Mathematics & Statistics (School of)http://hdl.handle.net/10023/282018-06-24T18:49:20Z2018-06-24T18:49:20ZOrigin and ion charge state evolution of solar wind transients during 4 - 7 August 2011Rodkin, D.Goryaev, F.Pagano, P.Gibb, G.Slemzin, V.Shugay, Y.Veselovsky, I.Mackay, D. H.http://hdl.handle.net/10023/144322018-06-22T23:18:37Z2017-07-01T00:00:00ZWe present a study of the complex event consisting of several solar wind transients detected by the Advanced Composition Explorer (ACE) on 4 - 7 August 2011, which caused a geomagnetic storm with Dst=-110 nT. The supposed coronal sources, three flares and coronal mass ejections (CMEs), occurred on 2 - 4 August 2011 in active region (AR) 11261. To investigate the solar origin and formation of these transients, we study the kinematic and thermodynamic properties of the expanding coronal structures using the Solar Dynamics Observatory/Atmospheric Imaging Assembly (SDO/AIA) EUV images and differential emission measure (DEM) diagnostics. The Helioseismic and Magnetic Imager (HMI) magnetic field maps were used as the input data for the 3D magnetohydrodynamic (MHD) model to describe the flux rope ejection (Pagano, Mackay, and Poedts, 2013b). We characterize the early phase of the flux rope ejection in the corona, where the usual three-component CME structure formed. The fluxrope was ejected with a speed of about 200 km s-1 to the height of 0.25 R⊙. The kinematics of the modeled CME front agrees well with the Solar Terrestrial Relations Observatory (STEREO) EUV measurements. Using the results of the plasma diagnostics and MHD modeling, we calculate the ion charge ratios of carbon and oxygen as well as the mean charge state of iron ions of the 2 August 2011 CME, taking into account the processes of heating, cooling, expansion, ionization, and recombination of the moving plasma in the corona up to the frozen-in region. We estimate a probable heating rate of the CME plasma in the low corona by matching the calculated ion composition parameters of the CME with those measured in situ for the solar wind transients. We also consider the similarities and discrepancies between the results of the MHD simulation and the observations.
This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 647214). The computational work for this article was carried out on the joint STFC and SFC (SRIF) funded clusters at the University of St Andrews (Scotland, UK). The work is partially supported by RFBR grants 17-02-00787, 14-02-00945 and the P7 Program of the Russian Academy of Sciences.
2017-07-01T00:00:00ZRodkin, D.Goryaev, F.Pagano, P.Gibb, G.Slemzin, V.Shugay, Y.Veselovsky, I.Mackay, D. H.We present a study of the complex event consisting of several solar wind transients detected by the Advanced Composition Explorer (ACE) on 4 - 7 August 2011, which caused a geomagnetic storm with Dst=-110 nT. The supposed coronal sources, three flares and coronal mass ejections (CMEs), occurred on 2 - 4 August 2011 in active region (AR) 11261. To investigate the solar origin and formation of these transients, we study the kinematic and thermodynamic properties of the expanding coronal structures using the Solar Dynamics Observatory/Atmospheric Imaging Assembly (SDO/AIA) EUV images and differential emission measure (DEM) diagnostics. The Helioseismic and Magnetic Imager (HMI) magnetic field maps were used as the input data for the 3D magnetohydrodynamic (MHD) model to describe the flux rope ejection (Pagano, Mackay, and Poedts, 2013b). We characterize the early phase of the flux rope ejection in the corona, where the usual three-component CME structure formed. The fluxrope was ejected with a speed of about 200 km s-1 to the height of 0.25 R⊙. The kinematics of the modeled CME front agrees well with the Solar Terrestrial Relations Observatory (STEREO) EUV measurements. Using the results of the plasma diagnostics and MHD modeling, we calculate the ion charge ratios of carbon and oxygen as well as the mean charge state of iron ions of the 2 August 2011 CME, taking into account the processes of heating, cooling, expansion, ionization, and recombination of the moving plasma in the corona up to the frozen-in region. We estimate a probable heating rate of the CME plasma in the low corona by matching the calculated ion composition parameters of the CME with those measured in situ for the solar wind transients. We also consider the similarities and discrepancies between the results of the MHD simulation and the observations.Computational modelling of cancer development and growth : modelling at multiple scales and multiscale modellingSzymanska, ZuzannaCytowski, MaciejMitchell, ElaineMacnamara, Cicely K.Chaplain, Mark A. J.http://hdl.handle.net/10023/143642018-06-21T23:19:46Z2018-05-01T00:00:00ZIn this paper, we present two mathematical models related to different aspects and scales of cancer growth. The first model is a stochastic spatiotemporal model of both a synthetic gene regulatory network (the example of a three-gene repressilator is given) and an actual gene regulatory network, the NF- κB pathway. The second model is a force-based individual-based model of the development of a solid avascular tumour with specific application to tumour cords, i.e. a mass of cancer cells growing around a central blood vessel. In each case, we compare our computational simulation results with experimental data. In the final discussion section, we outline how to take the work forward through the development of a multiscale model focussed at the cell level. This would incorporate key intracellular signalling pathways associated with cancer within each cell (e.g. p53–Mdm2, NF- κB) and through the use of high-performance computing be capable of simulating up to 109 cells, i.e. the tissue scale. In this way, mathematical models at multiple scales would be combined to formulate a multiscale computational model.
MAJC and CKM gratefully acknowledge support of EPSRC grant no. EP/N014642/1 (EPSRC Centre for Multiscale Soft Tissue Mechanics – With Application to Heart & Cancer).
2018-05-01T00:00:00ZSzymanska, ZuzannaCytowski, MaciejMitchell, ElaineMacnamara, Cicely K.Chaplain, Mark A. J.In this paper, we present two mathematical models related to different aspects and scales of cancer growth. The first model is a stochastic spatiotemporal model of both a synthetic gene regulatory network (the example of a three-gene repressilator is given) and an actual gene regulatory network, the NF- κB pathway. The second model is a force-based individual-based model of the development of a solid avascular tumour with specific application to tumour cords, i.e. a mass of cancer cells growing around a central blood vessel. In each case, we compare our computational simulation results with experimental data. In the final discussion section, we outline how to take the work forward through the development of a multiscale model focussed at the cell level. This would incorporate key intracellular signalling pathways associated with cancer within each cell (e.g. p53–Mdm2, NF- κB) and through the use of high-performance computing be capable of simulating up to 109 cells, i.e. the tissue scale. In this way, mathematical models at multiple scales would be combined to formulate a multiscale computational model.Photometry of star clustersEvans, Thomas Harry Hope Lloydhttp://hdl.handle.net/10023/142832018-06-19T23:17:59Z1968-01-01T00:00:00ZThe suitability of the Cassegrain Schmidt telescopes at St. Andrews University Observatory for the measurement of stellar magnitudes and colours by in-focus multicolour photography has been examined. A major requirement is that the photographic plate should coincide with the focal surface. Thermal effects in the Scott Lang Telescope and optical and mechanical problems in the James Gregory Telescope cause difficulty in, attaining this. These difficulties have been overcome in the case of the Scott Lang Telescope but no certain method for focussing the James Gregory Telescope was found. The photometric field limited by field error, is approximately one degree in diameter in each case. Colour equations between the instrumental and standard B, V systems depend on magnitude and, in the case of the Scott Lang Telescope, on exposure time as well. The methods used to measure UBV magnitudes and colours with the Radcliffe 74-inch reflector are described and the accuracy of the results discussed. Magnitudes and colours of stars brighter than V - 15.5 in the open cluster IC 2581 have been measured, together with MK spectral types for a few of the brighter stars. The interstellar absorption provides a criterion for the recognition of cluster members. A discrepancy between the shape of the cluster main sequence and that of the zero age main sequence is attributed to an error in the derivation of the standard zero age main sequence. The cluster is found to be at a distance of 2500 parsecs and may form part of the Carinae complex. The positions of the brightest stars in the colour magnitude diagram are discussed in the light of modern theories of stellar evolution and an age of approximately 10 million years is deduced. The colour magnitude diagram of the open cluster NGC 6383 has been obtained for stars brighter than V - 18.1; the limiting magnitudes in B and U are 19.7 and 17.9, respectively. MK spectral types have permitted the cluster membership of several bright B stars to be established; some stars of later type are non-members. The observation of this cluster are more complete than for most young clusters studied to date, but the poorness of the cluster and the unfavourable distribution of interstellar absorption with distance make it impossible to be certain of the membership of stars fainter than V = 13. The lack of stars fainter than V = 12.8 on the zero age main sequence indicates a contraction age of 5 million years. The distance is 1300 parsecs, like those of other young groups in the vicinity. The dense dust clouds which divide the Milky Way in Scorpius are immediately beyond this. Several faint variable stars may be of the T Tauri type.
1968-01-01T00:00:00ZEvans, Thomas Harry Hope LloydThe suitability of the Cassegrain Schmidt telescopes at St. Andrews University Observatory for the measurement of stellar magnitudes and colours by in-focus multicolour photography has been examined. A major requirement is that the photographic plate should coincide with the focal surface. Thermal effects in the Scott Lang Telescope and optical and mechanical problems in the James Gregory Telescope cause difficulty in, attaining this. These difficulties have been overcome in the case of the Scott Lang Telescope but no certain method for focussing the James Gregory Telescope was found. The photometric field limited by field error, is approximately one degree in diameter in each case. Colour equations between the instrumental and standard B, V systems depend on magnitude and, in the case of the Scott Lang Telescope, on exposure time as well. The methods used to measure UBV magnitudes and colours with the Radcliffe 74-inch reflector are described and the accuracy of the results discussed. Magnitudes and colours of stars brighter than V - 15.5 in the open cluster IC 2581 have been measured, together with MK spectral types for a few of the brighter stars. The interstellar absorption provides a criterion for the recognition of cluster members. A discrepancy between the shape of the cluster main sequence and that of the zero age main sequence is attributed to an error in the derivation of the standard zero age main sequence. The cluster is found to be at a distance of 2500 parsecs and may form part of the Carinae complex. The positions of the brightest stars in the colour magnitude diagram are discussed in the light of modern theories of stellar evolution and an age of approximately 10 million years is deduced. The colour magnitude diagram of the open cluster NGC 6383 has been obtained for stars brighter than V - 18.1; the limiting magnitudes in B and U are 19.7 and 17.9, respectively. MK spectral types have permitted the cluster membership of several bright B stars to be established; some stars of later type are non-members. The observation of this cluster are more complete than for most young clusters studied to date, but the poorness of the cluster and the unfavourable distribution of interstellar absorption with distance make it impossible to be certain of the membership of stars fainter than V = 13. The lack of stars fainter than V = 12.8 on the zero age main sequence indicates a contraction age of 5 million years. The distance is 1300 parsecs, like those of other young groups in the vicinity. The dense dust clouds which divide the Milky Way in Scorpius are immediately beyond this. Several faint variable stars may be of the T Tauri type.Solar intense magnetic fieldsWebb, Andrew Roberthttp://hdl.handle.net/10023/142772018-06-19T23:17:54Z1980-01-01T00:00:00ZThe nature of motions in intense magnetic fields is investigated. For a flux tube in a uniform atmosphere a dispersion relation is derived for the modes of vibration and analytic approximations are obtained for a slender tube. In a stratified atmosphere an expansion procedure is used to derive an equation for the vertical velocity perturbation. The behaviour of motions within the flux tube is shown to depend upon a transition frequency 𝜔[sub]v such that vertically propagating waves are possible only for frequencies greater than 𝜔[sub]v. Also, the nature of convective instability in a slender magnetic flux tube is explored. A sufficient condition for stability is derived for the case of an arbitrary temperature profile in the external medium. For a tube of infinite depth, with a uniform-temperature gradient inside the tube equal to that in the exterior, a necessary and sufficient condition for convective stability to occur inside the tube is derived. Under the assumptions of the model, intense flux tubes are convectively stable if sufficiently shallow (with depths 1 - 2 x 10³ km or less). Tubes that extend deeper into the convection zone are potentially (convectively) unstable, but may be stabilised for sufficiently strong magnetic fields. Radiative damping of waves is important in the upper photosphere and the effect of radiative relaxation on the propagation of waves in an intense flux tube is examined both for a uniform and stratified atmosphere. The cut-off frequency is generalized to include the effects of radiative relaxation. The phase-shift between velocity oscillations at two different levels and the phase difference between temperature and velocity perturbations are derived and compared with the available observations. Finally, the consequences of the observed steady downflow are discussed.
1980-01-01T00:00:00ZWebb, Andrew RobertThe nature of motions in intense magnetic fields is investigated. For a flux tube in a uniform atmosphere a dispersion relation is derived for the modes of vibration and analytic approximations are obtained for a slender tube. In a stratified atmosphere an expansion procedure is used to derive an equation for the vertical velocity perturbation. The behaviour of motions within the flux tube is shown to depend upon a transition frequency 𝜔[sub]v such that vertically propagating waves are possible only for frequencies greater than 𝜔[sub]v. Also, the nature of convective instability in a slender magnetic flux tube is explored. A sufficient condition for stability is derived for the case of an arbitrary temperature profile in the external medium. For a tube of infinite depth, with a uniform-temperature gradient inside the tube equal to that in the exterior, a necessary and sufficient condition for convective stability to occur inside the tube is derived. Under the assumptions of the model, intense flux tubes are convectively stable if sufficiently shallow (with depths 1 - 2 x 10³ km or less). Tubes that extend deeper into the convection zone are potentially (convectively) unstable, but may be stabilised for sufficiently strong magnetic fields. Radiative damping of waves is important in the upper photosphere and the effect of radiative relaxation on the propagation of waves in an intense flux tube is examined both for a uniform and stratified atmosphere. The cut-off frequency is generalized to include the effects of radiative relaxation. The phase-shift between velocity oscillations at two different levels and the phase difference between temperature and velocity perturbations are derived and compared with the available observations. Finally, the consequences of the observed steady downflow are discussed.Nonlinear stability of flows over rigid and flexible boundariesThomas, Michael Dhttp://hdl.handle.net/10023/142732018-06-19T23:17:42Z1990-01-01T00:00:00ZThis work assesses the importance of nonlinearity in the stability of flows over compliant and rigid walls, and comprises three main parts. The first part considers inviscid flow with a free surface over a flexible boundary. The dispersion relation is obtained, and the conditions for linear instability investigated. The linear dispersion relation is then used to show that the conditions for nonlinear three-wave resonance are often met. In some circumstances, the resonance may be of 'explosive' sort, involving waves of opposite energy sign; but non-explosive resonant configurations are most common. Next, the wave- amplitude evolution equations for three-wave resonance are derived, firstly by a 'direct' approach, and then via a variational (averaged Lagrangian) method. Results agree with those of Case & Chiu (1977) for capillary-gravity waves, and Craik & Adam (1979), for three-layer fluid flow, on taking the appropriate limits. We also consider a nonlinear model for the flexible boundary. In the second part, stability of Blasius flow over a compliant surface is studied. This extension of rigid-wall work of Craik (1971) and Hendriks (appendix to Usher & Craik 1975) determines the quadratic interaction coefficients of three-wave resonance, and complements the linear analysis of Carpenter & Garrad (1985, 1986) and others. First, the linear eigenvalue spectrum is investigated for various values of the wall parameters. Then, resonant triads are located and the quadratic interaction coefficients determined numerically. By way of introduction some rigid-wall results are also presented, extending those of Hendriks.
1990-01-01T00:00:00ZThomas, Michael DThis work assesses the importance of nonlinearity in the stability of flows over compliant and rigid walls, and comprises three main parts. The first part considers inviscid flow with a free surface over a flexible boundary. The dispersion relation is obtained, and the conditions for linear instability investigated. The linear dispersion relation is then used to show that the conditions for nonlinear three-wave resonance are often met. In some circumstances, the resonance may be of 'explosive' sort, involving waves of opposite energy sign; but non-explosive resonant configurations are most common. Next, the wave- amplitude evolution equations for three-wave resonance are derived, firstly by a 'direct' approach, and then via a variational (averaged Lagrangian) method. Results agree with those of Case & Chiu (1977) for capillary-gravity waves, and Craik & Adam (1979), for three-layer fluid flow, on taking the appropriate limits. We also consider a nonlinear model for the flexible boundary. In the second part, stability of Blasius flow over a compliant surface is studied. This extension of rigid-wall work of Craik (1971) and Hendriks (appendix to Usher & Craik 1975) determines the quadratic interaction coefficients of three-wave resonance, and complements the linear analysis of Carpenter & Garrad (1985, 1986) and others. First, the linear eigenvalue spectrum is investigated for various values of the wall parameters. Then, resonant triads are located and the quadratic interaction coefficients determined numerically. By way of introduction some rigid-wall results are also presented, extending those of Hendriks.Time dependent heating of the solar coronaWalsh, Robert Williamhttp://hdl.handle.net/10023/142672018-06-19T23:17:33Z1996-01-01T00:00:00ZThe problem of how the Sun's corona is heated is of central importance in Solar Physics research. In this thesis, a model is constructed of a typical coronal magnetic loop in order to investigate the response of coronal plasma to a time-dependent heating source. It is not the aim of the research to study in detail a particular heating mechanism but rather to understand the important features arising from time-dependent heating in general. A time-varying energy input into the coronal loop is required because it is likely that none of the suggested theoretical heating methods can provide a constant supply of heat to the corona. The magnetic field is taken to be strong enough that the loop dynamics reduce to a one-dimensional problem along the field. In addition, it is assumed that the radiative timescale in the corona is much longer than the sound travel time and thus, the plasma evolves isobarically. The thermal equilibria profiles along the coronal loop are then investigated for a simplified form of the optically thin radiation. Initially, a heating function that displays a regular, sinusoidal variation in time is introduced and it is found that there is a critical heating frequency above which a hot coronal loop solution can be maintained and below which the plasma temperature cools to chromospheric values. Pulse heating and the deposition of random-sized energy quanta in a loop are also investigated. An evaluation of the isobaric assumption to the corona is presented by allowing sound waves to propagate back and forth along the loop. It is found that the system can exhibit isobaric-like behaviour provided the acoustic timescale is short enough. Possible extensions of the developed loop model are discussed as well as the implications of time-dependent heating upon observations from the SOHO satellite.
1996-01-01T00:00:00ZWalsh, Robert WilliamThe problem of how the Sun's corona is heated is of central importance in Solar Physics research. In this thesis, a model is constructed of a typical coronal magnetic loop in order to investigate the response of coronal plasma to a time-dependent heating source. It is not the aim of the research to study in detail a particular heating mechanism but rather to understand the important features arising from time-dependent heating in general. A time-varying energy input into the coronal loop is required because it is likely that none of the suggested theoretical heating methods can provide a constant supply of heat to the corona. The magnetic field is taken to be strong enough that the loop dynamics reduce to a one-dimensional problem along the field. In addition, it is assumed that the radiative timescale in the corona is much longer than the sound travel time and thus, the plasma evolves isobarically. The thermal equilibria profiles along the coronal loop are then investigated for a simplified form of the optically thin radiation. Initially, a heating function that displays a regular, sinusoidal variation in time is introduced and it is found that there is a critical heating frequency above which a hot coronal loop solution can be maintained and below which the plasma temperature cools to chromospheric values. Pulse heating and the deposition of random-sized energy quanta in a loop are also investigated. An evaluation of the isobaric assumption to the corona is presented by allowing sound waves to propagate back and forth along the loop. It is found that the system can exhibit isobaric-like behaviour provided the acoustic timescale is short enough. Possible extensions of the developed loop model are discussed as well as the implications of time-dependent heating upon observations from the SOHO satellite.Time-dependent MHD wave coupling in non-uniform mediaMann, Ian R.http://hdl.handle.net/10023/142642018-06-19T23:17:43Z1996-01-01T00:00:00ZThis thesis studies the time dependent evolution of MHD waves in cold, fully compressible non-uniform plasmas. We used a 1-D box model (e.g., Southwood (1974)) to study wave mode coupling, and concentrate upon developing an understanding of the underlying physics that governs waves in the Earth's magnetosphere. We begin by discussing the form of the (often singular) governing eigenmodes of the system, and subsequently use these eigenmodes as a basis with which to construct the solution to a variety of initial value problems. We consider a detailed analysis of both the widths and the internal length scales developed by cavity mode driven held line resonances (FLRs), and compare our results to observations presented in the literature. We find that (especially asymptotically in time) the coupled waves derive their dominant characteristics from the form of undriven decoupled toroidal Alfvén eigenmodes. Ideal numerical solutions show that fine spatial scales are developed across the background magnetic field, and we demonstrate that this is accurately estimated as the decoupled phase mixing length
L[sub]p[sub]h = 2π/𝜔ⁱ[sub]A = d 𝜔[sub]A/dx
We also discuss the likely ionospheric and kinetic modifications to our theory. Later, we consider the evolution of poloidal Alfvén waves having large azimuthal wavenumber (𝜆). We find that the 𝜆 → ∞ decoupled poloidal Alfvén wave evaluation (Dungey, 1967) is modified for finite 𝜆 lambda, approaching decoupled toroidal field line oscillations for large t. We define a poloidal lifetime 𝛵, when toroidal and poloidal displacements become equal, and demonstrate that this is when the phase mixing length is equal to 2pi/lambda. We examine numerically the poloidal Alfvén wave evolution for 𝜆 ≫ k[sub]z, and k[sub]≳ lambda, when k[sub]x(x,t = 0) ≪ lambda or k[sub]z. We interpret the lambda ≪ kz results (applicable to the Earth's magnetosphere) in the context of poloidal Alfvén wave observations, and compare our study to the numerical analysis of Ding et al. (1995). We conclude the thesis by undertaking an asymptotic derivation of the large 𝜆 solutions by using the method of multiple time scales. We find our analytic solutions are in excellent agreement with those determined numerically. A central result of the thesis is the importance and dominance of the phase mixing length for time dependent solutions, irrespective of the value of 𝜆.
1996-01-01T00:00:00ZMann, Ian R.This thesis studies the time dependent evolution of MHD waves in cold, fully compressible non-uniform plasmas. We used a 1-D box model (e.g., Southwood (1974)) to study wave mode coupling, and concentrate upon developing an understanding of the underlying physics that governs waves in the Earth's magnetosphere. We begin by discussing the form of the (often singular) governing eigenmodes of the system, and subsequently use these eigenmodes as a basis with which to construct the solution to a variety of initial value problems. We consider a detailed analysis of both the widths and the internal length scales developed by cavity mode driven held line resonances (FLRs), and compare our results to observations presented in the literature. We find that (especially asymptotically in time) the coupled waves derive their dominant characteristics from the form of undriven decoupled toroidal Alfvén eigenmodes. Ideal numerical solutions show that fine spatial scales are developed across the background magnetic field, and we demonstrate that this is accurately estimated as the decoupled phase mixing length
L[sub]p[sub]h = 2π/𝜔ⁱ[sub]A = d 𝜔[sub]A/dx
We also discuss the likely ionospheric and kinetic modifications to our theory. Later, we consider the evolution of poloidal Alfvén waves having large azimuthal wavenumber (𝜆). We find that the 𝜆 → ∞ decoupled poloidal Alfvén wave evaluation (Dungey, 1967) is modified for finite 𝜆 lambda, approaching decoupled toroidal field line oscillations for large t. We define a poloidal lifetime 𝛵, when toroidal and poloidal displacements become equal, and demonstrate that this is when the phase mixing length is equal to 2pi/lambda. We examine numerically the poloidal Alfvén wave evolution for 𝜆 ≫ k[sub]z, and k[sub]≳ lambda, when k[sub]x(x,t = 0) ≪ lambda or k[sub]z. We interpret the lambda ≪ kz results (applicable to the Earth's magnetosphere) in the context of poloidal Alfvén wave observations, and compare our study to the numerical analysis of Ding et al. (1995). We conclude the thesis by undertaking an asymptotic derivation of the large 𝜆 solutions by using the method of multiple time scales. We find our analytic solutions are in excellent agreement with those determined numerically. A central result of the thesis is the importance and dominance of the phase mixing length for time dependent solutions, irrespective of the value of 𝜆.Magnetic neutral points and nonuniform reconnectionStrachan, N. R.http://hdl.handle.net/10023/142502018-06-19T23:17:17Z1994-01-01T00:00:00ZEver since the first recorded observation of a solar flare in September 1859, it has been a key question - for physics as a whole and for astrophsics in particular - to ask what mechanism lies behind the sudden, violent release of energy from the sun. It has become increasingly apparent that the complex structure of the solar magnetic field lies at the heart of the answer. The process of magnetic reconnection has, over the years, become the accepted explanation by which magnetic energy can be released on both large and small scales in astrophysical and laboratory plasmas. The results of reconnection can be seen, for instance, in star formation, solar flares and the earth's aurorae; indeed the 1859 flare was followed by exceptional auroral activity. The mechanism of magnetic reconnection was first postulated by Giovanelli (1947) as a way of releasing the magnetic energy stored in the Sun. He, and later Dungey (1953), realised that the behaviour of the plasma in the vicinity of a magnetic neutral or null point, where the field disappears, is quite different from other regions of space. In this thesis the nature of magnetic neutral points and their role in the process of reconnection is investigated. Firstly, a general classification of magnetic neutral points is presented. The chapter includes equilibrium and steady-state solutions for two-dimensional magnetic neutral points. The differences in the field behaviour close to each type of neutral point are explained and criteria for the existence of steady-state solutions and equilibria involving pressure balance are presented. In the last section, a self-similar solution for a collapsed X-point is explored. The X-point necessarily becomes cusp-like in nature if shearing is applied in the ignorable direction. Two reconnection models are considered. The first is an extension of the Priest-Lee model (1990). It incorporates large pressure gradients in the inflow corresponding to the Forbes-Priest Almost-Uniform Model. The investigation includes both analytical and numerical solutions and a study of the separatrix jet. In the numerical study, current spikes are found at the end of the current sheets and a much increased reconnection rate is found analytically in the extreme flux file-up limit. The second reconnection model presented is also based on the Priest-Lee configuration. A uniform field is imposed on the basic structure producing a cusp-point with a non-zero field strength as the neutral point is approached from above. This results in the removal of the singularity in the flow above the separatrix. A non-singular solution is found analytically for a double-cusp. A much larger reconnection rate is found and a numerical solution is presented.
1994-01-01T00:00:00ZStrachan, N. R.Ever since the first recorded observation of a solar flare in September 1859, it has been a key question - for physics as a whole and for astrophsics in particular - to ask what mechanism lies behind the sudden, violent release of energy from the sun. It has become increasingly apparent that the complex structure of the solar magnetic field lies at the heart of the answer. The process of magnetic reconnection has, over the years, become the accepted explanation by which magnetic energy can be released on both large and small scales in astrophysical and laboratory plasmas. The results of reconnection can be seen, for instance, in star formation, solar flares and the earth's aurorae; indeed the 1859 flare was followed by exceptional auroral activity. The mechanism of magnetic reconnection was first postulated by Giovanelli (1947) as a way of releasing the magnetic energy stored in the Sun. He, and later Dungey (1953), realised that the behaviour of the plasma in the vicinity of a magnetic neutral or null point, where the field disappears, is quite different from other regions of space. In this thesis the nature of magnetic neutral points and their role in the process of reconnection is investigated. Firstly, a general classification of magnetic neutral points is presented. The chapter includes equilibrium and steady-state solutions for two-dimensional magnetic neutral points. The differences in the field behaviour close to each type of neutral point are explained and criteria for the existence of steady-state solutions and equilibria involving pressure balance are presented. In the last section, a self-similar solution for a collapsed X-point is explored. The X-point necessarily becomes cusp-like in nature if shearing is applied in the ignorable direction. Two reconnection models are considered. The first is an extension of the Priest-Lee model (1990). It incorporates large pressure gradients in the inflow corresponding to the Forbes-Priest Almost-Uniform Model. The investigation includes both analytical and numerical solutions and a study of the separatrix jet. In the numerical study, current spikes are found at the end of the current sheets and a much increased reconnection rate is found analytically in the extreme flux file-up limit. The second reconnection model presented is also based on the Priest-Lee configuration. A uniform field is imposed on the basic structure producing a cusp-point with a non-zero field strength as the neutral point is approached from above. This results in the removal of the singularity in the flow above the separatrix. A non-singular solution is found analytically for a double-cusp. A much larger reconnection rate is found and a numerical solution is presented.Aspects of the MHD stability of coronal and laboratory plasmasClifford, Leo J.http://hdl.handle.net/10023/142482018-06-19T23:16:39Z1993-01-01T00:00:00ZThe magnetohydrodynamic (MHD) model is a simple mathematical model that treats a plasma as a perfectly conducting fluid acted upon by magnetic and pressure-driven forces. Many instabilities in plasmas can be predicted using this model. In this Thesis, aspects of the linear stability of solar and laboratory plasmas are studied using the MHD model. Firstly, we investigate the thermal instability of coronal plasmas with line-tied magnetic fields and with anisotropical heat conduction, using an analytical analysis which concentrates on isobaric perturbations, and a time-dependent numerical code. We find that including perpendicular thermal conduction means that condensations are restricted to a narrow layer around the region where the local isobaric growth rate is largest and that, while the growth rate of the thermal mode is largely unaffected by perpendicular thermal conduction, this may be an important factor in determining the lengthscale for the width of condensations. Secondly, the effect of a finitely conducting wall on the linear stability of Spheromak and Reversed Field Finch equilibria is investigated. We find growth rates for the modes that are present because of the finite resistivity of the wall, which grow proportionally to the "long" time constant of the wall. Finally, we apply a tractable method, derived by De Bruyne (1990), for investigating the stability of 2-D line-tied magnetic fields, to cylindrically symmetric spheromak equilibria. The method involves the solution of two sets of ordinary differential equations, integrated along the field lines, which give necessary and sufficient conditions for stability. The role of plasma pressure and of the width of the entrance region are investigated.
1993-01-01T00:00:00ZClifford, Leo J.The magnetohydrodynamic (MHD) model is a simple mathematical model that treats a plasma as a perfectly conducting fluid acted upon by magnetic and pressure-driven forces. Many instabilities in plasmas can be predicted using this model. In this Thesis, aspects of the linear stability of solar and laboratory plasmas are studied using the MHD model. Firstly, we investigate the thermal instability of coronal plasmas with line-tied magnetic fields and with anisotropical heat conduction, using an analytical analysis which concentrates on isobaric perturbations, and a time-dependent numerical code. We find that including perpendicular thermal conduction means that condensations are restricted to a narrow layer around the region where the local isobaric growth rate is largest and that, while the growth rate of the thermal mode is largely unaffected by perpendicular thermal conduction, this may be an important factor in determining the lengthscale for the width of condensations. Secondly, the effect of a finitely conducting wall on the linear stability of Spheromak and Reversed Field Finch equilibria is investigated. We find growth rates for the modes that are present because of the finite resistivity of the wall, which grow proportionally to the "long" time constant of the wall. Finally, we apply a tractable method, derived by De Bruyne (1990), for investigating the stability of 2-D line-tied magnetic fields, to cylindrically symmetric spheromak equilibria. The method involves the solution of two sets of ordinary differential equations, integrated along the field lines, which give necessary and sufficient conditions for stability. The role of plasma pressure and of the width of the entrance region are investigated.Ducted magnetoacoustic waves in the solar coronaSmith, Jason M.http://hdl.handle.net/10023/142462018-06-19T23:17:27Z1997-01-01T00:00:00ZThis thesis investigates the ducting of magnetoacoustic waves in coronal structures. The propagation of waves in current sheets and coronal loops has been examined in order to understand wave ducting in structured plasmas, and to provide an explanation of the observed oscillatory behaviour in the solar corona. Firstly a comprehensive review of the observations of loops and oscillations in the corona is given. An investigation into how the curvature of the loop alters the ducting of magnetoacoustic waves is then presented by studying the effect of the length, width and the density enhancement of the loop and also the frequency of oscillation. The effect of the curvature is to generate wave leakage from the loop. The guiding of magnetoacoustic waves by a current sheet is also considered. An investigation into the type of modes which may propagate and the time scales of oscillation is performed. Impulsively generated waves exhibit similar temporal signatures to observations of X-ray and radio emission. Periods of oscillation for all the ducted wave models are in good agreement with reported observations. The effect of a random boundary motion on a magnetospheric cavity is examined through numerical simulations. A broadband driving spectrum excites the quasi-monochromatic fast modes whose frequencies lie within the driving spectrum. These fast modes couple to an Alfvén mode if the frequency lies within the Alfvén continuum. The position of the resonant field lines and the Alfvén mode eigenfunction may be accurately calculated by assuming a periodic boundary motion. To conclude the work in this thesis the three-dimensional magnetic topologies surrounding neutral points are studied. The local linear magnetic structure about the null is found to depend only on a 3 X 3 matrix containing four parameters. The type of topology is dependent upon the nature of the eigenvalues and eigenvectors of this matrix.
1997-01-01T00:00:00ZSmith, Jason M.This thesis investigates the ducting of magnetoacoustic waves in coronal structures. The propagation of waves in current sheets and coronal loops has been examined in order to understand wave ducting in structured plasmas, and to provide an explanation of the observed oscillatory behaviour in the solar corona. Firstly a comprehensive review of the observations of loops and oscillations in the corona is given. An investigation into how the curvature of the loop alters the ducting of magnetoacoustic waves is then presented by studying the effect of the length, width and the density enhancement of the loop and also the frequency of oscillation. The effect of the curvature is to generate wave leakage from the loop. The guiding of magnetoacoustic waves by a current sheet is also considered. An investigation into the type of modes which may propagate and the time scales of oscillation is performed. Impulsively generated waves exhibit similar temporal signatures to observations of X-ray and radio emission. Periods of oscillation for all the ducted wave models are in good agreement with reported observations. The effect of a random boundary motion on a magnetospheric cavity is examined through numerical simulations. A broadband driving spectrum excites the quasi-monochromatic fast modes whose frequencies lie within the driving spectrum. These fast modes couple to an Alfvén mode if the frequency lies within the Alfvén continuum. The position of the resonant field lines and the Alfvén mode eigenfunction may be accurately calculated by assuming a periodic boundary motion. To conclude the work in this thesis the three-dimensional magnetic topologies surrounding neutral points are studied. The local linear magnetic structure about the null is found to depend only on a 3 X 3 matrix containing four parameters. The type of topology is dependent upon the nature of the eigenvalues and eigenvectors of this matrix.Inverse polarity prominence equilibriaSchönfelder, Apollonia Maria Oktaviahttp://hdl.handle.net/10023/142432018-06-19T23:17:18Z1995-01-01T00:00:00ZIt has been supposed since the middle of this century that it is the global magnetic field surrounding a quiescent prominence that provides the force to prevent its collapse due to the sun’s gravitational field. Many theoretical models, assuming that the prominence plasma is supported in a dip in the magnetic field lines associated by the magnetic tension force, have since been put forward. The aim of this thesis is to propose further models of quiescent prominences to widen our understanding and knowledge of these remarkable features.
A short overview over the magnetohydrodynamic equations used to describe solar prominences, or most of the solar phenomena for that matter, are discussed in chapter 2, and a short summary of prominence observations and attempts to model them is given in chapter 3.
A brief description of the numerical code used in chapters 5 and 7 is given in chapter 4.
Observations of Kim (1990) and Leroy (1985) have found that most large quiescent prominences are of inverse polarity type for which the magnetic field passes through the prominence in the opposite direction to that expected from the photospheric magnetic field. Many theoretical models have been proposed, but failed. Hence, in chapter 5 we investigate first – without the inclusion of a prominence sheet – when an inverse polarity magnetic field must have the correct topology for an inverse polarity configuration before the formation of the prominence itself. Only very recently, the first basic successful model of an I-type polarity prominence was proposed by Low (1993). In chapter 6 we examine this model and investigate current sheets more complicated and realistic than the one used by Low. These analytical models deal with the force-free solution, which is matched onto an external, unsheared, potential coronal magnetic field. These solutions are mathematically interesting and allow an investigation of different profiles of the current intensity of the magnetic field vector and of the mass density in the sheet. The prominence properties predicted by these models have been examined and have been found to match the observational values. The mathematics of current sheets in general is also briefly discussed.
Chapter 7 deals with numerical solutions of inverse polarity prominences embedded in a force-free magnetic flux tube, matched onto an unsheared potential coronal field. Unfortunately the solutions gained are quite sensitive to the boundary conditions imposed on them through the numerical box, showing a loss of convergence and a tendency for the solution to blow up.
Finally, a short summary as well as possible future work is given in chapter 8.
1995-01-01T00:00:00ZSchönfelder, Apollonia Maria OktaviaIt has been supposed since the middle of this century that it is the global magnetic field surrounding a quiescent prominence that provides the force to prevent its collapse due to the sun’s gravitational field. Many theoretical models, assuming that the prominence plasma is supported in a dip in the magnetic field lines associated by the magnetic tension force, have since been put forward. The aim of this thesis is to propose further models of quiescent prominences to widen our understanding and knowledge of these remarkable features.
A short overview over the magnetohydrodynamic equations used to describe solar prominences, or most of the solar phenomena for that matter, are discussed in chapter 2, and a short summary of prominence observations and attempts to model them is given in chapter 3.
