DSpace Community:
http://hdl.handle.net/10023/28
Sat, 25 Oct 2014 19:11:40 GMT
20141025T19:11:40Z
DSpace Community:
http://researchrepository.standrews.ac.uk:80/retrieve/13/Mathematics and statistics.gif
http://hdl.handle.net/10023/28

Exact dimensionality and projections of random selfsimilar measures and sets
http://hdl.handle.net/10023/5514
Abstract: 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.
Mon, 01 Sep 2014 00:00:00 GMT
http://hdl.handle.net/10023/5514
20140901T00:00:00Z
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
Abstract: 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
Abstract: 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
Abstract: 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.
Description: 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
Abstract: 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.
Description: 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
Abstract: 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
Abstract: 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
Abstract: 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 weakfiled regime
http://hdl.handle.net/10023/5358
Abstract: 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.
Description: 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
Abstract: 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.
Description: 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
Abstract: 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.
Description: 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
Abstract: 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.
Description: 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
Abstract: 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.
Description: 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
Abstract: 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
Abstract: 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
Abstract: 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.
Description: 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
Abstract: 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.
Description: 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
Abstract: 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.
Description: 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
Abstract: 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.
Description: 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
Abstract: 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
Abstract: 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.
Description: 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
Abstract: 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.
Description: 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
Abstract: 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.
Description: 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
Abstract: 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
Abstract: 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, 01 Jan 2014 00:00:00 GMT
http://hdl.handle.net/10023/5186
20140101T00:00:00Z
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
Abstract: 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, 01 Jan 2014 00:00:00 GMT
http://hdl.handle.net/10023/5185
20140101T00:00:00Z
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
Abstract: 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
Abstract: 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, 01 Jan 2014 00:00:00 GMT
http://hdl.handle.net/10023/5183
20140101T00:00:00Z
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
Abstract: 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
Abstract: 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.
Description: 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
Abstract: 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.
Description: 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
Abstract: 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.
Description: 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
Abstract: 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.
Description: 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
Abstract: 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.
Description: 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
Abstract: 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.
Description: 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
Abstract: 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.
Description: 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
Abstract: 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.
Description: 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
Abstract: 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
Abstract: 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
Abstract: 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.
Description: 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
Abstract: 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
Abstract: 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.
Description: 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
Abstract: 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
Abstract: 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.
Description: 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
Abstract: 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
Abstract: 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
Abstract: 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
Abstract: 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.
Description: 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
Abstract: 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
Abstract: 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.
Description: 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
Abstract: 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.
Description: 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
Description: 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
Abstract: 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.
Description: 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
Abstract: 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.
Description: 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
Abstract: 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.
Description: 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
Abstract: 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
Abstract: 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
Abstract: 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
Abstract: 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
Abstract: 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.
Description: 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
Abstract: 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
Abstract: 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.
Description: 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
Abstract: 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
Abstract: 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
Abstract: 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
Abstract: 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
Abstract: 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
Abstract: 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
Abstract: 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
Abstract: 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
Abstract: 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
Abstract: 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
Abstract: 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
Abstract: 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
Abstract: 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
Abstract: 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
Abstract: 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
Abstract: 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.
Description: 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
Abstract: 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
Abstract: 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
Abstract: 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.
Description: APC paid through BIS OA funds.
Fri, 01 Nov 2013 00:00:00 GMT
http://hdl.handle.net/10023/4356
20131101T00:00:00Z
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
Abstract: 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
Abstract: 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
Abstract: 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
Abstract: The waveinduced flow over a fixed bottom boundary beneath an internal solitary wave of elevation propagating in an unsheared, twolayer, stably stratified fluid is investigated experimentally. Measurements of the velocity field close to the bottom boundary are presented to illustrate that in the lower layer the fluid velocity near the bottom reverses direction as the wave decelerates while higher in the water column the fluid velocity is in the same direction as the wave propagation. The observation is similar in nature to that for waveinduced flow beneath a surface solitary wave. Contrary to theoretical predictions for internal solitary waves, no evidence for either boundary layer separation or vortex formation is found beneath the front half of the wave in the adverse pressure gradient region of the flow.
Mon, 01 Feb 2010 00:00:00 GMT
http://hdl.handle.net/10023/4331
20100201T00:00:00Z
Carr, Magda
Davies, P A
The waveinduced flow over a fixed bottom boundary beneath an internal solitary wave of elevation propagating in an unsheared, twolayer, stably stratified fluid is investigated experimentally. Measurements of the velocity field close to the bottom boundary are presented to illustrate that in the lower layer the fluid velocity near the bottom reverses direction as the wave decelerates while higher in the water column the fluid velocity is in the same direction as the wave propagation. The observation is similar in nature to that for waveinduced flow beneath a surface solitary wave. Contrary to theoretical predictions for internal solitary waves, no evidence for either boundary layer separation or vortex formation is found beneath the front half of the wave in the adverse pressure gradient region of the flow.

Generalized dimensions of images of measures under Gaussian processes
http://hdl.handle.net/10023/4319
Abstract: We show that for certain Gaussian random processes and fields X:RN→Rd, Dq(μx) = min {d, 1/α Dq (μ)} a.s., for an index α which depends on Hölder properties and strong local nondeterminism of X, where q>1, where Dq denotes generalized qdimension μX is the image of the measure μ under X. In particular this holds for indexα fractional Brownian motion, for fractional Riesz–Bessel motions and for certain infinity scale fractional Brownian motions.
Description: 26 pages
Sat, 15 Feb 2014 00:00:00 GMT
http://hdl.handle.net/10023/4319
20140215T00:00:00Z
Falconer, Kenneth
Xiao, Yimin
We show that for certain Gaussian random processes and fields X:RN→Rd, Dq(μx) = min {d, 1/α Dq (μ)} a.s., for an index α which depends on Hölder properties and strong local nondeterminism of X, where q>1, where Dq denotes generalized qdimension μX is the image of the measure μ under X. In particular this holds for indexα fractional Brownian motion, for fractional Riesz–Bessel motions and for certain infinity scale fractional Brownian motions.

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

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

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

Maximum likelihood estimation of markrecapturerecovery models in the presence of continuous covariates
http://hdl.handle.net/10023/4073
Abstract: We consider markrecapturerecovery (MRR) data of animals where the model parameters are a function of individual timevarying continuous covariates. For such covariates, the covariate value is unobserved if the corresponding individual is unobserved, in which case the survival probability cannot be evaluated. For continuousvalued covariates, the corresponding likelihood can only be expressed in the form of an integral that is analytically intractable, and, to date, no maximum likelihood approach that uses all the information in the data has been developed. Assuming a firstorder Markov process for the covariate values, we accomplish this task by formulating the MRR setting in a statespace framework and considering an approximate likelihood approach which essentially discretizes the range of covariate values, reducing the integral to a summation. The likelihood can then be efficiently calculated and maximized using standard techniques for hidden Markov models. We initially assess the approach using simulated data before applying to real data relating to Soay sheep, specifying the survival probability as a function of body mass. Models that have previously been suggested for the corresponding covariate process are typically of the form of di.usive random walks. We consider an alternative nondi.usive AR(1)type model which appears to provide a significantly better fit to the Soay sheep data.
Description: Supplementary material: R code for model fitting. Sample R code for simulating MRR data and fitting the corresponding model using the HMMbased approach (with MRR model as described in Section 3). Digital Object Identifier: doi:10.1214/13AOAS644SUPP
Tue, 01 Jan 2013 00:00:00 GMT
http://hdl.handle.net/10023/4073
20130101T00:00:00Z
Langrock, Roland
King, Ruth
We consider markrecapturerecovery (MRR) data of animals where the model parameters are a function of individual timevarying continuous covariates. For such covariates, the covariate value is unobserved if the corresponding individual is unobserved, in which case the survival probability cannot be evaluated. For continuousvalued covariates, the corresponding likelihood can only be expressed in the form of an integral that is analytically intractable, and, to date, no maximum likelihood approach that uses all the information in the data has been developed. Assuming a firstorder Markov process for the covariate values, we accomplish this task by formulating the MRR setting in a statespace framework and considering an approximate likelihood approach which essentially discretizes the range of covariate values, reducing the integral to a summation. The likelihood can then be efficiently calculated and maximized using standard techniques for hidden Markov models. We initially assess the approach using simulated data before applying to real data relating to Soay sheep, specifying the survival probability as a function of body mass. Models that have previously been suggested for the corresponding covariate process are typically of the form of di.usive random walks. We consider an alternative nondi.usive AR(1)type model which appears to provide a significantly better fit to the Soay sheep data.

Prioritizing global marine mammal habitats using density maps in place of range maps
http://hdl.handle.net/10023/4068
Abstract: Despite lessons from terrestrial systems, conservation efforts in marine systems continue to focus on identifying priority sites for protection based on high species richness inferred from range maps. Range maps oversimplify spatial variability in animal distributions by assuming uniform distribution within range and de facto giving equal weight to critical and marginal habitats. We used Marxan ver. 2.43 to compare species richnessbased systematic reserve network solutions using information about marine mammal range and relative abundance. At a global scale, reserve network solutions were strongly sensitive to model inputs and assumptions. Solutions based on different input data overlapped by a third at most, with agreement as low as 10% in some cases. At a regional scale, species richness was inversely related to density, such that species richness hotspots excluded highestdensity areas for all species. Based on these findings, we caution that speciesrichness estimates derived from range maps and used as input in conservation planning exercises may inadvertently lead to protection of largely marginal habitat.
Description: RW was supported by a Marie Curie International Incoming Fellowship within the 7th European Community Framework Programme FP7PEOPLE2009IIF
Sat, 01 Mar 2014 00:00:00 GMT
http://hdl.handle.net/10023/4068
20140301T00:00:00Z
Williams, Robert
Grand, Joanna
Hooker, Sascha Kate
Buckland, Stephen Terrence
Reeves, Randall R.
RojasBracho, Lorenzo
Sandilands, Doug
Kaschner, Kristin
Despite lessons from terrestrial systems, conservation efforts in marine systems continue to focus on identifying priority sites for protection based on high species richness inferred from range maps. Range maps oversimplify spatial variability in animal distributions by assuming uniform distribution within range and de facto giving equal weight to critical and marginal habitats. We used Marxan ver. 2.43 to compare species richnessbased systematic reserve network solutions using information about marine mammal range and relative abundance. At a global scale, reserve network solutions were strongly sensitive to model inputs and assumptions. Solutions based on different input data overlapped by a third at most, with agreement as low as 10% in some cases. At a regional scale, species richness was inversely related to density, such that species richness hotspots excluded highestdensity areas for all species. Based on these findings, we caution that speciesrichness estimates derived from range maps and used as input in conservation planning exercises may inadvertently lead to protection of largely marginal habitat.

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

Inhomogeneous parabolic equations on unbounded metric measure spaces
http://hdl.handle.net/10023/4061
Abstract: We study the inhomogeneous semilinear parabolic equation ut = Δu + up + f(x), with source term f independent of time and subject to f(x) ≥ 0 and with u(0, x) = φ(x) ≥ 0, for the very general setting of a metric measure space. By establishing Harnacktype inequalities in time t and some powerful estimates, we give sufficient conditions for nonexistence, local existence and global existence of weak solutions, depending on the value of p relative to a critical exponent.
Mon, 01 Oct 2012 00:00:00 GMT
http://hdl.handle.net/10023/4061
20121001T00:00:00Z
Falconer, Kenneth John
Hu, Jiaxin
Sun, Yuhua
We study the inhomogeneous semilinear parabolic equation ut = Δu + up + f(x), with source term f independent of time and subject to f(x) ≥ 0 and with u(0, x) = φ(x) ≥ 0, for the very general setting of a metric measure space. By establishing Harnacktype inequalities in time t and some powerful estimates, we give sufficient conditions for nonexistence, local existence and global existence of weak solutions, depending on the value of p relative to a critical exponent.

Using energetic models to investigate the survival and reproduction of beaked whales (family Ziphiidae)
http://hdl.handle.net/10023/4053
Abstract: Mass stranding of several species of beaked whales (family Ziphiidae) associated with exposure to anthropogenic sounds has raised concern for the conservation of these species. However, little is known about the species’ life histories, prey or habitat requirements. Without this knowledge, it becomes difficult to assess the effects of anthropogenic sound, since there is no way to determine whether the disturbance is impacting the species’ physical or environmental requirements. Here we take a bioenergetics approach to address this gap in our knowledge, as the elusive, deepdiving nature of beaked whales has made it hard to study these effects directly. We develop a model for Ziphiidae linking feeding energetics to the species’ requirements for survival and reproduction, since these life history traits would be the most likely to be impacted by nonlethal disturbances. Our models suggest that beaked whale reproduction requires energy dense prey, and that poor resource availability would lead to an extension of the intercalving interval. Further, given current information, it seems that some beaked whale species require relatively high quality habitat in order to meet their requirements for survival and reproduction. As a result, even a small nonlethal disturbance that results in displacement of whales from preferred habitats could potentially impact a population if a significant proportion of that population was affected. We explored the impact of varying ecological parameters and model assumptions on survival and reproduction, and find that calf and fetus survival appear more readily affected than the survival of adult females.
Wed, 17 Jul 2013 00:00:00 GMT
http://hdl.handle.net/10023/4053
20130717T00:00:00Z
New, Leslie Frances
Moretti, David
Hooker, Sascha Kate
Costa, Daniel P.
Simmons, Samantha E.
Mass stranding of several species of beaked whales (family Ziphiidae) associated with exposure to anthropogenic sounds has raised concern for the conservation of these species. However, little is known about the species’ life histories, prey or habitat requirements. Without this knowledge, it becomes difficult to assess the effects of anthropogenic sound, since there is no way to determine whether the disturbance is impacting the species’ physical or environmental requirements. Here we take a bioenergetics approach to address this gap in our knowledge, as the elusive, deepdiving nature of beaked whales has made it hard to study these effects directly. We develop a model for Ziphiidae linking feeding energetics to the species’ requirements for survival and reproduction, since these life history traits would be the most likely to be impacted by nonlethal disturbances. Our models suggest that beaked whale reproduction requires energy dense prey, and that poor resource availability would lead to an extension of the intercalving interval. Further, given current information, it seems that some beaked whale species require relatively high quality habitat in order to meet their requirements for survival and reproduction. As a result, even a small nonlethal disturbance that results in displacement of whales from preferred habitats could potentially impact a population if a significant proportion of that population was affected. We explored the impact of varying ecological parameters and model assumptions on survival and reproduction, and find that calf and fetus survival appear more readily affected than the survival of adult females.

Spatial models for distance sampling data : recent developments and future directions
http://hdl.handle.net/10023/4046
Abstract: Our understanding of a biological population can be greatly enhanced by modelling their distribution in space and as a function of environmental covariates. Density surface models consist of a spatial model of the abundance of a biological population which has been corrected for uncertain detection via distance sampling methods. We offer a comparison of recent advances in the field and consider the likely directions of future research. In particular we consider spatial modelling techniques that may be advantageous to applied ecologists such as quantification of uncertainty in a twostage model and smoothing in areas with complex boundaries. The methods discussed are available in an \textsf{R} package developed by the authors and are largely implemented in the popular Windows package Distance (or are soon to be incorporated). Density surface modelling enables applied ecologists to reliably estimate abundances and create maps of animal/plant distribution. Such models can also be used to investigate the relationships between distribution and environmental covariates.
Fri, 01 Nov 2013 00:00:00 GMT
http://hdl.handle.net/10023/4046
20131101T00:00:00Z
Miller, David Lawrence
Burt, M Louise
Rexstad, Eric
Thomas, Len
Our understanding of a biological population can be greatly enhanced by modelling their distribution in space and as a function of environmental covariates. Density surface models consist of a spatial model of the abundance of a biological population which has been corrected for uncertain detection via distance sampling methods. We offer a comparison of recent advances in the field and consider the likely directions of future research. In particular we consider spatial modelling techniques that may be advantageous to applied ecologists such as quantification of uncertainty in a twostage model and smoothing in areas with complex boundaries. The methods discussed are available in an \textsf{R} package developed by the authors and are largely implemented in the popular Windows package Distance (or are soon to be incorporated). Density surface modelling enables applied ecologists to reliably estimate abundances and create maps of animal/plant distribution. Such models can also be used to investigate the relationships between distribution and environmental covariates.

A default prior distribution for contingency tables with dependent factor levels
http://hdl.handle.net/10023/4042
Abstract: A default prior distribution is proposed for the Bayesian analysis of contingency tables. The prior is specified to allow for dependence between levels of the factors. Different dependence structures are considered, including conditional autoregressive and distance correlation structures. To demonstrate the prior distribution, a dataset is considered involving estimating the number of injecting drug users in the eleven National Health Service board regions of Scotland using an incomplete contingency table where the dependence structure relates to geographical regions.
Description: Both authors were partly funded by MRCfunded addictions cluster, NIQUAD (Grant No. G1000021).
Wed, 01 Jan 2014 00:00:00 GMT
http://hdl.handle.net/10023/4042
20140101T00:00:00Z
Overstall, Antony
King, Ruth
A default prior distribution is proposed for the Bayesian analysis of contingency tables. The prior is specified to allow for dependence between levels of the factors. Different dependence structures are considered, including conditional autoregressive and distance correlation structures. To demonstrate the prior distribution, a dataset is considered involving estimating the number of injecting drug users in the eleven National Health Service board regions of Scotland using an incomplete contingency table where the dependence structure relates to geographical regions.

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

Combining individual animal movement and ancillary biotelemetry data to investigate populationlevel activity budgets
http://hdl.handle.net/10023/3993
Abstract: Recent technological advances have permitted the collection of detailed animal location and ancillary biotelemetry data that facilitate inference about animal movement and associated behaviors. However, these rich sources of individual information, location, and biotelemetry data, are typically analyzed independently, with populationlevel inferences remaining largely post hoc. We describe a hierarchical modeling approach, which is able to integrate location and ancillary biotelemetry (e.g., physiological or accelerometer) data from many individuals. We can thus obtain robust estimates of (1) populationlevel movement parameters and (2) activity budgets for a set of behaviors among which animals transition as they respond to changes in their internal and external environment. Measurement error and missing data are easily accommodated using a statespace formulation of the proposed hierarchical model. Using Bayesian analysis methods, we demonstrate our modeling approach with location and dive activity data from 17 harbor seals (Phoca vitulina) in the United Kingdom. Based jointly on movement and diving activity, we identified three distinct movement behavior states: resting, foraging, and transit, and estimated populationlevel activity budgets to these three states. Because harbor seals are known to dive for both foraging and transit (but not usually for resting), we compared these results to a similar population level analysis utilizing only location data. We found that a large proportion of time steps were mischaracterized when behavior states were inferred from horizontal trajectory alone, with 33% of time steps exhibiting a majority of dive activity assigned to the resting state. Only 1% of these time steps were assigned to resting when inferred from both trajectory and dive activity data using our integrated modeling approach. There is mounting evidence of the potential perils of inferring animal behavior based on trajectory alone, but there fortunately now exist many flexible analytical techniques for extracting more out of the increasing wealth of information afforded by recent advances in biologging technology.
Mon, 01 Apr 2013 00:00:00 GMT
http://hdl.handle.net/10023/3993
20130401T00:00:00Z
McClintock, Brett Thomas
Russell, Deborah Jill Fraser
Matthiopoulos, Jason
King, Ruth
Recent technological advances have permitted the collection of detailed animal location and ancillary biotelemetry data that facilitate inference about animal movement and associated behaviors. However, these rich sources of individual information, location, and biotelemetry data, are typically analyzed independently, with populationlevel inferences remaining largely post hoc. We describe a hierarchical modeling approach, which is able to integrate location and ancillary biotelemetry (e.g., physiological or accelerometer) data from many individuals. We can thus obtain robust estimates of (1) populationlevel movement parameters and (2) activity budgets for a set of behaviors among which animals transition as they respond to changes in their internal and external environment. Measurement error and missing data are easily accommodated using a statespace formulation of the proposed hierarchical model. Using Bayesian analysis methods, we demonstrate our modeling approach with location and dive activity data from 17 harbor seals (Phoca vitulina) in the United Kingdom. Based jointly on movement and diving activity, we identified three distinct movement behavior states: resting, foraging, and transit, and estimated populationlevel activity budgets to these three states. Because harbor seals are known to dive for both foraging and transit (but not usually for resting), we compared these results to a similar population level analysis utilizing only location data. We found that a large proportion of time steps were mischaracterized when behavior states were inferred from horizontal trajectory alone, with 33% of time steps exhibiting a majority of dive activity assigned to the resting state. Only 1% of these time steps were assigned to resting when inferred from both trajectory and dive activity data using our integrated modeling approach. There is mounting evidence of the potential perils of inferring animal behavior based on trajectory alone, but there fortunately now exist many flexible analytical techniques for extracting more out of the increasing wealth of information afforded by recent advances in biologging technology.

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

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

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

Population status of Pan troglodytes verus in Lagoas de Cufada Natural Park, GuineaBissau
http://hdl.handle.net/10023/3974
Abstract: The western chimpanzee, Pan troglodytes verus, has been classified as Endangered on the IUCN Red List since 1988. Intensive agriculture, commercial plantations, logging, and mining have eliminated or degraded the habitats suitable for P. t. verus over a large part of its range. In this study we assessed the effect of landuse change on the population size and density of chimpanzees at Lagoas de Cufada Natural Park (LCNP), GuineaBissau. We further explored chimpanzee distribution in relation to landscapelevel proxies of human disturbance. Nest count and distancesampling methods were employed along 11 systematically placed linear transects in 2010 and 2011. Estimated nest decay rate was 293.9 days (%CV = 58.8). Based on this estimate of decay time and using the StandingCrop Nest Count Method, we obtained a habitatweighted average chimpanzee density estimate for 2011 of 0.22 nest building chimpanzees/km2 (95% CI 0.08–0.62), corresponding to 137 (95% CI 51.0–390.0) chimpanzees for LCNP. Human disturbance had a negative influence on chimpanzee distribution as nests were built farther away from human settlements, roads, and rivers than if they were randomly distributed, coinciding with the distribution of the remaining patches of dense canopy forest. We conclude that the continuous disappearance of suitable habitat (e.g. the replacement of LCNP's dense forests by monocultures of cashew plantations) may be compromising the future of one of the most threatened Guinean coastal chimpanzee populations. We discuss strategies to ensure longterm conservation in this important refuge for this chimpanzee subspecies at its westernmost margin of geographic distribution.
Thu, 01 Aug 2013 00:00:00 GMT
http://hdl.handle.net/10023/3974
20130801T00:00:00Z
Carvalho, Joana S.
Marques, Tiago A.
Vicente, Luis
The western chimpanzee, Pan troglodytes verus, has been classified as Endangered on the IUCN Red List since 1988. Intensive agriculture, commercial plantations, logging, and mining have eliminated or degraded the habitats suitable for P. t. verus over a large part of its range. In this study we assessed the effect of landuse change on the population size and density of chimpanzees at Lagoas de Cufada Natural Park (LCNP), GuineaBissau. We further explored chimpanzee distribution in relation to landscapelevel proxies of human disturbance. Nest count and distancesampling methods were employed along 11 systematically placed linear transects in 2010 and 2011. Estimated nest decay rate was 293.9 days (%CV = 58.8). Based on this estimate of decay time and using the StandingCrop Nest Count Method, we obtained a habitatweighted average chimpanzee density estimate for 2011 of 0.22 nest building chimpanzees/km2 (95% CI 0.08–0.62), corresponding to 137 (95% CI 51.0–390.0) chimpanzees for LCNP. Human disturbance had a negative influence on chimpanzee distribution as nests were built farther away from human settlements, roads, and rivers than if they were randomly distributed, coinciding with the distribution of the remaining patches of dense canopy forest. We conclude that the continuous disappearance of suitable habitat (e.g. the replacement of LCNP's dense forests by monocultures of cashew plantations) may be compromising the future of one of the most threatened Guinean coastal chimpanzee populations. We discuss strategies to ensure longterm conservation in this important refuge for this chimpanzee subspecies at its westernmost margin of geographic distribution.

Strong renewal theorems and Lyapunov spectra for alphaFarey and alphaLuroth systems
http://hdl.handle.net/10023/3933
Abstract: In this paper, we introduce and study the alphaFarey map and its associated jump transformation, the alphaLuroth map, for an arbitrary countable partition alpha of the unit interval with atoms which accumulate only at the origin. These maps represent linearized generalizations of the Farey map and the Gauss map from elementary number theory. First, a thorough analysis of some of their topological and ergodic theoretical properties is given, including establishing exactness for both types of these maps. The first main result then is to establish weak and strong renewal laws for what we have called alphasumlevel sets for the alphaLuroth map. Similar results have previously been obtained for the Farey map and the Gauss map by using infinite ergodic theory. In this respect, a side product of the paper is to allow for greater transparency of some of the core ideas of infinite ergodic theory. The second remaining result is to obtain a complete description of the Lyapunov spectra of the alphaFarey map and the alphaLuroth map in terms of the thermodynamical formalism. We show how to derive these spectra and then give various examples which demonstrate the diversity of their behaviours in dependence on the chosen partition alpha.
Fri, 01 Jun 2012 00:00:00 GMT
http://hdl.handle.net/10023/3933
20120601T00:00:00Z
Kesseboehmer, Marc
Munday, Sara
Stratmann, Bernd O.
In this paper, we introduce and study the alphaFarey map and its associated jump transformation, the alphaLuroth map, for an arbitrary countable partition alpha of the unit interval with atoms which accumulate only at the origin. These maps represent linearized generalizations of the Farey map and the Gauss map from elementary number theory. First, a thorough analysis of some of their topological and ergodic theoretical properties is given, including establishing exactness for both types of these maps. The first main result then is to establish weak and strong renewal laws for what we have called alphasumlevel sets for the alphaLuroth map. Similar results have previously been obtained for the Farey map and the Gauss map by using infinite ergodic theory. In this respect, a side product of the paper is to allow for greater transparency of some of the core ideas of infinite ergodic theory. The second remaining result is to obtain a complete description of the Lyapunov spectra of the alphaFarey map and the alphaLuroth map in terms of the thermodynamical formalism. We show how to derive these spectra and then give various examples which demonstrate the diversity of their behaviours in dependence on the chosen partition alpha.

Dimension and measure for generic continuous images
http://hdl.handle.net/10023/3902
Abstract: We consider the Banach space consisting of continuous functions from an arbitrary uncountable compact metric space, X, into Rn. The key question is 'what is the generic dimension of f(X)?' and we consider two different approaches to answering it: Baire category and prevalence. In the Baire category setting we prove that typically the packing and upper box dimensions are as large as possible, n, but find that the behaviour of the Hausdorff, lower box and topological dimensions is considerably more subtle. In fact, they are typically equal to the minimum of n and the topological dimension of X. We also study, the typical Hausdorff and packing measures of f (X) and, in particular, give necessary and sufficient conditions for them to be zero, positive and finite, or infinite. It is interesting to compare the Baire category results with results in the prevalence setting. As such we also discuss a result of Dougherty on the prevalent topological dimension of f (X) and give some simple applications concerning the prevalent dimensions of graphs of realvalued continuous functions on compact metric spaces, allowing us to extend a recent result of Bayart and Heurteaux.
Description: This work is supported by EPSRC Doctoral Training Grants
Tue, 01 Jan 2013 00:00:00 GMT
http://hdl.handle.net/10023/3902
20130101T00:00:00Z
Balka, Richard
Farkas, Abel
Fraser, Jonathan M.
Hyde, James T.
We consider the Banach space consisting of continuous functions from an arbitrary uncountable compact metric space, X, into Rn. The key question is 'what is the generic dimension of f(X)?' and we consider two different approaches to answering it: Baire category and prevalence. In the Baire category setting we prove that typically the packing and upper box dimensions are as large as possible, n, but find that the behaviour of the Hausdorff, lower box and topological dimensions is considerably more subtle. In fact, they are typically equal to the minimum of n and the topological dimension of X. We also study, the typical Hausdorff and packing measures of f (X) and, in particular, give necessary and sufficient conditions for them to be zero, positive and finite, or infinite. It is interesting to compare the Baire category results with results in the prevalence setting. As such we also discuss a result of Dougherty on the prevalent topological dimension of f (X) and give some simple applications concerning the prevalent dimensions of graphs of realvalued continuous functions on compact metric spaces, allowing us to extend a recent result of Bayart and Heurteaux.

