate descriptions of the process. In others, BSP models yield better fits. In general, the discrete case admits a simple spatial Poisson model for counts and does not require BSP model extensions.
Tue, 01 Jan 1991 00:00:00 GMT
http://hdl.handle.net/10023/7294
19910101T00:00:00Z
Lawson, Andrew B.
This work concerns the analysis of point events which are distributed on a planar region and are thought to be related to a fixed point. Data examples are considered from Epidemiology, where morbidity events are thought to be related to a pollution source, and Ecology and Geology where events associated with a central point are to be modelled. We have developed a variety of Heterogeneous Poisson Process (HEPP) models for the above examples. In particular, I have developed interaction and 8dependence models for angularlinear correlation, with their ML estimation and associated score/W aId tests. In the Epidemiological case we have developed casecontrol models and tests. The possibility of secondorder effects being important has also led to the development of Bayesian Spatial Prior (BSP) models. In addition, we have developed a new deviance residual for HEPP models and explored the use of GLIM for modelling purposes. A variety of results were found in data analysis. In some cases HEPP models provide adequate descriptions of the process. In others, BSP models yield better fits. In general, the discrete case admits a simple spatial Poisson model for counts and does not require BSP model extensions.

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

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

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

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

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

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

Large scale surveys for cetaceans : line transect assumptions, reliability of abundance estimates and improving survey efficiency – A response to MacLeod
http://hdl.handle.net/10023/7159
Sat, 01 Feb 2014 00:00:00 GMT
http://hdl.handle.net/10023/7159
20140201T00:00:00Z
Hammond, Philip Steven
Gillespie, Douglas Michael
Lovell, Philip
Samarra, Filipa Isabel Pereira
Swift, Rene James
Macleod, Kelly
Tasker, Mark L
Berggren, Per
Borchers, David Louis
Burt, M Louise
Paxton, Charles G. M.
Canadas, Ana
Desportes, Genevieve
Donovan, Greg P
Gilles, Anita
Lehnert, Kristina
Siebert, Ursula
Gordon, Jonathan Charles David
Leaper, Russell
Leopold, Mardik
Scheidat, Meike
Oien, Nils
Ridoux, Vincent
Rogan, Emer
Skov, Henrik
Teilmann, Jonas
Van Canneyt, Olivier
Vazquez, Jose Antonio

Detectability in audiovisual surveys of tropical rainforest birds : the influence of species, weather and habitat characteristics
http://hdl.handle.net/10023/7147
Indices of relative abundance do not control for variation in detectability, which can bias density estimates such that ecological processes are difficult to infer. Distance sampling methods can be used to correct for detectability, but in rainforest, where dense vegetation and diverse assemblages complicate sampling, information is lacking about factors affecting their application. Rare species present an additional challenge, as data may be too sparse to fit detection functions. We present analyses of distance sampling data collected for a diverse tropical rainforest bird assemblage across broad elevational and latitudinal gradients in North Queensland, Australia. Using audio and visual detections, we assessed the influence of various factors on Effective Strip Width (ESW), an intuitively useful parameter, since it can be used to calculate an estimate of density from count data. Body size and species exerted the most important influence on ESW, with larger species detectable over greater distances than smaller species. Secondarily, wet weather and high shrub density decreased ESW for most species. ESW for several species also differed between summer and winter, possibly due to seasonal differences in calling behavior. Distance sampling proved logistically intensive in these environments, but large differences in ESW between species confirmed the need to correct for detection probability to obtain accurate density estimates. Our results suggest an evidencebased approach to controlling for factors influencing detectability, and avenues for further work including modeling detectability as a function of species characteristics such as body size and call characteristics. Such models may be useful in developing a calibration for nondistance sampling data and for estimating detectability of rare species.
This research was funded by the Australian Government’s National Environmental Research Program, the Stuart Leslie Bird Research Award from Birds Australia (http://www.birdsaustralia.com.au/), the Earthwatch Institute (http://www.earthwatch.org/australia/), the Marine and Tropical Sciences Research Facility (MTSRF: http://www.rrrc.org.au/mtsrf). In addition, TAM was partially sponsored by national funds through the Fundação Nacional para a Ciência e Tecnologia, Portugal – FCT under the project (PEstOE/MAT/UI0006/2011). Date of Acceptance: 27/04/2015
Thu, 25 Jun 2015 00:00:00 GMT
http://hdl.handle.net/10023/7147
20150625T00:00:00Z
Anderson, Alexander S.
Marques, Tiago A.
Shoo, Luke P.
Williams, Stephen E.
Indices of relative abundance do not control for variation in detectability, which can bias density estimates such that ecological processes are difficult to infer. Distance sampling methods can be used to correct for detectability, but in rainforest, where dense vegetation and diverse assemblages complicate sampling, information is lacking about factors affecting their application. Rare species present an additional challenge, as data may be too sparse to fit detection functions. We present analyses of distance sampling data collected for a diverse tropical rainforest bird assemblage across broad elevational and latitudinal gradients in North Queensland, Australia. Using audio and visual detections, we assessed the influence of various factors on Effective Strip Width (ESW), an intuitively useful parameter, since it can be used to calculate an estimate of density from count data. Body size and species exerted the most important influence on ESW, with larger species detectable over greater distances than smaller species. Secondarily, wet weather and high shrub density decreased ESW for most species. ESW for several species also differed between summer and winter, possibly due to seasonal differences in calling behavior. Distance sampling proved logistically intensive in these environments, but large differences in ESW between species confirmed the need to correct for detection probability to obtain accurate density estimates. Our results suggest an evidencebased approach to controlling for factors influencing detectability, and avenues for further work including modeling detectability as a function of species characteristics such as body size and call characteristics. Such models may be useful in developing a calibration for nondistance sampling data and for estimating detectability of rare species.

Evaluating the utility of B/Ca ratios in planktic foraminifera as a proxy for the carbonate system : a case study of Globigerinoides ruber
http://hdl.handle.net/10023/7133
B/Ca ratios in foraminifera have attracted considerable scientific attention as a proxy for past ocean carbonate system. However, the carbonate system controls on B/Ca ratios are not straightforward, with Δ[ CO32] ([ CO32]in situ  [ CO32]at saturation) correlating best with B/Ca ratios in benthic foraminifera, rather than pH, B(OH)4/HCO3, or B(OH)4/DIC (as a simple model of boron speciation in seawater and incorporation into CaCO3 would predict). Furthermore, culture experiments have shown that in planktic foraminifera properties such as salinity and [B]SW can have profound effects on B/Ca ratios beyond those predicted by simple partition coefficients. Here, we investigate the controls on B/Ca ratios in G. ruber via a combination of culture experiments and coretop measurements, and add to a growing body of evidence that suggests B/Ca ratios in symbiontbearing foraminiferal carbonate are not a straightforward proxy for past seawater carbonate system conditions. We find that while B/Ca ratios in culture experiments covary with pH, in open ocean sediments this relationship is not seen. In fact, our B/Ca data correlate best with [ PO43] (a previously undocumented association) and in most regions, salinity. These findings might suggest a precipitation rate or crystallographic control on boron incorporation into foraminiferal calcite. Regardless, our results underscore the need for caution when attempting to interpret B/Ca records in terms of the ocean carbonate system, at the very least in the case of mixedlayer planktic foraminifera.
This research was funded by NERC, Grant Number: NE/D00876X/2.
Wed, 01 Apr 2015 00:00:00 GMT
http://hdl.handle.net/10023/7133
20150401T00:00:00Z
Henehan, M.J.
Foster, G.L.
Rae, J.W.B.
Prentice, K.C.
Erez, J.
Bostock, H.C.
Marshall, B.J.
Wilson, P.A.
B/Ca ratios in foraminifera have attracted considerable scientific attention as a proxy for past ocean carbonate system. However, the carbonate system controls on B/Ca ratios are not straightforward, with Δ[ CO32] ([ CO32]in situ  [ CO32]at saturation) correlating best with B/Ca ratios in benthic foraminifera, rather than pH, B(OH)4/HCO3, or B(OH)4/DIC (as a simple model of boron speciation in seawater and incorporation into CaCO3 would predict). Furthermore, culture experiments have shown that in planktic foraminifera properties such as salinity and [B]SW can have profound effects on B/Ca ratios beyond those predicted by simple partition coefficients. Here, we investigate the controls on B/Ca ratios in G. ruber via a combination of culture experiments and coretop measurements, and add to a growing body of evidence that suggests B/Ca ratios in symbiontbearing foraminiferal carbonate are not a straightforward proxy for past seawater carbonate system conditions. We find that while B/Ca ratios in culture experiments covary with pH, in open ocean sediments this relationship is not seen. In fact, our B/Ca data correlate best with [ PO43] (a previously undocumented association) and in most regions, salinity. These findings might suggest a precipitation rate or crystallographic control on boron incorporation into foraminiferal calcite. Regardless, our results underscore the need for caution when attempting to interpret B/Ca records in terms of the ocean carbonate system, at the very least in the case of mixedlayer planktic foraminifera.

Generalized energy inequalities and higher multifractal moments
http://hdl.handle.net/10023/7095
We present a class of generalized energy inequalities and indicate their use in investigating higher multifractal moments, in particular Lqdimensions of images of measures under Brownian processes, Lqdimensions of almost selfaﬃne measures, and moments of random cascade measures
Sat, 02 Aug 2014 00:00:00 GMT
http://hdl.handle.net/10023/7095
20140802T00:00:00Z
Falconer, Kenneth John
We present a class of generalized energy inequalities and indicate their use in investigating higher multifractal moments, in particular Lqdimensions of images of measures under Brownian processes, Lqdimensions of almost selfaﬃne measures, and moments of random cascade measures

Doubleobserver line transect surveys with Markovmodulated Poisson process models for overdispersed animal availability
http://hdl.handle.net/10023/7085
We develop maximum likelihood methods for line transect surveys in which animals go undetected at distance zero, either because they are stochastically unavailable while within view or because they are missed when they are available. These incorporate a Markovmodulated Poisson process model for animal availability, allowing more clustered availability events than is possible with Poisson availability models. They include a markrecapture component arising from the independentobserver survey, leading to more accurate estimation of detection probability given availability. We develop models for situations in which (a) multiple detections of the same individual are possible and (b) some or all of the availability process parameters are estimated from the line transect survey itself, rather than from independent data. We investigate estimator performance by simulation, and compare the multipledetection estimators with estimators that use only initial detections of individuals, and with a singleobserver estimator. Simultaneous estimation of detection function parameters and availability model parameters is shown to be feasible from the line transect survey alone with multiple detections and doubleobserver data but not with singleobserver data. Recording multiple detections of individuals improves estimator precision substantially when estimating the availability model parameters from survey data, and we recommend that these data be gathered. We apply the methods to estimate detection probability from a doubleobserver survey of North Atlantic minke whales, and find that doubleobserver data greatly improve estimator precision here too.
Tue, 01 Dec 2015 00:00:00 GMT
http://hdl.handle.net/10023/7085
20151201T00:00:00Z
Borchers, David Louis
Langrock, Roland
We develop maximum likelihood methods for line transect surveys in which animals go undetected at distance zero, either because they are stochastically unavailable while within view or because they are missed when they are available. These incorporate a Markovmodulated Poisson process model for animal availability, allowing more clustered availability events than is possible with Poisson availability models. They include a markrecapture component arising from the independentobserver survey, leading to more accurate estimation of detection probability given availability. We develop models for situations in which (a) multiple detections of the same individual are possible and (b) some or all of the availability process parameters are estimated from the line transect survey itself, rather than from independent data. We investigate estimator performance by simulation, and compare the multipledetection estimators with estimators that use only initial detections of individuals, and with a singleobserver estimator. Simultaneous estimation of detection function parameters and availability model parameters is shown to be feasible from the line transect survey alone with multiple detections and doubleobserver data but not with singleobserver data. Recording multiple detections of individuals improves estimator precision substantially when estimating the availability model parameters from survey data, and we recommend that these data be gathered. We apply the methods to estimate detection probability from a doubleobserver survey of North Atlantic minke whales, and find that doubleobserver data greatly improve estimator precision here too.

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

The maximal subgroups of the classical groups in dimension 13, 14 and 15
http://hdl.handle.net/10023/7067
One might easily argue that the Classification of Finite Simple Groups is
one of the most important theorems of group theory. Given that any finite
group can be deconstructed into its simple composition factors, it is of great
importance to have a detailed knowledge of the structure of finite simple
groups.
One of the classes of finite groups that appear in the classification theorem
are the simple classical groups, which are matrix groups preserving
some form. This thesis will shed some new light on almost simple classical
groups in dimension 13, 14 and 15. In particular we will determine their
maximal subgroups.
We will build on the results by Bray, Holt, and RoneyDougal who
calculated the maximal subgroups of all almost simple finite classical groups
in dimension less than 12. Furthermore, Aschbacher proved that the maximal
subgroups of almost simple classical groups lie in nine classes. The maximal
subgroups in the first eight classes, i.e. the subgroups of geometric type,
were determined by Kleidman and Liebeck for
dimension greater than 13.
Therefore this thesis concentrates on the ninth class of Aschbacher’s
Theorem. This class roughly consists of subgroups which are almost simple
modulo scalars and do not preserve a geometric structure. As our final
result we will give tables containing all maximal subgroups of almost simple
classical groups in dimension 13, 14 and 15.
Mon, 30 Nov 2015 00:00:00 GMT
http://hdl.handle.net/10023/7067
20151130T00:00:00Z
Schröder, Anna Katharina
One might easily argue that the Classification of Finite Simple Groups is
one of the most important theorems of group theory. Given that any finite
group can be deconstructed into its simple composition factors, it is of great
importance to have a detailed knowledge of the structure of finite simple
groups.
One of the classes of finite groups that appear in the classification theorem
are the simple classical groups, which are matrix groups preserving
some form. This thesis will shed some new light on almost simple classical
groups in dimension 13, 14 and 15. In particular we will determine their
maximal subgroups.
We will build on the results by Bray, Holt, and RoneyDougal who
calculated the maximal subgroups of all almost simple finite classical groups
in dimension less than 12. Furthermore, Aschbacher proved that the maximal
subgroups of almost simple classical groups lie in nine classes. The maximal
subgroups in the first eight classes, i.e. the subgroups of geometric type,
were determined by Kleidman and Liebeck for
dimension greater than 13.
Therefore this thesis concentrates on the ninth class of Aschbacher’s
Theorem. This class roughly consists of subgroups which are almost simple
modulo scalars and do not preserve a geometric structure. As our final
result we will give tables containing all maximal subgroups of almost simple
classical groups in dimension 13, 14 and 15.

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

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

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

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

Chronic exposure to imidacloprid increases neuronal vulnerability to mitochondrial dysfunction in the bumblebee (Bombus terrestris)
http://hdl.handle.net/10023/6986
The global decline in the abundance and diversity of insect pollinators could result from habitat loss, disease, and pesticide exposure. The contribution of the neonicotinoid insecticides (e.g., clothianidin and imidacloprid) to this decline is controversial, and key to understanding their risk is whether the astonishingly low levels found in the nectar and pollen of plants is sufficient to deliver neuroactive levels to their site of action: the bee brain. Here we show that bumblebees (Bombusterrestris audax) fed field levels [10 nM, 2.1 ppb (w/w)] of neonicotinoid accumulate between 4 and 10 nM in their brains within 3 days. Acute (minutes) exposure of cultured neurons to 10 nM clothianidin, but not imidacloprid, causes a nicotinic acetylcholine receptordependent rapid mitochondrial depolarization. However, a chronic (2 days) exposure to 1 nM imidacloprid leads to a receptordependent increased sensitivity to a normally innocuous level of acetylcholine, which now also causes rapid mitochondrial depolarization in neurons. Finally, colonies exposed to this level of imidacloprid show deficits in colony growth and nest condition compared with untreated colonies. These findings provide a mechanistic explanation for the poor navigation and foraging observed in neonicotinoid treated bumblebee colonies.
This work was funded jointly by the Biotechnology and Biological Sciences Research Council, the Department for Environment, Food and Rural Affairs, the Natural Environment Research Council, the Scottish Government, and The Wellcome Trust, under the Insect Pollinators Initiative (United Kingdom) Grant BB/ 1000313/1 (to C.N.C.).
Fri, 01 May 2015 00:00:00 GMT
http://hdl.handle.net/10023/6986
20150501T00:00:00Z
Moffat, C.
Goncalves Pacheco, J.
Sharpe, S.
Samson, A.J.
Bollan, K.A.
Huang, J.
Buckland, Stephen Terrence
Connolly, C.N.
The global decline in the abundance and diversity of insect pollinators could result from habitat loss, disease, and pesticide exposure. The contribution of the neonicotinoid insecticides (e.g., clothianidin and imidacloprid) to this decline is controversial, and key to understanding their risk is whether the astonishingly low levels found in the nectar and pollen of plants is sufficient to deliver neuroactive levels to their site of action: the bee brain. Here we show that bumblebees (Bombusterrestris audax) fed field levels [10 nM, 2.1 ppb (w/w)] of neonicotinoid accumulate between 4 and 10 nM in their brains within 3 days. Acute (minutes) exposure of cultured neurons to 10 nM clothianidin, but not imidacloprid, causes a nicotinic acetylcholine receptordependent rapid mitochondrial depolarization. However, a chronic (2 days) exposure to 1 nM imidacloprid leads to a receptordependent increased sensitivity to a normally innocuous level of acetylcholine, which now also causes rapid mitochondrial depolarization in neurons. Finally, colonies exposed to this level of imidacloprid show deficits in colony growth and nest condition compared with untreated colonies. These findings provide a mechanistic explanation for the poor navigation and foraging observed in neonicotinoid treated bumblebee colonies.

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

Dots and lines : geometric semigroup theory and finite presentability
http://hdl.handle.net/10023/6923
Geometric semigroup theory means different things to different people, but it is agreed that it involves associating a geometric structure to a semigroup and deducing properties of the semigroup based on that structure.
One such property is finite presentability. In geometric group theory, the geometric structure of choice is the Cayley graph of the group. It is known that in group theory finite presentability is an invariant under quasiisometry of Cayley graphs.
We choose to associate a metric space to a semigroup based on a Cayley graph of that semigroup. This metric space is constructed by removing directions, multiple edges and loops from the Cayley graph. We call this a skeleton of the semigroup.
We show that finite presentability of certain types of direct products, completely (0)simple, and Clifford semigroups is preserved under isomorphism of skeletons. A major tool employed in this is the ŠvarcMilnor Lemma.
We present an example that shows that in general, finite presentability is not an invariant property under isomorphism of skeletons of semigroups, and in fact is not an invariant property under quasiisometry of Cayley graphs for semigroups.
We give several skeletons and describe fully the semigroups that can be associated to these.
Fri, 26 Jun 2015 00:00:00 GMT
http://hdl.handle.net/10023/6923
20150626T00:00:00Z
Awang, Jennifer S.
Geometric semigroup theory means different things to different people, but it is agreed that it involves associating a geometric structure to a semigroup and deducing properties of the semigroup based on that structure.
One such property is finite presentability. In geometric group theory, the geometric structure of choice is the Cayley graph of the group. It is known that in group theory finite presentability is an invariant under quasiisometry of Cayley graphs.
We choose to associate a metric space to a semigroup based on a Cayley graph of that semigroup. This metric space is constructed by removing directions, multiple edges and loops from the Cayley graph. We call this a skeleton of the semigroup.
We show that finite presentability of certain types of direct products, completely (0)simple, and Clifford semigroups is preserved under isomorphism of skeletons. A major tool employed in this is the ŠvarcMilnor Lemma.
We present an example that shows that in general, finite presentability is not an invariant property under isomorphism of skeletons of semigroups, and in fact is not an invariant property under quasiisometry of Cayley graphs for semigroups.
We give several skeletons and describe fully the semigroups that can be associated to these.