A brief description of the numerical code used in chapters 5 and 7 is given in chapter 4.
Observations of Kim (1990) and Leroy (1985) have found that most large quiescent prominences are of inverse polarity type for which the magnetic field passes through the prominence in the opposite direction to that expected from the photospheric magnetic field. Many theoretical models have been proposed, but failed. Hence, in chapter 5 we investigate first – without the inclusion of a prominence sheet – when an inverse polarity magnetic field must have the correct topology for an inverse polarity configuration before the formation of the prominence itself. Only very recently, the first basic successful model of an I-type polarity prominence was proposed by Low (1993). In chapter 6 we examine this model and investigate current sheets more complicated and realistic than the one used by Low. These analytical models deal with the force-free solution, which is matched onto an external, unsheared, potential coronal magnetic field. These solutions are mathematically interesting and allow an investigation of different profiles of the current intensity of the magnetic field vector and of the mass density in the sheet. The prominence properties predicted by these models have been examined and have been found to match the observational values. The mathematics of current sheets in general is also briefly discussed.
Chapter 7 deals with numerical solutions of inverse polarity prominences embedded in a force-free magnetic flux tube, matched onto an unsheared potential coronal field. Unfortunately the solutions gained are quite sensitive to the boundary conditions imposed on them through the numerical box, showing a loss of convergence and a tendency for the solution to blow up.
Finally, a short summary as well as possible future work is given in chapter 8.The magnetohydrostatic equilibrium of quiescent solar prominencesRidgway, Christopherhttp://hdl.handle.net/10023/142392018-06-19T23:17:21Z1992-01-01T00:00:00ZSince the mid 1900's it has been supposed that the global magnetic field surrounding a quiescent prominence provides the force required to prevent its collapse under the influence of the Sun's gravitational field. Many theoretical models of this magnetic field have been produced in which it is assumed that the prominence plasma is supported in a dip in the field lines by the associated magnetic tension force. It is the aim of this thesis to propose further models of the magnetic field in order to extend our knowledge and understanding of prominences. In doing so we present three distinct models. The first is an extension of the twisted flux tube model for prominences proposed by Priest et al. (1989). Here we present analytical solutions to the magnetohydrostatic equilibrium equation within the tube using the so- called generating function method in which we select two distinct functional forms of the longitudinal field component. Unlike the solutions found by Priest et al., we allow for large deviations of the field from cylindrical symmetry. The prominence is represented by a finite vertical sheet of mass and current and we show that it is possible for such a sheet to be in static equilibrium everywhere along its vertical extent. Next we consider the model of van Ballegooijen and Martens in which photospheric motions drive a reconnection process leading to the formation of a helical magnetic structure capable of supporting dense prominence plasma in the low points of the helical windings. Under the assumption of cylindrical symmetry we analyse two methods of solving the magnetohydrostatic equilibrium equation in which the positions of the field line footpoints at the photosphere are imposed. Using a combination of analytical and numerical techniques, we study the quasi-static evolution of the model as the height of the helical axis increases. Unlike the numerical analysis of van Ballegooijen and Martens we are able to produce inverse polarity configurations without the problem of singular field components at the helical axis. Lastly we present an analysis of the interaction of a finite, vertical sheet of mass and current (representing a prominence) with an external constant-current force-free field. We formalise two distinct boundary-value problems in which the distribution of the normal magnetic field component along the photosphere is imposed along with the distribution of either the normal magnetic field component across the prominence or the prominence surface current. In both cases we demonstrate for particular boundary conditions that it is possible for equilibrium solutions to exist of both normal and inverse polarity in which dense material is supported everywhere along the prominence sheet. In particular we are, for the first time, able to produce an inverse polarity equilibrium configuration in which the field components are locally bounded and closed field lines exist above the prominence sheet while an X-type neutral point lies below it.
1992-01-01T00:00:00ZRidgway, ChristopherSince the mid 1900's it has been supposed that the global magnetic field surrounding a quiescent prominence provides the force required to prevent its collapse under the influence of the Sun's gravitational field. Many theoretical models of this magnetic field have been produced in which it is assumed that the prominence plasma is supported in a dip in the field lines by the associated magnetic tension force. It is the aim of this thesis to propose further models of the magnetic field in order to extend our knowledge and understanding of prominences. In doing so we present three distinct models. The first is an extension of the twisted flux tube model for prominences proposed by Priest et al. (1989). Here we present analytical solutions to the magnetohydrostatic equilibrium equation within the tube using the so- called generating function method in which we select two distinct functional forms of the longitudinal field component. Unlike the solutions found by Priest et al., we allow for large deviations of the field from cylindrical symmetry. The prominence is represented by a finite vertical sheet of mass and current and we show that it is possible for such a sheet to be in static equilibrium everywhere along its vertical extent. Next we consider the model of van Ballegooijen and Martens in which photospheric motions drive a reconnection process leading to the formation of a helical magnetic structure capable of supporting dense prominence plasma in the low points of the helical windings. Under the assumption of cylindrical symmetry we analyse two methods of solving the magnetohydrostatic equilibrium equation in which the positions of the field line footpoints at the photosphere are imposed. Using a combination of analytical and numerical techniques, we study the quasi-static evolution of the model as the height of the helical axis increases. Unlike the numerical analysis of van Ballegooijen and Martens we are able to produce inverse polarity configurations without the problem of singular field components at the helical axis. Lastly we present an analysis of the interaction of a finite, vertical sheet of mass and current (representing a prominence) with an external constant-current force-free field. We formalise two distinct boundary-value problems in which the distribution of the normal magnetic field component along the photosphere is imposed along with the distribution of either the normal magnetic field component across the prominence or the prominence surface current. In both cases we demonstrate for particular boundary conditions that it is possible for equilibrium solutions to exist of both normal and inverse polarity in which dense material is supported everywhere along the prominence sheet. In particular we are, for the first time, able to produce an inverse polarity equilibrium configuration in which the field components are locally bounded and closed field lines exist above the prominence sheet while an X-type neutral point lies below it.Wave-particle dynamics in a hot inhomogenous fusion plasmaTaylor, Michael Anthonyhttp://hdl.handle.net/10023/142352018-06-19T23:17:23Z1996-01-01T00:00:00ZAn outstanding problem in the field of nuclear fusion research is the precise mechanism by which a hot, magnetically inhomogeneous plasma is heated when illuminated by a constant beam of small amplitude radio waves matched in frequency to harmonics of the ion Larmor frequency. An accurate model must include microscopic dynamics and inevitably a kinetic theory is required. Highly energetic ions (> 1MeV) born from fusion reactions or powered by gyroresonance have large Larmor radii (> 10cm) which are comparable in size to the wavelength of the incident radiation. In particular we will focus on fast magnetosonic waves. Exact full wave equations describing a thermal plasma in a weakly inhomogeneous field are presently at least fourth order integro-differential equations (Sauter, 1992). These are computationally taxing. Recently a method was proposed to reduce the problem to a second order integro-differential equation at the expense of information related to the propagation of mode-converted waves (Holt, 1992). We present here a generalisation of the theory to allow for arbitrary velocity-dependent equilibria while at the same time retaining a general functional form for the field profile. We consider the specific case of a bi-Maxwellian plasma immersed in a linearly inhomogenous magnetic field. We find that thermal anisotropy produces resonance localisation when the perpendicular ion temperature is greater than that parallel to the ambient field. A study of the symmetry properties of the conductivity tensor reveals that the Onsager reciprocal relations are obeyed only for an isotropic plasma in an inhomogeneous field. This is a generalisation of the result obtained by Nambu (1995). We present a generalisation of the reduction method to include effects due to changes in wave amplitude. We find that we are able to include the odd-order field derivatives responsible for energy conservation. Our numerical study of fundamental Helium-3 gyroresonance in a majority Deuterium plasma reveals that we have > 99.9% energy conservation in all cases. We show that locally-uniform theory can be very inaccurate (≃ 70% in one case presented in our recent paper, Cairns et al., 1995) particularly for higher energy ions whose non-locality is more extreme. We present a representative sample of results for minority heating and mode conversion heating schemes. We report the appearance of an unexpected cut-off on the low field side of the minority gyroresonance which may have important consequences for antennae presently placed on the outside of Tokamaks.
1996-01-01T00:00:00ZTaylor, Michael AnthonyAn outstanding problem in the field of nuclear fusion research is the precise mechanism by which a hot, magnetically inhomogeneous plasma is heated when illuminated by a constant beam of small amplitude radio waves matched in frequency to harmonics of the ion Larmor frequency. An accurate model must include microscopic dynamics and inevitably a kinetic theory is required. Highly energetic ions (> 1MeV) born from fusion reactions or powered by gyroresonance have large Larmor radii (> 10cm) which are comparable in size to the wavelength of the incident radiation. In particular we will focus on fast magnetosonic waves. Exact full wave equations describing a thermal plasma in a weakly inhomogeneous field are presently at least fourth order integro-differential equations (Sauter, 1992). These are computationally taxing. Recently a method was proposed to reduce the problem to a second order integro-differential equation at the expense of information related to the propagation of mode-converted waves (Holt, 1992). We present here a generalisation of the theory to allow for arbitrary velocity-dependent equilibria while at the same time retaining a general functional form for the field profile. We consider the specific case of a bi-Maxwellian plasma immersed in a linearly inhomogenous magnetic field. We find that thermal anisotropy produces resonance localisation when the perpendicular ion temperature is greater than that parallel to the ambient field. A study of the symmetry properties of the conductivity tensor reveals that the Onsager reciprocal relations are obeyed only for an isotropic plasma in an inhomogeneous field. This is a generalisation of the result obtained by Nambu (1995). We present a generalisation of the reduction method to include effects due to changes in wave amplitude. We find that we are able to include the odd-order field derivatives responsible for energy conservation. Our numerical study of fundamental Helium-3 gyroresonance in a majority Deuterium plasma reveals that we have > 99.9% energy conservation in all cases. We show that locally-uniform theory can be very inaccurate (≃ 70% in one case presented in our recent paper, Cairns et al., 1995) particularly for higher energy ions whose non-locality is more extreme. We present a representative sample of results for minority heating and mode conversion heating schemes. We report the appearance of an unexpected cut-off on the low field side of the minority gyroresonance which may have important consequences for antennae presently placed on the outside of Tokamaks.Models of X-ray bright points and concelling magnetic featuresParnell, Clare E.http://hdl.handle.net/10023/142322018-06-19T23:17:02Z1995-01-01T00:00:00ZSmall brightenings called x-ray bright points (Golub et al, 1974) occur in the solar corona. They are observed with the soft x-ray telescope on Skylab to be approximately 22 Mm in diameter with a brighter inner core of width 4-7 Mm although with the Normal Incidence X-ray Telescope their dimensions are observed to be typically 6 Mm x 9 Mm. By comparison with magnetograms of the photosphere it has been noticed recently that there is a high correlation between the occurrence of x-ray bright points and the mutual reduction of flux between two opposite polarity magnetic fragments. These fragments are originally unconnected magnetically, but move towards each other and simultaneously lose equal amounts of flux (cancel): they are called cancelling magnetic features (Martin et al, 1984). The observations relating to these features were reviewed by Priest et al. (1994) who suggested that they naturally evolve through three phases: the pre-interaction, interaction and cancellation phases. From this evidence qualitative pictures of the magnetic field structure for an x-ray bright point and associated cancelling magnetic feature were established. The aim of this thesis has been to build on the ideas of Priest et al. (1994) to produce a detailed theoretical model of an x-ray bright point and a cancelling magnetic feature. The magnetic field structures are estimated, and the position and lifetime of the bright point are calculated, as is the total amount of energy released during the bright point. This work is also extended to study more complex cancelling configurations representing the main basic types of cancelling magnetic feature. The results of these models determine the factors that affect the lifetime and position of a bright point and indicate which types of cancelling magnetic features are most likely to produce bright points that are long-lived, lie directly above the cancellation site and occur simultaneously with the cancellation phase. The complex structure of a bright point cannot be explained from the above two-dimensional models: thus two recently observed bright points were studied to see if the above model could be extended into three dimensions to explain the structure seen in soft x-ray images. The available observational data was used and leads to reasonable explanations for the complex shapes of both bright points. Finally, a more realistic model for the overlying field was set up involving a model of the field above a supergranule cell field with fragments of finite width. The interaction of an ephemeral region within this field was then studied and led to five different scenarios. The results obtained reaffirmed those found in the previous simpler models and suggest where bright points may appear in a cell relative to the cancelling magnetic feature and for how long the bright points might last. Predictions for the lifetimes of cancelling magnetic features are also made, indicating when the cancelling magnetic feature occurs relative to the bright point.
1995-01-01T00:00:00ZParnell, Clare E.Small brightenings called x-ray bright points (Golub et al, 1974) occur in the solar corona. They are observed with the soft x-ray telescope on Skylab to be approximately 22 Mm in diameter with a brighter inner core of width 4-7 Mm although with the Normal Incidence X-ray Telescope their dimensions are observed to be typically 6 Mm x 9 Mm. By comparison with magnetograms of the photosphere it has been noticed recently that there is a high correlation between the occurrence of x-ray bright points and the mutual reduction of flux between two opposite polarity magnetic fragments. These fragments are originally unconnected magnetically, but move towards each other and simultaneously lose equal amounts of flux (cancel): they are called cancelling magnetic features (Martin et al, 1984). The observations relating to these features were reviewed by Priest et al. (1994) who suggested that they naturally evolve through three phases: the pre-interaction, interaction and cancellation phases. From this evidence qualitative pictures of the magnetic field structure for an x-ray bright point and associated cancelling magnetic feature were established. The aim of this thesis has been to build on the ideas of Priest et al. (1994) to produce a detailed theoretical model of an x-ray bright point and a cancelling magnetic feature. The magnetic field structures are estimated, and the position and lifetime of the bright point are calculated, as is the total amount of energy released during the bright point. This work is also extended to study more complex cancelling configurations representing the main basic types of cancelling magnetic feature. The results of these models determine the factors that affect the lifetime and position of a bright point and indicate which types of cancelling magnetic features are most likely to produce bright points that are long-lived, lie directly above the cancellation site and occur simultaneously with the cancellation phase. The complex structure of a bright point cannot be explained from the above two-dimensional models: thus two recently observed bright points were studied to see if the above model could be extended into three dimensions to explain the structure seen in soft x-ray images. The available observational data was used and leads to reasonable explanations for the complex shapes of both bright points. Finally, a more realistic model for the overlying field was set up involving a model of the field above a supergranule cell field with fragments of finite width. The interaction of an ephemeral region within this field was then studied and led to five different scenarios. The results obtained reaffirmed those found in the previous simpler models and suggest where bright points may appear in a cell relative to the cancelling magnetic feature and for how long the bright points might last. Predictions for the lifetimes of cancelling magnetic features are also made, indicating when the cancelling magnetic feature occurs relative to the bright point.Aspects of MHD wave propagation in solar atmospheric studiesMundie, Cheryl Annhttp://hdl.handle.net/10023/142272018-06-19T23:16:34Z1998-01-01T00:00:00ZThe theme of this thesis is ideal linear MHD wave propagation in structured media, using models relevant to structures in the solar atmosphere. We derive dispersion relations governing the ideal linear MHD modes for stationary states which are discretely structured in velocity and other plasma properties, in a direction transverse to the magnetic field, with field-aligned steady flow; the discrete structures considered are the single interface, uniform slab and uniform cylinder. This represents an extension of earlier models for the static case (Edwin 1984), by the inclusion of structured flows. The basic effects of flow are described, drawing on a discussion of the dispersion relations. The dispersion relations for the case of incompressible surface modes are examined in detail. We identify the qualitative effects of flow, including the onset of instability, by tracing the evolution of stable solutions and their propagation windows, as the relative flow is increased. Our analysis is presented in terms of a general formulation applicable to all three geometries (interface, slab and cylinder), revealing the combined role of dispersion and the ratio of densities in the two media. We go on to consider the relevance of the incompressible approximation to compressible surface modes, with particular reference to the static case of a single interface one side of which is field-free. We present and investigate analytical solutions for several special cases. The properties of the solutions obtained are compared with those for the equivalent incompressible case. Finally, we turn to the topic of global oscillations of quiescent prominences. A uniform slab model (Joarder 1993) yields, under conditions appropriate to the prominence-coronal inhomogeneity with the magnetic field threading the prominence being line-tied in the photosphere, modes which are analogous to the oscillations of a uniform string loaded with a point mass, and a formula approximating the period is given. We investigate the robustness of this formula for various plasma density profiles, assessing the applicability of the results from the uniform slab calculation to more realistic density profiles of the prominence-coronal inhomogeneity.
1998-01-01T00:00:00ZMundie, Cheryl AnnThe theme of this thesis is ideal linear MHD wave propagation in structured media, using models relevant to structures in the solar atmosphere. We derive dispersion relations governing the ideal linear MHD modes for stationary states which are discretely structured in velocity and other plasma properties, in a direction transverse to the magnetic field, with field-aligned steady flow; the discrete structures considered are the single interface, uniform slab and uniform cylinder. This represents an extension of earlier models for the static case (Edwin 1984), by the inclusion of structured flows. The basic effects of flow are described, drawing on a discussion of the dispersion relations. The dispersion relations for the case of incompressible surface modes are examined in detail. We identify the qualitative effects of flow, including the onset of instability, by tracing the evolution of stable solutions and their propagation windows, as the relative flow is increased. Our analysis is presented in terms of a general formulation applicable to all three geometries (interface, slab and cylinder), revealing the combined role of dispersion and the ratio of densities in the two media. We go on to consider the relevance of the incompressible approximation to compressible surface modes, with particular reference to the static case of a single interface one side of which is field-free. We present and investigate analytical solutions for several special cases. The properties of the solutions obtained are compared with those for the equivalent incompressible case. Finally, we turn to the topic of global oscillations of quiescent prominences. A uniform slab model (Joarder 1993) yields, under conditions appropriate to the prominence-coronal inhomogeneity with the magnetic field threading the prominence being line-tied in the photosphere, modes which are analogous to the oscillations of a uniform string loaded with a point mass, and a formula approximating the period is given. We investigate the robustness of this formula for various plasma density profiles, assessing the applicability of the results from the uniform slab calculation to more realistic density profiles of the prominence-coronal inhomogeneity.Magnetohydrodynamic surface waves in the solar atmosphereMiles, Alan J.http://hdl.handle.net/10023/142252018-06-19T23:16:22Z1991-01-01T00:00:00ZIn this thesis the nature of magnetoacoustic surface waves at a single magnetic interface is examined for the case of parallel propagation. Above the interface is an isothermal medium permeated by a horizontal magnetic field. The lower region is a field-free medium of different density to the magnetic atmosphere. We consider both the incompressible and compressible situations and the effect of including gravity. In each case a transcendental dispersion relation is solved numerically for a range of parameters and the resulting dispersion curves plotted. In the first chapter we provide a general introduction to the work, reviewing previous work in this area and considering applications of surface waves. In the second chapter we consider the existence of surface waves for the case when the media are incompressible either side of the interface. We consider the cases of both uniform and non-uniform distributions of densities and the effect of including gravity. We show that the f-mode exists in a restricted band of horizontal wavenumber. In the subsequent chapters we consider the effect of compressibility on surface waves. The media either side of the interface are taken to be isothermal. In the absence of gravity the interface may support one or two surface modes determined by the relative temperatures and magnetism of the two media. This case is studied in Chapter 3 where phase-speeds and penetration depths of the waves and the associated pressure perturbations are investigated for a variety of field strengths and sound speeds. In Chapters 4 and 5 we consider the effect of gravity on the compressible modes described in Chapter 3. In Chapter 4 an exact dispersion relation is obtained for the case of a constant Alfven speed, whilst in Chapter 5 the case of a uniform magnetic field is considered. In the absence of the magnetic field the transcendental dispersion relation may be reduced to a polynomial. This polynomial possesses two acceptable solutions, only one of which may exist at any given circumstance depending on the densities either side of the interface. If the gas density within the field exceeds that in the field-free medium, then the f-mode may propagate; otherwise, a magnetic surface gravity mode propagates. As in the incompressible case, the f-mode exists in a restricted band of horizontal wavenumber. An analytical form for the wave speed of the f-mode is obtained for small values of the Alfven speed. It is shown that the f-mode is related to the fast magnetoacoustic surface wave, merging into that mode at short wavelengths.
1991-01-01T00:00:00ZMiles, Alan J.In this thesis the nature of magnetoacoustic surface waves at a single magnetic interface is examined for the case of parallel propagation. Above the interface is an isothermal medium permeated by a horizontal magnetic field. The lower region is a field-free medium of different density to the magnetic atmosphere. We consider both the incompressible and compressible situations and the effect of including gravity. In each case a transcendental dispersion relation is solved numerically for a range of parameters and the resulting dispersion curves plotted. In the first chapter we provide a general introduction to the work, reviewing previous work in this area and considering applications of surface waves. In the second chapter we consider the existence of surface waves for the case when the media are incompressible either side of the interface. We consider the cases of both uniform and non-uniform distributions of densities and the effect of including gravity. We show that the f-mode exists in a restricted band of horizontal wavenumber. In the subsequent chapters we consider the effect of compressibility on surface waves. The media either side of the interface are taken to be isothermal. In the absence of gravity the interface may support one or two surface modes determined by the relative temperatures and magnetism of the two media. This case is studied in Chapter 3 where phase-speeds and penetration depths of the waves and the associated pressure perturbations are investigated for a variety of field strengths and sound speeds. In Chapters 4 and 5 we consider the effect of gravity on the compressible modes described in Chapter 3. In Chapter 4 an exact dispersion relation is obtained for the case of a constant Alfven speed, whilst in Chapter 5 the case of a uniform magnetic field is considered. In the absence of the magnetic field the transcendental dispersion relation may be reduced to a polynomial. This polynomial possesses two acceptable solutions, only one of which may exist at any given circumstance depending on the densities either side of the interface. If the gas density within the field exceeds that in the field-free medium, then the f-mode may propagate; otherwise, a magnetic surface gravity mode propagates. As in the incompressible case, the f-mode exists in a restricted band of horizontal wavenumber. An analytical form for the wave speed of the f-mode is obtained for small values of the Alfven speed. It is shown that the f-mode is related to the fast magnetoacoustic surface wave, merging into that mode at short wavelengths.Some aspects of solar flare and prominence theoryMilne, Alexander Mitchellhttp://hdl.handle.net/10023/142222018-06-19T23:16:28Z1980-01-01T00:00:00ZSolar flares and solar prominences are amongst the best known features of solar activity. Despite this familiarity, however, there are still significant gaps in our knowledge of these phenomena. In this thesis some theoretical aspects of these events are considered. We first consider solar prominences. We propose a model for the static equilibrium of quiescent prominences which will simultaneously explain the support mechanism for the dense prominence material and take account roughly of the required energy balance. This model contains two parameters, namely the coronal plasma beta and the horizontal shear angle 𝜙, that the magnetic fieldlines make with the prominence normal. We obtain limits on both these parameters which, when exceeded, imply that no equilibrium state is possible. The results obtained provide a possible explanation for several prominence features. For the remainder of the thesis we consider one aspect of the solar flare problem, namely the possibility of a trigger mechanism for the rapid release of energy in a flare. One candidate for this mechanism is the sudden release of energy stored in excess of potential by a force-free magnetic field which becomes unstable as a result of photospheric motions. For this reason we seek simple analytic solutions to the force-free field equations which may exhibit such an instability. An alternative trigger mechanism, which requires the presence of a current sheet, is given by the emerging flux model for solar flares. We thus develop a one-dimensional model for current sheets in general, where the conditions within the current sheet are given in terms of several non-dimensional parameters which describe the external conditions. These results are then applied to the emerging flux model.
1980-01-01T00:00:00ZMilne, Alexander MitchellSolar flares and solar prominences are amongst the best known features of solar activity. Despite this familiarity, however, there are still significant gaps in our knowledge of these phenomena. In this thesis some theoretical aspects of these events are considered. We first consider solar prominences. We propose a model for the static equilibrium of quiescent prominences which will simultaneously explain the support mechanism for the dense prominence material and take account roughly of the required energy balance. This model contains two parameters, namely the coronal plasma beta and the horizontal shear angle 𝜙, that the magnetic fieldlines make with the prominence normal. We obtain limits on both these parameters which, when exceeded, imply that no equilibrium state is possible. The results obtained provide a possible explanation for several prominence features. For the remainder of the thesis we consider one aspect of the solar flare problem, namely the possibility of a trigger mechanism for the rapid release of energy in a flare. One candidate for this mechanism is the sudden release of energy stored in excess of potential by a force-free magnetic field which becomes unstable as a result of photospheric motions. For this reason we seek simple analytic solutions to the force-free field equations which may exhibit such an instability. An alternative trigger mechanism, which requires the presence of a current sheet, is given by the emerging flux model for solar flares. We thus develop a one-dimensional model for current sheets in general, where the conditions within the current sheet are given in terms of several non-dimensional parameters which describe the external conditions. These results are then applied to the emerging flux model.Polynomial generated polygonsSoares, Benedict J.http://hdl.handle.net/10023/141982018-06-18T23:17:17Z1999-01-01T00:00:00ZA turtle geometric construction on the plane, called a polynomial generated polygon (PGP) and represented by 𝒫[sub]f,[sub]pᵐ, is generated from the sequence obtained from evaluating f(𝓍) ∈ ℤ [𝓍] over ℤ modulo pᵐ where p is a prime and m ∈ ℕ. Computational methods are developed to pre-calculate the symmetries exhibited by [sub]f,[sub]pᵐ for a given f and pᵐ.
These include procedures to find whether [sub]f,[sub]pᵐ is bounded or unbounded, the degree of rotational symmetry present, whether lines of reflectional symmetry can be observed, and in the case of 𝒫[sub]f,[sub]pᵐ unbounded, whether the PGP has a glide reflection.
Methods are also sought to find a suitable f and pᵐ to produce a desired 'feasible' shape in a PGP construction, and how the same shape might be generated modulo pᵐ⁺ᵏ if it cannot be produced modulo pᵐ.
1999-01-01T00:00:00ZSoares, Benedict J.A turtle geometric construction on the plane, called a polynomial generated polygon (PGP) and represented by 𝒫[sub]f,[sub]pᵐ, is generated from the sequence obtained from evaluating f(𝓍) ∈ ℤ [𝓍] over ℤ modulo pᵐ where p is a prime and m ∈ ℕ. Computational methods are developed to pre-calculate the symmetries exhibited by [sub]f,[sub]pᵐ for a given f and pᵐ.
These include procedures to find whether [sub]f,[sub]pᵐ is bounded or unbounded, the degree of rotational symmetry present, whether lines of reflectional symmetry can be observed, and in the case of 𝒫[sub]f,[sub]pᵐ unbounded, whether the PGP has a glide reflection.
Methods are also sought to find a suitable f and pᵐ to produce a desired 'feasible' shape in a PGP construction, and how the same shape might be generated modulo pᵐ⁺ᵏ if it cannot be produced modulo pᵐ.Nonlinear magnetic reconnectionColin, A. M.http://hdl.handle.net/10023/141952018-06-18T23:16:47Z1987-01-01T00:00:00ZIn many astrophysical problems magnetic reconnection plays a major role. Despite this reconnection theory remains incompletely understood, partly due to the strong non-linearity of the governing equations and the resulting difficulties in demonstrating analytical solutions. This thesis examines some fundamental aspects of reconnection theory: namely, the dynamics of driven and spontaneously reconnecting systems. We first consider the dynamics of a driven reconnecting system by numerically modelling a configuration consisting of two oppositely oriented flux systems with a variety of different boundary conditions and internal parameters. The results indicate that the rate of reconnection is chiefly dependent on the magnetic Reynolds number, but that the plasma flow is weakly dependent on this parameter, being more affected by the curvature of Incoming magnetic field. Scaling laws for the dimensions of the diffusion region are derived, and the existence of several reconnection regimes is shown. Using the same computer code we also simulate tearing modes in Cartesian geometry under different boundary conditions. By imposing a suitable perturbation a magnetic island is generated. The plasma flows show marked differences for the different boundary conditions implemented. Lastly, we examine some aspects of the coalescence instability. The usual flux function taken to represent a tearing node Island in the linear growth phase is shown to be erroneous, and we derive a correct expression. We show that under certain conditions there exists a threshold to coalescence that depends on the island wavenumbers and the associated perturbation.
1987-01-01T00:00:00ZColin, A. M.In many astrophysical problems magnetic reconnection plays a major role. Despite this reconnection theory remains incompletely understood, partly due to the strong non-linearity of the governing equations and the resulting difficulties in demonstrating analytical solutions. This thesis examines some fundamental aspects of reconnection theory: namely, the dynamics of driven and spontaneously reconnecting systems. We first consider the dynamics of a driven reconnecting system by numerically modelling a configuration consisting of two oppositely oriented flux systems with a variety of different boundary conditions and internal parameters. The results indicate that the rate of reconnection is chiefly dependent on the magnetic Reynolds number, but that the plasma flow is weakly dependent on this parameter, being more affected by the curvature of Incoming magnetic field. Scaling laws for the dimensions of the diffusion region are derived, and the existence of several reconnection regimes is shown. Using the same computer code we also simulate tearing modes in Cartesian geometry under different boundary conditions. By imposing a suitable perturbation a magnetic island is generated. The plasma flows show marked differences for the different boundary conditions implemented. Lastly, we examine some aspects of the coalescence instability. The usual flux function taken to represent a tearing node Island in the linear growth phase is shown to be erroneous, and we derive a correct expression. We show that under certain conditions there exists a threshold to coalescence that depends on the island wavenumbers and the associated perturbation.The nonlinear thermal evolution of coronal structuresMendoza Briceño, César Augustohttp://hdl.handle.net/10023/141932018-06-18T23:17:18Z1996-01-01T00:00:00ZThe thermal equilibrium and evolution of coronal structure is studied in this thesis. A symmetric and constant cross-sectional coronal loop is considered and, because of the strong magnetic field, the plasma is confined to move along the field lines, so that a one-dimensional problem can be assumed. We begin by giving a brief description of the Sun and corresponding phenomena. Then a discussion of the basic MHD equations is given. Here, it is assumed that the heating function is spatially dependent and the cooling function is due to an optically thin plasma. The thermal equilibrium of uniform-pressure coronal loop is investigated. The effects due to varying the values of the parameters involved in the governing equations are studied. It is found that there is a critical decay length of the heating below which a hot coronal loop does not exist. It is suggested that thermal non-equilibrium occurs, allowing the existence of catastrophic cooling. A study of the stability of the equilibrium up to the second order approximation is presented, and it is found that the response of the structure not only depends on the amplitude of the disturbance, but also on whether the disturbance increases or decreases the static temperature. The thermal evolution of the above structure is also investigated by assuming that the inertial terms are small. The previous results related to the critical heating decay length are verified. The numerical simulation shows that an initial hot plasma evolves to a new equilibrium which has a cool summit. This equilibrium is identified as a prominence-like solution. Further investigations are made in order to show how the structure can either evolve to a hot or a cool summit temperature depending on whether the initial conditions are above or below threshold values. The evolution of a disturbance increasing or decreasing an initial equilibrium temperature is followed numerically verifying the prediction made in the stability analysis. Furthermore, the effect of gravity is considered in the thermal equilibrium of loop. Similar results were found as studied for a constant-pressure loop. However, it was found that the critical values in which thermal non-equilibrium can occur is increased. A magnetic dip is also included in this model and the thermal equilibrium is studied. Finally, extensions of the present work is presented and some preliminary results are discussed.
1996-01-01T00:00:00ZMendoza Briceño, César AugustoThe thermal equilibrium and evolution of coronal structure is studied in this thesis. A symmetric and constant cross-sectional coronal loop is considered and, because of the strong magnetic field, the plasma is confined to move along the field lines, so that a one-dimensional problem can be assumed. We begin by giving a brief description of the Sun and corresponding phenomena. Then a discussion of the basic MHD equations is given. Here, it is assumed that the heating function is spatially dependent and the cooling function is due to an optically thin plasma. The thermal equilibrium of uniform-pressure coronal loop is investigated. The effects due to varying the values of the parameters involved in the governing equations are studied. It is found that there is a critical decay length of the heating below which a hot coronal loop does not exist. It is suggested that thermal non-equilibrium occurs, allowing the existence of catastrophic cooling. A study of the stability of the equilibrium up to the second order approximation is presented, and it is found that the response of the structure not only depends on the amplitude of the disturbance, but also on whether the disturbance increases or decreases the static temperature. The thermal evolution of the above structure is also investigated by assuming that the inertial terms are small. The previous results related to the critical heating decay length are verified. The numerical simulation shows that an initial hot plasma evolves to a new equilibrium which has a cool summit. This equilibrium is identified as a prominence-like solution. Further investigations are made in order to show how the structure can either evolve to a hot or a cool summit temperature depending on whether the initial conditions are above or below threshold values. The evolution of a disturbance increasing or decreasing an initial equilibrium temperature is followed numerically verifying the prediction made in the stability analysis. Furthermore, the effect of gravity is considered in the thermal equilibrium of loop. Similar results were found as studied for a constant-pressure loop. However, it was found that the critical values in which thermal non-equilibrium can occur is increased. A magnetic dip is also included in this model and the thermal equilibrium is studied. Finally, extensions of the present work is presented and some preliminary results are discussed.Alfvén waves in low-mass star-forming regionsMartin, Clare E.http://hdl.handle.net/10023/141902018-06-18T23:17:15Z1999-01-01T00:00:00ZLow-mass star-forming regions have a lifetime which is greater than their dynamical time and must therefore be, in an average sense, in mechanical equilibrium. The work presented here proposes that an equilibrium exists between the self-gravity, gas pressure, and the magnetic field and the waves it supports. Specifically the equilibrium in the direction perpendicular to the ordered magnetic field is given by the Lorentz force, while that parallel to the field is given by an Alfvén wave pressure force. The work detailed in this thesis models a low-mass star-forming region as a one-dimensional gas slab with a magnetic field lying perpendicular to the layer. Analytical, self-consistent models are formulated to study the equilibrium parallel to the background magnetic field. It is found that both short-wavelength (modelled using the WKB approximation) and large-amplitude, long-wavelength Alfvén waves can provide the necessary support parallel to the magnetic field, generating model cloud thicknesses that are consistent with the observations. The effect of damping by the linear process of ion-neutral friction is considered. It is found that the damping of the waves is not a necessary condition for the support of the cloud although it is an advantage. The possible sources of these waves are discussed. The Alfvén waves are also found to make an important contribution to the heating of a low-mass star-forming region. By modelling the dominant heating and cooling mechanisms in a molecular cloud, it is discovered that a cloud supported against its self-gravity by short-wavelength Alfvén waves will be hotter at its outer edge than in the central regions. These models successfully describe a low-mass star-forming region in equilibrium between its self-gravity, the gas pressure and an Alfvén wave pressure force. The question of the stability of such an equilibrium is considered, specifically that of an isothermal gas slab supported by short-wavelength Alfvén waves. The initial results suggest that the presence of a magnetic field and its associated Alfvén waves have a stabilising effect on the layer, and encourage further consideration of the role of Alfvén waves in low-mass star-forming regions.
1999-01-01T00:00:00ZMartin, Clare E.Low-mass star-forming regions have a lifetime which is greater than their dynamical time and must therefore be, in an average sense, in mechanical equilibrium. The work presented here proposes that an equilibrium exists between the self-gravity, gas pressure, and the magnetic field and the waves it supports. Specifically the equilibrium in the direction perpendicular to the ordered magnetic field is given by the Lorentz force, while that parallel to the field is given by an Alfvén wave pressure force. The work detailed in this thesis models a low-mass star-forming region as a one-dimensional gas slab with a magnetic field lying perpendicular to the layer. Analytical, self-consistent models are formulated to study the equilibrium parallel to the background magnetic field. It is found that both short-wavelength (modelled using the WKB approximation) and large-amplitude, long-wavelength Alfvén waves can provide the necessary support parallel to the magnetic field, generating model cloud thicknesses that are consistent with the observations. The effect of damping by the linear process of ion-neutral friction is considered. It is found that the damping of the waves is not a necessary condition for the support of the cloud although it is an advantage. The possible sources of these waves are discussed. The Alfvén waves are also found to make an important contribution to the heating of a low-mass star-forming region. By modelling the dominant heating and cooling mechanisms in a molecular cloud, it is discovered that a cloud supported against its self-gravity by short-wavelength Alfvén waves will be hotter at its outer edge than in the central regions. These models successfully describe a low-mass star-forming region in equilibrium between its self-gravity, the gas pressure and an Alfvén wave pressure force. The question of the stability of such an equilibrium is considered, specifically that of an isothermal gas slab supported by short-wavelength Alfvén waves. The initial results suggest that the presence of a magnetic field and its associated Alfvén waves have a stabilising effect on the layer, and encourage further consideration of the role of Alfvén waves in low-mass star-forming regions.Basic magnetic field configurations for solar filament channels and filamentsMackay, Duncan Hendryhttp://hdl.handle.net/10023/141882018-06-18T23:17:12Z1997-01-01T00:00:00ZThe three-dimensional magnetic structure of solar filament channels and filaments is considered. A simple analytical potential model of a filament channel is setup with line sources representing the overlying arcades and point sources the flux of the filament. A possible explanation of the distinct upper and lower bounds of a filament is given. A more detailed numerical force-free model with discrete flux sources is then developed and the effect of magnetic shear on the separatrix surface explored. Dextral channels are shown to exist for a wider range of negative values of the force-free alpha and sinistral channels for positive values of alpha. Potential models of a variety of coronal structures are then considered. The bending of a filament is modelled and a method of determining the horizontal component of a filament's magnetic field is proposed. Next, the observed opposite skew of arcades lying above switchbacks of polarity inversion lines is shown to be produced by a local flux imbalance at the corner of the switchback. Then, the magnetic structure of a particular filament in a filament channel is modelled using observations from a photospheric magnetogram. It is shown that dips in the filaments magnetic field could result from opposite polarity fragments lying below the filament. Finally, the formation of a specific filament channel and filament is modelled. The formation of the channel is shown to be due to the emergence of new flux in a sheared state. It is shown that convergence and reconnections between the new flux and old remnant flux is required for the filament to form. The field lines that represent the filament form a thin vertical sheet of flux. The changing angle of inclination of the sheet gives the appearance of twist. The method of formation is then generalised to other cases and it is shown that a hemispheric pattern consistent with the results of Martin et al. (1995) can be obtained.