A generalised likelihood framework for partially observed capturerecapturerecovery models
http://hdl.handle.net/10023/3877
Abstract: We provide a closed form likelihood expression for multistate markrecapturerecovery data when the state of an individual may be only partially observed. The corresponding su cient statistics are presented in addition to a matrix formulation which facilitates an e cient calculation of the likelihood. This likelihood framework provides a consistent and uni ed framework with many standard models applied to markrecapturerecovery data as special cases.
Wed, 01 Jan 2014 00:00:00 GMT
http://hdl.handle.net/10023/3877
20140101T00:00:00Z
King, Ruth
McCrea, R S
We provide a closed form likelihood expression for multistate markrecapturerecovery data when the state of an individual may be only partially observed. The corresponding su cient statistics are presented in addition to a matrix formulation which facilitates an e cient calculation of the likelihood. This likelihood framework provides a consistent and uni ed framework with many standard models applied to markrecapturerecovery data as special cases.

Dimension theory and fractal constructions based on selfaffine carpets
http://hdl.handle.net/10023/3869
Abstract: The aim of this thesis is to develop the dimension theory of selfaffine carpets in several directions. Selfaffine carpets are an important class of planar selfaffine sets which have received a great deal of attention in the literature on fractal geometry over the last 30 years. These constructions are important for several reasons. In particular, they provide a bridge between the relatively wellunderstood world of selfsimilar sets and the far from understood world of general selfaffine sets. These carpets are designed in such a way as to facilitate the computation of their dimensions, and they display many interesting and surprising features which the simpler selfsimilar constructions do not have. For example, they can have distinct Hausdorff and packing dimensions and the Hausdorff and packing measures are typically infinite in the critical dimensions. Furthermore, they often provide exceptions to the seminal result of Falconer from 1988 which gives the `generic' dimensions of selfaffine sets in a natural setting. The work in this thesis will be based on five research papers I wrote during my time as a PhD student.
The first contribution of this thesis will be to introduce a new class of selfaffine carpets, which we call boxlike selfaffine sets, and compute their box and packing dimensions via a modified singular value function. This not only generalises current results on selfaffine carpets, but also helps to reconcile the `exceptional constructions' with Falconer's singular value function approach in the generic case. This will appear in Chapter 2 and is based on a paper which appeared in 'Nonlinearity' in 2012.
In Chapter 3 we continue studying the dimension theory of selfaffine sets by computing the Assouad and lower dimensions of certain classes. The Assouad and lower dimensions have not received much attention in the literature on fractals to date and their importance has been more related to quasiconformal maps and embeddability problems. This appears to be changing, however, and so our results constitute a timely and important contribution to a growing body of literature on the subject. The material in this Chapter will be based on a paper which has been accepted for publication in 'Transactions of the American Mathematical Society'.
In Chapters 46 we move away from the classical setting of iterated function systems to consider two more exotic constructions, namely, inhomogeneous attractors and random 1variable attractors, with the aim of developing the dimension theory of selfaffine carpets in these directions.
In order to put our work into context, in Chapter 4 we consider inhomogeneous selfsimilar sets and significantly generalise the results on box dimensions obtained by Olsen and Snigireva, answering several questions posed in the literature in the process. We then move to the selfaffine setting and, in Chapter 5, investigate the dimensions of inhomogeneous selfaffine carpets and prove that new phenomena can occur in this setting which do not occur in the setting of selfsimilar sets. The material in Chapter 4 will be based on a paper which appeared in 'Studia Mathematica' in 2012, and the material in Chapter 5 is based on a paper, which is in preparation.
Finally, in Chapter 6 we consider random selfaffine sets. The traditional approach to random iterated function systems is probabilistic, but here we allow the randomness in the construction to be provided by the topological structure of the sample space, employing ideas from Baire category. We are able to obtain very general results in this setting, relaxing the conditions on the maps from `affine' to `biLipschitz'. In order to get precise results on the Hausdorff and packing measures of typical attractors, we need to specialise to the setting of random selfsimilar sets and we show again that several interesting and new phenomena can occur when we relax to the setting of random selfaffine carpets. The material in this Chapter will be based on a paper which has been accepted for publication by 'Ergodic Theory and Dynamical Systems'.
Fri, 29 Nov 2013 00:00:00 GMT
http://hdl.handle.net/10023/3869
20131129T00:00:00Z
Fraser, Jonathan M.
The aim of this thesis is to develop the dimension theory of selfaffine carpets in several directions. Selfaffine carpets are an important class of planar selfaffine sets which have received a great deal of attention in the literature on fractal geometry over the last 30 years. These constructions are important for several reasons. In particular, they provide a bridge between the relatively wellunderstood world of selfsimilar sets and the far from understood world of general selfaffine sets. These carpets are designed in such a way as to facilitate the computation of their dimensions, and they display many interesting and surprising features which the simpler selfsimilar constructions do not have. For example, they can have distinct Hausdorff and packing dimensions and the Hausdorff and packing measures are typically infinite in the critical dimensions. Furthermore, they often provide exceptions to the seminal result of Falconer from 1988 which gives the `generic' dimensions of selfaffine sets in a natural setting. The work in this thesis will be based on five research papers I wrote during my time as a PhD student.
The first contribution of this thesis will be to introduce a new class of selfaffine carpets, which we call boxlike selfaffine sets, and compute their box and packing dimensions via a modified singular value function. This not only generalises current results on selfaffine carpets, but also helps to reconcile the `exceptional constructions' with Falconer's singular value function approach in the generic case. This will appear in Chapter 2 and is based on a paper which appeared in 'Nonlinearity' in 2012.
In Chapter 3 we continue studying the dimension theory of selfaffine sets by computing the Assouad and lower dimensions of certain classes. The Assouad and lower dimensions have not received much attention in the literature on fractals to date and their importance has been more related to quasiconformal maps and embeddability problems. This appears to be changing, however, and so our results constitute a timely and important contribution to a growing body of literature on the subject. The material in this Chapter will be based on a paper which has been accepted for publication in 'Transactions of the American Mathematical Society'.
In Chapters 46 we move away from the classical setting of iterated function systems to consider two more exotic constructions, namely, inhomogeneous attractors and random 1variable attractors, with the aim of developing the dimension theory of selfaffine carpets in these directions.
In order to put our work into context, in Chapter 4 we consider inhomogeneous selfsimilar sets and significantly generalise the results on box dimensions obtained by Olsen and Snigireva, answering several questions posed in the literature in the process. We then move to the selfaffine setting and, in Chapter 5, investigate the dimensions of inhomogeneous selfaffine carpets and prove that new phenomena can occur in this setting which do not occur in the setting of selfsimilar sets. The material in Chapter 4 will be based on a paper which appeared in 'Studia Mathematica' in 2012, and the material in Chapter 5 is based on a paper, which is in preparation.
Finally, in Chapter 6 we consider random selfaffine sets. The traditional approach to random iterated function systems is probabilistic, but here we allow the randomness in the construction to be provided by the topological structure of the sample space, employing ideas from Baire category. We are able to obtain very general results in this setting, relaxing the conditions on the maps from `affine' to `biLipschitz'. In order to get precise results on the Hausdorff and packing measures of typical attractors, we need to specialise to the setting of random selfsimilar sets and we show again that several interesting and new phenomena can occur when we relax to the setting of random selfaffine carpets. The material in this Chapter will be based on a paper which has been accepted for publication by 'Ergodic Theory and Dynamical Systems'.

Estimating resource acquisition and atsea body condition of a marine predator
http://hdl.handle.net/10023/3867
Abstract: (1) Body condition plays a fundamental role in many ecological and evolutionary processes at a variety of scales and across a broad range of animal taxa. An understanding of how body condition changes at fine spatial and temporal scales as a result of interaction with the environment provides necessary information about how animals acquire resources. (2) However, comparatively little is known about intra and interindividual variation of condition in marine systems. Where condition has been studied, changes typically are recorded at relatively coarse timescales. By quantifying how finescale interaction with the environment influences condition, we can broaden our understanding of how animals acquire resources and allocate them to body stores. (3) Here we used a hierarchical Bayesian statespace model to estimate the body condition as measured by the size of an animal's lipid store in two closely related species of marine predator that occupy different hemispheres: northern elephant seals (Mirounga angustirostris) and southern elephant seals (Mirounga leonina). The observation model linked drift dives to lipid stores. The process model quantified daily changes in lipid stores as a function of the physiological condition of the seal (lipid:lean tissue ratio, departure lipid and departure mass), its foraging location, two measures of behaviour and environmental covariates. (4) We found that physiological condition significantly impacted lipid gain at two timescales – daily and at departure from the colony – that foraging location was significantly associated with lipid gain in both species of elephant seals and that longterm behavioural phase was associated with positive lipid gain in northern and southern elephant seals. In northern elephant seals, the occurrence of shortterm behavioural states assumed to represent foraging were correlated with lipid gain. Lipid gain was a function of covariates in both species. Southern elephant seals performed fewer drift dives than northern elephant seals and gained lipids at a lower rate. (5) We have demonstrated a new way to obtain time series of body condition estimates for a marine predator at fine spatial and temporal scales. This modelling approach accounts for uncertainty at many levels and has the potential to integrate physiological and movement ecology of top predators. The observation model we used was specific to elephant seals, but the process model can readily be applied to other species, providing an opportunity to understand how animals respond to their environment at a fine spatial scale.
Description: This article was made open access through BIS OA funding.
Tue, 01 Jan 2013 00:00:00 GMT
http://hdl.handle.net/10023/3867
20130101T00:00:00Z
Schick, Robert Schilling
New, Leslie
Thomas, Len
Costa, Daniel
Hindell, Mark
McMahon, Clive
Robinson, Patrick
Simmons, Samantha
Thums, Michele
Harwood, John
Clark, James
(1) Body condition plays a fundamental role in many ecological and evolutionary processes at a variety of scales and across a broad range of animal taxa. An understanding of how body condition changes at fine spatial and temporal scales as a result of interaction with the environment provides necessary information about how animals acquire resources. (2) However, comparatively little is known about intra and interindividual variation of condition in marine systems. Where condition has been studied, changes typically are recorded at relatively coarse timescales. By quantifying how finescale interaction with the environment influences condition, we can broaden our understanding of how animals acquire resources and allocate them to body stores. (3) Here we used a hierarchical Bayesian statespace model to estimate the body condition as measured by the size of an animal's lipid store in two closely related species of marine predator that occupy different hemispheres: northern elephant seals (Mirounga angustirostris) and southern elephant seals (Mirounga leonina). The observation model linked drift dives to lipid stores. The process model quantified daily changes in lipid stores as a function of the physiological condition of the seal (lipid:lean tissue ratio, departure lipid and departure mass), its foraging location, two measures of behaviour and environmental covariates. (4) We found that physiological condition significantly impacted lipid gain at two timescales – daily and at departure from the colony – that foraging location was significantly associated with lipid gain in both species of elephant seals and that longterm behavioural phase was associated with positive lipid gain in northern and southern elephant seals. In northern elephant seals, the occurrence of shortterm behavioural states assumed to represent foraging were correlated with lipid gain. Lipid gain was a function of covariates in both species. Southern elephant seals performed fewer drift dives than northern elephant seals and gained lipids at a lower rate. (5) We have demonstrated a new way to obtain time series of body condition estimates for a marine predator at fine spatial and temporal scales. This modelling approach accounts for uncertainty at many levels and has the potential to integrate physiological and movement ecology of top predators. The observation model we used was specific to elephant seals, but the process model can readily be applied to other species, providing an opportunity to understand how animals respond to their environment at a fine spatial scale.

Using hierarchical bayes to understand movement, health, and survival in the endangered North Atlantic right whale
http://hdl.handle.net/10023/3860
Abstract: Body condition is an indicator of health, and it plays a key role in many vital processes for mammalian species. While evidence of individual body condition can be obtained, these observations provide just brief glimpses into the health state of the animal. An analytical framework is needed for understanding how health of animals changes over space and time.Through knowledge of individual health we can better understand the status of populations. This is particularly important in endangered species, where the consequences of disruption of critical biological functions can push groups of animals rapidly toward extinction. Here we built a statespace model that provides estimates of movement, health, and survival. We assimilated 30+ years of photographic evidence of body condition and three additional visual health parameters in individual North Atlantic right whales, together with survey data, to infer the true health status as it changes over space and time. We also included the effect of reproductive status and entanglement status on health. At the population level, we estimated differential movement patterns in males and females. At the individual level, we estimated the likely animal locations each month. We estimated the relationship between observed and latent health status. Observations of body condition, skin condition, cyamid infestation on the blowholes, and rake marks all provided measures of the true underlying health. The resulting time series of individual health highlight both normal variations in health status and how anthropogenic stressors can affect the health and, ultimately, the survival of individuals. This modeling approach provides information for monitoring of health in right whales, as well as a framework for integrating observational data at the level of individuals up through the health status of the population. This framework can be broadly applied to a variety of systems – terrestrial and marine – where sporadic observations of individuals exist.
Description: This article was made open access through BIS OA funding.
Sat, 01 Jun 2013 00:00:00 GMT
http://hdl.handle.net/10023/3860
20130601T00:00:00Z
Schick, Robert Schilling
Kraus, Scott D.
Rolland, Rosalind M.
Knowlton, Amy R.
Hamilton, Philip K.
Pettis, Heather M.
Kenney, Robert D.
Clark, James S.
Body condition is an indicator of health, and it plays a key role in many vital processes for mammalian species. While evidence of individual body condition can be obtained, these observations provide just brief glimpses into the health state of the animal. An analytical framework is needed for understanding how health of animals changes over space and time.Through knowledge of individual health we can better understand the status of populations. This is particularly important in endangered species, where the consequences of disruption of critical biological functions can push groups of animals rapidly toward extinction. Here we built a statespace model that provides estimates of movement, health, and survival. We assimilated 30+ years of photographic evidence of body condition and three additional visual health parameters in individual North Atlantic right whales, together with survey data, to infer the true health status as it changes over space and time. We also included the effect of reproductive status and entanglement status on health. At the population level, we estimated differential movement patterns in males and females. At the individual level, we estimated the likely animal locations each month. We estimated the relationship between observed and latent health status. Observations of body condition, skin condition, cyamid infestation on the blowholes, and rake marks all provided measures of the true underlying health. The resulting time series of individual health highlight both normal variations in health status and how anthropogenic stressors can affect the health and, ultimately, the survival of individuals. This modeling approach provides information for monitoring of health in right whales, as well as a framework for integrating observational data at the level of individuals up through the health status of the population. This framework can be broadly applied to a variety of systems – terrestrial and marine – where sporadic observations of individuals exist.

Cetacean abundance and distribution in European Atlantic shelf waters to inform conservation and management
http://hdl.handle.net/10023/3859
Abstract: The European Union (EU) Habitats Directive requires Member States to monitor and maintain at favourable conservation status those species identified to be in need of protection, including all cetaceans. In July 2005 we surveyed the entire EU Atlantic continental shelf to generate robust estimates of abundance for harbour porpoise and other cetacean species. The survey used line transect sampling methods and purpose built data collection equipment designed to minimise bias in estimates of abundance. Shipboard transects covered 19,725 km in sea conditions ⩽Beaufort 4 in an area of 1,005,743 km2. Aerial transects covered 15,802 km in good/moderate conditions (⩽Beaufort 3) in an area of 364,371 km2. Thirteen cetacean species were recorded; abundance was estimated for harbour porpoise (375,358; CV = 0.197), bottlenose dolphin (16,485; CV = 0.422), whitebeaked dolphin (16,536; CV = 0.303), shortbeaked common dolphin (56,221; CV = 0.234) and minke whale (18,958; CV = 0.347). Abundance in 2005 was similar to that estimated in July 1994 for harbour porpoise, whitebeaked dolphin and minke whale in a comparable area. However, modelbased density surfaces showed a marked difference in harbour porpoise distribution between 1994 and 2005. Our results allow EU Member States to discharge their responsibilities under the Habitats Directive and inform other international organisations concerning the assessment of conservation status of cetaceans and the impact of bycatch at a large spatial scale. The lack of evidence for a change in harbour porpoise abundance in EU waters as a whole does not exclude the possibility of an impact of bycatch in some areas. Monitoring bycatch and estimation of abundance continue to be essential.
Description: This article was made open access through BIS OA funding.
Thu, 01 Aug 2013 00:00:00 GMT
http://hdl.handle.net/10023/3859
20130801T00:00:00Z
Hammond, Philip Steven
Macleod, Kelly
Berggren, Per
Borchers, David Louis
Burt, M Louise
Cañadas, Ana
Desportes, Genevieve
Donovan, Greg P
Gilles, Anita
Gillespie, Douglas Michael
Gordon, Jonathan Charles David
Hiby, Lex
Kuklik, Iwona
Leaper, Russell
Lehnert, Kristina
Leopold, Mardik
Lovell, Philip
Øien, Nils
Paxton, Charles G. M.
Ridoux, Vincent
Rogan, Emer
Samarra, Filipa Isabel Pereira
Scheidat, Meike
Sequeira, Marina
Siebert, Ursula
Skov, Henrik
Swift, Rene James
Tasker, Mark
Teilmann, Jonas
Van Canneyt, Olivier
Vázquez, José Antonio
The European Union (EU) Habitats Directive requires Member States to monitor and maintain at favourable conservation status those species identified to be in need of protection, including all cetaceans. In July 2005 we surveyed the entire EU Atlantic continental shelf to generate robust estimates of abundance for harbour porpoise and other cetacean species. The survey used line transect sampling methods and purpose built data collection equipment designed to minimise bias in estimates of abundance. Shipboard transects covered 19,725 km in sea conditions ⩽Beaufort 4 in an area of 1,005,743 km2. Aerial transects covered 15,802 km in good/moderate conditions (⩽Beaufort 3) in an area of 364,371 km2. Thirteen cetacean species were recorded; abundance was estimated for harbour porpoise (375,358; CV = 0.197), bottlenose dolphin (16,485; CV = 0.422), whitebeaked dolphin (16,536; CV = 0.303), shortbeaked common dolphin (56,221; CV = 0.234) and minke whale (18,958; CV = 0.347). Abundance in 2005 was similar to that estimated in July 1994 for harbour porpoise, whitebeaked dolphin and minke whale in a comparable area. However, modelbased density surfaces showed a marked difference in harbour porpoise distribution between 1994 and 2005. Our results allow EU Member States to discharge their responsibilities under the Habitats Directive and inform other international organisations concerning the assessment of conservation status of cetaceans and the impact of bycatch at a large spatial scale. The lack of evidence for a change in harbour porpoise abundance in EU waters as a whole does not exclude the possibility of an impact of bycatch in some areas. Monitoring bycatch and estimation of abundance continue to be essential.

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

Evidence for densitydependent changes in body condition and pregnancy rate of North Atlantic fin whales over four decades of varying environmental conditions
http://hdl.handle.net/10023/3854
Abstract: A central theme in ecology is the search for pattern in the response of a species to changing environmental conditions. Natural resource management and endangered species conservation require an understanding of densitydependent and densityindependent factors that regulate populations. Marine mammal populations are expected to express density dependence in the same way as terrestrial mammals, but logistical difficulties in data acquisition for many large whale species have hindered attempts to identify populationregulation mechanisms. We explored relationships between body condition (inferred from patterns in blubber thickness) and per capita prey abundance, and between pregnancy rate and body condition in North Atlantic fin whales as environmental conditions and population size varied between 1967 and 2010. Blubber thickness in both males and females declined at low per capita prey availability, and in breedingage females, pregnancy rate declined at low blubber thickness, demonstrating a densitydependent response of pregnancy to prey limitation mediated through body condition. To the best of our knowledge, this is the first time a quantitative relationship among per capita prey abundance, body condition, and pregnancy rate has been documented for whales. As longlived predators, marine mammals can act as indicators of the state of marine ecosystems. Improving our understanding of the relationships that link prey, body condition, and population parameters such as pregnancy rate and survival will become increasingly useful as these systems are affected by natural and anthropogenic change. Quantifying linkages among prey, fitness and vital rates will improve our ability to predict population consequences of subtle, sublethal impacts of ocean noise and other anthropogenic stressors.
Fri, 01 Mar 2013 00:00:00 GMT
http://hdl.handle.net/10023/3854
20130301T00:00:00Z
Williams, Robert
Vikingsson, Gisli A.
Gislason, Astthor
Lockyer, Christina
New, Leslie
Thomas, Len
Hammond, Philip Steven
A central theme in ecology is the search for pattern in the response of a species to changing environmental conditions. Natural resource management and endangered species conservation require an understanding of densitydependent and densityindependent factors that regulate populations. Marine mammal populations are expected to express density dependence in the same way as terrestrial mammals, but logistical difficulties in data acquisition for many large whale species have hindered attempts to identify populationregulation mechanisms. We explored relationships between body condition (inferred from patterns in blubber thickness) and per capita prey abundance, and between pregnancy rate and body condition in North Atlantic fin whales as environmental conditions and population size varied between 1967 and 2010. Blubber thickness in both males and females declined at low per capita prey availability, and in breedingage females, pregnancy rate declined at low blubber thickness, demonstrating a densitydependent response of pregnancy to prey limitation mediated through body condition. To the best of our knowledge, this is the first time a quantitative relationship among per capita prey abundance, body condition, and pregnancy rate has been documented for whales. As longlived predators, marine mammals can act as indicators of the state of marine ecosystems. Improving our understanding of the relationships that link prey, body condition, and population parameters such as pregnancy rate and survival will become increasingly useful as these systems are affected by natural and anthropogenic change. Quantifying linkages among prey, fitness and vital rates will improve our ability to predict population consequences of subtle, sublethal impacts of ocean noise and other anthropogenic stressors.

Blue whales respond to simulated midfrequency military sonar
http://hdl.handle.net/10023/3837
Abstract: Midfrequency military (1–10 kHz) sonars have been associated with lethal mass strandings of deepdiving toothed whales, but the effects on endangered baleen whale species are virtually unknown. Here, we used controlled exposure experiments with simulated military sonar and other midfrequency sounds to measure behavioural responses of tagged blue whales (Balaenoptera musculus) in feeding areas within the Southern California Bight. Despite using source levels orders of magnitude below some operational military systems, our results demonstrate that midfrequency sound can significantly affect blue whale behaviour, especially during deep feeding modes. When a response occurred, behavioural changes varied widely from cessation of deep feeding to increased swimming speed and directed travel away from the sound source. The variability of these behavioural responses was largely influenced by a complex interaction of behavioural state, the type of midfrequency sound and received sound level. Sonarinduced disruption of feeding and displacement from highquality prey patches could have significant and previously undocumented impacts on baleen whale foraging ecology, individual fitness and population health.
Tue, 01 Jan 2013 00:00:00 GMT
http://hdl.handle.net/10023/3837
20130101T00:00:00Z
Goldbogen, Jeremy A.
Southall, Brandon L.
De Ruiter, Stacy Lynn
Calambokidis, John
Friedlaender, Ari S.
Hazen, Elliott L.
Falcone, Erin A.
Schorr, Gregory S.
Douglas, Annie
Moretti, David J.
Kyburg, Chris
McKenna, Megan F.
Tyack, Peter Lloyd
Midfrequency military (1–10 kHz) sonars have been associated with lethal mass strandings of deepdiving toothed whales, but the effects on endangered baleen whale species are virtually unknown. Here, we used controlled exposure experiments with simulated military sonar and other midfrequency sounds to measure behavioural responses of tagged blue whales (Balaenoptera musculus) in feeding areas within the Southern California Bight. Despite using source levels orders of magnitude below some operational military systems, our results demonstrate that midfrequency sound can significantly affect blue whale behaviour, especially during deep feeding modes. When a response occurred, behavioural changes varied widely from cessation of deep feeding to increased swimming speed and directed travel away from the sound source. The variability of these behavioural responses was largely influenced by a complex interaction of behavioural state, the type of midfrequency sound and received sound level. Sonarinduced disruption of feeding and displacement from highquality prey patches could have significant and previously undocumented impacts on baleen whale foraging ecology, individual fitness and population health.

First direct measurements of behavioural responses by Cuvier's beaked whales to midfrequency active sonar
http://hdl.handle.net/10023/3836
Abstract: Most marine mammal strandings coincident with naval sonar exercises have involved Cuvier's beaked whales (Ziphius cavirostris). We recorded animal movement and acoustic data on two tagged Ziphius and obtained the first direct measurements of behavioural responses of this species to midfrequency active (MFA) sonar signals. Each recording included a 30min playback (one 1.6s simulated MFA sonar signal repeated every 25 s); one whale was also incidentally exposed to MFA sonar from distant naval exercises. Whales responded strongly to playbacks at low received levels (RLs; 89–127 dB re 1 µPa): after ceasing normal fluking and echolocation, they swam rapidly, silently away, extending both dive duration and subsequent nonforaging interval. Distant sonar exercises (78–106 dB re 1 µPa) did not elicit such responses, suggesting that context may moderate reactions. The observed responses to playback occurred at RLs well below current regulatory thresholds; equivalent responses to operational sonars could elevate stranding risk and reduce foraging efficiency.
Tue, 01 Jan 2013 00:00:00 GMT
http://hdl.handle.net/10023/3836
20130101T00:00:00Z
De Ruiter, Stacy Lynn
Southall, Brandon L.
Calambokidis, John
Zimmer, Walter M. X.
Sadykova, Dinara
Falcone, Erin A.
Friedlaender, Ari S.
Joseph, John E.
Moretti, David
Schorr, Gregory S.
Thomas, Len
Tyack, Peter Lloyd
Most marine mammal strandings coincident with naval sonar exercises have involved Cuvier's beaked whales (Ziphius cavirostris). We recorded animal movement and acoustic data on two tagged Ziphius and obtained the first direct measurements of behavioural responses of this species to midfrequency active (MFA) sonar signals. Each recording included a 30min playback (one 1.6s simulated MFA sonar signal repeated every 25 s); one whale was also incidentally exposed to MFA sonar from distant naval exercises. Whales responded strongly to playbacks at low received levels (RLs; 89–127 dB re 1 µPa): after ceasing normal fluking and echolocation, they swam rapidly, silently away, extending both dive duration and subsequent nonforaging interval. Distant sonar exercises (78–106 dB re 1 µPa) did not elicit such responses, suggesting that context may moderate reactions. The observed responses to playback occurred at RLs well below current regulatory thresholds; equivalent responses to operational sonars could elevate stranding risk and reduce foraging efficiency.

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

Minimal and random generation of permutation and matrix groups
http://hdl.handle.net/10023/3823
Abstract: We prove explicit bounds on the numbers of elements needed to generate various types of finite permutation groups and finite completely reducible matrix groups, and present examples to show that they are sharp in all cases. The bounds are linear in the degree of the permutation or matrix group in general, and logarithmic when the group is primitive. They can be combined with results of Lubotzky to produce explicit bounds on the number of random elements required to generate these groups with a specified probability. These results have important applications to computational group theory. Our proofs are inductive and largely theoretical, but we use computer calculations to establish the bounds in a number of specific small cases.
Thu, 01 Aug 2013 00:00:00 GMT
http://hdl.handle.net/10023/3823
20130801T00:00:00Z
Holt, Derek
RoneyDougal, Colva Mary
We prove explicit bounds on the numbers of elements needed to generate various types of finite permutation groups and finite completely reducible matrix groups, and present examples to show that they are sharp in all cases. The bounds are linear in the degree of the permutation or matrix group in general, and logarithmic when the group is primitive. They can be combined with results of Lubotzky to produce explicit bounds on the number of random elements required to generate these groups with a specified probability. These results have important applications to computational group theory. Our proofs are inductive and largely theoretical, but we use computer calculations to establish the bounds in a number of specific small cases.