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

Spatial variation in maximum dive depth in gray seals in relation to foraging.
http://hdl.handle.net/10023/6886
Habitat preference maps are a way of representing animals’ space use in two dimensions. For marine animals, the third dimension is an important aspect of spatial ecology. We used dive data from seven gray seals Halichoerus grypus (a primarily benthic forager) collected with GPS phone tags (Sea Mammal Research Unit) to investigate the distribution of the maximum depth visited in each dive. We modeled maximum dive depth as a function of spatiotemporal covariates using a generalized additive mixed model (GAMM) with individual as a random effect. Bathymetry, horizontal displacement, latitude and longitude, Julian day, sediment type, and light conditions accounted for 37% of the variability in the data. Persistent patterns of autocorrelation in the raw data suggest that individual intrinsic rhythm might be an important factor, not captured by external covariates. The strength of using this statistical method to generate spatial predictions of the distribution of maximum dive depth is its applicability to other plunge and pursuit divers. Despite being predictions of a point estimate, these maps provide some insight into the third dimension of habitat use in marine animals. The capacity to predict this aspect of vertical habitat use may help avoid conflict between animal habitat and coastal or offshore developments
Theoni Photopoulou was funded by SMRU Ltd in the form of a Ph.D. studentship, 2008–2012.
Tue, 01 Jul 2014 00:00:00 GMT
http://hdl.handle.net/10023/6886
20140701T00:00:00Z
Photopoulou, Theoni
Fedak, Mike
Thomas, Len
Matthiopoulos, Jason
Habitat preference maps are a way of representing animals’ space use in two dimensions. For marine animals, the third dimension is an important aspect of spatial ecology. We used dive data from seven gray seals Halichoerus grypus (a primarily benthic forager) collected with GPS phone tags (Sea Mammal Research Unit) to investigate the distribution of the maximum depth visited in each dive. We modeled maximum dive depth as a function of spatiotemporal covariates using a generalized additive mixed model (GAMM) with individual as a random effect. Bathymetry, horizontal displacement, latitude and longitude, Julian day, sediment type, and light conditions accounted for 37% of the variability in the data. Persistent patterns of autocorrelation in the raw data suggest that individual intrinsic rhythm might be an important factor, not captured by external covariates. The strength of using this statistical method to generate spatial predictions of the distribution of maximum dive depth is its applicability to other plunge and pursuit divers. Despite being predictions of a point estimate, these maps provide some insight into the third dimension of habitat use in marine animals. The capacity to predict this aspect of vertical habitat use may help avoid conflict between animal habitat and coastal or offshore developments

Estimating population sizes of lions Panthera leo and spotted hyaenas Crocuta crocuta in Uganda’s savannah parks, using lure count methods
http://hdl.handle.net/10023/6885
Despite > 60 years of conservation in Uganda’s national parks the populations of lions and spotted hyaenas in these areas have never been estimated using a census method. Estimates for some sites have been extrapolated to other protected areas and educated guesses have been made but there has been nothing more definitive. We used a lure count analysis method of callup counts to estimate populations of the lion Panthera leo and spotted hyaena Crocuta crocuta in the parks where reasonable numbers of these species exist: Queen Elizabeth Protected Area, Murchison Falls Conservation Area and Kidepo Valley National Park. We estimated a total of 408 lions and 324 hyaenas for these three conservation areas. It is unlikely that other conservation areas in Uganda host >10 lions or > 40 hyaenas. The Queen Elizabeth Protected Area had the largest populations of lions and hyaenas: 140 and 211, respectively. It is estimated that lion numbers have declined by 30% in this protected area since the late 1990s and there are increasing concerns for the longterm viability of both species in Uganda.
Funding: United States Agency for International Development
Tue, 01 Jul 2014 00:00:00 GMT
http://hdl.handle.net/10023/6885
20140701T00:00:00Z
Omoya, Edward Okot
Mudumba, Tutilo
Buckland, Stephen T
Mulondo, Paul
Plumptre, Andrew J
Despite > 60 years of conservation in Uganda’s national parks the populations of lions and spotted hyaenas in these areas have never been estimated using a census method. Estimates for some sites have been extrapolated to other protected areas and educated guesses have been made but there has been nothing more definitive. We used a lure count analysis method of callup counts to estimate populations of the lion Panthera leo and spotted hyaena Crocuta crocuta in the parks where reasonable numbers of these species exist: Queen Elizabeth Protected Area, Murchison Falls Conservation Area and Kidepo Valley National Park. We estimated a total of 408 lions and 324 hyaenas for these three conservation areas. It is unlikely that other conservation areas in Uganda host >10 lions or > 40 hyaenas. The Queen Elizabeth Protected Area had the largest populations of lions and hyaenas: 140 and 211, respectively. It is estimated that lion numbers have declined by 30% in this protected area since the late 1990s and there are increasing concerns for the longterm viability of both species in Uganda.

Inflations of geometric grid classes of permutations
http://hdl.handle.net/10023/6862
Geometric grid classes and the substitution decomposition have both been shown to be fundamental in the understanding of the structure of permutation classes. In particular, these are the two main tools in the recent classification of permutation classes of growth rate less than κ ≈ 2.20557 (a specific algebraic integer at which infinite antichains first appear). Using language and ordertheoretic methods, we prove that the substitution closures of geometric grid classes are well partially ordered, finitely based, and that all their subclasses have algebraic generating functions. We go on to show that the inflation of a geometric grid class by a strongly rational class is well partially ordered, and that all its subclasses have rational generating functions. This latter fact allows us to conclude that every permutation class with growth rate less than κ has a rational generating function. This bound is tight as there are permutation classes with growth rate κ which have nonrational generating functions.
All three authors were partially supported by EPSRC via the grant EP/J006440/1.
Sun, 01 Feb 2015 00:00:00 GMT
http://hdl.handle.net/10023/6862
20150201T00:00:00Z
Albert, M.D.
Ruskuc, Nik
Vatter, V.
Geometric grid classes and the substitution decomposition have both been shown to be fundamental in the understanding of the structure of permutation classes. In particular, these are the two main tools in the recent classification of permutation classes of growth rate less than κ ≈ 2.20557 (a specific algebraic integer at which infinite antichains first appear). Using language and ordertheoretic methods, we prove that the substitution closures of geometric grid classes are well partially ordered, finitely based, and that all their subclasses have algebraic generating functions. We go on to show that the inflation of a geometric grid class by a strongly rational class is well partially ordered, and that all its subclasses have rational generating functions. This latter fact allows us to conclude that every permutation class with growth rate less than κ has a rational generating function. This bound is tight as there are permutation classes with growth rate κ which have nonrational generating functions.

Annual report on the implementation of Council Regulation (EC) No 812/2004 during 2014
http://hdl.handle.net/10023/6855
Mon, 01 Jun 2015 00:00:00 GMT
http://hdl.handle.net/10023/6855
20150601T00:00:00Z
Northridge, Simon
Kingston, Al
Thomas, Len

Subalgebras of FApresentable algebras
http://hdl.handle.net/10023/6852
Automatic presentations, also called FApresentations, were introduced to extend finite model theory to infinite structures whilst retaining the solubility of fundamental decision problems. This paper studies FApresentable algebras. First, an example is given to show that the class of finitely generated FApresentable algebras is not closed under forming finitely generated subalgebras, even within the class of algebras with only unary operations. In contrast, a finitely generated subalgebra of an FApresentable algebra with a single unary operation is itself FApresentable. Furthermore, it is proven that the class of unary FApresentable algebras is closed under forming finitely generated subalgebras and that the membership problem for such subalgebras is decidable.
Sun, 01 Jun 2014 00:00:00 GMT
http://hdl.handle.net/10023/6852
20140601T00:00:00Z
Cain, A.J.
Ruskuc, Nik
Automatic presentations, also called FApresentations, were introduced to extend finite model theory to infinite structures whilst retaining the solubility of fundamental decision problems. This paper studies FApresentable algebras. First, an example is given to show that the class of finitely generated FApresentable algebras is not closed under forming finitely generated subalgebras, even within the class of algebras with only unary operations. In contrast, a finitely generated subalgebra of an FApresentable algebra with a single unary operation is itself FApresentable. Furthermore, it is proven that the class of unary FApresentable algebras is closed under forming finitely generated subalgebras and that the membership problem for such subalgebras is decidable.

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

Developing and enhancing biodiversity monitoring programmes : a collaborative assessment of priorities
http://hdl.handle.net/10023/6756
Biodiversity is changing at unprecedented rates, and it is increasingly important that these changes are quantified through monitoring programmes. Previous recommendations for developing or enhancing these programmes focus either on the end goals, that is the intended use of the data, or on how these goals are achieved, for example through volunteer involvement in citizen science, but not both. These recommendations are rarely prioritized. We used a collaborative approach, involving 52 experts in biodiversity monitoring in the UK, to develop a list of attributes of relevance to any biodiversity monitoring programme and to order these attributes by their priority. We also ranked the attributes according to their importance in monitoring biodiversity in the UK. Experts involved included data users, funders, programme organizers and participants in data collection. They covered expertise in a wide range of taxa. We developed a final list of 25 attributes of biodiversity monitoring schemes, ordered from the most elemental (those essential for monitoring schemes; e.g. articulate the objectives and gain sufficient participants) to the most aspirational (e.g. electronic data capture in the field, reporting change annually). This ordered list is a practical framework which can be used to support the development of monitoring programmes. People's ranking of attributes revealed a difference between those who considered attributes with benefits to end users to be most important (e.g. people from governmental organizations) and those who considered attributes with greatest benefit to participants to be most important (e.g. people involved with volunteer biological recording schemes). This reveals a distinction between focussing on aims and the pragmatism in achieving those aims. Synthesis and applications. The ordered list of attributes developed in this study will assist in prioritizing resources to develop biodiversity monitoring programmes (including citizen science). The potential conflict between end users of data and participants in data collection that we discovered should be addressed by involving the diversity of stakeholders at all stages of programme development. This will maximize the chance of successfully achieving the goals of biodiversity monitoring programmes.
This work was supported by the UK Department for Environment, Food and Rural Affairs (Defra) [grant number WC1014] and the Natural Environment Research Council through National Capability funding to the Centre for Ecology and Hydrology.
Mon, 01 Jun 2015 00:00:00 GMT
http://hdl.handle.net/10023/6756
20150601T00:00:00Z
Pocock, Michael J. O.
Newson, Stuart E.
Henderson, Ian G.
Peyton, Jodey
Sutherland, William J.
Noble, David G.
Ball, Stuart G.
Beckmann, Björn C.
Biggs, Jeremy
Brereton, Tom
Bullock, David J.
Buckland, Stephen T.
Edwards, Mike
Eaton, Mark A.
Harvey, Martin C.
Hill, Mark O.
Horlock, Martin
Hubble, David S.
Julian, Angela M.
Mackey, Edward C.
Mann, Darren J.
Marshall, Matthew J.
Medlock, Jolyon M.
O'Mahony, Elaine M.
Pacheco, Marina
Porter, Keith
Prentice, Steve
Procter, Deborah A.
Roy, Helen E.
Southway, Sue E.
Shortall, Chris R.
Stewart, Alan J. A.
Wembridge, David E.
Wright, Mark A.
Roy, David B.
Biodiversity is changing at unprecedented rates, and it is increasingly important that these changes are quantified through monitoring programmes. Previous recommendations for developing or enhancing these programmes focus either on the end goals, that is the intended use of the data, or on how these goals are achieved, for example through volunteer involvement in citizen science, but not both. These recommendations are rarely prioritized. We used a collaborative approach, involving 52 experts in biodiversity monitoring in the UK, to develop a list of attributes of relevance to any biodiversity monitoring programme and to order these attributes by their priority. We also ranked the attributes according to their importance in monitoring biodiversity in the UK. Experts involved included data users, funders, programme organizers and participants in data collection. They covered expertise in a wide range of taxa. We developed a final list of 25 attributes of biodiversity monitoring schemes, ordered from the most elemental (those essential for monitoring schemes; e.g. articulate the objectives and gain sufficient participants) to the most aspirational (e.g. electronic data capture in the field, reporting change annually). This ordered list is a practical framework which can be used to support the development of monitoring programmes. People's ranking of attributes revealed a difference between those who considered attributes with benefits to end users to be most important (e.g. people from governmental organizations) and those who considered attributes with greatest benefit to participants to be most important (e.g. people involved with volunteer biological recording schemes). This reveals a distinction between focussing on aims and the pragmatism in achieving those aims. Synthesis and applications. The ordered list of attributes developed in this study will assist in prioritizing resources to develop biodiversity monitoring programmes (including citizen science). The potential conflict between end users of data and participants in data collection that we discovered should be addressed by involving the diversity of stakeholders at all stages of programme development. This will maximize the chance of successfully achieving the goals of biodiversity monitoring programmes.

Bayesian methods for hierarchical distance sampling models
http://hdl.handle.net/10023/6714
The few distance sampling studies that use Bayesian methods typically consider only line transect sampling with a halfnormal detection function. We present a Bayesian approach to analyse distance sampling data applicable to line and point transects, exact and interval distance data and any detection function possibly including covariates affecting detection probabilities. We use an integrated likelihood which combines the detection and count models. For the latter, counts are related to covariates in a loglinear mixed effect Poisson model which accommodates correlated counts. We use a MetropolisHastings algorithm for updating parameters and a reversible jump algorithm to include model selection for both the detection function and count models. The approach is applied to a largescale experimental design study of northern bobwhite coveys where the interest was to assess the effect of establishing herbaceous buffers around agricultural fields in several states in the US on bird densities. Results were compared with those from an existing maximum likelihood approach that analyses the detection and count models in two stages. Both methods revealed an increase of covey densities on buffered fields. Our approach gave estimates with higher precision even though it does not condition on a known detection function for the count model.
Cornelia S. Oedekoven was supported by a studentship jointly funded by the University of St Andrews and EPSRC (EPSRC grant EP/C522702/1), through the National Centre for Statistical Ecology.
Sun, 01 Jun 2014 00:00:00 GMT
http://hdl.handle.net/10023/6714
20140601T00:00:00Z
Oedekoven, Cornelia Sabrina
Buckland, Stephen Terrence
MacKenzie, Monique Lea
King, Ruth
Evans, Kristine
Burger, Wes
The few distance sampling studies that use Bayesian methods typically consider only line transect sampling with a halfnormal detection function. We present a Bayesian approach to analyse distance sampling data applicable to line and point transects, exact and interval distance data and any detection function possibly including covariates affecting detection probabilities. We use an integrated likelihood which combines the detection and count models. For the latter, counts are related to covariates in a loglinear mixed effect Poisson model which accommodates correlated counts. We use a MetropolisHastings algorithm for updating parameters and a reversible jump algorithm to include model selection for both the detection function and count models. The approach is applied to a largescale experimental design study of northern bobwhite coveys where the interest was to assess the effect of establishing herbaceous buffers around agricultural fields in several states in the US on bird densities. Results were compared with those from an existing maximum likelihood approach that analyses the detection and count models in two stages. Both methods revealed an increase of covey densities on buffered fields. Our approach gave estimates with higher precision even though it does not condition on a known detection function for the count model.

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

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

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

Using accelerometers to determine the calling behavior of tagged baleen whales
http://hdl.handle.net/10023/6623
Lowfrequency acoustic signals generated by baleen whales can propagate over vast distances, making the assignment of calls to specific individuals problematic. Here, we report the novel use of acoustic recording tags equipped with highresolution accelerometers to detect vibrations from the surface of two tagged fin whales that directly match the timing of recorded acoustic signals. A tag deployed on a buoy in the vicinity of calling fin whales and a recording from a tag that had just fallen off a whale were able to detect calls acoustically but did not record corresponding accelerometer signals that were measured on calling individuals. Across the hundreds of calls measured on two tagged fin whales, the accelerometer response was generally anisotropic across all three axes, appeared to depend on tag placement and increased with the level of received sound. These data demonstrate that highsample rate accelerometry can provide important insights into the acoustic behavior of baleen whales that communicate at low frequencies. This method helps identify vocalizing whales, which in turn enables the quantification of call rates, a fundamental component of models used to estimate baleen whale abundance and distribution from passive acoustic monitoring.
Tue, 15 Jul 2014 00:00:00 GMT
http://hdl.handle.net/10023/6623
20140715T00:00:00Z
Goldbogen, Jeremy
De Ruiter, Stacy Lynn
Stimpert, Alison
Calambokidis, John
Friedlaender, Ari
Schorr, Greg
Moretti, David
Tyack, Peter Lloyd
Southall, Brandon
Lowfrequency acoustic signals generated by baleen whales can propagate over vast distances, making the assignment of calls to specific individuals problematic. Here, we report the novel use of acoustic recording tags equipped with highresolution accelerometers to detect vibrations from the surface of two tagged fin whales that directly match the timing of recorded acoustic signals. A tag deployed on a buoy in the vicinity of calling fin whales and a recording from a tag that had just fallen off a whale were able to detect calls acoustically but did not record corresponding accelerometer signals that were measured on calling individuals. Across the hundreds of calls measured on two tagged fin whales, the accelerometer response was generally anisotropic across all three axes, appeared to depend on tag placement and increased with the level of received sound. These data demonstrate that highsample rate accelerometry can provide important insights into the acoustic behavior of baleen whales that communicate at low frequencies. This method helps identify vocalizing whales, which in turn enables the quantification of call rates, a fundamental component of models used to estimate baleen whale abundance and distribution from passive acoustic monitoring.

Cayley automaton semigroups
http://hdl.handle.net/10023/6558
Let S be a semigroup, C(S) the automaton constructed from the right Cayley
graph of S with respect to all of S as the generating set and ∑(C(S)) the
automaton semigroup constructed from C(S). Such semigroups are termed
Cayley automaton semigroups. For a given semigroup S we aim to establish
connections between S and ∑(C(S)).
For a finite monogenic semigroup S with a nontrivial cyclic subgroup C[sub]n we
show that ∑(C(S)) is a small extension of a free semigroup of rank n, and
that in the case of a trivial subgroup ∑(C(S)) is finite.
The notion of invariance is considered and we examine those semigroups S
satisfying S ≅ ∑(C(S)). We classify which bands satisfy this, showing that
they are those bands with faithful leftregular representations, but exhibit
examples outwith this classification. In doing so we answer an open problem
of Cain.
Following this, we consider iterations of the construction and show that for
any n there exists a semigroup where we can iterate the construction n times
before reaching a semigroup satisfying S ≅ ∑(C(S)). We also give an example of a semigroup where repeated iteration never produces a semigroup
satisfying S ≅ ∑(C(S)).
Cayley automaton semigroups of infinite semigroups are also considered and
we generalise and extend a result of Silva and Steinberg to cancellative semigroups. We also construct the Cayley automaton semigroup of the bicyclic
monoid, showing in particular that it is not finitely generated.
Fri, 26 Jun 2015 00:00:00 GMT
http://hdl.handle.net/10023/6558
20150626T00:00:00Z
McLeman, Alexander Lewis Andrew
Let S be a semigroup, C(S) the automaton constructed from the right Cayley
graph of S with respect to all of S as the generating set and ∑(C(S)) the
automaton semigroup constructed from C(S). Such semigroups are termed
Cayley automaton semigroups. For a given semigroup S we aim to establish
connections between S and ∑(C(S)).
For a finite monogenic semigroup S with a nontrivial cyclic subgroup C[sub]n we
show that ∑(C(S)) is a small extension of a free semigroup of rank n, and
that in the case of a trivial subgroup ∑(C(S)) is finite.
The notion of invariance is considered and we examine those semigroups S
satisfying S ≅ ∑(C(S)). We classify which bands satisfy this, showing that
they are those bands with faithful leftregular representations, but exhibit
examples outwith this classification. In doing so we answer an open problem
of Cain.
Following this, we consider iterations of the construction and show that for
any n there exists a semigroup where we can iterate the construction n times
before reaching a semigroup satisfying S ≅ ∑(C(S)). We also give an example of a semigroup where repeated iteration never produces a semigroup
satisfying S ≅ ∑(C(S)).
Cayley automaton semigroups of infinite semigroups are also considered and
we generalise and extend a result of Silva and Steinberg to cancellative semigroups. We also construct the Cayley automaton semigroup of the bicyclic
monoid, showing in particular that it is not finitely generated.

Nested rowcolumn designs for nearfactorial experiments with two treatment factors and one control treatment
http://hdl.handle.net/10023/6556
This paper presents some methods of designing experiments in a block design with nested rows and columns. The treatments consist of all combinations of levels of two treatment factors, with an additional control treatment.
The authors also thank Queen Mary, University of London, the University of St Andrews and the Poznan University of Life Sciences for financial support. The second author was also supported by the BritishPolish Young Scientists Programme, grant WAR/342/116.
Thu, 01 Oct 2015 00:00:00 GMT
http://hdl.handle.net/10023/6556
20151001T00:00:00Z
Bailey, Rosemary Anne
Lacka, Agnieszka
This paper presents some methods of designing experiments in a block design with nested rows and columns. The treatments consist of all combinations of levels of two treatment factors, with an additional control treatment.