1997-01-01T00:00:00ZMackay, Duncan HendryThe three-dimensional magnetic structure of solar filament channels and filaments is considered. A simple analytical potential model of a filament channel is setup with line sources representing the overlying arcades and point sources the flux of the filament. A possible explanation of the distinct upper and lower bounds of a filament is given. A more detailed numerical force-free model with discrete flux sources is then developed and the effect of magnetic shear on the separatrix surface explored. Dextral channels are shown to exist for a wider range of negative values of the force-free alpha and sinistral channels for positive values of alpha. Potential models of a variety of coronal structures are then considered. The bending of a filament is modelled and a method of determining the horizontal component of a filament's magnetic field is proposed. Next, the observed opposite skew of arcades lying above switchbacks of polarity inversion lines is shown to be produced by a local flux imbalance at the corner of the switchback. Then, the magnetic structure of a particular filament in a filament channel is modelled using observations from a photospheric magnetogram. It is shown that dips in the filaments magnetic field could result from opposite polarity fragments lying below the filament. Finally, the formation of a specific filament channel and filament is modelled. The formation of the channel is shown to be due to the emergence of new flux in a sheared state. It is shown that convergence and reconnections between the new flux and old remnant flux is required for the filament to form. The field lines that represent the filament form a thin vertical sheet of flux. The changing angle of inclination of the sheet gives the appearance of twist. The method of formation is then generalised to other cases and it is shown that a hemispheric pattern consistent with the results of Martin et al. (1995) can be obtained.Aspects of magnetic field theory in solar and laboratory plasmasLothian, Robert M.http://hdl.handle.net/10023/141832018-06-18T23:17:16Z1990-01-01T00:00:00ZUsing the Magnetohydrodynamic model, two problems in the behaviour of magnetic field structures are investigated. Firstly, the stability of tokamak equilibria to coupled tearing modes is calculated. Secondly, the equilibrium structure of a solar coronal loop is examined. The flux co-ordinate method is used to construct toroidal equilibria of the type found in large aspect ratio tokamaks. In such a field configuration, the analysis of tearing modes is complicated by the coupling of different poloidal fourier modes. The effect of coupling through elliptic shaping of plasma surfaces is calculated. For certain current profiles, this effect may cause instability. The response of coronal loops to twisting at their photospheric footpoints is investigated. Long loops are shown to have an essentially 1-D nature. This observation is used to develop a 1-D, line-tied model for such loops. This model is used to conduct an extensive survey of the non-linear twist regime, including the effects of enhanced fluid pressure. The possibility of non-equilibrium, which would provide energy for coronal heating and compact flares, is examined. When the physical variable of footpoint displacement is specified, no loss of equilibrium is found by twisting. Loss of equilibrium is found for high pressures, which we do not, however, expect to find in the corona.
1990-01-01T00:00:00ZLothian, Robert M.Using the Magnetohydrodynamic model, two problems in the behaviour of magnetic field structures are investigated. Firstly, the stability of tokamak equilibria to coupled tearing modes is calculated. Secondly, the equilibrium structure of a solar coronal loop is examined. The flux co-ordinate method is used to construct toroidal equilibria of the type found in large aspect ratio tokamaks. In such a field configuration, the analysis of tearing modes is complicated by the coupling of different poloidal fourier modes. The effect of coupling through elliptic shaping of plasma surfaces is calculated. For certain current profiles, this effect may cause instability. The response of coronal loops to twisting at their photospheric footpoints is investigated. Long loops are shown to have an essentially 1-D nature. This observation is used to develop a 1-D, line-tied model for such loops. This model is used to conduct an extensive survey of the non-linear twist regime, including the effects of enhanced fluid pressure. The possibility of non-equilibrium, which would provide energy for coronal heating and compact flares, is examined. When the physical variable of footpoint displacement is specified, no loss of equilibrium is found by twisting. Loss of equilibrium is found for high pressures, which we do not, however, expect to find in the corona.Exact solutions for axisymmetric and nonpolytropic astrophysical windsLima, João José de Faria Graça Afonsohttp://hdl.handle.net/10023/141802018-06-18T23:17:07Z1995-01-01T00:00:00ZAstrophysical outflows are common in a large variety of objects with very different length-scales. They can be almost spherical, as in the case of the solar wind, or show a high degree of anisotropy as in pre-main sequence stars, star-forming regions or even extragalactic objects. This work is aimed at finding exact solutions of the axisymmetric wind equations in which all variables depend not only on the distance to the central object but on latitude as well. The geometry of the stream/field-lines is taken as helicoidal and this seems to be a good approximation in some examples of collimated flows. From a simple hydrodynamic approach, a straightforward technique based on separation of the variables yields the most general solution of the wind equations under the above assumptions. The way the different variables depend on latitude is controlled by three anisotropy parameters which are related to typical ratios at the base of the atmosphere. The density needs to be higher at the equator than at the pole for the outflow to be able to accelerate. In these circumstances, the radial velocity always increases from equator to pole. Contrary to Parker's model of the solar wind, the solution does not pass through any critical point, since no polytropic law is assumed. However, the general behaviour is similar, with a high acceleration at the base and the velocity rapidly attaining an almost constant asymptotic value. The heating rate that sustains this rapid increase is mostly concentrated near the surface of the central object. The inclusion of the magnetic field in the analysis introduces two critical points: the Alfvenic point and an extra X -type point filtering the solution that gives a vanishing pressure at infinity. If the density anisotropy is too low the wind is unable to accelerate to large asymptotic values. The dependence of the angular velocity of the roots of the fieldlines with latitude reproduces well the observed rotation profile of photospheric magnetic features. The mass loss rate can be substantially increased if the structure of the outflow is highly anisotropic. Some applications to the solar wind are also discussed. In particular, recent results from ULYSSES (pointing out that solar speed increases with latitude while the density decreases from equator to the pole) are in good agreement with the general behaviour of the solutions presented in this work.
1995-01-01T00:00:00ZLima, João José de Faria Graça AfonsoAstrophysical outflows are common in a large variety of objects with very different length-scales. They can be almost spherical, as in the case of the solar wind, or show a high degree of anisotropy as in pre-main sequence stars, star-forming regions or even extragalactic objects. This work is aimed at finding exact solutions of the axisymmetric wind equations in which all variables depend not only on the distance to the central object but on latitude as well. The geometry of the stream/field-lines is taken as helicoidal and this seems to be a good approximation in some examples of collimated flows. From a simple hydrodynamic approach, a straightforward technique based on separation of the variables yields the most general solution of the wind equations under the above assumptions. The way the different variables depend on latitude is controlled by three anisotropy parameters which are related to typical ratios at the base of the atmosphere. The density needs to be higher at the equator than at the pole for the outflow to be able to accelerate. In these circumstances, the radial velocity always increases from equator to pole. Contrary to Parker's model of the solar wind, the solution does not pass through any critical point, since no polytropic law is assumed. However, the general behaviour is similar, with a high acceleration at the base and the velocity rapidly attaining an almost constant asymptotic value. The heating rate that sustains this rapid increase is mostly concentrated near the surface of the central object. The inclusion of the magnetic field in the analysis introduces two critical points: the Alfvenic point and an extra X -type point filtering the solution that gives a vanishing pressure at infinity. If the density anisotropy is too low the wind is unable to accelerate to large asymptotic values. The dependence of the angular velocity of the roots of the fieldlines with latitude reproduces well the observed rotation profile of photospheric magnetic features. The mass loss rate can be substantially increased if the structure of the outflow is highly anisotropic. Some applications to the solar wind are also discussed. In particular, recent results from ULYSSES (pointing out that solar speed increases with latitude while the density decreases from equator to the pole) are in good agreement with the general behaviour of the solutions presented in this work.Chromospheric effects on global solar oscillationsJohnston, Alanhttp://hdl.handle.net/10023/141732018-06-18T23:16:48Z1994-01-01T00:00:00ZA study has been made of the global solar oscillations known as p-modes. The Sun is represented by a plane-parallel stratified plasma. Solutions are found to the magnetohydrodynamic equations of motion in such a plasma, and normal mode frequencies are calculated by applying realistic boundary conditions to these solutions. The normal modes model solar p-modes. For a model consisting of an isothermal chromosphere with a uniform horizontal magnetic field, it is demonstrated that modes may form at all frequencies. Consideration is also given to the related problem of vertical propagation of fast magnetoacoustic waves in a uniform magnetic field. An investigation is carried out into the observed solar cycle variations in the frequencies of p-modes in the classical, low frequency range (1-5 mHz). A possible mechanism for the observed "turnover" effect is discussed. Through the use of a modified Bohr- Sommerfeld condition, the effect of a non-isothermal chromosphere is also considered, and a physical description of chromospheric effects on p-mode frequencies is given. The formation of modes above the acoustic cut-off frequency is investigated. The theoretically calcidated forms of frequency shift curves in this high frequency range agree well with observations. The special case of modes of degree zero is also briefly examined. A mathematical formulation for such modes is constructed, and frequency shifts are determined for a simple chromospheric model atmosphere.
1994-01-01T00:00:00ZJohnston, AlanA study has been made of the global solar oscillations known as p-modes. The Sun is represented by a plane-parallel stratified plasma. Solutions are found to the magnetohydrodynamic equations of motion in such a plasma, and normal mode frequencies are calculated by applying realistic boundary conditions to these solutions. The normal modes model solar p-modes. For a model consisting of an isothermal chromosphere with a uniform horizontal magnetic field, it is demonstrated that modes may form at all frequencies. Consideration is also given to the related problem of vertical propagation of fast magnetoacoustic waves in a uniform magnetic field. An investigation is carried out into the observed solar cycle variations in the frequencies of p-modes in the classical, low frequency range (1-5 mHz). A possible mechanism for the observed "turnover" effect is discussed. Through the use of a modified Bohr- Sommerfeld condition, the effect of a non-isothermal chromosphere is also considered, and a physical description of chromospheric effects on p-mode frequencies is given. The formation of modes above the acoustic cut-off frequency is investigated. The theoretically calcidated forms of frequency shift curves in this high frequency range agree well with observations. The special case of modes of degree zero is also briefly examined. A mathematical formulation for such modes is constructed, and frequency shifts are determined for a simple chromospheric model atmosphere.Theoretical modelling of global oscillations in solar prominencesJoarder, Parthasarathihttp://hdl.handle.net/10023/141692018-06-18T23:16:21Z1994-01-01T00:00:00ZThis thesis aims to provide a basic theoretical explanation for the oscillatory motions observed in solar quiescent prominences. The prominence is treated as a simple plasma slab embedded in a hotter and rarer uniform coronal plasma. Both the slab and its environment are permeated by a uniform magnetic field. The field lines are anchored at rigid walls placed on either side of the plasma slab and representing the photospheric line-tying effect. The magnetohydrodynamic modes of oscillation of the plasma slab are then examined for different orientations of the magnetic field with respect to the long axis of the slab. Particularly interesting in this study is the appearance of the 'string MHD' modes that are analogous to the fundamental vibrations of a mass- loaded stretched elastic string. Such modes appear whenever the magnetic field vector is inclined to the long axis of the slab, thus producing a magnetic field component in the direction transverse to the axis of the slab. Observationally, this inclination of the field is generally small. For realistic values of the angle of inclination of the magnetic field lines, the 'string Alfven' mode and an 'internal slow' mode yield periods in the range 1/2-2 hr. These modes may correspond to the observed long period (40-90 minutes) oscillations in quiescent prominences. Intermediate periodicities, in the range 8-20 min, may be associated with an 'internal Alfven' mode and a 'fast string' mode of the prominence slab. The observed short periodicities, in the range 2-5 min, may correspond to an 'internal fast' mode in prominences. Having thus established a foundation for the theoretical modelling of prominence oscillations in terms of the magnetohydrodynamic modes of oscillation of a non-gravitating plasma slab, we discuss several factors, such as the effects of gravitational stratification, the curvature of the magnetic field lines, and the fine-structures in a prominence, that may complicate a description of its oscillatory modes. Some preliminary investigations of simple magnetohydrostatic equilibrium models suggest that gravity and the curvature of the magnetic field lines play only a secondary role in determining the periods of the oscillatory modes in prominences, the basic structure of the modes being similar to that present in simple slab models.
1994-01-01T00:00:00ZJoarder, ParthasarathiThis thesis aims to provide a basic theoretical explanation for the oscillatory motions observed in solar quiescent prominences. The prominence is treated as a simple plasma slab embedded in a hotter and rarer uniform coronal plasma. Both the slab and its environment are permeated by a uniform magnetic field. The field lines are anchored at rigid walls placed on either side of the plasma slab and representing the photospheric line-tying effect. The magnetohydrodynamic modes of oscillation of the plasma slab are then examined for different orientations of the magnetic field with respect to the long axis of the slab. Particularly interesting in this study is the appearance of the 'string MHD' modes that are analogous to the fundamental vibrations of a mass- loaded stretched elastic string. Such modes appear whenever the magnetic field vector is inclined to the long axis of the slab, thus producing a magnetic field component in the direction transverse to the axis of the slab. Observationally, this inclination of the field is generally small. For realistic values of the angle of inclination of the magnetic field lines, the 'string Alfven' mode and an 'internal slow' mode yield periods in the range 1/2-2 hr. These modes may correspond to the observed long period (40-90 minutes) oscillations in quiescent prominences. Intermediate periodicities, in the range 8-20 min, may be associated with an 'internal Alfven' mode and a 'fast string' mode of the prominence slab. The observed short periodicities, in the range 2-5 min, may correspond to an 'internal fast' mode in prominences. Having thus established a foundation for the theoretical modelling of prominence oscillations in terms of the magnetohydrodynamic modes of oscillation of a non-gravitating plasma slab, we discuss several factors, such as the effects of gravitational stratification, the curvature of the magnetic field lines, and the fine-structures in a prominence, that may complicate a description of its oscillatory modes. Some preliminary investigations of simple magnetohydrostatic equilibrium models suggest that gravity and the curvature of the magnetic field lines play only a secondary role in determining the periods of the oscillatory modes in prominences, the basic structure of the modes being similar to that present in simple slab models.Magnetic surface effects on solar oscillationsJain, Rekhahttp://hdl.handle.net/10023/141532018-06-18T23:16:08Z1993-01-01T00:00:00ZThis thesis is concerned with the effects of magnetic atmospheres on solar oscillations. The behaviour of magnetohydrodynamic surface waves propagating on a single magnetic interface is discussed ignoring the effects of gravity. The effects of non-parallel propagation (where the wave vector is at an angle to the magnetic field direction) are considered. The effects of chromospheric magnetic fields on solar p- and f-modes in a stratified atmosphere are examined for three different models. In the first of these models, the chromosphere is assumed to be isothermal and permeated by a uniform and horizontal magnetic field. A dispersion relation for the p-modes trapped below such an atmosphere is derived. Asymptotic and numerical solutions for the p-modes are discussed in detail. An increase in chromospheric magnetic field strength leads to an increase in the frequency of the p-modes, whereas an increase in the chromospheric temperature leads to a decrease in the frequencies of these modes. Comparison with observational data suggests that both these effects may indeed take place. The second model is set up for magnetic fields which decrease with height in such a way that the Alfven speed remains constant. In addition to magnetic effects, the effects of non-parallel propagation on and f-modes are considered in the presence of such a non-uniform magnetic field. After deriving a very general dispersion relation, various asymptotic and numerical solutions have been obtained and the possible effects of magnetic fields and non-parallel propagation on these modes are examined. The presence of a horizontal non-uniform chromospheric field produces changes in the frequencies of the p- and f-modes, reducing the frequencies of p-modes and increasing the frequency of the f-mode. Besides depending upon magnetic field strength, frequencies also depend on both the mode's order n and its degree l. The effects of non-parallel propagation are found to be most significant for the f-mode and the low order p-modes. The magnetic structure of the chromosphere has been further generalised by combining the two models described above. In this three layer model, a dispersion relation is derived in a general manner and discussed in detail for the p-modes. The role of magnetoacoustic cut-off frequency is studied. Again, the results are qualitatively similar to those found from observation.
1993-01-01T00:00:00ZJain, RekhaThis thesis is concerned with the effects of magnetic atmospheres on solar oscillations. The behaviour of magnetohydrodynamic surface waves propagating on a single magnetic interface is discussed ignoring the effects of gravity. The effects of non-parallel propagation (where the wave vector is at an angle to the magnetic field direction) are considered. The effects of chromospheric magnetic fields on solar p- and f-modes in a stratified atmosphere are examined for three different models. In the first of these models, the chromosphere is assumed to be isothermal and permeated by a uniform and horizontal magnetic field. A dispersion relation for the p-modes trapped below such an atmosphere is derived. Asymptotic and numerical solutions for the p-modes are discussed in detail. An increase in chromospheric magnetic field strength leads to an increase in the frequency of the p-modes, whereas an increase in the chromospheric temperature leads to a decrease in the frequencies of these modes. Comparison with observational data suggests that both these effects may indeed take place. The second model is set up for magnetic fields which decrease with height in such a way that the Alfven speed remains constant. In addition to magnetic effects, the effects of non-parallel propagation on and f-modes are considered in the presence of such a non-uniform magnetic field. After deriving a very general dispersion relation, various asymptotic and numerical solutions have been obtained and the possible effects of magnetic fields and non-parallel propagation on these modes are examined. The presence of a horizontal non-uniform chromospheric field produces changes in the frequencies of the p- and f-modes, reducing the frequencies of p-modes and increasing the frequency of the f-mode. Besides depending upon magnetic field strength, frequencies also depend on both the mode's order n and its degree l. The effects of non-parallel propagation are found to be most significant for the f-mode and the low order p-modes. The magnetic structure of the chromosphere has been further generalised by combining the two models described above. In this three layer model, a dispersion relation is derived in a general manner and discussed in detail for the p-modes. The role of magnetoacoustic cut-off frequency is studied. Again, the results are qualitatively similar to those found from observation.Thermal instabilities in the solar coronaIreland, Richard C.http://hdl.handle.net/10023/141502018-06-18T23:15:57Z1995-01-01T00:00:00ZIn this thesis, several problems relating to thermal instabilities in the solar corona are examined. Chapter 1 gives a brief description of the Sun and corresponding events with particular attention focused on prominences, their formation and eruption. Various problems concerning thermal instabilities are then tackled in the later Chapters. In Chapter 2, the basic MHD equations are introduced and a physical description of the thermal instability mechanism given. The MHD equations are linearised in a uniform, infinite medium and the basic instability criteria obtained. Chapter 3 investigates the normal mode spectrum for the linearised MHD equations for a cylindrical equilibrium. This spectrum is examined for zero perpendicular thermal conduction, with both zero and non-zero scalar resistivity. Particular attention is paid to the continuous branches of this spectrum, or continuous spectra. For zero resistivity there are three types of continuous spectra present, namely the Alfven, slow and thermal continua. It is shown that when dissipation due to resistivity is included, the slow and Alfven continua are removed and the thermal continuum is shifted to a different position (where the shift is independent of the exact value of resistivity). The 'old' location of the thermal continuum is covered by a dense set of nearly singular discrete modes called a quasi-continuum, for equilibria with the thermal time scale much smaller than the Alfven time scale. This quasi-continuum is investigated numerically and the eigenfunctions are shown to have rapid spatial oscillating behaviour. These oscillations are confined to the most unstable part of the equilibrium based on the Field criterion and may be the cause of fine structure in prominences. In Chapter 4, the normal mode spectrum for the linearised MHD equations is examined for a plasma in a cylindrical equilibrium. The equations describing these normal modes are solved numerically using a finite element code. In the ideal case the Hain-Lust equation is expanded and a WKB solution obtained for large axial wave numbers. This is compared to the numerical solutions. In the non-ideal case, the ballooning equations describing localised modes are manipulated in an arcade geometry and a dispersion relation derived. It is illustrated that as the axial wave number k is increased, the fundamental thermal and Alfven modes can coalesce to form overstable magnetothermal modes. The ratio between the magnetic and thermal terms is varied and the existence of the magnetothermal modes examined. The corresponding growth rates are predicted by a WKB solution to the ballooning equations. The interaction of thermal and magnetic instabilities and the existence of these magnetothermal modes may be significant in the eruption of prominences into solar flares. Chapter 5 extends the work presented in Chapter 4 to include the effects of line-tying in a coronal arcade. The ballooning equations which were introduced in Chapter 4 are manipulated to give a dispersion relation. This relation is a quadratic in the square of the azimuthal wave number m if parallel thermal conduction is neglected and a cubic in m2 if parallel conduction is included. Rigid wall boundary conditions are applied to this dispersion relation. This dispersion relation is then solved numerically subject to these boundary conditions and the solutions plotted. Unfortunately the expression for the thermal continuum in line-tied arcades is required since the thermal continuum must play an important role in the proceedings. This calculation is left for future work. From the results obtained, it can be seen that the thermal instability can play a major part in prominence formation and destruction. The thermal instability may help create the prominence. Resistivity and perpendicular thermal conduction can cause of the observed fine scale structure. Finally, a neighbouring thermal instability may trigger a magnetic instability that causes the prominence to erupt.
1995-01-01T00:00:00ZIreland, Richard C.In this thesis, several problems relating to thermal instabilities in the solar corona are examined. Chapter 1 gives a brief description of the Sun and corresponding events with particular attention focused on prominences, their formation and eruption. Various problems concerning thermal instabilities are then tackled in the later Chapters. In Chapter 2, the basic MHD equations are introduced and a physical description of the thermal instability mechanism given. The MHD equations are linearised in a uniform, infinite medium and the basic instability criteria obtained. Chapter 3 investigates the normal mode spectrum for the linearised MHD equations for a cylindrical equilibrium. This spectrum is examined for zero perpendicular thermal conduction, with both zero and non-zero scalar resistivity. Particular attention is paid to the continuous branches of this spectrum, or continuous spectra. For zero resistivity there are three types of continuous spectra present, namely the Alfven, slow and thermal continua. It is shown that when dissipation due to resistivity is included, the slow and Alfven continua are removed and the thermal continuum is shifted to a different position (where the shift is independent of the exact value of resistivity). The 'old' location of the thermal continuum is covered by a dense set of nearly singular discrete modes called a quasi-continuum, for equilibria with the thermal time scale much smaller than the Alfven time scale. This quasi-continuum is investigated numerically and the eigenfunctions are shown to have rapid spatial oscillating behaviour. These oscillations are confined to the most unstable part of the equilibrium based on the Field criterion and may be the cause of fine structure in prominences. In Chapter 4, the normal mode spectrum for the linearised MHD equations is examined for a plasma in a cylindrical equilibrium. The equations describing these normal modes are solved numerically using a finite element code. In the ideal case the Hain-Lust equation is expanded and a WKB solution obtained for large axial wave numbers. This is compared to the numerical solutions. In the non-ideal case, the ballooning equations describing localised modes are manipulated in an arcade geometry and a dispersion relation derived. It is illustrated that as the axial wave number k is increased, the fundamental thermal and Alfven modes can coalesce to form overstable magnetothermal modes. The ratio between the magnetic and thermal terms is varied and the existence of the magnetothermal modes examined. The corresponding growth rates are predicted by a WKB solution to the ballooning equations. The interaction of thermal and magnetic instabilities and the existence of these magnetothermal modes may be significant in the eruption of prominences into solar flares. Chapter 5 extends the work presented in Chapter 4 to include the effects of line-tying in a coronal arcade. The ballooning equations which were introduced in Chapter 4 are manipulated to give a dispersion relation. This relation is a quadratic in the square of the azimuthal wave number m if parallel thermal conduction is neglected and a cubic in m2 if parallel conduction is included. Rigid wall boundary conditions are applied to this dispersion relation. This dispersion relation is then solved numerically subject to these boundary conditions and the solutions plotted. Unfortunately the expression for the thermal continuum in line-tied arcades is required since the thermal continuum must play an important role in the proceedings. This calculation is left for future work. From the results obtained, it can be seen that the thermal instability can play a major part in prominence formation and destruction. The thermal instability may help create the prominence. Resistivity and perpendicular thermal conduction can cause of the observed fine scale structure. Finally, a neighbouring thermal instability may trigger a magnetic instability that causes the prominence to erupt.Heating of turbulent solar and laboratory plasmasInverarity, Gordon W.http://hdl.handle.net/10023/141462018-06-18T23:15:32Z1995-01-01T00:00:00ZThe model of Heyvaerts and Priest (1992) for steady-state heating of the turbulent medium within a sheared solar coronal arcade structure is here developed. The energy input into the corona is calculated at the large scales of the model. At the smaller scales the effects of coronal turbulence are modelled in the form of an enhanced turbulent viscosity and magnetic diffusivity, which are related to the injected power density in the steady state. Matching the expressions for the injected and dissipated power enables the calculation of a heating power consistent with both boundary motions and turbulent effects with a minimum of arbitrary parameters - the price to be paid is that the inertial range spectrum must be prescribed and imposed at all scales. While it is capable of reproducing the observed levels of coronal heating (300 Wm⁻² 3x10⁵ erg cm⁻² s⁻ⁱ for the quiet Sun, 800 Wm⁻² (8 x 10⁵ erg cm⁻² s⁻ⁱ) for a coronal hole and 10⁴ Wm ⁻² (10⁷ erg cm⁻² s⁻ⁱ) for an active region (Withbroe and Noyes, 1977)), there are some mathematical and physical difficulties present. These are eliminated as far as is possible and it is found that the final results for heating levels differ little from the original model although there is a much greater consistency between the imposed and predicted energy power spectra. The modified approach is applied to the problems of photospheric motions twisting a coronal flux tube and of rapid motions injecting Alfven waves into an arcade. In the former case comparable levels of heating are obtained. For a driven and damped standing wave, however, desired levels of heating are only obtained when a global resonance occurs. Attempts are also made to find similar steady-state equilibria possessing flow for fusion experiments in order to apply the above procedure to investigate turbulence in laboratory plasmas. This has been hampered by the difficulty in finding simple appropriate equilibria with many scales present.
1995-01-01T00:00:00ZInverarity, Gordon W.The model of Heyvaerts and Priest (1992) for steady-state heating of the turbulent medium within a sheared solar coronal arcade structure is here developed. The energy input into the corona is calculated at the large scales of the model. At the smaller scales the effects of coronal turbulence are modelled in the form of an enhanced turbulent viscosity and magnetic diffusivity, which are related to the injected power density in the steady state. Matching the expressions for the injected and dissipated power enables the calculation of a heating power consistent with both boundary motions and turbulent effects with a minimum of arbitrary parameters - the price to be paid is that the inertial range spectrum must be prescribed and imposed at all scales. While it is capable of reproducing the observed levels of coronal heating (300 Wm⁻² 3x10⁵ erg cm⁻² s⁻ⁱ for the quiet Sun, 800 Wm⁻² (8 x 10⁵ erg cm⁻² s⁻ⁱ) for a coronal hole and 10⁴ Wm ⁻² (10⁷ erg cm⁻² s⁻ⁱ) for an active region (Withbroe and Noyes, 1977)), there are some mathematical and physical difficulties present. These are eliminated as far as is possible and it is found that the final results for heating levels differ little from the original model although there is a much greater consistency between the imposed and predicted energy power spectra. The modified approach is applied to the problems of photospheric motions twisting a coronal flux tube and of rapid motions injecting Alfven waves into an arcade. In the former case comparable levels of heating are obtained. For a driven and damped standing wave, however, desired levels of heating are only obtained when a global resonance occurs. Attempts are also made to find similar steady-state equilibria possessing flow for fusion experiments in order to apply the above procedure to investigate turbulence in laboratory plasmas. This has been hampered by the difficulty in finding simple appropriate equilibria with many scales present.Constraining the pass-band of future space-based coronagraphs for observations of solar eruptions in the FeXIV 530.3 nm “green line”Bemporad, AlessandroPagano, PaoloGiordano, SilvioFineschi, Silvanohttp://hdl.handle.net/10023/141392018-06-16T23:15:15Z2017-10-01T00:00:00ZObservations of the solar corona in the FeXIV 530.3 nm “green line” have been very important in the past, and are planned for future coronagraphs on-board forthcoming space missions such as PROBA-3 and Aditya. For these instruments, a very important parameter to be optimized is the spectral width of the band-pass filter to be centred over the “green line”. Focusing on solar eruptions, motions occurring along the line of sight will Doppler shift the line profiles producing an emission that will partially fall out of the narrower pass-band, while broader pass-band will provide observations with reduced spectral purity. To address these issues, we performed numerical (MHD) simulation of CME emission in the “green line” and produced synthetic images assuming 4 different widths of the pass-band (Δλ = 20 Å, 10 Å, 5 Å, and 2 Å). It turns out that, as expected, during solar eruptions a significant fraction of “green line” emission will be lost using narrower filters; on the other hand these images will have a higher spectral purity and will contain emission coming from parcels of plasma expanding only along the plane of the sky. This will provide a better definition of single filamentary features and will help isolating single slices of plasma through the eruption, thus reducing the problem of superposition of different features along the line of sight and helping physical interpretation of limb events. For these reasons, we suggest to use narrower band passes (Δλ ≤ 2 Å) for the observations of solar eruptions with future coronagraphs.
This research has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 647214) and from the UK Science and Technology Facilities Council.
2017-10-01T00:00:00ZBemporad, AlessandroPagano, PaoloGiordano, SilvioFineschi, SilvanoObservations of the solar corona in the FeXIV 530.3 nm “green line” have been very important in the past, and are planned for future coronagraphs on-board forthcoming space missions such as PROBA-3 and Aditya. For these instruments, a very important parameter to be optimized is the spectral width of the band-pass filter to be centred over the “green line”. Focusing on solar eruptions, motions occurring along the line of sight will Doppler shift the line profiles producing an emission that will partially fall out of the narrower pass-band, while broader pass-band will provide observations with reduced spectral purity. To address these issues, we performed numerical (MHD) simulation of CME emission in the “green line” and produced synthetic images assuming 4 different widths of the pass-band (Δλ = 20 Å, 10 Å, 5 Å, and 2 Å). It turns out that, as expected, during solar eruptions a significant fraction of “green line” emission will be lost using narrower filters; on the other hand these images will have a higher spectral purity and will contain emission coming from parcels of plasma expanding only along the plane of the sky. This will provide a better definition of single filamentary features and will help isolating single slices of plasma through the eruption, thus reducing the problem of superposition of different features along the line of sight and helping physical interpretation of limb events. For these reasons, we suggest to use narrower band passes (Δλ ≤ 2 Å) for the observations of solar eruptions with future coronagraphs.Attributing changes in the distribution of species abundance to weather variables using the example of British breeding birdsOedekoven, Cornelia S.Elston, David A.Harrison, Philip J.Brewer, Mark J.Buckland, Stephen T.Johnston, AlisonFoster, SimonPearce-Higgins, James W.http://hdl.handle.net/10023/141382018-06-16T23:32:03Z2017-12-01T00:00:00Z1. Modelling spatio-temporal changes in species abundance and attributing those changes to potential drivers such as climate, is an important but difficult problem. The standard approach for incorporating climatic variables into such models is to include each weather variable as a single covariate whose effect is expressed through a low-order polynomial or smoother in an additive model. This, however, confounds the spatial and temporal effects of the covariates. 2. We developed a novel approach to distinguish between three types of change in any particular weather covariate. We decomposed the weather covariate into three new covariates by separating out temporal variation in weather (averaging over space), spatial variation in weather (averaging over years) and a space-time anomaly term (residual variation). These three covariates were each fitted separately in the models. We illustrate the approach using generalized additive models applied to count data for a selection of species from the UK’s Breeding Bird Survey, 1994-2013. The weather covariates considered were the mean temperatures during the preceding winter and temperatures and rainfall during the preceding breeding season. We compare models that include these covariates directly with models including decomposed components of the same covariates, considering both linear and smooth relationships. 3. The lowest QAIC values were always associated with a decomposed weather covariate model. Different relationships between counts and the three new covariates provided strong evidence that the effects of changes in covariate values depended on whether changes took place in space, in time, or in the space-time anomaly. These results promote caution in predicting species distribution and abundance in future climate, based on relationships that are largely determined by environmental variation over space. 4. Our methods estimate the effect of temporal changes in weather, whilst accounting for spatial effects of long-term climate, improving inference on overall and/or localised effects of climate change. With increasing availability of large-scale data sets, need is growing for appropriate analytical tools. The proposed decomposition of the weather variables represents an important advance by eliminating the confounding issue often inherent in large-scale data sets.
The BBS is undertaken by the British Trust for Ornithology (BTO) and jointly funded by the BTO, the Joint Nature Conservation Committee and the Royal Society for the Protection of Birds.
2017-12-01T00:00:00ZOedekoven, Cornelia S.Elston, David A.Harrison, Philip J.Brewer, Mark J.Buckland, Stephen T.Johnston, AlisonFoster, SimonPearce-Higgins, James W.1. Modelling spatio-temporal changes in species abundance and attributing those changes to potential drivers such as climate, is an important but difficult problem. The standard approach for incorporating climatic variables into such models is to include each weather variable as a single covariate whose effect is expressed through a low-order polynomial or smoother in an additive model. This, however, confounds the spatial and temporal effects of the covariates. 2. We developed a novel approach to distinguish between three types of change in any particular weather covariate. We decomposed the weather covariate into three new covariates by separating out temporal variation in weather (averaging over space), spatial variation in weather (averaging over years) and a space-time anomaly term (residual variation). These three covariates were each fitted separately in the models. We illustrate the approach using generalized additive models applied to count data for a selection of species from the UK’s Breeding Bird Survey, 1994-2013. The weather covariates considered were the mean temperatures during the preceding winter and temperatures and rainfall during the preceding breeding season. We compare models that include these covariates directly with models including decomposed components of the same covariates, considering both linear and smooth relationships. 3. The lowest QAIC values were always associated with a decomposed weather covariate model. Different relationships between counts and the three new covariates provided strong evidence that the effects of changes in covariate values depended on whether changes took place in space, in time, or in the space-time anomaly. These results promote caution in predicting species distribution and abundance in future climate, based on relationships that are largely determined by environmental variation over space. 4. Our methods estimate the effect of temporal changes in weather, whilst accounting for spatial effects of long-term climate, improving inference on overall and/or localised effects of climate change. With increasing availability of large-scale data sets, need is growing for appropriate analytical tools. The proposed decomposition of the weather variables represents an important advance by eliminating the confounding issue often inherent in large-scale data sets.WKB estimates to the critical length of twisted solar coronal loopsHerbert, Simon I.http://hdl.handle.net/10023/140922018-06-21T23:17:28Z1995-01-01T00:00:00ZThe solar corona exhibits many different phenomena, observable from the Earth or space. Magnetohydrodynamic stability theory provides a method of investigating these phenomena by using it to test proposed mathematical models. WKB is a way of approximating the solutions of second order linear homogeneous differential equations with large parameters and so together with MHD stability theory, models for solar coronal loops can be investigated. In this thesis, the problem of a line tied twisted coronal loop is studied within the framework of ideal MHD using a WKB approximation to estimate the critical length at which the various magnetic fields become unstable. The problem will be split into two halves: (i) force-free and (ii) non force-free fields. Using a finite element/Fourier method, the full MHD equations will be solved numerically and the results compared with analytical solutions.