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

Estimating wildlife distribution and abundance from line transect surveys conducted from platforms of opportunity
http://hdl.handle.net/10023/3727
Abstract: Line transect data obtained from 'platforms of opportunity' are useful for the monitoring
of long term trends in dolphin populations which occur over vast areas, yet analyses of
such data axe problematic due to violation of fundamental assumptions of line transect
methodology. In this thesis we develop methods which allow estimates of dolphin relative
abundance to be obtained when certain assumptions of line transect sampling are violated.
Generalised additive models are used to model encounter rate and mean school size as
a function of spatially and temporally referenced covariates. The estimated relationship
between the response and the environmental and locational covariates is then used to
obtain a predicted surface for the response over the entire survey region. Given those
predicted surfaces, a density surface can then be obtained and an estimate of abundance
computed by numerically integrating over the entire survey region. This approach is
particularly useful when search effort is not random, in which case standard line transect
methods would yield biased estimates.
Estimates of f (0) (the inverse of the effective strip (half)width), an essential component
of the line transect estimator, may also be biased due to heterogeneity in detection probabilities.
We developed a conditional likelihood approach in which covariate effects are
directly incorporated into the estimation procedure. Simulation results indicated that the
method performs well in the presence of sizebias. When multiple covariates are used, it
is important that covariate selection be carried out.
As an example we applied the methods described above to eastern tropical Pacific dolphin
stocks. However, uncertainty in stock identification has never been directly incorporated
into methods used to obtain estimates of relative or absolute abundance. Therefore we
illustrate an approach in which trends in dolphin relative abundance axe monitored by
small areas, rather than stocks.
Mon, 01 Jan 2001 00:00:00 GMT
http://hdl.handle.net/10023/3727
20010101T00:00:00Z
Marques, Fernanda F. C.
Line transect data obtained from 'platforms of opportunity' are useful for the monitoring
of long term trends in dolphin populations which occur over vast areas, yet analyses of
such data axe problematic due to violation of fundamental assumptions of line transect
methodology. In this thesis we develop methods which allow estimates of dolphin relative
abundance to be obtained when certain assumptions of line transect sampling are violated.
Generalised additive models are used to model encounter rate and mean school size as
a function of spatially and temporally referenced covariates. The estimated relationship
between the response and the environmental and locational covariates is then used to
obtain a predicted surface for the response over the entire survey region. Given those
predicted surfaces, a density surface can then be obtained and an estimate of abundance
computed by numerically integrating over the entire survey region. This approach is
particularly useful when search effort is not random, in which case standard line transect
methods would yield biased estimates.
Estimates of f (0) (the inverse of the effective strip (half)width), an essential component
of the line transect estimator, may also be biased due to heterogeneity in detection probabilities.
We developed a conditional likelihood approach in which covariate effects are
directly incorporated into the estimation procedure. Simulation results indicated that the
method performs well in the presence of sizebias. When multiple covariates are used, it
is important that covariate selection be carried out.
As an example we applied the methods described above to eastern tropical Pacific dolphin
stocks. However, uncertainty in stock identification has never been directly incorporated
into methods used to obtain estimates of relative or absolute abundance. Therefore we
illustrate an approach in which trends in dolphin relative abundance axe monitored by
small areas, rather than stocks.

Bayesian point process modelling of ecological communities
http://hdl.handle.net/10023/3710
Abstract: The modelling of biological communities is important to further the understanding
of species coexistence and the mechanisms involved in maintaining
biodiversity. This involves considering not only interactions between individual
biological organisms, but also the incorporation of covariate information,
if available, in the modelling process. This thesis explores the use
of point processes to model interactions in bivariate point patterns within
a Bayesian framework, and, where applicable, in conjunction with covariate
data. Specifically, we distinguish between symmetric and asymmetric species
interactions and model these using appropriate point processes. In this thesis
we consider both pairwise and area interaction point processes to allow for
inhibitory interactions and both inhibitory and attractive interactions.
It is envisaged that the analyses and innovations presented in this thesis
will contribute to the parsimonious modelling of biological communities.
Fri, 28 Jun 2013 00:00:00 GMT
http://hdl.handle.net/10023/3710
20130628T00:00:00Z
Nightingale, Glenna Faith
The modelling of biological communities is important to further the understanding
of species coexistence and the mechanisms involved in maintaining
biodiversity. This involves considering not only interactions between individual
biological organisms, but also the incorporation of covariate information,
if available, in the modelling process. This thesis explores the use
of point processes to model interactions in bivariate point patterns within
a Bayesian framework, and, where applicable, in conjunction with covariate
data. Specifically, we distinguish between symmetric and asymmetric species
interactions and model these using appropriate point processes. In this thesis
we consider both pairwise and area interaction point processes to allow for
inhibitory interactions and both inhibitory and attractive interactions.
It is envisaged that the analyses and innovations presented in this thesis
will contribute to the parsimonious modelling of biological communities.

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

Finiteness conditions for unions of semigroups
http://hdl.handle.net/10023/3687
Abstract: In this thesis we prove the following:
The semigroup which is a disjoint union of two or three copies of a group is a Clifford semigroup, Rees matrix semigroup or a combination between a Rees matrix semigroup and a group. Furthermore, the semigroup which is a disjoint union of finitely many copies of a finitely presented (residually finite) group is finitely presented (residually finite) semigroup.
The constructions of the semigroup which is a disjoint union of two copies of the free monogenic semigroup are parallel to the constructions of the semigroup which is a disjoint union of two copies of a group, i.e. such a semigroup is Clifford (strong semilattice of groups) or Rees matrix semigroup. However, the semigroup which is a disjoint union of three copies of the free monogenic semigroup is not just a strong semillatice of semigroups, Rees matrix semigroup or combination between a Rees matrix semigroup and a semigroup, but there are two more semigroups which do not arise from the constructions of the semigroup which is a disjoint union of three copies of a group. We also classify semigroups which are disjoint unions of two or three copies of the free monogenic semigroup. There are three types of semigroups which are unions of two copies of the free monogenic semigroup and nine types of semigroups which are unions of three copies of the free monogenic semigroup. For each type of such semigroups we exhibit a presentation defining semigroups of this type.
The semigroup which is a disjoint union of finitely many copies of the free monogenic semigroup is finitely presented, residually finite, hopfian, has soluble word problem and has soluble subsemigroup membership problem.
Fri, 28 Jun 2013 00:00:00 GMT
http://hdl.handle.net/10023/3687
20130628T00:00:00Z
AbuGhazalh, Nabilah Hani
In this thesis we prove the following:
The semigroup which is a disjoint union of two or three copies of a group is a Clifford semigroup, Rees matrix semigroup or a combination between a Rees matrix semigroup and a group. Furthermore, the semigroup which is a disjoint union of finitely many copies of a finitely presented (residually finite) group is finitely presented (residually finite) semigroup.
The constructions of the semigroup which is a disjoint union of two copies of the free monogenic semigroup are parallel to the constructions of the semigroup which is a disjoint union of two copies of a group, i.e. such a semigroup is Clifford (strong semilattice of groups) or Rees matrix semigroup. However, the semigroup which is a disjoint union of three copies of the free monogenic semigroup is not just a strong semillatice of semigroups, Rees matrix semigroup or combination between a Rees matrix semigroup and a semigroup, but there are two more semigroups which do not arise from the constructions of the semigroup which is a disjoint union of three copies of a group. We also classify semigroups which are disjoint unions of two or three copies of the free monogenic semigroup. There are three types of semigroups which are unions of two copies of the free monogenic semigroup and nine types of semigroups which are unions of three copies of the free monogenic semigroup. For each type of such semigroups we exhibit a presentation defining semigroups of this type.
The semigroup which is a disjoint union of finitely many copies of the free monogenic semigroup is finitely presented, residually finite, hopfian, has soluble word problem and has soluble subsemigroup membership problem.

Adventures in applying iteration lemmas
http://hdl.handle.net/10023/3671
Abstract: The word problem of a finitely generated group is commonly defined to be a formal language over a finite generating set.
The class of finite groups has been characterised as the class of finitely generated groups that have word problem decidable by a finite state automaton.
We give a natural generalisation of the notion of word problem from finitely generated groups to finitely generated semigroups by considering relations of strings. We characterise the class of finite semigroups by the class of finitely generated semigroups whose word problem is decidable by finite state automata.
We then examine the class of semigroups with word problem decidable by asynchronous two tape finite state automata. Algebraic properties of semigroups in this class are considered, towards an algebraic characterisation.
We take the next natural step to further extend the classes of semigroups under consideration to semigroups that have word problem decidable by a finite collection of asynchronous automata working independently.
A central tool used in the derivation of structural results are socalled iteration lemmas.
We define a hierarchy of the considered classes of semigroups and connect our original results with previous research.
Fri, 28 Jun 2013 00:00:00 GMT
http://hdl.handle.net/10023/3671
20130628T00:00:00Z
Pfeiffer, Markus Johannes
The word problem of a finitely generated group is commonly defined to be a formal language over a finite generating set.
The class of finite groups has been characterised as the class of finitely generated groups that have word problem decidable by a finite state automaton.
We give a natural generalisation of the notion of word problem from finitely generated groups to finitely generated semigroups by considering relations of strings. We characterise the class of finite semigroups by the class of finitely generated semigroups whose word problem is decidable by finite state automata.
We then examine the class of semigroups with word problem decidable by asynchronous two tape finite state automata. Algebraic properties of semigroups in this class are considered, towards an algebraic characterisation.
We take the next natural step to further extend the classes of semigroups under consideration to semigroups that have word problem decidable by a finite collection of asynchronous automata working independently.
A central tool used in the derivation of structural results are socalled iteration lemmas.
We define a hierarchy of the considered classes of semigroups and connect our original results with previous research.

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

Animal population estimation using markrecapture and plantcapture
http://hdl.handle.net/10023/3655
Abstract: Markrecapture is a method of population estimation that involves capturing a number
of animals from a population of unknown size on several occasions, and marking
those animals that are caught each time. By observing the number of marked
animals that are subsequently seen, estimates of the total population size can be
made. There are various subclasses of the markrecapture method called the Otisclass
of models (Otis, Burnham, White & Anderson 1978). These relate to the
assumed behaviour of the individuals in the target population.
More recent work has generalised the theory of markrecapture to the socalled
plantcapture, where a known number of animals are preinserted into the target
population. Sampling is then carried out as normal, but with additional information
coming from knowledge of the number of planted individuals.
The theory underpinning plantcapture is less welldeveloped than markrecapture,
with the difference on population estimation of the former over the latter not often
tested. This thesis shows that, under fixed and random samplesize models, the
inclusion of plants can improve the mean point population estimation of various
estimators. The estimator of Pathak (1964) is generalised to allow for the inclusion
of plants into the target population. The results show that mean estimates from
most estimators, under most models, can be improved with the inclusion of plants,
and the sample standard deviations of the simulations can be reduced. This improvement
in mean point population estimation is particularly pronounced when
the number of animals captured is low.
Sample coverage, which is the proportion of distinct animals caught during sampling,
is also often sought by practitioners. Given here is a generalisation of the
inverse population estimator of Pathak (1964) to plantcapture and a proposed new
inverse population estimator, which can be used as estimates of the coverage of a
sample.
Sun, 01 Jan 2012 00:00:00 GMT
http://hdl.handle.net/10023/3655
20120101T00:00:00Z
Gormley, Richard
Markrecapture is a method of population estimation that involves capturing a number
of animals from a population of unknown size on several occasions, and marking
those animals that are caught each time. By observing the number of marked
animals that are subsequently seen, estimates of the total population size can be
made. There are various subclasses of the markrecapture method called the Otisclass
of models (Otis, Burnham, White & Anderson 1978). These relate to the
assumed behaviour of the individuals in the target population.
More recent work has generalised the theory of markrecapture to the socalled
plantcapture, where a known number of animals are preinserted into the target
population. Sampling is then carried out as normal, but with additional information
coming from knowledge of the number of planted individuals.
The theory underpinning plantcapture is less welldeveloped than markrecapture,
with the difference on population estimation of the former over the latter not often
tested. This thesis shows that, under fixed and random samplesize models, the
inclusion of plants can improve the mean point population estimation of various
estimators. The estimator of Pathak (1964) is generalised to allow for the inclusion
of plants into the target population. The results show that mean estimates from
most estimators, under most models, can be improved with the inclusion of plants,
and the sample standard deviations of the simulations can be reduced. This improvement
in mean point population estimation is particularly pronounced when
the number of animals captured is low.
Sample coverage, which is the proportion of distinct animals caught during sampling,
is also often sought by practitioners. Given here is a generalisation of the
inverse population estimator of Pathak (1964) to plantcapture and a proposed new
inverse population estimator, which can be used as estimates of the coverage of a
sample.

Estimating anglerfish abundance from trawl surveys, and related problems
http://hdl.handle.net/10023/3652
Abstract: The content of this thesis was motivated by the need to estimate anglerfish abundance
from stratified random trawl surveys of the anglerfish stock which occupies
the northern European shelf (Fernandes et al., 2007). The survey was conducted
annually from 2005 to 2010 in order to obtain agestructured estimates of absolute
abundance for this stock. An estimation method is considered to incorporate statistical models for herding, lengthbased net retention probability and missing age data and uncertainty from all of these sources in variance estimation.
A key component of abundance estimation is the estimation of capture probability.
Capture probability is estimated from the experimental survey data using various
logistic regression models with haul as a random effect. Conditional on the estimated
capture probability, a number of abundance estimators are developed and applied to
the anglerfish data. The abundance estimators differ in the way that the haul effect is incorporated. The performance of these estimators is investigated by simulation. An estimator with form similar to that conventionally used to estimate abundance from distance sampling surveys is found to perform best.
The estimators developed for the anglerfish survey data which incorporate random
effects in capture probability have wider application than trawl surveys. We examine
the analytic properties of these estimators when the capture/detection probability is
known. We apply these estimators to three different types of survey data in addition
to the anglerfish data, with different forms of random effects and investigate their
performance by simulation. We find that a generalization of the form of estimator
typically used on line transect surveys performs best overall. It has low bias, and
also the lowest bias and mean squared error among all the estimators we considered.
Sun, 01 Jan 2012 00:00:00 GMT
http://hdl.handle.net/10023/3652
20120101T00:00:00Z
Yuan, Yuan
The content of this thesis was motivated by the need to estimate anglerfish abundance
from stratified random trawl surveys of the anglerfish stock which occupies
the northern European shelf (Fernandes et al., 2007). The survey was conducted
annually from 2005 to 2010 in order to obtain agestructured estimates of absolute
abundance for this stock. An estimation method is considered to incorporate statistical models for herding, lengthbased net retention probability and missing age data and uncertainty from all of these sources in variance estimation.
A key component of abundance estimation is the estimation of capture probability.
Capture probability is estimated from the experimental survey data using various
logistic regression models with haul as a random effect. Conditional on the estimated
capture probability, a number of abundance estimators are developed and applied to
the anglerfish data. The abundance estimators differ in the way that the haul effect is incorporated. The performance of these estimators is investigated by simulation. An estimator with form similar to that conventionally used to estimate abundance from distance sampling surveys is found to perform best.
The estimators developed for the anglerfish survey data which incorporate random
effects in capture probability have wider application than trawl surveys. We examine
the analytic properties of these estimators when the capture/detection probability is
known. We apply these estimators to three different types of survey data in addition
to the anglerfish data, with different forms of random effects and investigate their
performance by simulation. We find that a generalization of the form of estimator
typically used on line transect surveys performs best overall. It has low bias, and
also the lowest bias and mean squared error among all the estimators we considered.

Mixed effect models in distance sampling
http://hdl.handle.net/10023/3618
Abstract: Recently, much effort has been expended for improving conventional distance sampling methods, e.g. by replacing the designbased approach with a modelbased approach where observed counts are related to environmental covariates (Hedley and Buckland, 2004) or by incorporating covariates in the detection function model (Marques and Buckland, 2003).
While these models have generally been limited to include fixed effects, we propose
four different methods for analysing distance sampling data using mixed effects models. These include an extension of the twostage approach (Buckland et al., 2009),
where we include site random effects in the secondstage count model to account for
correlated counts at the same sites. We also present two integrated approaches which
include site random effects in the count model. These approaches combine the analysis stages for the detection and count models and allow simultaneous estimation of all
parameters. Furthermore, we develop a detection function model that incorporates
random effects. We also propose a novel Bayesian approach to analysing distance sampling data which uses a MetropolisHastings algorithm for updating model parameters and a reversible jump Markov chain Monte Carlo (RJMCMC) algorithm for assessing model uncertainty. Lastly, we propose using hierarchical centering as a novel technique for improving model mixing and hence facilitating an RJMCMC algorithm for mixed models.
We analyse two case studies, both largescale point transect surveys, where the interest lies in establishing the effects of conservation buffers on agricultural fields. For each case study, we compare the results from one integrated approach to those from
the extended twostage approach. We find that these may differ in parameter estimates for covariates that were both in the detection and the count model and in model probabilities when model uncertainty was included in inference. The performance of the random effects based detection function is assessed via simulation and when heterogeneity in the data is present, one of the new estimators yields improved results compared to conventional distance sampling estimators.
Tue, 01 Jan 2013 00:00:00 GMT
http://hdl.handle.net/10023/3618
20130101T00:00:00Z
Oedekoven, Cornelia Sabrina
Recently, much effort has been expended for improving conventional distance sampling methods, e.g. by replacing the designbased approach with a modelbased approach where observed counts are related to environmental covariates (Hedley and Buckland, 2004) or by incorporating covariates in the detection function model (Marques and Buckland, 2003).
While these models have generally been limited to include fixed effects, we propose
four different methods for analysing distance sampling data using mixed effects models. These include an extension of the twostage approach (Buckland et al., 2009),
where we include site random effects in the secondstage count model to account for
correlated counts at the same sites. We also present two integrated approaches which
include site random effects in the count model. These approaches combine the analysis stages for the detection and count models and allow simultaneous estimation of all
parameters. Furthermore, we develop a detection function model that incorporates
random effects. We also propose a novel Bayesian approach to analysing distance sampling data which uses a MetropolisHastings algorithm for updating model parameters and a reversible jump Markov chain Monte Carlo (RJMCMC) algorithm for assessing model uncertainty. Lastly, we propose using hierarchical centering as a novel technique for improving model mixing and hence facilitating an RJMCMC algorithm for mixed models.
We analyse two case studies, both largescale point transect surveys, where the interest lies in establishing the effects of conservation buffers on agricultural fields. For each case study, we compare the results from one integrated approach to those from
the extended twostage approach. We find that these may differ in parameter estimates for covariates that were both in the detection and the count model and in model probabilities when model uncertainty was included in inference. The performance of the random effects based detection function is assessed via simulation and when heterogeneity in the data is present, one of the new estimators yields improved results compared to conventional distance sampling estimators.

Ends of semigroups
http://hdl.handle.net/10023/3590
Abstract: The aim of this thesis is to understand the algebraic structure of a semigroup
by studying the geometric properties of its Cayley graph. 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 Hopfs 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.
We classify all semigroups with one end and make use of this classification
to prove various finiteness properties for semigroups with one end.
We also consider the ends of digraphs with certain algebraic properties.
We prove that two quasiisometric digraphs have isomorphic end sets. We also prove that vertex transitive digraphs have 1, 2 or infinitely many ends and construct a topology that reflects the properties of the ends of a digraph.
Tue, 01 Jan 2013 00:00:00 GMT
http://hdl.handle.net/10023/3590
20130101T00:00:00Z
Craik, Simon
The aim of this thesis is to understand the algebraic structure of a semigroup
by studying the geometric properties of its Cayley graph. 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 Hopfs 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.
We classify all semigroups with one end and make use of this classification
to prove various finiteness properties for semigroups with one end.
We also consider the ends of digraphs with certain algebraic properties.
We prove that two quasiisometric digraphs have isomorphic end sets. We also prove that vertex transitive digraphs have 1, 2 or infinitely many ends and construct a topology that reflects the properties of the ends of a digraph.

Random generation and chief length of finite groups
http://hdl.handle.net/10023/3578
Abstract: Part I of this thesis studies P[subscript(G)](d), the probability of generating a nonabelian
simple group G with d randomly chosen elements, and extends this
idea to consider the conditional probability P[subscript(G,Soc(G))](d), the probability
of generating an almost simple group G by d randomly chosen elements,
given that they project onto a generating set of G/Soc(G). In particular
we show that for a 2generated almost simple group, P[subscript(G,Soc(G))](2) 53≥90,
with equality if and only if G = A₆ or S₆. Furthermore P[subscript(G,Soc(G))](2) 9≥10
except for 30 almost simple groups G, and we specify this list and provide
exact values for P[subscript(G,Soc(G))](2) in these cases. We conclude Part I by showing
that for all almost simple groups P[subscript(G,Soc(G))](3)≥139/150.
In Part II we consider a related notion. Given a probability ε, we wish
to determine d[superscript(ε)] (G), the number of random elements needed to generate a finite group G with failure probabilty at most ε. A generalisation of a result
of Lubotzky bounds d[superscript(ε)](G) in terms of l(G), the chief length of G, and d(G),
the minimal number of generators needed to generate G. We obtain bounds
on the chief length of permutation groups in terms of the degree n, and
bounds on the chief length of completely reducible matrix groups in terms
of the dimension and field size. Combining these with existing bounds on
d(G), we obtain bounds on d[superscript(ε)] (G) for permutation groups and completely
reducible matrix groups.
Tue, 01 Jan 2013 00:00:00 GMT
http://hdl.handle.net/10023/3578
20130101T00:00:00Z
Menezes, Nina E.
Part I of this thesis studies P[subscript(G)](d), the probability of generating a nonabelian
simple group G with d randomly chosen elements, and extends this
idea to consider the conditional probability P[subscript(G,Soc(G))](d), the probability
of generating an almost simple group G by d randomly chosen elements,
given that they project onto a generating set of G/Soc(G). In particular
we show that for a 2generated almost simple group, P[subscript(G,Soc(G))](2) 53≥90,
with equality if and only if G = A₆ or S₆. Furthermore P[subscript(G,Soc(G))](2) 9≥10
except for 30 almost simple groups G, and we specify this list and provide
exact values for P[subscript(G,Soc(G))](2) in these cases. We conclude Part I by showing
that for all almost simple groups P[subscript(G,Soc(G))](3)≥139/150.
In Part II we consider a related notion. Given a probability ε, we wish
to determine d[superscript(ε)] (G), the number of random elements needed to generate a finite group G with failure probabilty at most ε. A generalisation of a result
of Lubotzky bounds d[superscript(ε)](G) in terms of l(G), the chief length of G, and d(G),
the minimal number of generators needed to generate G. We obtain bounds
on the chief length of permutation groups in terms of the degree n, and
bounds on the chief length of completely reducible matrix groups in terms
of the dimension and field size. Combining these with existing bounds on
d(G), we obtain bounds on d[superscript(ε)] (G) for permutation groups and completely
reducible matrix groups.

Multistable processes and localizability
http://hdl.handle.net/10023/3560
Abstract: We use characteristic functions to construct alphamultistable measures and integrals, where the measures behave locally like stable measures, but with the stability index alpha(x) varying with x. This enables us to construct alphamultistable processes on R, that is processes whose scaling limit at time t is an alpha(t)stable process. We present several examples of such multistable processes and examine their localisability.
Sun, 01 Jan 2012 00:00:00 GMT
http://hdl.handle.net/10023/3560
20120101T00:00:00Z
Falconer, Kenneth John
Liu, Lining
We use characteristic functions to construct alphamultistable measures and integrals, where the measures behave locally like stable measures, but with the stability index alpha(x) varying with x. This enables us to construct alphamultistable processes on R, that is processes whose scaling limit at time t is an alpha(t)stable process. We present several examples of such multistable processes and examine their localisability.

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

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

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

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

Estimating animal population density using passive acoustics
http://hdl.handle.net/10023/3496
Abstract: Reliable estimation of the size or density of wild animal populations is very important for effective wildlife management, conservation and ecology. Currently, the most widely used methods for obtaining such estimates involve either sighting animals from transect lines or some form of capturerecapture on marked or uniquely identifiable individuals. However, many species are difficult to sight, and cannot be easily marked or recaptured. Some of these species produce readily identifiable sounds, providing an opportunity to use passive acoustic data to estimate animal density. In addition, even for species for which other visually based methods are feasible, passive acoustic methods offer the potential for greater detection ranges in some environments (e.g. underwater or in dense forest), and hence potentially better precision. Automated data collection means that surveys can take place at times and in places where it would be too expensive or dangerous to send human observers. Here, we present an overview of animal density estimation using passive acoustic data, a relatively new and fastdeveloping field. We review the types of data and methodological approaches currently available to researchers and we provide a framework for acousticsbased density estimation, illustrated with examples from realworld case studies. We mention moving sensor platforms (e.g. towed acoustics), but then focus on methods involving sensors at fixed locations, particularly hydrophones to survey marine mammals, as acousticbased density estimation research to date has been concentrated in this area. Primary among these are methods based on distance sampling and spatially explicit capturerecapture. The methods are also applicable to other aquatic and terrestrial soundproducing taxa. We conclude that, despite being in its infancy, density estimation based on passive acoustic data likely will become an important method for surveying a number of diverse taxa, such as sea mammals, fish, birds, amphibians, and insects, especially in situations where inferences are required over long periods of time. There is considerable work ahead, with several potentially fruitful research areas, including the development of (i) hardware and software for data acquisition, (ii) efficient, calibrated, automated detection and classification systems, and (iii) statistical approaches optimized for this application. Further, survey design will need to be developed, and research is needed on the acoustic behaviour of target species. Fundamental research on vocalization rates and group sizes, and the relation between these and other factors such as season or behaviour state, is critical. Evaluation of the methods under known density scenarios will be important for empirically validating the approaches presented here
Wed, 01 May 2013 00:00:00 GMT
http://hdl.handle.net/10023/3496
20130501T00:00:00Z
Marques, Tiago A.
Thomas, Len
Martin, Stephen
Mellinger, David
Ward, Jessica
Moretti, David
Harris, Danielle Veronica
Tyack, Peter Lloyd
Reliable estimation of the size or density of wild animal populations is very important for effective wildlife management, conservation and ecology. Currently, the most widely used methods for obtaining such estimates involve either sighting animals from transect lines or some form of capturerecapture on marked or uniquely identifiable individuals. However, many species are difficult to sight, and cannot be easily marked or recaptured. Some of these species produce readily identifiable sounds, providing an opportunity to use passive acoustic data to estimate animal density. In addition, even for species for which other visually based methods are feasible, passive acoustic methods offer the potential for greater detection ranges in some environments (e.g. underwater or in dense forest), and hence potentially better precision. Automated data collection means that surveys can take place at times and in places where it would be too expensive or dangerous to send human observers. Here, we present an overview of animal density estimation using passive acoustic data, a relatively new and fastdeveloping field. We review the types of data and methodological approaches currently available to researchers and we provide a framework for acousticsbased density estimation, illustrated with examples from realworld case studies. We mention moving sensor platforms (e.g. towed acoustics), but then focus on methods involving sensors at fixed locations, particularly hydrophones to survey marine mammals, as acousticbased density estimation research to date has been concentrated in this area. Primary among these are methods based on distance sampling and spatially explicit capturerecapture. The methods are also applicable to other aquatic and terrestrial soundproducing taxa. We conclude that, despite being in its infancy, density estimation based on passive acoustic data likely will become an important method for surveying a number of diverse taxa, such as sea mammals, fish, birds, amphibians, and insects, especially in situations where inferences are required over long periods of time. There is considerable work ahead, with several potentially fruitful research areas, including the development of (i) hardware and software for data acquisition, (ii) efficient, calibrated, automated detection and classification systems, and (iii) statistical approaches optimized for this application. Further, survey design will need to be developed, and research is needed on the acoustic behaviour of target species. Fundamental research on vocalization rates and group sizes, and the relation between these and other factors such as season or behaviour state, is critical. Evaluation of the methods under known density scenarios will be important for empirically validating the approaches presented here

Estimating prevalence of injecting drug users and associated heroinrelated death rates in England by using regional data and incorporating prior information
http://hdl.handle.net/10023/3494
Abstract: Injecting drug users (IDUs) have a direct social and economic effect yet can typically be regarded as a hidden population within a community. We estimate the size of the IDU population across the nine different Government Office regions of England in 2005–2006 by using capture–recapture methods with age (ranging from 15 to 64 years) and gender as covariate information. We consider a Bayesian model averaging approach using loglinear models, where we can include explicit prior information within the analysis in relation to the total IDU population (elicited from the number of drugrelated deaths and injectors’ drugrelated death rates). Estimation at the regional level allows for regional heterogeneity with these regional estimates aggregated to obtain a posterior mean estimate for the number of England's IDUs of 195840 with 95% credible interval (181700, 210480). There is significant variation in the estimated regional prevalence of current IDUs per million of population aged 15–64 years, and in injecting drugrelated death rates across the gender × age crossclassifications. The propensity of an IDU to be seen by at least one source also exhibits strong regional variability with London having the lowest propensity of being observed (posterior mean probability 0.21) and the South West the highest propensity (posterior mean 0.46).
Wed, 01 Jan 2014 00:00:00 GMT
http://hdl.handle.net/10023/3494
20140101T00:00:00Z
King, Ruth
Bird, Sheila
Overstall, Antony
Hay, Gordon
Hutchinson, Sharon
Injecting drug users (IDUs) have a direct social and economic effect yet can typically be regarded as a hidden population within a community. We estimate the size of the IDU population across the nine different Government Office regions of England in 2005–2006 by using capture–recapture methods with age (ranging from 15 to 64 years) and gender as covariate information. We consider a Bayesian model averaging approach using loglinear models, where we can include explicit prior information within the analysis in relation to the total IDU population (elicited from the number of drugrelated deaths and injectors’ drugrelated death rates). Estimation at the regional level allows for regional heterogeneity with these regional estimates aggregated to obtain a posterior mean estimate for the number of England's IDUs of 195840 with 95% credible interval (181700, 210480). There is significant variation in the estimated regional prevalence of current IDUs per million of population aged 15–64 years, and in injecting drugrelated death rates across the gender × age crossclassifications. The propensity of an IDU to be seen by at least one source also exhibits strong regional variability with London having the lowest propensity of being observed (posterior mean probability 0.21) and the South West the highest propensity (posterior mean 0.46).