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

Carl Friedrich Geiser and Ferdinand Rudio : the men behind the first International Congress of Mathematicians
http://hdl.handle.net/10023/6536
The first International Congress of Mathematicians (ICM) was held in Zurich in 1897, setting the standards for all future ICMs. Whilst giving an overview of the congress itself, this thesis focuses on the Swiss organisers, who were predominantly university professors and secondary school teachers. As this thesis aims to offer some insight into their lives, it includes their biographies, highlighting their individual contributions to the congress. Furthermore, it explains why Zurich was chosen as the first host city and how the committee proceeded with the congress organisation.
Two of the main organisers were the Swiss geometers Carl Friedrich Geiser (18431934) and Ferdinand Rudio (18561929). In addition to the congress, they also made valuable contributions to mathematical education, and in Rudio’s case, the history of mathematics. Therefore, this thesis focuses primarily on these two mathematicians.
As for Geiser, the relationship to his greatuncle Jakob Steiner is explained in more detail. Furthermore, his contributions to the administration of the Swiss Federal Institute of Technology are summarised. Due to the overarching theme of mathematical education and collaborations in this thesis, Geiser’s schoolbook "Einleitung in die synthetische Geometrie" is considered in more detail and Geiser’s methods are highlighted.
A selection of Rudio’s contributions to the history of mathematics is studied as well. His book "Archimedes, Huygens, Lambert, Legendre" is analysed and compared to E W Hobson’s treatise "Squaring the Circle". Furthermore, Rudio’s papers relating to the commentary of Simplicius on quadratures by Antiphon and Hippocrates are considered, focusing on Rudio’s translation of the commentary and on "Die Möndchen des Hippokrates". The thesis concludes with an analysis of Rudio’s popular lectures "Leonhard Euler" and "Über den Antheil der mathematischen Wissenschaften an der Kultur der Renaissance", which are prime examples of his approach to the history of mathematics.
Fri, 26 Jun 2015 00:00:00 GMT
http://hdl.handle.net/10023/6536
20150626T00:00:00Z
Eminger, Stefanie Ursula
The first International Congress of Mathematicians (ICM) was held in Zurich in 1897, setting the standards for all future ICMs. Whilst giving an overview of the congress itself, this thesis focuses on the Swiss organisers, who were predominantly university professors and secondary school teachers. As this thesis aims to offer some insight into their lives, it includes their biographies, highlighting their individual contributions to the congress. Furthermore, it explains why Zurich was chosen as the first host city and how the committee proceeded with the congress organisation.
Two of the main organisers were the Swiss geometers Carl Friedrich Geiser (18431934) and Ferdinand Rudio (18561929). In addition to the congress, they also made valuable contributions to mathematical education, and in Rudio’s case, the history of mathematics. Therefore, this thesis focuses primarily on these two mathematicians.
As for Geiser, the relationship to his greatuncle Jakob Steiner is explained in more detail. Furthermore, his contributions to the administration of the Swiss Federal Institute of Technology are summarised. Due to the overarching theme of mathematical education and collaborations in this thesis, Geiser’s schoolbook "Einleitung in die synthetische Geometrie" is considered in more detail and Geiser’s methods are highlighted.
A selection of Rudio’s contributions to the history of mathematics is studied as well. His book "Archimedes, Huygens, Lambert, Legendre" is analysed and compared to E W Hobson’s treatise "Squaring the Circle". Furthermore, Rudio’s papers relating to the commentary of Simplicius on quadratures by Antiphon and Hippocrates are considered, focusing on Rudio’s translation of the commentary and on "Die Möndchen des Hippokrates". The thesis concludes with an analysis of Rudio’s popular lectures "Leonhard Euler" and "Über den Antheil der mathematischen Wissenschaften an der Kultur der Renaissance", which are prime examples of his approach to the history of mathematics.

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

The effect of animal movement on line transect estimates of abundance
http://hdl.handle.net/10023/6466
Line transect sampling is a distance sampling method for estimating the abundance of wild animal populations. One key assumption of this method is that all animals are detected at their initial location. Animal movement independent of the transect and observer can thus cause substantial bias. We present an analytic expression for this bias when detection within the transect is certain (strip transect sampling) and use simulation to quantify bias when detection falls off with distance from the line (line transect sampling). We also explore the nonlinear relationship between bias, detection, and animal movement by varying detectability and movement type. We consider animals that move in randomly orientated straight lines, which provides an upper bound on bias, and animals that are constrained to a home range of random radius. We find that bias is reduced when animal movement is constrained, and bias is considerably smaller in line transect sampling than strip transect sampling provided that mean animal speed is less than observer speed. By contrast, when mean animal speed exceeds observer speed the bias in line transect sampling becomes comparable with, and may exceed, that of strip transect sampling. Bias from independent animal movement is reduced by the observer searching further perpendicular to the transect, searching a shorter distance ahead and by ignoring animals that may overtake the observer from behind. However, when animals move in response to the observer, the standard practice of searching further ahead should continue as the bias from responsive movement is often greater than that from independent movement.
This work was supported by the University of St Andrews (http://www.standrews.ac.uk/; RG, STB, LT) and by a summer scholarship and PhD grant from The Carnegie Trust for the Universities of Scotland (http://www.carnegietrust.org/) to RG.
Mon, 23 Mar 2015 00:00:00 GMT
http://hdl.handle.net/10023/6466
20150323T00:00:00Z
Glennie, R.
Buckland, S.T.
Thomas, L.
Line transect sampling is a distance sampling method for estimating the abundance of wild animal populations. One key assumption of this method is that all animals are detected at their initial location. Animal movement independent of the transect and observer can thus cause substantial bias. We present an analytic expression for this bias when detection within the transect is certain (strip transect sampling) and use simulation to quantify bias when detection falls off with distance from the line (line transect sampling). We also explore the nonlinear relationship between bias, detection, and animal movement by varying detectability and movement type. We consider animals that move in randomly orientated straight lines, which provides an upper bound on bias, and animals that are constrained to a home range of random radius. We find that bias is reduced when animal movement is constrained, and bias is considerably smaller in line transect sampling than strip transect sampling provided that mean animal speed is less than observer speed. By contrast, when mean animal speed exceeds observer speed the bias in line transect sampling becomes comparable with, and may exceed, that of strip transect sampling. Bias from independent animal movement is reduced by the observer searching further perpendicular to the transect, searching a shorter distance ahead and by ignoring animals that may overtake the observer from behind. However, when animals move in response to the observer, the standard practice of searching further ahead should continue as the bias from responsive movement is often greater than that from independent movement.

Mixture models for distance sampling detection functions
http://hdl.handle.net/10023/6463
We present a new class of models for the detection function in distance sampling surveys of wildlife populations, based on finite mixtures of simple parametric key functions such as the halfnormal. The models share many of the features of the widelyused “key function plus series adjustment” (K+A) formulation: they are flexible, produce plausible shapes with a small number of parameters, allow incorporation of covariates in addition to distance and can be fitted using maximum likelihood. One important advantage over the K+A approach is that the mixtures are automatically monotonic nonincreasing and nonnegative, so constrained optimization is not required to ensure distance sampling assumptions are honoured. We compare the mixture formulation to the K+A approach using simulations to evaluate its applicability in a wide set of challenging situations. We also reanalyze four previously problematic realworld case studies. We find mixtures outperform K+A methods in many cases, particularly spiked line transect data (i.e., where detectability drops rapidly at small distances) and larger sample sizes. We recommend that current standard model selection methods for distance sampling detection functions are extended to include mixture models in the candidate set.
Funding: EPSRC DTG
Fri, 20 Mar 2015 00:00:00 GMT
http://hdl.handle.net/10023/6463
20150320T00:00:00Z
Miller, David Lawrence
Thomas, Len
We present a new class of models for the detection function in distance sampling surveys of wildlife populations, based on finite mixtures of simple parametric key functions such as the halfnormal. The models share many of the features of the widelyused “key function plus series adjustment” (K+A) formulation: they are flexible, produce plausible shapes with a small number of parameters, allow incorporation of covariates in addition to distance and can be fitted using maximum likelihood. One important advantage over the K+A approach is that the mixtures are automatically monotonic nonincreasing and nonnegative, so constrained optimization is not required to ensure distance sampling assumptions are honoured. We compare the mixture formulation to the K+A approach using simulations to evaluate its applicability in a wide set of challenging situations. We also reanalyze four previously problematic realworld case studies. We find mixtures outperform K+A methods in many cases, particularly spiked line transect data (i.e., where detectability drops rapidly at small distances) and larger sample sizes. We recommend that current standard model selection methods for distance sampling detection functions are extended to include mixture models in the candidate set.

Most switching classes with primitive automorphism groups contain graphs with trivial groups
http://hdl.handle.net/10023/6429
The operation of switching a graph Gamma with respect to a subset X of the vertex set interchanges edges and nonedges between X and its complement, leaving the rest of the graph unchanged. This is an equivalence relation on the set of graphs on a given vertex set, so we can talk about the automorphism group of a switching class of graphs. It might be thought that switching classes with many automorphisms would have the property that all their graphs also have many automorphisms. But the main theorem of this paper shows a different picture: with finitely many exceptions, if a nontrivial switching class S has primitive automorphism group, then it contains a graph whose automorphism group is trivial. We also find all the exceptional switching classes; up to complementation, there are just six.
Mon, 01 Jun 2015 00:00:00 GMT
http://hdl.handle.net/10023/6429
20150601T00:00:00Z
Cameron, Peter Jephson
Spiga, Pablo
The operation of switching a graph Gamma with respect to a subset X of the vertex set interchanges edges and nonedges between X and its complement, leaving the rest of the graph unchanged. This is an equivalence relation on the set of graphs on a given vertex set, so we can talk about the automorphism group of a switching class of graphs. It might be thought that switching classes with many automorphisms would have the property that all their graphs also have many automorphisms. But the main theorem of this paper shows a different picture: with finitely many exceptions, if a nontrivial switching class S has primitive automorphism group, then it contains a graph whose automorphism group is trivial. We also find all the exceptional switching classes; up to complementation, there are just six.

Random coeffcient models for complex longitudinal data
http://hdl.handle.net/10023/6386
Longitudinal data are common in biological research. However, real data sets vary considerably in terms of their structure and complexity and present many challenges for statistical modelling. This thesis proposes a series of methods using random coefficients for modelling two broad types of longitudinal response: normally distributed measurements and binary recapture data.
Biased inference can occur in linear mixedeffects modelling if subjects are drawn from a number of unknown subpopulations, or if the residual covariance is poorly specified. To address some of the shortcomings of previous approaches in terms of model selection and flexibility, this thesis presents methods for: (i) determining the presence of latent grouping structures using a twostep approach, involving regression splines for modelling functional random effects and mixture modelling of the fitted random effects; and (ii) flexible of modelling of the residual covariance matrix using regression splines to specify smooth and potentially nonmonotonic variance and correlation functions.
Spatially explicit capturerecapture methods for estimating the density of animal populations have shown a rapid increase in popularity over recent years. However, further refinements to existing theory and fitting software are required to apply these methods in many situations. This thesis presents: (i) an analysis of recapture data from an acoustic survey of gibbons using supplementary data in the form of estimated angles to detections, (ii) the development of a multioccasion likelihood including a model for stochastic availability using a partially observed random effect (interpreted in terms of calling behaviour in the case of gibbons), and (iii) an analysis of recapture data from a population of radiotagged skates using a conditional likelihood that allows the density of animal activity centres to be modelled as functions of time, space and animallevel covariates.
Fri, 27 Jun 2014 00:00:00 GMT
http://hdl.handle.net/10023/6386
20140627T00:00:00Z
Kidney, Darren
Longitudinal data are common in biological research. However, real data sets vary considerably in terms of their structure and complexity and present many challenges for statistical modelling. This thesis proposes a series of methods using random coefficients for modelling two broad types of longitudinal response: normally distributed measurements and binary recapture data.
Biased inference can occur in linear mixedeffects modelling if subjects are drawn from a number of unknown subpopulations, or if the residual covariance is poorly specified. To address some of the shortcomings of previous approaches in terms of model selection and flexibility, this thesis presents methods for: (i) determining the presence of latent grouping structures using a twostep approach, involving regression splines for modelling functional random effects and mixture modelling of the fitted random effects; and (ii) flexible of modelling of the residual covariance matrix using regression splines to specify smooth and potentially nonmonotonic variance and correlation functions.
Spatially explicit capturerecapture methods for estimating the density of animal populations have shown a rapid increase in popularity over recent years. However, further refinements to existing theory and fitting software are required to apply these methods in many situations. This thesis presents: (i) an analysis of recapture data from an acoustic survey of gibbons using supplementary data in the form of estimated angles to detections, (ii) the development of a multioccasion likelihood including a model for stochastic availability using a partially observed random effect (interpreted in terms of calling behaviour in the case of gibbons), and (iii) an analysis of recapture data from a population of radiotagged skates using a conditional likelihood that allows the density of animal activity centres to be modelled as functions of time, space and animallevel covariates.

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

Peter Guthrie Tait : new insights into aspects of his life and work : and associated topics in the history of mathematics
http://hdl.handle.net/10023/6330
In this thesis I present new insights into aspects of Peter Guthrie Tait’s life and work, derived principally from largelyunexplored primary source material: Tait’s scrapbook, the Tait–Maxwell schoolbook and Tait’s pocket notebook. By way of associated historical insights, I also come to discuss the innovative and farreaching mathematics of the elusive Frenchman, C.V. Mourey.
P. G. Tait (1831–1901) F.R.S.E., Professor of Mathematics at the Queen’s College, Belfast (1854–1860) and of Natural Philosophy at the University of Edinburgh (1860–1901), was one of the leading physicists and mathematicians in Europe in the nineteenth century. His expertise encompassed the breadth of physical science and mathematics. However, since the nineteenth century he has been unfortunately overlooked—overshadowed, perhaps, by the brilliance of his personal friends, James Clerk Maxwell (1831–1879), Sir William Rowan Hamilton (1805–1865) and William Thomson (1824–1907), later Lord Kelvin.
Here I present the results of extensive research into the Tait family history. I explore the spiritual aspect of Tait’s life in connection with The Unseen Universe (1875) which Tait coauthored with Balfour Stewart (1828–1887). I also reveal Tait’s surprising involvement in statistics and give an account of his introduction to complex numbers, as a schoolboy at the Edinburgh Academy. A highlight of the thesis is a reevaluation of C.V. Mourey’s 1828 work, La Vraie Théorie des quantités négatives et des quantités prétendues imaginaires, which I consider from the perspective of algebraic reform. The thesis also contains: (i) a transcription of an unpublished paper by Hamilton on the fundamental theorem of algebra which was inspired by Mourey and (ii) new biographical information on Mourey.
Fri, 26 Jun 2015 00:00:00 GMT
http://hdl.handle.net/10023/6330
20150626T00:00:00Z
Lewis, Elizabeth Faith
In this thesis I present new insights into aspects of Peter Guthrie Tait’s life and work, derived principally from largelyunexplored primary source material: Tait’s scrapbook, the Tait–Maxwell schoolbook and Tait’s pocket notebook. By way of associated historical insights, I also come to discuss the innovative and farreaching mathematics of the elusive Frenchman, C.V. Mourey.
P. G. Tait (1831–1901) F.R.S.E., Professor of Mathematics at the Queen’s College, Belfast (1854–1860) and of Natural Philosophy at the University of Edinburgh (1860–1901), was one of the leading physicists and mathematicians in Europe in the nineteenth century. His expertise encompassed the breadth of physical science and mathematics. However, since the nineteenth century he has been unfortunately overlooked—overshadowed, perhaps, by the brilliance of his personal friends, James Clerk Maxwell (1831–1879), Sir William Rowan Hamilton (1805–1865) and William Thomson (1824–1907), later Lord Kelvin.
Here I present the results of extensive research into the Tait family history. I explore the spiritual aspect of Tait’s life in connection with The Unseen Universe (1875) which Tait coauthored with Balfour Stewart (1828–1887). I also reveal Tait’s surprising involvement in statistics and give an account of his introduction to complex numbers, as a schoolboy at the Edinburgh Academy. A highlight of the thesis is a reevaluation of C.V. Mourey’s 1828 work, La Vraie Théorie des quantités négatives et des quantités prétendues imaginaires, which I consider from the perspective of algebraic reform. The thesis also contains: (i) a transcription of an unpublished paper by Hamilton on the fundamental theorem of algebra which was inspired by Mourey and (ii) new biographical information on Mourey.

On residual finiteness of monoids, their Schützenberger groups and associated actions
http://hdl.handle.net/10023/6310
In this paper we discuss connections between the following properties: (RFM) residual finiteness of a monoid M ; (RFSG) residual finiteness of Schützenberger groups of M ; and (RFRL) residual finiteness of the natural actions of M on its Green's R and Lclasses. The general question is whether (RFM) implies (RFSG) and/or (RFRL), and vice versa. We consider these questions in all the possible combinations of the following situations: M is an arbitrary monoid; M is an arbitrary regular monoid; every Jclass of M has finitely many R and Lclasses; M has finitely many left and right ideals. In each case we obtain complete answers, which are summarised in a table.
RG was supported by an EPSRC Postdoctoral Fellowship EP/E043194/1 held at the University of St Andrews, Scotland.
Sun, 01 Jun 2014 00:00:00 GMT
http://hdl.handle.net/10023/6310
20140601T00:00:00Z
Gray, R
Ruskuc, Nik
In this paper we discuss connections between the following properties: (RFM) residual finiteness of a monoid M ; (RFSG) residual finiteness of Schützenberger groups of M ; and (RFRL) residual finiteness of the natural actions of M on its Green's R and Lclasses. The general question is whether (RFM) implies (RFSG) and/or (RFRL), and vice versa. We consider these questions in all the possible combinations of the following situations: M is an arbitrary monoid; M is an arbitrary regular monoid; every Jclass of M has finitely many R and Lclasses; M has finitely many left and right ideals. In each case we obtain complete answers, which are summarised in a table.

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

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

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

Bayesian hierarchical modelling of continuous nonnegative longitudinal data with a spike at zero : an application to a study of birds visiting gardens in winter
http://hdl.handle.net/10023/6164
The development of methods for dealing with continuous data with a spike at zero has lagged behind those for overdispersed or zeroinflated count data. We consider longitudinal ecological data corresponding to an annual average of 26 weekly maximum counts of birds, and are hence effectively continuous, bounded below by zero but also with a discrete mass at zero. We develop a Bayesian hierarchical Tweedie regression model that can directly accommodate the excess number of zeros common to this type of data, whilst accounting for both spatial and temporal correlation. Implementation of the model is conducted in a Markov chain Monte Carlo (MCMC) framework, using reversible jump MCMC to explore uncertainty across both parameter and model spaces. This regression modelling framework is very flexible and removes the need to make strong assumptions about meanvariance relationships a priori. It can also directly account for the spike at zero, whilst being easily applicable to other types of data and other model formulations. Whilst a correlative study such as this cannot prove causation, our results suggest that an increase in an avian predator may have led to an overall decrease in the number of one of its prey species visiting garden feeding stations in the United Kingdom. This may reflect a change in behaviour of house sparrows to avoid feeding stations frequented by sparrowhawks, or a reduction in house sparrow population size as a result of sparrowhawk increase.
Tue, 01 Mar 2016 00:00:00 GMT
http://hdl.handle.net/10023/6164
20160301T00:00:00Z
Swallow, Benjamin Thomas
Buckland, Stephen Terrence
King, Ruth
Toms, Mike
The development of methods for dealing with continuous data with a spike at zero has lagged behind those for overdispersed or zeroinflated count data. We consider longitudinal ecological data corresponding to an annual average of 26 weekly maximum counts of birds, and are hence effectively continuous, bounded below by zero but also with a discrete mass at zero. We develop a Bayesian hierarchical Tweedie regression model that can directly accommodate the excess number of zeros common to this type of data, whilst accounting for both spatial and temporal correlation. Implementation of the model is conducted in a Markov chain Monte Carlo (MCMC) framework, using reversible jump MCMC to explore uncertainty across both parameter and model spaces. This regression modelling framework is very flexible and removes the need to make strong assumptions about meanvariance relationships a priori. It can also directly account for the spike at zero, whilst being easily applicable to other types of data and other model formulations. Whilst a correlative study such as this cannot prove causation, our results suggest that an increase in an avian predator may have led to an overall decrease in the number of one of its prey species visiting garden feeding stations in the United Kingdom. This may reflect a change in behaviour of house sparrows to avoid feeding stations frequented by sparrowhawks, or a reduction in house sparrow population size as a result of sparrowhawk increase.