1995-01-01T00:00:00ZHerbert, Simon I.The solar corona exhibits many different phenomena, observable from the Earth or space. Magnetohydrodynamic stability theory provides a method of investigating these phenomena by using it to test proposed mathematical models. WKB is a way of approximating the solutions of second order linear homogeneous differential equations with large parameters and so together with MHD stability theory, models for solar coronal loops can be investigated. In this thesis, the problem of a line tied twisted coronal loop is studied within the framework of ideal MHD using a WKB approximation to estimate the critical length at which the various magnetic fields become unstable. The problem will be split into two halves: (i) force-free and (ii) non force-free fields. Using a finite element/Fourier method, the full MHD equations will be solved numerically and the results compared with analytical solutions.Solar coronal stability problemsHardie, Ian S.http://hdl.handle.net/10023/140902018-06-14T23:20:33Z1993-01-01T00:00:00ZMagnetohydrodynamic stability theory provides a powerful tool for understanding and testing hypothesized mathematical and physical models of observed phenomena on the surface of the Sun. In this thesis, the problem of applying the 'correct' boundary conditions at the photospheric/coronal interface used in modelling coronal arcades is tackled. Then some aspects of the stability of coronal loops and arcades are investigated using a Fourier truncated series approximation for the equation of motion. The problem involving the boundary conditions has been the subject of a controversy for the past decade with two principal conditions suggested, the 'rigid-wall' conditions where all perturbations vanish at the interface, and 'flow-through' conditions where flows parallel to the equilibrium magnetic field take place. By modelling the photosphere and corona as two different density regions and then varying the ratio of the densities of the two regions, growth rates and eigen-functions of both ideal and resistive modes are investigated in order to follow the evolution of the modes as the density ratio is increased. In order to simplify the analysis, the 2-D equations are reduced to 1-D equations by taking a WKB approximation for the spatial variations across the field to give a localized ballooning approach with ordinary differential equations along the fieldlines. Stability of coronal loops to kink modes transformed to localized modes by increasing the poloidal wavenumber, m, is investigated. Two fields generated numerically from the Grad-Shafranov equation and three analytic fields are investigated in detail and the effect of pressure on the marginal loop length is found, both for near force-free conditions such as is found in the solar corona, and away from force-free conditions. It was found that for near force-free conditions, kink modes are the most unstable with localized modes the most stable. As pressure and pressure gradients become important, there is a reversal in the most unstable modes with localized modes the most unstable.
1993-01-01T00:00:00ZHardie, Ian S.Magnetohydrodynamic stability theory provides a powerful tool for understanding and testing hypothesized mathematical and physical models of observed phenomena on the surface of the Sun. In this thesis, the problem of applying the 'correct' boundary conditions at the photospheric/coronal interface used in modelling coronal arcades is tackled. Then some aspects of the stability of coronal loops and arcades are investigated using a Fourier truncated series approximation for the equation of motion. The problem involving the boundary conditions has been the subject of a controversy for the past decade with two principal conditions suggested, the 'rigid-wall' conditions where all perturbations vanish at the interface, and 'flow-through' conditions where flows parallel to the equilibrium magnetic field take place. By modelling the photosphere and corona as two different density regions and then varying the ratio of the densities of the two regions, growth rates and eigen-functions of both ideal and resistive modes are investigated in order to follow the evolution of the modes as the density ratio is increased. In order to simplify the analysis, the 2-D equations are reduced to 1-D equations by taking a WKB approximation for the spatial variations across the field to give a localized ballooning approach with ordinary differential equations along the fieldlines. Stability of coronal loops to kink modes transformed to localized modes by increasing the poloidal wavenumber, m, is investigated. Two fields generated numerically from the Grad-Shafranov equation and three analytic fields are investigated in detail and the effect of pressure on the marginal loop length is found, both for near force-free conditions such as is found in the solar corona, and away from force-free conditions. It was found that for near force-free conditions, kink modes are the most unstable with localized modes the most stable. As pressure and pressure gradients become important, there is a reversal in the most unstable modes with localized modes the most unstable.Instability and wave-growth within some oscillatory fluid flowsForster, Graham Keithhttp://hdl.handle.net/10023/140872018-06-14T23:18:59Z1996-01-01T00:00:00ZOscillatory fluid flows arise naturally in many systems. Whether or not these systems are stable is an important question and external periodic forcing of the flow may result in rich and complicated behaviours. Here three distinct oscillatory fluid flows are examined in detail, with the stability of each being established using a range of analytical and computational methods. The first system comprises standing surface capillary-gravity waves in second-harmonic resonance subject to Faraday excitation. Using the perturbation technique of multiple scales, the amplitude equations for the system are derived. At exact resonance, and with the absence of damping, the only fixed point of the equations is found to be the origin. A computational approach reveals that the amplitudes of the two waves remain either bounded or grow to infinity depending on initial data. With the introduction of detuning and damping into the system families of fixed points now exist and some special cases are considered. The second class of flows are unbounded time-periodic flows with fixed ellipsoidal stream surfaces, and having spatially uniform but time-periodic strain rates. Using a recently developed method based on theoretical study of the Schrodinger equation with quasi-periodic potential, a computational approach is adopted which determines the stability of the flow to three-dimensional plane wave disturbances. Results for the growth rate and winding number of the disturbance clearly reveal the regions of instability. It is found that almost all these flows are highly unstable. The third class is another set of three-dimensional time-periodic flows with spatially uniform strain rates. These flows are non-axisymmetric and have sinusoidally-fluctuating rates of strain directed along the fixed coordinate axes. The same computational method is employed and it is found that instability increases along with the non-axisymmetric nature of the flow.
1996-01-01T00:00:00ZForster, Graham KeithOscillatory fluid flows arise naturally in many systems. Whether or not these systems are stable is an important question and external periodic forcing of the flow may result in rich and complicated behaviours. Here three distinct oscillatory fluid flows are examined in detail, with the stability of each being established using a range of analytical and computational methods. The first system comprises standing surface capillary-gravity waves in second-harmonic resonance subject to Faraday excitation. Using the perturbation technique of multiple scales, the amplitude equations for the system are derived. At exact resonance, and with the absence of damping, the only fixed point of the equations is found to be the origin. A computational approach reveals that the amplitudes of the two waves remain either bounded or grow to infinity depending on initial data. With the introduction of detuning and damping into the system families of fixed points now exist and some special cases are considered. The second class of flows are unbounded time-periodic flows with fixed ellipsoidal stream surfaces, and having spatially uniform but time-periodic strain rates. Using a recently developed method based on theoretical study of the Schrodinger equation with quasi-periodic potential, a computational approach is adopted which determines the stability of the flow to three-dimensional plane wave disturbances. Results for the growth rate and winding number of the disturbance clearly reveal the regions of instability. It is found that almost all these flows are highly unstable. The third class is another set of three-dimensional time-periodic flows with spatially uniform strain rates. These flows are non-axisymmetric and have sinusoidally-fluctuating rates of strain directed along the fixed coordinate axes. The same computational method is employed and it is found that instability increases along with the non-axisymmetric nature of the flow.The effects of magnetic fields on oscillations in the solar atmosphereEvans, David J.http://hdl.handle.net/10023/140822018-06-14T23:20:32Z1990-01-01T00:00:00ZA study has been made of wave propagation in two regions of the solar atmosphere in which magnetic forces are significant. Sunspot observations indicate a rich variety of characteristic modes of oscillation roughly divided into three categories: three minute umbral oscillations, five minute umbral oscillations and penumbral waves. Outside of intense magnetic flux concentrations the oscillation spectrum is dominated by the five minute period. These waves are trapped in a cavity whose upper boundary may be affected by the magnetism of the chromosphere. A sunspot has been modelled by a uniform cylindrical flux tube. The allowable modes of oscillation are found to vary as the atmospheric parameters change with depth. Umbral three minute oscillations are interpreted as slow body modes. The umbral five minute oscillations arise through a complicated interaction with acoustic waves outside the sunspot. This drives fast body modes as well as waves simply passing through the flux tube. The former may propagate upwards and become fast surface waves. Fast and slow surface waves may explain some of the oscillations of the penumbra. The magnetic structure of the chromosphere has been modelled as an isothermal atmosphere permeated by a uniform and horizontal magnetic field. A dispersion relation for the trapped waves below such an atmosphere has been derived and both asymptotic and numerical solutions found. The effect of a uniform magnetic field is to increase the frequency of the trapped modes. A physical explanation for these changes in frequency has been put forward. Observational evidence may indicate that such effects are indeed seen. This model has been further generalised to take some account of the variation in canopy height which has been observed.
1990-01-01T00:00:00ZEvans, David J.A study has been made of wave propagation in two regions of the solar atmosphere in which magnetic forces are significant. Sunspot observations indicate a rich variety of characteristic modes of oscillation roughly divided into three categories: three minute umbral oscillations, five minute umbral oscillations and penumbral waves. Outside of intense magnetic flux concentrations the oscillation spectrum is dominated by the five minute period. These waves are trapped in a cavity whose upper boundary may be affected by the magnetism of the chromosphere. A sunspot has been modelled by a uniform cylindrical flux tube. The allowable modes of oscillation are found to vary as the atmospheric parameters change with depth. Umbral three minute oscillations are interpreted as slow body modes. The umbral five minute oscillations arise through a complicated interaction with acoustic waves outside the sunspot. This drives fast body modes as well as waves simply passing through the flux tube. The former may propagate upwards and become fast surface waves. Fast and slow surface waves may explain some of the oscillations of the penumbra. The magnetic structure of the chromosphere has been modelled as an isothermal atmosphere permeated by a uniform and horizontal magnetic field. A dispersion relation for the trapped waves below such an atmosphere has been derived and both asymptotic and numerical solutions found. The effect of a uniform magnetic field is to increase the frequency of the trapped modes. A physical explanation for these changes in frequency has been put forward. Observational evidence may indicate that such effects are indeed seen. This model has been further generalised to take some account of the variation in canopy height which has been observed.Magnetic helicity and force-free equilibria in the solar corona and in laboratory devicesDixon, Andrew Michaelhttp://hdl.handle.net/10023/140802018-06-14T23:19:04Z1988-01-01T00:00:00ZForce-free equilibria are believed to be important in both an astrophysical and a laboratory context as minimum-energy configurations (see, for example, Woltjer, 1958; Taylor, 1974). Associated is the study of magnetic helicity and its invariance. In Chapter Two of this thesis we put forward a means of heating the corona by the rotation of the foot-points of a coronal "sunspot" magnetic field anchored in the photosphere. The method adopted is essentially that of Heyvaerts and Priest (1984), employing Taylor's Hypothesis (Taylor, 1974) and a magnetic helicity evolution equation. A characteristic of the Reversed-Field Pinch device is the appearance, at high enough values of the quantity "volt-seconds over toroidal flux", of a helical distortion to the basic axi-symmetric state. In Chapter Three we look for corresponding behaviour in the "sunspot equilibrium" of the previous chapter, with limited success. However, we go on to formulate a method of calculating general axi-symmetric fields above a sunspot given the normal field component at the photosphere. Chapters Four, Five and Six are concerned with equilibrium force-free fields in a sphere. The main aim here is the calculation minimum-energy configurations having magnetic flux crossing the boundary, and so we employ "relative helicity" (Berger and Field, 1984). In Chapter Four we consider the "P1(cos𝜃)" boundary radial field, finding that the minimum-energy state is always purely symmetric. In Chapter Five we treat the "P2(cos𝜃)" boundary condition. We find in this case that a "mixed state" is theoretically possible for high enough values of the helicity. In Chapter Six, we consider a general boundary field, which we use to model point sources of magnetic flux at the boundary of a spheromak, finding that in practice an axi-symmetric configuration is always the minimum-energy state. Finally, in Chapter Seven we present an extension to the theorem of Woltjer (1958), concerning the minimization of the magnetic energy of a magnetic structure, to include the case of a free boundary subjected to external pressure forces. To illustrate the theory, we have provided three applications, the first to a finite cylindrical flux and the remainder to possible spheromak configurations.
1988-01-01T00:00:00ZDixon, Andrew MichaelForce-free equilibria are believed to be important in both an astrophysical and a laboratory context as minimum-energy configurations (see, for example, Woltjer, 1958; Taylor, 1974). Associated is the study of magnetic helicity and its invariance. In Chapter Two of this thesis we put forward a means of heating the corona by the rotation of the foot-points of a coronal "sunspot" magnetic field anchored in the photosphere. The method adopted is essentially that of Heyvaerts and Priest (1984), employing Taylor's Hypothesis (Taylor, 1974) and a magnetic helicity evolution equation. A characteristic of the Reversed-Field Pinch device is the appearance, at high enough values of the quantity "volt-seconds over toroidal flux", of a helical distortion to the basic axi-symmetric state. In Chapter Three we look for corresponding behaviour in the "sunspot equilibrium" of the previous chapter, with limited success. However, we go on to formulate a method of calculating general axi-symmetric fields above a sunspot given the normal field component at the photosphere. Chapters Four, Five and Six are concerned with equilibrium force-free fields in a sphere. The main aim here is the calculation minimum-energy configurations having magnetic flux crossing the boundary, and so we employ "relative helicity" (Berger and Field, 1984). In Chapter Four we consider the "P1(cos𝜃)" boundary radial field, finding that the minimum-energy state is always purely symmetric. In Chapter Five we treat the "P2(cos𝜃)" boundary condition. We find in this case that a "mixed state" is theoretically possible for high enough values of the helicity. In Chapter Six, we consider a general boundary field, which we use to model point sources of magnetic flux at the boundary of a spheromak, finding that in practice an axi-symmetric configuration is always the minimum-energy state. Finally, in Chapter Seven we present an extension to the theorem of Woltjer (1958), concerning the minimization of the magnetic energy of a magnetic structure, to include the case of a free boundary subjected to external pressure forces. To illustrate the theory, we have provided three applications, the first to a finite cylindrical flux and the remainder to possible spheromak configurations.MHD flows in the solar atmosphereDel Zanna, Lucahttp://hdl.handle.net/10023/140752018-06-14T23:19:03Z1997-01-01T00:00:00ZIn this thesis, different aspects of the physics of flows in the solar atmosphere are examined. These are described by means of the set of (ideal) magnetohydrodynamics (MHD) and throughout the thesis there is a progressive refinement in the mathematical methods to solve these equations. First, an analysis of symmetric MHD equilibria is presented and the difficulties that are found in solving the steady equations, both analytically and numerically, are discussed in detail. A novel method to find exact solutions in the incompressible case is presented and families of solutions are given in different geometries. Then, attention is turned to flows in coronal magnetic structures, namely quiescent prominences (closed fieldlines) and polar plumes (open fieldlines), and MHD models for these structures are developed by following two different methods: for the former a semi- analytic approach while for the latter a linearisation through a low 𝛽 assumption. In the prominence model, the effects of a subsonic flow along the fieldlines supporting the structure are studied and the results are compared both with a previous static model and with the observed flow speeds. For the plume model, flows are supposed to be transonic along the open fieldlines and their behaviour is studied for different distributions of temperature, density and magnetic flux. However, here the main goal is to demonstrate that coronal plumes are essentially magnetic features and some results of the model are compared with observations. Finally, a time dependent MHD code in spherical coordinates is presented. The aim is to study the interaction of the solar wind with the large scale coronal magnetic structures and the propagation of MHD waves. As a test in 1-D, simulations of the dynamic response of a spherically symmetric extended corona to changes at the outer pressure are studied, following a previous analytic work.
1997-01-01T00:00:00ZDel Zanna, LucaIn this thesis, different aspects of the physics of flows in the solar atmosphere are examined. These are described by means of the set of (ideal) magnetohydrodynamics (MHD) and throughout the thesis there is a progressive refinement in the mathematical methods to solve these equations. First, an analysis of symmetric MHD equilibria is presented and the difficulties that are found in solving the steady equations, both analytically and numerically, are discussed in detail. A novel method to find exact solutions in the incompressible case is presented and families of solutions are given in different geometries. Then, attention is turned to flows in coronal magnetic structures, namely quiescent prominences (closed fieldlines) and polar plumes (open fieldlines), and MHD models for these structures are developed by following two different methods: for the former a semi- analytic approach while for the latter a linearisation through a low 𝛽 assumption. In the prominence model, the effects of a subsonic flow along the fieldlines supporting the structure are studied and the results are compared both with a previous static model and with the observed flow speeds. For the plume model, flows are supposed to be transonic along the open fieldlines and their behaviour is studied for different distributions of temperature, density and magnetic flux. However, here the main goal is to demonstrate that coronal plumes are essentially magnetic features and some results of the model are compared with observations. Finally, a time dependent MHD code in spherical coordinates is presented. The aim is to study the interaction of the solar wind with the large scale coronal magnetic structures and the propagation of MHD waves. As a test in 1-D, simulations of the dynamic response of a spherically symmetric extended corona to changes at the outer pressure are studied, following a previous analytic work.The nonuniform magnetohydrodynamic nature of the solar atmosphereDe Ville, Andrewhttp://hdl.handle.net/10023/140732018-06-14T23:19:34Z1991-01-01T00:00:00ZThe nonuniform structure observed in the solar atmosphere, and in particular the corona, is thought to arise due to the interaction between the magnetic field and plasma. Using a linear theory, the nature of these interactions is investigated, and it is shown how coronal structure may be modelled in a simple way by extended standing disturbances. The effect of inertial forces in considered in both a Cartesian and cylindrical geometries, and a first correction due to gravity is calculated. The restrictions of a linear theory may be overcome by finding exact solutions. Solutions are presented which may model plasma flows in closed, partially open and open magnetic field line structures. A new method for finding particular classes of exact steady solutions in a gravitationally stratified, isothermal atmosphere is presented, along with some examples of possible solutions.
1991-01-01T00:00:00ZDe Ville, AndrewThe nonuniform structure observed in the solar atmosphere, and in particular the corona, is thought to arise due to the interaction between the magnetic field and plasma. Using a linear theory, the nature of these interactions is investigated, and it is shown how coronal structure may be modelled in a simple way by extended standing disturbances. The effect of inertial forces in considered in both a Cartesian and cylindrical geometries, and a first correction due to gravity is calculated. The restrictions of a linear theory may be overcome by finding exact solutions. Solutions are presented which may model plasma flows in closed, partially open and open magnetic field line structures. A new method for finding particular classes of exact steady solutions in a gravitationally stratified, isothermal atmosphere is presented, along with some examples of possible solutions.Aspects of solar coronal stability theoryDe Bruyne, Peter J. J.http://hdl.handle.net/10023/140712018-06-14T23:18:47Z1991-01-01T00:00:00ZSolar coronal stability theory is a powerful tool for understanding the complex behaviour of the Sun's atmosphere. It enables one to discover the driving forces behind some intriguing phenomena and to gauge the soundness of theoretical models for observed structures. In this thesis, the linear stability analysis of line-tied symmetric magnetohydrostatic equilibria is studied within the framework of ideal MHD, aimed at its application to the solar corona. Firstly, a tractable stability procedure based on a variational method is devised. It provides a necessary condition for stability to disturbances localised about a particular flux surface, and a sufficient condition for stability to all accessible perturbations that vanish at the photosphere. The tests require the minimisation of a line integral along the magnetic field lines. For 1-D equilibria, this can be performed analytically, and simple stability criteria are obtained. The necessary condition then serves as an extended Suydam criterion, incorporating the stabilising effect of line-tying. For 2-D equilibria, the minimisation requires the integration of a system of ordinary differential equations along the field lines. This stability technique is applied to arcade, loop, and prominence models, yielding tight bounds on the equilibrium parameters. Secondly, global modes in 1-D coronal loops are investigated using a normal mode method, in order to clarify their link with localised interchange modes. For nearly force-free fields it is shown that instability to localised modes implies the existence of a fast growing global kink mode driven in the neighbourhood of the radius predicted by the local analysis. This confers a new significance on the study of localised interchange modes and the associated extended Suydam criterion.
1991-01-01T00:00:00ZDe Bruyne, Peter J. J.Solar coronal stability theory is a powerful tool for understanding the complex behaviour of the Sun's atmosphere. It enables one to discover the driving forces behind some intriguing phenomena and to gauge the soundness of theoretical models for observed structures. In this thesis, the linear stability analysis of line-tied symmetric magnetohydrostatic equilibria is studied within the framework of ideal MHD, aimed at its application to the solar corona. Firstly, a tractable stability procedure based on a variational method is devised. It provides a necessary condition for stability to disturbances localised about a particular flux surface, and a sufficient condition for stability to all accessible perturbations that vanish at the photosphere. The tests require the minimisation of a line integral along the magnetic field lines. For 1-D equilibria, this can be performed analytically, and simple stability criteria are obtained. The necessary condition then serves as an extended Suydam criterion, incorporating the stabilising effect of line-tying. For 2-D equilibria, the minimisation requires the integration of a system of ordinary differential equations along the field lines. This stability technique is applied to arcade, loop, and prominence models, yielding tight bounds on the equilibrium parameters. Secondly, global modes in 1-D coronal loops are investigated using a normal mode method, in order to clarify their link with localised interchange modes. For nearly force-free fields it is shown that instability to localised modes implies the existence of a fast growing global kink mode driven in the neighbourhood of the radius predicted by the local analysis. This confers a new significance on the study of localised interchange modes and the associated extended Suydam criterion.Hysteresis and mode competition in Faraday wavesDecent, Stephen Paulhttp://hdl.handle.net/10023/140542018-06-14T23:20:39Z1996-01-01T00:00:00ZFaraday waves arise on the surface of a liquid in a container that is undergoing vertical periodic oscillations. We investigate two-dimensional Faraday waves in a long rectangular container, both theoretically and experimentally. Hysteresis occurs when both finite amplitude solutions and the flat surface solution are available. We derive a nonlinear model of a standing wave, extending the Lagrangian method of Miles (1976). The model is used to investigate hysteresis. It is found necessary to retain cubic damping, cubic forcing and the fifth-order conservative term in order to achieve agreement with experiments. The fifth-order conservative term was omitted from all previous studies of Faraday waves. Stable limit cycles are found to arise from this single-mode equation. We examine the structure of this new solution in detail, both analytically and numerically. We describe local bifurcations using a multiple time scales analysis and global bifurcations using Melnikov's method. The coefficients of linear and cubic damping are derived for a standing wave in a rectangular container by considering energy dissipation in the main body of the fluid (due to potential flow and streaming) and in boundary layers at the sidewalls and at the surface. Surface contamination, due to the presence of a thin viscoelastic surface film, creates a boundary layer at the surface which causes enhanced dissipation comparable to, or greater than, that caused by the boundary layers at the walls of the container. Three-mode interaction equations are used to model intermittency and complex modulations which are found to arise from a sideband instability mechanism similar to that of Eckhaus (1963) and Benjamin & Feir (1967). The role of cubic and fifth-order nonlinear terms on this instability mechanism is examined. Theoretical results are found to compare quite favourably with experimental data.
1996-01-01T00:00:00ZDecent, Stephen PaulFaraday waves arise on the surface of a liquid in a container that is undergoing vertical periodic oscillations. We investigate two-dimensional Faraday waves in a long rectangular container, both theoretically and experimentally. Hysteresis occurs when both finite amplitude solutions and the flat surface solution are available. We derive a nonlinear model of a standing wave, extending the Lagrangian method of Miles (1976). The model is used to investigate hysteresis. It is found necessary to retain cubic damping, cubic forcing and the fifth-order conservative term in order to achieve agreement with experiments. The fifth-order conservative term was omitted from all previous studies of Faraday waves. Stable limit cycles are found to arise from this single-mode equation. We examine the structure of this new solution in detail, both analytically and numerically. We describe local bifurcations using a multiple time scales analysis and global bifurcations using Melnikov's method. The coefficients of linear and cubic damping are derived for a standing wave in a rectangular container by considering energy dissipation in the main body of the fluid (due to potential flow and streaming) and in boundary layers at the sidewalls and at the surface. Surface contamination, due to the presence of a thin viscoelastic surface film, creates a boundary layer at the surface which causes enhanced dissipation comparable to, or greater than, that caused by the boundary layers at the walls of the container. Three-mode interaction equations are used to model intermittency and complex modulations which are found to arise from a sideband instability mechanism similar to that of Eckhaus (1963) and Benjamin & Feir (1967). The role of cubic and fifth-order nonlinear terms on this instability mechanism is examined. Theoretical results are found to compare quite favourably with experimental data.The influence of thermal and magnetic layers on solar oscillation frequenciesDaniell, Markhttp://hdl.handle.net/10023/140512018-06-14T23:20:28Z1998-01-01T00:00:00ZIn this thesis, a study is made of the global solar oscillations known as p-modes, modelled by a plane-parallel stratified plasma, within which is embedded a horizontal layered magnetic field. A magnetohydrodynamic formalism is used to investigate the models. The main aim of the thesis is to model the turnover effect in the frequency shifts of the p-modes observed over the course of the solar cycle. Radial oscillations (modes of degree zero) of the Sun are studied for several atmospheric temperature and magnetic field profiles. It is found that the turnover in frequency shifts may be obtained by an increase in the strength of the atmospheric horizontal magnetic field (assumed to be uniform), coupled with a simultaneous increase in atmospheric temperature. The effect of a thin superadiabatic layer in the upper convection zone on p-mode frequencies is also considered. For this model we study modes of general degree, and find that the observed rise and subsequent downturn in the frequency shifts can be duplicated, in the absence of a magnetic field, by simultaneously steepening the temperature gradient of the superadiabatic layer and increasing the atmospheric temperature. In the presence of a magnetic field, where the atmosphere is permeated by a uniform horizontal magnetic field, turnover is reproduced by a combination of an increase in magnetic field strength, a steepening of the temperature gradient in the superadiabatic region, and an increase in atmospheric temperature. The unstable superadiabatic layer also gives rise to convective modes, which are considered briefly. Finally, a model incorporating a magnetic layer residing at the base of the convection zone is constructed and its influence on the frequencies of p-modes assessed. By simply changing the magnetic field strength of this layer, we are unable to reproduce the observed solar cycle variations in p-mode frequencies. The buried magnetic layer supports surface and body magnetoacoustic waves, and a brief study is made of their properties.
1998-01-01T00:00:00ZDaniell, MarkIn this thesis, a study is made of the global solar oscillations known as p-modes, modelled by a plane-parallel stratified plasma, within which is embedded a horizontal layered magnetic field. A magnetohydrodynamic formalism is used to investigate the models. The main aim of the thesis is to model the turnover effect in the frequency shifts of the p-modes observed over the course of the solar cycle. Radial oscillations (modes of degree zero) of the Sun are studied for several atmospheric temperature and magnetic field profiles. It is found that the turnover in frequency shifts may be obtained by an increase in the strength of the atmospheric horizontal magnetic field (assumed to be uniform), coupled with a simultaneous increase in atmospheric temperature. The effect of a thin superadiabatic layer in the upper convection zone on p-mode frequencies is also considered. For this model we study modes of general degree, and find that the observed rise and subsequent downturn in the frequency shifts can be duplicated, in the absence of a magnetic field, by simultaneously steepening the temperature gradient of the superadiabatic layer and increasing the atmospheric temperature. In the presence of a magnetic field, where the atmosphere is permeated by a uniform horizontal magnetic field, turnover is reproduced by a combination of an increase in magnetic field strength, a steepening of the temperature gradient in the superadiabatic region, and an increase in atmospheric temperature. The unstable superadiabatic layer also gives rise to convective modes, which are considered briefly. Finally, a model incorporating a magnetic layer residing at the base of the convection zone is constructed and its influence on the frequencies of p-modes assessed. By simply changing the magnetic field strength of this layer, we are unable to reproduce the observed solar cycle variations in p-mode frequencies. The buried magnetic layer supports surface and body magnetoacoustic waves, and a brief study is made of their properties.Energy-balance models of the solar coronaWragg, M. A.http://hdl.handle.net/10023/140472018-06-14T23:20:29Z1982-01-01T00:00:00ZSolar coronal observations have shown that the corona has a highly complex structure which presumably owes its existence to the magnetic field. Models in thermal and hydrostatic equilibrium are here calculated in order to try and explain many of these observations. Coronal holes occur where open field lines reach out into space. The model of McWhirter, et al. (1975) for the inner corona in such a configuration is generalised to allow different types and magnitudes of heating as well as different area divergences and flows. It is found that hot, fast upflows cannot always exist in thermal equilibrium. The choice of boundary conditions can appreciably alter the results, and so different choices are compared. Most of the corona, especially in active regions, appears to consist of coronal loops. Subtle relations for energy balance models of such loops are found to exist between the physical parameters of a loop's length, base density, and heat input. No solution exists at coronal temperatures in certain cases, which may explain the observations of very cool loops. The effect of a loop's geometry and field line divergence on the structure is found. Results predicted from scaling laws are compared, and the uniqueness of the solution for a loop with a fixed mass is studied. The error in the predicted emission measure through assuming uniform pressure is shown to be considerable. The life-time of a loop can often be many days, suggesting the existence of a thermally stable state. A global stability analysis is performed, and it is found that a loop's stability may depend critically upon its length. Thermally isolated loops, which are the most unstable type, can be thermally stable, provided their pressure falls off sufficiently rapidly with height (due to hydrostatic equilibrium).
1982-01-01T00:00:00ZWragg, M. A.Solar coronal observations have shown that the corona has a highly complex structure which presumably owes its existence to the magnetic field. Models in thermal and hydrostatic equilibrium are here calculated in order to try and explain many of these observations. Coronal holes occur where open field lines reach out into space. The model of McWhirter, et al. (1975) for the inner corona in such a configuration is generalised to allow different types and magnitudes of heating as well as different area divergences and flows. It is found that hot, fast upflows cannot always exist in thermal equilibrium. The choice of boundary conditions can appreciably alter the results, and so different choices are compared. Most of the corona, especially in active regions, appears to consist of coronal loops. Subtle relations for energy balance models of such loops are found to exist between the physical parameters of a loop's length, base density, and heat input. No solution exists at coronal temperatures in certain cases, which may explain the observations of very cool loops. The effect of a loop's geometry and field line divergence on the structure is found. Results predicted from scaling laws are compared, and the uniqueness of the solution for a loop with a fixed mass is studied. The error in the predicted emission measure through assuming uniform pressure is shown to be considerable. The life-time of a loop can often be many days, suggesting the existence of a thermally stable state. A global stability analysis is performed, and it is found that a loop's stability may depend critically upon its length. Thermally isolated loops, which are the most unstable type, can be thermally stable, provided their pressure falls off sufficiently rapidly with height (due to hydrostatic equilibrium).Solar coronal loopsHood, Alan W.http://hdl.handle.net/10023/140442018-06-14T13:19:44Z1980-01-01T00:00:00ZIn the past few years it has been realised that loop structures are an important feature of the solar corona. Presumably, these structures outline the local magnetic field and in this thesis some theoretical aspects of solar coronal loops are considered. The starting point is to model the static equilibrium, in a 1 - D structure, and determine the temperature and density by solving the energy balance equation. The basic state is determined by two dimensionless parameters, namely the ratio of optically thin radiation to thermal conduction, and the ratio of mechanical heating to radiation, An important result is that when critical values of the parameters are exceeded thermal non-equilibrium- ensues and the loop rapidly cools from coronal temperatures ~ 10⁶K to below 10⁵K. A simple 2 - D model extends this work and results provide a possible explanation for several loop features. The thermal stability of coronal loops is investigated by developing two simple methods which apply to a wide class of equilibria. Stability is found to depend on the boundary conditions adopted but not critically on the form of the heating. A loop is shown to be stable if its conductive flux is large enough that it lies on the upper- of two equilibrium branches. Solar coronal loops are observed to be remarkably stable structures. A magneto hydrodynamic stability analysis of a model loop by the energy method suggests that the main reason for stability is the fact that the ends of the loop are anchored in the dense photosphere. Two-ribbon flares follow the eruption of an active region filament, which may lie along a magnetic flux tube. It is suggested that the eruption is caused by the kink instability, which sets in when the amount of magnetic twist in the flux tube exceeds a critical value. Occasionally active region loops may become unstable and give rise to small loop flares, which may also be a result of the kink instability. A more realistic model of an active region filament, that takes account of the overlying magnetic field, shows that instability may occur if either the twist or the height of the filament exceed critical values. Finally, the possibility that a solar flare is triggered by thermal non-equilibrium, instead of by magnetic instability, is investigated. This is demonstrated by solving approximately the energy equation for a loop under a balance between thermal conduction, optically thin radiation and a heating source. It is found that, if one starts with a cool equilibrium at a temperature about 10⁴K and gradually increases the heating or decreases the loop pressure (or decreases the loop length), ultimately critical conditions are reached beyond which no cool equilibrium exists. The plasma rapidly heats up to a new quasi-equilibrium at typically 10⁷K. During such a thermal flaring, any magnetic disruption or particle acceleration is of secondary importance.
1980-01-01T00:00:00ZHood, Alan W.In the past few years it has been realised that loop structures are an important feature of the solar corona. Presumably, these structures outline the local magnetic field and in this thesis some theoretical aspects of solar coronal loops are considered. The starting point is to model the static equilibrium, in a 1 - D structure, and determine the temperature and density by solving the energy balance equation. The basic state is determined by two dimensionless parameters, namely the ratio of optically thin radiation to thermal conduction, and the ratio of mechanical heating to radiation, An important result is that when critical values of the parameters are exceeded thermal non-equilibrium- ensues and the loop rapidly cools from coronal temperatures ~ 10⁶K to below 10⁵K. A simple 2 - D model extends this work and results provide a possible explanation for several loop features. The thermal stability of coronal loops is investigated by developing two simple methods which apply to a wide class of equilibria. Stability is found to depend on the boundary conditions adopted but not critically on the form of the heating. A loop is shown to be stable if its conductive flux is large enough that it lies on the upper- of two equilibrium branches. Solar coronal loops are observed to be remarkably stable structures. A magneto hydrodynamic stability analysis of a model loop by the energy method suggests that the main reason for stability is the fact that the ends of the loop are anchored in the dense photosphere. Two-ribbon flares follow the eruption of an active region filament, which may lie along a magnetic flux tube. It is suggested that the eruption is caused by the kink instability, which sets in when the amount of magnetic twist in the flux tube exceeds a critical value. Occasionally active region loops may become unstable and give rise to small loop flares, which may also be a result of the kink instability. A more realistic model of an active region filament, that takes account of the overlying magnetic field, shows that instability may occur if either the twist or the height of the filament exceed critical values. Finally, the possibility that a solar flare is triggered by thermal non-equilibrium, instead of by magnetic instability, is investigated. This is demonstrated by solving approximately the energy equation for a loop under a balance between thermal conduction, optically thin radiation and a heating source. It is found that, if one starts with a cool equilibrium at a temperature about 10⁴K and gradually increases the heating or decreases the loop pressure (or decreases the loop length), ultimately critical conditions are reached beyond which no cool equilibrium exists. The plasma rapidly heats up to a new quasi-equilibrium at typically 10⁷K. During such a thermal flaring, any magnetic disruption or particle acceleration is of secondary importance.Three-dimensional topology of solar coronal magnetic fieldsBrown, Daniel Stephenhttp://hdl.handle.net/10023/140362018-06-14T23:18:36Z1999-01-01T00:00:00ZThis thesis investigates the topology of the magnetic field in the solar corona. It is important have an understanding of how the highly complex coronal magnetic field behaves in order to study many fundamental coronal phenomena, such as coronal heating events, solar flares and polar plumes. The magnetic fields due to three or four discrete sources are investigated and the corresponding topological states are found. The locations of these states in parameter space is calculated and the bifurcations between states are analysed. A complete analysis has been undertaken for the three-source case and a selective one for the four-source case in order to identify new non-generic behaviour. The thesis goes on to study the topological behaviour of a coronal bright point. Different phases during the lifetime of the bright point are identified and the responsible topological behaviour due to the movement of the magnetic fragments in the photosphere is discussed.