Decomposition tables for experiments : II. Two–one randomizations
http://hdl.handle.net/10023/3479
Abstract: We investigate structure for pairs of randomizations that do not follow each other in a chain. These are unrandomizedinclusive, independent, coincident or double randomizations. This involves taking several structures that satisfy particular relations and combining them to form the appropriate orthogonal decomposition of the data space for the experiment. We show how to establish the decomposition table giving the sources of variation, their relationships and their degrees of freedom, so that competing designs can be evaluated. This leads to recommendations for when the different types of multiple randomization should be used.
Fri, 01 Oct 2010 00:00:00 GMT
http://hdl.handle.net/10023/3479
20101001T00:00:00Z
Brien, C. J.
Bailey, Rosemary Anne
We investigate structure for pairs of randomizations that do not follow each other in a chain. These are unrandomizedinclusive, independent, coincident or double randomizations. This involves taking several structures that satisfy particular relations and combining them to form the appropriate orthogonal decomposition of the data space for the experiment. We show how to establish the decomposition table giving the sources of variation, their relationships and their degrees of freedom, so that competing designs can be evaluated. This leads to recommendations for when the different types of multiple randomization should be used.

Decomposition tables for experiments : I. A chain of randomizations
http://hdl.handle.net/10023/3478
Abstract: One aspect of evaluating the design for an experiment is the discovery of the relationships between subspaces of the data space. Initially we establish the notation and methods for evaluating an experiment with a single randomization. Starting with two structures, or orthogonal decompositions of the data space, we describe how to combine them to form the overall decomposition for a singlerandomization experiment that is "structure balanced." The relationships between the two structures are characterized using efficiency factors. The decomposition is encapsulated in a decomposition table. Then, for experiments that involve multiple randomizations forming a chain, we take several structures that pairwise are structure balanced and combine them to establish the form of the orthogonal decomposition for the experiment. In particular, it is proven that the properties of the design for Such an experiment are derived in a straightforward manner from those of the individual designs. We show how to formulate an extended decomposition table giving the sources of variation, their relationships and their degrees of freedom, so that competing designs can be evaluated.
Tue, 01 Dec 2009 00:00:00 GMT
http://hdl.handle.net/10023/3478
20091201T00:00:00Z
Brien, C. J.
Bailey, Rosemary Anne
One aspect of evaluating the design for an experiment is the discovery of the relationships between subspaces of the data space. Initially we establish the notation and methods for evaluating an experiment with a single randomization. Starting with two structures, or orthogonal decompositions of the data space, we describe how to combine them to form the overall decomposition for a singlerandomization experiment that is "structure balanced." The relationships between the two structures are characterized using efficiency factors. The decomposition is encapsulated in a decomposition table. Then, for experiments that involve multiple randomizations forming a chain, we take several structures that pairwise are structure balanced and combine them to establish the form of the orthogonal decomposition for the experiment. In particular, it is proven that the properties of the design for Such an experiment are derived in a straightforward manner from those of the individual designs. We show how to formulate an extended decomposition table giving the sources of variation, their relationships and their degrees of freedom, so that competing designs can be evaluated.

Estimating seasonal abundance of a central place forager using counts and telemetry data
http://hdl.handle.net/10023/3454
Abstract: Obtaining population estimates of species that are not easily observed directly can be problematic. However, central place foragers can often be observed some of the time, e.g. when seals are hauled out. In these instances, population estimates can be derived from counts, combined with information on the proportion of time that animals can be observed. We present a modelling framework to estimate seasonal absolute abundance using counts and information from satellite telemetry data. The method was tested on a harbour seal population in an area of southeast Scotland. Counts were made monthly, between November 2001 and June 2003, when seals were hauled out on land and were corrected for the proportion of time the seals were at sea using satellite telemetry. Harbour seals (n=25) were tagged with satellite relay data loggers between November 2001 and March 2003. To estimate the proportion of time spent hauled out, time at sea on foraging trips was modelled separately from haulout behaviour close to haulout sites because of the different factors affecting these processes. A generalised linear mixed model framework was developed to capture the longitudinal nature of the data and the repeated measures across individuals. Despite seasonal variability in the number of seals counted at haulout sites, the model generated estimates of abundance, with an overall mean of 846 (95% CI: 767 to 979). The methodology shows the value of using count and telemetry data collected concurrently for estimating absolute abundance, information that is essential to assess interactions between predators, fish stocks and fisheries.
Description: R.J.S. was supported by a Natural Environment Research Council studentship.
Thu, 01 Jan 2009 00:00:00 GMT
http://hdl.handle.net/10023/3454
20090101T00:00:00Z
Sharples, RJ
MacKenzie, Monique Lea
Hammond, Philip Steven
Obtaining population estimates of species that are not easily observed directly can be problematic. However, central place foragers can often be observed some of the time, e.g. when seals are hauled out. In these instances, population estimates can be derived from counts, combined with information on the proportion of time that animals can be observed. We present a modelling framework to estimate seasonal absolute abundance using counts and information from satellite telemetry data. The method was tested on a harbour seal population in an area of southeast Scotland. Counts were made monthly, between November 2001 and June 2003, when seals were hauled out on land and were corrected for the proportion of time the seals were at sea using satellite telemetry. Harbour seals (n=25) were tagged with satellite relay data loggers between November 2001 and March 2003. To estimate the proportion of time spent hauled out, time at sea on foraging trips was modelled separately from haulout behaviour close to haulout sites because of the different factors affecting these processes. A generalised linear mixed model framework was developed to capture the longitudinal nature of the data and the repeated measures across individuals. Despite seasonal variability in the number of seals counted at haulout sites, the model generated estimates of abundance, with an overall mean of 846 (95% CI: 767 to 979). The methodology shows the value of using count and telemetry data collected concurrently for estimating absolute abundance, information that is essential to assess interactions between predators, fish stocks and fisheries.

Quantifying biodiversity trends in time and space
http://hdl.handle.net/10023/3414
Abstract: The global loss of biodiversity calls for robust largescale diversity assessment. Biological diversity is a multifaceted concept; defined as the “variety of life”, answering questions such as “How much is there?” or more precisely “Have we succeeded in reducing the rate of its decline?” is not straightforward. While various aspects of biodiversity give rise to numerous ways of quantification, we focus on temporal (and spatial) trends and their changes in species diversity.
Traditional diversity indices summarise information contained in the species abundance distribution, i.e. each species' proportional contribution to total abundance. Estimated from data, these indices can be biased if variation in detection probability is ignored. We discuss differences between diversity indices and demonstrate possible adjustments for detectability.
Additionally, most indices focus on the most abundant species in ecological communities. We introduce a new set of diversity measures, based on a family of goodnessoffit statistics. A function of a free parameter, this family allows us to vary the sensitivity of these measures to dominance and rarity of species.
Their performance is studied by assessing temporal trends in diversity for five communities of British breeding birds based on 14 years of survey data, where they are applied alongside the current headline index, a geometric mean of relative abundances. Revealing the contributions of both rare and common species to biodiversity trends, these "goodnessoffit" measures provide novel insights into how ecological communities change over time.
Biodiversity is not only subject to temporal changes, but it also varies across space. We take first steps towards estimating spatial diversity trends. Finally, processes maintaining biodiversity act locally, at specific spatial scales. Contrary to abundancebased summary statistics, spatial characteristics of ecological communities may distinguish these processes. We suggest a generalisation to a spatial summary, the crosspair overlap distribution, to render it more flexible to spatial scale.
Fri, 30 Nov 2012 00:00:00 GMT
http://hdl.handle.net/10023/3414
20121130T00:00:00Z
Studeny, Angelika C.
The global loss of biodiversity calls for robust largescale diversity assessment. Biological diversity is a multifaceted concept; defined as the “variety of life”, answering questions such as “How much is there?” or more precisely “Have we succeeded in reducing the rate of its decline?” is not straightforward. While various aspects of biodiversity give rise to numerous ways of quantification, we focus on temporal (and spatial) trends and their changes in species diversity.
Traditional diversity indices summarise information contained in the species abundance distribution, i.e. each species' proportional contribution to total abundance. Estimated from data, these indices can be biased if variation in detection probability is ignored. We discuss differences between diversity indices and demonstrate possible adjustments for detectability.
Additionally, most indices focus on the most abundant species in ecological communities. We introduce a new set of diversity measures, based on a family of goodnessoffit statistics. A function of a free parameter, this family allows us to vary the sensitivity of these measures to dominance and rarity of species.
Their performance is studied by assessing temporal trends in diversity for five communities of British breeding birds based on 14 years of survey data, where they are applied alongside the current headline index, a geometric mean of relative abundances. Revealing the contributions of both rare and common species to biodiversity trends, these "goodnessoffit" measures provide novel insights into how ecological communities change over time.
Biodiversity is not only subject to temporal changes, but it also varies across space. We take first steps towards estimating spatial diversity trends. Finally, processes maintaining biodiversity act locally, at specific spatial scales. Contrary to abundancebased summary statistics, spatial characteristics of ecological communities may distinguish these processes. We suggest a generalisation to a spatial summary, the crosspair overlap distribution, to render it more flexible to spatial scale.

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

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

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

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

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

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

Generating transformation semigroups using endomorphisms of preorders, graphs, and tolerances
http://hdl.handle.net/10023/3383
Abstract: Let ΩΩ be the semigroup of all mappings of a countably infinite set Ω. If U and V are subsemigroups of ΩΩ, then we write U≈V if there exists a finite subset F of ΩΩ such that the subsemigroup generated by U and F equals that generated by V and F. The relative rank of U in ΩΩ is the least cardinality of a subset A of ΩΩ such that the union of U and A generates ΩΩ. In this paper we study the notions of relative rank and the equivalence ≈ for semigroups of endomorphisms of binary relations on Ω. The semigroups of endomorphisms of preorders, bipartite graphs, and tolerances on Ω are shown to lie in two equivalence classes under ≈. Moreover such semigroups have relative rank 0, 1, 2, or d in ΩΩ where d is the minimum cardinality of a dominating family for NN. We give examples of preorders, bipartite graphs, and tolerances on Ω where the relative ranks of their endomorphism semigroups in ΩΩ are 0, 1, 2, and d. We show that the endomorphism semigroups of graphs, in general, fall into at least four classes under ≈ and that there exist graphs where the relative rank of the endomorphism semigroup is 2ℵ0.
Wed, 01 Sep 2010 00:00:00 GMT
http://hdl.handle.net/10023/3383
20100901T00:00:00Z
Mitchell, James David
Morayne, Michal
Peresse, Yann Hamon
Quick, Martyn
Let ΩΩ be the semigroup of all mappings of a countably infinite set Ω. If U and V are subsemigroups of ΩΩ, then we write U≈V if there exists a finite subset F of ΩΩ such that the subsemigroup generated by U and F equals that generated by V and F. The relative rank of U in ΩΩ is the least cardinality of a subset A of ΩΩ such that the union of U and A generates ΩΩ. In this paper we study the notions of relative rank and the equivalence ≈ for semigroups of endomorphisms of binary relations on Ω. The semigroups of endomorphisms of preorders, bipartite graphs, and tolerances on Ω are shown to lie in two equivalence classes under ≈. Moreover such semigroups have relative rank 0, 1, 2, or d in ΩΩ where d is the minimum cardinality of a dominating family for NN. We give examples of preorders, bipartite graphs, and tolerances on Ω where the relative ranks of their endomorphism semigroups in ΩΩ are 0, 1, 2, and d. We show that the endomorphism semigroups of graphs, in general, fall into at least four classes under ≈ and that there exist graphs where the relative rank of the endomorphism semigroup is 2ℵ0.

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

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

Fitting complex ecological point process models with integrated nested Laplace approximation
http://hdl.handle.net/10023/3364
Abstract: Summary 1. We highlight an emerging statistical method, integrated nested Laplace approximation (INLA), which is ideally suited for fitting complex models to many of the rich spatial data sets that ecologists wish to analyse. 2. INLA is an approximation method that nevertheless provides very exact estimates. In this article, we describe the INLA methodology highlighting where it offers opportunities for drawing inference from (spatial) ecological data that would previously have been too complex to make practical model fitting feasible. 3. We use INLA to fit a complex joint model to the spatial pattern formed by a plant species, Thymus carnosus, as well as to the health status of each individual. 4. The key ecological result revealed by our spatial analysis of these data, relates to the distancetowater covariate. We find that T. carnosus plants are generally healthier when they are further away from the water. 5. We suggest that this may be the result of a combination of (1) plants having alternative rooting strategies depending on how close to water they grow and (2) the rooting strategy determining how well the plants were able to tolerate an unusually dry summer. 6. We anticipate INLA becoming widely used within spatial ecological analysis over the next decade and suggest that both ecologists and statisticians will benefit greatly from working collaboratively to further develop and apply these emerging statistical methods.
Mon, 01 Apr 2013 00:00:00 GMT
http://hdl.handle.net/10023/3364
20130401T00:00:00Z
Illian, Janine Baerbel
Martino, Sara
Sørbye, Sigrunn H.
GallegoFernández, Juan B.
Zunzunegui, Maria
Esquivias, M. Paz
Travis, Justin M.
Summary 1. We highlight an emerging statistical method, integrated nested Laplace approximation (INLA), which is ideally suited for fitting complex models to many of the rich spatial data sets that ecologists wish to analyse. 2. INLA is an approximation method that nevertheless provides very exact estimates. In this article, we describe the INLA methodology highlighting where it offers opportunities for drawing inference from (spatial) ecological data that would previously have been too complex to make practical model fitting feasible. 3. We use INLA to fit a complex joint model to the spatial pattern formed by a plant species, Thymus carnosus, as well as to the health status of each individual. 4. The key ecological result revealed by our spatial analysis of these data, relates to the distancetowater covariate. We find that T. carnosus plants are generally healthier when they are further away from the water. 5. We suggest that this may be the result of a combination of (1) plants having alternative rooting strategies depending on how close to water they grow and (2) the rooting strategy determining how well the plants were able to tolerate an unusually dry summer. 6. We anticipate INLA becoming widely used within spatial ecological analysis over the next decade and suggest that both ecologists and statisticians will benefit greatly from working collaboratively to further develop and apply these emerging statistical methods.

Endomorphisms of Fraïssé limits and automorphism groups of algebraically closed relational structures
http://hdl.handle.net/10023/3358
Abstract: Let Ω be the Fraïssé limit of a class of relational structures. We seek to
answer the following semigroup theoretic question about Ω. What are the group Hclasses, i.e. the maximal subgroups, of End(Ω)? Fraïssé limits for which we answer this question include the random graph
R, the random directed graph D, the random tournament T, the random bipartite graph B, Henson's graphs G[subscript n] (for n greater or equal to 3) and the total order Q. The maximal subgroups of End(Ω) are closely connected to the automorphism groups of the relational structures induced by the images of idempotents from End(Ω). It has been shown that the relational structure induced by the image of an idempotent from End(Ω) is algebraically closed. Accordingly, we investigate which groups can be realised as the automorphism group of an algebraically closed relational structure in order to
determine the maximal subgroups of End(Ω) in each case. In particular, we show that if Γ is a countable graph and Ω = R,D,B,
then there exist 2[superscript alephnaught] maximal subgroups of End(Ω) which are isomorphic to Aut(Γ). Additionally, we provide a complete description of the subsets
of Q which are the image of an idempotent from End(Q). We call these subsets retracts of Q and show that if Ω is a total order and f is an embedding of Ω into Q such that im f is a retract of Q, then there exist 2[superscript alephnaught] maximal subgroups of End(Q) isomorphic to Aut(Ω). We also show that any countable maximal subgroup of End(Q) must be isomorphic to Zⁿ for some natural number n. As a consequence of the methods developed, we are also able to show that when Ω = R,D,B,Q there exist 2[superscript alephnaught] regular Dclasses of End(Ω) and when Ω = R,D,B there exist 2[superscript alephnaught] Jclasses of End(Ω). Additionally we show
that if Ω = R,D then all regular Dclasses contain 2[superscript alephnaught] group Hclasses. On the other hand, we show that when
Ω = B,Q there exist regular Dclasses
which contain countably many group Hclasses.
Fri, 30 Nov 2012 00:00:00 GMT
http://hdl.handle.net/10023/3358
20121130T00:00:00Z
McPhee, Jillian Dawn
Let Ω be the Fraïssé limit of a class of relational structures. We seek to
answer the following semigroup theoretic question about Ω. What are the group Hclasses, i.e. the maximal subgroups, of End(Ω)? Fraïssé limits for which we answer this question include the random graph
R, the random directed graph D, the random tournament T, the random bipartite graph B, Henson's graphs G[subscript n] (for n greater or equal to 3) and the total order Q. The maximal subgroups of End(Ω) are closely connected to the automorphism groups of the relational structures induced by the images of idempotents from End(Ω). It has been shown that the relational structure induced by the image of an idempotent from End(Ω) is algebraically closed. Accordingly, we investigate which groups can be realised as the automorphism group of an algebraically closed relational structure in order to
determine the maximal subgroups of End(Ω) in each case. In particular, we show that if Γ is a countable graph and Ω = R,D,B,
then there exist 2[superscript alephnaught] maximal subgroups of End(Ω) which are isomorphic to Aut(Γ). Additionally, we provide a complete description of the subsets
of Q which are the image of an idempotent from End(Q). We call these subsets retracts of Q and show that if Ω is a total order and f is an embedding of Ω into Q such that im f is a retract of Q, then there exist 2[superscript alephnaught] maximal subgroups of End(Q) isomorphic to Aut(Ω). We also show that any countable maximal subgroup of End(Q) must be isomorphic to Zⁿ for some natural number n. As a consequence of the methods developed, we are also able to show that when Ω = R,D,B,Q there exist 2[superscript alephnaught] regular Dclasses of End(Ω) and when Ω = R,D,B there exist 2[superscript alephnaught] Jclasses of End(Ω). Additionally we show
that if Ω = R,D then all regular Dclasses contain 2[superscript alephnaught] group Hclasses. On the other hand, we show that when
Ω = B,Q there exist regular Dclasses
which contain countably many group Hclasses.

A family of spatial biodiversity measures based on graphs
http://hdl.handle.net/10023/3350
Abstract: While much research in ecology has focused on spatially explicit modelling as well as on measures of biodiversity, the concept of spatial (or local) biodiversity has been discussed very little. This paper generalises existing measures of spatial biodiversity and introduces a family of spatial biodiversity measures by flexibly defining the notion of the individuals’ neighbourhood within the framework of graphs associated to a spatial point pattern. We consider two nonindependent aspects of spatial biodiversity, scattering, i.e. the spatial arrangement of the individuals in the study area and exposure, the local diversity in an individual’s neighbourhood. A simulation study reveals that measures based on the most commonly used neighbourhood defined by the geometric graph do not distinguish well between scattering and exposure. This problem is much less pronounced when other graphs are used. In an analysis of the spatial diversity in a rainforest, the results based on the geometric graph have been shown to spuriously indicate a decrease in spatial biodiversity when no such trend was detected by the other types of neighbourhoods. We also show that the choice neighbourhood markedly impacts on the classification of species according to how strongly and in what way different species spatially structure species diversity. Clearly, in an analysis of spatial or local diversity an appropriate choice of local neighbourhood is crucial in particular in terms of the biological interpretation of the results. Due to its general definition, the approach discussed here offers the necessary flexibility that allows suitable and varying neighbourhood structures to be chosen.
Sat, 01 Dec 2012 00:00:00 GMT
http://hdl.handle.net/10023/3350
20121201T00:00:00Z
Rajala, T
Illian, Janine Baerbel
While much research in ecology has focused on spatially explicit modelling as well as on measures of biodiversity, the concept of spatial (or local) biodiversity has been discussed very little. This paper generalises existing measures of spatial biodiversity and introduces a family of spatial biodiversity measures by flexibly defining the notion of the individuals’ neighbourhood within the framework of graphs associated to a spatial point pattern. We consider two nonindependent aspects of spatial biodiversity, scattering, i.e. the spatial arrangement of the individuals in the study area and exposure, the local diversity in an individual’s neighbourhood. A simulation study reveals that measures based on the most commonly used neighbourhood defined by the geometric graph do not distinguish well between scattering and exposure. This problem is much less pronounced when other graphs are used. In an analysis of the spatial diversity in a rainforest, the results based on the geometric graph have been shown to spuriously indicate a decrease in spatial biodiversity when no such trend was detected by the other types of neighbourhoods. We also show that the choice neighbourhood markedly impacts on the classification of species according to how strongly and in what way different species spatially structure species diversity. Clearly, in an analysis of spatial or local diversity an appropriate choice of local neighbourhood is crucial in particular in terms of the biological interpretation of the results. Due to its general definition, the approach discussed here offers the necessary flexibility that allows suitable and varying neighbourhood structures to be chosen.

Multispecies functional response of the minke whale Balaenoptera acutorostrata based on smallscale foraging studies
http://hdl.handle.net/10023/3345
Abstract: Atlantic minke whales are important predators in the Barents Sea ecosystem; capelin Mallotus villosus, krill Thysanoessa sp. and Meganyctephanes norvegica and herring Clupea harengus are their major prey. Their consumption of commercial species may present an economic problem for the local fishery. In order to estimate this consumption and understand the potential consequences for prey dynamics, it is essential to determine the multispecies functional response of the whales. The parameterisation of a functional response requires measurements of consumption rates and prey availability. In this localised study, undigested stomach contents were used to assess the amount of each prey that had been consumed immediately prior to capture. To determine the availability of prey to the whales, standard acoustic surveys were run in the same area within 2 d of the capture of the whales. The spatial distribution of prey was modelled using generalised additive models (GAMs). In order to generate a measure of prey availability and the uncertainty in this value, a simple model was assumed for whale movement, and prey abundance was sampled over space according to a Gaussian kernel. A multispecies functional response (MSFR) model was then fitted to the consumption and prey availability data using Bayesian methods. Simple simulations, based on the fitted MSFR, indicate that minke whales may deplete local capelin aggregations at small spatial scales. This is the first time that a multispecies functional response has been fitted for a cetacean predator, and the methods outlined here may prove useful for modelling marine mammalfish interactions in other systems.
Sun, 01 Jul 2007 00:00:00 GMT
http://hdl.handle.net/10023/3345
20070701T00:00:00Z
Smout, Sophie Caroline
Lindstrom, Ulf
Atlantic minke whales are important predators in the Barents Sea ecosystem; capelin Mallotus villosus, krill Thysanoessa sp. and Meganyctephanes norvegica and herring Clupea harengus are their major prey. Their consumption of commercial species may present an economic problem for the local fishery. In order to estimate this consumption and understand the potential consequences for prey dynamics, it is essential to determine the multispecies functional response of the whales. The parameterisation of a functional response requires measurements of consumption rates and prey availability. In this localised study, undigested stomach contents were used to assess the amount of each prey that had been consumed immediately prior to capture. To determine the availability of prey to the whales, standard acoustic surveys were run in the same area within 2 d of the capture of the whales. The spatial distribution of prey was modelled using generalised additive models (GAMs). In order to generate a measure of prey availability and the uncertainty in this value, a simple model was assumed for whale movement, and prey abundance was sampled over space according to a Gaussian kernel. A multispecies functional response (MSFR) model was then fitted to the consumption and prey availability data using Bayesian methods. Simple simulations, based on the fitted MSFR, indicate that minke whales may deplete local capelin aggregations at small spatial scales. This is the first time that a multispecies functional response has been fitted for a cetacean predator, and the methods outlined here may prove useful for modelling marine mammalfish interactions in other systems.

Estimating demographic parameters for capturerecapture data in the presence of multiple mark types
http://hdl.handle.net/10023/3344
Abstract: In markrecapture studies, various techniques can be used to uniquely identify individual animals, such as ringing, tagging or photoidentification using natural markings. In some longterm studies more than one type of marking procedure may be implemented during the study period. In these circumstances, ignoring the different mark types can produce biased survival estimates since the assumption that the different mark types are equally catchable (homogeneous capture probability across mark types) may be incorrect.We implement an integrated approach where we simultaneously analyse data obtained using three different marking techniques, assuming that animals can be crossclassified across the different mark types. We discriminate between competing models using the AIC statistic. This technique also allows us to estimate both relative markloss probabilities and relative recapture efficiency rates for the different marking methods.We initially perform a simulation study to explore the different biases that can be introduced if we assume a homogeneous recapture probability over mark type, before applying the method to a real dataset. We make use of data obtained from an intensive longterm observational study of UK female grey seals (Halichoerus grypus) at a single breeding colony, where three different methods are used to identify individuals within a single study: branding, tagging and photoidentification based on seal coat pattern or pelage.
Wed, 01 Jun 2011 00:00:00 GMT
http://hdl.handle.net/10023/3344
20110601T00:00:00Z
Smout, Sophie Caroline
King, Ruth
Pomeroy, Patrick
In markrecapture studies, various techniques can be used to uniquely identify individual animals, such as ringing, tagging or photoidentification using natural markings. In some longterm studies more than one type of marking procedure may be implemented during the study period. In these circumstances, ignoring the different mark types can produce biased survival estimates since the assumption that the different mark types are equally catchable (homogeneous capture probability across mark types) may be incorrect.We implement an integrated approach where we simultaneously analyse data obtained using three different marking techniques, assuming that animals can be crossclassified across the different mark types. We discriminate between competing models using the AIC statistic. This technique also allows us to estimate both relative markloss probabilities and relative recapture efficiency rates for the different marking methods.We initially perform a simulation study to explore the different biases that can be introduced if we assume a homogeneous recapture probability over mark type, before applying the method to a real dataset. We make use of data obtained from an intensive longterm observational study of UK female grey seals (Halichoerus grypus) at a single breeding colony, where three different methods are used to identify individuals within a single study: branding, tagging and photoidentification based on seal coat pattern or pelage.