Statistical ecology comes of age
http://hdl.handle.net/10023/6128
The desire to predict the consequences of global environmental change has been the driver towards more realistic models embracing the variability and uncertainties inherent in ecology. Statistical ecology has gelled over the past decade as a discipline that moves away from describing patterns towards modelling the ecological processes that generate these patterns. Following the fourth International Statistical Ecology Conference (1 –4 July 2014) in Montpellier, France, we analyse current trends in statistical ecology. Important advances in the analysis of individual movement, and in the modelling of population dynamics and species distributions, are made possible by the increasing use of hierarchical and hidden process models. Exciting research perspectives include the development of methods to interpret citizen science data and of efficient, flexible computational algorithms for model fitting. Statistical ecology has come of age: it now provides a general and mathematically rigorous framework linking ecological theory and empirical data.
Wed, 24 Dec 2014 00:00:00 GMT
http://hdl.handle.net/10023/6128
20141224T00:00:00Z
Gimenez, Olivier
Buckland, Stephen Terrence
Morgan, Byron J. T.
Bez, Nicolas
Bertrand, Sophie
Choquet, Remi
Dray, Stephane
Etienne, MariePierre
Fewster, Rachel
Gosselin, Frederic
Merigot, Bastien
Monestiez, Pascal
Morales, Juan M.
Mortier, Frederic
Munoz, Francois
Ovaskainen, Otso
Pavoine, Sandrine
Pradel, Roger
Schurr, Frank M.
Thomas, Len
Thuiller, Wilfried
Trenkel, Verena
de Valpine, Perry
Rexstad, Eric
The desire to predict the consequences of global environmental change has been the driver towards more realistic models embracing the variability and uncertainties inherent in ecology. Statistical ecology has gelled over the past decade as a discipline that moves away from describing patterns towards modelling the ecological processes that generate these patterns. Following the fourth International Statistical Ecology Conference (1 –4 July 2014) in Montpellier, France, we analyse current trends in statistical ecology. Important advances in the analysis of individual movement, and in the modelling of population dynamics and species distributions, are made possible by the increasing use of hierarchical and hidden process models. Exciting research perspectives include the development of methods to interpret citizen science data and of efficient, flexible computational algorithms for model fitting. Statistical ecology has come of age: it now provides a general and mathematically rigorous framework linking ecological theory and empirical data.

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

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

Interannual and seasonal trends in cetacean distribution, density and abundance off southern California
http://hdl.handle.net/10023/6088
Trends in cetacean density and distribution off southern California were assessed through visual linetransect surveys during thirtyseven California Cooperative Oceanic Fisheries Investigations (CalCOFI) cruises from July 2004–November 2013. From sightings of the six most commonly encountered cetacean species, seasonal, annual and overall density estimates were calculated. Blue whales (Balaenoptera musculus), fin whales (Balaenoptera physalus) and humpback whales (Megaptera novaeangliae) were the most frequently sighted baleen whales with overall densities of 0.91/1000 km2 (CV=0.27), 2.73/1000 km2 (CV=0.19), and 1.17/1000 km2 (CV=0.21) respectively. Species specific density estimates, stratified by cruise, were analyzed using a generalized additive model to estimate longterm trends and correct for seasonal imbalances. Variances were estimated using a nonparametric bootstrap with one day of effort as the sampling unit. Blue whales were primarily observed during summer and fall while fin and humpback whales were observed yearround with peaks in density during summer and spring respectively. Shortbeaked common dolphins (Delphinus delphis), Pacific whitesided dolphins (Lagenorhynchus obliquidens) and Dall’s porpoise (Phocoenoidesdalli) were the most frequently encountered small cetaceans with overall densities of 705.83/1000 km2 (CV=0.22), 51.98/1000 km2 (CV=0.27), and 21.37/1000 km2 (CV=0.19) respectively. Seasonally, shortbeaked common dolphins were most abundant in winter whereas Pacific whitesided dolphins and Dall’s porpoise were most abundant during spring. There were no significant longterm changes in blue whale, fin whale, humpback whale, shortbeaked common dolphin or Dall’s porpoise densities while Pacific whitesided dolphins exhibited a significant decrease in density across the tenyear study. The results from this study were fundamentally consistent with earlier studies, but provide greater temporal and seasonal resolution
Funding was provided by the Chief of Naval Operations Environmental Readiness Division, the United States Navy’s Pacific Fleet, the Naval Postgraduate School Grant #N00244111027, and the Naval Facilities Engineering Command Living Marine Resources Program.
Sun, 01 Feb 2015 00:00:00 GMT
http://hdl.handle.net/10023/6088
20150201T00:00:00Z
Campbell, G.S.
Thomas, L.
Whitaker, K.
Douglas, A.B.
Calambokidis, J.
Hildebrand, J.A.
Trends in cetacean density and distribution off southern California were assessed through visual linetransect surveys during thirtyseven California Cooperative Oceanic Fisheries Investigations (CalCOFI) cruises from July 2004–November 2013. From sightings of the six most commonly encountered cetacean species, seasonal, annual and overall density estimates were calculated. Blue whales (Balaenoptera musculus), fin whales (Balaenoptera physalus) and humpback whales (Megaptera novaeangliae) were the most frequently sighted baleen whales with overall densities of 0.91/1000 km2 (CV=0.27), 2.73/1000 km2 (CV=0.19), and 1.17/1000 km2 (CV=0.21) respectively. Species specific density estimates, stratified by cruise, were analyzed using a generalized additive model to estimate longterm trends and correct for seasonal imbalances. Variances were estimated using a nonparametric bootstrap with one day of effort as the sampling unit. Blue whales were primarily observed during summer and fall while fin and humpback whales were observed yearround with peaks in density during summer and spring respectively. Shortbeaked common dolphins (Delphinus delphis), Pacific whitesided dolphins (Lagenorhynchus obliquidens) and Dall’s porpoise (Phocoenoidesdalli) were the most frequently encountered small cetaceans with overall densities of 705.83/1000 km2 (CV=0.22), 51.98/1000 km2 (CV=0.27), and 21.37/1000 km2 (CV=0.19) respectively. Seasonally, shortbeaked common dolphins were most abundant in winter whereas Pacific whitesided dolphins and Dall’s porpoise were most abundant during spring. There were no significant longterm changes in blue whale, fin whale, humpback whale, shortbeaked common dolphin or Dall’s porpoise densities while Pacific whitesided dolphins exhibited a significant decrease in density across the tenyear study. The results from this study were fundamentally consistent with earlier studies, but provide greater temporal and seasonal resolution

Codimension formulae for the intersection of fractal subsets of Cantor spaces
http://hdl.handle.net/10023/6030
We examine the dimensions of the intersection of a subset E of an mary Cantor space Cm with the image of a subset F under a random isometry with respect to a natural metric. We obtain almost sure upper bounds for the Hausdorff and upper boxcounting dimensions of the intersection, and a lower bound for the essential supremum of the Hausdorff dimension. The dimensions of the intersections are typically max{dim E +dim F dim Cm, 0}, akin to other codimension theorems. The upper estimates come from the expected sizes of coverings, whilst the lower estimate is more intricate, using martingales to define a random measure on the intersection to facilitate a potential theoretic argument.
Mon, 01 Feb 2016 00:00:00 GMT
http://hdl.handle.net/10023/6030
20160201T00:00:00Z
Donoven, Casey
Falconer, Kenneth John
We examine the dimensions of the intersection of a subset E of an mary Cantor space Cm with the image of a subset F under a random isometry with respect to a natural metric. We obtain almost sure upper bounds for the Hausdorff and upper boxcounting dimensions of the intersection, and a lower bound for the essential supremum of the Hausdorff dimension. The dimensions of the intersections are typically max{dim E +dim F dim Cm, 0}, akin to other codimension theorems. The upper estimates come from the expected sizes of coverings, whilst the lower estimate is more intricate, using martingales to define a random measure on the intersection to facilitate a potential theoretic argument.

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

Hölder differentiability of selfconformal devil's staircases
http://hdl.handle.net/10023/5980
In this paper we consider the probability distribution function of a Gibbs measure supported on a selfconformal set given by an iterated function system (devil's staircase) applied to a compact subset of ℝ. We use thermodynamic multifractal formalism to calculate the Hausdorff dimension of the sets Sα 0, Sα ∞ and Sα, the set of points at which this function has, respectively, Hölder derivative 0, ∞ or no derivative in the general sense. This extends recent work by Darst, Dekking, Falconer, Kesseböhmer and Stratmann, and Yao, Zhang and Li by considering arbitrary such Gibbs measures given by a potential function independent of the geometric potential.
Sat, 01 Mar 2014 00:00:00 GMT
http://hdl.handle.net/10023/5980
20140301T00:00:00Z
Troscheit, S.
In this paper we consider the probability distribution function of a Gibbs measure supported on a selfconformal set given by an iterated function system (devil's staircase) applied to a compact subset of ℝ. We use thermodynamic multifractal formalism to calculate the Hausdorff dimension of the sets Sα 0, Sα ∞ and Sα, the set of points at which this function has, respectively, Hölder derivative 0, ∞ or no derivative in the general sense. This extends recent work by Darst, Dekking, Falconer, Kesseböhmer and Stratmann, and Yao, Zhang and Li by considering arbitrary such Gibbs measures given by a potential function independent of the geometric potential.

Higher biodiversity is required to sustain multiple ecosystem processes across temperature regimes
http://hdl.handle.net/10023/5975
Biodiversity loss is occurring rapidly worldwide, yet it is uncertain whether few or many species are required to sustain ecosystem functioning in the face of environmental change. The importance of biodiversity might be enhanced when multiple ecosystem processes (termed multifunctionality) and environmental contexts are considered, yet no studies have quantified this explicitly to date. We measured five key processes and their combined multifunctionality at three temperatures (5, 10 and 15 °C) in freshwater aquaria containing different animal assemblages (14 benthic macroinvertebrate species). For single processes, biodiversity effects were weak and were best predicted by additivebased models, i.e. polyculture performances represented the sum of their monoculture parts. There were, however, significant effects of biodiversity on multifunctionality at the low and the high (but not the intermediate) temperature. Variation in the contribution of species to processes across temperatures meant that greater biodiversity was required to sustain multifunctionality across different temperatures than was the case for single processes. This suggests that previous studies might have underestimated the importance of biodiversity in sustaining ecosystem functioning in a changing environment.
The authors thank the Natural Environment Research Council for financial support awarded to G. W. (Grant reference: NE/D013305/1) that funded D. M. P.'s research. Accepted 11 July 2014.
Thu, 01 Jan 2015 00:00:00 GMT
http://hdl.handle.net/10023/5975
20150101T00:00:00Z
Perkins, D.M.
Bailey, R.A.
Dossena, M.
Gamfeldt, L.
Reiss, J.
Trimmer, M.
Woodward, G.
Biodiversity loss is occurring rapidly worldwide, yet it is uncertain whether few or many species are required to sustain ecosystem functioning in the face of environmental change. The importance of biodiversity might be enhanced when multiple ecosystem processes (termed multifunctionality) and environmental contexts are considered, yet no studies have quantified this explicitly to date. We measured five key processes and their combined multifunctionality at three temperatures (5, 10 and 15 °C) in freshwater aquaria containing different animal assemblages (14 benthic macroinvertebrate species). For single processes, biodiversity effects were weak and were best predicted by additivebased models, i.e. polyculture performances represented the sum of their monoculture parts. There were, however, significant effects of biodiversity on multifunctionality at the low and the high (but not the intermediate) temperature. Variation in the contribution of species to processes across temperatures meant that greater biodiversity was required to sustain multifunctionality across different temperatures than was the case for single processes. This suggests that previous studies might have underestimated the importance of biodiversity in sustaining ecosystem functioning in a changing environment.

Assouad type dimensions and homogeneity of fractals
http://hdl.handle.net/10023/5941
We investigate several aspects of the Assouad dimension and the lower dimension, which together form a natural 'dimension pair'. In particular, we compute these dimensions for certain classes of selfaffine sets and quasiselfsimilar sets and study their relationships with other notions of dimension, such as the Hausdorff dimension for example. We also investigate some basic properties of these dimensions including their behaviour regarding unions and products and their set theoretic complexity.
The author was supported by an EPSRC Doctoral Training Grant
Mon, 01 Dec 2014 00:00:00 GMT
http://hdl.handle.net/10023/5941
20141201T00:00:00Z
Fraser, Jonathan M.
We investigate several aspects of the Assouad dimension and the lower dimension, which together form a natural 'dimension pair'. In particular, we compute these dimensions for certain classes of selfaffine sets and quasiselfsimilar sets and study their relationships with other notions of dimension, such as the Hausdorff dimension for example. We also investigate some basic properties of these dimensions including their behaviour regarding unions and products and their set theoretic complexity.

Analysing markrecapturerecovery data in the presence of missing covariate data via multiple imputation
http://hdl.handle.net/10023/5932
We consider mark–recapture–recovery data with additional individual timevarying continuous covariate data. For such data it is common to specify the model parameters, and in particular the survival probabilities, as a function of these covariates to incorporate individual heterogeneity. However, an issue arises in relation to missing covariate values, for (at least) the times when an individual is not observed, leading to an analytically intractable likelihood. We propose a twostep multiple imputation approach to obtain estimates of the demographic parameters. Firstly, a model is fitted to only the observed covariate values. Conditional on the fitted covariate model, multiple “complete” datasets are generated (i.e. all missing covariate values are imputed). Secondly, for each complete dataset, a closed form complete data likelihood can be maximised to obtain estimates of the model parameters which are subsequently combined to obtain an overall estimate of the parameters. Associated standard errors and 95 % confidence intervals are obtained using a nonparametric bootstrap. A simulation study is undertaken to assess the performance of the proposed twostep approach. We apply the method to data collected on a wellstudied population of Soay sheep and compare the results with a Bayesian data augmentation approach. Supplementary materials accompanying this paper appear online.
Sun, 01 Mar 2015 00:00:00 GMT
http://hdl.handle.net/10023/5932
20150301T00:00:00Z
Worthington, Hannah
King, Ruth
Buckland, Stephen Terrence
We consider mark–recapture–recovery data with additional individual timevarying continuous covariate data. For such data it is common to specify the model parameters, and in particular the survival probabilities, as a function of these covariates to incorporate individual heterogeneity. However, an issue arises in relation to missing covariate values, for (at least) the times when an individual is not observed, leading to an analytically intractable likelihood. We propose a twostep multiple imputation approach to obtain estimates of the demographic parameters. Firstly, a model is fitted to only the observed covariate values. Conditional on the fitted covariate model, multiple “complete” datasets are generated (i.e. all missing covariate values are imputed). Secondly, for each complete dataset, a closed form complete data likelihood can be maximised to obtain estimates of the model parameters which are subsequently combined to obtain an overall estimate of the parameters. Associated standard errors and 95 % confidence intervals are obtained using a nonparametric bootstrap. A simulation study is undertaken to assess the performance of the proposed twostep approach. We apply the method to data collected on a wellstudied population of Soay sheep and compare the results with a Bayesian data augmentation approach. Supplementary materials accompanying this paper appear online.

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

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

Negative ion sound solitary waves revisited
http://hdl.handle.net/10023/5845
Some years ago, a group including the present author and Padma Shukla showed that a suitable nonthermal electron distribution allows the formation of ion sound solitary waves with either positive or negative density perturbations, whereas with Maxwellian electrons only a positive density perturbation is possible. The present paper discusses the qualitative features of this distribution allowing the negative waves and shared with suitable twotemperature distributions.
Sun, 01 Dec 2013 00:00:00 GMT
http://hdl.handle.net/10023/5845
20131201T00:00:00Z
Cairns, R. A.
Some years ago, a group including the present author and Padma Shukla showed that a suitable nonthermal electron distribution allows the formation of ion sound solitary waves with either positive or negative density perturbations, whereas with Maxwellian electrons only a positive density perturbation is possible. The present paper discusses the qualitative features of this distribution allowing the negative waves and shared with suitable twotemperature distributions.

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

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

An explicit upper bound for the Helfgott delta in SL(2,p)
http://hdl.handle.net/10023/5819
Helfgott proved that there exists a δ>0 such that if S is a symmetric generating subset of SL(2,p) containing 1 then either S3=SL(2,p) or S3 ≥S1+δ. It is known that δ ≥ 1/3024. Here we show that δ ≤(log2(7)1)/6 ≈ 0.3012 and we present evidence suggesting that this might be the true value of δ.
Thu, 01 Jan 2015 00:00:00 GMT
http://hdl.handle.net/10023/5819
20150101T00:00:00Z
Button, Jack
RoneyDougal, Colva
Helfgott proved that there exists a δ>0 such that if S is a symmetric generating subset of SL(2,p) containing 1 then either S3=SL(2,p) or S3 ≥S1+δ. It is known that δ ≥ 1/3024. Here we show that δ ≤(log2(7)1)/6 ≈ 0.3012 and we present evidence suggesting that this might be the true value of δ.

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

A unifying model for capturerecapture and distance sampling surveys of wildlife populations
http://hdl.handle.net/10023/5797
Spatially explicit capturerecapture (SECR) methods extend traditional capturerecapture methods for estimating population density by using information contained in the location of traps. The The central feature of the improvement is estimation from the locations of traps at which animals were and were not captured to estimate of the distance over which animals are susceptible to capture. We show that standard SECR models are a special case of a more general class of model in which animal detection is not certain, but some information is available about the location of detected animals. The model class accommodates a range of spatial data types and includes as a special case markrecapture distance sampling, where distances to detected animals are recorded by multiple observers. Other examples of additional information that can be included are bearing to detected animals, strength of acoustic signals received from detected animals, and time of arrival of acoustic signals at detectors. Errors in variables are easily incorporated. We illustrate the versatility of the model and method through a number of applications, in each case using real and simulated data, and comparing our results with those from previous studies where these are available.
Funding: Partfunded by Fundacao Nacional para a Cienca e Technologia, Portugal (FCT) under the project PEst OE/MAT/UI0006/2011 (Marques) and the UK Engineering and Physical Sciences Research Council EP/I000917/1
Thu, 01 Jan 2015 00:00:00 GMT
http://hdl.handle.net/10023/5797
20150101T00:00:00Z
Borchers, D. L.
Stevenson, B.C.
Kidney, D.
Thomas, L.
Marques, T.A.
Spatially explicit capturerecapture (SECR) methods extend traditional capturerecapture methods for estimating population density by using information contained in the location of traps. The The central feature of the improvement is estimation from the locations of traps at which animals were and were not captured to estimate of the distance over which animals are susceptible to capture. We show that standard SECR models are a special case of a more general class of model in which animal detection is not certain, but some information is available about the location of detected animals. The model class accommodates a range of spatial data types and includes as a special case markrecapture distance sampling, where distances to detected animals are recorded by multiple observers. Other examples of additional information that can be included are bearing to detected animals, strength of acoustic signals received from detected animals, and time of arrival of acoustic signals at detectors. Errors in variables are easily incorporated. We illustrate the versatility of the model and method through a number of applications, in each case using real and simulated data, and comparing our results with those from previous studies where these are available.

Maximal subsemigroups of the semigroup of all mappings on an infinite set
http://hdl.handle.net/10023/5793
We classify the maximal subsemigroups of the semigroup ΩΩ of all mappings on an infinite set Ω that contain one of the following groups: the symmetric group on Ω, the setwise stabilizer of a nonempty finite subset of Ω, the stabilizer of a finite partition of Ω, or the stabilizer of an ultrafilter on Ω. If G is any of these groups, then we also characterise the mappings f,g ∈ ΩΩ such that the semigroup G, f, g generated by G ∪ {f,g} equals ΩΩ. We also show that the setwise stabiliser of a nonempty finite set, the almost stabiliser of a finite partition, and the stabiliser of an ultrafilter are maximal subsemigroups of the symmetric group.
Sun, 01 Mar 2015 00:00:00 GMT
http://hdl.handle.net/10023/5793
20150301T00:00:00Z
East, J.
Mitchell, James David
Péresse, Y.
We classify the maximal subsemigroups of the semigroup ΩΩ of all mappings on an infinite set Ω that contain one of the following groups: the symmetric group on Ω, the setwise stabilizer of a nonempty finite subset of Ω, the stabilizer of a finite partition of Ω, or the stabilizer of an ultrafilter on Ω. If G is any of these groups, then we also characterise the mappings f,g ∈ ΩΩ such that the semigroup G, f, g generated by G ∪ {f,g} equals ΩΩ. We also show that the setwise stabiliser of a nonempty finite set, the almost stabiliser of a finite partition, and the stabiliser of an ultrafilter are maximal subsemigroups of the symmetric group.