1999-01-01T00:00:00ZBrown, Daniel StephenThis thesis investigates the topology of the magnetic field in the solar corona. It is important have an understanding of how the highly complex coronal magnetic field behaves in order to study many fundamental coronal phenomena, such as coronal heating events, solar flares and polar plumes. The magnetic fields due to three or four discrete sources are investigated and the corresponding topological states are found. The locations of these states in parameter space is calculated and the bifurcations between states are analysed. A complete analysis has been undertaken for the three-source case and a selective one for the four-source case in order to identify new non-generic behaviour. The thesis goes on to study the topological behaviour of a coronal bright point. Different phases during the lifetime of the bright point are identified and the responsible topological behaviour due to the movement of the magnetic fragments in the photosphere is discussed.External and internal magnetohydrostatic models of quiescent solar prominencesCartledge, Nicholas P.http://hdl.handle.net/10023/140292018-06-13T23:19:57Z1996-01-01T00:00:00ZQuiescent solar prominences are amongst the most interesting and yet least understood of the phenomena observed on the Sun and provide both the theorist and the observer with equally demanding challenges. The theoretical study of prominences is an important branch of solar physics as it contributes significantly to the overall understanding of the Sun and its atmosphere. One only needs to be presented with the illuminating fact that there is more mass contained in these bodies than in the remainder of the entire corona to be convinced of their importance. Although many of the physical mechanisms associated with prominence theory are important in their own right, they are also of much wider relevance for various other astrophysical phenomena. For example, radiative and magnetic instabilities are explored in detail in the context of solar prominences; yet clearly these are important processes that relate to many other branches of astrophysics. Prominences are intimately associated with solar flares which occur when a prominence loses equilibrium. Also, prominence eruptions are very important as they are closely connected with coronal mass ejections. These account for a large fraction of the total mass lost from the Sun and so are extremely important events, particularly when one considers the consequences as this plasma interacts with the Earth's environment. It is the period of global equilibrium of quiescent prominences, though, that is the focus of this thesis. Various models are proposed to help understand both the topology and supporting mechanisms of the external, coronal magnetic field, and also the internal prominence structure and the way in which the two regimes fit together. In Chapter 3 we extend a model for the equilibrium of a prominence sheet in a twisted magnetic flux-tube, given by Ridgway, Priest and Amari (1991), to incorporate a current sheet of finite height. This removes the discontinuity at the edge of the tube and provides a shear-free outer boundary which enables the tube to be matched onto a background potential field. In addition, internal prominence solutions are found by expanding the sheet to a finite width and matching suitable magnetic profiles across this region. Next we consider a global model for the magnetic field structure surrounding a polar-crown prominence. We examine potential configurations generated from typical distributions of photospheric flux, and select solutions for which there is a location of dipped magnetic field where prominence material may collect and form. Once such a configuration is available, it is necessary to construct the ensuing prominence solution. We achieve this in Chapter 4 by considering a simplified form for the photospheric field. We show that the equilibrium contains a weighted, curved prominence sheet supported in the location of dipped magnetic field. The equilibrium requires an enhanced magnetic pressure below the sheet to support the component of weight in the normal direction. The internal equilibrium of curved or inclined prominence material has not been considered previously and so we formulate, in Chapter 6, a simple one-dimensional isothermal solution for a cut across the prominence. This is developed to allow for variations along the sheet and in this way an internal solution for the curved prominence of Chapter 4 is given, which matches onto the external potential polar-crown field. Finally, in Chapter 7, we rewrite this solution in terms of its constituent internal and external components and show how the composite solution switches between the two in a region of overlap, or transition region. From this, the internal plasma properties are deduced and realistic profiles for the pressure, density and temperature are obtained.
1996-01-01T00:00:00ZCartledge, Nicholas P.Quiescent solar prominences are amongst the most interesting and yet least understood of the phenomena observed on the Sun and provide both the theorist and the observer with equally demanding challenges. The theoretical study of prominences is an important branch of solar physics as it contributes significantly to the overall understanding of the Sun and its atmosphere. One only needs to be presented with the illuminating fact that there is more mass contained in these bodies than in the remainder of the entire corona to be convinced of their importance. Although many of the physical mechanisms associated with prominence theory are important in their own right, they are also of much wider relevance for various other astrophysical phenomena. For example, radiative and magnetic instabilities are explored in detail in the context of solar prominences; yet clearly these are important processes that relate to many other branches of astrophysics. Prominences are intimately associated with solar flares which occur when a prominence loses equilibrium. Also, prominence eruptions are very important as they are closely connected with coronal mass ejections. These account for a large fraction of the total mass lost from the Sun and so are extremely important events, particularly when one considers the consequences as this plasma interacts with the Earth's environment. It is the period of global equilibrium of quiescent prominences, though, that is the focus of this thesis. Various models are proposed to help understand both the topology and supporting mechanisms of the external, coronal magnetic field, and also the internal prominence structure and the way in which the two regimes fit together. In Chapter 3 we extend a model for the equilibrium of a prominence sheet in a twisted magnetic flux-tube, given by Ridgway, Priest and Amari (1991), to incorporate a current sheet of finite height. This removes the discontinuity at the edge of the tube and provides a shear-free outer boundary which enables the tube to be matched onto a background potential field. In addition, internal prominence solutions are found by expanding the sheet to a finite width and matching suitable magnetic profiles across this region. Next we consider a global model for the magnetic field structure surrounding a polar-crown prominence. We examine potential configurations generated from typical distributions of photospheric flux, and select solutions for which there is a location of dipped magnetic field where prominence material may collect and form. Once such a configuration is available, it is necessary to construct the ensuing prominence solution. We achieve this in Chapter 4 by considering a simplified form for the photospheric field. We show that the equilibrium contains a weighted, curved prominence sheet supported in the location of dipped magnetic field. The equilibrium requires an enhanced magnetic pressure below the sheet to support the component of weight in the normal direction. The internal equilibrium of curved or inclined prominence material has not been considered previously and so we formulate, in Chapter 6, a simple one-dimensional isothermal solution for a cut across the prominence. This is developed to allow for variations along the sheet and in this way an internal solution for the curved prominence of Chapter 4 is given, which matches onto the external potential polar-crown field. Finally, in Chapter 7, we rewrite this solution in terms of its constituent internal and external components and show how the composite solution switches between the two in a region of overlap, or transition region. From this, the internal plasma properties are deduced and realistic profiles for the pressure, density and temperature are obtained.Dynamical processes in the solar atmosphereCargill, P. (Peter)http://hdl.handle.net/10023/140242018-06-13T23:18:51Z1982-01-01T00:00:00ZIt has become clear that the closed-field regions of the solar atmosphere are not static (as was once thought) but that many types of steady and unsteady flows and other dynamical, processes such as flares are continually occurring, in them. This thesis investigates some theoretical aspects of these dynamical phenomena. Steady, one-dimensional flow along a coronal loop is investigated first of all. Such a flow may be driven by a pressure difference between the foot points, and a wide range of shocked and unshocked flows are found. The presence of steady flows removes the symmetry present in most static loop models, and these models are shown to form only one class of a much wider range of dynamic solutions to the equations of motion. Thermal non-equilibrium in hot coronal loops occurs if the pressure in a loop becomes too big. The non-linear evolution of this non-equilibrium state is followed, and the loop is found to cool from of order 10[super]6 K to below 10[super]5 K in a few hours. An upflow is driven, and non-equilibrium is suggested as a means of formation of either cool loop cores or prominences. Thermal non-equilibrium is also discussed as a possible mechanism for the simple-loop flare. It is suggested that a cool equilibrium at a temperature of a few times 10[super]4 K can flare to over. 10[super]7 K if the mechanical heating in the cool loop becomes too large. The evolution is followed and the loop is found to flare to over 10[super]7 K in approximately 5 minutes. Magnetohydrodynamic shock waves have long been regarded as a potentially efficient heating mechanism. Their behaviour is re-examined here, and it is found that certain types of shock can release very large amounts of energy. These results are then applied to the heating of "post"-flare loops, for which temperatures of 10[super]7 K at the loop summit may be obtained. Finally, some solutions of the magnetostatic equation are discussed, and it is pointed out that if the gas pressure is too big then magnetostatic equilibrium will break down. It is suggested that the subsequent evolution may give rise to a surge or other mass ejection.
1982-01-01T00:00:00ZCargill, P. (Peter)It has become clear that the closed-field regions of the solar atmosphere are not static (as was once thought) but that many types of steady and unsteady flows and other dynamical, processes such as flares are continually occurring, in them. This thesis investigates some theoretical aspects of these dynamical phenomena. Steady, one-dimensional flow along a coronal loop is investigated first of all. Such a flow may be driven by a pressure difference between the foot points, and a wide range of shocked and unshocked flows are found. The presence of steady flows removes the symmetry present in most static loop models, and these models are shown to form only one class of a much wider range of dynamic solutions to the equations of motion. Thermal non-equilibrium in hot coronal loops occurs if the pressure in a loop becomes too big. The non-linear evolution of this non-equilibrium state is followed, and the loop is found to cool from of order 10[super]6 K to below 10[super]5 K in a few hours. An upflow is driven, and non-equilibrium is suggested as a means of formation of either cool loop cores or prominences. Thermal non-equilibrium is also discussed as a possible mechanism for the simple-loop flare. It is suggested that a cool equilibrium at a temperature of a few times 10[super]4 K can flare to over. 10[super]7 K if the mechanical heating in the cool loop becomes too large. The evolution is followed and the loop is found to flare to over 10[super]7 K in approximately 5 minutes. Magnetohydrodynamic shock waves have long been regarded as a potentially efficient heating mechanism. Their behaviour is re-examined here, and it is found that certain types of shock can release very large amounts of energy. These results are then applied to the heating of "post"-flare loops, for which temperatures of 10[super]7 K at the loop summit may be obtained. Finally, some solutions of the magnetostatic equation are discussed, and it is pointed out that if the gas pressure is too big then magnetostatic equilibrium will break down. It is suggested that the subsequent evolution may give rise to a surge or other mass ejection.Topological configurations of coronal magnetic fields and current sheetsBungey, Timothy N.http://hdl.handle.net/10023/140212018-06-13T23:18:40Z1996-01-01T00:00:00ZThe question of topology in the coronal magnetic field is addressed in this thesis. Magnetic reconnection, which plays a major role in many of the fascinating phenomena seen in the solar atmosphere, is likely to occur at the boundaries between different topological regions of the magnetic field. By modelling the coronal field using discrete sources of flux, to represent the concentrations seen at the photospheric surface, we study the varying topological structures present in the field. We generate a criterion for determining the presence of null points above the photospheric surface and establish that any separatrix surfaces present in the field are due to the presence of either null points, or regions where the field tangentially grazes the surface. We follow the evolution of these separatrix surfaces and, in particular, determine the existence of a well-defined separator field line in the absence of coronal null points. Finally, we look locally at the configuration of the magnetic field in the region surrounding a straight current sheet. We derive an analytical expression to describe the topology of both potential and constant-current force-free fields in the neighbourhood of a sheet, and in so doing generalise the previously known expressions.
1996-01-01T00:00:00ZBungey, Timothy N.The question of topology in the coronal magnetic field is addressed in this thesis. Magnetic reconnection, which plays a major role in many of the fascinating phenomena seen in the solar atmosphere, is likely to occur at the boundaries between different topological regions of the magnetic field. By modelling the coronal field using discrete sources of flux, to represent the concentrations seen at the photospheric surface, we study the varying topological structures present in the field. We generate a criterion for determining the presence of null points above the photospheric surface and establish that any separatrix surfaces present in the field are due to the presence of either null points, or regions where the field tangentially grazes the surface. We follow the evolution of these separatrix surfaces and, in particular, determine the existence of a well-defined separator field line in the absence of coronal null points. Finally, we look locally at the configuration of the magnetic field in the region surrounding a straight current sheet. We derive an analytical expression to describe the topology of both potential and constant-current force-free fields in the neighbourhood of a sheet, and in so doing generalise the previously known expressions.Parametric instabilities in inhomogenous plasmasBegg, Iain M.http://hdl.handle.net/10023/140162018-06-13T23:19:31Z1976-01-01T00:00:00ZThis thesis will deal with certain problems of parametric instabilities in the inhomogeneous plasma. A large amplitude, 'pump' wave can deposit some of its energy into the plasma through resonance with two lower frequency waves (which may be damped). This type of process is a parametric decay of the pump wave and has applications in many fields. We consider, predominantly, that of laser fusion, in which the pump wave is electromagnetic and incident on the plasma. The objective is to deposit as much energy as possible within the plasma. Instabilities reducing this energy input are therefore of importance and it is, mostly, to these that this thesis will turn. They are mostly scattering processes in which one of the decay modes is electromagnetic. We examine the stimulated Brillouin backscattering process (the other decay mode being an ion accoustic wave) from a reference frame in which the plasma is streaming outwards. It is found that, if this velocity is near the sound velocity, the ion acoustic wave has a frequency Doppler-shifted to zero, the electromagnetic waves then having equal frequencies. In such a situation, any reflection of the pump wave at the critical surface will enhance the initial level of the backscattered wave. We find that, allowing for this, there is considerable enhancement of backscatter from the plasma, with consequent energy loss to the pump. Since the effect is noticeably unaffected by 'off- resonance' situations, it is felt that this process could mount a barrier to possible applications. We next consider the stimulated Compton scattering process, where the pump is scattered off the 'bare' or thermal electrons in the plasma. It is found that this rather weak instability occurs predominantly only when electron plasma waves are heavily dampled. Substantial reflection only occurs for high pump powers. Whilst there is little loss to the pump energy, there is substantial perturbation to the background distribution function. However, at the high powers involved filamentation and modulation of the pump can occur with a resulting enhancement of the scattering. Finally, we consider the effect on the decay instability (photon → plasmon + phonon) of the presence of substantial filamentation of the critical surface. It is found that the growth rate is substantially reduced.
1976-01-01T00:00:00ZBegg, Iain M.This thesis will deal with certain problems of parametric instabilities in the inhomogeneous plasma. A large amplitude, 'pump' wave can deposit some of its energy into the plasma through resonance with two lower frequency waves (which may be damped). This type of process is a parametric decay of the pump wave and has applications in many fields. We consider, predominantly, that of laser fusion, in which the pump wave is electromagnetic and incident on the plasma. The objective is to deposit as much energy as possible within the plasma. Instabilities reducing this energy input are therefore of importance and it is, mostly, to these that this thesis will turn. They are mostly scattering processes in which one of the decay modes is electromagnetic. We examine the stimulated Brillouin backscattering process (the other decay mode being an ion accoustic wave) from a reference frame in which the plasma is streaming outwards. It is found that, if this velocity is near the sound velocity, the ion acoustic wave has a frequency Doppler-shifted to zero, the electromagnetic waves then having equal frequencies. In such a situation, any reflection of the pump wave at the critical surface will enhance the initial level of the backscattered wave. We find that, allowing for this, there is considerable enhancement of backscatter from the plasma, with consequent energy loss to the pump. Since the effect is noticeably unaffected by 'off- resonance' situations, it is felt that this process could mount a barrier to possible applications. We next consider the stimulated Compton scattering process, where the pump is scattered off the 'bare' or thermal electrons in the plasma. It is found that this rather weak instability occurs predominantly only when electron plasma waves are heavily dampled. Substantial reflection only occurs for high pump powers. Whilst there is little loss to the pump energy, there is substantial perturbation to the background distribution function. However, at the high powers involved filamentation and modulation of the pump can occur with a resulting enhancement of the scattering. Finally, we consider the effect on the decay instability (photon → plasmon + phonon) of the presence of substantial filamentation of the critical surface. It is found that the growth rate is substantially reduced.Magnetic annihilation and reconnectionAnderson, Craighttp://hdl.handle.net/10023/140142018-06-13T23:18:39Z1994-01-01T00:00:00ZThis thesis presents several analytical models of magnetic annihilation and reconnection and studies their properties. The models investigated are 1. Steady-state magnetic annihilation. The assumption of straight field lines reduces the resistive, viscous MHD equations to two ordinary differential equations, one for the flow and one for the magnetic field. These equations can be solved exactly (for the case of a simple stagnation-point flow) and asymptotically (for a more general stagnation-point flow). In both cases the reconnection rates can be fast due to advection effects which create large magnetic gradients. 2. Time-dependent magnetic annihilation. The assumption of straight field lines whose strength can vary with time reduces the MHD equations to two partial differential equations, one for the flow and one for the magnetic field. The time-modulated simple stagnation-point flow is shown to be an exact solution and the equation for the magnetic field is then solved on infinite and finite intervals. For the infinite interval the reconnection rates are shown to be dependent on the nature of the advected initial field. Also examined are self-similar solutions and the effect of variation of diffusivity with time. 3. Annihilation in a compressible, inviscid plasma. Here, the assumption of straight field lines and an inviscid, compressible flow reduce the MHD equations to a pair of non-linear coupled partial differential equations. Further assuming that the density only varies in one direction and the flow is of a stagnation-point type allow these equations to be solved approximately analytically and exactly numerically. It is shown that the magnetic field and reconnection rates are the same in both the compressible and incompressible cases and that the density of the plasma is greatest within the current sheet. 4. Steady-state magnetic reconnection. For an incompressible flow the MHD equations can be reduced to two coupled non-linear partial differential equations. These two equations are studied by seeking asymptotic solutions around the annihilation solution and then looking for series solutions to the first-order equations. It is found that the magnetic field always has a magnetic cusp and never possesses an x-type neutral point. 5. Reconnection in a viscous plasma. Assuming that the viscous forces dominate, the induction equation and equation of motion decouple and become linear. The magnetic field is obtained for the case of a simple stagnation-point flow. It is shown that if the inflow magnetic field is taken to be straight then the magnetic field within the region tends towards the annihilation solution as the magnetic Reynolds number increases. 6. Magnetic flipping. A previous ideal model of magnetic flipping is refined so that it becomes an exact solution of the MHD equations. In the refined model the streamlines are straight rather than curved. Assuming straight streamlines, the MHD equations reduce to two linear ordinary differential equations, one for the flow and one for the magnetic field. These are then solved exactly analytically to find a flow containing a viscous boundary layer and a magnetic field that contains an x-type neutral point. The angle between the separatrices of the field is determined by the Reynolds and magnetic Reynolds numbers. It is shown that most of the ohmic heating occurs within the viscous boundary layer.
1994-01-01T00:00:00ZAnderson, CraigThis thesis presents several analytical models of magnetic annihilation and reconnection and studies their properties. The models investigated are 1. Steady-state magnetic annihilation. The assumption of straight field lines reduces the resistive, viscous MHD equations to two ordinary differential equations, one for the flow and one for the magnetic field. These equations can be solved exactly (for the case of a simple stagnation-point flow) and asymptotically (for a more general stagnation-point flow). In both cases the reconnection rates can be fast due to advection effects which create large magnetic gradients. 2. Time-dependent magnetic annihilation. The assumption of straight field lines whose strength can vary with time reduces the MHD equations to two partial differential equations, one for the flow and one for the magnetic field. The time-modulated simple stagnation-point flow is shown to be an exact solution and the equation for the magnetic field is then solved on infinite and finite intervals. For the infinite interval the reconnection rates are shown to be dependent on the nature of the advected initial field. Also examined are self-similar solutions and the effect of variation of diffusivity with time. 3. Annihilation in a compressible, inviscid plasma. Here, the assumption of straight field lines and an inviscid, compressible flow reduce the MHD equations to a pair of non-linear coupled partial differential equations. Further assuming that the density only varies in one direction and the flow is of a stagnation-point type allow these equations to be solved approximately analytically and exactly numerically. It is shown that the magnetic field and reconnection rates are the same in both the compressible and incompressible cases and that the density of the plasma is greatest within the current sheet. 4. Steady-state magnetic reconnection. For an incompressible flow the MHD equations can be reduced to two coupled non-linear partial differential equations. These two equations are studied by seeking asymptotic solutions around the annihilation solution and then looking for series solutions to the first-order equations. It is found that the magnetic field always has a magnetic cusp and never possesses an x-type neutral point. 5. Reconnection in a viscous plasma. Assuming that the viscous forces dominate, the induction equation and equation of motion decouple and become linear. The magnetic field is obtained for the case of a simple stagnation-point flow. It is shown that if the inflow magnetic field is taken to be straight then the magnetic field within the region tends towards the annihilation solution as the magnetic Reynolds number increases. 6. Magnetic flipping. A previous ideal model of magnetic flipping is refined so that it becomes an exact solution of the MHD equations. In the refined model the streamlines are straight rather than curved. Assuming straight streamlines, the MHD equations reduce to two linear ordinary differential equations, one for the flow and one for the magnetic field. These are then solved exactly analytically to find a flow containing a viscous boundary layer and a magnetic field that contains an x-type neutral point. The angle between the separatrices of the field is determined by the Reynolds and magnetic Reynolds numbers. It is shown that most of the ohmic heating occurs within the viscous boundary layer.Plasma drift waves and instabilitiesAllan, Williamhttp://hdl.handle.net/10023/140112018-06-13T23:18:44Z1974-01-01T00:00:00ZThe work of this thesis is concerned with the investigation of the propagation of waves in a magnetized plasma containing various parameter gradients, and with the stability of ion acoustic waves in a weakly collisional plasma with a strong temperature gradient. The thesis is divided into three sections. In the first section the intention is to derive in a compact and unambiguous tensor form the dispersion relation describing the propagation of waves in a magnetized plasma containing three-dimensional density and temperature gradients, an E̲⏜ B̲ drift, and differing temperatures parallel and perpendicular to the magnetic field. This is achieved by introducing and extending the polarized co-ordinate system first proposed by Buneman in 1961, and then carrying through the standard procedure of integration along unperturbed trajectories. The "local" approximation of Krall and Rosenbluth is used in order that an analytic result may be derived. The dispersion relation obtained includes certain moment tensors whose elements may be evaluated independently of the gradients involved in the problem. These elements may then be listed and the list referred to in order to obtain the elements required for a specific problem. The second section is concerned with the use of the theory and results of J.P. Dougherty to show that in the high-frequency regime the introduction of a small amount of collisions into a plasma is sufficient to disrupt the gyro-resonances which allow the existence of Bernstein waves at multiples of the gyro-frequencies perpendicular and near- perpendicular to the magnetic field. It is shown that a collision frequency v such that (k 𝜌) ⁻² ≲ v/Ω < (k 𝜌) ⁻¹ where k 𝜌 >> 1 is sufficient to do this; k is the wave-number, 𝜌 the Larmor radius, and the gyro-frequency. It is also shown that in this case the ion-acoustic dispersion relation is valid even for propagation perpendicular to the magnetic field. In the final section the result of the second section is used to derive a dispersion relation for high-frequency wave propagation in a weakly-collisional plasma containing an electron temperature gradient. The dispersion relation is solved numerically for various electron-ion temperature ratios and electron temperature gradient drift velocities. Earlier predictions, based on analytic calculations for small temperature ratios and drift velocities, are confirmed and some new results presented. In particular, it is shown that a temperature gradient is a more effective destabilizing agent then a simple drift between ions and electrons. Dispersion plots are given, along with analytic and physical explanations of their form; finally neutral stability curves are presented. The thesis concludes with a summary of the results obtained.
1974-01-01T00:00:00ZAllan, WilliamThe work of this thesis is concerned with the investigation of the propagation of waves in a magnetized plasma containing various parameter gradients, and with the stability of ion acoustic waves in a weakly collisional plasma with a strong temperature gradient. The thesis is divided into three sections. In the first section the intention is to derive in a compact and unambiguous tensor form the dispersion relation describing the propagation of waves in a magnetized plasma containing three-dimensional density and temperature gradients, an E̲⏜ B̲ drift, and differing temperatures parallel and perpendicular to the magnetic field. This is achieved by introducing and extending the polarized co-ordinate system first proposed by Buneman in 1961, and then carrying through the standard procedure of integration along unperturbed trajectories. The "local" approximation of Krall and Rosenbluth is used in order that an analytic result may be derived. The dispersion relation obtained includes certain moment tensors whose elements may be evaluated independently of the gradients involved in the problem. These elements may then be listed and the list referred to in order to obtain the elements required for a specific problem. The second section is concerned with the use of the theory and results of J.P. Dougherty to show that in the high-frequency regime the introduction of a small amount of collisions into a plasma is sufficient to disrupt the gyro-resonances which allow the existence of Bernstein waves at multiples of the gyro-frequencies perpendicular and near- perpendicular to the magnetic field. It is shown that a collision frequency v such that (k 𝜌) ⁻² ≲ v/Ω < (k 𝜌) ⁻¹ where k 𝜌 >> 1 is sufficient to do this; k is the wave-number, 𝜌 the Larmor radius, and the gyro-frequency. It is also shown that in this case the ion-acoustic dispersion relation is valid even for propagation perpendicular to the magnetic field. In the final section the result of the second section is used to derive a dispersion relation for high-frequency wave propagation in a weakly-collisional plasma containing an electron temperature gradient. The dispersion relation is solved numerically for various electron-ion temperature ratios and electron temperature gradient drift velocities. Earlier predictions, based on analytic calculations for small temperature ratios and drift velocities, are confirmed and some new results presented. In particular, it is shown that a temperature gradient is a more effective destabilizing agent then a simple drift between ions and electrons. Dispersion plots are given, along with analytic and physical explanations of their form; finally neutral stability curves are presented. The thesis concludes with a summary of the results obtained.Aspects of current sheet theoryTur, T. J.http://hdl.handle.net/10023/140002018-06-13T23:19:42Z1977-01-01T00:00:00ZCurrent sheets are widely believed to play an important role in astrophysics when regions of magnetic flux are in motion. Several models based on the formation of current sheets have been proposed to explain such phenomena as geomagnetic storms, solar flares and prominences. In this thesis three aspects of current sheet theory are studied with particular reference to the solar flare problem. Firstly the development of two-dimensional current sheets is investigated for several simple configurations. These include converging line current sources, converging and diverging line dipole sources and a dipole of increasing moment situated in either a uniform magnetic field or a constant dipole field. These last two may be thought of as modelling the emergence of bipolar flux from beneath the photosphere, a phenomena frequently observed prior to solar flares. The length, position and shape of the current sheet is determined from the requirement that the magnetic field be frozen-into the plasma. The sheet is found to be curved, except in the symmetrical case of converging line sources. In addition, the extra energy due to the presence of the current sheet is determined. Comparison with estimates of the energy dissipated during a flare indicate that the formation of current sheets may store an adequate amount of preflare magnetic energy, provided no reconnection occurs during the formation process. A three-dimensional axi-symmetric model for current sheet formation is then considered. Two equal and co-directional dipoles approach along the axis of symmetry to form an annular current sheet between them. The equations determining the magnetic field for this configuration are reduced to a single integral equation for the current density in the sheet as a function of radial distance from the axis. A numerical method is used to solve this integral equation. The inner and outer radii of the sheet are then determined from the conditions of flux conservation as for the two-dimensional case. Finally the energetics of a current sheet that forms between newly emerging flux and an ambient field are considered. As more and more flux emerges, so the sheet rises in the solar atmosphere. The various contributions to the thermal energy balance in the sheet are approximated and the resulting equation is solved for the internal temperature of the sheet. It is found that, for certain choices of the ambient magnetic field strength and velocity, the internal temperature increases until, when the sheet reaches some critical height, no neighbouring stable state exists. The temperature then increases rapidly seeking a hotter branch of the solution curve. During this dynamic heating the threshold temperature for the onset of microinstabilities may be attained. It is suggested that this may be a suitable trigger mechanism for the recently proposed "emerging flux" model of a solar flare.
1977-01-01T00:00:00ZTur, T. J.Current sheets are widely believed to play an important role in astrophysics when regions of magnetic flux are in motion. Several models based on the formation of current sheets have been proposed to explain such phenomena as geomagnetic storms, solar flares and prominences. In this thesis three aspects of current sheet theory are studied with particular reference to the solar flare problem. Firstly the development of two-dimensional current sheets is investigated for several simple configurations. These include converging line current sources, converging and diverging line dipole sources and a dipole of increasing moment situated in either a uniform magnetic field or a constant dipole field. These last two may be thought of as modelling the emergence of bipolar flux from beneath the photosphere, a phenomena frequently observed prior to solar flares. The length, position and shape of the current sheet is determined from the requirement that the magnetic field be frozen-into the plasma. The sheet is found to be curved, except in the symmetrical case of converging line sources. In addition, the extra energy due to the presence of the current sheet is determined. Comparison with estimates of the energy dissipated during a flare indicate that the formation of current sheets may store an adequate amount of preflare magnetic energy, provided no reconnection occurs during the formation process. A three-dimensional axi-symmetric model for current sheet formation is then considered. Two equal and co-directional dipoles approach along the axis of symmetry to form an annular current sheet between them. The equations determining the magnetic field for this configuration are reduced to a single integral equation for the current density in the sheet as a function of radial distance from the axis. A numerical method is used to solve this integral equation. The inner and outer radii of the sheet are then determined from the conditions of flux conservation as for the two-dimensional case. Finally the energetics of a current sheet that forms between newly emerging flux and an ambient field are considered. As more and more flux emerges, so the sheet rises in the solar atmosphere. The various contributions to the thermal energy balance in the sheet are approximated and the resulting equation is solved for the internal temperature of the sheet. It is found that, for certain choices of the ambient magnetic field strength and velocity, the internal temperature increases until, when the sheet reaches some critical height, no neighbouring stable state exists. The temperature then increases rapidly seeking a hotter branch of the solution curve. During this dynamic heating the threshold temperature for the onset of microinstabilities may be attained. It is suggested that this may be a suitable trigger mechanism for the recently proposed "emerging flux" model of a solar flare.Thermal and resistive instabilities in the solar atmosphereSmith, E. A.http://hdl.handle.net/10023/139982018-06-13T23:19:37Z1977-01-01T00:00:00ZThe magnetic field greatly influences the plasma in the solar atmosphere and in this thesis we consider the effect of the field on the stability of the plasma. The many observations that have been made suggest that two types of field structure play a major role. Firstly a current sheet - this has field lines which change direction in a thin, current forming region, but are fairly uniform outside. We consider the case where the field strength is zero along the neutral line so that a gas pressure gradient is required across the sheet to balance the magnetic pressure gradient. Secondly a force-free field - here the magnetic force is zero, which requires the magnetic pressure to be much larger than the gas pressure. In the neutral current sheet we examine the thermal instability and the tearing-mode instability. While in the force-free magnetic arch system we look for a thermal instability which can occur when the foot points of the arch are sheared. When we investigated the thermal stability of the current sheet we found that as its length increases it passes through a series of stable equilibria until a value, L[sub]max, is reached when the sheet cools down to a max new stable equilibrium. For coronal conditions, values for L[sub]max and max cooling time are in fair agreement with the observed values for quiescent prominences. We calculate the growth rate of the tearing-mode instability in a neutral current sheet with no energy sources or sinks and find that the maximum growth rate can be significantly larger in the current sheet than in the sheared field of constant magnitude considered by others. Also the growth rate decreases when the ratio of gas to magnetic pressure is reduced. We find that the growth rate is significantly inhibited if the current sheet has a transverse magnetic field which is large enough. Lastly we examine the thermal balance in a sheared, force-free magnetic field and show that thermal instability can occur if the field is sheared enough. We assume thermal equilibrium between radiative loss and thermal conduction and we take gravity balanced by a pressure gradient. If, for example, the density at the base of the field is ten times larger than the normal coronal value, as it may be in coronal condensations, then there is instability if the shear angle is greater than 63 °. The presence of a large enough mechanical heating is found to prevent the instability occurring.
1977-01-01T00:00:00ZSmith, E. A.The magnetic field greatly influences the plasma in the solar atmosphere and in this thesis we consider the effect of the field on the stability of the plasma. The many observations that have been made suggest that two types of field structure play a major role. Firstly a current sheet - this has field lines which change direction in a thin, current forming region, but are fairly uniform outside. We consider the case where the field strength is zero along the neutral line so that a gas pressure gradient is required across the sheet to balance the magnetic pressure gradient. Secondly a force-free field - here the magnetic force is zero, which requires the magnetic pressure to be much larger than the gas pressure. In the neutral current sheet we examine the thermal instability and the tearing-mode instability. While in the force-free magnetic arch system we look for a thermal instability which can occur when the foot points of the arch are sheared. When we investigated the thermal stability of the current sheet we found that as its length increases it passes through a series of stable equilibria until a value, L[sub]max, is reached when the sheet cools down to a max new stable equilibrium. For coronal conditions, values for L[sub]max and max cooling time are in fair agreement with the observed values for quiescent prominences. We calculate the growth rate of the tearing-mode instability in a neutral current sheet with no energy sources or sinks and find that the maximum growth rate can be significantly larger in the current sheet than in the sheared field of constant magnitude considered by others. Also the growth rate decreases when the ratio of gas to magnetic pressure is reduced. We find that the growth rate is significantly inhibited if the current sheet has a transverse magnetic field which is large enough. Lastly we examine the thermal balance in a sheared, force-free magnetic field and show that thermal instability can occur if the field is sheared enough. We assume thermal equilibrium between radiative loss and thermal conduction and we take gravity balanced by a pressure gradient. If, for example, the density at the base of the field is ten times larger than the normal coronal value, as it may be in coronal condensations, then there is instability if the shear angle is greater than 63 °. The presence of a large enough mechanical heating is found to prevent the instability occurring.Numerical studies of the Fokker-Planck equationMcGowan, Alastair Davidhttp://hdl.handle.net/10023/139952018-06-13T23:19:58Z1992-01-01T00:00:00ZJorna and Wood recently developed a program that numerically solved the Fokker-Planck equation in spherical geometry. In this thesis, we describe how the original program has been redeveloped to produce a program that is an order of magnitude quicker and that has superior energy and density conservation. The revised version of the program has been used to extend the work of Jorna and Wood on thermal conduction in laser produced plasmas. It has been shown that the effect of curvature on heat flow can be described from a purely geometrical argument and that for aspect ratios similar to those found in targets, the heat flow is reduced by approximately 10%. Also, it has been shown, in contradiction with Jorna and Wood, that the inclusion of the anisotropic portion of the Rosenbluth potentials does not have a significant effect on the heat flow. Even for highly anisotropic plasmas, the inclusion of the anisotropic portion only increases the heat flow by 10%. In addition, the revised version of the program has been used to study the energy relaxation of model distributions It has been shown that the relaxation time of most non - thermal distributions depends on the detailed structure of the distribution and that the normal Spitzer collision time can under-estimate or over-estimate the time required for energy relaxation.
1992-01-01T00:00:00ZMcGowan, Alastair DavidJorna and Wood recently developed a program that numerically solved the Fokker-Planck equation in spherical geometry. In this thesis, we describe how the original program has been redeveloped to produce a program that is an order of magnitude quicker and that has superior energy and density conservation. The revised version of the program has been used to extend the work of Jorna and Wood on thermal conduction in laser produced plasmas. It has been shown that the effect of curvature on heat flow can be described from a purely geometrical argument and that for aspect ratios similar to those found in targets, the heat flow is reduced by approximately 10%. Also, it has been shown, in contradiction with Jorna and Wood, that the inclusion of the anisotropic portion of the Rosenbluth potentials does not have a significant effect on the heat flow. Even for highly anisotropic plasmas, the inclusion of the anisotropic portion only increases the heat flow by 10%. In addition, the revised version of the program has been used to study the energy relaxation of model distributions It has been shown that the relaxation time of most non - thermal distributions depends on the detailed structure of the distribution and that the normal Spitzer collision time can under-estimate or over-estimate the time required for energy relaxation.Nonlinear plasma waves and their applicationsAmin, Mohamed Ruhulhttp://hdl.handle.net/10023/139932018-06-13T23:19:50Z1999-01-01T00:00:00ZThe possibility of beat wave current drive in tokamaks is considered in this thesis in steady state 2D geometry. The problem is considered by including in the analysis the 2D toroidal inhomogeneity effect and the effect of finite spatial width of the pump microwave pulses on the beat wave excitation. Both a Langmuir beat wave as well as an obliquely propagating upper-hybrid cyclotron beat wave are considered in this study. The three wave coupled system of equations in a magnetized plasma has been derived and solved numerically for this purpose. It has been found that Langmuir type beat wave excited by two almost antiparallel pump microwaves is more efficient for action transfer than a cyclotron beat wave. It has also been found that for the same input parameters, right hand polarized pumps are more efficient than left hand polarized pump microwaves for depositing power in the beat wave. The second part of the thesis considers the relativistic excitation mechanism of a large amplitude plasma wake field by a single ultra-short laser pulse. This type of large amplitude wake field has been proposed for particle acceleration to very high energies for future generation of accelerators. The problem has been modeled self consistently in ID geometry and the relevant coupled system of equations have been solved numerically. It has been found that the shape of the laser pulse profile and the ratio of the ambient plasma frequency to the incident laser frequency play an important role for the excitation of the wake-field and the stability of the laser pulse profile.
1999-01-01T00:00:00ZAmin, Mohamed RuhulThe possibility of beat wave current drive in tokamaks is considered in this thesis in steady state 2D geometry. The problem is considered by including in the analysis the 2D toroidal inhomogeneity effect and the effect of finite spatial width of the pump microwave pulses on the beat wave excitation. Both a Langmuir beat wave as well as an obliquely propagating upper-hybrid cyclotron beat wave are considered in this study. The three wave coupled system of equations in a magnetized plasma has been derived and solved numerically for this purpose. It has been found that Langmuir type beat wave excited by two almost antiparallel pump microwaves is more efficient for action transfer than a cyclotron beat wave. It has also been found that for the same input parameters, right hand polarized pumps are more efficient than left hand polarized pump microwaves for depositing power in the beat wave. The second part of the thesis considers the relativistic excitation mechanism of a large amplitude plasma wake field by a single ultra-short laser pulse. This type of large amplitude wake field has been proposed for particle acceleration to very high energies for future generation of accelerators. The problem has been modeled self consistently in ID geometry and the relevant coupled system of equations have been solved numerically. It has been found that the shape of the laser pulse profile and the ratio of the ambient plasma frequency to the incident laser frequency play an important role for the excitation of the wake-field and the stability of the laser pulse profile.The effects of the Kelvin-Helmholtz instability of the magnetosphereMills, Katharine J.http://hdl.handle.net/10023/139902018-06-13T23:18:53Z1999-01-01T00:00:00ZIn this thesis, the behaviour of Kelvin-Helmholtz unstable modes on the magnetospheric flanks and in the magnetotail are investigated. A model of a straight bounded magnetosphere connected to a semi-infinite field-free magnetosheath which is flowing with a uniform speed is used. First the magnetosphere is taken to be uniform with the magnetic field perpendicular to the flow in the magnetosheath and it is shown that the increase in Pc5 wave power observed for high solar wind flow speeds correlates well with the onset of instability of the fast body modes. A condition for the exact onset of instability of these modes is derived and the behaviour of fast surface and slow body and surface modes is also investigated. Using a non-uniform magnetosphere, it is shown that these unstable body modes may couple to field line resonances. The fastest growing modes are found to have a common azimuthal phase speed which depends only on the local conditions at the magnetopause and may be predicted using the theory of over-reflection. A finite width boundary layer is then added to the uniform magnetosphere model to investigate the space-time evolution of wave-packets on the magnetopause. Fast surface mode wave-packets are found to grow rapidly as they convect around the flanks so that non-linear effects will be important. Fast cavity mode wave-packets will remain relatively small on the flanks, explaining the robustness of the body of the magnetosphere here. Slow modes are found to grow very little in this region. Finally, a uniform magnetosphere with the magnetic field parallel to the flow in the magnetosheath is considered. Here, the fast modes are unlikely to be Kelvin-Helmholtz unstable for realistic flow speeds, and the magnetopause boundary may be reasonably assumed to be perfectly reflecting. The low value of the plasma pressure is this region suggests that slow modes will be unimportant.