Every group is a maximal subgroup of the free idempotent generated semigroup over a band
http://hdl.handle.net/10023/3342
Abstract: Given an arbitrary group G we construct a semigroup of idempotents (band) BG with the property that the free idempotent generated semigroup over BG has a maximal subgroup isomorphic to G. If G is finitely presented then BG is finite. This answers several questions from recent papers in the area.
Wed, 01 May 2013 00:00:00 GMT
http://hdl.handle.net/10023/3342
20130501T00:00:00Z
Dolinka, I
Ruskuc, Nik
Given an arbitrary group G we construct a semigroup of idempotents (band) BG with the property that the free idempotent generated semigroup over BG has a maximal subgroup isomorphic to G. If G is finitely presented then BG is finite. This answers several questions from recent papers in the area.

On disjoint unions of finitely many copies of the free monogenic semigroup
http://hdl.handle.net/10023/3341
Abstract: Every semigroup which is a finite disjoint union of copies of the free monogenic semigroup (natural numbers under addition) is finitely presented and residually finite.
Thu, 01 Aug 2013 00:00:00 GMT
http://hdl.handle.net/10023/3341
20130801T00:00:00Z
Abughazalah, Nabilah
Ruskuc, Nik
Every semigroup which is a finite disjoint union of copies of the free monogenic semigroup (natural numbers under addition) is finitely presented and residually finite.

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

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

Ideals and finiteness conditions for subsemigroups
http://hdl.handle.net/10023/3335
Abstract: In this paper we consider a number of finiteness conditions for semigroups related to their ideal structure, and ask whether such conditions are preserved by sub or supersemigroups with finite Rees or Green index. Specific properties under consideration include stability, D=J and minimal conditions on ideals.
Wed, 01 Jan 2014 00:00:00 GMT
http://hdl.handle.net/10023/3335
20140101T00:00:00Z
Gray, Robert Duncan
Maltcev, Victor
D. Mitchell, J.
Ruskuc, N.
In this paper we consider a number of finiteness conditions for semigroups related to their ideal structure, and ask whether such conditions are preserved by sub or supersemigroups with finite Rees or Green index. Specific properties under consideration include stability, D=J and minimal conditions on ideals.

The geometric mean of relative abundance indices : a biodiversity measure with a difference
http://hdl.handle.net/10023/3310
Abstract: The 2010 Biodiversity Target of the Convention on Biological Diversity (CBD), set in 2002, which stated that there should be ‘a significant reduction of the current rate of biodiversity loss' by 2010, highlighted the need for informative and tractable metrics that can be used to evaluate change in biological diversity. While the subsequent Aichi 2020 targets are more wideranging, they also seek to reduce the rate of biodiversity loss. The geometric mean of relative abundance indices, G, is increasingly being used to examine trends in biological diversity and to assess whether biodiversity targets are being met. Here, we explore the mathematical and statistical properties of G that make it useful for judging temporal change in biological diversity, and we discuss its advantages and limitations relative to other measures. We demonstrate that the index reflects trends in both abundance and evenness, and that it is not prone to bias when detectability of individuals varies by species. We note that it allows data from different surveys to be combined to generate a composite index. However, the index exhibits high variance and unstable behaviour when rarelyrecorded species are included in the analyses. Read More: http://www.esajournals.org/doi/abs/10.1890/ES1100186.1
Description: This work is partly supported by the European Research Council
Fri, 02 Sep 2011 00:00:00 GMT
http://hdl.handle.net/10023/3310
20110902T00:00:00Z
Buckland, Stephen Terrence
Studeny, Angelika Caroline
Magurran, Anne
Illian, Janine Baerbel
Newson, Stuart
The 2010 Biodiversity Target of the Convention on Biological Diversity (CBD), set in 2002, which stated that there should be ‘a significant reduction of the current rate of biodiversity loss' by 2010, highlighted the need for informative and tractable metrics that can be used to evaluate change in biological diversity. While the subsequent Aichi 2020 targets are more wideranging, they also seek to reduce the rate of biodiversity loss. The geometric mean of relative abundance indices, G, is increasingly being used to examine trends in biological diversity and to assess whether biodiversity targets are being met. Here, we explore the mathematical and statistical properties of G that make it useful for judging temporal change in biological diversity, and we discuss its advantages and limitations relative to other measures. We demonstrate that the index reflects trends in both abundance and evenness, and that it is not prone to bias when detectability of individuals varies by species. We note that it allows data from different surveys to be combined to generate a composite index. However, the index exhibits high variance and unstable behaviour when rarelyrecorded species are included in the analyses. Read More: http://www.esajournals.org/doi/abs/10.1890/ES1100186.1

Using INLA to fit a complex point process model with temporally varying effects – a case study
http://hdl.handle.net/10023/3306
Abstract: Integrated nested Laplace approximation (INLA) provides a fast and yet quite exact approach to fitting complex latent Gaussian models which comprise many statistical models in a Bayesian context, including log Gaussian Cox processes. This paper discusses how a joint log Gaussian Cox process model may be fitted to independent replicated point patterns. We illustrate the approach by fitting a model to data on the locations of muskoxen (Ovibos moschatus) herds in Zackenberg valley, Northeast Greenland and by detailing how this model is specified within the Rinterface RINLA. The paper strongly focuses on practical problems involved in the modelling process, including issues of spatial scale, edge effects and prior choices, and finishes with a discussion on models with varying boundary conditions.
Sun, 01 Jul 2012 00:00:00 GMT
http://hdl.handle.net/10023/3306
20120701T00:00:00Z
Illian, Janine Baerbel
Soerbye, S
Rue, H
Hendrichsen, D
Integrated nested Laplace approximation (INLA) provides a fast and yet quite exact approach to fitting complex latent Gaussian models which comprise many statistical models in a Bayesian context, including log Gaussian Cox processes. This paper discusses how a joint log Gaussian Cox process model may be fitted to independent replicated point patterns. We illustrate the approach by fitting a model to data on the locations of muskoxen (Ovibos moschatus) herds in Zackenberg valley, Northeast Greenland and by detailing how this model is specified within the Rinterface RINLA. The paper strongly focuses on practical problems involved in the modelling process, including issues of spatial scale, edge effects and prior choices, and finishes with a discussion on models with varying boundary conditions.

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

Quantifying temporal change in biodiversity : challenges and opportunities
http://hdl.handle.net/10023/3284
Abstract: Growing concern about biodiversity loss underscores the need to quantify and understand temporal change. Here, we review the opportunities presented by biodiversity time series, and address three related issues: (i) recognizing the characteristics of temporal data; (ii) selecting appropriate statistical procedures for analysing temporal data; and (iii) inferring and forecasting biodiversity change. With regard to the first issue, we draw attention to defining characteristics of biodiversity time series—lack of physical boundaries, unidimensionality, autocorrelation and directionality—that inform the choice of analytic methods. Second, we explore methods of quantifying change in biodiversity at different timescales, noting that autocorrelation can be viewed as a feature that sheds light on the underlying structure of temporal change. Finally, we address the transition from inferring to forecasting biodiversity change, highlighting potential pitfalls associated with phaseshifts and novel conditions.
Mon, 07 Jan 2013 00:00:00 GMT
http://hdl.handle.net/10023/3284
20130107T00:00:00Z
Dornelas, Maria
Magurran, Anne
Buckland, Stephen Terrence
Chao, Anne
Chazdon, Robin L
Colwell, Robert K
Curtis, Tom
Gaston, Kevin J
Gotelli, Nicolas J
Kosnik, Matthew A
McGill, Brian
McCune, Jenny L
Morlon, Hélène
Mumby, Peter J
Øvreås, Lise
Studeny, Angelika
Vellend, Mark
Growing concern about biodiversity loss underscores the need to quantify and understand temporal change. Here, we review the opportunities presented by biodiversity time series, and address three related issues: (i) recognizing the characteristics of temporal data; (ii) selecting appropriate statistical procedures for analysing temporal data; and (iii) inferring and forecasting biodiversity change. With regard to the first issue, we draw attention to defining characteristics of biodiversity time series—lack of physical boundaries, unidimensionality, autocorrelation and directionality—that inform the choice of analytic methods. Second, we explore methods of quantifying change in biodiversity at different timescales, noting that autocorrelation can be viewed as a feature that sheds light on the underlying structure of temporal change. Finally, we address the transition from inferring to forecasting biodiversity change, highlighting potential pitfalls associated with phaseshifts and novel conditions.

The functional response of a generalist predator
http://hdl.handle.net/10023/3269
Abstract: Background: Predators can have profound impacts on the dynamics of their prey that depend on how predator consumption is affected by prey density (the predator's functional response). Consumption by a generalist predator is expected to depend on the densities of all its major prey species (its multispecies functional response, or MSFR), but most studies of generalists have focussed on their functional response to only one prey species. Methodology and principal findings: Using Bayesian methods, we fit an MSFR to field data from an avian predator (the hen harrier Circus cyaneus) feeding on three different prey species. We use a simple graphical approach to show that ignoring the effects of alternative prey can give a misleading impression of the predator's effect on the prey of interest. For example, in our system, a “predator pit” for one prey species only occurs when the availability of other prey species is low. Conclusions and significance: The Bayesian approach is effective in fitting the MSFR model to field data. It allows flexibility in modelling overdispersion, incorporates additional biological information into the parameter priors, and generates estimates of uncertainty in the model's predictions. These features of robustness and data efficiency make our approach ideal for the study of longlived predators, for which data may be sparse and management/conservation priorities pressing.
Thu, 27 May 2010 00:00:00 GMT
http://hdl.handle.net/10023/3269
20100527T00:00:00Z
Smout, Sophie Caroline
Asseburg, C
Matthiopoulos, Jason
Fernández, Carmen
Redpath, S
Thirgood, S
Harwood, John
Background: Predators can have profound impacts on the dynamics of their prey that depend on how predator consumption is affected by prey density (the predator's functional response). Consumption by a generalist predator is expected to depend on the densities of all its major prey species (its multispecies functional response, or MSFR), but most studies of generalists have focussed on their functional response to only one prey species. Methodology and principal findings: Using Bayesian methods, we fit an MSFR to field data from an avian predator (the hen harrier Circus cyaneus) feeding on three different prey species. We use a simple graphical approach to show that ignoring the effects of alternative prey can give a misleading impression of the predator's effect on the prey of interest. For example, in our system, a “predator pit” for one prey species only occurs when the availability of other prey species is low. Conclusions and significance: The Bayesian approach is effective in fitting the MSFR model to field data. It allows flexibility in modelling overdispersion, incorporates additional biological information into the parameter priors, and generates estimates of uncertainty in the model's predictions. These features of robustness and data efficiency make our approach ideal for the study of longlived predators, for which data may be sparse and management/conservation priorities pressing.

A nontechnical overview of spatially explicit capturerecapture models
http://hdl.handle.net/10023/3259
Abstract: Most capturerecapture studies are inherently spatial in nature, with capture probabilities depending on the location of traps relative to animals. The spatial component of the studies has until recently, however, not been incorporated in statistical capturerecapture models. This paper reviews capturerecapture models that do include an explicit spatial component. This is done in a nontechnical way, omitting much of the algebraic detail and focussing on the model formulation rather than on the estimation methods (which include inverse prediction, maximum likelihood and Bayesian methods). One can view spatially explicit capturerecapture (SECR) models as an endpoint of a series of spatial sampling models, starting with circular plot survey models and moving through conventional distance sampling models, with and without measurement errors, through markrecapture distance sampling (MRDS) models. This paper attempts a synthesis of these models in what I hope is a style accessible to nonspecialists, placing SECR models in the context of other spatial sampling models.
Wed, 01 Feb 2012 00:00:00 GMT
http://hdl.handle.net/10023/3259
20120201T00:00:00Z
Borchers, David
Most capturerecapture studies are inherently spatial in nature, with capture probabilities depending on the location of traps relative to animals. The spatial component of the studies has until recently, however, not been incorporated in statistical capturerecapture models. This paper reviews capturerecapture models that do include an explicit spatial component. This is done in a nontechnical way, omitting much of the algebraic detail and focussing on the model formulation rather than on the estimation methods (which include inverse prediction, maximum likelihood and Bayesian methods). One can view spatially explicit capturerecapture (SECR) models as an endpoint of a series of spatial sampling models, starting with circular plot survey models and moving through conventional distance sampling models, with and without measurement errors, through markrecapture distance sampling (MRDS) models. This paper attempts a synthesis of these models in what I hope is a style accessible to nonspecialists, placing SECR models in the context of other spatial sampling models.

Attractors of directed graph IFSs that are not standard IFS attractors and their Hausdorff measure
http://hdl.handle.net/10023/3237
Abstract: For directed graph iterated function systems (IFSs) defined on R, we prove that a class of 2vertex directed graph IFSs have attractors that cannot be the attractors of standard (1vertex directed graph) IFSs, with or without separation conditions. We also calculate their exact Hausdorff measure. Thus we are able to identify a new class of attractors for which the exact Hausdorff measure is known.
Description: "GCB was supported by an EPSRC Doctoral Training Grant whilst undertaking this work"
Tue, 01 Jan 2013 00:00:00 GMT
http://hdl.handle.net/10023/3237
20130101T00:00:00Z
Boore, Graeme
Falconer, Kenneth John
For directed graph iterated function systems (IFSs) defined on R, we prove that a class of 2vertex directed graph IFSs have attractors that cannot be the attractors of standard (1vertex directed graph) IFSs, with or without separation conditions. We also calculate their exact Hausdorff measure. Thus we are able to identify a new class of attractors for which the exact Hausdorff measure is known.

Topics in combinatorial semigroup theory
http://hdl.handle.net/10023/3226
Abstract: In this thesis we discuss various topics from Combinatorial Semigroup Theory: automaton semigroups; finiteness conditions and their preservation under certain semigroup theoretic notions of index; Markov semigroups; wordhyperbolic semigroups; decision problems for finitely presented
and onerelator monoids. First, in order to show that general ideas from Combinatorial Semigroup Theory can apply to uncountable semigroups, at the beginning of the thesis we discuss semigroups with Bergman’s property. We prove that an automaton semigroup generated by a Cayley machine
of a finite semigroup S is itself finite if and only if S is aperiodic, which yields a new characterisation of finite aperiodic monoids. Using this, we derive some further results about Cayley automaton semigroups.
We investigate how various semigroup finiteness conditions, linked to
the notion of ideal, are preserved under finite Rees and Green indices. We
obtain a surprising result that J = D is preserved by supersemigroups of finite Green index, but it is not preserved by subsemigroups of finite Rees index even in the finitely generated case. We also consider the question of preservation of hopficity for finite Rees index. We prove that in general hopficity is preserved neither by finite Rees index subsemigroups, nor by finite Rees index extensions. However, under finite generation assumption,
hopficity is preserved by finite Rees index extensions. Still, there is
an example of a finitely generated hopfian semigroup with a nonhopfian subsemigroup of finite Rees index. We prove also that monoids presented by confluent contextfree monadic rewriting systems are wordhyperbolic, and provide an example of such a monoid, which does not admit a wordhyperbolic structure with uniqueness.
This answers in the negative a question of Duncan & Gilman. We initiate in this thesis a study of Markov semigroups. We investigate
how the property of being Markov is preserved under finite Rees and
Green indices. For various semigroup properties P we examine whether P , ¬P are Markov properties, and whether P is decidable for finitely presented and
onerelator monoids.
Fri, 30 Nov 2012 00:00:00 GMT
http://hdl.handle.net/10023/3226
20121130T00:00:00Z
Maltcev, Victor
In this thesis we discuss various topics from Combinatorial Semigroup Theory: automaton semigroups; finiteness conditions and their preservation under certain semigroup theoretic notions of index; Markov semigroups; wordhyperbolic semigroups; decision problems for finitely presented
and onerelator monoids. First, in order to show that general ideas from Combinatorial Semigroup Theory can apply to uncountable semigroups, at the beginning of the thesis we discuss semigroups with Bergman’s property. We prove that an automaton semigroup generated by a Cayley machine
of a finite semigroup S is itself finite if and only if S is aperiodic, which yields a new characterisation of finite aperiodic monoids. Using this, we derive some further results about Cayley automaton semigroups.
We investigate how various semigroup finiteness conditions, linked to
the notion of ideal, are preserved under finite Rees and Green indices. We
obtain a surprising result that J = D is preserved by supersemigroups of finite Green index, but it is not preserved by subsemigroups of finite Rees index even in the finitely generated case. We also consider the question of preservation of hopficity for finite Rees index. We prove that in general hopficity is preserved neither by finite Rees index subsemigroups, nor by finite Rees index extensions. However, under finite generation assumption,
hopficity is preserved by finite Rees index extensions. Still, there is
an example of a finitely generated hopfian semigroup with a nonhopfian subsemigroup of finite Rees index. We prove also that monoids presented by confluent contextfree monadic rewriting systems are wordhyperbolic, and provide an example of such a monoid, which does not admit a wordhyperbolic structure with uniqueness.
This answers in the negative a question of Duncan & Gilman. We initiate in this thesis a study of Markov semigroups. We investigate
how the property of being Markov is preserved under finite Rees and
Green indices. For various semigroup properties P we examine whether P , ¬P are Markov properties, and whether P is decidable for finitely presented and
onerelator monoids.

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

Workshop on new developments in cetacean survey methods
http://hdl.handle.net/10023/3216
Abstract: This report contains the slides from a workshop on New Developments in Cetacean Survey Methods held on 27th November 2011 at the 19th Biennial Conference on the Biology of Marine Mammals, Tampa, Florida. Review talks were given on Passive Acoustic Density Estimation (Len Thomas); Dealing with g(0)<1: Perception Bias (Stephen Buckland); Dealing with g(0)<1: Availability Bias (Hans Skaug); Dealing with Measurement Error (David Borchers); and Density Surface Modelling (Jay Barlow). The sessions were followed by a discussion, and this is summarized at the end of the report.
Sat, 01 Jan 2011 00:00:00 GMT
http://hdl.handle.net/10023/3216
20110101T00:00:00Z
Borchers, David Louis
Thomas, Len
Buckland, Stephen Terrence
Skaug, Hans
Barlow, Jay
This report contains the slides from a workshop on New Developments in Cetacean Survey Methods held on 27th November 2011 at the 19th Biennial Conference on the Biology of Marine Mammals, Tampa, Florida. Review talks were given on Passive Acoustic Density Estimation (Len Thomas); Dealing with g(0)<1: Perception Bias (Stephen Buckland); Dealing with g(0)<1: Availability Bias (Hans Skaug); Dealing with Measurement Error (David Borchers); and Density Surface Modelling (Jay Barlow). The sessions were followed by a discussion, and this is summarized at the end of the report.

The propagation and damping of slow magnetoacoustic waves in the solar atmosphere
http://hdl.handle.net/10023/3215
Abstract: The propagation and damping of slow magnetoacoustic waves in the solar atmosphere is investigated, with
particular emphasis placed on waves with periodicities of five minutes. The basic model of a uniform
temperature loop is extended by the addition of an equilibrium temperature gradient allowing study of
wave propagation from the transition region to the corona. The inclusion of thermal conduction produces
a phase shift between the perturbations in velocity, density and temperature, which for a nonuniform
equilibrium temperature varies along the loop and may be observable as a phase shift between intensity and
Doppler shift observations. Forward modelling of the simulation results, for both constant and nonconstant
equilibrium temperature profiles, is undertaken in order to establish the observational consequences for
TRACE, SoHO/CDS and Hinode/EIS. Slow waves propagating in a nonuniform equilibrium temperature
loop are seen to damp rapidly in the corona, however, as a result of the ionisation balance, the inclusion of
damping can actually increase the amplitude of some parts of the oscillation.
The ability of several data analysis techniques to identify oscillation signatures are examined. In particular,
empirical mode decomposition was found to be a very useful technique for extracting oscillations from a
wide range of data sets and is capable of intrinsically determining background trends. Cospatial and cotemporal
TRACE 171 A, CDS and EIS data are analysed for evidence of propagating slow waves. Slow
waves with periods of 210 s to 370 s are found with amplitudes of 1.2% to 3.4% in the corona and 2.3% to
6.0% in the transition region.
Fri, 30 Nov 2012 00:00:00 GMT
http://hdl.handle.net/10023/3215
20121130T00:00:00Z
Owen, Nicholas Robert
The propagation and damping of slow magnetoacoustic waves in the solar atmosphere is investigated, with
particular emphasis placed on waves with periodicities of five minutes. The basic model of a uniform
temperature loop is extended by the addition of an equilibrium temperature gradient allowing study of
wave propagation from the transition region to the corona. The inclusion of thermal conduction produces
a phase shift between the perturbations in velocity, density and temperature, which for a nonuniform
equilibrium temperature varies along the loop and may be observable as a phase shift between intensity and
Doppler shift observations. Forward modelling of the simulation results, for both constant and nonconstant
equilibrium temperature profiles, is undertaken in order to establish the observational consequences for
TRACE, SoHO/CDS and Hinode/EIS. Slow waves propagating in a nonuniform equilibrium temperature
loop are seen to damp rapidly in the corona, however, as a result of the ionisation balance, the inclusion of
damping can actually increase the amplitude of some parts of the oscillation.
The ability of several data analysis techniques to identify oscillation signatures are examined. In particular,
empirical mode decomposition was found to be a very useful technique for extracting oscillations from a
wide range of data sets and is capable of intrinsically determining background trends. Cospatial and cotemporal
TRACE 171 A, CDS and EIS data are analysed for evidence of propagating slow waves. Slow
waves with periods of 210 s to 370 s are found with amplitudes of 1.2% to 3.4% in the corona and 2.3% to
6.0% in the transition region.

Wave propagation, phase mixing and dissipation in Hall MHD
http://hdl.handle.net/10023/3182
Abstract: In this thesis the effect of the Hall term in the generalised Ohm’s law on Alfvén (shear) and fast wave propagation and dissipation in the ion cyclotron frequency range is investigated.
The damping of an initially Gaussian field perturbation in a uniform Hall MHD plasma is treated analytically. Subsequently a 2D Lagrangian remap code (Lare2d) is used to study the damping and phase mixing of initially Gaussian field perturbations and a harmonic series of boundarydriven perturbations in a uniform field (in the presence of a transverse equilibrium density gradient). The same code is then used to study a range of initially shear and fastwave perturbations in the vicinity of a magnetic Xtype null point.
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 kδ where k is wavenumber and δ is ion skin depth. A similar decay law applies to whistler perturbations in the limit kδ>>>1.
We demonstrate that in both geometries considered, the inclusion of the Hall term reduces the effectiveness of phasemixing in plasma heating. The reduction in the damping rate in the uniform ﬁeld (nonuniform density) cases, arising from dispersive effects, tends to zero in both the weak and strong phase mixing limits. In the Hall MHD Xpoint case, minimal reductions are seen for initially shear wave pulses, suggesting that little or no phasemixing takes place. Nonlinear fast wave pulses which interact with the initial Xpoint destabilise the local field sufficiently to generate multiple null pairs; subsequent oscillatory current sheet behaviour appears unaffected by earlier differences between the MHD and Hall MHD cases.
Fri, 22 Jun 2012 00:00:00 GMT
http://hdl.handle.net/10023/3182
20120622T00:00:00Z
Threlfall, James W.
In this thesis the effect of the Hall term in the generalised Ohm’s law on Alfvén (shear) and fast wave propagation and dissipation in the ion cyclotron frequency range is investigated.
The damping of an initially Gaussian field perturbation in a uniform Hall MHD plasma is treated analytically. Subsequently a 2D Lagrangian remap code (Lare2d) is used to study the damping and phase mixing of initially Gaussian field perturbations and a harmonic series of boundarydriven perturbations in a uniform field (in the presence of a transverse equilibrium density gradient). The same code is then used to study a range of initially shear and fastwave perturbations in the vicinity of a magnetic Xtype null point.
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 kδ where k is wavenumber and δ is ion skin depth. A similar decay law applies to whistler perturbations in the limit kδ>>>1.
We demonstrate that in both geometries considered, the inclusion of the Hall term reduces the effectiveness of phasemixing in plasma heating. The reduction in the damping rate in the uniform ﬁeld (nonuniform density) cases, arising from dispersive effects, tends to zero in both the weak and strong phase mixing limits. In the Hall MHD Xpoint case, minimal reductions are seen for initially shear wave pulses, suggesting that little or no phasemixing takes place. Nonlinear fast wave pulses which interact with the initial Xpoint destabilise the local field sufficiently to generate multiple null pairs; subsequent oscillatory current sheet behaviour appears unaffected by earlier differences between the MHD and Hall MHD cases.

Collisionless distribution function for the relativistic forcefree Harris sheet
http://hdl.handle.net/10023/3154
Abstract: A selfconsistent collisionless distribution function for the relativistic analogue of the forcefree Harris sheet is presented. This distribution function is the relativistic generalization of the distribution function for the nonrelativistic collisionless forcefree Harris sheet recently found by Harrison and Neukirch [Phys. Rev. Lett. 102, 135003 (2009)], as it has the same dependence on the particle energy and canonical momenta. We present a detailed calculation which shows that the proposed distribution function generates the required current density profile (and thus magnetic field profile) in a frame of reference in which the electric potential vanishes identically. The connection between the parameters of the distribution function and the macroscopic parameters such as the current sheet thickness is discussed. (C) 2012 American Institute of Physics. [doi: 10.1063/1.3677268]
Sun, 01 Jan 2012 00:00:00 GMT
http://hdl.handle.net/10023/3154
20120101T00:00:00Z
Stark, C. R.
Neukirch, T.
A selfconsistent collisionless distribution function for the relativistic analogue of the forcefree Harris sheet is presented. This distribution function is the relativistic generalization of the distribution function for the nonrelativistic collisionless forcefree Harris sheet recently found by Harrison and Neukirch [Phys. Rev. Lett. 102, 135003 (2009)], as it has the same dependence on the particle energy and canonical momenta. We present a detailed calculation which shows that the proposed distribution function generates the required current density profile (and thus magnetic field profile) in a frame of reference in which the electric potential vanishes identically. The connection between the parameters of the distribution function and the macroscopic parameters such as the current sheet thickness is discussed. (C) 2012 American Institute of Physics. [doi: 10.1063/1.3677268]

A detailed investigation of the properties of a VlasovMaxwell equilibrium for the forcefree Harris sheet
http://hdl.handle.net/10023/3153
Abstract: A detailed discussion is presented of the VlasovMaxwell equilibrium for the forcefree Harris sheet recently found by Harrison and Neukirch [Phys. Rev. Lett. 102, 135003 (2009)]. The derivation of the distribution function and a discussion of its general properties and their dependence on the distribution function parameters will be given. In particular, the distribution function can be singlepeaked or multipeaked in two of the velocity components, with possible implications for stability. The dependence of the shape of the distribution function on the values of its parameters will be investigated and the relation to macroscopic quantities such as the current sheet thickness will be discussed.
Tue, 01 Dec 2009 00:00:00 GMT
http://hdl.handle.net/10023/3153
20091201T00:00:00Z
Neukirch, Thomas
Wilson, F.
Harrison, M. G.
A detailed discussion is presented of the VlasovMaxwell equilibrium for the forcefree Harris sheet recently found by Harrison and Neukirch [Phys. Rev. Lett. 102, 135003 (2009)]. The derivation of the distribution function and a discussion of its general properties and their dependence on the distribution function parameters will be given. In particular, the distribution function can be singlepeaked or multipeaked in two of the velocity components, with possible implications for stability. The dependence of the shape of the distribution function on the values of its parameters will be investigated and the relation to macroscopic quantities such as the current sheet thickness will be discussed.