Acoustic and foraging behavior of a Baird’s beaked whale, Berardius bairdii, exposed to simulated sonar
http://hdl.handle.net/10023/5787
Beaked whales are hypothesized to be particularly sensitive to anthropogenic noise, based on previous strandings and limited experimental and observational data. However, few species have been studied in detail. We describe the underwater behavior of a Baird's beaked whale (Berardius bairdii) from the first deployment of a multisensor acoustic tag on this species. The animal exhibited shallow (23 ± 15 m max depth), intermediate (324 ± 49 m), and deep (1138 ± 243 m) dives. Echolocation clicks were produced with a mean interclick interval of approximately 300 ms and peak frequency of 25 kHz. Two deep dives included presumed foraging behavior, with echolocation pulsed sounds (presumed prey capture attempts) associated with increased maneuvering, and sustained inverted swimming during the bottom phase of the dive. A controlled exposure to simulated midfrequency active sonar (3.5–4 kHz) was conducted 4 hours after tag deployment, and within 3 minutes of exposure onset, the tagged whale increased swim speed and body movement, and continued to show unusual dive behavior for each of its next three dives, one of each type. These are the first data on the acoustic foraging behavior in this largest beaked whale species, and the first experimental demonstration of a response to simulated sonar.
Research was supported by the US Navy Chief of Naval Operations, Environmental Readiness Program, the Office of Naval Research, the Naval Postgraduate School, and the National Research Council.
Thu, 13 Nov 2014 00:00:00 GMT
http://hdl.handle.net/10023/5787
20141113T00:00:00Z
Stimpert, Alison
De Ruiter, Stacy Lynn
Southall, Brandon
Moretti, David
Falcone, Erin
Goldbogen, Jeremy
Friedlaender, Ari
Schorr, Greg
Calambokidis, John
Beaked whales are hypothesized to be particularly sensitive to anthropogenic noise, based on previous strandings and limited experimental and observational data. However, few species have been studied in detail. We describe the underwater behavior of a Baird's beaked whale (Berardius bairdii) from the first deployment of a multisensor acoustic tag on this species. The animal exhibited shallow (23 ± 15 m max depth), intermediate (324 ± 49 m), and deep (1138 ± 243 m) dives. Echolocation clicks were produced with a mean interclick interval of approximately 300 ms and peak frequency of 25 kHz. Two deep dives included presumed foraging behavior, with echolocation pulsed sounds (presumed prey capture attempts) associated with increased maneuvering, and sustained inverted swimming during the bottom phase of the dive. A controlled exposure to simulated midfrequency active sonar (3.5–4 kHz) was conducted 4 hours after tag deployment, and within 3 minutes of exposure onset, the tagged whale increased swim speed and body movement, and continued to show unusual dive behavior for each of its next three dives, one of each type. These are the first data on the acoustic foraging behavior in this largest beaked whale species, and the first experimental demonstration of a response to simulated sonar.

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

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

Optimal crossover designs for full interaction models
http://hdl.handle.net/10023/5768
We consider repeated measurement designs when a residual or carryover effect may be present in at most one later period. Since assuming an additive model may be unrealistic for some applications and leads to biased estimation of treatment effects, we consider a model with interactions between carryover and direct treatment effects. When the aim of the experiment is to study the effects of a treatment used alone, we obtain universally optimal approximate designs. We also propose some efficient designs with a reduced number of subjects.
July 2014
Sat, 01 Nov 2014 00:00:00 GMT
http://hdl.handle.net/10023/5768
20141101T00:00:00Z
Bailey, Rosemary Anne
Druilhet, Pierre
We consider repeated measurement designs when a residual or carryover effect may be present in at most one later period. Since assuming an additive model may be unrealistic for some applications and leads to biased estimation of treatment effects, we consider a model with interactions between carryover and direct treatment effects. When the aim of the experiment is to study the effects of a treatment used alone, we obtain universally optimal approximate designs. We also propose some efficient designs with a reduced number of subjects.

Computing in permutation groups without memory
http://hdl.handle.net/10023/5727
Memoryless computation is a new technique to compute any function of a set of registers by updating one register at a time while using no memory. Its aim is to emulate how computations are performed in modern cores, since they typically involve updates of single registers. The memoryless computation model can be fully expressed in terms of transformation semigroups, or in the case of bijective functions, permutation groups. In this paper, we consider how efficiently permutations can be computed without memory. We determine the minimum number of basic updates required to compute any permutation, or any even permutation. The small number of required instructions shows that very small instruction sets could be encoded on cores to perform memoryless computation. We then start looking at a possible compromise between the size of the instruction set and the length of the resulting programs. We consider updates only involving a limited number of registers. In particular, we show that binary instructions are not enough to compute all permutations without memory when the alphabet size is even. These results, though expressed as properties of special generating sets of the symmetric or alternating groups, provide guidelines on the implementation of memoryless computation.
Funding: UK Engineering and Physical Sciences Research Council (EP/K033956/1)
Sun, 02 Nov 2014 00:00:00 GMT
http://hdl.handle.net/10023/5727
20141102T00:00:00Z
Cameron, Peter Jephson
Fairbairn, Ben
Gadouleau, Maximilien
Memoryless computation is a new technique to compute any function of a set of registers by updating one register at a time while using no memory. Its aim is to emulate how computations are performed in modern cores, since they typically involve updates of single registers. The memoryless computation model can be fully expressed in terms of transformation semigroups, or in the case of bijective functions, permutation groups. In this paper, we consider how efficiently permutations can be computed without memory. We determine the minimum number of basic updates required to compute any permutation, or any even permutation. The small number of required instructions shows that very small instruction sets could be encoded on cores to perform memoryless computation. We then start looking at a possible compromise between the size of the instruction set and the length of the resulting programs. We consider updates only involving a limited number of registers. In particular, we show that binary instructions are not enough to compute all permutations without memory when the alphabet size is even. These results, though expressed as properties of special generating sets of the symmetric or alternating groups, provide guidelines on the implementation of memoryless computation.

Computing in matrix groups without memory
http://hdl.handle.net/10023/5715
Memoryless computation is a novel means of computing any function of a set of registers by updating one register at a time while using no memory. We aim to emulate how computations are performed on modern cores, since they typically involve updates of single registers. The computation model of memoryless computation can be fully expressed in terms of transformation semigroups, or in the case of bijective functions, permutation groups. In this paper, we view registers as elements of a finite field and we compute linear permutations without memory. We first determine the maximum complexity of a linear function when only linear instructions are allowed. We also determine which linear functions are hardest to compute when the field in question is the binary field and the number of registers is even. Secondly, we investigate some matrix groups, thus showing that the special linear group is internally computable but not fast. Thirdly, we determine the smallest set of instructions required to generate the special and general linear groups. These results are important for memoryless computation, for they show that linear functions can be computed very fast or that very few instructions are needed to compute any linear function. They thus indicate new advantages of using memoryless computation.
Funding: UK Engineering and Physical Sciences Research Council award EP/K033956/1
Sun, 02 Nov 2014 00:00:00 GMT
http://hdl.handle.net/10023/5715
20141102T00:00:00Z
Cameron, Peter Jephson
Fairbairn, Ben
Gadouleau, Maximilien
Memoryless computation is a novel means of computing any function of a set of registers by updating one register at a time while using no memory. We aim to emulate how computations are performed on modern cores, since they typically involve updates of single registers. The computation model of memoryless computation can be fully expressed in terms of transformation semigroups, or in the case of bijective functions, permutation groups. In this paper, we view registers as elements of a finite field and we compute linear permutations without memory. We first determine the maximum complexity of a linear function when only linear instructions are allowed. We also determine which linear functions are hardest to compute when the field in question is the binary field and the number of registers is even. Secondly, we investigate some matrix groups, thus showing that the special linear group is internally computable but not fast. Thirdly, we determine the smallest set of instructions required to generate the special and general linear groups. These results are important for memoryless computation, for they show that linear functions can be computed very fast or that very few instructions are needed to compute any linear function. They thus indicate new advantages of using memoryless computation.

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

The probability of generating a finite simple group
http://hdl.handle.net/10023/5658
We study the probability of generating a finite simple group, together with its generalisation PG,socG(d), the conditional probability of generating an almost simple finite group G by d elements, given that these elements generate G/ socG. We prove that PG,socG(2) ⩾ 53/90, with equality if and only if G is A6 or S6, and establish a similar result for PG,socG(3). Positive answers to longstanding questions of Wiegold on direct products, and of Mel’nikov on profinite groups, follow easily from our results.
Fri, 01 Nov 2013 00:00:00 GMT
http://hdl.handle.net/10023/5658
20131101T00:00:00Z
Menezes, Nina Emma
Quick, Martyn
RoneyDougal, Colva Mary
We study the probability of generating a finite simple group, together with its generalisation PG,socG(d), the conditional probability of generating an almost simple finite group G by d elements, given that these elements generate G/ socG. We prove that PG,socG(2) ⩾ 53/90, with equality if and only if G is A6 or S6, and establish a similar result for PG,socG(3). Positive answers to longstanding questions of Wiegold on direct products, and of Mel’nikov on profinite groups, follow easily from our results.

Most primitive groups are full automorphism groups of edgetransitive hypergraphs
http://hdl.handle.net/10023/5580
We prove that, for a primitive permutation group G acting on a set of size n, other than the alternating group, the probability that Aut(X,YG) = G for a random subset Y of X, tends to 1 as n tends to infinity. So the property of the title holds for all primitive groups except the alternating groups and finitely many others. This answers a question of M. Klin. Moreover, we give an upper bound n1/2+ε for the minimum size of the edges in such a hypergraph. This is essentially best possible.
Thu, 01 Jan 2015 00:00:00 GMT
http://hdl.handle.net/10023/5580
20150101T00:00:00Z
Babai, Laszlo
Cameron, Peter Jephson
We prove that, for a primitive permutation group G acting on a set of size n, other than the alternating group, the probability that Aut(X,YG) = G for a random subset Y of X, tends to 1 as n tends to infinity. So the property of the title holds for all primitive groups except the alternating groups and finitely many others. This answers a question of M. Klin. Moreover, we give an upper bound n1/2+ε for the minimum size of the edges in such a hypergraph. This is essentially best possible.

Exact dimensionality and projections of random selfsimilar measures and sets
http://hdl.handle.net/10023/5514
We study the geometric properties of random multiplicative cascade measures defined on selfsimilar sets. We show that such measures and their projections and sections are almost surely exactdimensional, generalizing Feng and Hu's result for selfsimilar measures. This, together with a compact group extension argument, enables us to generalize Hochman and Shmerkin's theorems on projections of deterministic selfsimilar measures to these random measures without requiring any separation conditions on the underlying sets. We give applications to selfsimilar sets and fractal percolation, including new results on projections, C1images and distance sets.
Wed, 01 Oct 2014 00:00:00 GMT
http://hdl.handle.net/10023/5514
20141001T00:00:00Z
Falconer, Kenneth
Jin, Xiong
We study the geometric properties of random multiplicative cascade measures defined on selfsimilar sets. We show that such measures and their projections and sections are almost surely exactdimensional, generalizing Feng and Hu's result for selfsimilar measures. This, together with a compact group extension argument, enables us to generalize Hochman and Shmerkin's theorems on projections of deterministic selfsimilar measures to these random measures without requiring any separation conditions on the underlying sets. We give applications to selfsimilar sets and fractal percolation, including new results on projections, C1images and distance sets.

The cooling of coronal plasmas. IV. Catastrophic cooling of loops
http://hdl.handle.net/10023/5503
We examine the radiative cooling of coronal loops and demonstrate that the recently identified catastrophic cooling is due to the inability of a loop to sustain radiative/enthalpy cooling below a critical temperature, which can be >1 MK in flares, 0.51 MK in active regions, and 0.1 MK in long tenuous loops. Catastrophic cooling is characterized by a rapid fall in coronal temperature, while the coronal density changes by a small amount. Analytic expressions for the critical temperature are derived and show good agreement with numerical results. This effect considerably limits the lifetime of coronal plasmas below the critical temperature.
Sat, 20 Jul 2013 00:00:00 GMT
http://hdl.handle.net/10023/5503
20130720T00:00:00Z
Cargill, P.J.
Bradshaw, S.J.
We examine the radiative cooling of coronal loops and demonstrate that the recently identified catastrophic cooling is due to the inability of a loop to sustain radiative/enthalpy cooling below a critical temperature, which can be >1 MK in flares, 0.51 MK in active regions, and 0.1 MK in long tenuous loops. Catastrophic cooling is characterized by a rapid fall in coronal temperature, while the coronal density changes by a small amount. Analytic expressions for the critical temperature are derived and show good agreement with numerical results. This effect considerably limits the lifetime of coronal plasmas below the critical temperature.

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

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

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

On the nature of reconnection at a solar coronal null point above a separatrix dome
http://hdl.handle.net/10023/5459
Threedimensional magnetic null points are ubiquitous in the solar corona and in any generic mixedpolarity magnetic field. We consider magnetic reconnection at an isolated coronal null point whose fan field lines form a dome structure. Using analytical and computational models, we demonstrate several features of spinefan reconnection at such a null, including the fact that substantial magnetic flux transfer from one region of field line connectivity to another can occur. The flux transfer occurs across the current sheet that forms around the null point during spinefan reconnection, and there is no separator present. Also, flipping of magnetic field lines takes place in a manner similar to that observed in the quasiseparatrix layer or sliprunning reconnection.
Tue, 10 Sep 2013 00:00:00 GMT
http://hdl.handle.net/10023/5459
20130910T00:00:00Z
Pontin, D. I.
Priest, E. R.
Galsgaard, K.
Threedimensional magnetic null points are ubiquitous in the solar corona and in any generic mixedpolarity magnetic field. We consider magnetic reconnection at an isolated coronal null point whose fan field lines form a dome structure. Using analytical and computational models, we demonstrate several features of spinefan reconnection at such a null, including the fact that substantial magnetic flux transfer from one region of field line connectivity to another can occur. The flux transfer occurs across the current sheet that forms around the null point during spinefan reconnection, and there is no separator present. Also, flipping of magnetic field lines takes place in a manner similar to that observed in the quasiseparatrix layer or sliprunning reconnection.

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

On magnetic reconnection and flux rope topology in solar flux emergence
http://hdl.handle.net/10023/5393
We present an analysis of the formation of atmospheric flux ropes in a magnetohydrodynamic solar flux emergence simulation. The simulation domain ranges from the top of the solar interior to the low corona. A twisted magnetic flux tube emerges from the solar interior and into the atmosphere where it interacts with the ambient magnetic field. By studying the connectivity of the evolving magnetic field, we are able to better understand the process of flux rope formation in the solar atmosphere. In the simulation, two flux ropes are produced as a result of flux emergence. Each has a different evolution resulting in different topological structures. These are determined by plasma flows and magnetic reconnection. As the flux rope is the basic structure of the coronal mass ejection, we discuss the implications of our findings for solar eruptions.
Fri, 21 Feb 2014 00:00:00 GMT
http://hdl.handle.net/10023/5393
20140221T00:00:00Z
MacTaggart, David
Haynes, Andrew Lewis
We present an analysis of the formation of atmospheric flux ropes in a magnetohydrodynamic solar flux emergence simulation. The simulation domain ranges from the top of the solar interior to the low corona. A twisted magnetic flux tube emerges from the solar interior and into the atmosphere where it interacts with the ambient magnetic field. By studying the connectivity of the evolving magnetic field, we are able to better understand the process of flux rope formation in the solar atmosphere. In the simulation, two flux ropes are produced as a result of flux emergence. Each has a different evolution resulting in different topological structures. These are determined by plasma flows and magnetic reconnection. As the flux rope is the basic structure of the coronal mass ejection, we discuss the implications of our findings for solar eruptions.

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

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

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

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

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

Active region emission measure distributions and implications for nanoflare heating
http://hdl.handle.net/10023/5305
The temperature dependence of the emission measure (EM) in the core of active regions coronal loops is an important diagnostic of heating processes. Observations indicate that EM(T) ~ T a below approximately 4 MK, with 2 < a < 5. Zerodimensional hydrodynamic simulations of nanoflare trains are used to demonstrate the dependence of a on the time between individual nanoflares (NT) and the distribution of nanoflare energies. If TN is greater than a few thousand seconds, a < 3. For smaller values, trains of equally spaced nanoflares cannot account for the observed range of a if the distribution of nanoflare energies is either constant, randomly distributed, or a power law. Power law distributions where there is a delay between consecutive nanoflares proportional to the energy of the second nanoflare do lead to the observed range of a. However, TN must then be of the order of hundreds to no more than a few thousand seconds. If a nanoflare leads to the relaxation of a stressed coronal field to a nearpotential state, the time taken to build up the required magnetic energy is thus too long to account for the EM measurements. Instead, it is suggested that a nanoflare involves the relaxation from one stressed coronal state to another, dissipating only a small fraction of the available magnetic energy. A consequence is that nanoflare energies may be smaller than previously envisioned.
Thu, 20 Mar 2014 00:00:00 GMT
http://hdl.handle.net/10023/5305
20140320T00:00:00Z
Cargill, P.J.
The temperature dependence of the emission measure (EM) in the core of active regions coronal loops is an important diagnostic of heating processes. Observations indicate that EM(T) ~ T a below approximately 4 MK, with 2 < a < 5. Zerodimensional hydrodynamic simulations of nanoflare trains are used to demonstrate the dependence of a on the time between individual nanoflares (NT) and the distribution of nanoflare energies. If TN is greater than a few thousand seconds, a < 3. For smaller values, trains of equally spaced nanoflares cannot account for the observed range of a if the distribution of nanoflare energies is either constant, randomly distributed, or a power law. Power law distributions where there is a delay between consecutive nanoflares proportional to the energy of the second nanoflare do lead to the observed range of a. However, TN must then be of the order of hundreds to no more than a few thousand seconds. If a nanoflare leads to the relaxation of a stressed coronal field to a nearpotential state, the time taken to build up the required magnetic energy is thus too long to account for the EM measurements. Instead, it is suggested that a nanoflare involves the relaxation from one stressed coronal state to another, dissipating only a small fraction of the available magnetic energy. A consequence is that nanoflare energies may be smaller than previously envisioned.

Space exploration using parallel orbits : a study in parallel symbolic computing
http://hdl.handle.net/10023/5303
Orbit enumerations represent an important class of mathematical algorithms which is widely used in computational discrete mathematics. In this paper, we present a new sharedmemory implementation of a generic Orbit skeleton in the GAP computer algebra system [5]. By defining a skeleton, we are easily able to capture a wide variety of concrete Orbit enumerations that can exploit the same underlying parallel implementation. We also propose a generic cost model for predicting the speedups that our Orbit skeleton will deliver for a given application on a given parallel system. We demonstrate the scalability of our implementation on a 64core sharedmemory machine. Our results show that we are able to obtain good speedups over sequential GAP programs (up to 25.27 on 64 cores).
Sun, 01 Sep 2013 00:00:00 GMT
http://hdl.handle.net/10023/5303
20130901T00:00:00Z
Janjic, Vladimir
Brown, Christopher Mark
Neunhoeffer, Max
Hammond, Kevin
Linton, Stephen Alexander
Loidl, HansWolfgang
Orbit enumerations represent an important class of mathematical algorithms which is widely used in computational discrete mathematics. In this paper, we present a new sharedmemory implementation of a generic Orbit skeleton in the GAP computer algebra system [5]. By defining a skeleton, we are easily able to capture a wide variety of concrete Orbit enumerations that can exploit the same underlying parallel implementation. We also propose a generic cost model for predicting the speedups that our Orbit skeleton will deliver for a given application on a given parallel system. We demonstrate the scalability of our implementation on a 64core sharedmemory machine. Our results show that we are able to obtain good speedups over sequential GAP programs (up to 25.27 on 64 cores).