1999-01-01T00:00:00ZMills, Katharine J.In this thesis, the behaviour of Kelvin-Helmholtz unstable modes on the magnetospheric flanks and in the magnetotail are investigated. A model of a straight bounded magnetosphere connected to a semi-infinite field-free magnetosheath which is flowing with a uniform speed is used. First the magnetosphere is taken to be uniform with the magnetic field perpendicular to the flow in the magnetosheath and it is shown that the increase in Pc5 wave power observed for high solar wind flow speeds correlates well with the onset of instability of the fast body modes. A condition for the exact onset of instability of these modes is derived and the behaviour of fast surface and slow body and surface modes is also investigated. Using a non-uniform magnetosphere, it is shown that these unstable body modes may couple to field line resonances. The fastest growing modes are found to have a common azimuthal phase speed which depends only on the local conditions at the magnetopause and may be predicted using the theory of over-reflection. A finite width boundary layer is then added to the uniform magnetosphere model to investigate the space-time evolution of wave-packets on the magnetopause. Fast surface mode wave-packets are found to grow rapidly as they convect around the flanks so that non-linear effects will be important. Fast cavity mode wave-packets will remain relatively small on the flanks, explaining the robustness of the body of the magnetosphere here. Slow modes are found to grow very little in this region. Finally, a uniform magnetosphere with the magnetic field parallel to the flow in the magnetosheath is considered. Here, the fast modes are unlikely to be Kelvin-Helmholtz unstable for realistic flow speeds, and the magnetopause boundary may be reasonably assumed to be perfectly reflecting. The low value of the plasma pressure is this region suggests that slow modes will be unimportant.Study of solitary waves in space plasmasMamun, A. A.http://hdl.handle.net/10023/139872018-06-13T23:18:32Z1997-01-01T00:00:00ZTheoretical investigations have been made of arbitrary amplitude electrostatic solitary waves in non-thermal plasmas, which may be of relevance to ionospheric and magnetospheric plasmas, and dusty plasmas, which are most common in earth's and cometary environments as well as in planetary rings, for understanding the nonlinear features of localised electrostatic disturbances in such space plasma systems. This thesis starts with an introductory chapter where a very brief historical review of solitary waves in plasmas has been presented. The study of arbitrary amplitude electrostatic solitary waves in non-thermal plasma has considered a plasma system consisting of warm adiabatic ions and non- thermal electrons. It is found that a non-thermal electron distribution may change the nature of ion-acoustic solitary waves. If the ions are assumed to respond as a fluid to perturbations in the potential, with no significant trapping in a potential well, then a thermal plasma only supports solitary waves with a density peak. However, with a suitable distribution of non-thermal electrons, solitary waves with both density peaks and density depressions may exist. This study has also included a numerical analysis showing how these electrostatic solitary structures evolve with time. The investigation has then been extended to magnetised plasmas to study the effects of magnetic field on obliquely propagating electrostatic solitary structures. This attempt first employed the reductive perturbation method and investigated the nonlinear properties of small but finite amplitude obliquely propagating solitary waves in this magnetised non-thermal plasma model. This study is then generalised to arbitrary amplitude solitary waves by the numerical solution of the full nonlinear system of equations. This numerical method has also been utilised to present a similar study in another popular plasma model, namely the two-electron-temperature plasma model. The study of arbitrary amplitude solitary waves in a dusty plasma has considered another plasma system which consists of an inertial dust fluid and ions with Maxwellian distribution and has investigated the nonlinear properties of dust- acoustic solitary waves. A numerical study has also been made to show how these dust-acoustic solitary waves evolve with time. The effects of non-thermal and vortex-like ion distributions are then incorporated into this study. The study of arbitrary amplitude electrostatic solitary waves in this thesis has finally been concluded with some brief discussion of our results and proposal for further studies, which are expected to generalise and develop our present work to some other extents, in this versatile area of research.
1997-01-01T00:00:00ZMamun, A. A.Theoretical investigations have been made of arbitrary amplitude electrostatic solitary waves in non-thermal plasmas, which may be of relevance to ionospheric and magnetospheric plasmas, and dusty plasmas, which are most common in earth's and cometary environments as well as in planetary rings, for understanding the nonlinear features of localised electrostatic disturbances in such space plasma systems. This thesis starts with an introductory chapter where a very brief historical review of solitary waves in plasmas has been presented. The study of arbitrary amplitude electrostatic solitary waves in non-thermal plasma has considered a plasma system consisting of warm adiabatic ions and non- thermal electrons. It is found that a non-thermal electron distribution may change the nature of ion-acoustic solitary waves. If the ions are assumed to respond as a fluid to perturbations in the potential, with no significant trapping in a potential well, then a thermal plasma only supports solitary waves with a density peak. However, with a suitable distribution of non-thermal electrons, solitary waves with both density peaks and density depressions may exist. This study has also included a numerical analysis showing how these electrostatic solitary structures evolve with time. The investigation has then been extended to magnetised plasmas to study the effects of magnetic field on obliquely propagating electrostatic solitary structures. This attempt first employed the reductive perturbation method and investigated the nonlinear properties of small but finite amplitude obliquely propagating solitary waves in this magnetised non-thermal plasma model. This study is then generalised to arbitrary amplitude solitary waves by the numerical solution of the full nonlinear system of equations. This numerical method has also been utilised to present a similar study in another popular plasma model, namely the two-electron-temperature plasma model. The study of arbitrary amplitude solitary waves in a dusty plasma has considered another plasma system which consists of an inertial dust fluid and ions with Maxwellian distribution and has investigated the nonlinear properties of dust- acoustic solitary waves. A numerical study has also been made to show how these dust-acoustic solitary waves evolve with time. The effects of non-thermal and vortex-like ion distributions are then incorporated into this study. The study of arbitrary amplitude electrostatic solitary waves in this thesis has finally been concluded with some brief discussion of our results and proposal for further studies, which are expected to generalise and develop our present work to some other extents, in this versatile area of research.Steady models for magnetic reconnectionJardine, Moirahttp://hdl.handle.net/10023/139852018-06-13T23:18:40Z1989-01-01T00:00:00ZMagnetic reconnection is a fundamental physical process by which stored magnetic energy may be released. It is already known that different reconnection regimes result from changes in the nature of the plasma inflow towards the reconnection site. In this thesis, we examine both how the outflow region responds to changes both in the inflow and outflow boundary conditions and also how introducing compressibility affects the results. We find that if the inflow is converging, the outflow velocity is least, the width of the outflow region is greatest and the ratio of outflowing thermal to kinetic energy is greatest. Also, there is one free outflow parameter which would naturally be specified by the velocity of plasma leaving the reconnection site. We suggest that reverse currents seen in numerical simulations may result from the specification of an extra boundary condition. In addition, we find that the main effects of including compressibility are: to enhance convergence or divergence of the inflow; to increase the maximum reconnection rate where the inflow is converging; to increase the flow speed near the reconnection site where the inflow is diverging; to give faster, narrower outflow jets; to increase variations between regimes in the energy conversion and to increase the ratio of thermal to kinetic energy in the outflow jet.
1989-01-01T00:00:00ZJardine, MoiraMagnetic reconnection is a fundamental physical process by which stored magnetic energy may be released. It is already known that different reconnection regimes result from changes in the nature of the plasma inflow towards the reconnection site. In this thesis, we examine both how the outflow region responds to changes both in the inflow and outflow boundary conditions and also how introducing compressibility affects the results. We find that if the inflow is converging, the outflow velocity is least, the width of the outflow region is greatest and the ratio of outflowing thermal to kinetic energy is greatest. Also, there is one free outflow parameter which would naturally be specified by the velocity of plasma leaving the reconnection site. We suggest that reverse currents seen in numerical simulations may result from the specification of an extra boundary condition. In addition, we find that the main effects of including compressibility are: to enhance convergence or divergence of the inflow; to increase the maximum reconnection rate where the inflow is converging; to increase the flow speed near the reconnection site where the inflow is diverging; to give faster, narrower outflow jets; to increase variations between regimes in the energy conversion and to increase the ratio of thermal to kinetic energy in the outflow jet.Microinstabilities in high power electron cyclotron heating of plasmasMiller, Andrew Gilberthttp://hdl.handle.net/10023/139772018-06-12T23:19:06Z1991-01-01T00:00:00ZElectron cyclotron resonance heating has been successfully used in a number of experiments, firstly to raise the plasma temperature and secondly to drive currents noninductively. Recently the microwaves in tokamak experiment (MTX) has been proposed at the Lawrence Livermore Laboratory, which will involve pulsed heating at powers much higher than have previously been possible, using a Free Electron Laser (PEL). The physics of such an experiment differs greatly from the physics of experiments using less powerful but continuous operation gyrotron sources. An analytical model of the interaction between a wave and an electron is presented on the assumption that the wave amplitude experienced along the electron guiding centre changes slowly with time as it passes through the beam. This model is tested numerically by integrating the equations of motion governing the electron's motion as it interacts with the wave. Finally this model is used to predict the possible growth of instabilities in a plasma heated by a FEL. The growth rates of these waves may be large enough to act on the plasma in time scales much shorter than typical electron collision times.
1991-01-01T00:00:00ZMiller, Andrew GilbertElectron cyclotron resonance heating has been successfully used in a number of experiments, firstly to raise the plasma temperature and secondly to drive currents noninductively. Recently the microwaves in tokamak experiment (MTX) has been proposed at the Lawrence Livermore Laboratory, which will involve pulsed heating at powers much higher than have previously been possible, using a Free Electron Laser (PEL). The physics of such an experiment differs greatly from the physics of experiments using less powerful but continuous operation gyrotron sources. An analytical model of the interaction between a wave and an electron is presented on the assumption that the wave amplitude experienced along the electron guiding centre changes slowly with time as it passes through the beam. This model is tested numerically by integrating the equations of motion governing the electron's motion as it interacts with the wave. Finally this model is used to predict the possible growth of instabilities in a plasma heated by a FEL. The growth rates of these waves may be large enough to act on the plasma in time scales much shorter than typical electron collision times.A gyrokinetic analysis of electron plasma waves at resonance in magnetic field gradientsMcDonald, Darrenhttp://hdl.handle.net/10023/139752018-06-12T23:19:12Z1995-01-01T00:00:00ZTo produce nuclear fusion in a Tokamak reactor requires the heating of a plasma to a temperature of the order of 10 keV. Electron cyclotron resonant heating (ECRH), in which the plasma is heated by radio waves in resonance with the Larmor frequency of the plasma's electrons, is one scheme under consideration for achieving this. A description of such a heating scheme requires a theory to explain the propagation and absorption of high frequency waves in a plasma in the presence of a magnetic field gradient. A WKB analysis can describe some of the processes involved but a complete explanation requires the use of full wave equations. In this thesis we shall develop a technique for deriving such equations which will be shown to be simpler and more general than calculations performed by earlier workers. The technique relies on including the effect of the magnetic gradient across the Larmor orbit of the electrons in the resonance condition of the wave, the so called Gyrokinetic correction, which has been ignored in calculations by previous workers. Once derived, the equations are solved numerically and the results applied to a number of experiments currently being performed on Tokamak fusion. In addition, we shall also look at the energy loss processes of runaway electrons, which have been shown experimentally to be shorter than would be expected.
1995-01-01T00:00:00ZMcDonald, DarrenTo produce nuclear fusion in a Tokamak reactor requires the heating of a plasma to a temperature of the order of 10 keV. Electron cyclotron resonant heating (ECRH), in which the plasma is heated by radio waves in resonance with the Larmor frequency of the plasma's electrons, is one scheme under consideration for achieving this. A description of such a heating scheme requires a theory to explain the propagation and absorption of high frequency waves in a plasma in the presence of a magnetic field gradient. A WKB analysis can describe some of the processes involved but a complete explanation requires the use of full wave equations. In this thesis we shall develop a technique for deriving such equations which will be shown to be simpler and more general than calculations performed by earlier workers. The technique relies on including the effect of the magnetic gradient across the Larmor orbit of the electrons in the resonance condition of the wave, the so called Gyrokinetic correction, which has been ignored in calculations by previous workers. Once derived, the equations are solved numerically and the results applied to a number of experiments currently being performed on Tokamak fusion. In addition, we shall also look at the energy loss processes of runaway electrons, which have been shown experimentally to be shorter than would be expected.The theory of electron heating in collisonless plasma shock wavesBuckner, A. J. F.http://hdl.handle.net/10023/139732018-06-12T23:19:09Z1993-01-01T00:00:00ZEquations are derived to describe the evolution of an electron distribution function under the action of electromagnetic instabilities in a non-uniform plasma using an extension of the quasilinear theory of Kennel and Engelmann. Variations in both the electron density and temperature and the background magnetic field are taken into account. These equations are simplified in the limit of small electron beta so that an electrostatic approximation is justified. Methods are then presented which allow the solution of these equations (or, in principle, the more complex electromagnetic equations). In particular, a method of solving the kinetic dispersion relation for an arbitrary background (first-order) distribution function with the minimum of additional assumptions and approximations is described in detail. The electrostatic equations are solved for a number of different cases in order to study the action of the modified two stream instability on the electron distribution function. Throughout, realistic values of the ratios of electron to ion mass and electron plasma to cyclotron frequency ratio are used. The applications to collisionless plasma shock waves are discussed, and it is found that the modified two stream instability can produce the (relatively small) amounts of electron heating observed at quasi-perpendicular terrestrial bow shocks, and the flat-topped electron distribution functions seen to evolve. Extensions to the model which would greatly improve its applicability and accuracy, as well as the amount of computational effort required, are discussed.
1993-01-01T00:00:00ZBuckner, A. J. F.Equations are derived to describe the evolution of an electron distribution function under the action of electromagnetic instabilities in a non-uniform plasma using an extension of the quasilinear theory of Kennel and Engelmann. Variations in both the electron density and temperature and the background magnetic field are taken into account. These equations are simplified in the limit of small electron beta so that an electrostatic approximation is justified. Methods are then presented which allow the solution of these equations (or, in principle, the more complex electromagnetic equations). In particular, a method of solving the kinetic dispersion relation for an arbitrary background (first-order) distribution function with the minimum of additional assumptions and approximations is described in detail. The electrostatic equations are solved for a number of different cases in order to study the action of the modified two stream instability on the electron distribution function. Throughout, realistic values of the ratios of electron to ion mass and electron plasma to cyclotron frequency ratio are used. The applications to collisionless plasma shock waves are discussed, and it is found that the modified two stream instability can produce the (relatively small) amounts of electron heating observed at quasi-perpendicular terrestrial bow shocks, and the flat-topped electron distribution functions seen to evolve. Extensions to the model which would greatly improve its applicability and accuracy, as well as the amount of computational effort required, are discussed.Rotational flow in fluid dynamicsMurray, J. D. (James Dickson)http://hdl.handle.net/10023/139672018-06-12T23:18:46Z1955-01-01T00:00:00ZThe thesis is divided into four chapters. Chapter I gives a brief résumé of the state of rotational flow theory up to 1955. Chapter II contains a study of the constant shear flow past cylinders with various cross sections. Chapter III contains a method for obtaining the stream functions for cylinders in a variable shear flow when the latter approximates firstly to a linear vorticity distribution, and secondly to the rotational flow present in a boundary layer. Further, it illustrates the nature of the difficulties likely to be encountered in trying to obtain analytical solutions of problems where the rotation is of a more complicated nature. Finally, Chapter IV contains a relaxation solution to the two-dimensional isentropic compressible rotational flow of a gas through a channel containing a constriction, it also illustrates the complexity of the numerical work required in obtaining relaxation solutions of compressible flow problems with rotation.
1955-01-01T00:00:00ZMurray, J. D. (James Dickson)The thesis is divided into four chapters. Chapter I gives a brief résumé of the state of rotational flow theory up to 1955. Chapter II contains a study of the constant shear flow past cylinders with various cross sections. Chapter III contains a method for obtaining the stream functions for cylinders in a variable shear flow when the latter approximates firstly to a linear vorticity distribution, and secondly to the rotational flow present in a boundary layer. Further, it illustrates the nature of the difficulties likely to be encountered in trying to obtain analytical solutions of problems where the rotation is of a more complicated nature. Finally, Chapter IV contains a relaxation solution to the two-dimensional isentropic compressible rotational flow of a gas through a channel containing a constriction, it also illustrates the complexity of the numerical work required in obtaining relaxation solutions of compressible flow problems with rotation.Mode conversion of plasma wavesWoods, Anna Mariahttp://hdl.handle.net/10023/139652018-06-12T23:18:41Z1987-01-01T00:00:00ZLinear mode conversion processes are much studied in plasma physics because they determine the efficiency of any radio frequency heating scheme. Mode coupling model equations, extracted with varying degrees of rigour from the Maxwell-linearized kinetic equations, are usually fourth or higher order O.D.E's. These are solved by complicated methods to obtain transmission, conversion, reflection and absorption coefficients. Recently, Fuchs et al and Cairns and Lashmore-Davies (C.L-D.) have postulated second order O.D.E's to describe pairwise coupling events. The second order theories have reproduced results previously obtained by much more sophisticated treatments. In this thesis, we firstly examine the hybrid resonances in a cold plasma and show that they have a mode conversion interpretation in the framework of the C.L-D. model. The Budden tunnelling coefficients are recovered for this case. Next, mode conversion between the fast and slow electromagnetic waves in the lower hybrid frequency range is considered. This phenomenon determines the accessibility of the lower hybrid resonance to the slow wave, and is also of theoretical interest because the mode coupling differs in certain aspects from cases previously investigated by C.L-D. A second order approximation to the dispersion relation is used in the mode conversion region leading to Weber's equation from which transmission coefficients are then obtained in various cases. Finally, we provide justification for the use of Weber's equation. The exact fourth order system of O.D.E's for the problem is set down, and a linear transformation, which is an extension of that given by Heading, reveals the second order nature of the coupling process. Numerical solutions of the fourth order system yield transmission coefficients in excellent agreement with the second order theory, and also demonstrate that the electric field variation across the mode conversion region is well approximated, via the above transformation, by our second order theory.
1987-01-01T00:00:00ZWoods, Anna MariaLinear mode conversion processes are much studied in plasma physics because they determine the efficiency of any radio frequency heating scheme. Mode coupling model equations, extracted with varying degrees of rigour from the Maxwell-linearized kinetic equations, are usually fourth or higher order O.D.E's. These are solved by complicated methods to obtain transmission, conversion, reflection and absorption coefficients. Recently, Fuchs et al and Cairns and Lashmore-Davies (C.L-D.) have postulated second order O.D.E's to describe pairwise coupling events. The second order theories have reproduced results previously obtained by much more sophisticated treatments. In this thesis, we firstly examine the hybrid resonances in a cold plasma and show that they have a mode conversion interpretation in the framework of the C.L-D. model. The Budden tunnelling coefficients are recovered for this case. Next, mode conversion between the fast and slow electromagnetic waves in the lower hybrid frequency range is considered. This phenomenon determines the accessibility of the lower hybrid resonance to the slow wave, and is also of theoretical interest because the mode coupling differs in certain aspects from cases previously investigated by C.L-D. A second order approximation to the dispersion relation is used in the mode conversion region leading to Weber's equation from which transmission coefficients are then obtained in various cases. Finally, we provide justification for the use of Weber's equation. The exact fourth order system of O.D.E's for the problem is set down, and a linear transformation, which is an extension of that given by Heading, reveals the second order nature of the coupling process. Numerical solutions of the fourth order system yield transmission coefficients in excellent agreement with the second order theory, and also demonstrate that the electric field variation across the mode conversion region is well approximated, via the above transformation, by our second order theory.Some exact solutions in the one-dimensional unsteady motion of a gasWeir, David Gordonhttp://hdl.handle.net/10023/139642018-06-12T23:19:05Z1961-01-01T00:00:00ZIn this thesis, we present certain exact solutions of the mathematical equations governing the one-dimensional unsteady flow of a compressible fluid. In Chapter 2 we introduce the well-known simplification of the equations (1.1.10), (1.1.11) and (1.1.12) which occurs when the entropy is assumed to be constant, and conditions for parching solutions of the equations along characteristics are obtained. These results are used to generalise a problem solved by Mackie. In chapter 3 we meet the concept of a shook, and exact solutions are obtained for two problems in which shocks occur in non-uniform flows. In chapter 4 the case of waves in shallow water which has differential equations similar to those of gas flow is discussed. The results of the previous section are applied to this case and a problem attacked which permits a comparison to be made of the results obtained by this theory and a simpler linearized theory. Finally in chapter 5 we examine a method introduced by Martin for dealing with certain non-isentropic flows. Some new exact solutions of non-isentropic flows are thus obtained.
1961-01-01T00:00:00ZWeir, David GordonIn this thesis, we present certain exact solutions of the mathematical equations governing the one-dimensional unsteady flow of a compressible fluid. In Chapter 2 we introduce the well-known simplification of the equations (1.1.10), (1.1.11) and (1.1.12) which occurs when the entropy is assumed to be constant, and conditions for parching solutions of the equations along characteristics are obtained. These results are used to generalise a problem solved by Mackie. In chapter 3 we meet the concept of a shook, and exact solutions are obtained for two problems in which shocks occur in non-uniform flows. In chapter 4 the case of waves in shallow water which has differential equations similar to those of gas flow is discussed. The results of the previous section are applied to this case and a problem attacked which permits a comparison to be made of the results obtained by this theory and a simpler linearized theory. Finally in chapter 5 we examine a method introduced by Martin for dealing with certain non-isentropic flows. Some new exact solutions of non-isentropic flows are thus obtained.Stability of some free-surface flowsSmith, Frank Ian Pitthttp://hdl.handle.net/10023/139602018-06-12T23:19:08Z1969-01-01T00:00:00ZThe subject matter of this thesis is concerned with the stability of fluid flows; more particularly , with the stability of liquid films which have an interface with air. We will therefore begin by formulating the basic equations and ideas which pertain to this class of problems. Later in this chapter, a summary will be given of the topics dealt with in this dissertation.
1969-01-01T00:00:00ZSmith, Frank Ian PittThe subject matter of this thesis is concerned with the stability of fluid flows; more particularly , with the stability of liquid films which have an interface with air. We will therefore begin by formulating the basic equations and ideas which pertain to this class of problems. Later in this chapter, a summary will be given of the topics dealt with in this dissertation.The unsteady expansion of a gas into a near vacuumMcLaughlin, Raymondhttp://hdl.handle.net/10023/139562018-06-12T23:18:13Z1975-01-01T00:00:00ZThis thesis is concerned with the unsteady expansion of an initially uniform, stationary gas into a low density, stationary atmosphere, studied from the viewpoint of inviscid gasdynamics. It is found that, there are two regions in the k-𝜎 parameter space having distinct forms for the large time solution, when the atmospheric density is initially proportional to r⁻[super]k, r being the spatial coordinate, k being constant and 𝜎, the geometry index, has its usual meaning. First of all a constant asymptotic shock velocity is assumed and matched expansions, for large r, are constructed. Inner expansions, valid near the shock, are matched to zeroth and first orders with the outer expansions which are valid near the contact front. Zeroth order matching, which, yields the constant asymptotic shock velocity, is possible only in a restricted region of the k-𝜎parameter space and this situation is clarified by appealing to the similarity solutions which are extended to cover cases which have not been dealt with previously.
In the other region of the k-𝜎 parameter space the asymptotic shock velocity is proportional to r[super]∈ where ∈, a positive constant, is found from the similarity solutions as a function of k, γ ,𝜎. An attempt is made at constructing matched asymptotic expansions for large r. The inner solution can be obtained, apart from the evaluation of certain constants, to zeroth and first orders but the outer solution is inaccessible and can only be determined from the full inviscid solution. However it is shown that there exists a solution to the outer equations which matches with the inner solution up to first order. In both cases matching of the first order inner terms to the outer solution produces an eigenvalue problem, the solution of which is not attempted here. Finally full numerical solutions of the inviscid equations, one for each case, were produced using the method of backward drawn characteristics, devised by Hartree, and it will be seen that they compare most favourably with the asymptotic analysis.
1975-01-01T00:00:00ZMcLaughlin, RaymondThis thesis is concerned with the unsteady expansion of an initially uniform, stationary gas into a low density, stationary atmosphere, studied from the viewpoint of inviscid gasdynamics. It is found that, there are two regions in the k-𝜎 parameter space having distinct forms for the large time solution, when the atmospheric density is initially proportional to r⁻[super]k, r being the spatial coordinate, k being constant and 𝜎, the geometry index, has its usual meaning. First of all a constant asymptotic shock velocity is assumed and matched expansions, for large r, are constructed. Inner expansions, valid near the shock, are matched to zeroth and first orders with the outer expansions which are valid near the contact front. Zeroth order matching, which, yields the constant asymptotic shock velocity, is possible only in a restricted region of the k-𝜎parameter space and this situation is clarified by appealing to the similarity solutions which are extended to cover cases which have not been dealt with previously.
In the other region of the k-𝜎 parameter space the asymptotic shock velocity is proportional to r[super]∈ where ∈, a positive constant, is found from the similarity solutions as a function of k, γ ,𝜎. An attempt is made at constructing matched asymptotic expansions for large r. The inner solution can be obtained, apart from the evaluation of certain constants, to zeroth and first orders but the outer solution is inaccessible and can only be determined from the full inviscid solution. However it is shown that there exists a solution to the outer equations which matches with the inner solution up to first order. In both cases matching of the first order inner terms to the outer solution produces an eigenvalue problem, the solution of which is not attempted here. Finally full numerical solutions of the inviscid equations, one for each case, were produced using the method of backward drawn characteristics, devised by Hartree, and it will be seen that they compare most favourably with the asymptotic analysis.Hodograph methods applied to flow past finite wedgesMackie, A. G. (Andrew George)http://hdl.handle.net/10023/139462018-06-12T23:18:31Z1953-01-01T00:00:00Z1953-01-01T00:00:00ZMackie, A. G. (Andrew George)Two parameter integral methods in laminar boundary layer theoryLister, William Macraehttp://hdl.handle.net/10023/139442018-06-12T23:18:51Z1971-01-01T00:00:00ZThe work of this thesis is concerned, with the investigation and attempted improvement of an integral method for solving the two dimensional, incompressible laminar boundary layer equations of fluid dynamics. The method which is based on a theoretical two parameter representation of well-known boundary layer properties was first produced by Professor S. N. Curle. Its range of application, reliability and accuracy rely on four universal functions which have been derived from known exact solutions to the boundary layer equations, and are given tabulated in terms of a pressure gradient parameter 𝞴. This thesis seeks to improve these properties by making adjustments to the tabulated functions and also considers the extension of the method to certain compressible boundary layer problems. The first chapter contains the development of, and background to the method and gives a critical assessment of the existing functions. This analysis indicates that the method may be improved by supplying more data for certain ranges of 𝞴 from which the functions may be calculated; by improving the fitting process; and by the provision for small values of 𝞴 of an analytic form for a shape parameter H which the method involves.
To supply more data two new solutions for the flows u₁ = U₀ (1+𝜉) and u₁ = u₀ (𝜉+𝜉³) where 𝜉 is a non-dimensional co-ordinate in the direction of the flow, are investigated. The resulting work produces some interesting examples of the use of series expansions in boundary layer theory and these, and the results produced, are given in the second chapter. The fitting of the functions is carried out in chapter three. Polynomial models in terms of 𝞴 are fitted by least squares techniques to data from seven solutions and are adjusted to ensure an analytic form for H for small values of 𝞴. A comparison of results using new and old tables Indicates that an improvement has been made. The transformation relating certain compressible and incompressible flows is next examined and the extension of the method to such problems considered. An idea due to Stewartson for assessing the relative accuracies of methods under such circumstances indicates that the method should be highly accurate, a result confirmed by the calculation of the compressible flow u₁ = u₀ (1-𝜉) at a leading edge Mach number of four. The thesis is concluded with a review of the work carried out and the results obtained.
1971-01-01T00:00:00ZLister, William MacraeThe work of this thesis is concerned, with the investigation and attempted improvement of an integral method for solving the two dimensional, incompressible laminar boundary layer equations of fluid dynamics. The method which is based on a theoretical two parameter representation of well-known boundary layer properties was first produced by Professor S. N. Curle. Its range of application, reliability and accuracy rely on four universal functions which have been derived from known exact solutions to the boundary layer equations, and are given tabulated in terms of a pressure gradient parameter 𝞴. This thesis seeks to improve these properties by making adjustments to the tabulated functions and also considers the extension of the method to certain compressible boundary layer problems. The first chapter contains the development of, and background to the method and gives a critical assessment of the existing functions. This analysis indicates that the method may be improved by supplying more data for certain ranges of 𝞴 from which the functions may be calculated; by improving the fitting process; and by the provision for small values of 𝞴 of an analytic form for a shape parameter H which the method involves.
To supply more data two new solutions for the flows u₁ = U₀ (1+𝜉) and u₁ = u₀ (𝜉+𝜉³) where 𝜉 is a non-dimensional co-ordinate in the direction of the flow, are investigated. The resulting work produces some interesting examples of the use of series expansions in boundary layer theory and these, and the results produced, are given in the second chapter. The fitting of the functions is carried out in chapter three. Polynomial models in terms of 𝞴 are fitted by least squares techniques to data from seven solutions and are adjusted to ensure an analytic form for H for small values of 𝞴. A comparison of results using new and old tables Indicates that an improvement has been made. The transformation relating certain compressible and incompressible flows is next examined and the extension of the method to such problems considered. An idea due to Stewartson for assessing the relative accuracies of methods under such circumstances indicates that the method should be highly accurate, a result confirmed by the calculation of the compressible flow u₁ = u₀ (1-𝜉) at a leading edge Mach number of four. The thesis is concluded with a review of the work carried out and the results obtained.The evaporation kinetics of liquid helium IIHunter, George Huttonhttp://hdl.handle.net/10023/139412018-06-12T23:18:42Z1968-01-01T00:00:00ZThis work is concerned with the evaporation and condensation processes occurring when liquid helium II is in equilibrium with its saturated vapour. We define the condensation coefficient a as the fraction of atoms incident on the liquid vapour interface which cross it to form part of the liquid. Experiments to measure are described, and the results are discussed in terms of microscopic condensation processes. The measurements are made by reflecting second sound pulses from the liquid vapour surface at normal incidence and measuring the reflection coefficient. An account is given of the phenomenological theories of Osborne (1962a) and Chernikova (1964), which describe the reflection of second sound from the surface and the associated effect, its transformation into first sound in the gas. Neither of these agree with the experimental results, and Osborne's theory is modified by taking account of the conditions in the gas a small fraction of a mean free path above the surface (rather than many mean free paths above the surface, as in Osborne's original theory). Thus modified, the theory is shown to be in agreement with the measurements of the reflection coefficient. Also described are measurements made in second sound pulses generated at the interface by first sound pulses, themselves generated at the interface by second sound, propagated up the tube, and reflected from its closed and back to the surface. From the time intervals between these pulses the velocity of first sound in the vapour is deduced, and found to be in agreement with previous work. Measurements of pulse amplitude corroborate the reflection coefficient measurements, and taking the two sets of measurements together wo have concluded that a is probably 1 and not less than 0.8 between 1.0°K and 2.14°K. The microscopic processes by which condensation can take place are considered. Experiments due to beaker (unpublished, see Osborne, 1962a) and Osborne (1962b) are described, which indicate that the vapour exchanges momentum with normal fluid only. We have therefore supposed that processes in which a gas atom condenses to form excitations must conserve energy and momentum. Processes involving both bulk excitations and surface excitations are considered, but effects due to the finite lifetime of the excitations and the linewidth of the excitations spectrum are neglected. No attempt has been made to calculate the matrix elements for condensation processes, but plausible estimates have been made of their relative magnitudes. In particular, only processes involving one gas atom and one or two excitations have been considered. Using the requirements of conservation of energy and momentum, it is shown that as the temperature decreases, a decreasing fraction of the incident atom have enough energy to form two excitations, and condensation must take place by the collision of an atom with an existing excitation. A rough estimate of the collision probability for such a process leads to the conclusion that at 1°K, a should be about 0.2. This disagreement with experiment has not been resolved. Finally, some remarks are made about the implications for other work on liquid helium II, and some suggestions for future work.
1968-01-01T00:00:00ZHunter, George HuttonThis work is concerned with the evaporation and condensation processes occurring when liquid helium II is in equilibrium with its saturated vapour. We define the condensation coefficient a as the fraction of atoms incident on the liquid vapour interface which cross it to form part of the liquid. Experiments to measure are described, and the results are discussed in terms of microscopic condensation processes. The measurements are made by reflecting second sound pulses from the liquid vapour surface at normal incidence and measuring the reflection coefficient. An account is given of the phenomenological theories of Osborne (1962a) and Chernikova (1964), which describe the reflection of second sound from the surface and the associated effect, its transformation into first sound in the gas. Neither of these agree with the experimental results, and Osborne's theory is modified by taking account of the conditions in the gas a small fraction of a mean free path above the surface (rather than many mean free paths above the surface, as in Osborne's original theory). Thus modified, the theory is shown to be in agreement with the measurements of the reflection coefficient. Also described are measurements made in second sound pulses generated at the interface by first sound pulses, themselves generated at the interface by second sound, propagated up the tube, and reflected from its closed and back to the surface. From the time intervals between these pulses the velocity of first sound in the vapour is deduced, and found to be in agreement with previous work. Measurements of pulse amplitude corroborate the reflection coefficient measurements, and taking the two sets of measurements together wo have concluded that a is probably 1 and not less than 0.8 between 1.0°K and 2.14°K. The microscopic processes by which condensation can take place are considered. Experiments due to beaker (unpublished, see Osborne, 1962a) and Osborne (1962b) are described, which indicate that the vapour exchanges momentum with normal fluid only. We have therefore supposed that processes in which a gas atom condenses to form excitations must conserve energy and momentum. Processes involving both bulk excitations and surface excitations are considered, but effects due to the finite lifetime of the excitations and the linewidth of the excitations spectrum are neglected. No attempt has been made to calculate the matrix elements for condensation processes, but plausible estimates have been made of their relative magnitudes. In particular, only processes involving one gas atom and one or two excitations have been considered. Using the requirements of conservation of energy and momentum, it is shown that as the temperature decreases, a decreasing fraction of the incident atom have enough energy to form two excitations, and condensation must take place by the collision of an atom with an existing excitation. A rough estimate of the collision probability for such a process leads to the conclusion that at 1°K, a should be about 0.2. This disagreement with experiment has not been resolved. Finally, some remarks are made about the implications for other work on liquid helium II, and some suggestions for future work.Hydrodynamics of liquid helium IIGriffiths, D. J. (Derek John)http://hdl.handle.net/10023/139382018-06-20T10:29:59Z1964-01-01T00:00:00ZObservations have been made of the behaviour of a fine quartz fibre, weighted at its lower end and suspended inside a short, horizontal tunnel in which counterblow of the normal and superfluid components of liquid helium II can be produced by a heater. Section I of this thesis is an introduction to the hydrodynamic of liquid helium II. In section II the interaction with such a fibre of quantized vortex lines in the superfluid is discussed, and the effect of a short heat pulse on the fibre when it is carrying superfluid circulation in calculated approximately. The different responses of the fibre to turbulence in the normal fluid and in the superfluid are contrasted.
In section III, after a description of the apparatus and the experimental method, measurements, deduced from the response to heat pulses, of the circulation about the fibre from 1.3°K to2.1°K are reported. At all temperatures circulations of the expected order from magnitude are observed to grow and decay with time. At 1.3°K apparent circulations of up to about 1/5 quantum occur. In undisturbed helium the largest circulations are more stable than other values, persisting for up to five minutes. Measurement of the same circulation both by the heat-pulse method and by the deflection of the fibre in a steady heat current suggests that the large, persistent circulations may in fact be equal to one quantum. The sense of the observed circulations about the fibre at 1.3°K is strongly biased, this bias being probably associated with the heater geometry. In small heat current no change in the bins or persistence of circulation can be detected, but in currents above 11/2-3 mW/cm², depending on the heater, the circulation about the fibre is both more variable and of the opposite bias to that in undisturbed helium. This behaviour continues for 100 sec or more after the heat current has been switched off. At higher temperatures there are indications that the behaviour might be similar if it were possible for the helium to region its undisturbed condition after being stirred up by turbulent heat currents. In fact this seems other to be impossible, or to require many hundreds of seconds, and the situation is therefore rather confused.