A nonlinear forcefree field model for the solar magnetic carpet
http://hdl.handle.net/10023/3114
Abstract: The magnetic carpet is defined to be the smallscale photospheric magnetic field of the quiet Sun. Observations of the magnetic carpet show it to be highly dynamic, where the time taken for all flux within the magnetic carpet to be replaced is on the order of just a few hours. The magnetic carpet is continually evolving due to the Sun's underlying convection and the interaction of smallscale magnetic features with one another. Due to this, the smallscale coronal field of the magnetic carpet is also expected to be highly dynamic and complex. Previous modelling has shown that much of the flux from the magnetic carpet is stored along lowlying closed connections between magnetic features. This indicates that significant coronal heating could occur low down in the smallscale corona. In this thesis, a new twocomponent magnetic field model is developed for the evolution of the magnetic carpet. A 2D model is constructed to realistically simulate the evolution of the photospheric field of the magnetic carpet, where many of the parameters for the model are taken from observational studies. The photospheric model contains a granular and supergranular flow profile to describe the motion of the smallscale magnetic features, and includes the processes of flux emergence, cancellation, coalescence and fragmentation. This 2D model then couples to a 3D model as the lower boundary condition, which drives the evolution of the coronal field through a series of nonlinear forcefree states, via a magnetofrictional relaxation technique. We first apply the magnetofrictional technique to consider the coronal evolution of three basic smallscale photospheric processes: emergence, cancellation and flyby. We consider the interaction of the magnetic features with an overlying coronal magnetic field, and quantify magnetic energy buildup, storage and dissipation. The magnetofrictional technique is then applied to synthetic magnetograms produced from the 2D model, to simulate the evolution of the coronal field in a situation involving many hundreds of magnetic features. We conduct a preliminary analysis of the resultant 3D simulations, considering the magnetic energy stored and dissipated, as well as regions of enhanced velocity and electric current density within the coronal volume. The simulations show that the socalled 'quiet Sun' is not quiet and a significant amount of complex interactions take place.
Fri, 22 Jun 2012 00:00:00 GMT
http://hdl.handle.net/10023/3114
20120622T00:00:00Z
Meyer, Karen Alison
The magnetic carpet is defined to be the smallscale photospheric magnetic field of the quiet Sun. Observations of the magnetic carpet show it to be highly dynamic, where the time taken for all flux within the magnetic carpet to be replaced is on the order of just a few hours. The magnetic carpet is continually evolving due to the Sun's underlying convection and the interaction of smallscale magnetic features with one another. Due to this, the smallscale coronal field of the magnetic carpet is also expected to be highly dynamic and complex. Previous modelling has shown that much of the flux from the magnetic carpet is stored along lowlying closed connections between magnetic features. This indicates that significant coronal heating could occur low down in the smallscale corona. In this thesis, a new twocomponent magnetic field model is developed for the evolution of the magnetic carpet. A 2D model is constructed to realistically simulate the evolution of the photospheric field of the magnetic carpet, where many of the parameters for the model are taken from observational studies. The photospheric model contains a granular and supergranular flow profile to describe the motion of the smallscale magnetic features, and includes the processes of flux emergence, cancellation, coalescence and fragmentation. This 2D model then couples to a 3D model as the lower boundary condition, which drives the evolution of the coronal field through a series of nonlinear forcefree states, via a magnetofrictional relaxation technique. We first apply the magnetofrictional technique to consider the coronal evolution of three basic smallscale photospheric processes: emergence, cancellation and flyby. We consider the interaction of the magnetic features with an overlying coronal magnetic field, and quantify magnetic energy buildup, storage and dissipation. The magnetofrictional technique is then applied to synthetic magnetograms produced from the 2D model, to simulate the evolution of the coronal field in a situation involving many hundreds of magnetic features. We conduct a preliminary analysis of the resultant 3D simulations, considering the magnetic energy stored and dissipated, as well as regions of enhanced velocity and electric current density within the coronal volume. The simulations show that the socalled 'quiet Sun' is not quiet and a significant amount of complex interactions take place.

A highly adaptive three dimensional hybrid vortex method for inviscid flows and helically symmetric vortex equilibria
http://hdl.handle.net/10023/3091
Abstract: This thesis is concerned with threedimensional vortex dynamics, in particular the modelling of vortex structures in an inviscid context. We are motivated by the open problem of regularity of the inviscid equations, i.e. whether or not these equations possess solutions. This problem is manifest in small scales, where vortex filaments are stretched and intensify as they are drawn into increasingly thin tendrils. This creates great difficulty in the investigation of such flows. Our only means of experimentation is to perform numerical simulations, which require exceptionally high resolution to capture the small scale vortex structures.
A new numerical method to solve the inviscid Euler equations for threedimensional, incompressible fluids is presented, with special emphasis on spatial adaptivity to resolve as broad a range of scales as possible in a completely selfsimilar fashion. We present a hybrid vortex method whereby we discretise the vorticity in Lagrangian filaments and perform and inversion to compute velocity on an arbitrary unstructured finitevolume grid. This allows for a twofold adaptivity strategy. First, although naturally spatially adaptive by definition, the vorticity filaments undergo ‘renoding’. We redistribute nodes along the filament to concentrate their density in regions of high curvature. Secondly the Eulerian mesh is adapted to follow high strain by increasing resolution based on local filament dimensions. These features allow vortex stretching and folding to be resolved in a completely automatic and selfsimilar way. The method is validated via well known vortex rings and newly discovered helical vortex equilibria are also used to test the method.
We begin by presenting this new class of threedimensional vortex equilibria which possess helical symmetry. Such vortices are observed in propeller and wind turbine wakes, and their equilibria shapes have until now been unknown. These vortices are described by contours bounding regions of uniform axial vorticity. Material conservation of axial vorticity enables equilibria to be calculated simply by a restriction on the helical stream function. The states are parameterised by their mean radius and centroid position. In the case of a single vortex, the parameter space cannot be fully filled by our numerical approach. We conjecture that multiply connected contours will characterise equilibria where the algorithm fails. We also consider multiple vortices, evenly azimuthally spaced about the origin. In such cases instabilities often lead to a single helical vortex.
Fri, 22 Jun 2012 00:00:00 GMT
http://hdl.handle.net/10023/3091
20120622T00:00:00Z
Lucas, Daniel
This thesis is concerned with threedimensional vortex dynamics, in particular the modelling of vortex structures in an inviscid context. We are motivated by the open problem of regularity of the inviscid equations, i.e. whether or not these equations possess solutions. This problem is manifest in small scales, where vortex filaments are stretched and intensify as they are drawn into increasingly thin tendrils. This creates great difficulty in the investigation of such flows. Our only means of experimentation is to perform numerical simulations, which require exceptionally high resolution to capture the small scale vortex structures.
A new numerical method to solve the inviscid Euler equations for threedimensional, incompressible fluids is presented, with special emphasis on spatial adaptivity to resolve as broad a range of scales as possible in a completely selfsimilar fashion. We present a hybrid vortex method whereby we discretise the vorticity in Lagrangian filaments and perform and inversion to compute velocity on an arbitrary unstructured finitevolume grid. This allows for a twofold adaptivity strategy. First, although naturally spatially adaptive by definition, the vorticity filaments undergo ‘renoding’. We redistribute nodes along the filament to concentrate their density in regions of high curvature. Secondly the Eulerian mesh is adapted to follow high strain by increasing resolution based on local filament dimensions. These features allow vortex stretching and folding to be resolved in a completely automatic and selfsimilar way. The method is validated via well known vortex rings and newly discovered helical vortex equilibria are also used to test the method.
We begin by presenting this new class of threedimensional vortex equilibria which possess helical symmetry. Such vortices are observed in propeller and wind turbine wakes, and their equilibria shapes have until now been unknown. These vortices are described by contours bounding regions of uniform axial vorticity. Material conservation of axial vorticity enables equilibria to be calculated simply by a restriction on the helical stream function. The states are parameterised by their mean radius and centroid position. In the case of a single vortex, the parameter space cannot be fully filled by our numerical approach. We conjecture that multiply connected contours will characterise equilibria where the algorithm fails. We also consider multiple vortices, evenly azimuthally spaced about the origin. In such cases instabilities often lead to a single helical vortex.

Spatial patterns and species coexistence : using spatial statistics to identify underlying ecological processes in plant communities
http://hdl.handle.net/10023/3084
Abstract: The use of spatial statistics to investigate ecological processes in plant communities is becoming increasingly widespread. In diverse communities such as tropical rainforests, analysis of spatial structure may help to unravel the various processes that act and interact to maintain high levels of diversity. In particular, a number of contrasting mechanisms have been suggested to explain species coexistence, and these differ greatly in their practical implications for the ecology and conservation of tropical forests. Traditional firstorder measures of community structure have proved unable to distinguish these mechanisms in practice, but statistics that describe spatial structure may be able to do so. This is of great interest and relevance as spatially explicit data become available for a range of ecological communities and analysis methods for these data become more accessible.
This thesis investigates the potential for inference about underlying ecological processes in plant communities using spatial statistics. Current methodologies for spatial analysis are reviewed and extended, and are used to characterise the spatial signals of the principal theorised mechanisms of coexistence. The sensitivity of a range of spatial statistics to these signals is assessed, and the strength of such signals in natural communities is investigated.
The spatial signals of the processes considered here are found to be strong and robust to modelled stochastic variation. Several new and existing spatial statistics are found to be sensitive to these signals, and offer great promise for inference about underlying processes from empirical data. The relative strengths of particular processes are found to vary between natural communities, with any one theory being insufficient to explain observed patterns. This thesis extends both understanding of species coexistence in diverse plant communities and the methodology for assessing underlying process in particular cases. It demonstrates that the potential of spatial statistics in ecology is great and largely unexplored.
Thu, 01 Nov 2012 00:00:00 GMT
http://hdl.handle.net/10023/3084
20121101T00:00:00Z
Brown, Calum
The use of spatial statistics to investigate ecological processes in plant communities is becoming increasingly widespread. In diverse communities such as tropical rainforests, analysis of spatial structure may help to unravel the various processes that act and interact to maintain high levels of diversity. In particular, a number of contrasting mechanisms have been suggested to explain species coexistence, and these differ greatly in their practical implications for the ecology and conservation of tropical forests. Traditional firstorder measures of community structure have proved unable to distinguish these mechanisms in practice, but statistics that describe spatial structure may be able to do so. This is of great interest and relevance as spatially explicit data become available for a range of ecological communities and analysis methods for these data become more accessible.
This thesis investigates the potential for inference about underlying ecological processes in plant communities using spatial statistics. Current methodologies for spatial analysis are reviewed and extended, and are used to characterise the spatial signals of the principal theorised mechanisms of coexistence. The sensitivity of a range of spatial statistics to these signals is assessed, and the strength of such signals in natural communities is investigated.
The spatial signals of the processes considered here are found to be strong and robust to modelled stochastic variation. Several new and existing spatial statistics are found to be sensitive to these signals, and offer great promise for inference about underlying processes from empirical data. The relative strengths of particular processes are found to vary between natural communities, with any one theory being insufficient to explain observed patterns. This thesis extends both understanding of species coexistence in diverse plant communities and the methodology for assessing underlying process in particular cases. It demonstrates that the potential of spatial statistics in ecology is great and largely unexplored.

Vessel noise affects beaked whale behavior : Results of a dedicated acoustic response study
http://hdl.handle.net/10023/3078
Abstract: Some beaked whale species are susceptible to the detrimental effects of anthropogenic noise. Most studies have concentrated on the effects of military sonar, but other forms of acoustic disturbance (e.g. shipping noise) may disrupt behavior. An experiment involving the exposure of target whale groups to intense vesselgenerated noise tested how these exposures influenced the foraging behavior of Blainville’s beaked whales (Mesoplodon densirostris) in the Tongue of the Ocean (Bahamas). A military array of bottommounted hydrophones was used to measure the response based upon changes in the spatial and temporal pattern of vocalizations. The archived acoustic data were used to compute metrics the echolocationbased foraging behavior for 16 targeted groups, 10 groups further away on the range, and 26 nonexposed groups. The duration of foraging bouts was not significantly affected by the exposure. Changes in the hydrophone over which the group was most frequently detected occurred as the animals moved around within a foraging bout, and their number was significantly less the closer the whales were to the sound source. Nonexposed groups also had significantly more changes in the primary hydrophone than exposed groups irrespective of distance. Our results suggested that broadband ship noise caused a significant change in beaked whale behavior up to at least 5.2 kilometers away from the vessel. The observed change could potentially correspond to a restriction in the movement of groups, a period of more directional travel, a reduction in the number of individuals clicking within the group, or a response to changes in prey movement.
Fri, 03 Aug 2012 00:00:00 GMT
http://hdl.handle.net/10023/3078
20120803T00:00:00Z
Pirotta, Enrico
Milor, Rachel
Quick, Nicola Jane
Moretti, David
Dimarzio, Nancy
Tyack, Peter Lloyd
Boyd, Ian
Hastie, Gordon Drummond
Some beaked whale species are susceptible to the detrimental effects of anthropogenic noise. Most studies have concentrated on the effects of military sonar, but other forms of acoustic disturbance (e.g. shipping noise) may disrupt behavior. An experiment involving the exposure of target whale groups to intense vesselgenerated noise tested how these exposures influenced the foraging behavior of Blainville’s beaked whales (Mesoplodon densirostris) in the Tongue of the Ocean (Bahamas). A military array of bottommounted hydrophones was used to measure the response based upon changes in the spatial and temporal pattern of vocalizations. The archived acoustic data were used to compute metrics the echolocationbased foraging behavior for 16 targeted groups, 10 groups further away on the range, and 26 nonexposed groups. The duration of foraging bouts was not significantly affected by the exposure. Changes in the hydrophone over which the group was most frequently detected occurred as the animals moved around within a foraging bout, and their number was significantly less the closer the whales were to the sound source. Nonexposed groups also had significantly more changes in the primary hydrophone than exposed groups irrespective of distance. Our results suggested that broadband ship noise caused a significant change in beaked whale behavior up to at least 5.2 kilometers away from the vessel. The observed change could potentially correspond to a restriction in the movement of groups, a period of more directional travel, a reduction in the number of individuals clicking within the group, or a response to changes in prey movement.

Growth of generating sets for direct powers of classical algebraic structures
http://hdl.handle.net/10023/3058
Abstract: For an algebraic structure A denote by d(A) the smallest size of a generating set for A, and let d(A)=(d(A),d(A2),d(A3),…), where An denotes a direct power of A. In this paper we investigate the asymptotic behaviour of the sequence d(A) when A is one of the classical structures—a group, ring, module, algebra or Lie algebra. We show that if A is finite then d(A) grows either linearly or logarithmically. In the infinite case constant growth becomes another possibility; in particular, if A is an infinite simple structure belonging to one of the above classes then d(A) is eventually constant. Where appropriate we frame our exposition within the general theory of congruence permutable varieties.
Sun, 01 Aug 2010 00:00:00 GMT
http://hdl.handle.net/10023/3058
20100801T00:00:00Z
Quick, Martyn
Ruskuc, Nik
For an algebraic structure A denote by d(A) the smallest size of a generating set for A, and let d(A)=(d(A),d(A2),d(A3),…), where An denotes a direct power of A. In this paper we investigate the asymptotic behaviour of the sequence d(A) when A is one of the classical structures—a group, ring, module, algebra or Lie algebra. We show that if A is finite then d(A) grows either linearly or logarithmically. In the infinite case constant growth becomes another possibility; in particular, if A is an infinite simple structure belonging to one of the above classes then d(A) is eventually constant. Where appropriate we frame our exposition within the general theory of congruence permutable varieties.

Numerical simulation of shearinduced instabilities in internal solitary waves
http://hdl.handle.net/10023/3054
Abstract: A numerical method that employs a combination of contour advection and pseudospectral techniques is used to simulate shearinduced instabilities in an internal solitary wave (ISW). A threelayer configuration for the background stratification, in which a linearly stratified intermediate layer is sandwiched between two homogeneous ones, is considered throughout. The flow is assumed to satisfy the inviscid, incompressible, Oberbeck–Boussinesq equations in two dimensions. Simulations are initialized by fully nonlinear, steadystate, ISWs. The results of the simulations show that the instability takes place in the pycnocline and manifests itself as Kelvin–Helmholtz billows. The billows form near the trough of the wave, subsequently grow and disturb the tail. Both the critical Richardson number (Ric) and the critical amplitude required for instability are found to be functions of the ratio of the undisturbed layer thicknesses. It is shown, therefore, that the constant, critical bound for instability in ISWs given in Barad & Fringer (J. Fluid Mech., vol. 644, 2010, pp. 61–95), namely Ric = 0.1 ± 0.01 , is not a sufficient condition for instability. It is also shown that the critical value of Lx/λ required for instability, where Lx is the length of the region in a wave in which Ri < 1/4 and λ is the halfwidth of the wave, is sensitive to the ratio of the layer thicknesses. Similarly, a linear stability analysis reveals that δiTw (where δi is the growth rate of the instability averaged over Tw, the period in which parcels of fluid are subjected to Ri < 1/4) is very sensitive to the transition between the undisturbed pycnocline and the homogeneous layers, and the amplitude of the wave. Therefore, the alternative tests for instability presented in Fructus et al. (J. Fluid Mech., vol. 620, 2009, pp. 1–29) and Barad & Fringer (J. Fluid Mech., vol. 644, 2010, pp. 61–95), respectively, namely Lx/λ ≥ 0.86 and δiTw > 5 , are shown to be valid only for a limited parameter range.
Description: This work was supported by the UK Engineering and Physical Sciences Research Council [grant number EP/F030622/1]
Sun, 25 Sep 2011 00:00:00 GMT
http://hdl.handle.net/10023/3054
20110925T00:00:00Z
Carr, Magda
King, Stuart Edward
Dritschel, David Gerard
A numerical method that employs a combination of contour advection and pseudospectral techniques is used to simulate shearinduced instabilities in an internal solitary wave (ISW). A threelayer configuration for the background stratification, in which a linearly stratified intermediate layer is sandwiched between two homogeneous ones, is considered throughout. The flow is assumed to satisfy the inviscid, incompressible, Oberbeck–Boussinesq equations in two dimensions. Simulations are initialized by fully nonlinear, steadystate, ISWs. The results of the simulations show that the instability takes place in the pycnocline and manifests itself as Kelvin–Helmholtz billows. The billows form near the trough of the wave, subsequently grow and disturb the tail. Both the critical Richardson number (Ric) and the critical amplitude required for instability are found to be functions of the ratio of the undisturbed layer thicknesses. It is shown, therefore, that the constant, critical bound for instability in ISWs given in Barad & Fringer (J. Fluid Mech., vol. 644, 2010, pp. 61–95), namely Ric = 0.1 ± 0.01 , is not a sufficient condition for instability. It is also shown that the critical value of Lx/λ required for instability, where Lx is the length of the region in a wave in which Ri < 1/4 and λ is the halfwidth of the wave, is sensitive to the ratio of the layer thicknesses. Similarly, a linear stability analysis reveals that δiTw (where δi is the growth rate of the instability averaged over Tw, the period in which parcels of fluid are subjected to Ri < 1/4) is very sensitive to the transition between the undisturbed pycnocline and the homogeneous layers, and the amplitude of the wave. Therefore, the alternative tests for instability presented in Fructus et al. (J. Fluid Mech., vol. 620, 2009, pp. 1–29) and Barad & Fringer (J. Fluid Mech., vol. 644, 2010, pp. 61–95), respectively, namely Lx/λ ≥ 0.86 and δiTw > 5 , are shown to be valid only for a limited parameter range.

Continued fractions which correspond to two series expansions and the strong Hamburger moment problem
http://hdl.handle.net/10023/2977
Abstract: Just as the denominator polynomials of a Jfraction are
orthogonal polynomials with respect to some moment functional, the
denominator polynomials of an Mfraction are shown to satisfy a skew
orthogonality relation with respect to a stronger moment functional.
Many of the properties of the numerators and denominators of an M
fraction are also studied using this pseudo orthogonality relation
of the denominator polynomials. Properties of the zeros of the
denominator polynomials when the associated moment functional is
positive definite are also considered.
A type of continued fraction, referred to as a Jfraction, is
shown to correspond to a power series about the origin and to another
power series about infinity such that the successive convergents of
this fraction include two more additional terms of anyone of the
power series. Given the power series expansions, a method of
obtaining such a Jfraction, whenever it exists, is also looked at.
The first complete proof of the so called strong Hamburger moment
problem using a continued fraction is given. In this case the
continued fraction is a Jfraction.
Finally a special class of Jfraction, referred to as positive
definite Jfractions, is studied in detail.
The four chapters of this thesis are divided into sections.
Each section is given a section number which is made up of the
chapter number followed by the number of the section within the
chapter. The equations in the thesis have an equation number
consisting of the section number followed by the number of the
equation within that section.
In Chapter One, in addition to looking at some of the
historical and recent developments of corresponding continued
fractions and their applications, we also present some preliminaries.
Chapter Two deals with a different approach of understanding
the properties of the numerators and denominators of corresponding
(two point) rational functions and, continued fractions. This
approach, which is based on a pseudo orthogonality relation of the
denominator polynomials of the corresponding rational functions,
provides an insight into understanding the moment problems. In
particular, results are established which suggest a possible type
of continued fraction for solving the strong Hamburger moment
problem.
In the third chapter we study in detail the existence
conditions and corresponding properties of this new type of continued
fraction, which we call Jfractions. A method of derivation of one
of these 3fractions is also considered. In the same chapter we also
look at the all important application of solving the strong Hamburger
moment problem, using these 3fractions.
The fourth and final chapter is devoted entirely to the study
of the convergence behaviour of a certain class of Jfractions,
namely positive definite Jfractions. This study also provides some
interesting convergence criteria for a real and regular 3fraction.
Finally a word concerning the literature on continued fractions
and moment problems. The more recent and uptodate exposition on
the analytic theory of continued fractions and their applications is
the text of Jones and Thron [1980]. The two volumes of Baker and
GravesMorris [1981] provide a very good treatment on one of the
computational aspects of the continued fractions, namely Pade
approximants. There are also the earlier texts of Wall [1948] and
Khovanskii [1963], in which the former gives an extensive insight
into the analytic theory of continued fractions while the latter,
being simpler, remains the ideal book for the beginner. In his
treatise on Applied and Computational Complex Analysis, Henrici
[1977] has also included an excellent chapter on continued fractions.
Wall [1948] also includes a few chapters on moment problems and
related areas. A much wider treatment of the classical moment
problems is provided in the excellent texts of Shohat and Tamarkin
[1943] and Akhieser [1965].
Sun, 01 Jan 1984 00:00:00 GMT
http://hdl.handle.net/10023/2977
19840101T00:00:00Z
Sri Ranga, A.
Just as the denominator polynomials of a Jfraction are
orthogonal polynomials with respect to some moment functional, the
denominator polynomials of an Mfraction are shown to satisfy a skew
orthogonality relation with respect to a stronger moment functional.
Many of the properties of the numerators and denominators of an M
fraction are also studied using this pseudo orthogonality relation
of the denominator polynomials. Properties of the zeros of the
denominator polynomials when the associated moment functional is
positive definite are also considered.
A type of continued fraction, referred to as a Jfraction, is
shown to correspond to a power series about the origin and to another
power series about infinity such that the successive convergents of
this fraction include two more additional terms of anyone of the
power series. Given the power series expansions, a method of
obtaining such a Jfraction, whenever it exists, is also looked at.
The first complete proof of the so called strong Hamburger moment
problem using a continued fraction is given. In this case the
continued fraction is a Jfraction.
Finally a special class of Jfraction, referred to as positive
definite Jfractions, is studied in detail.
The four chapters of this thesis are divided into sections.
Each section is given a section number which is made up of the
chapter number followed by the number of the section within the
chapter. The equations in the thesis have an equation number
consisting of the section number followed by the number of the
equation within that section.
In Chapter One, in addition to looking at some of the
historical and recent developments of corresponding continued
fractions and their applications, we also present some preliminaries.
Chapter Two deals with a different approach of understanding
the properties of the numerators and denominators of corresponding
(two point) rational functions and, continued fractions. This
approach, which is based on a pseudo orthogonality relation of the
denominator polynomials of the corresponding rational functions,
provides an insight into understanding the moment problems. In
particular, results are established which suggest a possible type
of continued fraction for solving the strong Hamburger moment
problem.
In the third chapter we study in detail the existence
conditions and corresponding properties of this new type of continued
fraction, which we call Jfractions. A method of derivation of one
of these 3fractions is also considered. In the same chapter we also
look at the all important application of solving the strong Hamburger
moment problem, using these 3fractions.
The fourth and final chapter is devoted entirely to the study
of the convergence behaviour of a certain class of Jfractions,
namely positive definite Jfractions. This study also provides some
interesting convergence criteria for a real and regular 3fraction.
Finally a word concerning the literature on continued fractions
and moment problems. The more recent and uptodate exposition on
the analytic theory of continued fractions and their applications is
the text of Jones and Thron [1980]. The two volumes of Baker and
GravesMorris [1981] provide a very good treatment on one of the
computational aspects of the continued fractions, namely Pade
approximants. There are also the earlier texts of Wall [1948] and
Khovanskii [1963], in which the former gives an extensive insight
into the analytic theory of continued fractions while the latter,
being simpler, remains the ideal book for the beginner. In his
treatise on Applied and Computational Complex Analysis, Henrici
[1977] has also included an excellent chapter on continued fractions.
Wall [1948] also includes a few chapters on moment problems and
related areas. A much wider treatment of the classical moment
problems is provided in the excellent texts of Shohat and Tamarkin
[1943] and Akhieser [1965].

Presentations and efficiency of semigroups
http://hdl.handle.net/10023/2843
Abstract: In this thesis we consider in detail the following two problems for semigroups:
(i) When are semigroups finitely generated and presented?
(ii) Which families of semigroups can be efficiently presented?
We also consider some other finiteness conditions for semigroups, homology of
semigroups and wreath product of groups.
In Chapter 2 we investigate finite presentability and some other finiteness conditions
for the Odirect union of semigroups with zero. In Chapter 3 we investigate
finite generation and presentability of Rees matrix semigroups over semigroups.
We find necessary and sufficient conditions for finite generation and presentability.
In Chapter 4 we investigate some other finiteness conditions for Rees matrix
semigroups.
In Chapter 5 we consider groups as semigroups and investigate their semigroup
efficiency. In Chapter 6 we look at "proper" semigroups, that is semigroups
that are not groups. We first give examples of efficient and inefficient "proper"
semigroups by computing their homology and finding their minimal presentations.
In Chapter 7 we compute the second homology of finite simple semigroups and
find a "small" presentation for them. If that "small" presentation has a special
relation, we prove that finite simple semigroups are efficient. Finally, in Chapter
8, we investigate the efficiency of wreath products of finite groups as groups and
as semigroups. We give more examples of efficient groups and inefficient groups.
Thu, 01 Jan 1998 00:00:00 GMT
http://hdl.handle.net/10023/2843
19980101T00:00:00Z
Ayik, Hayrullah
In this thesis we consider in detail the following two problems for semigroups:
(i) When are semigroups finitely generated and presented?
(ii) Which families of semigroups can be efficiently presented?
We also consider some other finiteness conditions for semigroups, homology of
semigroups and wreath product of groups.
In Chapter 2 we investigate finite presentability and some other finiteness conditions
for the Odirect union of semigroups with zero. In Chapter 3 we investigate
finite generation and presentability of Rees matrix semigroups over semigroups.
We find necessary and sufficient conditions for finite generation and presentability.
In Chapter 4 we investigate some other finiteness conditions for Rees matrix
semigroups.
In Chapter 5 we consider groups as semigroups and investigate their semigroup
efficiency. In Chapter 6 we look at "proper" semigroups, that is semigroups
that are not groups. We first give examples of efficient and inefficient "proper"
semigroups by computing their homology and finding their minimal presentations.
In Chapter 7 we compute the second homology of finite simple semigroups and
find a "small" presentation for them. If that "small" presentation has a special
relation, we prove that finite simple semigroups are efficient. Finally, in Chapter
8, we investigate the efficiency of wreath products of finite groups as groups and
as semigroups. We give more examples of efficient groups and inefficient groups.