Catastrophe versus instability for the eruption of a toroidal solar magnetic flux rope
http://hdl.handle.net/10023/5291
The onset of a solar eruption is formulated here as either a magnetic catastrophe or as an instability. Both start with the same equation of force balance governing the underlying equilibria. Using a toroidal flux rope in an external bipolar or quadrupolar field as a model for the currentcarrying flux, we demonstrate the occurrence of a fold catastrophe by loss of equilibrium for several representative evolutionary sequences in the stable domain of parameter space. We verify that this catastrophe and the torus instability occur at the same point; they are thus equivalent descriptions for the onset condition of solar eruptions.
B.K. acknowledges support by the Chinese Academy of Sciences under grant No. 2012T1J0017. He also acknowledges support by the DFG, the STFC, and the NSF. J.L.'s work was supported by 973 Program grants 2013CB815103 and 2011CB811403, NSFC grants 11273055, and 11333007, and CAS grant KJCX2EWT07 to Yunnan Observatory. E.R.P. is grateful to the Leverhulme Trust for financial support. The contribution of T.T. was supported by NASA's HTP, LWS, and SR&T programs and by NSF.
Tue, 01 Jul 2014 00:00:00 GMT
http://hdl.handle.net/10023/5291
20140701T00:00:00Z
Kliem, B.
Lin, J.
Forbes, T. G.
Priest, E. R.
Toeroek, T.
The onset of a solar eruption is formulated here as either a magnetic catastrophe or as an instability. Both start with the same equation of force balance governing the underlying equilibria. Using a toroidal flux rope in an external bipolar or quadrupolar field as a model for the currentcarrying flux, we demonstrate the occurrence of a fold catastrophe by loss of equilibrium for several representative evolutionary sequences in the stable domain of parameter space. We verify that this catastrophe and the torus instability occur at the same point; they are thus equivalent descriptions for the onset condition of solar eruptions.

Loss cone evolution and particle escape in collapsing magnetic trap models in solar flares
http://hdl.handle.net/10023/5275
Context. Collapsing magnetic traps (CMTs) have been suggested as one possible mechanism responsible for the acceleration of highenergy particles during solar flares. An important question regarding the CMT acceleration mechanism is which particle orbits escape and which are trapped during the time evolution of a CMT. While some models predict the escape of the majority of particle orbits, other more sophisticated CMT models show that, in particular, the highestenergy particles remain trapped at all times. The exact prediction is not straightforward because both the loss cone angle and the particle orbit pitch angle evolve in time in a CMT. Aims. Our aim is to gain a better understanding of the conditions leading to either particle orbit escape or trapping in CMTs. Methods. We present a detailed investigation of the time evolution of particle orbit pitch angles in the CMT model of Giuliani and collaborators and compare this with the time evolution of the loss cone angle. The nonrelativistic guiding centre approximation is used to calculate the particle orbits. We also use simplified models to corroborate the findings of the particle orbit calculations. Results. We find that there is a critical initial pitch angle for each field line of a CMT that divides trapped and escaping particle orbits. This critical initial pitch angle is greater than the initial loss cone angle, but smaller than the asymptotic (final) loss cone angle for that field line. As the final loss cone angle in CMTs is larger than the initial loss cone angle, particle orbits with pitch angles that cross into the loss cone during their time evolution will escape whereas all other particle orbits are trapped. We find that in realistic CMT models, Fermi acceleration will only dominate in the initial phase of the CMT evolution and, in this case, can reduce the pitch angle, but that betatron acceleration will dominate for later stages of the CMT evolution leading to a systematic increase of the pitch angle. Whether a particle escapes or remains trapped depends critically on the relative importance of the two acceleration mechanisms, which cannot be decoupled in more sophisticated CMT models.
This work was financially supported by the UK’s Science and Technology Facilities Council.
Wed, 12 Mar 2014 00:00:00 GMT
http://hdl.handle.net/10023/5275
20140312T00:00:00Z
Neukirch, Thomas
Eradat Oskoui, Solmaz
Grady, Keith James
Context. Collapsing magnetic traps (CMTs) have been suggested as one possible mechanism responsible for the acceleration of highenergy particles during solar flares. An important question regarding the CMT acceleration mechanism is which particle orbits escape and which are trapped during the time evolution of a CMT. While some models predict the escape of the majority of particle orbits, other more sophisticated CMT models show that, in particular, the highestenergy particles remain trapped at all times. The exact prediction is not straightforward because both the loss cone angle and the particle orbit pitch angle evolve in time in a CMT. Aims. Our aim is to gain a better understanding of the conditions leading to either particle orbit escape or trapping in CMTs. Methods. We present a detailed investigation of the time evolution of particle orbit pitch angles in the CMT model of Giuliani and collaborators and compare this with the time evolution of the loss cone angle. The nonrelativistic guiding centre approximation is used to calculate the particle orbits. We also use simplified models to corroborate the findings of the particle orbit calculations. Results. We find that there is a critical initial pitch angle for each field line of a CMT that divides trapped and escaping particle orbits. This critical initial pitch angle is greater than the initial loss cone angle, but smaller than the asymptotic (final) loss cone angle for that field line. As the final loss cone angle in CMTs is larger than the initial loss cone angle, particle orbits with pitch angles that cross into the loss cone during their time evolution will escape whereas all other particle orbits are trapped. We find that in realistic CMT models, Fermi acceleration will only dominate in the initial phase of the CMT evolution and, in this case, can reduce the pitch angle, but that betatron acceleration will dominate for later stages of the CMT evolution leading to a systematic increase of the pitch angle. Whether a particle escapes or remains trapped depends critically on the relative importance of the two acceleration mechanisms, which cannot be decoupled in more sophisticated CMT models.

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

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

Free products in R. Thompson’s group V
http://hdl.handle.net/10023/5237
We investigate some product structures in R. Thompson's group $ V$, primarily by studying the topological dynamics associated with $ V$'s action on the Cantor set C. We draw attention to the class D(V,C) of groups which have embeddings as demonstrative subgroups of V whose class can be used to assist in forming various products. Note that D(V,C) contains all finite groups, the free group on two generators, and Q/Z, and is closed under passing to subgroups and under taking direct products of any member by any finite member. If G≤V and H ∈ D(V,C), then G~H embeds into V. Finally, if G, H ∈ D(V,C), then G*H embeds in V. Using a dynamical approach, we also show the perhaps surprising result that Z2 * Z does not embed in V, even though V has many embedded copies of Z2 and has many embedded copies of free products of various pairs of its subgroups.
Fri, 01 Nov 2013 00:00:00 GMT
http://hdl.handle.net/10023/5237
20131101T00:00:00Z
Bleak, Collin Patrick
SalazarDiaz, Olga
We investigate some product structures in R. Thompson's group $ V$, primarily by studying the topological dynamics associated with $ V$'s action on the Cantor set C. We draw attention to the class D(V,C) of groups which have embeddings as demonstrative subgroups of V whose class can be used to assist in forming various products. Note that D(V,C) contains all finite groups, the free group on two generators, and Q/Z, and is closed under passing to subgroups and under taking direct products of any member by any finite member. If G≤V and H ∈ D(V,C), then G~H embeds into V. Finally, if G, H ∈ D(V,C), then G*H embeds in V. Using a dynamical approach, we also show the perhaps surprising result that Z2 * Z does not embed in V, even though V has many embedded copies of Z2 and has many embedded copies of free products of various pairs of its subgroups.

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

Indeterminacy and instability in Petschek reconnection
http://hdl.handle.net/10023/5234
We explain two puzzling aspects of Petschek's model for fast reconnection. One is its failure to occur in plasma simulations with uniform resistivity. The other is its inability to provide anything more than an upper limit for the reconnection rate. We have found that previously published analytical solutions based on Petschek's model are structurally unstable if the electrical resistivity is uniform. The structural instability is associated with the presence of an essential singularity at the Xline that is unphysical. By requiring that such a singularity does not exist, we obtain a formula that predicts a specific rate of reconnection. For uniform resistivity, reconnection can only occur at the slow, SweetParker rate. For nonuniform resistivity, reconnection can occur at a much faster rate provided that the resistivity profile is not too flat near the Xline. If this condition is satisfied, then the scale length of the nonuniformity determines the reconnection rate.
This work was supported by NSF Grants ATM0734032 and AGS0962698, NASA Grants NNX08AG44G and NNX10AC04G to the University of New Hampshire, and subcontract SVT7702 from the Smithsonian Astrophysical Observatory in support of their NASA Grants NNM07AA02C and NNM07AB07C. D. B. Seaton was supported by PRODEX Grant C90193 managed by the European Space Agency in collaboration with the Belgian Federal Science Policy Office, and by Grant FP7/20072013 from the European Commission's Seventh Framework Program under the agreement eHeroes (Project No. 284461). Additional support was provided by the Leverhulme Trust to E. R. Priest.
Mon, 13 May 2013 00:00:00 GMT
http://hdl.handle.net/10023/5234
20130513T00:00:00Z
Forbes, T.G.
Priest, E.R.
Seaton, D.B.
Litvinenko, Y.E.
We explain two puzzling aspects of Petschek's model for fast reconnection. One is its failure to occur in plasma simulations with uniform resistivity. The other is its inability to provide anything more than an upper limit for the reconnection rate. We have found that previously published analytical solutions based on Petschek's model are structurally unstable if the electrical resistivity is uniform. The structural instability is associated with the presence of an essential singularity at the Xline that is unphysical. By requiring that such a singularity does not exist, we obtain a formula that predicts a specific rate of reconnection. For uniform resistivity, reconnection can only occur at the slow, SweetParker rate. For nonuniform resistivity, reconnection can occur at a much faster rate provided that the resistivity profile is not too flat near the Xline. If this condition is satisfied, then the scale length of the nonuniformity determines the reconnection rate.

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

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

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

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

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

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

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

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

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

The effects of acoustic misclassification on cetacean species abundance estimation
http://hdl.handle.net/10023/5163
To estimate the density or abundance of a cetacean species using acoustic detection data, it is necessary to correctly identify the species that are detected. Developing an automated species classifier with 100% correct classification rate for any species is likely to stay out of reach. It is therefore necessary to consider the effect of misidentified detections on the number of observed data and consequently on abundance or density estimation, and develop methods to cope with these misidentifications. If misclassification rates are known, it is possible to estimate the true numbers of detected calls without bias. However, misclassification and uncertainties in the level of misclassification increase the variance of the estimates. If the true numbers of calls from different species are similar, then a small amount of misclassification between species and a small amount of uncertainty around the classification probabilities does not have an overly detrimental effect on the overall variance. However, if there is a difference in the encounter rate between species calls and/or a large amount of uncertainty in misclassification rates, then the variance of the estimates becomes very large and this dramatically increases the variance of the final abundance estimate.
This work was funded through the Natural Environment Research Council and SMRU Ltd.
Wed, 25 Dec 2013 00:00:00 GMT
http://hdl.handle.net/10023/5163
20131225T00:00:00Z
Caillat, Marjolaine Annie
Thomas, Len
Gillespie, Douglas Michael
To estimate the density or abundance of a cetacean species using acoustic detection data, it is necessary to correctly identify the species that are detected. Developing an automated species classifier with 100% correct classification rate for any species is likely to stay out of reach. It is therefore necessary to consider the effect of misidentified detections on the number of observed data and consequently on abundance or density estimation, and develop methods to cope with these misidentifications. If misclassification rates are known, it is possible to estimate the true numbers of detected calls without bias. However, misclassification and uncertainties in the level of misclassification increase the variance of the estimates. If the true numbers of calls from different species are similar, then a small amount of misclassification between species and a small amount of uncertainty around the classification probabilities does not have an overly detrimental effect on the overall variance. However, if there is a difference in the encounter rate between species calls and/or a large amount of uncertainty in misclassification rates, then the variance of the estimates becomes very large and this dramatically increases the variance of the final abundance estimate.

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

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

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

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

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

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

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

Fitting models of multiplehypotheses to partial population data : investigating the causes of cycles in red grouse
http://hdl.handle.net/10023/5119
There are two postulated causes for the observed periodic fluctuations (cycles) in red grouse (Lagopus lagopus scoticus). The first involves interaction with the parasitic nematode Trichostrongylus tenuis. The second invokes delayed regulation through the effect of male aggressiveness on territoriality. Empirical evidence exists to support both hypotheses, and each hypothesis has been modeled deterministically. However, little effort has gone into looking at the combined effects of the two mechanisms or formally fitting the corresponding models to field data. Here we present a model for red grouse dynamics that includes both parasites and territoriality. To explore the single and combined hypotheses, we specify three versions of this model and fit them to data using Bayesian statespace modeling, a method that allows statistical inference to be performed on mechanistic models such as ours. Output from the three models is then examined to determine their goodness of fit and the biological plausibility of the parameter values required by each to fit the population data. While all three models are capable of emulating the observed cyclic dynamics, only the model including both aggression and parasites does so under consistently realistic parameter values, providing theoretical support for the idea that both mechanisms shape red grouse cycles.
Tue, 01 Sep 2009 00:00:00 GMT
http://hdl.handle.net/10023/5119
20090901T00:00:00Z
New, L
Matthiopoulos, Jason
Redpath, S
Buckland, Stephen Terrence
There are two postulated causes for the observed periodic fluctuations (cycles) in red grouse (Lagopus lagopus scoticus). The first involves interaction with the parasitic nematode Trichostrongylus tenuis. The second invokes delayed regulation through the effect of male aggressiveness on territoriality. Empirical evidence exists to support both hypotheses, and each hypothesis has been modeled deterministically. However, little effort has gone into looking at the combined effects of the two mechanisms or formally fitting the corresponding models to field data. Here we present a model for red grouse dynamics that includes both parasites and territoriality. To explore the single and combined hypotheses, we specify three versions of this model and fit them to data using Bayesian statespace modeling, a method that allows statistical inference to be performed on mechanistic models such as ours. Output from the three models is then examined to determine their goodness of fit and the biological plausibility of the parameter values required by each to fit the population data. While all three models are capable of emulating the observed cyclic dynamics, only the model including both aggression and parasites does so under consistently realistic parameter values, providing theoretical support for the idea that both mechanisms shape red grouse cycles.

Doseresponse relationships for the onset of avoidance of sonar by freeranging killer whales
http://hdl.handle.net/10023/5092
Eight experimentally controlled exposures to 1−2 kHz or 6−7 kHz sonar signals were conducted with four killer whale groups. The source level and proximity of the source were increased during each exposure in order to reveal response thresholds. Detailed inspection of movements during each exposure session revealed sustained changes in speed and travel direction judged to be avoidance responses during six of eight sessions. Following methods developed for PhaseI clinical trials in human medicine, response thresholds ranging from 94 to 164 dB re 1 μPa received sound pressure level (SPL) were fitted to Bayesian doseresponse functions. Thresholds did not consistently differ by sonar frequency or whether a group had previously been exposed, with a mean SPL response threshold of 142 ± 15 dB (mean ± s.d.). High levels of between and withinindividual variability were identified, indicating that thresholds depended upon other undefined contextual variables. The doseresponse functions indicate that some killer whales started to avoid sonar at received SPL below thresholds assumed by the U.S. Navy. The predicted extent of habitat over which avoidance reactions occur depends upon whether whales responded to proximity or received SPL of the sonar or both, but was large enough to raise concerns about biological consequences to the whales.
The authors acknowledge the support of the MASTS pooling initiative (The Marine Alliance for Science and Technology for Scotland) in the completion of this study. MASTS is funded by the Scottish Funding Council (grant reference HR09011) and contributing institutions.
Sat, 01 Feb 2014 00:00:00 GMT
http://hdl.handle.net/10023/5092
20140201T00:00:00Z
Miller, Patrick
Antunes, Ricardo Nuno
Wensveen, Paulus Jacobus
Samarra, Filipa Isabel Pereira
Alves, Ana Catarina De Carvalho
Tyack, Peter Lloyd
Kvadsheim, Petter H.
Kleivane, Lars
Lam, FransPeter A.
Ainslie, Michael A.
Thomas, Len
Eight experimentally controlled exposures to 1−2 kHz or 6−7 kHz sonar signals were conducted with four killer whale groups. The source level and proximity of the source were increased during each exposure in order to reveal response thresholds. Detailed inspection of movements during each exposure session revealed sustained changes in speed and travel direction judged to be avoidance responses during six of eight sessions. Following methods developed for PhaseI clinical trials in human medicine, response thresholds ranging from 94 to 164 dB re 1 μPa received sound pressure level (SPL) were fitted to Bayesian doseresponse functions. Thresholds did not consistently differ by sonar frequency or whether a group had previously been exposed, with a mean SPL response threshold of 142 ± 15 dB (mean ± s.d.). High levels of between and withinindividual variability were identified, indicating that thresholds depended upon other undefined contextual variables. The doseresponse functions indicate that some killer whales started to avoid sonar at received SPL below thresholds assumed by the U.S. Navy. The predicted extent of habitat over which avoidance reactions occur depends upon whether whales responded to proximity or received SPL of the sonar or both, but was large enough to raise concerns about biological consequences to the whales.

conting : an R package for Bayesian analysis of complete and incomplete contingency tables
http://hdl.handle.net/10023/5050
The aim of this paper is to demonstrate the R package conting for the Bayesian analysis of complete and incomplete contingency tables using hierarchical loglinear models. This package allows a user to identify interactions between categorical factors (via complete contingency tables) and to estimate closed population sizes using capturerecapture studies (via incomplete contingency tables). The models are fitted using Markov chain Monte Carlo methods. In particular, implementations of the MetropolisHastings and reversible jump algorithms appropriate for loglinear models are employed. The conting package is demonstrated on four real examples.
Sun, 01 Jun 2014 00:00:00 GMT
http://hdl.handle.net/10023/5050
20140601T00:00:00Z
Overstall, Antony
King, Ruth
The aim of this paper is to demonstrate the R package conting for the Bayesian analysis of complete and incomplete contingency tables using hierarchical loglinear models. This package allows a user to identify interactions between categorical factors (via complete contingency tables) and to estimate closed population sizes using capturerecapture studies (via incomplete contingency tables). The models are fitted using Markov chain Monte Carlo methods. In particular, implementations of the MetropolisHastings and reversible jump algorithms appropriate for loglinear models are employed. The conting package is demonstrated on four real examples.

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

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

Using hidden Markov models to deal with availability bias on line transect surveys
http://hdl.handle.net/10023/5017
We develop estimators for line transect surveys of animals that are stochastically unavailable for detection while within detection range. The detection process is formulated as a hidden Markov model with a binary statedependent observation model that depends on both perpendicular and forward distances. This provides a parametric method of dealing with availability bias when estimates of availability process parameters are available even if series of availability events themselves are not. We apply the estimators to an aerial and a shipboard survey of whales, and investigate their properties by simulation. They are shown to be more general and more flexible than existing estimators based on parametric models of the availability process. We also find that methods using availability correction factors can be very biased when surveys are not close to being instantaneous, as can estimators that assume temporal independence in availability when there is temporal dependence.
This work was supported by EPSRC grant EP/I000917/1
Tue, 01 Jan 2013 00:00:00 GMT
http://hdl.handle.net/10023/5017
20130101T00:00:00Z
Borchers, David Louis
Zucchini, Walter
HeideJørgensen, M.P.
Cañadas, A.
Langrock, Roland
We develop estimators for line transect surveys of animals that are stochastically unavailable for detection while within detection range. The detection process is formulated as a hidden Markov model with a binary statedependent observation model that depends on both perpendicular and forward distances. This provides a parametric method of dealing with availability bias when estimates of availability process parameters are available even if series of availability events themselves are not. We apply the estimators to an aerial and a shipboard survey of whales, and investigate their properties by simulation. They are shown to be more general and more flexible than existing estimators based on parametric models of the availability process. We also find that methods using availability correction factors can be very biased when surveys are not close to being instantaneous, as can estimators that assume temporal independence in availability when there is temporal dependence.

J J Thomson and the Discovery of the Electron
http://hdl.handle.net/10023/4991
One experiment, more than any other, is often associated with the `discovery of the electron' in 1897. This is J J Thomson's determination of the mass to charge ratio (m/e) of cathode rays by deflecting them in magnetic and electric fields. Yet this experiment was performed two months after Thomson first announced that cathode rays were very small, negatively charged particles. So why was it important? I look at Thomson's route to, and conduct of, the experiment, and then at how his ideas were received.
Fri, 01 Jan 1999 00:00:00 GMT
http://hdl.handle.net/10023/4991
19990101T00:00:00Z
Falconer, Isobel Jessie
One experiment, more than any other, is often associated with the `discovery of the electron' in 1897. This is J J Thomson's determination of the mass to charge ratio (m/e) of cathode rays by deflecting them in magnetic and electric fields. Yet this experiment was performed two months after Thomson first announced that cathode rays were very small, negatively charged particles. So why was it important? I look at Thomson's route to, and conduct of, the experiment, and then at how his ideas were received.