In still higher heat currents measurement of superfluid circulation by heat pulses is impossible because the fibre is continuously agitated in a random way. From measurements of the rms deflections of the bob on the end of the fibre a critical heat current for the onset of such turbulence is found at 1.3°K. At higher temperatures the sensitivity is too low for the transition itself, if any, to be detected, but an upper limit to the critical heat current is given. At 1.3°K and 2.1°K the rms deflection increases monotonically with increasing heat currents, but at intermediate temperatures it is variable, because the bob is often hardly agitated for long periods during apparently supercritical heat currents. This is called quiescent behaviour.
When a supercritical heat current is a delay before agitation of the fibre begins. The delay time, which is often not very well defined, has been measured as a function of the heat current. When the current is switched off the agitation of the bob decoys in a few seconds, but at 1.3°K the circulation about the fibre is small and variable for 100 sec or more, until the persistence and bias characteristic of undisturbed helium regained. These results are discussed in section IV.
1964-01-01T00:00:00ZGriffiths, D. J. (Derek John)Observations have been made of the behaviour of a fine quartz fibre, weighted at its lower end and suspended inside a short, horizontal tunnel in which counterblow of the normal and superfluid components of liquid helium II can be produced by a heater. Section I of this thesis is an introduction to the hydrodynamic of liquid helium II. In section II the interaction with such a fibre of quantized vortex lines in the superfluid is discussed, and the effect of a short heat pulse on the fibre when it is carrying superfluid circulation in calculated approximately. The different responses of the fibre to turbulence in the normal fluid and in the superfluid are contrasted.
In section III, after a description of the apparatus and the experimental method, measurements, deduced from the response to heat pulses, of the circulation about the fibre from 1.3°K to2.1°K are reported. At all temperatures circulations of the expected order from magnitude are observed to grow and decay with time. At 1.3°K apparent circulations of up to about 1/5 quantum occur. In undisturbed helium the largest circulations are more stable than other values, persisting for up to five minutes. Measurement of the same circulation both by the heat-pulse method and by the deflection of the fibre in a steady heat current suggests that the large, persistent circulations may in fact be equal to one quantum. The sense of the observed circulations about the fibre at 1.3°K is strongly biased, this bias being probably associated with the heater geometry. In small heat current no change in the bins or persistence of circulation can be detected, but in currents above 11/2-3 mW/cm², depending on the heater, the circulation about the fibre is both more variable and of the opposite bias to that in undisturbed helium. This behaviour continues for 100 sec or more after the heat current has been switched off. At higher temperatures there are indications that the behaviour might be similar if it were possible for the helium to region its undisturbed condition after being stirred up by turbulent heat currents. In fact this seems other to be impossible, or to require many hundreds of seconds, and the situation is therefore rather confused.
In still higher heat currents measurement of superfluid circulation by heat pulses is impossible because the fibre is continuously agitated in a random way. From measurements of the rms deflections of the bob on the end of the fibre a critical heat current for the onset of such turbulence is found at 1.3°K. At higher temperatures the sensitivity is too low for the transition itself, if any, to be detected, but an upper limit to the critical heat current is given. At 1.3°K and 2.1°K the rms deflection increases monotonically with increasing heat currents, but at intermediate temperatures it is variable, because the bob is often hardly agitated for long periods during apparently supercritical heat currents. This is called quiescent behaviour.
When a supercritical heat current is a delay before agitation of the fibre begins. The delay time, which is often not very well defined, has been measured as a function of the heat current. When the current is switched off the agitation of the bob decoys in a few seconds, but at 1.3°K the circulation about the fibre is small and variable for 100 sec or more, until the persistence and bias characteristic of undisturbed helium regained. These results are discussed in section IV.Approximate methods in high speed flowBurnside, Robert R.http://hdl.handle.net/10023/139312018-06-18T14:04:50Z1962-01-01T00:00:00ZIn many problems arising in the theory of compressible flow, the equations characterising the solution of the system are so intractable that recourse must be made to some approximate method which allows the essential features of the flow to be preserved, whilst to some degree, simplifying the mathematics. It is with certain methods of this type that this thesis is concerned.
In the subsequent work, we shall assume that the effects due to viscosity and heat conduction are so small as to be negligible. These assumptions may be shown to be largely valid except in those domains of the flow-field where the modified system of equations predicts regions in which the solution is in general multivalued. In the modified system, however, such ‘regions’ are avoided by the introduction of mathematical discontinuities and, assuming that the jump conditions across them can be determines, are sufficient to provide single-valued solutions valid everywhere, except at the discontinuity. The methods to be presented are formulated in the plane consisting of one space variable and one time variable.
1962-01-01T00:00:00ZBurnside, Robert R.In many problems arising in the theory of compressible flow, the equations characterising the solution of the system are so intractable that recourse must be made to some approximate method which allows the essential features of the flow to be preserved, whilst to some degree, simplifying the mathematics. It is with certain methods of this type that this thesis is concerned.
In the subsequent work, we shall assume that the effects due to viscosity and heat conduction are so small as to be negligible. These assumptions may be shown to be largely valid except in those domains of the flow-field where the modified system of equations predicts regions in which the solution is in general multivalued. In the modified system, however, such ‘regions’ are avoided by the introduction of mathematical discontinuities and, assuming that the jump conditions across them can be determines, are sufficient to provide single-valued solutions valid everywhere, except at the discontinuity. The methods to be presented are formulated in the plane consisting of one space variable and one time variable.Aspects of natural convention and of non-linear hydridynamic stabilityUsher, J. R.http://hdl.handle.net/10023/139222018-06-12T23:17:26Z1974-01-01T00:00:00ZIn Part I of this thesis, steady and time-dependent, natural-convection similarity flows with mass transfer are discussed. Similarity flows for natural convection on families of two-dimensional bodies with closed lower ends are enumerated, when both a temperature distribution and a suction velocity distribution are prescribed at the body surface. For steady similarity flow on a heated vertical flat plate, with mass transfer at the surface, a numerical procedure is introduced for determining the velocity and temperature profiles. These results are presented in Figs. 2 and 3. Other similarity flows may be found by the same method.
A simplification, valid for “strong” suction, is discussed. An extension of Mangler’s transformation [1948] is given which reduces the equations governing axisymmetric flow to those for two-dimensional flow in steady natural convection.
In Part II non-linear resonant instability in parallel shear flows is discussed. A.D.D.Craik’s (see Usher and Craik [I]) modified version of Bateman’s [1956] variational formulation for viscous flows is employed to derive the second-order interaction equations governing the temporal evolution of a resonant wave triad in a sheer flow. (An extension of Craik’s variational formulation to free surface flows is presented but is not required in the subsequent analysis for the resonance problem). This problem was treated previously using a ‘direct’ approach (employing the Navier-Stokes equations) by Craik [1971]. The major advantage of the present method over the ‘direct’ method is the substantial reduction in algebraic complexity. Also, a justification of the validity of Craik’s previous analysis is given.
For this same resonance problem, third-order interaction equations are derived by the *direct* method since, to this order of approximation, little advantage is to be gained from the variational formulation. The resonance theory is thereby developed to the same order of approximation as the non-resonant third-order theory of Stuart [1960, 1962].
An asymptotic analysis for large Reynolds numbers reveals that the magnitudes of the third-order interaction coefficients – like certain of those at second-order – are remarkably large. Such results lead to a discussion of the regions of validity of the perturbation analysis. Also some light is shed on the roles played by resonance and three-dimensionality in the non-linear instability of shear flows.
1974-01-01T00:00:00ZUsher, J. R.In Part I of this thesis, steady and time-dependent, natural-convection similarity flows with mass transfer are discussed. Similarity flows for natural convection on families of two-dimensional bodies with closed lower ends are enumerated, when both a temperature distribution and a suction velocity distribution are prescribed at the body surface. For steady similarity flow on a heated vertical flat plate, with mass transfer at the surface, a numerical procedure is introduced for determining the velocity and temperature profiles. These results are presented in Figs. 2 and 3. Other similarity flows may be found by the same method.
A simplification, valid for “strong” suction, is discussed. An extension of Mangler’s transformation [1948] is given which reduces the equations governing axisymmetric flow to those for two-dimensional flow in steady natural convection.
In Part II non-linear resonant instability in parallel shear flows is discussed. A.D.D.Craik’s (see Usher and Craik [I]) modified version of Bateman’s [1956] variational formulation for viscous flows is employed to derive the second-order interaction equations governing the temporal evolution of a resonant wave triad in a sheer flow. (An extension of Craik’s variational formulation to free surface flows is presented but is not required in the subsequent analysis for the resonance problem). This problem was treated previously using a ‘direct’ approach (employing the Navier-Stokes equations) by Craik [1971]. The major advantage of the present method over the ‘direct’ method is the substantial reduction in algebraic complexity. Also, a justification of the validity of Craik’s previous analysis is given.
For this same resonance problem, third-order interaction equations are derived by the *direct* method since, to this order of approximation, little advantage is to be gained from the variational formulation. The resonance theory is thereby developed to the same order of approximation as the non-resonant third-order theory of Stuart [1960, 1962].
An asymptotic analysis for large Reynolds numbers reveals that the magnitudes of the third-order interaction coefficients – like certain of those at second-order – are remarkably large. Such results lead to a discussion of the regions of validity of the perturbation analysis. Also some light is shed on the roles played by resonance and three-dimensionality in the non-linear instability of shear flows.Ion dynamics in collisionless shock wavesSherwell, Davidhttp://hdl.handle.net/10023/139172018-06-11T23:17:53Z1976-01-01T00:00:00ZIn a laminar model of a collisionless magnetosonic shock wave, ion equations of motion are integrated through shock-like profiles. Conservation relations and Maxwell's equations allow a self-consistent determination of unknown downstream ion distribution functions fᵢ, ion temperature Tᵢ, and electric potential jump 𝛷. Favourable comparison of model Tᵢ, 𝛷.
Favourable comparison of model Tᵢ, 𝛷 , with experiment establishes (at low 𝛽 ≲ O.3, 𝛽=8 π N
[sub] l k (T[sub]e₂+Tᵢ[sub]l)/B₁²)
importance of laminar ion dynamics. Heating is due to distortion of Maxwellian distributions when entropy is conserved; in particular shock dynamics is dominated by a fast "tail" of reflected ions. The solutions for fᵢ are considered. The "stability" of the model to its assumptions (linear profiles, shock thickness (L[sub]s)) is shown. When reflections occur a self-consistent length emerges. The solutions Tᵢ, 𝛷 are extensively studied at various Mach numbers for different values of 𝛽. Laminar ion heating is very efficient and at high 𝛽 can exceed proper conservation levels due to ion reflections; at high 𝛽(≥ 𝛽 *) the electric potential is unable to slow the ions to conservation levels. The model predicts significant reflected ion currents in the plane of the shock. The boundary 𝛽 * is determined. Then laminar ion dynamics on the scale of the electron heating length (~10 C/w[sub]p ₑ) cannot occur for 𝛽 > 𝛽 *. Dependence on L[sub]s and T ₑ₁,/Tᵢ₁ is considered. The nature of non-laminar 𝛽 >𝛽* shocks is considered. Collisions are found to be important in laboratory shocks, and are efficient in slowing the reflected ions. In the absence of collisions, ion instabilities must be considered. It is shown that turbulent slowing of the fast ions cannot take place in L[sub]s alone. Further it is shown possible to construct a shock so that non-laminar mechanisms cannot occur significantly. Then the laminar model is re-instated. A decoupling of ion and electron heating lengths is proposed. Reflection heating in the Earth's Bow Shock (𝛽>𝛽*) is modelled, and is comparable with experiment.
1976-01-01T00:00:00ZSherwell, DavidIn a laminar model of a collisionless magnetosonic shock wave, ion equations of motion are integrated through shock-like profiles. Conservation relations and Maxwell's equations allow a self-consistent determination of unknown downstream ion distribution functions fᵢ, ion temperature Tᵢ, and electric potential jump 𝛷. Favourable comparison of model Tᵢ, 𝛷.
Favourable comparison of model Tᵢ, 𝛷 , with experiment establishes (at low 𝛽 ≲ O.3, 𝛽=8 π N
[sub] l k (T[sub]e₂+Tᵢ[sub]l)/B₁²)
importance of laminar ion dynamics. Heating is due to distortion of Maxwellian distributions when entropy is conserved; in particular shock dynamics is dominated by a fast "tail" of reflected ions. The solutions for fᵢ are considered. The "stability" of the model to its assumptions (linear profiles, shock thickness (L[sub]s)) is shown. When reflections occur a self-consistent length emerges. The solutions Tᵢ, 𝛷 are extensively studied at various Mach numbers for different values of 𝛽. Laminar ion heating is very efficient and at high 𝛽 can exceed proper conservation levels due to ion reflections; at high 𝛽(≥ 𝛽 *) the electric potential is unable to slow the ions to conservation levels. The model predicts significant reflected ion currents in the plane of the shock. The boundary 𝛽 * is determined. Then laminar ion dynamics on the scale of the electron heating length (~10 C/w[sub]p ₑ) cannot occur for 𝛽 > 𝛽 *. Dependence on L[sub]s and T ₑ₁,/Tᵢ₁ is considered. The nature of non-laminar 𝛽 >𝛽* shocks is considered. Collisions are found to be important in laboratory shocks, and are efficient in slowing the reflected ions. In the absence of collisions, ion instabilities must be considered. It is shown that turbulent slowing of the fast ions cannot take place in L[sub]s alone. Further it is shown possible to construct a shock so that non-laminar mechanisms cannot occur significantly. Then the laminar model is re-instated. A decoupling of ion and electron heating lengths is proposed. Reflection heating in the Earth's Bow Shock (𝛽>𝛽*) is modelled, and is comparable with experiment.Investigations on classical symmetries theory of quantizationGuest, P. B.http://hdl.handle.net/10023/139132018-06-11T23:17:38Z1972-01-01T00:00:00ZThe thesis divides naturally into two parts. Part I raises, and in some cases answers, questions concerning symmetry in classical mechanics. The main result (Theorem 6.4) shows that the assumption of the existence of a realization puts an upper limit on the rank of the algebra.
The heart of the thesis (covering three-quarters of the volume) is section II on the quantization of classical systems. §1 lists axioms desirable in any quantization rule for the 'functions of the q's'. The momentum observables are introduced in §2 prior to their quantization in §4. §5 essentially shows how conventional quantum mechanics fits into this scheme of things. By progressive specialization from a general manifold to a vector space, from a general quantization scheme to one which is linear on the linear momentum functions, and finally to an entirely well-behaved (admissible) quantization rule, into which conventional quantum mechanics fits nicely, we obtain in §7-§9 results which become progressively more and more powerful. The final theorem (Theorem 9.2) is perhaps the most significant of all. This result states that there exists a class of functions, which contains all functions of the q's and functions of the p's and all momentum observables and which is closed with respect to any linear canonical transformation L; a rule A assigning a unique self-adjoint operator to each such function f; a unitary operator WL corresponding to L and an equation
𝛬(𝑓 ∘ 𝐿) = 𝑊[sub]𝐿⁻ 𝛬 𝑓 𝑊[sub]𝐿
1972-01-01T00:00:00ZGuest, P. B.The thesis divides naturally into two parts. Part I raises, and in some cases answers, questions concerning symmetry in classical mechanics. The main result (Theorem 6.4) shows that the assumption of the existence of a realization puts an upper limit on the rank of the algebra.
The heart of the thesis (covering three-quarters of the volume) is section II on the quantization of classical systems. §1 lists axioms desirable in any quantization rule for the 'functions of the q's'. The momentum observables are introduced in §2 prior to their quantization in §4. §5 essentially shows how conventional quantum mechanics fits into this scheme of things. By progressive specialization from a general manifold to a vector space, from a general quantization scheme to one which is linear on the linear momentum functions, and finally to an entirely well-behaved (admissible) quantization rule, into which conventional quantum mechanics fits nicely, we obtain in §7-§9 results which become progressively more and more powerful. The final theorem (Theorem 9.2) is perhaps the most significant of all. This result states that there exists a class of functions, which contains all functions of the q's and functions of the p's and all momentum observables and which is closed with respect to any linear canonical transformation L; a rule A assigning a unique self-adjoint operator to each such function f; a unitary operator WL corresponding to L and an equation
𝛬(𝑓 ∘ 𝐿) = 𝑊[sub]𝐿⁻ 𝛬 𝑓 𝑊[sub]𝐿An algebraic formulation of asmptotically separable quantum mechanicsMcLean, R. G. Derekhttp://hdl.handle.net/10023/139092018-06-11T23:17:34Z1984-01-01T00:00:00ZThis thesis explores the possibility of an algebraic formulation of non-relativistic quantum theory in which certain paradoxes associated with non-locality may be resolved. It is shown that the localisation of a free quantum mechanical wave function at large time coincides approximately with the localisation of an ensemble of classical particles having the same momentum range. This result is used to give a formal definition of spatially separating states and spatially separating particles. We then study certain C*-algebras on which expectation values converge in an infinite time limit. By considering such algebras which contain local observables it is possible to introduce states at infinity as limits of states described by wave functions. In such a state at infinity there is zero probability of a position measurement finding the system in any bounded region in configuration space. It is shown that a C*-algebra exists on which any coherent superposition of spatially separating states will converge in an infinite time limit to a mixture of disjoint states. This allows us to obtain an asymptotic resolution of de Broglie's paradox and the Einstein, Podolsy and Rosen paradox. These results are obtained for the simplest types of quantum systems i.e. a one particle system without spin having configuration space IRⁿ and a system consisting of two such particles which may be distinguished from each other.
1984-01-01T00:00:00ZMcLean, R. G. DerekThis thesis explores the possibility of an algebraic formulation of non-relativistic quantum theory in which certain paradoxes associated with non-locality may be resolved. It is shown that the localisation of a free quantum mechanical wave function at large time coincides approximately with the localisation of an ensemble of classical particles having the same momentum range. This result is used to give a formal definition of spatially separating states and spatially separating particles. We then study certain C*-algebras on which expectation values converge in an infinite time limit. By considering such algebras which contain local observables it is possible to introduce states at infinity as limits of states described by wave functions. In such a state at infinity there is zero probability of a position measurement finding the system in any bounded region in configuration space. It is shown that a C*-algebra exists on which any coherent superposition of spatially separating states will converge in an infinite time limit to a mixture of disjoint states. This allows us to obtain an asymptotic resolution of de Broglie's paradox and the Einstein, Podolsy and Rosen paradox. These results are obtained for the simplest types of quantum systems i.e. a one particle system without spin having configuration space IRⁿ and a system consisting of two such particles which may be distinguished from each other.Geometrical and topological properties of fractal percolationOrzechowski, Mark E.http://hdl.handle.net/10023/139072018-06-11T23:17:26Z1998-01-01T00:00:00ZThe basic 'fractal percolation' process was first proposed by Mandelbrot in 1974 and takes the following form. Let M ≥2 and P ∈ [0,1]; we start with the unit square C₀ = [0,1]²; Divide C₀ into M² equal closed squares, each of side-length M⁻¹ , in the natural way and retain each of these squares with probability p, or else remove it with probability 1 - p. We let C₁ be the union of those squares retained. The process is now repeated within each square of C₁ to give a new set C₂⊆C₁, consisting of squares of side-length M⁻². Iterating the construction in the obvious way, we obtain a decreasing sequence of sets C₀⊇ C₁ ⊇ C₂ ⊇ … with limit C[sub]∞ = ∩[sub]n≥₁C[sub]n.
The set C[sub]∞ is an example of a random Cantor set, and is typically highly intricate in nature. It may be empty, dust-like or highly connected, depending on the value of p; percolation is said to occur if C[sub]∞ contains large connected components linking opposite sides of the unit square.
In this thesis we shall investigate some of the geometrical and topological properties of C[sub]∞ that hold either almost surely (with probability 1) or with non-zero probability. In particular, the following results are established. We obtain (almost sure) lower and upper bounds on the box-counting dimension of the 'straightest' crossings in C[sub]∞ whenever percolation occurs; we also look at the distribution of the sizes of the connected components and the probability of percolation. In the three-dimensional version of the process, we establish the existence of two distinct phases of percolation, corresponding to the occurrence of paths and surfaces (or 'sheets') in the limit set, and study the limiting behaviour of the phase transition to sheet percolation as M → ∞. We also consider the results of some computer simulations of fractal percolation and present a number of generalisations of the basic process and other closely related constructions.
1998-01-01T00:00:00ZOrzechowski, Mark E.The basic 'fractal percolation' process was first proposed by Mandelbrot in 1974 and takes the following form. Let M ≥2 and P ∈ [0,1]; we start with the unit square C₀ = [0,1]²; Divide C₀ into M² equal closed squares, each of side-length M⁻¹ , in the natural way and retain each of these squares with probability p, or else remove it with probability 1 - p. We let C₁ be the union of those squares retained. The process is now repeated within each square of C₁ to give a new set C₂⊆C₁, consisting of squares of side-length M⁻². Iterating the construction in the obvious way, we obtain a decreasing sequence of sets C₀⊇ C₁ ⊇ C₂ ⊇ … with limit C[sub]∞ = ∩[sub]n≥₁C[sub]n.
The set C[sub]∞ is an example of a random Cantor set, and is typically highly intricate in nature. It may be empty, dust-like or highly connected, depending on the value of p; percolation is said to occur if C[sub]∞ contains large connected components linking opposite sides of the unit square.
In this thesis we shall investigate some of the geometrical and topological properties of C[sub]∞ that hold either almost surely (with probability 1) or with non-zero probability. In particular, the following results are established. We obtain (almost sure) lower and upper bounds on the box-counting dimension of the 'straightest' crossings in C[sub]∞ whenever percolation occurs; we also look at the distribution of the sizes of the connected components and the probability of percolation. In the three-dimensional version of the process, we establish the existence of two distinct phases of percolation, corresponding to the occurrence of paths and surfaces (or 'sheets') in the limit set, and study the limiting behaviour of the phase transition to sheet percolation as M → ∞. We also consider the results of some computer simulations of fractal percolation and present a number of generalisations of the basic process and other closely related constructions.Graph directed self-conformal multifractalsCole, Julianhttp://hdl.handle.net/10023/139032018-06-11T23:17:58Z1999-01-01T00:00:00ZIn this thesis we study the multifractal structure of graph directed self-conformal measures. We begin by introducing a number of notions from geometric measure theory. In particular, several notions of dimension, graph directed iterated function schemes, and the thermodynamic formalism. We then give an historical introduction to multifractal analysis. Finally, we develop our own contribution to multifractal analysis. Our own contribution to multifractal analysis can be broken into three parts; the proof of two multifractal density theorems, the calculation of the multifractal spectrum of self-conformal measures coded by graph directed iterated function schemes, and the introduction of a relative multifractal formalism together with an investigation of the relative multifractal structure of one graph directed self-conformal measure with respect to another. Specifically, in Chapter 5 we show that by interpreting the multifractal Hausdorff and packing measures Olsen introduced in [0195] as Henstock-Thomson variation measures we are able to obtain two stronger density theorems than those obtained by Olsen. In Chapter 6 we give full details of the calculation of the multifractal spectrum of graph directed self-conformal measures satisfying the strong open set condition and show that the multifractal Hausdorff and packing measures introduced by Olsen in [0195] take positive and finite values at the critical dimension provided that the self-conformal measures satisfy the strong separation condition. In Chapter 7 we formalise the idea of performing multifractal analysis with respect to an arbitrary reference measure by developing a formalism for the multifractal analysis of one measure with respect to another. This formalism is based on the ideas of the 'multifractal formalism' as first introduced by Halsey et. al. [HJKPS86] and closely parallels Olsen's formal treatment of this formalism in [0195]. In Chapter 8 we illustrate our relative multifractal formalism by investigating the relative multifractal structure of one graph directed self-conformal measure with respect to another where the two measures are based on the same graph directed self-conformal iterated function scheme which satisfies the strong open set condition.
1999-01-01T00:00:00ZCole, JulianIn this thesis we study the multifractal structure of graph directed self-conformal measures. We begin by introducing a number of notions from geometric measure theory. In particular, several notions of dimension, graph directed iterated function schemes, and the thermodynamic formalism. We then give an historical introduction to multifractal analysis. Finally, we develop our own contribution to multifractal analysis. Our own contribution to multifractal analysis can be broken into three parts; the proof of two multifractal density theorems, the calculation of the multifractal spectrum of self-conformal measures coded by graph directed iterated function schemes, and the introduction of a relative multifractal formalism together with an investigation of the relative multifractal structure of one graph directed self-conformal measure with respect to another. Specifically, in Chapter 5 we show that by interpreting the multifractal Hausdorff and packing measures Olsen introduced in [0195] as Henstock-Thomson variation measures we are able to obtain two stronger density theorems than those obtained by Olsen. In Chapter 6 we give full details of the calculation of the multifractal spectrum of graph directed self-conformal measures satisfying the strong open set condition and show that the multifractal Hausdorff and packing measures introduced by Olsen in [0195] take positive and finite values at the critical dimension provided that the self-conformal measures satisfy the strong separation condition. In Chapter 7 we formalise the idea of performing multifractal analysis with respect to an arbitrary reference measure by developing a formalism for the multifractal analysis of one measure with respect to another. This formalism is based on the ideas of the 'multifractal formalism' as first introduced by Halsey et. al. [HJKPS86] and closely parallels Olsen's formal treatment of this formalism in [0195]. In Chapter 8 we illustrate our relative multifractal formalism by investigating the relative multifractal structure of one graph directed self-conformal measure with respect to another where the two measures are based on the same graph directed self-conformal iterated function scheme which satisfies the strong open set condition.Parametric models of surfacesRobertson, Stewart A. (Stewart Alexander)http://hdl.handle.net/10023/138972018-06-11T23:17:17Z1957-01-01T00:00:00Z1957-01-01T00:00:00ZRobertson, Stewart A. (Stewart Alexander)Finite difference techniques of improved accuracyLambert, J. D.http://hdl.handle.net/10023/138882018-06-11T23:16:39Z1963-01-01T00:00:00ZIt is the major purpose of this thesis to propose finite difference techniques of improved accuracy for the numerical solution of ordinary differential equations, and for the numerical evaluation of definite integrals, the former problem being discussed in Chapter II, and the latter in Chapter IV. In Chapter III the stability of the formulae evolved in Chapter II is studied.
1963-01-01T00:00:00ZLambert, J. D.It is the major purpose of this thesis to propose finite difference techniques of improved accuracy for the numerical solution of ordinary differential equations, and for the numerical evaluation of definite integrals, the former problem being discussed in Chapter II, and the latter in Chapter IV. In Chapter III the stability of the formulae evolved in Chapter II is studied.Polynomial interpolation on a triangular regionYahaya, Daudhttp://hdl.handle.net/10023/138872018-06-11T23:17:02Z1994-01-01T00:00:00ZIt is well known that given f there is a unique polynomial of degree at most n which interpolates f on the standard triangle with uniform nodes (i, j), i, j ≥ 0, i + j ≤n. This leads us to the study of polynomial interpolation on a "triangular" domain with the nodes,
S = {([i], [j]): i, j ≥ 0, i + j ≤n}, [k] = [k][sub]q = (1-qᵏ)/(1-q), q > 0, which includes the standard triangle as a special case. In Chapter 2 of this thesis we derive a forward difference formula (of degree at most n) in the x and y directions for the interpolating polynomial P[sub]n on S. We also construct a Lagrange form of an interpolating polynomial which uses hyperbolas (although its coefficients are of degree up to 2n) and discuss a Neville-Aitken algorithm. In Chapter 3 we derive the Newton formula for the interpolating polynomial P[sub]n on the set of distinct points {(xᵢ, y[sub]j): i, j ≥ 0, i + j ≤n}. In particular if xᵢ = [i][sub]p and y[sub]j = [j]q, we show that Newton's form of P[sub]n reduces to a forward difference formula. We show further that we can express the interpolating polynomial on S itself in a Lagrange form and although its coefficients Ln/ij are not as simple as those of the first Lagrange form, they all have degree n. Moreover, Ln/ij can all be expressed in terms of Lm/0,0, 0 ≤ m ≤ n. In Chapter 4 we show that P[sub]n has a limit when both p, q → 0. We then verify that the interpolation properties of the limit form depend on the appropriate partial derivatives of f(x, y). In Chapter 5 we study integration rules I[sub]n of interpolatory type on the triangle S[sub] = {(x, y): 0 ≤ x ≤y ≤ [n]). For 1 ≤ n ≤5, we calculate the weights wn/ij for I[sub]n in terms of the parameter q and study certain general properties which govern wn/ij on S[sub]n. Finally, Chapter 6 deals with the behaviour of the Lebesgue functions 𝜆[sub]n(x, y; q) and the corresponding Lebesgue constant. We prove a property concerning where 𝜆[sub]n takes the value 1 at points other than the interpolation nodes. We also analyse the discontinuity of the directional derivative of 𝜆[sub]n on S[sub]n.
1994-01-01T00:00:00ZYahaya, DaudIt is well known that given f there is a unique polynomial of degree at most n which interpolates f on the standard triangle with uniform nodes (i, j), i, j ≥ 0, i + j ≤n. This leads us to the study of polynomial interpolation on a "triangular" domain with the nodes,
S = {([i], [j]): i, j ≥ 0, i + j ≤n}, [k] = [k][sub]q = (1-qᵏ)/(1-q), q > 0, which includes the standard triangle as a special case. In Chapter 2 of this thesis we derive a forward difference formula (of degree at most n) in the x and y directions for the interpolating polynomial P[sub]n on S. We also construct a Lagrange form of an interpolating polynomial which uses hyperbolas (although its coefficients are of degree up to 2n) and discuss a Neville-Aitken algorithm. In Chapter 3 we derive the Newton formula for the interpolating polynomial P[sub]n on the set of distinct points {(xᵢ, y[sub]j): i, j ≥ 0, i + j ≤n}. In particular if xᵢ = [i][sub]p and y[sub]j = [j]q, we show that Newton's form of P[sub]n reduces to a forward difference formula. We show further that we can express the interpolating polynomial on S itself in a Lagrange form and although its coefficients Ln/ij are not as simple as those of the first Lagrange form, they all have degree n. Moreover, Ln/ij can all be expressed in terms of Lm/0,0, 0 ≤ m ≤ n. In Chapter 4 we show that P[sub]n has a limit when both p, q → 0. We then verify that the interpolation properties of the limit form depend on the appropriate partial derivatives of f(x, y). In Chapter 5 we study integration rules I[sub]n of interpolatory type on the triangle S[sub] = {(x, y): 0 ≤ x ≤y ≤ [n]). For 1 ≤ n ≤5, we calculate the weights wn/ij for I[sub]n in terms of the parameter q and study certain general properties which govern wn/ij on S[sub]n. Finally, Chapter 6 deals with the behaviour of the Lebesgue functions 𝜆[sub]n(x, y; q) and the corresponding Lebesgue constant. We prove a property concerning where 𝜆[sub]n takes the value 1 at points other than the interpolation nodes. We also analyse the discontinuity of the directional derivative of 𝜆[sub]n on S[sub]n.Some contributions to the theory and application of polynomial approximationPhillips, G. M. (George McArtney)http://hdl.handle.net/10023/138832018-06-11T23:17:11Z1969-01-01T00:00:00ZThe fundamental theorem, as far as this work is concerned, is Weierstrass' theorem (1885) on the approximability of continuous functions by polynomials. Since the time of Weierstrass (1815-97) and his equally important contemporary Chebyshev (1821-94), the topic of approximation has grown enormously into a subject of considerable interest to both pure and applied mathematicians. The subject matter of this thesis, being exclusively concerned with polynomial approximations to a single-valued, function of one real variable, is on the side of 'applied' side of approximation theory. The first chapter lists the definitions and theorems required subsequently. Chapter is devoted to estimates for the maximum error in minimax polynomial approximations. Extensions of this are used to obtain crude error estimates for cubic spline approximations. The following chapter extends the minimax results to deal also with best L[sub]p polynomial approximations, which include beat least squares (L₂) and best modulus of integral (L₁) approximations as special cases. Chapter 4 is different in character. It is on the practical problem of approximating to convex or nearly convex data.
1969-01-01T00:00:00ZPhillips, G. M. (George McArtney)The fundamental theorem, as far as this work is concerned, is Weierstrass' theorem (1885) on the approximability of continuous functions by polynomials. Since the time of Weierstrass (1815-97) and his equally important contemporary Chebyshev (1821-94), the topic of approximation has grown enormously into a subject of considerable interest to both pure and applied mathematicians. The subject matter of this thesis, being exclusively concerned with polynomial approximations to a single-valued, function of one real variable, is on the side of 'applied' side of approximation theory. The first chapter lists the definitions and theorems required subsequently. Chapter is devoted to estimates for the maximum error in minimax polynomial approximations. Extensions of this are used to obtain crude error estimates for cubic spline approximations. The following chapter extends the minimax results to deal also with best L[sub]p polynomial approximations, which include beat least squares (L₂) and best modulus of integral (L₁) approximations as special cases. Chapter 4 is different in character. It is on the practical problem of approximating to convex or nearly convex data.Some consequences of symmetry in strong Stieltjes distributionsBracciali, Cleonice Fátima Braccialihttp://hdl.handle.net/10023/138812018-06-11T23:17:06Z1998-01-01T00:00:00ZThe main purpose of this work is to study a class of strong Stieltjes distributions 𝜓(t), defined on an interval (a, b) ⊆ (0, ∞), where 0 < 𝛽 < b ≤ ∞ and a = 𝛽²/b which satisfy the symmetric property
(dψ(t))/t[super]ω=-(dψ(β^2/t))/((β^2/t)[super]ω), tε (a,b), 2ωε𝓩
We investigate the consequences of this symmetric property on the orthogonal L-polynomials related to distributions ψ(t)and which are the denominators of the two-point Pade approximants for the power series that arise in the moment problem. We examine relations involving the coefficients of the continued fractions that correspond to these power series. We also study the consequences of the symmetry on the associated quadrature formulae.
1998-01-01T00:00:00ZBracciali, Cleonice Fátima BraccialiThe main purpose of this work is to study a class of strong Stieltjes distributions 𝜓(t), defined on an interval (a, b) ⊆ (0, ∞), where 0 < 𝛽 < b ≤ ∞ and a = 𝛽²/b which satisfy the symmetric property
(dψ(t))/t[super]ω=-(dψ(β^2/t))/((β^2/t)[super]ω), tε (a,b), 2ωε𝓩
We investigate the consequences of this symmetric property on the orthogonal L-polynomials related to distributions ψ(t)and which are the denominators of the two-point Pade approximants for the power series that arise in the moment problem. We examine relations involving the coefficients of the continued fractions that correspond to these power series. We also study the consequences of the symmetry on the associated quadrature formulae.Some aspects of the Jacobian conjecture: (the geometry of automorphisms of ℂ²)Ali, A. Hamid A. Hussainhttp://hdl.handle.net/10023/138782018-06-11T23:16:44Z1987-01-01T00:00:00ZWe consider the affine varieties which arise by considering invertible polynomial maps from ℂ² to itself of less than or equal to a given-degree. These varieties arise naturally in the investigation of the long-standing Jacobian Conjecture. We start with some calculations in the lower degree cases. These calculations provide a proof of the Jacobian conjecture in these cases and suggest how the investigation in the higher degree cases should proceed. We then show how invertible polynomial maps can be decomposed as products of what we call triangular maps and we are able to prove a uniqueness result which gives a stronger version of Jung's theorem [j] which is one of the most important results in this area. Our proof also gives a new derivation of Jung's theorem from Segre's lemma. We give a different decomposition of an invertible polynomial map as a composition of "irreducible maps" and we are able to write down standard forms for these irreducibles. We use these standard forms to give a description of the structure of the varieties of invertible maps. We consider some interesting group actions on our varieties and show how these fit in with the structure we describe. Finally, we look at the problem of identifying polynomial maps of finite order. Our description of the structure of the above varieties allows us to solve this problem completely and we are able to show that the only elements of finite order are those which arise from conjugating linear elements of finite order.