Solar flare particle acceleration in collapsing magnetic traps
http://hdl.handle.net/10023/2839
Abstract: The topic of this thesis is a detailed investigation of different aspects of the particle acceleration mechanisms operating in Collapsing Magnetic Traps (CMTs), which have been suggested as one possible mechanism for particle acceleration during solar flares.
The acceleration processes in CMTs are investigated using guiding centre test particle calculations.
Results including terms of different orders in the guiding centre approximation are compared to help identify which of the terms are important for the acceleration of particles. For a basic 2D CMT model the effects of different initial conditions (position, kinetic energy and pitch angle) of particles are investigated in detail. The main result is that the particles that gain most energy are those with initial pitch angles close to 90° and start in weak field regions in the centre of the CMT. The dominant acceleration mechanism for these particles is betatron acceleration, but other
particles also show signatures of Fermi acceleration.
The basic CMT model is then extended by (a) including a magnetic field component in the invariant direction and (b) by making it asymmetric. It is found that the addition of a guide field does not change the characteristics of particle acceleration very much, but for the asymmetric models the associated energy gain is found to be much smaller than in symmetric models, because the
particles can no longer remain very close to the trap centre throughout their orbit.
The test particle method is then also applied to a CMT model from the literature which contains a magnetic Xline and open and closed field lines and the results are compared with the previous results and the findings in the literature.
Finally, the theoretical framework of CMT models is extended to 2.5D models with shear flow and to fully 3D models, allowing the construction of more realistic CMT models in the future.
Fri, 22 Jun 2012 00:00:00 GMT
http://hdl.handle.net/10023/2839
20120622T00:00:00Z
Grady, Keith J.
The topic of this thesis is a detailed investigation of different aspects of the particle acceleration mechanisms operating in Collapsing Magnetic Traps (CMTs), which have been suggested as one possible mechanism for particle acceleration during solar flares.
The acceleration processes in CMTs are investigated using guiding centre test particle calculations.
Results including terms of different orders in the guiding centre approximation are compared to help identify which of the terms are important for the acceleration of particles. For a basic 2D CMT model the effects of different initial conditions (position, kinetic energy and pitch angle) of particles are investigated in detail. The main result is that the particles that gain most energy are those with initial pitch angles close to 90° and start in weak field regions in the centre of the CMT. The dominant acceleration mechanism for these particles is betatron acceleration, but other
particles also show signatures of Fermi acceleration.
The basic CMT model is then extended by (a) including a magnetic field component in the invariant direction and (b) by making it asymmetric. It is found that the addition of a guide field does not change the characteristics of particle acceleration very much, but for the asymmetric models the associated energy gain is found to be much smaller than in symmetric models, because the
particles can no longer remain very close to the trap centre throughout their orbit.
The test particle method is then also applied to a CMT model from the literature which contains a magnetic Xline and open and closed field lines and the results are compared with the previous results and the findings in the literature.
Finally, the theoretical framework of CMT models is extended to 2.5D models with shear flow and to fully 3D models, allowing the construction of more realistic CMT models in the future.

Semigroups of orderdecreasing transformations
http://hdl.handle.net/10023/2834
Abstract: Let X be a totally ordered set and consider the semigroups of orderdecreasing (increasing) full (partial, partial onetoone) transformations of X. In this
Thesis the study of orderincreasing full (partial, partial onetoone) transformations
has been reduced to that of orderdecreasing full (partial, partial onetoone)
transformations and the study of orderdecreasing partial transformations to that of
orderdecreasing full transformations for both the finite and infinite cases.
For the finite orderdecreasing full (partial onetoone) transformation
semigroups, we obtain results analogous to Howie (1971) and Howie and McFadden
(1990) concerning products of idempotents (quasiidempotents), and concerning
combinatorial and rank properties. By contrast with the semigroups of orderpreserving
transformations and the full transformation semigroup, the semigroups of orderdecreasing
full (partial onetoone) transformations and their Rees quotient semigroups
are not regular. They are, however, abundant (type A) semigroups in the sense of
Fountain (1982,1979). An explicit characterisation of the minimum semilattice
congruence on the finite semigroups of orderdecreasing transformations and their Rees
quotient semigroups is obtained.
If X is an infinite chain then the semigroup S of orderdecreasing full
transformations need not be abundant. A necessary and sufficient condition on X is
obtained for S to be abundant. By contrast, for every chain X the semigroup of
orderdecreasing partial onetoone transformations is type A.
The ranks of the nilpotent subsemigroups of the finite semigroups of orderdecreasing
full (partial onetoone) transformations have been investigated.
Wed, 01 Jan 1992 00:00:00 GMT
http://hdl.handle.net/10023/2834
19920101T00:00:00Z
Umar, Abdullahi
Let X be a totally ordered set and consider the semigroups of orderdecreasing (increasing) full (partial, partial onetoone) transformations of X. In this
Thesis the study of orderincreasing full (partial, partial onetoone) transformations
has been reduced to that of orderdecreasing full (partial, partial onetoone)
transformations and the study of orderdecreasing partial transformations to that of
orderdecreasing full transformations for both the finite and infinite cases.
For the finite orderdecreasing full (partial onetoone) transformation
semigroups, we obtain results analogous to Howie (1971) and Howie and McFadden
(1990) concerning products of idempotents (quasiidempotents), and concerning
combinatorial and rank properties. By contrast with the semigroups of orderpreserving
transformations and the full transformation semigroup, the semigroups of orderdecreasing
full (partial onetoone) transformations and their Rees quotient semigroups
are not regular. They are, however, abundant (type A) semigroups in the sense of
Fountain (1982,1979). An explicit characterisation of the minimum semilattice
congruence on the finite semigroups of orderdecreasing transformations and their Rees
quotient semigroups is obtained.
If X is an infinite chain then the semigroup S of orderdecreasing full
transformations need not be abundant. A necessary and sufficient condition on X is
obtained for S to be abundant. By contrast, for every chain X the semigroup of
orderdecreasing partial onetoone transformations is type A.
The ranks of the nilpotent subsemigroups of the finite semigroups of orderdecreasing
full (partial onetoone) transformations have been investigated.

Semigroup presentations
http://hdl.handle.net/10023/2821
Abstract: In this thesis we consider in detail the following two fundamental problems for
semigroup presentations:
1. Given a semigroup find a presentation defining it.
2. Given a presentation describe the semigroup defined by it.
We also establish two links between these two approaches: semigroup constructions
and computational methods.
After an introduction to semigroup presentations in Chapter 3, in Chapters 4
and 5 we consider the first of the two approaches. The semigroups we examine in
these two chapters include completely Osimple semigroups, transformation semigroups,
matrix semigroups and various endomorphism semigroups. In Chapter 6
we find presentations for the following semi group constructions: wreath product,
BruckReilly extension, Schiitzenberger product, strong semilattices of monoids,
Rees matrix semigroups, ideal extensions and subsemigroups. We investigate in
more detail presentations for subsemigroups in Chapters 7 and 10, where we prove
a number of ReidemeisterSchreier type results for semigroups. In Chapter 9
we examine the connection between the semi group and the group defined by the
same presentation. The general results from Chapters 6, 7, 9 and 10 are applied
in Chapters 8, 11, 12 and 13 to subsemigroups of free semigroups, Fibonacci
semigroups, semigroups defined by Coxeter type presentations and one relator
products of cyclic groups. Finally, in Chapter 14 we describe the ToddCoxeter
enumeration procedure and introduce three modifications of this procedure.
Sun, 01 Jan 1995 00:00:00 GMT
http://hdl.handle.net/10023/2821
19950101T00:00:00Z
Ruškuc, Nik
In this thesis we consider in detail the following two fundamental problems for
semigroup presentations:
1. Given a semigroup find a presentation defining it.
2. Given a presentation describe the semigroup defined by it.
We also establish two links between these two approaches: semigroup constructions
and computational methods.
After an introduction to semigroup presentations in Chapter 3, in Chapters 4
and 5 we consider the first of the two approaches. The semigroups we examine in
these two chapters include completely Osimple semigroups, transformation semigroups,
matrix semigroups and various endomorphism semigroups. In Chapter 6
we find presentations for the following semi group constructions: wreath product,
BruckReilly extension, Schiitzenberger product, strong semilattices of monoids,
Rees matrix semigroups, ideal extensions and subsemigroups. We investigate in
more detail presentations for subsemigroups in Chapters 7 and 10, where we prove
a number of ReidemeisterSchreier type results for semigroups. In Chapter 9
we examine the connection between the semi group and the group defined by the
same presentation. The general results from Chapters 6, 7, 9 and 10 are applied
in Chapters 8, 11, 12 and 13 to subsemigroups of free semigroups, Fibonacci
semigroups, semigroups defined by Coxeter type presentations and one relator
products of cyclic groups. Finally, in Chapter 14 we describe the ToddCoxeter
enumeration procedure and introduce three modifications of this procedure.

Green index in semigroups : generators, presentations and automatic structures
http://hdl.handle.net/10023/2760
Abstract: The Green index of a subsemigroup T of a semigroup S is given by counting strong orbits in the complement S n T under the natural actions of T on S via right and left multiplication. This partitions the complement S nT into Trelative H classes, in the sense of Wallace, and with each such class there is a naturally associated group called the relative Schützenberger group. If the Rees index ΙS n TΙ is finite, T also has finite Green index in S. If S is a group and T a subgroup then T has finite Green index in S if and only if it has finite group index in S. Thus Green index provides a common generalisation of Rees index and group index. We prove a rewriting theorem which shows how generating sets for S may be used to obtain generating sets for T and the Schützenberger groups, and vice versa. We also give a method for constructing a presentation for S from given presentations of T and the Schützenberger groups. These results are then used to show that several important properties are preserved when passing to finite Green index subsemigroups or extensions, including: finite generation, solubility of the word problem, growth type, automaticity (for subsemigroups), finite presentability (for extensions) and finite Malcev presentability (in the case of groupembeddable semigroups).
Sun, 01 Jan 2012 00:00:00 GMT
http://hdl.handle.net/10023/2760
20120101T00:00:00Z
Cain, A.J.
Gray, R
Ruskuc, Nik
The Green index of a subsemigroup T of a semigroup S is given by counting strong orbits in the complement S n T under the natural actions of T on S via right and left multiplication. This partitions the complement S nT into Trelative H classes, in the sense of Wallace, and with each such class there is a naturally associated group called the relative Schützenberger group. If the Rees index ΙS n TΙ is finite, T also has finite Green index in S. If S is a group and T a subgroup then T has finite Green index in S if and only if it has finite group index in S. Thus Green index provides a common generalisation of Rees index and group index. We prove a rewriting theorem which shows how generating sets for S may be used to obtain generating sets for T and the Schützenberger groups, and vice versa. We also give a method for constructing a presentation for S from given presentations of T and the Schützenberger groups. These results are then used to show that several important properties are preserved when passing to finite Green index subsemigroups or extensions, including: finite generation, solubility of the word problem, growth type, automaticity (for subsemigroups), finite presentability (for extensions) and finite Malcev presentability (in the case of groupembeddable semigroups).

The visible part of plane selfsimilar sets
http://hdl.handle.net/10023/2756
Abstract: Given a compact subset F of R2, the visible part VθF of F from direction θ is the set of x in F such that the halfline from x in direction θ intersects F only at x. It is suggested that if dimH F ≥ 1 then dimH VθF = 1 for almost all θ , where dimH denotes Hausdorff dimension. We conrm this when F is a selfsimilar set satisfying the convex open set condition and such that the orthogonal projection of F onto every line is an interval. In particular the underlying similarities may involve arbitrary rotations and F need not be connected.
Description: JMF was supported by an EPSRC grant whilst undertaking this work.
Tue, 01 Jan 2013 00:00:00 GMT
http://hdl.handle.net/10023/2756
20130101T00:00:00Z
Falconer, Kenneth John
Fraser, Jonathan Macdonald
Given a compact subset F of R2, the visible part VθF of F from direction θ is the set of x in F such that the halfline from x in direction θ intersects F only at x. It is suggested that if dimH F ≥ 1 then dimH VθF = 1 for almost all θ , where dimH denotes Hausdorff dimension. We conrm this when F is a selfsimilar set satisfying the convex open set condition and such that the orthogonal projection of F onto every line is an interval. In particular the underlying similarities may involve arbitrary rotations and F need not be connected.

Global analysis of cetacean linetransect surveys : detecting trends in cetacean density
http://hdl.handle.net/10023/2747
Abstract: Measuring the effect of anthropogenic change on cetacean populations is hampered by our lack of understanding about population status and a lack of power in the available data to detect trends in abundance. Often longterm data from repeated surveys are lacking, and alternative approaches to trend detection must be considered. We utilised an existing database of line transect survey records to determine whether temporal trends could be detected when survey effort from around the world was combined. We extracted density estimates for 25 species and fitted generalised additive models (GAMs) to investigate whether taxonomic, spatial or methodological differences among systematic linetransect surveys affect estimates of density and whether we can identify temporal trends in the data once these factors are accounted for. The selected GAM consisted of 2 parts: an intercept term that was a complex interaction of taxonomic, spatial and methodological factors and a smooth temporal term with trends varying by family and ocean basin. We discuss the trends found and assess the suitability of published density estimates for detecting temporal trends using retrospective power analysis. In conclusion, increasing sample size through combining survey effort across a global scale does not necessarily result in sufficient power to detect trends because of the extent of variability across surveys, species and oceans. Instead, results from repeated dedicated surveys designed specifically for the species and geographical region of interest should be used to inform conservation and management.
Mon, 07 May 2012 00:00:00 GMT
http://hdl.handle.net/10023/2747
20120507T00:00:00Z
Jewell, Rebecca Lucy
Thomas, Len
Harris, Catriona M
Kaschner, Kristin
Wiff, Rodrigo Alexis
Hammond, Philip Steven
Quick, Nicola Jane
Measuring the effect of anthropogenic change on cetacean populations is hampered by our lack of understanding about population status and a lack of power in the available data to detect trends in abundance. Often longterm data from repeated surveys are lacking, and alternative approaches to trend detection must be considered. We utilised an existing database of line transect survey records to determine whether temporal trends could be detected when survey effort from around the world was combined. We extracted density estimates for 25 species and fitted generalised additive models (GAMs) to investigate whether taxonomic, spatial or methodological differences among systematic linetransect surveys affect estimates of density and whether we can identify temporal trends in the data once these factors are accounted for. The selected GAM consisted of 2 parts: an intercept term that was a complex interaction of taxonomic, spatial and methodological factors and a smooth temporal term with trends varying by family and ocean basin. We discuss the trends found and assess the suitability of published density estimates for detecting temporal trends using retrospective power analysis. In conclusion, increasing sample size through combining survey effort across a global scale does not necessarily result in sufficient power to detect trends because of the extent of variability across surveys, species and oceans. Instead, results from repeated dedicated surveys designed specifically for the species and geographical region of interest should be used to inform conservation and management.

Applications of statistics in flood frequency analysis
http://hdl.handle.net/10023/2666
Abstract: Estimation of the probability of occurrence of future flood events at one
or more locations across a river system is frequently required for the design of
bridges, culverts, spillways, dams and other engineering works. This study
investigates some of the statistical aspects for estimating the flood frequency
distribution at a single site and on regional basis.
It is demonstrated that generalized logistic (GL) distribution has many
properties well suited for the modelling of flood frequency data. The GL
distribution performs better than the other commonly recommended flood frequency
distributions in terms of several key properties. Specifically, it is capable of
reproducing almost the same degree of skewness typically present in observed
flood data. It appears to be more robust to the presence of extreme outliers in the
upper tail of the distribution. It has a relatively simpler mathematical form. Thus all
the well known methods of parameter estimation can be easily implemented.
It is shown that the method of probability weighted moments (PWM)
using the conventionally recommended plotting position substantially effects the
estimation of the shape parameter of the generalized extreme value (GEV)
distribution by relocating the annual maximum flood series. A location invariant
plotting position is introduced to use in estimating, by the method of PWM, the
parameters of the GEV and the GL distributions.
Tests based on empirical distribution function (EDF) statistics are
proposed to assess the goodness of fit of the flood frequency distributions. A
modified EDF test is derived that gives greater emphasis to the upper tail of a
distribution which is more important for flood frequency prediction. Significance
points are derived for the GEV and GL distributions when the parameters are to be
estimated from the sample data by the method of PWMs. The critical points are
considerably smaller than for the case where the parameters of a distribution are
assumed to be specified. Approximate formulae over the whole range of the
distribution for these tests are also developed which can be used for regional
assessment of GEV and GL models based on all the annual maximum series
simultaneously in a hydrological region.
In order to pool atsite flood data across a region into a single series for
regional analysis, the effect of standardization by atsite mean on the estimation of
the regional shape parameter of the GEV distribution is examined. Our simulation
study based on various synthetic regions reveals that the standardization by the atsite
mean underestimates the shape parameter of the GEV by about 30% of its true
value and also contributes to the separation of skewness of observed and simulated
floods. A two parameter standardization by the atsite estimates of location and
scale parameters is proposed. It does not distort the shape of the flood frequency
data in the pooling process. Therefore, it offers significantly improved estimate of
the shape parameter, allows pooling data with heterogeneous coefficients of
variation and helps to explain the separation of skewness effect.
Regions on the basis of flood statistics LCV and USKEW are derived
for Scotland and North England. Only about 50% of the basins could be correctly
identified as belonging to these regions by a set of seven catchment characteristics.
The alternative approach of grouping basins solely on the basis of physical
properties is preferable. Six physically homogeneous groups of basins are
identified by WARD's multivariate clustering algorithm using the same seven
characteristics. These regions have hydrological homogeneity in addition to their
physical homogeneity. Dimensionless regional flood frequency curves are produced
by fitting GEV and GL distributions for each region. The GEV regional growth
curves imply a larger return period for a given magnitude flood. When floods are
described by GL model the respective return periods are considerably smaller.
Sun, 01 Jan 1989 00:00:00 GMT
http://hdl.handle.net/10023/2666
19890101T00:00:00Z
Ahmad, Muhammad Idrees
Estimation of the probability of occurrence of future flood events at one
or more locations across a river system is frequently required for the design of
bridges, culverts, spillways, dams and other engineering works. This study
investigates some of the statistical aspects for estimating the flood frequency
distribution at a single site and on regional basis.
It is demonstrated that generalized logistic (GL) distribution has many
properties well suited for the modelling of flood frequency data. The GL
distribution performs better than the other commonly recommended flood frequency
distributions in terms of several key properties. Specifically, it is capable of
reproducing almost the same degree of skewness typically present in observed
flood data. It appears to be more robust to the presence of extreme outliers in the
upper tail of the distribution. It has a relatively simpler mathematical form. Thus all
the well known methods of parameter estimation can be easily implemented.
It is shown that the method of probability weighted moments (PWM)
using the conventionally recommended plotting position substantially effects the
estimation of the shape parameter of the generalized extreme value (GEV)
distribution by relocating the annual maximum flood series. A location invariant
plotting position is introduced to use in estimating, by the method of PWM, the
parameters of the GEV and the GL distributions.
Tests based on empirical distribution function (EDF) statistics are
proposed to assess the goodness of fit of the flood frequency distributions. A
modified EDF test is derived that gives greater emphasis to the upper tail of a
distribution which is more important for flood frequency prediction. Significance
points are derived for the GEV and GL distributions when the parameters are to be
estimated from the sample data by the method of PWMs. The critical points are
considerably smaller than for the case where the parameters of a distribution are
assumed to be specified. Approximate formulae over the whole range of the
distribution for these tests are also developed which can be used for regional
assessment of GEV and GL models based on all the annual maximum series
simultaneously in a hydrological region.
In order to pool atsite flood data across a region into a single series for
regional analysis, the effect of standardization by atsite mean on the estimation of
the regional shape parameter of the GEV distribution is examined. Our simulation
study based on various synthetic regions reveals that the standardization by the atsite
mean underestimates the shape parameter of the GEV by about 30% of its true
value and also contributes to the separation of skewness of observed and simulated
floods. A two parameter standardization by the atsite estimates of location and
scale parameters is proposed. It does not distort the shape of the flood frequency
data in the pooling process. Therefore, it offers significantly improved estimate of
the shape parameter, allows pooling data with heterogeneous coefficients of
variation and helps to explain the separation of skewness effect.
Regions on the basis of flood statistics LCV and USKEW are derived
for Scotland and North England. Only about 50% of the basins could be correctly
identified as belonging to these regions by a set of seven catchment characteristics.
The alternative approach of grouping basins solely on the basis of physical
properties is preferable. Six physically homogeneous groups of basins are
identified by WARD's multivariate clustering algorithm using the same seven
characteristics. These regions have hydrological homogeneity in addition to their
physical homogeneity. Dimensionless regional flood frequency curves are produced
by fitting GEV and GL distributions for each region. The GEV regional growth
curves imply a larger return period for a given magnitude flood. When floods are
described by GL model the respective return periods are considerably smaller.

A general discretetime modeling framework for animal movement using multistate random walks
http://hdl.handle.net/10023/2605
Abstract: Recent developments in animal tracking technology have permitted the collection of detailed data on the movement paths of individuals from many species. However, analysis methods for these data have not developed at a similar pace, largely due to a lack of suitable candidate models, coupled with the technical difficulties of fitting such models to data. To facilitate a general modeling framework, we propose that complex movement paths can be conceived as a series of movement strategies among which animals transition as they are affected by changes in their internal and external environment. We synthesize previously existing and novel methodologies to develop a general suite of mechanistic models based on biased and correlated random walks that allow different behavioral states for directed (e.g., migration), exploratory (e.g., dispersal), arearestricted (e.g., foraging), and other types of movement. Using this “toolbox” of nested model components, multistate movement models may be custombuilt for a wide variety of species and applications. As a unified statespace modeling framework, it allows the simultaneous investigation of numerous hypotheses about animal movement from imperfectly observed data, including time allocations to different movement behavior states, transitions between states, the use of memory or navigation, and strengths of attraction (or repulsion) to specific locations. The inclusion of covariate information permits further investigation of specific hypotheses related to factors driving different types of movement behavior. Using reversible jump Markov chain Monte Carlo methods to facilitate Bayesian model selection and multimodel inference, we apply the proposed methodology to real data by adapting it to the natural history of the grey seal (Halichoerus grypus) in the North Sea. Although previous grey seal studies tended to focus on correlated movements, we found overwhelming evidence that bias towards haulout or foraging locations better explained seal movement than simple or correlated random walks. Posterior model probabilities also provided evidence that seals transition among directed, arearestricted, and exploratory movements associated with haulout, foraging, and other behaviors. With this intuitive framework for modeling and interpreting animal movement, we believe the development and application of bespoke movement models will become more accessible to ecologists and nonstatisticians.
Wed, 01 Aug 2012 00:00:00 GMT
http://hdl.handle.net/10023/2605
20120801T00:00:00Z
McClintock, Brett Thomas
King, Ruth
Thomas, Len
Matthiopoulos, Jason
McConnell, Bernie J
Morales, Juan
Recent developments in animal tracking technology have permitted the collection of detailed data on the movement paths of individuals from many species. However, analysis methods for these data have not developed at a similar pace, largely due to a lack of suitable candidate models, coupled with the technical difficulties of fitting such models to data. To facilitate a general modeling framework, we propose that complex movement paths can be conceived as a series of movement strategies among which animals transition as they are affected by changes in their internal and external environment. We synthesize previously existing and novel methodologies to develop a general suite of mechanistic models based on biased and correlated random walks that allow different behavioral states for directed (e.g., migration), exploratory (e.g., dispersal), arearestricted (e.g., foraging), and other types of movement. Using this “toolbox” of nested model components, multistate movement models may be custombuilt for a wide variety of species and applications. As a unified statespace modeling framework, it allows the simultaneous investigation of numerous hypotheses about animal movement from imperfectly observed data, including time allocations to different movement behavior states, transitions between states, the use of memory or navigation, and strengths of attraction (or repulsion) to specific locations. The inclusion of covariate information permits further investigation of specific hypotheses related to factors driving different types of movement behavior. Using reversible jump Markov chain Monte Carlo methods to facilitate Bayesian model selection and multimodel inference, we apply the proposed methodology to real data by adapting it to the natural history of the grey seal (Halichoerus grypus) in the North Sea. Although previous grey seal studies tended to focus on correlated movements, we found overwhelming evidence that bias towards haulout or foraging locations better explained seal movement than simple or correlated random walks. Posterior model probabilities also provided evidence that seals transition among directed, arearestricted, and exploratory movements associated with haulout, foraging, and other behaviors. With this intuitive framework for modeling and interpreting animal movement, we believe the development and application of bespoke movement models will become more accessible to ecologists and nonstatisticians.