Beyond sumfree sets in the natural numbers
http://hdl.handle.net/10023/4986
For an interval [1,N]⊆N, sets S⊆[1,N] with the property that {(x,y)∈S2:x+y∈S}=0, known as sumfree sets, have attracted considerable attention. In this paper, we generalize this notion by considering r(S)={(x,y)∈S2:x+y∈S}, and analyze its behaviour as S ranges over the subsets of [1,N]. We obtain a comprehensive description of the spectrum of attainable rvalues, constructive existence results and structural characterizations for sets attaining extremal and nearextremal values.
Fri, 07 Feb 2014 00:00:00 GMT
http://hdl.handle.net/10023/4986
20140207T00:00:00Z
Huczynska, Sophie
For an interval [1,N]⊆N, sets S⊆[1,N] with the property that {(x,y)∈S2:x+y∈S}=0, known as sumfree sets, have attracted considerable attention. In this paper, we generalize this notion by considering r(S)={(x,y)∈S2:x+y∈S}, and analyze its behaviour as S ranges over the subsets of [1,N]. We obtain a comprehensive description of the spectrum of attainable rvalues, constructive existence results and structural characterizations for sets attaining extremal and nearextremal values.

Injecting drug users in Scotland, 2006 : listing, number, demography, and opiaterelated deathrates
http://hdl.handle.net/10023/4904
Using Bayesian capture–recapture analysis, we estimated the number of current injecting drug users (IDUs) in Scotland in 2006 from the crosscounts of 5670 IDUs listed on four datasources: social enquiry reports (901 IDUs listed), hospital records (953), drug treatment agencies (3504), and recent Hepatitis C virus (HCV) diagnoses (827 listed as IDUrisk). Further, we accessed exact numbers of opiaterelated drugsrelated deaths (DRDs) in 2006 and 2007 to improve estimation of Scotland's DRD rates per 100 current IDUs. Using all four datasources, and modelaveraging of standard hierarchical loglinear models to allow for pairwise interactions between datasources and/or demographic classifications, Scotland had an estimated 31700 IDUs in 2006 (95% credible interval: 24900–38700); but 25000 IDUs (95% CI: 20700–35000) by excluding recent HCV diagnoses whose IDUrisk can refer to past injecting. Only in the younger agegroup (15–34 years) were Scotland's opiaterelated DRD rates significantly lower for females than males. Older males’ opiaterelated DRD rate was 1.9 (1.24–2.40) per 100 current IDUs without or 1.3 (0.94–1.64) with inclusion of recent HCV diagnoses. If, indeed, Scotland had only 25000 current IDUs in 2006, with only 8200 of them aged 35+ years, the opiaterelated DRD rate is higher among this older age group than has been appreciated hitherto. There is counterbalancing good news for the public health: the hitherto sharp increase in older current IDUs had stalled by 2006.
Sat, 01 Jun 2013 00:00:00 GMT
http://hdl.handle.net/10023/4904
20130601T00:00:00Z
King, Ruth
Bird, Sheila
Overstall, Antony
Hay, Gordon
Hutchinson, Sharon
Using Bayesian capture–recapture analysis, we estimated the number of current injecting drug users (IDUs) in Scotland in 2006 from the crosscounts of 5670 IDUs listed on four datasources: social enquiry reports (901 IDUs listed), hospital records (953), drug treatment agencies (3504), and recent Hepatitis C virus (HCV) diagnoses (827 listed as IDUrisk). Further, we accessed exact numbers of opiaterelated drugsrelated deaths (DRDs) in 2006 and 2007 to improve estimation of Scotland's DRD rates per 100 current IDUs. Using all four datasources, and modelaveraging of standard hierarchical loglinear models to allow for pairwise interactions between datasources and/or demographic classifications, Scotland had an estimated 31700 IDUs in 2006 (95% credible interval: 24900–38700); but 25000 IDUs (95% CI: 20700–35000) by excluding recent HCV diagnoses whose IDUrisk can refer to past injecting. Only in the younger agegroup (15–34 years) were Scotland's opiaterelated DRD rates significantly lower for females than males. Older males’ opiaterelated DRD rate was 1.9 (1.24–2.40) per 100 current IDUs without or 1.3 (0.94–1.64) with inclusion of recent HCV diagnoses. If, indeed, Scotland had only 25000 current IDUs in 2006, with only 8200 of them aged 35+ years, the opiaterelated DRD rate is higher among this older age group than has been appreciated hitherto. There is counterbalancing good news for the public health: the hitherto sharp increase in older current IDUs had stalled by 2006.

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

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

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

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

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

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

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

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

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

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

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

On the commutator lengths of certain classes of finitely presented groups
http://hdl.handle.net/10023/4719
For a finite group G = 〈X〉 (X ≠ G), the least positive integer ML(G) is called the maximum length of G with respect to the generating set X if every element of G maybe represented as a product of at most ML(G) elements of X. The maximum length of G, denoted by ML (G), is defined to be the minimum of {ML(G) G = 〈X〉, X ≠ G, X ≠ G  {1}}. The wellknown commutator length of a group G, denoted by c (G), satisfies the inequality c (G) ≤ ML(G′), where G′ is the derived subgroup of G. In this paper we study the properties of ML (G) and by using this inequality we give upper bounds for the commutator lengths of certain classes of finite groups. In some cases these upper bounds involve the interesting sequences of Fibonacci and Lucas numbers.
Sun, 01 Jan 2006 00:00:00 GMT
http://hdl.handle.net/10023/4719
20060101T00:00:00Z
Doostie, H.
Campbell, P.P.
For a finite group G = 〈X〉 (X ≠ G), the least positive integer ML(G) is called the maximum length of G with respect to the generating set X if every element of G maybe represented as a product of at most ML(G) elements of X. The maximum length of G, denoted by ML (G), is defined to be the minimum of {ML(G) G = 〈X〉, X ≠ G, X ≠ G  {1}}. The wellknown commutator length of a group G, denoted by c (G), satisfies the inequality c (G) ≤ ML(G′), where G′ is the derived subgroup of G. In this paper we study the properties of ML (G) and by using this inequality we give upper bounds for the commutator lengths of certain classes of finite groups. In some cases these upper bounds involve the interesting sequences of Fibonacci and Lucas numbers.

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

An approximate Bayesian method applied to estimating the trajectories of four British grey seal (Halichoerus grypus) populations from pup counts.
http://hdl.handle.net/10023/4688
1. For British grey seals, as with many pinniped species, population monitoring is implemented by aerial surveys of pups at breeding colonies. Scaling pup counts up to population estimates requires assumptions about population structure; this is straightforward when populations are growing exponentially, but not when growth slows, since it is unclear whether density dependence affects pup survival or fecundity. 2. We present an approximate Bayesian method for fitting pup trajectories, estimating adult population size and investigating alternative biological models. The method is equivalent to fitting a density dependent Leslie matrix model, within a Bayesian framework, but with the forms of the density dependent effects as outputs rather than assumptions. 3. This approach requires fewer assumptions than the state space models currently used, and produces similar estimates. The simplifications made the models easier to fit, reducing their computational intensity and allowing regional differences in demographic parameters to be considered. 4. The approach is not restricted to situations where only a single component of the population is observable, but, particularly in those cases, provides a practical method for extracting information from limited datasets. 5. We discuss the potential and limitations of the method and suggest that this approach provides a useful tool for at least the preliminary analysis of similar datasets.
Sat, 01 Jan 2011 00:00:00 GMT
http://hdl.handle.net/10023/4688
20110101T00:00:00Z
Lonergan, Michael Edward
Thompson, David
Thomas, Leonard Joseph
Duck, Callan David
1. For British grey seals, as with many pinniped species, population monitoring is implemented by aerial surveys of pups at breeding colonies. Scaling pup counts up to population estimates requires assumptions about population structure; this is straightforward when populations are growing exponentially, but not when growth slows, since it is unclear whether density dependence affects pup survival or fecundity. 2. We present an approximate Bayesian method for fitting pup trajectories, estimating adult population size and investigating alternative biological models. The method is equivalent to fitting a density dependent Leslie matrix model, within a Bayesian framework, but with the forms of the density dependent effects as outputs rather than assumptions. 3. This approach requires fewer assumptions than the state space models currently used, and produces similar estimates. The simplifications made the models easier to fit, reducing their computational intensity and allowing regional differences in demographic parameters to be considered. 4. The approach is not restricted to situations where only a single component of the population is observable, but, particularly in those cases, provides a practical method for extracting information from limited datasets. 5. We discuss the potential and limitations of the method and suggest that this approach provides a useful tool for at least the preliminary analysis of similar datasets.

On the probability of generating a monolithic group
http://hdl.handle.net/10023/4626
A group L is primitive monolithic if L has a unique minimal normal subgroup, N , and trivial Frattini subgroup. By PL,N(k) we denote the conditional probability that k randomly chosen elements of L generate L , given that they project onto generators for L/N. In this article we show that PL,N(k) is controlled by PY,S(2), where N≅Sr and Y is a 2generated almost simple group with socle S that is contained in the normalizer in L of the first direct factor of N . Information aboutPL,N(k) for L primitive monolithic yields various types of information about the generation of arbitrary finite and profinite groups.
This research was supported through EPSRC grant EP/I03582X/1. The APC was paid through RCUK open access block grant funds.
Sun, 01 Jun 2014 00:00:00 GMT
http://hdl.handle.net/10023/4626
20140601T00:00:00Z
Detomi, Eloisa
Lucchini, Andrea
RoneyDougal, Colva Mary
A group L is primitive monolithic if L has a unique minimal normal subgroup, N , and trivial Frattini subgroup. By PL,N(k) we denote the conditional probability that k randomly chosen elements of L generate L , given that they project onto generators for L/N. In this article we show that PL,N(k) is controlled by PY,S(2), where N≅Sr and Y is a 2generated almost simple group with socle S that is contained in the normalizer in L of the first direct factor of N . Information aboutPL,N(k) for L primitive monolithic yields various types of information about the generation of arbitrary finite and profinite groups.

Modelling group dynamic animal movement
http://hdl.handle.net/10023/4555
1). Group dynamics are a fundamental aspect of many species' movements. The need to adequately model individuals' interactions with other group members has been recognized, particularly in order to differentiate the role of social forces in individual movement from environmental factors. However, to date, practical statistical methods, which can include group dynamics in animal movement models, have been lacking. 2). We consider a flexible modelling framework that distinguishes a grouplevel model, describing the movement of the group's centre, and an individuallevel model, such that each individual makes its movement decisions relative to the group centroid. The basic idea is framed within the flexible class of hidden Markov models, extending previous work on modelling animal movement by means of multistate random walks. 3). While in simulation experiments parameter estimators exhibit some bias in nonideal scenarios, we show that generally the estimation of models of this type is both feasible and ecologically informative. 4). We illustrate the approach using real movement data from 11 reindeer (Rangifer tarandus). Results indicate a directional bias towards a group centroid for reindeer in an encamped state. Though the attraction to the group centroid is relatively weak, our model successfully captures groupinfluenced movement dynamics. Specifically, as compared to a regular mixture of correlated random walks, the group dynamic model more accurately predicts the nondiffusive behaviour of a cohesive mobile group. 5). As technology continues to develop, it will become easier and less expensive to tag multiple individuals within a group in order to follow their movements. Our work provides a first inferential framework for understanding the relative influences of individual versus grouplevel movement decisions. This framework can be extended to include covariates corresponding to environmental influences or body condition. As such, this framework allows for a broader understanding of the many internal and external factors that can influence an individual's movement.
Sat, 01 Feb 2014 00:00:00 GMT
http://hdl.handle.net/10023/4555
20140201T00:00:00Z
Langrock, Roland
Hopcraft, Grant
Blackwell, Paul
Goodall, Victoria
King, Ruth
Niu, Mu
Patterson, Toby
Pedersen, Martin
Skarin, Anna
Schick, Robert Schilling
1). Group dynamics are a fundamental aspect of many species' movements. The need to adequately model individuals' interactions with other group members has been recognized, particularly in order to differentiate the role of social forces in individual movement from environmental factors. However, to date, practical statistical methods, which can include group dynamics in animal movement models, have been lacking. 2). We consider a flexible modelling framework that distinguishes a grouplevel model, describing the movement of the group's centre, and an individuallevel model, such that each individual makes its movement decisions relative to the group centroid. The basic idea is framed within the flexible class of hidden Markov models, extending previous work on modelling animal movement by means of multistate random walks. 3). While in simulation experiments parameter estimators exhibit some bias in nonideal scenarios, we show that generally the estimation of models of this type is both feasible and ecologically informative. 4). We illustrate the approach using real movement data from 11 reindeer (Rangifer tarandus). Results indicate a directional bias towards a group centroid for reindeer in an encamped state. Though the attraction to the group centroid is relatively weak, our model successfully captures groupinfluenced movement dynamics. Specifically, as compared to a regular mixture of correlated random walks, the group dynamic model more accurately predicts the nondiffusive behaviour of a cohesive mobile group. 5). As technology continues to develop, it will become easier and less expensive to tag multiple individuals within a group in order to follow their movements. Our work provides a first inferential framework for understanding the relative influences of individual versus grouplevel movement decisions. This framework can be extended to include covariates corresponding to environmental influences or body condition. As such, this framework allows for a broader understanding of the many internal and external factors that can influence an individual's movement.

Living on the edge : Roe deer (Capreolus capreolus) density in the margins of Its geographical range
http://hdl.handle.net/10023/4523
Over the last decades roe deer (Capreolus capreolus) populations have increased in number and distribution throughout Europe. Such increases have profound impacts on ecosystems, both positive and negative. Therefore monitoring roe deer populations is essential for the appropriate management of this species, in order to achieve a balance between conservation and mitigation of the negative impacts. Despite being required for an effective management plan, the study of roe deer ecology in Portugal is at an early stage, and hence there is still a complete lack of knowledge of roe deer density within its known range. Distance sampling of pellet groups coupled with production and decay rates for pellet groups provided density estimates for roe deer in northeastern Portugal (Lombada National Hunting Area  LNHA, Serra de Montesinho – SM and Serra da Nogueira – SN; LNHA and SM located in Montesinho Natural Park). The estimated roe deer density using a stratified detection function was 1.23/100 ha for LNHA, 4.87/100 ha for SM and 4.25/100 ha in SN, with 95% confidence intervals (CI) of 0.68 to 2.21, 3.08 to 7.71 and 2.25 to 8.03, respectively. For the entire area, the estimated density was about 3.51/100 ha (95% CI  2.26–5.45). This method can provide estimates of roe deer density, which will ultimately support management decisions. However, effective monitoring should be based on longterm studies that are able to detect population fluctuations. This study represents the initial phase of roe deer monitoring at the edge of its European range and intends to fill the gap in this species ecology, as the gathering of similar data over a number of years will provide the basis for stronger inferences. Monitoring should be continued, although the study area should be increased to evaluate the accuracy of estimates and assess the impact of management actions.
Sat, 01 Feb 2014 00:00:00 GMT
http://hdl.handle.net/10023/4523
20140201T00:00:00Z
Valente, Ana M.
Fonseca, Carlos
Marques, Tiago A.
Santos, João P.
Rodrigues, Rogério
Torres, Rita Tinoco
Over the last decades roe deer (Capreolus capreolus) populations have increased in number and distribution throughout Europe. Such increases have profound impacts on ecosystems, both positive and negative. Therefore monitoring roe deer populations is essential for the appropriate management of this species, in order to achieve a balance between conservation and mitigation of the negative impacts. Despite being required for an effective management plan, the study of roe deer ecology in Portugal is at an early stage, and hence there is still a complete lack of knowledge of roe deer density within its known range. Distance sampling of pellet groups coupled with production and decay rates for pellet groups provided density estimates for roe deer in northeastern Portugal (Lombada National Hunting Area  LNHA, Serra de Montesinho – SM and Serra da Nogueira – SN; LNHA and SM located in Montesinho Natural Park). The estimated roe deer density using a stratified detection function was 1.23/100 ha for LNHA, 4.87/100 ha for SM and 4.25/100 ha in SN, with 95% confidence intervals (CI) of 0.68 to 2.21, 3.08 to 7.71 and 2.25 to 8.03, respectively. For the entire area, the estimated density was about 3.51/100 ha (95% CI  2.26–5.45). This method can provide estimates of roe deer density, which will ultimately support management decisions. However, effective monitoring should be based on longterm studies that are able to detect population fluctuations. This study represents the initial phase of roe deer monitoring at the edge of its European range and intends to fill the gap in this species ecology, as the gathering of similar data over a number of years will provide the basis for stronger inferences. Monitoring should be continued, although the study area should be increased to evaluate the accuracy of estimates and assess the impact of management actions.

A risk function for behavioral disruption of Blainville’s beaked whales (Mesoplodon densirostris) from midfrequency active sonar
http://hdl.handle.net/10023/4522
There is increasing concern about the potential effects of noise pollution on marine life in the world’s oceans. For marine mammals, anthropogenic sounds may cause behavioral disruption, and this can be quantified using a risk function that relates sound exposure to a measured behavioral response. Beaked whales are a taxon of deep diving whales that may be particularly susceptible to naval sonar as the species has been associated with sonarrelated mass stranding events. Here we derive the first empirical risk function for Blainville’s beaked whales (Mesoplodon densirostris) by combining in situ data from passive acoustic monitoring of animal vocalizations and navy sonar operations with precise ship tracks and sound field modeling. The hydrophone array at the Atlantic Undersea Test and Evaluation Center, Bahamas, was used to locate vocalizing groups of Blainville’s beaked whales and identify sonar transmissions before, during, and after MidFrequency Active (MFA) sonar operations. Sonar transmission times and source levels were combined with ship tracks using a sound propagation model to estimate the received level (RL) at each hydrophone. A generalized additive model was fitted to data to model the presence or absence of the start of foraging dives in 30minute periods as a function of the corresponding sonar RL at the hydrophone closest to the center of each group. This model was then used to construct a risk function that can be used to estimate the probability of a behavioral change (cessation of foraging) the individual members of a Blainville’s beaked whale population might experience as a function of sonar RL. The function predicts a 0.5 probability of disturbance at a RL of 150dBrms re µPa (CI: 144 to 155) This is 15dB lower than the level used historically by the US Navy in their risk assessments but 10 dB higher than the current 140 dB stepfunction
Wed, 01 Jan 2014 00:00:00 GMT
http://hdl.handle.net/10023/4522
20140101T00:00:00Z
Moretti, David
Thomas, Len
Marques, Tiago A.
Harwood, John
Dilley, Ashley
Neales, Bert
Shaffer, Jessica
Mccarthy, E
New, Leslie Frances
Jarvis, S
Morrissey, Ron
There is increasing concern about the potential effects of noise pollution on marine life in the world’s oceans. For marine mammals, anthropogenic sounds may cause behavioral disruption, and this can be quantified using a risk function that relates sound exposure to a measured behavioral response. Beaked whales are a taxon of deep diving whales that may be particularly susceptible to naval sonar as the species has been associated with sonarrelated mass stranding events. Here we derive the first empirical risk function for Blainville’s beaked whales (Mesoplodon densirostris) by combining in situ data from passive acoustic monitoring of animal vocalizations and navy sonar operations with precise ship tracks and sound field modeling. The hydrophone array at the Atlantic Undersea Test and Evaluation Center, Bahamas, was used to locate vocalizing groups of Blainville’s beaked whales and identify sonar transmissions before, during, and after MidFrequency Active (MFA) sonar operations. Sonar transmission times and source levels were combined with ship tracks using a sound propagation model to estimate the received level (RL) at each hydrophone. A generalized additive model was fitted to data to model the presence or absence of the start of foraging dives in 30minute periods as a function of the corresponding sonar RL at the hydrophone closest to the center of each group. This model was then used to construct a risk function that can be used to estimate the probability of a behavioral change (cessation of foraging) the individual members of a Blainville’s beaked whale population might experience as a function of sonar RL. The function predicts a 0.5 probability of disturbance at a RL of 150dBrms re µPa (CI: 144 to 155) This is 15dB lower than the level used historically by the US Navy in their risk assessments but 10 dB higher than the current 140 dB stepfunction

Optimizing sampling design to deal with mistnet avoidance in Amazonian birds and bats
http://hdl.handle.net/10023/4520
Mist netting is a widely used technique to sample bird and bat assemblages. However, captures often decline with time because animals learn and avoid the locations of nets. This avoidance or net shyness can substantially decrease sampling efficiency. We quantified the daytoday decline in captures of Amazonian birds and bats with mist nets set at the same location for four consecutive days. We also evaluated how net avoidance influences the efficiency of surveys under different logistic scenarios using resampling techniques. Net avoidance caused substantial declines in bird and bat captures, although more accentuated in the latter. Most of the decline occurred between the first and second days of netting: 28% in birds and 47% in bats. Captures of commoner species were more affected. The numbers of species detected also declined. Moving nets daily to minimize the avoidance effect increased captures by 30% in birds and 70% in bats. However, moving the location of nets may cause a reduction in netting time and captures. When moving the nets caused the loss of one netting day it was no longer advantageous to move the nets frequently. In bird surveys that could even decrease the number of individuals captured and species detected. Net avoidance can greatly affect sampling efficiency but adjustments in survey design can minimize this. Whenever nets can be moved without losing netting time and the objective is to capture many individuals, they should be moved daily. If the main objective is to survey species present then nets should still be moved for bats, but not for birds. However, if relocating nets causes a significant loss of netting time, moving them to reduce effects of shyness will not improve sampling efficiency in either group. Overall, our findings can improve the design of mist netting sampling strategies in other tropical areas.
Wed, 18 Sep 2013 00:00:00 GMT
http://hdl.handle.net/10023/4520
20130918T00:00:00Z
Marques, Joao Tiago
Ramos Pereira, Maria J.
Marques, Tiago A.
Santos, Carlos David
Santana, Joana
Beja, Pedro
Palmeirim, Jorge M.
Mist netting is a widely used technique to sample bird and bat assemblages. However, captures often decline with time because animals learn and avoid the locations of nets. This avoidance or net shyness can substantially decrease sampling efficiency. We quantified the daytoday decline in captures of Amazonian birds and bats with mist nets set at the same location for four consecutive days. We also evaluated how net avoidance influences the efficiency of surveys under different logistic scenarios using resampling techniques. Net avoidance caused substantial declines in bird and bat captures, although more accentuated in the latter. Most of the decline occurred between the first and second days of netting: 28% in birds and 47% in bats. Captures of commoner species were more affected. The numbers of species detected also declined. Moving nets daily to minimize the avoidance effect increased captures by 30% in birds and 70% in bats. However, moving the location of nets may cause a reduction in netting time and captures. When moving the nets caused the loss of one netting day it was no longer advantageous to move the nets frequently. In bird surveys that could even decrease the number of individuals captured and species detected. Net avoidance can greatly affect sampling efficiency but adjustments in survey design can minimize this. Whenever nets can be moved without losing netting time and the objective is to capture many individuals, they should be moved daily. If the main objective is to survey species present then nets should still be moved for bats, but not for birds. However, if relocating nets causes a significant loss of netting time, moving them to reduce effects of shyness will not improve sampling efficiency in either group. Overall, our findings can improve the design of mist netting sampling strategies in other tropical areas.

Novel methods for species distribution mapping including spatial models in complex regions
http://hdl.handle.net/10023/4514
Species Distribution Modelling (SDM) plays a key role in a number of biological applications: assessment of temporal trends in distribution, environmental impact assessment and spatial conservation planning. From a statistical perspective, this thesis develops two methods for increasing the accuracy and reliability of maps of density surfaces and provides a solution to the problem of how to collate multiple density maps of the same region, obtained from differing sources. From a biological perspective, these statistical methods are used to analyse two marine mammal datasets to produce accurate maps for use in spatial conservation planning and temporal trend assessment.
The first new method, Complex Region Spatial Smoother [CReSS; ScottHayward et al., 2013], improves smoothing in areas where the real distance an animal must travel (`as the animal swims') between two points may be greater than the straight line distance between them, a problem that occurs in complex domains with coastline or islands. CReSS uses estimates of the geodesic distance between points, model averaging and local radial smoothing. Simulation is used to compare its performance with other traditional and recentlydeveloped smoothing techniques: Thin Plate Splines (TPS, Harder and Desmarais [1972]), Geodesic Low rank TPS (GLTPS; Wang and Ranalli [2007]) and the Soap lm smoother (SOAP; Wood et al. [2008]). GLTPS cannot be used in areas with islands and SOAP can be very hard to parametrise. CReSS outperforms all of the other methods on a range of simulations, based on their fit to the underlying function as measured by mean squared error, particularly for sparse data sets.
Smoothing functions need to be flexible when they are used to model density surfaces that are highly heterogeneous, in order to avoid biases due to under or overfitting. This issue was addressed using an adaptation of a Spatially Adaptive Local Smoothing Algorithm (SALSA, Walker et al. [2010]) in combination with the CReSS method (CReSSSALSA2D). Unlike traditional methods, such as Generalised Additive Modelling, the adaptive knot selection approach used in SALSA2D naturally accommodates local changes in the smoothness of the density surface that is being modelled. At the time of writing, there are no other methods available to deal with this issue in topographically complex regions. Simulation results show that CReSSSALSA2D performs better than CReSS (based on MSE scores), except at very high noise levels where there is an issue with overfitting.
There is an increasing need for a facility to combine multiple density surface maps of individual species in order to make best use of metadatabases, to maintain existing maps, and to extend their geographical coverage. This thesis develops a framework and methods for combining species distribution maps as new information becomes available. The methods use Bayes Theorem to combine density surfaces, taking account of the levels of precision associated with the different sets of estimates, and kernel smoothing to alleviate artefacts that may be created where pairs of surfaces join. The methods were used as part of an algorithm (the Dynamic Cetacean Abundance Predictor) designed for BAE Systems to aid in risk mitigation for naval exercises.
Two case studies show the capabilities of CReSS and CReSSSALSA2D when applied to real ecological data. In the first case study, CReSS was used in a Generalised Estimating Equation framework to identify a candidate Marine Protected Area for the Southern Resident Killer Whale population to the south of San Juan Island, off the Pacific coast of the United States. In the second case study, changes in the spatial and temporal distribution of harbour porpoise and minke whale in northwestern European waters over a period of 17 years (19942010) were modelled. CReSS and CReSSSALSA2D performed well in a large, topographically complex study area. Based on simulation results, maps produced using these methods are more accurate than if a traditional GAMbased method is used. The resulting maps identified particularly high densities of both harbour porpoise and minke whale in an area off the west coast of Scotland in 2010, that might be a candidate for inclusion into the
Scottish network of Nature Conservation Marine Protected Areas.
Tue, 05 Nov 2013 00:00:00 GMT
http://hdl.handle.net/10023/4514
20131105T00:00:00Z
ScottHayward, Lindesay Alexandra Sarah
Species Distribution Modelling (SDM) plays a key role in a number of biological applications: assessment of temporal trends in distribution, environmental impact assessment and spatial conservation planning. From a statistical perspective, this thesis develops two methods for increasing the accuracy and reliability of maps of density surfaces and provides a solution to the problem of how to collate multiple density maps of the same region, obtained from differing sources. From a biological perspective, these statistical methods are used to analyse two marine mammal datasets to produce accurate maps for use in spatial conservation planning and temporal trend assessment.
The first new method, Complex Region Spatial Smoother [CReSS; ScottHayward et al., 2013], improves smoothing in areas where the real distance an animal must travel (`as the animal swims') between two points may be greater than the straight line distance between them, a problem that occurs in complex domains with coastline or islands. CReSS uses estimates of the geodesic distance between points, model averaging and local radial smoothing. Simulation is used to compare its performance with other traditional and recentlydeveloped smoothing techniques: Thin Plate Splines (TPS, Harder and Desmarais [1972]), Geodesic Low rank TPS (GLTPS; Wang and Ranalli [2007]) and the Soap lm smoother (SOAP; Wood et al. [2008]). GLTPS cannot be used in areas with islands and SOAP can be very hard to parametrise. CReSS outperforms all of the other methods on a range of simulations, based on their fit to the underlying function as measured by mean squared error, particularly for sparse data sets.
Smoothing functions need to be flexible when they are used to model density surfaces that are highly heterogeneous, in order to avoid biases due to under or overfitting. This issue was addressed using an adaptation of a Spatially Adaptive Local Smoothing Algorithm (SALSA, Walker et al. [2010]) in combination with the CReSS method (CReSSSALSA2D). Unlike traditional methods, such as Generalised Additive Modelling, the adaptive knot selection approach used in SALSA2D naturally accommodates local changes in the smoothness of the density surface that is being modelled. At the time of writing, there are no other methods available to deal with this issue in topographically complex regions. Simulation results show that CReSSSALSA2D performs better than CReSS (based on MSE scores), except at very high noise levels where there is an issue with overfitting.
There is an increasing need for a facility to combine multiple density surface maps of individual species in order to make best use of metadatabases, to maintain existing maps, and to extend their geographical coverage. This thesis develops a framework and methods for combining species distribution maps as new information becomes available. The methods use Bayes Theorem to combine density surfaces, taking account of the levels of precision associated with the different sets of estimates, and kernel smoothing to alleviate artefacts that may be created where pairs of surfaces join. The methods were used as part of an algorithm (the Dynamic Cetacean Abundance Predictor) designed for BAE Systems to aid in risk mitigation for naval exercises.
Two case studies show the capabilities of CReSS and CReSSSALSA2D when applied to real ecological data. In the first case study, CReSS was used in a Generalised Estimating Equation framework to identify a candidate Marine Protected Area for the Southern Resident Killer Whale population to the south of San Juan Island, off the Pacific coast of the United States. In the second case study, changes in the spatial and temporal distribution of harbour porpoise and minke whale in northwestern European waters over a period of 17 years (19942010) were modelled. CReSS and CReSSSALSA2D performed well in a large, topographically complex study area. Based on simulation results, maps produced using these methods are more accurate than if a traditional GAMbased method is used. The resulting maps identified particularly high densities of both harbour porpoise and minke whale in an area off the west coast of Scotland in 2010, that might be a candidate for inclusion into the
Scottish network of Nature Conservation Marine Protected Areas.

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

Modelling catch sampling uncertainty in fisheries stock assessment : the AtlanticIberian sardine case
http://hdl.handle.net/10023/4474
The statistical assessment of harvested fish populations, such as the AtlanticIberian sardine (AIS)
stock, needs to deal with uncertainties inherent in fisheries systems. Uncertainties arising from
sampling errors and stochasticity in stock dynamics must be incorporated in stock assessment
models so that management decisions are based on realistic evaluation of the uncertainty about
the status of the stock. The main goal of this study is to develop a stock assessment framework
that accounts for some of the uncertainties associated with the AIS stock that are currently not
integrated into stock assessment models. In particular, it focuses on accounting for the uncertainty
arising from the catch data sampling process.
The central innovation the thesis is the development of a Bayesian integrated stock assessment
(ISA) model, in which an observation model explicitly links stock dynamics parameters
with statistical models for the various types of data observed from catches of the AIS stock.
This allows for systematic and statistically consistent propagation of the uncertainty inherent in
the catch sampling process across the whole stock assessment model, through to estimates of
biomass and stock parameters. The method is tested by simulations and found to provide reliable
and accurate estimates of stock parameters and associated uncertainty, while also outperforming
existing designedbased and modelbased estimation approaches.
The method is computationally very demanding and this is an obstacle to its adoption
by fisheries bodies. Once this obstacle is overcame, the ISA modelling framework developed
and presented in this thesis could provide an important contribution to the improvement in the
evaluation of uncertainty in fisheries stock assessments, not only of the AIS stock, but of any other
fish stock with similar data and dynamics structure. Furthermore, the models developed in this
study establish a solid conceptual platform to allow future development of more complex models
of fish population dynamics.
Tue, 01 Jan 2013 00:00:00 GMT
http://hdl.handle.net/10023/4474
20130101T00:00:00Z
Caneco, Bruno
The statistical assessment of harvested fish populations, such as the AtlanticIberian sardine (AIS)
stock, needs to deal with uncertainties inherent in fisheries systems. Uncertainties arising from
sampling errors and stochasticity in stock dynamics must be incorporated in stock assessment
models so that management decisions are based on realistic evaluation of the uncertainty about
the status of the stock. The main goal of this study is to develop a stock assessment framework
that accounts for some of the uncertainties associated with the AIS stock that are currently not
integrated into stock assessment models. In particular, it focuses on accounting for the uncertainty
arising from the catch data sampling process.
The central innovation the thesis is the development of a Bayesian integrated stock assessment
(ISA) model, in which an observation model explicitly links stock dynamics parameters
with statistical models for the various types of data observed from catches of the AIS stock.
This allows for systematic and statistically consistent propagation of the uncertainty inherent in
the catch sampling process across the whole stock assessment model, through to estimates of
biomass and stock parameters. The method is tested by simulations and found to provide reliable
and accurate estimates of stock parameters and associated uncertainty, while also outperforming
existing designedbased and modelbased estimation approaches.
The method is computationally very demanding and this is an obstacle to its adoption
by fisheries bodies. Once this obstacle is overcame, the ISA modelling framework developed
and presented in this thesis could provide an important contribution to the improvement in the
evaluation of uncertainty in fisheries stock assessments, not only of the AIS stock, but of any other
fish stock with similar data and dynamics structure. Furthermore, the models developed in this
study establish a solid conceptual platform to allow future development of more complex models
of fish population dynamics.

Incomplete contingency tables with censored cells with application to estimating the number of people who inject drugs in Scotland
http://hdl.handle.net/10023/4433
Estimating the size of hidden or difficult to reach populations is often of interest for economic, sociological or public health reasons. In order to estimate such populations, administrative data lists are often collated to form multilist crosscounts and displayed in the form of an incomplete contingency table. Loglinear models are typically fitted to such data to obtain an estimate of the total population size by estimating the number of individuals not observed by any of the datasources. This approach has been taken to estimate the current number of people who inject drugs (PWID) in Scotland, with the Hepatitis C virus (HCV) diagnosis database used as one of the datasources to identify PWID. However, the HCV diagnosis datasource does not distinguish between current and former PWID, which, if ignored, will lead to overestimation of the total population size of current PWID. We extend the standard modelfitting approach to allow for a datasource which contains a mixture of target and nontarget individuals (i.e. in this case; current and former PWID). We apply the proposed approach to data for PWID in Scotland in 2003, 2006 and 2009 and compare to the results from standard loglinear models.
Wed, 30 Apr 2014 00:00:00 GMT
http://hdl.handle.net/10023/4433
20140430T00:00:00Z
Overstall, Antony
King, Ruth
Bird, Sheila
Hutchinson, Sharon
Hay, Gordon
Estimating the size of hidden or difficult to reach populations is often of interest for economic, sociological or public health reasons. In order to estimate such populations, administrative data lists are often collated to form multilist crosscounts and displayed in the form of an incomplete contingency table. Loglinear models are typically fitted to such data to obtain an estimate of the total population size by estimating the number of individuals not observed by any of the datasources. This approach has been taken to estimate the current number of people who inject drugs (PWID) in Scotland, with the Hepatitis C virus (HCV) diagnosis database used as one of the datasources to identify PWID. However, the HCV diagnosis datasource does not distinguish between current and former PWID, which, if ignored, will lead to overestimation of the total population size of current PWID. We extend the standard modelfitting approach to allow for a datasource which contains a mixture of target and nontarget individuals (i.e. in this case; current and former PWID). We apply the proposed approach to data for PWID in Scotland in 2003, 2006 and 2009 and compare to the results from standard loglinear models.

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

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

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

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

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

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

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

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

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

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

Pelagic movements of pacific leatherback turtles (Dermochelys coriacea) reveal the complex role of prey and ocean currents
http://hdl.handle.net/10023/4356
Background: Leatherback turtles are renowned for their transoceanic migrations. However, despite numerous movement studies, the precise drivers of movement patterns in leatherbacks remain elusive. Many previous studies of leatherback turtles as well as other diving marine predators have analyzed surface movement patterns using only surface covariates. Since turtles and other marine predators spend the vast majority of their time diving under water, an analysis of movement patterns at depth should yield insight into what drives their movements. Results: We analyzed the movement paths of 15 postnesting adult female Pacific leatherback turtles, which were caught and tagged on three nesting beaches in Mexico. The temporal length of the tracks ranged from 32 to 436 days, and the spatial distance covered ranged from 1,532 km to 13,097 km. We analyzed these tracks using a movement model designed to yield inference on the parameters driving movement. Because the telemetry data included diving depths, we extended an earlier version of the model that examined surface only movements, and here analyze movements in 3dimensions. We tested the effect of dynamic environmental covariates from a coupled biophysical oceanographic model on patch choice in diving leatherback turtles, and compared the effects of parameters measured at the surface and at depth. The covariates included distance to future patch, temperature, salinity, meridional current velocity (current in the north–south direction), zonal current velocity (current in the east–west direction), phytoplankton density, diatom density, microplankton density, and mesozooplankton density. We found significant, i.e. nonzero, correlation between movement and the parameters for oceanic covariates in 8 of the tracks. Of particular note, for one turtle we observed a lack of correlation between movements and a modeled index of zooplankton at the surface, but a significant correlation between movements and zooplankton at depth. Two of the turtles express a preference for patches at depth with elevated diatoms, and 2 turtles prefer patches with higher mezozooplankton values at depth. In contrast, 4 turtles expressed a preference for elevated zooplankton patches at the surface, but not at depth. We suggest that our understanding of a marine predator’s response to the environment may change significantly depending upon the analytical frame of reference, i.e. whether relationships are examined at the surface, at depth, or at different temporal resolutions. Lastly, we tested the effects of accounting for ocean currents on the movement patterns and found that for 13 of the 15 turtles, the parameter governing distance to the next patch decreased. Conclusions: Our results suggest that relationships derived from the analysis of surface tracks may not entirely explain movement patterns of this highly migratory species. Accounting for choices in the water column has shown that for certain individual turtles, what appears to be favourable habitat at depth is quantitatively different from that at the surface. This has implications for the analysis of the movements and diving behaviour of any top marine predator. The leatherback turtle is a deep diving reptile, and it is important to understand the subsurface variables that influence their movements if we are to precisely map the spatial dimensions of favorable leatherback habitat. These results present a new view into the drivers of diving patterns in turtles, and in particular represent a way of analyzing movements at depth that can be extended to other diving species.
APC paid through BIS OA funds.
Wed, 20 Nov 2013 00:00:00 GMT
http://hdl.handle.net/10023/4356
20131120T00:00:00Z
Schick, Robert Schilling
Roberts, Jason
Eckert, Scott
Clark, James
Bailey, Helen
Chai, Fei
Shi, Li
Halpin, Patrick
Background: Leatherback turtles are renowned for their transoceanic migrations. However, despite numerous movement studies, the precise drivers of movement patterns in leatherbacks remain elusive. Many previous studies of leatherback turtles as well as other diving marine predators have analyzed surface movement patterns using only surface covariates. Since turtles and other marine predators spend the vast majority of their time diving under water, an analysis of movement patterns at depth should yield insight into what drives their movements. Results: We analyzed the movement paths of 15 postnesting adult female Pacific leatherback turtles, which were caught and tagged on three nesting beaches in Mexico. The temporal length of the tracks ranged from 32 to 436 days, and the spatial distance covered ranged from 1,532 km to 13,097 km. We analyzed these tracks using a movement model designed to yield inference on the parameters driving movement. Because the telemetry data included diving depths, we extended an earlier version of the model that examined surface only movements, and here analyze movements in 3dimensions. We tested the effect of dynamic environmental covariates from a coupled biophysical oceanographic model on patch choice in diving leatherback turtles, and compared the effects of parameters measured at the surface and at depth. The covariates included distance to future patch, temperature, salinity, meridional current velocity (current in the north–south direction), zonal current velocity (current in the east–west direction), phytoplankton density, diatom density, microplankton density, and mesozooplankton density. We found significant, i.e. nonzero, correlation between movement and the parameters for oceanic covariates in 8 of the tracks. Of particular note, for one turtle we observed a lack of correlation between movements and a modeled index of zooplankton at the surface, but a significant correlation between movements and zooplankton at depth. Two of the turtles express a preference for patches at depth with elevated diatoms, and 2 turtles prefer patches with higher mezozooplankton values at depth. In contrast, 4 turtles expressed a preference for elevated zooplankton patches at the surface, but not at depth. We suggest that our understanding of a marine predator’s response to the environment may change significantly depending upon the analytical frame of reference, i.e. whether relationships are examined at the surface, at depth, or at different temporal resolutions. Lastly, we tested the effects of accounting for ocean currents on the movement patterns and found that for 13 of the 15 turtles, the parameter governing distance to the next patch decreased. Conclusions: Our results suggest that relationships derived from the analysis of surface tracks may not entirely explain movement patterns of this highly migratory species. Accounting for choices in the water column has shown that for certain individual turtles, what appears to be favourable habitat at depth is quantitatively different from that at the surface. This has implications for the analysis of the movements and diving behaviour of any top marine predator. The leatherback turtle is a deep diving reptile, and it is important to understand the subsurface variables that influence their movements if we are to precisely map the spatial dimensions of favorable leatherback habitat. These results present a new view into the drivers of diving patterns in turtles, and in particular represent a way of analyzing movements at depth that can be extended to other diving species.

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

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

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

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