Coupling of the solar wind, magnetosphere and ionosphere by MHD waves
http://hdl.handle.net/10023/2571
Abstract: The solar wind, magnetosphere and ionosphere are coupled by magnetohydrodynamic waves, and this gives rise to new and often unexpected behaviours that cannot be produced by a single, isolated part of the system. This thesis examines two broad instances of coupling: fieldline resonance (FLR) which couples fast and Alfvén waves, and magnetosphereionosphere (MI) coupling via Alfvén waves.
The first part of this thesis investigates fieldline resonance for equilibria that vary in two dimensions perpendicular to the background magnetic field. This research confirms that our intuitive understanding of FLR from 1D is a good guide to events in 2D, and places 2D FLR onto a firm mathematical basis by systematic solution of the governing equations. It also reveals the new concept of ‘imprinting’ of spatial forms: spatial variations of the resonant Alfvén wave correlate strongly with the spatial form of the fast wave that drives the resonance.
MIcoupling gives rise to ionospheremagnetosphere (IM) waves, and we have made a detailed analysis of these waves for a 1D sheet Eregion. IMwaves are characterised by two quantities: a speed v_{IM} and an angular frequency ω_{IM} , for which we have obtained analytic expressions. For an ideal magnetosphere, IMwaves are advective and move in the direction of the electric field with speed v_{IM}. The advection speed is a nonlinear expression that decreases with heightintegrated Eregion plasmadensity, hence, wavepackets steepen on their trailing edge, rapidly accessing small lengthscales through wavebreaking. Inclusion of electron inertial effects in the magnetosphere introduces dispersion to IMwaves. In the strongly inertial limit (wavelength λ << λ_{e} , where λ_{e} is the electron inertial length at the base of the magnetosphere), the group velocity of linear waves goes to zero, and the waves oscillate at ω_{IM} which is an upper limit on the angular frequency of IMwaves for any wavelength. Estimates of v_{IM} show that this speed can be a significant fraction (perhaps half) of the E_{⊥} × B_{0} drift in the Eregion, producing speeds of up to several hundred metres per second. The upper limit on angular frequency, ωIM , is estimated to give periods from a few hundredths of a second to several minutes. IMwaves are damped by recombination and background ionisation, giving an efolding decay time that can vary from tens of seconds to tens of minutes.
We have also investigated the dynamics and steadystates that occur when the magnetosphereionosphere system is driven by largescale Alfvénic fieldaligned currents. Steadystates are dominated by two approximate solutions: an ‘upper’ solution that is valid in places where the Eregion is a near perfect conductor, and a ‘lower’ solution that is valid where Eregion depletion makes recombination negligible. These analytic solutions are extremely useful tools and the global steadystate can be constructed by matching these solutions across suitable boundarylayers. Furthermore, the upper solution reveals that Eregion density cavities form and widen (with associated broadening of the magnetospheric downward current channel) if the downward current density exceeds the maximum current density that can be supplied by background Eregion ionisation. We also supply expressions for the minimum Eregion plasmadensity and shortest lengthscale in the steadystate.
IMwaves and steadystates are extremely powerful tools for interpreting MIdynamics. When an Eregion density cavity widens through coupling to an ideal, singlefluid MHD magnetosphere, it does so by forming a discontinuity that steps between the upper and lower steadystates. This discontinuity acts as part of an ideal IMwave and moves in the direction of the electric field at a speed U = \sqrt{v_{IM}^{+} v_{IM}^{}}, which is the geometric mean of v_{IM} evaluated immediately to the left and right of the discontinuity. This widening speed is typically several hundreds of metres per second. If electron inertial effects are included in the magnetosphere, then the discontinuity is smoothed, and a series of undershoots and overshoots develops behind it. These undershoots and overshoots evolve as inertial IMwaves. Initially they are weakly inertial, with a wavelength of about λ_{e}, however, strong gradients of ω_{IM} cause IMwaves to phasemix, making their wavelength inversely proportional to time. Therefore, the waves rapidly become strongly inertial and oscillate at ω_{IM}. The inertial IMwaves drive upgoing Alfvén waves in the magnetosphere, which populate a region over the downward current channel, close to its edge. In this manner, the Eregion depletion mechanism, that we have detailed, creates smallscale Alfvén waves in largescale current systems, with properties determined by MIcoupling.
Tue, 30 Nov 2010 00:00:00 GMT
http://hdl.handle.net/10023/2571
20101130T00:00:00Z
Russell, Alexander J. B.
The solar wind, magnetosphere and ionosphere are coupled by magnetohydrodynamic waves, and this gives rise to new and often unexpected behaviours that cannot be produced by a single, isolated part of the system. This thesis examines two broad instances of coupling: fieldline resonance (FLR) which couples fast and Alfvén waves, and magnetosphereionosphere (MI) coupling via Alfvén waves.
The first part of this thesis investigates fieldline resonance for equilibria that vary in two dimensions perpendicular to the background magnetic field. This research confirms that our intuitive understanding of FLR from 1D is a good guide to events in 2D, and places 2D FLR onto a firm mathematical basis by systematic solution of the governing equations. It also reveals the new concept of ‘imprinting’ of spatial forms: spatial variations of the resonant Alfvén wave correlate strongly with the spatial form of the fast wave that drives the resonance.
MIcoupling gives rise to ionospheremagnetosphere (IM) waves, and we have made a detailed analysis of these waves for a 1D sheet Eregion. IMwaves are characterised by two quantities: a speed v_{IM} and an angular frequency ω_{IM} , for which we have obtained analytic expressions. For an ideal magnetosphere, IMwaves are advective and move in the direction of the electric field with speed v_{IM}. The advection speed is a nonlinear expression that decreases with heightintegrated Eregion plasmadensity, hence, wavepackets steepen on their trailing edge, rapidly accessing small lengthscales through wavebreaking. Inclusion of electron inertial effects in the magnetosphere introduces dispersion to IMwaves. In the strongly inertial limit (wavelength λ << λ_{e} , where λ_{e} is the electron inertial length at the base of the magnetosphere), the group velocity of linear waves goes to zero, and the waves oscillate at ω_{IM} which is an upper limit on the angular frequency of IMwaves for any wavelength. Estimates of v_{IM} show that this speed can be a significant fraction (perhaps half) of the E_{⊥} × B_{0} drift in the Eregion, producing speeds of up to several hundred metres per second. The upper limit on angular frequency, ωIM , is estimated to give periods from a few hundredths of a second to several minutes. IMwaves are damped by recombination and background ionisation, giving an efolding decay time that can vary from tens of seconds to tens of minutes.
We have also investigated the dynamics and steadystates that occur when the magnetosphereionosphere system is driven by largescale Alfvénic fieldaligned currents. Steadystates are dominated by two approximate solutions: an ‘upper’ solution that is valid in places where the Eregion is a near perfect conductor, and a ‘lower’ solution that is valid where Eregion depletion makes recombination negligible. These analytic solutions are extremely useful tools and the global steadystate can be constructed by matching these solutions across suitable boundarylayers. Furthermore, the upper solution reveals that Eregion density cavities form and widen (with associated broadening of the magnetospheric downward current channel) if the downward current density exceeds the maximum current density that can be supplied by background Eregion ionisation. We also supply expressions for the minimum Eregion plasmadensity and shortest lengthscale in the steadystate.
IMwaves and steadystates are extremely powerful tools for interpreting MIdynamics. When an Eregion density cavity widens through coupling to an ideal, singlefluid MHD magnetosphere, it does so by forming a discontinuity that steps between the upper and lower steadystates. This discontinuity acts as part of an ideal IMwave and moves in the direction of the electric field at a speed U = \sqrt{v_{IM}^{+} v_{IM}^{}}, which is the geometric mean of v_{IM} evaluated immediately to the left and right of the discontinuity. This widening speed is typically several hundreds of metres per second. If electron inertial effects are included in the magnetosphere, then the discontinuity is smoothed, and a series of undershoots and overshoots develops behind it. These undershoots and overshoots evolve as inertial IMwaves. Initially they are weakly inertial, with a wavelength of about λ_{e}, however, strong gradients of ω_{IM} cause IMwaves to phasemix, making their wavelength inversely proportional to time. Therefore, the waves rapidly become strongly inertial and oscillate at ω_{IM}. The inertial IMwaves drive upgoing Alfvén waves in the magnetosphere, which populate a region over the downward current channel, close to its edge. In this manner, the Eregion depletion mechanism, that we have detailed, creates smallscale Alfvén waves in largescale current systems, with properties determined by MIcoupling.

Topics in computational group theory : primitive permutation groups and matrix group normalisers
http://hdl.handle.net/10023/2561
Abstract: Part I of this thesis presents methods for finding the primitive permutation
groups of degree d, where 2500 ≤ d < 4096, using the O'NanScott Theorem
and Aschbacher's theorem. Tables of the groups G are given for each O'NanScott class. For the nonaffine groups, additional information is given: the
degree d of G, the shape of a stabiliser in G of the primitive action, the
shape of the normaliser N in S[subscript(d)] of G and the rank of N.
Part II presents a new algorithm NormaliserGL for computing the normaliser
in GL[subscript(n)](q) of a group G ≤ GL[subscript(n)](q). The algorithm is implemented in
the computational algebra system MAGMA and employs Aschbacher's theorem
to break the problem into several cases. The attached CD contains the
code for the algorithm as well as several test cases which demonstrate the
improvement over MAGMA's existing algorithm.
Tue, 01 Nov 2011 00:00:00 GMT
http://hdl.handle.net/10023/2561
20111101T00:00:00Z
Coutts, Hannah Jane
Part I of this thesis presents methods for finding the primitive permutation
groups of degree d, where 2500 ≤ d < 4096, using the O'NanScott Theorem
and Aschbacher's theorem. Tables of the groups G are given for each O'NanScott class. For the nonaffine groups, additional information is given: the
degree d of G, the shape of a stabiliser in G of the primitive action, the
shape of the normaliser N in S[subscript(d)] of G and the rank of N.
Part II presents a new algorithm NormaliserGL for computing the normaliser
in GL[subscript(n)](q) of a group G ≤ GL[subscript(n)](q). The algorithm is implemented in
the computational algebra system MAGMA and employs Aschbacher's theorem
to break the problem into several cases. The attached CD contains the
code for the algorithm as well as several test cases which demonstrate the
improvement over MAGMA's existing algorithm.

Status assessment of the Critically Endangered Azores Bullfinch Pyrrhula murina
http://hdl.handle.net/10023/2552
Abstract: The Azores Bullfinch is endemic to the island of São Miguel (Azores, Portugal). Its status was uplisted to Critically Endangered in 2005 on the basis of an extremely small and declining population that was considered to be restricted to a very small mountain range (43 km2), in a single location, within which the spread of invasive plants constituted a threat to habitat quality. Nevertheless, information was mostly inferred, or the product of, nonsystematic studies. In order to carry out a complete assessment of the conservation status we analysed: (i) population trend, calculated from annual monitoring 1991–2008, (ii) population size, and (iii) range size, obtaining estimates in a single morning study in 2008 involving the simultaneous participation of 48 observers. Contrary to previous inferences, the population is no longer decreasing, although quality of laurel forest habitat continues to decline due to the persistent threat of invasive species. Population size (mean ± SE) was estimated at 1,064 ± 304 individuals using distance sampling methods, although the estimate was very sensitive to the survey method used. Range size estimates (extent of occurrence and area of occupancy) were 144 km2 and 83 km2 respectively. Given the present information, we propose the downlisting of Azores Bullfinch to Endangered on the IUCN Red List.
Description: 'This work was part of the Azores Bullﬁnch monitoring programme included in the project LIFE NAT/P/000013 “Recovery of Azores Bullﬁnch’s habitat in the Special Protection Area of Pico da Vara / Ribeira do Guilherme”'
Sat, 01 Jan 2011 00:00:00 GMT
http://hdl.handle.net/10023/2552
20110101T00:00:00Z
Ceia, Ricardo S.
Ramos, Jaime A.
Heleno, Ruben H.
Hilton, Geoff M.
Marques, Tiago A.
The Azores Bullfinch is endemic to the island of São Miguel (Azores, Portugal). Its status was uplisted to Critically Endangered in 2005 on the basis of an extremely small and declining population that was considered to be restricted to a very small mountain range (43 km2), in a single location, within which the spread of invasive plants constituted a threat to habitat quality. Nevertheless, information was mostly inferred, or the product of, nonsystematic studies. In order to carry out a complete assessment of the conservation status we analysed: (i) population trend, calculated from annual monitoring 1991–2008, (ii) population size, and (iii) range size, obtaining estimates in a single morning study in 2008 involving the simultaneous participation of 48 observers. Contrary to previous inferences, the population is no longer decreasing, although quality of laurel forest habitat continues to decline due to the persistent threat of invasive species. Population size (mean ± SE) was estimated at 1,064 ± 304 individuals using distance sampling methods, although the estimate was very sensitive to the survey method used. Range size estimates (extent of occurrence and area of occupancy) were 144 km2 and 83 km2 respectively. Given the present information, we propose the downlisting of Azores Bullfinch to Endangered on the IUCN Red List.

Atmospheric transport and critical layer mixing in the troposphere and stratosphere
http://hdl.handle.net/10023/2538
Abstract: This thesis aims to improve the understanding of transport and critical layer mixing in the troposphere and stratosphere. A dynamical approach is taken based on potential vorticity which has long been recognised as the essential field inducing the flow and thermodynamic structure of the atmosphere. Within the dynamical framework of critical layer mixing of potential vorticity, three main topics are addressed.
First, an idealised model of critical layer mixing in the stratospheric surf zone is examined. The effect of the shear across the critical layer on the critical layer evolution itself is investigated. In particular it is found that at small shear barotropic instability occurs and the mixing efficiency of the critical layer increases due to the instability. The effect of finite deformation length is also considered which extends previous work.
Secondly, the dynamical coupling between the stratosphere and troposphere is examined by considering the effect of direct perturbations to stratospheric potential vorticity on the evolution of midlatitude baroclinic instability. Both zonally symmetric and asymmetric perturbations to the stratospheric potential vorticity are considered, the former representative of a strong polar vortex, the latter representative of the stratospheric state following a major sudden warming. A comparison of these perturbations gives some insight into the possible influence of pre or postsudden warming conditions on the tropospheric evolution.
Finally, the influence of the stratospheric potential vorticity distribution on lateral mixing and transport into and out of the tropical pipe, the low latitude ascending branch of the BrewerDobson circulation, is investigated. The stratospheric potential vorticity distribution in the tropical stratosphere is found to have a clear pattern according to the phase of the quasibiennial oscillation (QBO). The extent of the QBO influence is quantified, by analysing trajectories of Lagrangian particles using an online trajectory code recently implemented in the Met Office's Unified Model.
Fri, 22 Jun 2012 00:00:00 GMT
http://hdl.handle.net/10023/2538
20120622T00:00:00Z
Smy, Louise Ann
This thesis aims to improve the understanding of transport and critical layer mixing in the troposphere and stratosphere. A dynamical approach is taken based on potential vorticity which has long been recognised as the essential field inducing the flow and thermodynamic structure of the atmosphere. Within the dynamical framework of critical layer mixing of potential vorticity, three main topics are addressed.
First, an idealised model of critical layer mixing in the stratospheric surf zone is examined. The effect of the shear across the critical layer on the critical layer evolution itself is investigated. In particular it is found that at small shear barotropic instability occurs and the mixing efficiency of the critical layer increases due to the instability. The effect of finite deformation length is also considered which extends previous work.
Secondly, the dynamical coupling between the stratosphere and troposphere is examined by considering the effect of direct perturbations to stratospheric potential vorticity on the evolution of midlatitude baroclinic instability. Both zonally symmetric and asymmetric perturbations to the stratospheric potential vorticity are considered, the former representative of a strong polar vortex, the latter representative of the stratospheric state following a major sudden warming. A comparison of these perturbations gives some insight into the possible influence of pre or postsudden warming conditions on the tropospheric evolution.
Finally, the influence of the stratospheric potential vorticity distribution on lateral mixing and transport into and out of the tropical pipe, the low latitude ascending branch of the BrewerDobson circulation, is investigated. The stratospheric potential vorticity distribution in the tropical stratosphere is found to have a clear pattern according to the phase of the quasibiennial oscillation (QBO). The extent of the QBO influence is quantified, by analysing trajectories of Lagrangian particles using an online trajectory code recently implemented in the Met Office's Unified Model.

Generation problems for finite groups
http://hdl.handle.net/10023/2529
Abstract: It can be deduced from the Burnside Basis Theorem that if G is a finite pgroup with d(G)=r then given any generating set A for G there exists a subset of A of size r that generates G. We have denoted this property B. A group is said to have the basis property if all subgroups have property B. This thesis is a study into the nature of these two properties. Note all groups are finite unless stated otherwise.
We begin this thesis by providing examples of groups with and without property B and several results on the structure of groups with property B, showing that under certain conditions property B is inherited by quotients. This culminates with a result which shows that groups with property B that can be expressed as direct products are exactly those arising from the Burnside Basis Theorem.
We also seek to create a class of groups which have property B. We provide a method for constructing groups with property B and trivial Frattini subgroup using finite fields. We then classify all groups G where the quotient of G by the Frattini subgroup is isomorphic to this construction. We finally note that groups arising from this construction do not in general have the basis property.
Finally we look at groups with the basis property. We prove that groups with the basis property are soluble and consist only of elements of primepower order. We then exploit the classification of all such groups by Higman to provide a complete classification of groups with the basis property.
Wed, 30 Nov 2011 00:00:00 GMT
http://hdl.handle.net/10023/2529
20111130T00:00:00Z
McDougallBagnall, Jonathan M.
It can be deduced from the Burnside Basis Theorem that if G is a finite pgroup with d(G)=r then given any generating set A for G there exists a subset of A of size r that generates G. We have denoted this property B. A group is said to have the basis property if all subgroups have property B. This thesis is a study into the nature of these two properties. Note all groups are finite unless stated otherwise.
We begin this thesis by providing examples of groups with and without property B and several results on the structure of groups with property B, showing that under certain conditions property B is inherited by quotients. This culminates with a result which shows that groups with property B that can be expressed as direct products are exactly those arising from the Burnside Basis Theorem.
We also seek to create a class of groups which have property B. We provide a method for constructing groups with property B and trivial Frattini subgroup using finite fields. We then classify all groups G where the quotient of G by the Frattini subgroup is isomorphic to this construction. We finally note that groups arising from this construction do not in general have the basis property.
Finally we look at groups with the basis property. We prove that groups with the basis property are soluble and consist only of elements of primepower order. We then exploit the classification of all such groups by Higman to provide a complete classification of groups with the basis property.

Behind and beyond a theorem on groups related to trivalent graphs
http://hdl.handle.net/10023/2462
Abstract: In 2006 we completed the proof of a fivepart conjecture that was made in 1977 about a family of groups related to trivalent graphs. This family covers all 2generator, 2relator groups where one relator specifies that a generator is an involution and the other relator has three syllables. Our proof relies upon detailed but general computations in the groups under question. The proof is theoretical, but based upon explicit proofs produced by machine for individual cases. Here we explain how we derived the general proofs from specific cases. The conjecture essentially addressed only the finite groups in the family. Here we extend the results to infinite groups, effectively determining when members of this family of finitely presented groups are simply isomorphic to a specific quotient.
Mon, 01 Dec 2008 00:00:00 GMT
http://hdl.handle.net/10023/2462
20081201T00:00:00Z
Havas, George
Robertson, Edmund F.
Sutherland, Dale C.
In 2006 we completed the proof of a fivepart conjecture that was made in 1977 about a family of groups related to trivalent graphs. This family covers all 2generator, 2relator groups where one relator specifies that a generator is an involution and the other relator has three syllables. Our proof relies upon detailed but general computations in the groups under question. The proof is theoretical, but based upon explicit proofs produced by machine for individual cases. Here we explain how we derived the general proofs from specific cases. The conjecture essentially addressed only the finite groups in the family. Here we extend the results to infinite groups, effectively determining when members of this family of finitely presented groups are simply isomorphic to a specific quotient.

Lowerhybrid waves generated by anomalous Doppler resonance in auroral plasmas
http://hdl.handle.net/10023/2457
Abstract: This paper describes sonic aspects of lowerhybrid wave activity in space plasmas. Lowerhybrid waves are particularly important since they can transfer energy efficiently between electrons and ions in a collisionless magnetized plasma. We consider the 'fan' or anomalous Doppler resonance instability driven by energetic electron tails and show that it is responsible for the generation of lowerhybrid waves. We also demonstrate that observations of their intensity are sufficient to drive the modulational instability.
Sun, 01 Aug 2010 00:00:00 GMT
http://hdl.handle.net/10023/2457
20100801T00:00:00Z
Bingham, Robert
Cairns, R Alan
Vorgul, I.
Shapiro, V. D.
This paper describes sonic aspects of lowerhybrid wave activity in space plasmas. Lowerhybrid waves are particularly important since they can transfer energy efficiently between electrons and ions in a collisionless magnetized plasma. We consider the 'fan' or anomalous Doppler resonance instability driven by energetic electron tails and show that it is responsible for the generation of lowerhybrid waves. We also demonstrate that observations of their intensity are sufficient to drive the modulational instability.

Falling towards forgetfulness : synaptic decay prevents spontaneous recovery of memory
http://hdl.handle.net/10023/2455
Abstract: Long after a new language has been learned and forgotten, relearning a few words seems to trigger the recall of other words. This "freelunch learning'' (FLL) effect has been demonstrated both in humans and in neural network models. Specifically, previous work proved that linear networks that learn a set of associations, then partially forget them all, and finally relearn some of the associations, show improved performance on the remaining (i.e., nonrelearned) associations. Here, we prove that relearning forgotten associations decreases performance on nonrelearned associations; an effect we call negative freelunch learning. The difference between freelunch learning and the negative freelunch learning presented here is due to the particular method used to induce forgetting. Specifically, if forgetting is induced by isotropic drifting of weight vectors (i.e., by adding isotropic noise), then freelunch learning is observed. However, as proved here, if forgetting is induced by weight values that simply decay or fall towards zero, then negative freelunch learning is observed. From a biological perspective, and assuming that nervous systems are analogous to the networks used here, this suggests that evolution may have selected physiological mechanisms that involve forgetting using a form of synaptic drift rather than synaptic decay, because synaptic drift, but not synaptic decay, yields freelunch learning.
Description: No funding was received for this work.
Fri, 22 Aug 2008 00:00:00 GMT
http://hdl.handle.net/10023/2455
20080822T00:00:00Z
Stone, James V.
Jupp, Peter Edmund
Long after a new language has been learned and forgotten, relearning a few words seems to trigger the recall of other words. This "freelunch learning'' (FLL) effect has been demonstrated both in humans and in neural network models. Specifically, previous work proved that linear networks that learn a set of associations, then partially forget them all, and finally relearn some of the associations, show improved performance on the remaining (i.e., nonrelearned) associations. Here, we prove that relearning forgotten associations decreases performance on nonrelearned associations; an effect we call negative freelunch learning. The difference between freelunch learning and the negative freelunch learning presented here is due to the particular method used to induce forgetting. Specifically, if forgetting is induced by isotropic drifting of weight vectors (i.e., by adding isotropic noise), then freelunch learning is observed. However, as proved here, if forgetting is induced by weight values that simply decay or fall towards zero, then negative freelunch learning is observed. From a biological perspective, and assuming that nervous systems are analogous to the networks used here, this suggests that evolution may have selected physiological mechanisms that involve forgetting using a form of synaptic drift rather than synaptic decay, because synaptic drift, but not synaptic decay, yields freelunch learning.

Geometric grid classes of permutations
http://hdl.handle.net/10023/2450
Abstract: A geometric grid class consists of those permutations that can be drawn on a specified set of line segments of slope ±1 arranged in a rectangular pattern governed by a matrix. Using a mixture of geometric and language theoretic methods, we prove that such classes are specified by finite sets of forbidden permutations, are partially well ordered, and have rational generating functions. Furthermore, we show that these properties are inherited by the subclasses (under permutation involvement) of such classes, and establish the basic lattice theoretic properties of the collection of all such subclasses.
Fri, 01 Nov 2013 00:00:00 GMT
http://hdl.handle.net/10023/2450
20131101T00:00:00Z
Albert, M.H.
Atkinson, M.D.
Bouvel, M.
Ruskuc, Nik
Vatter, V.
A geometric grid class consists of those permutations that can be drawn on a specified set of line segments of slope ±1 arranged in a rectangular pattern governed by a matrix. Using a mixture of geometric and language theoretic methods, we prove that such classes are specified by finite sets of forbidden permutations, are partially well ordered, and have rational generating functions. Furthermore, we show that these properties are inherited by the subclasses (under permutation involvement) of such classes, and establish the basic lattice theoretic properties of the collection of all such subclasses.

Unary FApresentable semigroups
http://hdl.handle.net/10023/2375
Abstract: Automatic presentations, also called FApresentations, were introduced to extend nite model theory to innite structures whilst retaining the solubility of interesting decision problems. A particular focus of research has been the classication of those structures of some species that admit automatic presentations. Whilst some successes have been obtained, this appears to be a dicult problem in general. A restricted problem, also of signicant interest, is to ask this question for unary automatic presentations: automatic presentations over a oneletter alphabet. This paper studies unary FApresentable semigroups. We prove the following: Every unary FApresentable structure admits an injective unary automatic presentation where the language of representatives consists of every word over a oneletter alphabet. Unary FApresentable semigroups are locally nite, but nonnitely generated unary FApresentable semigroups may be innite. Every unary FApresentable semigroup satises some Burnside identity.We describe the Green's relations in unary FApresentable semigroups. We investigate the relationship between the class of unary FApresentable semigroups and various semigroup constructions. A classication is given of the unary FApresentable completely simple semigroups.
Fri, 08 Jun 2012 00:00:00 GMT
http://hdl.handle.net/10023/2375
20120608T00:00:00Z
Cain, Alan James
Ruskuc, Nik
Thomas, R.M.
Automatic presentations, also called FApresentations, were introduced to extend nite model theory to innite structures whilst retaining the solubility of interesting decision problems. A particular focus of research has been the classication of those structures of some species that admit automatic presentations. Whilst some successes have been obtained, this appears to be a dicult problem in general. A restricted problem, also of signicant interest, is to ask this question for unary automatic presentations: automatic presentations over a oneletter alphabet. This paper studies unary FApresentable semigroups. We prove the following: Every unary FApresentable structure admits an injective unary automatic presentation where the language of representatives consists of every word over a oneletter alphabet. Unary FApresentable semigroups are locally nite, but nonnitely generated unary FApresentable semigroups may be innite. Every unary FApresentable semigroup satises some Burnside identity.We describe the Green's relations in unary FApresentable semigroups. We investigate the relationship between the class of unary FApresentable semigroups and various semigroup constructions. A classication is given of the unary FApresentable completely simple semigroups.

Threedimensional solutions of the magnetohydrostatic equations : rigidly rotating magnetized coronae in spherical geometry
http://hdl.handle.net/10023/2269
Abstract: Context. Magnetohydrostatic (MHS) equilibria are often used to model astrophysical plasmas, for example, planetary magnetospheres or coronae of magnetized stars. However, finding realistic threedimensional solutions to the MHS equations is difficult, with only a few known analytical solutions and even finding numerical solution is far from easy. Aims. We extend the results of a previous paper on threedimensional solutions of the MHS equations around rigidly rotating massive cylinders to the much more realistic case of rigidly rotating massive spheres. An obvious application is to model the closed field line regions of the coronae of rapidly rotating stars. Methods. We used a number of simplifying assumptions to reduce the MHS equations to a single elliptic partial differential equation for a pseudopotential U, from which all physical quantities, such as the magnetic field, the plasma pressure, and the density, can be derived by differentiation. The most important assumptions made are stationarity in the corotating frame of reference, a particular form for the current density, and neglect of outflows. Results. In this paper we demonstrate that standard methods can be used to find numerical solutions to the fundamental equation of the theory. We present three simple different cases of magnetic field boundary conditions on the surface of the central sphere, corresponding to an aligned dipole field, a nonaligned dipole field, and a displaced dipole field. Our results show that it should be possible in the future to use this method without dramatically increasing the demands on computational resources to improve upon potential field models of rotating magnetospheres and coronae.
Fri, 01 Oct 2010 00:00:00 GMT
http://hdl.handle.net/10023/2269
20101001T00:00:00Z
AlSalti, Nasser
Neukirch, Thomas
Context. Magnetohydrostatic (MHS) equilibria are often used to model astrophysical plasmas, for example, planetary magnetospheres or coronae of magnetized stars. However, finding realistic threedimensional solutions to the MHS equations is difficult, with only a few known analytical solutions and even finding numerical solution is far from easy. Aims. We extend the results of a previous paper on threedimensional solutions of the MHS equations around rigidly rotating massive cylinders to the much more realistic case of rigidly rotating massive spheres. An obvious application is to model the closed field line regions of the coronae of rapidly rotating stars. Methods. We used a number of simplifying assumptions to reduce the MHS equations to a single elliptic partial differential equation for a pseudopotential U, from which all physical quantities, such as the magnetic field, the plasma pressure, and the density, can be derived by differentiation. The most important assumptions made are stationarity in the corotating frame of reference, a particular form for the current density, and neglect of outflows. Results. In this paper we demonstrate that standard methods can be used to find numerical solutions to the fundamental equation of the theory. We present three simple different cases of magnetic field boundary conditions on the surface of the central sphere, corresponding to an aligned dipole field, a nonaligned dipole field, and a displaced dipole field. Our results show that it should be possible in the future to use this method without dramatically increasing the demands on computational resources to improve upon potential field models of rotating magnetospheres and coronae.

On the relationship between equilibrium bifurcations and ideal MHD instabilities for linetied coronal loops
http://hdl.handle.net/10023/2268
Abstract: For axisymmetric models for coronal loops the relationship between the bifurcation points of magnetohydrodynamic (MHD) equilibrium sequences and the points of linear ideal MHD instability is investigated, imposing linetied boundary conditions. Using a wellstudied example based on the Gold aEuro parts per thousand Hoyle equilibrium, it is demonstrated that if the equilibrium sequence is calculated using the Grad aEuro parts per thousand Shafranov equation, the instability corresponds to the second bifurcation point and not the first bifurcation point, because the equilibrium boundary conditions allow for modes which are excluded from the linear ideal stability analysis. This is shown by calculating the bifurcating equilibrium branches and comparing the spatial structure of the solutions close to the bifurcation point with the spatial structure of the unstable mode. If the equilibrium sequence is calculated using Euler potentials, the first bifurcation point of the Grad aEuro parts per thousand Shafranov case is not found, and the first bifurcation point of the Euler potential description coincides with the ideal instability threshold. An explanation of this results in terms of linear bifurcation theory is given and the implications for the use of MHD equilibrium bifurcations to explain eruptive phenomena is briefly discussed.
Fri, 01 Jan 2010 00:00:00 GMT
http://hdl.handle.net/10023/2268
20100101T00:00:00Z
Neukirch, T.
Romeou, Z.
For axisymmetric models for coronal loops the relationship between the bifurcation points of magnetohydrodynamic (MHD) equilibrium sequences and the points of linear ideal MHD instability is investigated, imposing linetied boundary conditions. Using a wellstudied example based on the Gold aEuro parts per thousand Hoyle equilibrium, it is demonstrated that if the equilibrium sequence is calculated using the Grad aEuro parts per thousand Shafranov equation, the instability corresponds to the second bifurcation point and not the first bifurcation point, because the equilibrium boundary conditions allow for modes which are excluded from the linear ideal stability analysis. This is shown by calculating the bifurcating equilibrium branches and comparing the spatial structure of the solutions close to the bifurcation point with the spatial structure of the unstable mode. If the equilibrium sequence is calculated using Euler potentials, the first bifurcation point of the Grad aEuro parts per thousand Shafranov case is not found, and the first bifurcation point of the Euler potential description coincides with the ideal instability threshold. An explanation of this results in terms of linear bifurcation theory is given and the implications for the use of MHD equilibrium bifurcations to explain eruptive phenomena is briefly discussed.