1987-01-01T00:00:00ZAli, A. Hamid A. HussainWe consider the affine varieties which arise by considering invertible polynomial maps from ℂ² to itself of less than or equal to a given-degree. These varieties arise naturally in the investigation of the long-standing Jacobian Conjecture. We start with some calculations in the lower degree cases. These calculations provide a proof of the Jacobian conjecture in these cases and suggest how the investigation in the higher degree cases should proceed. We then show how invertible polynomial maps can be decomposed as products of what we call triangular maps and we are able to prove a uniqueness result which gives a stronger version of Jung's theorem [j] which is one of the most important results in this area. Our proof also gives a new derivation of Jung's theorem from Segre's lemma. We give a different decomposition of an invertible polynomial map as a composition of "irreducible maps" and we are able to write down standard forms for these irreducibles. We use these standard forms to give a description of the structure of the varieties of invertible maps. We consider some interesting group actions on our varieties and show how these fit in with the structure we describe. Finally, we look at the problem of identifying polynomial maps of finite order. Our description of the structure of the above varieties allows us to solve this problem completely and we are able to show that the only elements of finite order are those which arise from conjugating linear elements of finite order.On Riesz summabilityShawyer, Brucehttp://hdl.handle.net/10023/138252018-06-20T10:30:12Z1963-01-01T00:00:00ZThe thesis is divided into four chapters. The first contains notation and fundamental results. The others contain a number of theorems on Riesz summability, ordinary in the second, absolute in the third and strong in the fourth. The substance of chapter II has appeared in the Proceedings of the Glasgow Mathermatical Association [2].
1963-01-01T00:00:00ZShawyer, BruceThe thesis is divided into four chapters. The first contains notation and fundamental results. The others contain a number of theorems on Riesz summability, ordinary in the second, absolute in the third and strong in the fourth. The substance of chapter II has appeared in the Proceedings of the Glasgow Mathermatical Association [2].Global optimization using interval arithmeticMohd, Ismail Binhttp://hdl.handle.net/10023/138242018-06-07T23:16:42Z1987-01-01T00:00:00ZThis thesis contains a description of algorithm, MW, for bounding the global minimizers and globally minimum value of a twice continuously differentiable function f :Rⁿ → R¹ R1 in a compact sub-interval of Rⁿ. The algorithm MW is similar to the algorithm of Hansen (Han-80a] in that interval arithmetic is used together with certain of Hansen's ideas, but is different from Hansen's algorithm in that MW bounds the Kuhn Tucker points corresponding to the global minimizers of f in the given sab-interval. The Kuhn Tucker points are bounded with prescribed precision by using either of the algorithms KMSW [SheW-85c] or MAP [SheW-85b]. Numerical results which are obtained from Triplex [BaCM-82a] [MorC-83a] implementations of H and MW axe presented.
1987-01-01T00:00:00ZMohd, Ismail BinThis thesis contains a description of algorithm, MW, for bounding the global minimizers and globally minimum value of a twice continuously differentiable function f :Rⁿ → R¹ R1 in a compact sub-interval of Rⁿ. The algorithm MW is similar to the algorithm of Hansen (Han-80a] in that interval arithmetic is used together with certain of Hansen's ideas, but is different from Hansen's algorithm in that MW bounds the Kuhn Tucker points corresponding to the global minimizers of f in the given sab-interval. The Kuhn Tucker points are bounded with prescribed precision by using either of the algorithms KMSW [SheW-85c] or MAP [SheW-85b]. Numerical results which are obtained from Triplex [BaCM-82a] [MorC-83a] implementations of H and MW axe presented.Modifications of some algorithms for unconstrained optimizationMirnia-Harikandi, Khttp://hdl.handle.net/10023/138222018-06-07T23:17:02Z1979-01-01T00:00:00ZThis thesis contains an account of several modifications to two algorithms for unconstrained optimization, both of which are due to Gill and Murray. Chapter One contains a brief survey of unconstrained optimization and contains also some results which are used subsequently. Chapter Two contains an account of some work on iterative procedures for the solution of operator equations in Banach spaces due to Wolfe (1978a) in which it is suggested that it may be possible, in certain circumstances, to use high-order iterative procedures rather than Newton's method, thereby obtaining computational advantages. In Chapter Three the Newton-type algorithm of Gill and Murray (1974) is described and the ideas contained in Chapter Two are used to construct some modifications of this algorithm. Chapter Four contains some algorithms for the numerical estimation of both full and b and-type Hessian matrices. These algorithms may be used in conjunction with the optimization algorithms which are described in Chapters Three and Five. In Chapter Five the least-squares algorithm of Gill and Murray (1976) is described and the ideas contained in Chapter Two are used to construct some modifications of this algorithm. Chapter Six contains the computational results which were obtained by using the algorithms which are described in Chapters Three, Four and Five to solve the test problems which are listed in Appendices One and Two.
1979-01-01T00:00:00ZMirnia-Harikandi, KThis thesis contains an account of several modifications to two algorithms for unconstrained optimization, both of which are due to Gill and Murray. Chapter One contains a brief survey of unconstrained optimization and contains also some results which are used subsequently. Chapter Two contains an account of some work on iterative procedures for the solution of operator equations in Banach spaces due to Wolfe (1978a) in which it is suggested that it may be possible, in certain circumstances, to use high-order iterative procedures rather than Newton's method, thereby obtaining computational advantages. In Chapter Three the Newton-type algorithm of Gill and Murray (1974) is described and the ideas contained in Chapter Two are used to construct some modifications of this algorithm. Chapter Four contains some algorithms for the numerical estimation of both full and b and-type Hessian matrices. These algorithms may be used in conjunction with the optimization algorithms which are described in Chapters Three and Five. In Chapter Five the least-squares algorithm of Gill and Murray (1976) is described and the ideas contained in Chapter Two are used to construct some modifications of this algorithm. Chapter Six contains the computational results which were obtained by using the algorithms which are described in Chapters Three, Four and Five to solve the test problems which are listed in Appendices One and Two.Formal methods for deriving Green-type transitional and uniform asymptotic expansions from differential equationsJorna, Siebehttp://hdl.handle.net/10023/138212018-06-07T23:16:40Z1965-01-01T00:00:00ZIn the present work, we develop and illustrate powerful, but straightforward, formal methods for deriving asymptotic expansions from differential equations. In the second chapter, the ‘inverse Frobenius method’ for deriving Stokes expansions is exemplified. The main body of this thesis, however, consists of the development of the new Green-Liouville-Melin transform method, and its detailed application to modified Bessel functions, parabolic cylinder functions, Whittaker functions, Poiseuille functions, confluent hypergeometric functions, and also to periodic Mathieu functions and oblate spheroidal wave functions, all with at least one parameter large⁺. The wide scope of the method is evinced by the fact that treatment of the essentially eigenvalue problem posed by the two last-named cases requires no additional techniques. This method, as will be explained in detail in chapter 3, yields Green-type, transitional and uniform expansions.
The transitional expansions found in this way are usually of a simpler form than those derived by alternative processes (e.g. perturbation theory). To state an example, the asymptotic expansions for the periodic Mathieu functions ce(z,h) and se(z,h) valid near |z| = 1/2π that have been obtained in earlier work contain the complicated parabolic cylinder functions (c.f. Meixner 1948, Sips 1949, Dingle and Müller 1962). By contrast, our methods yield expansions of comparable applicability, but involving only elementary functions. To demonstrate their usefulness, we have fed these expansions into a digital computer and obtained extensive tables for ce(z,h) and se(z,h) in the range 50°≤ z ≤90° . Extracts from these tables and comparisons with correct results are given in §8.71.
Following the chapters on the introduction and applications of the Mellin transform technique, there is some preliminary work on a new method for determining the general term in Green-type expansions. The method is illustrated by detailed calculations for modified Bessel and parabolic cylinder functions.
In the final chapter, we present certain suggestions for further work.
1965-01-01T00:00:00ZJorna, SiebeIn the present work, we develop and illustrate powerful, but straightforward, formal methods for deriving asymptotic expansions from differential equations. In the second chapter, the ‘inverse Frobenius method’ for deriving Stokes expansions is exemplified. The main body of this thesis, however, consists of the development of the new Green-Liouville-Melin transform method, and its detailed application to modified Bessel functions, parabolic cylinder functions, Whittaker functions, Poiseuille functions, confluent hypergeometric functions, and also to periodic Mathieu functions and oblate spheroidal wave functions, all with at least one parameter large⁺. The wide scope of the method is evinced by the fact that treatment of the essentially eigenvalue problem posed by the two last-named cases requires no additional techniques. This method, as will be explained in detail in chapter 3, yields Green-type, transitional and uniform expansions.
The transitional expansions found in this way are usually of a simpler form than those derived by alternative processes (e.g. perturbation theory). To state an example, the asymptotic expansions for the periodic Mathieu functions ce(z,h) and se(z,h) valid near |z| = 1/2π that have been obtained in earlier work contain the complicated parabolic cylinder functions (c.f. Meixner 1948, Sips 1949, Dingle and Müller 1962). By contrast, our methods yield expansions of comparable applicability, but involving only elementary functions. To demonstrate their usefulness, we have fed these expansions into a digital computer and obtained extensive tables for ce(z,h) and se(z,h) in the range 50°≤ z ≤90° . Extracts from these tables and comparisons with correct results are given in §8.71.
Following the chapters on the introduction and applications of the Mellin transform technique, there is some preliminary work on a new method for determining the general term in Green-type expansions. The method is illustrated by detailed calculations for modified Bessel and parabolic cylinder functions.
In the final chapter, we present certain suggestions for further work.Presentations of linear groupsWilliams, Peter D.http://hdl.handle.net/10023/138142018-06-07T23:17:19Z1983-01-01T00:00:00ZIf d(M) denotes the rank of the Schur multiplicator of a finite group G, then a group is efficient if -def G = d(M). Efficient presentations of the simple groups PSL(2,p), p an odd prime > 3, were obtained by J.G. Sunday.This raised the question of whether or not all finite simple groups are efficient.
In this thesis, we investigate the deficiency of the groups PSL(2,pⁿ). J.A. Todd gave presentations for PSL(2,pⁿ) which use large numbers of generators and relations. Starting with these, we obtain, at best, deficiency -1 presentations for PSL(2,2ⁿ) (= SL(2,2ⁿ)) and deficiency -6 presentations for PSL(2,pⁿ), p an odd prime. If pⁿ = -1(mod 4), the latter can be reduced to a deficiency -4 presentation. Efficient presentations for PSL(2,25), PSL(2,27) and PSL(2,49) are obtained.
The Behr-Mennicke presentation for PSL(2,p) is one of the most fundamental in the sense that it forms the basis for others, such as those given by Sunday, Zassenhaus and Sidki. Behr and Mennicke derived their presentation indirectly, and it would be desirable to have a more direct proof. The groups G[sub]p(a) are defined as
< U, R, S | U³ = (UR)² = (US)² = Sᵖ = Rᵗ = (SaRU)³= 1, Sᵃ²R = RS >
where a ε GF(p)* and a²ᵗ = 1 (mod p) . We show that G[sub]p (2) is isomorphic with the Behr-Mennicke presentation for PSL(2,p), p > 3. Conditions are found to discover when Gp (a) is isomorphic with PSL(2,p) and, under these conditions, this provides a direct proof of the Behr-Mennicke presentations. For any odd positive integer m, we show that the groups SL(2,ℤ (m)) and PSL(2,ℤ(m)) are efficient.
1983-01-01T00:00:00ZWilliams, Peter D.If d(M) denotes the rank of the Schur multiplicator of a finite group G, then a group is efficient if -def G = d(M). Efficient presentations of the simple groups PSL(2,p), p an odd prime > 3, were obtained by J.G. Sunday.This raised the question of whether or not all finite simple groups are efficient.
In this thesis, we investigate the deficiency of the groups PSL(2,pⁿ). J.A. Todd gave presentations for PSL(2,pⁿ) which use large numbers of generators and relations. Starting with these, we obtain, at best, deficiency -1 presentations for PSL(2,2ⁿ) (= SL(2,2ⁿ)) and deficiency -6 presentations for PSL(2,pⁿ), p an odd prime. If pⁿ = -1(mod 4), the latter can be reduced to a deficiency -4 presentation. Efficient presentations for PSL(2,25), PSL(2,27) and PSL(2,49) are obtained.
The Behr-Mennicke presentation for PSL(2,p) is one of the most fundamental in the sense that it forms the basis for others, such as those given by Sunday, Zassenhaus and Sidki. Behr and Mennicke derived their presentation indirectly, and it would be desirable to have a more direct proof. The groups G[sub]p(a) are defined as
< U, R, S | U³ = (UR)² = (US)² = Sᵖ = Rᵗ = (SaRU)³= 1, Sᵃ²R = RS >
where a ε GF(p)* and a²ᵗ = 1 (mod p) . We show that G[sub]p (2) is isomorphic with the Behr-Mennicke presentation for PSL(2,p), p > 3. Conditions are found to discover when Gp (a) is isomorphic with PSL(2,p) and, under these conditions, this provides a direct proof of the Behr-Mennicke presentations. For any odd positive integer m, we show that the groups SL(2,ℤ (m)) and PSL(2,ℤ(m)) are efficient.A study of the infinite dimensional linear and symplectic groupsArrell, David G.http://hdl.handle.net/10023/138102018-06-07T23:16:43Z1979-01-01T00:00:00ZBy a linear group we shall mean essentially a group of invertible matrices over a ring. Thus, we include in our class of linear groups the 'classical' geometric groups. These are the general linear group, GL[sub]n(F), the orthogonal groups, 0[sub]n (F) and the syraplectic groups Sp[sub]n(F). The normal and subnormal subgroup structure of these groups is well known and has been the subject of much investigation since the turn of the century. We study here the normal and subnormal structure of some of their infinite dimensional counterparts, namely, the infinite dimensional linear group GL(Ω,R), for arbitrary rings R, and the infinite dimensional syraplectic group Sp(Ω,R), for commutative rings R with identity. We shall see that a key role in the classification of the normal and subnormal subgroups of GL(Ω,R) and Sp(Ω,R) is played by the 'elementary' normal subgroups E(Ω,R) and ESp(Ω,R). We shall also see that, in the case of the infinite dimensional linear group, the normal subgroup structure depends very much upon the way in which R is generated as a right R-module. We shall also give a presentation for the 'elementary' subgroup E(Ω,R) when R is a division ring.
1979-01-01T00:00:00ZArrell, David G.By a linear group we shall mean essentially a group of invertible matrices over a ring. Thus, we include in our class of linear groups the 'classical' geometric groups. These are the general linear group, GL[sub]n(F), the orthogonal groups, 0[sub]n (F) and the syraplectic groups Sp[sub]n(F). The normal and subnormal subgroup structure of these groups is well known and has been the subject of much investigation since the turn of the century. We study here the normal and subnormal structure of some of their infinite dimensional counterparts, namely, the infinite dimensional linear group GL(Ω,R), for arbitrary rings R, and the infinite dimensional syraplectic group Sp(Ω,R), for commutative rings R with identity. We shall see that a key role in the classification of the normal and subnormal subgroups of GL(Ω,R) and Sp(Ω,R) is played by the 'elementary' normal subgroups E(Ω,R) and ESp(Ω,R). We shall also see that, in the case of the infinite dimensional linear group, the normal subgroup structure depends very much upon the way in which R is generated as a right R-module. We shall also give a presentation for the 'elementary' subgroup E(Ω,R) when R is a division ring.A variable input boundary problem in contaminant transportWarner, G. C.http://hdl.handle.net/10023/138012018-06-07T23:16:52Z1997-01-01T00:00:00ZThis thesis considers the large-time behaviour of the equation
(∂(u+uᵖ) )/( ∂t ) + Q(t) ∂u/( ∂x) = ∂²u/∂x² p>0, r≥ -1
With 0 ≤ 𝓍 < ∞, t ≥ 0 and Q (t) ~ tʳ, t ∞. This equation models, after suitable scalings are introduced, the one-dimensional flow of a solute through a porous medium with the solute undergoing adsorption by the solid matrix. We consider two models for the contaminant input at 𝓍= 0, the first being continuous input and the second being an initial pulse of contaminant which terminates after a finite time. Thus the total mass of the solute both adsorbed and in solution is considered to be dependent on time. It is found that the asymptotic solution depends crucially on both p and r. In finding the asymptotic solution, a similarity variable is introduced which for p ≥ 1 may involve spatial translation. We also have that when p < 1 interfaces appear and hence we have bounded support, whilst for p≥1 we do not. The principal role of r is to determine the balance between diffusion and convection effects. In the continuous input case this balance is independent of p, whilst in the pulse problem p is also involved in determining the balance.
1997-01-01T00:00:00ZWarner, G. C.This thesis considers the large-time behaviour of the equation
(∂(u+uᵖ) )/( ∂t ) + Q(t) ∂u/( ∂x) = ∂²u/∂x² p>0, r≥ -1
With 0 ≤ 𝓍 < ∞, t ≥ 0 and Q (t) ~ tʳ, t ∞. This equation models, after suitable scalings are introduced, the one-dimensional flow of a solute through a porous medium with the solute undergoing adsorption by the solid matrix. We consider two models for the contaminant input at 𝓍= 0, the first being continuous input and the second being an initial pulse of contaminant which terminates after a finite time. Thus the total mass of the solute both adsorbed and in solution is considered to be dependent on time. It is found that the asymptotic solution depends crucially on both p and r. In finding the asymptotic solution, a similarity variable is introduced which for p ≥ 1 may involve spatial translation. We also have that when p < 1 interfaces appear and hence we have bounded support, whilst for p≥1 we do not. The principal role of r is to determine the balance between diffusion and convection effects. In the continuous input case this balance is independent of p, whilst in the pulse problem p is also involved in determining the balance.The prediction of thermal phase-change boundaries and associated temperature distributionsWood, A. S.http://hdl.handle.net/10023/137972018-06-07T23:16:53Z1984-01-01T00:00:00ZThe past three decades have seen a fast expanding interest in thermal problems exhibiting a change of phase, more commonly known as Stefan problems. With the rapid advance in computer technology the use and expansion of numerical simulation schemes has been responsible for large advances in this field. The increasing size of computers has led to more sophisticated and complex numerical solutions becoming feasible from a computational point of view. On the other hand, part of this interest has developed from industrial quarters where a knowledge of the location of a melting/freezing boundary may be of critical importance for certain processes. Much experimental work has been completed in this field. However, it is still useful to be able to obtain quick, accurate numerical solutions to such problems and it is with this in mind that this thesis is presented. Ideas from both of the above areas of interest are treated. In the first case a simple to program and computationally efficient numerical scheme is proposed for solving one dimensional Stefan problems and its merits are discussed in relation to several of the more common existing solution schemes. This scheme is then modified to cater for a two dimensional problem which crudely imitates a possible heating configuration in some industrial processes. The problem, with its attendant difficulties, is first approximated by a 'test' problem which is constructed so as to admit an analytic solution. This allows assessment of the numerical procedure in two dimensions. In the course of this work a pseudo-analytic solution was obtained for the original two dimensional problem. Finally, in collaboration with the British Gas Corporation, a complex industrial freezing problem is discussed concerning the flow of liquid through an enclosed channel. Some simplifying assumptions are proposed to reduce the problem to a form for which a relatively simple numerical scheme may be adopted. Several simulations are completed to examine the effect of varying physical parameters on the solution and in particular to test for situations of blockage or steady-state.
1984-01-01T00:00:00ZWood, A. S.The past three decades have seen a fast expanding interest in thermal problems exhibiting a change of phase, more commonly known as Stefan problems. With the rapid advance in computer technology the use and expansion of numerical simulation schemes has been responsible for large advances in this field. The increasing size of computers has led to more sophisticated and complex numerical solutions becoming feasible from a computational point of view. On the other hand, part of this interest has developed from industrial quarters where a knowledge of the location of a melting/freezing boundary may be of critical importance for certain processes. Much experimental work has been completed in this field. However, it is still useful to be able to obtain quick, accurate numerical solutions to such problems and it is with this in mind that this thesis is presented. Ideas from both of the above areas of interest are treated. In the first case a simple to program and computationally efficient numerical scheme is proposed for solving one dimensional Stefan problems and its merits are discussed in relation to several of the more common existing solution schemes. This scheme is then modified to cater for a two dimensional problem which crudely imitates a possible heating configuration in some industrial processes. The problem, with its attendant difficulties, is first approximated by a 'test' problem which is constructed so as to admit an analytic solution. This allows assessment of the numerical procedure in two dimensions. In the course of this work a pseudo-analytic solution was obtained for the original two dimensional problem. Finally, in collaboration with the British Gas Corporation, a complex industrial freezing problem is discussed concerning the flow of liquid through an enclosed channel. Some simplifying assumptions are proposed to reduce the problem to a form for which a relatively simple numerical scheme may be adopted. Several simulations are completed to examine the effect of varying physical parameters on the solution and in particular to test for situations of blockage or steady-state.Compressible boundary layers with sharp pressure gradientsReader-Harris, Michael Johnhttp://hdl.handle.net/10023/137952018-06-07T23:16:54Z1981-01-01T00:00:00ZThe work of this thesis was undertaken as a C.A.S.E. award project in collaboration with Rolls-Royce to examine compressible laminar boundary layers with sharp adverse pressure-gradients. Much of the work is devoted to the solution of two important particular problems. The first flow considered is that along a semi-infinite flat plate with uniform pressure when X < X₀ and with the pressure for X > X₀ being so chosen that the boundary layer is just on the point of separation for all X > X₀. Immediately downstream of X₀ there is a sharp pressure rise to which the flow reacts mainly in a thin inner sublayer; so inner and outer asymptotic expansions are derived and matched for the stream function and a function of the temperature. Throughout the thesis the ratio of the viscosity to the absolute temperature is taken to be a function of x, the distance along the wall, alone, and the Illingworth-Stewartson transformation is applied. The Prandtl number, σ, is taken to be of order unity and detailed results are presented for σ= 1 and 0.72. The second flow considered is that along a finite flat plate where the transformed external velocity U₁(X) is chosen such that
U₁(X) = u₀(-X/L)[super]ε, where O< ε <<1,
is the transformed length of the plate and X represents transformed distance downstream from the trailing edge. The skin friction, position of separation and heat transfer right up to separation are determined. On the basis of these two solutions, another solution which is not presented in detail, and a solution (due to Curie) to a fourth sharp pressure gradient problem, a general Stratford-type method for computing compressible boundary layers is derived, which may be used to predict the position of separation, skin friction, heat transfer, displacement and momentum thicknesses for a compressible boundary layer with an unfavourable pressure gradient. In all this work techniques of series analysis are used to good effect. This led us to look at another boundary-layer problem in which such techniques could be used, one in which two parallel infinite disks are initially rotating with angular velocity Ω about a common axis in incompressible fluid, the appropriate Reynolds number being very large. Suddenly the angular velocity of one of the disks is reversed. A new examination of this problem is presented in the appendix to the thesis.
1981-01-01T00:00:00ZReader-Harris, Michael JohnThe work of this thesis was undertaken as a C.A.S.E. award project in collaboration with Rolls-Royce to examine compressible laminar boundary layers with sharp adverse pressure-gradients. Much of the work is devoted to the solution of two important particular problems. The first flow considered is that along a semi-infinite flat plate with uniform pressure when X < X₀ and with the pressure for X > X₀ being so chosen that the boundary layer is just on the point of separation for all X > X₀. Immediately downstream of X₀ there is a sharp pressure rise to which the flow reacts mainly in a thin inner sublayer; so inner and outer asymptotic expansions are derived and matched for the stream function and a function of the temperature. Throughout the thesis the ratio of the viscosity to the absolute temperature is taken to be a function of x, the distance along the wall, alone, and the Illingworth-Stewartson transformation is applied. The Prandtl number, σ, is taken to be of order unity and detailed results are presented for σ= 1 and 0.72. The second flow considered is that along a finite flat plate where the transformed external velocity U₁(X) is chosen such that
U₁(X) = u₀(-X/L)[super]ε, where O< ε <<1,
is the transformed length of the plate and X represents transformed distance downstream from the trailing edge. The skin friction, position of separation and heat transfer right up to separation are determined. On the basis of these two solutions, another solution which is not presented in detail, and a solution (due to Curie) to a fourth sharp pressure gradient problem, a general Stratford-type method for computing compressible boundary layers is derived, which may be used to predict the position of separation, skin friction, heat transfer, displacement and momentum thicknesses for a compressible boundary layer with an unfavourable pressure gradient. In all this work techniques of series analysis are used to good effect. This led us to look at another boundary-layer problem in which such techniques could be used, one in which two parallel infinite disks are initially rotating with angular velocity Ω about a common axis in incompressible fluid, the appropriate Reynolds number being very large. Suddenly the angular velocity of one of the disks is reversed. A new examination of this problem is presented in the appendix to the thesis.The numerical solution of boundary value problems in partial differential equationsKeast, Patrickhttp://hdl.handle.net/10023/137932018-06-07T23:16:31Z1967-01-01T00:00:00Z1967-01-01T00:00:00ZKeast, PatrickOn the fast and accurate computer solution of partial differential systemsHill, Michael T.http://hdl.handle.net/10023/137912018-06-07T23:16:56Z1974-01-01T00:00:00ZTwo methods are presented for use on an electronic computer for the solution of partial differential systems. The first is concerned with accurate solutions of differential equations. It is equally applicable to ordinary differential equations and partial differential equations, and can be used for parabolic, hyperbolic or elliptic systems, and also for non-linear and mixed systems. It can be used in conjunction with existing schemes. Conversely, the method can be used as a very fast method of obtaining a rough solution of the system. It has an additional advantage over traditional higher order methods in that it does not require extra boundary conditions. The second method is concerned with the acceleration of the convergence rate in the solution of hyperbolic systems. The number of iterations has been reduced from tens of thousands with the traditional Lax-Wendroff methods to the order of twenty iterations. Analyses for both the differential and the difference systems are presented. Again the method is easily added to existing programs. The two methods may be used together to give one fast and accurate method.
1974-01-01T00:00:00ZHill, Michael T.Two methods are presented for use on an electronic computer for the solution of partial differential systems. The first is concerned with accurate solutions of differential equations. It is equally applicable to ordinary differential equations and partial differential equations, and can be used for parabolic, hyperbolic or elliptic systems, and also for non-linear and mixed systems. It can be used in conjunction with existing schemes. Conversely, the method can be used as a very fast method of obtaining a rough solution of the system. It has an additional advantage over traditional higher order methods in that it does not require extra boundary conditions. The second method is concerned with the acceleration of the convergence rate in the solution of hyperbolic systems. The number of iterations has been reduced from tens of thousands with the traditional Lax-Wendroff methods to the order of twenty iterations. Analyses for both the differential and the difference systems are presented. Again the method is easily added to existing programs. The two methods may be used together to give one fast and accurate method.Alternating direction methods for hyperbolic systemsGourlay, A. R.http://hdl.handle.net/10023/137882018-06-07T23:16:23Z1966-01-01T00:00:00Z1966-01-01T00:00:00ZGourlay, A. R.Alternating direction implicit methods for partial differential equationsFairweather, Graemehttp://hdl.handle.net/10023/137842018-06-07T23:16:27Z1966-01-01T00:00:00Z1966-01-01T00:00:00ZFairweather, GraemeThe use of non-polynomial interpolants in the numerical solution of ordinary differential equationsShaw, Brianhttp://hdl.handle.net/10023/137832018-06-07T23:17:28Z1966-01-01T00:00:00Z1966-01-01T00:00:00ZShaw, BrianFinite difference methods for non-linear hyperbolic systemsMorris, John Ll.http://hdl.handle.net/10023/137822018-06-07T14:37:42Z1968-01-01T00:00:00Z1968-01-01T00:00:00ZMorris, John Ll.Inner product quadrature formulasGribble, Julian de Gruchyhttp://hdl.handle.net/10023/137802018-06-07T23:16:56Z1979-01-01T00:00:00ZWe investigate an approach to approximating the integral
(0.1) ⨍[sub]R w(x)f(x)g(x)dx ≡ I (f;g),
where R is a region in one-dimensional Euclidean space, and w a weight function. Since (0.1) may be regarded as a continuous bi-linear functional in f and g we approximate it by a discrete bi-linear functional, which we term an Inner Product Quadrature Formula (I.P.Q.F.).
(0.2) Q(f;g) ≡ f̲ᵀAg̲,
Where f̲ᵀ = (Sₒ(f), . . . , s[sub]m(f))ᵀ
g̲ᵀ = (Tₒ(g), . . . , T[sub]n(g)) ᵀ
A = (aᵢ[sub]j)ᵐi=o,ⁿj=0,
And a[sub]i[sub]j are real numbers, 𝛴 ᵐi=0 𝛴ⁿj =0 |aᵢ [sub]j | > 0
The so-called elementary functionals {Sᵢ}ᵐi=0 and {T[sub]j}ⁿj=0 are two sets of linearly independent linear functionals, acting f and g respectively, defined over a certain subspace of functions to which f and g belong. The simplest example of these functionals is function evaluation at a given point.
The matrix A is determined by requiring (0.2) to be exact for certain classes of functions f and g, say
F𝜀𝛷𝛾 ≡ {𝛷₀, . . . , 𝛷ᵧ}, 𝛾≥0
G𝜀𝛹𝛿 ≡ {𝛹₀, . . . , 𝛹[sub] 𝛿} 𝛿≥0
In Chapter 1 we introduce the concept of I.P.Q.F. in more detail and make some general comments about approaches available when examining numerical integration. After explaining in some detail why we feel I.P.Q.F. are a useful tool in §2.1, we proceed in the remainder of Chapter 2 to investigate various conditions which may be placed on 𝛷ᵞ, 𝛹[super] 𝛿 {Sᵢ}ᵐi=0 and {T[sub]j}ⁿj=0 in order to guarantee the existence of I.P.Q.F. exact when F𝜀𝛷𝛾 and G𝜀𝛹𝛿.
In particular we investigate the question of maximizing 𝛾+ 𝛿. In the case where 𝛷ᵢ and 𝛹[sub]j are the standard monomials of degree i and j respectively, some results have already been published in B.I.T. (1977) p. 392-408. We investigate various choices of 𝛷ᵢ and 𝛹[sub]j :
(a) {𝛷ᵢ}ᵐ⁺¹ I = 0 (i.e. 𝛾 = m+1) and {𝛹[sub]j}ᵐ[sub]j = 0 (i.e. 𝛿 = m) being Tchebychev sets (§2.7),
(b) {𝛷ᵢ}²ᵐ⁺¹ I = 0 (i.e. 𝛾 = 2m+1) being a Tchebychev set and 𝛹[super]𝛿 contains only one function (i.e. 𝛿 = 0) (§2.6)
(c) 𝛷ᵢ ≡ (𝛷[sub]l)ⁱ, i=0,1, . . . and 𝛷ᵢ = 𝛹ᵢ, i= 0, 1, … (§2.8).
In Chapter 3 we consider the question of compounding I.P.Q.F. both in the classical sense, and, briefly, by examining spline functions, regarding them as providing a link between an I.P.Q.F on one hand and a compounded I.P.Q.F. on the other. Various methods of theoretically estimating the errors involved are considered in Chapter M-. In the fifth Chapter we examine various ways in which the concept of I.P.Q.F. might (or might not) be extended. Finally, we make some brief comments about the possible applications of I.P.Q.F., and give a few examples.
1979-01-01T00:00:00ZGribble, Julian de GruchyWe investigate an approach to approximating the integral
(0.1) ⨍[sub]R w(x)f(x)g(x)dx ≡ I (f;g),
where R is a region in one-dimensional Euclidean space, and w a weight function. Since (0.1) may be regarded as a continuous bi-linear functional in f and g we approximate it by a discrete bi-linear functional, which we term an Inner Product Quadrature Formula (I.P.Q.F.).
(0.2) Q(f;g) ≡ f̲ᵀAg̲,
Where f̲ᵀ = (Sₒ(f), . . . , s[sub]m(f))ᵀ
g̲ᵀ = (Tₒ(g), . . . , T[sub]n(g)) ᵀ
A = (aᵢ[sub]j)ᵐi=o,ⁿj=0,
And a[sub]i[sub]j are real numbers, 𝛴 ᵐi=0 𝛴ⁿj =0 |aᵢ [sub]j | > 0
The so-called elementary functionals {Sᵢ}ᵐi=0 and {T[sub]j}ⁿj=0 are two sets of linearly independent linear functionals, acting f and g respectively, defined over a certain subspace of functions to which f and g belong. The simplest example of these functionals is function evaluation at a given point.
The matrix A is determined by requiring (0.2) to be exact for certain classes of functions f and g, say
F𝜀𝛷𝛾 ≡ {𝛷₀, . . . , 𝛷ᵧ}, 𝛾≥0
G𝜀𝛹𝛿 ≡ {𝛹₀, . . . , 𝛹[sub] 𝛿} 𝛿≥0
In Chapter 1 we introduce the concept of I.P.Q.F. in more detail and make some general comments about approaches available when examining numerical integration. After explaining in some detail why we feel I.P.Q.F. are a useful tool in §2.1, we proceed in the remainder of Chapter 2 to investigate various conditions which may be placed on 𝛷ᵞ, 𝛹[super] 𝛿 {Sᵢ}ᵐi=0 and {T[sub]j}ⁿj=0 in order to guarantee the existence of I.P.Q.F. exact when F𝜀𝛷𝛾 and G𝜀𝛹𝛿.
In particular we investigate the question of maximizing 𝛾+ 𝛿. In the case where 𝛷ᵢ and 𝛹[sub]j are the standard monomials of degree i and j respectively, some results have already been published in B.I.T. (1977) p. 392-408. We investigate various choices of 𝛷ᵢ and 𝛹[sub]j :
(a) {𝛷ᵢ}ᵐ⁺¹ I = 0 (i.e. 𝛾 = m+1) and {𝛹[sub]j}ᵐ[sub]j = 0 (i.e. 𝛿 = m) being Tchebychev sets (§2.7),
(b) {𝛷ᵢ}²ᵐ⁺¹ I = 0 (i.e. 𝛾 = 2m+1) being a Tchebychev set and 𝛹[super]𝛿 contains only one function (i.e. 𝛿 = 0) (§2.6)
(c) 𝛷ᵢ ≡ (𝛷[sub]l)ⁱ, i=0,1, . . . and 𝛷ᵢ = 𝛹ᵢ, i= 0, 1, … (§2.8).
In Chapter 3 we consider the question of compounding I.P.Q.F. both in the classical sense, and, briefly, by examining spline functions, regarding them as providing a link between an I.P.Q.F on one hand and a compounded I.P.Q.F. on the other. Various methods of theoretically estimating the errors involved are considered in Chapter M-. In the fifth Chapter we examine various ways in which the concept of I.P.Q.F. might (or might not) be extended. Finally, we make some brief comments about the possible applications of I.P.Q.F., and give a few examples.Interval methods for non-linear systemsShearer, J. M.http://hdl.handle.net/10023/137792018-06-07T14:55:57Z1986-01-01T00:00:00ZIn numerical mathematics, there is a need for methods which provide a user with the solution to his problem without requiring him to understand the mathematics underlying the method of solution. Such a method involves computable tests to determine whether or not a solution exists in a given region, and whether, if it exists, such a solution may be found by using the given method. Two valuable tools for the implementation of such methods are interval mathematics and symbolic computation. In. practice all computers have memories of finite size and cannot perform exact arithmetic. Therefore, in addition to the error which is inherent in a given numerical method, namely truncation error, there is also the error due to rounding. Using interval arithmetic, computable tests which guarantee the existence of a solution to a given problem in a given region, and the convergence of a particular iterative method to this solution, become practically realizable. This is not possible using real arithmetic due to the accumulation of rounding error on a computer. The advent of packages which allow symbolic computations to be carried out on a given computer is an important advance for computational numerical mathematics. In particular, the ability to compute derivatives automatically removes the need for a user to supply them, thus eliminating a major source of error in the use of methods requiring first or higher derivatives. In this thesis some methods which use interval arithmetic and symbolic computation for the solution of systems of nonlinear algebraic equations are presented. Some algorithms based on the symmetric single-step algorithm are described. These methods however do not possess computable existence, uniqueness, and convergence tests. Algorithms which do possess such tests, based on the Krawczyk-Moore algorithm are also presented. A simple package which allows symbolic computations to be carried out is described. Several applications for such a package are given. In particular, an interval form of Brown's method is presented.
1986-01-01T00:00:00ZShearer, J. M.In numerical mathematics, there is a need for methods which provide a user with the solution to his problem without requiring him to understand the mathematics underlying the method of solution. Such a method involves computable tests to determine whether or not a solution exists in a given region, and whether, if it exists, such a solution may be found by using the given method. Two valuable tools for the implementation of such methods are interval mathematics and symbolic computation. In. practice all computers have memories of finite size and cannot perform exact arithmetic. Therefore, in addition to the error which is inherent in a given numerical method, namely truncation error, there is also the error due to rounding. Using interval arithmetic, computable tests which guarantee the existence of a solution to a given problem in a given region, and the convergence of a particular iterative method to this solution, become practically realizable. This is not possible using real arithmetic due to the accumulation of rounding error on a computer. The advent of packages which allow symbolic computations to be carried out on a given computer is an important advance for computational numerical mathematics. In particular, the ability to compute derivatives automatically removes the need for a user to supply them, thus eliminating a major source of error in the use of methods requiring first or higher derivatives. In this thesis some methods which use interval arithmetic and symbolic computation for the solution of systems of nonlinear algebraic equations are presented. Some algorithms based on the symmetric single-step algorithm are described. These methods however do not possess computable existence, uniqueness, and convergence tests. Algorithms which do possess such tests, based on the Krawczyk-Moore algorithm are also presented. A simple package which allows symbolic computations to be carried out is described. Several applications for such a package are given. In particular, an interval form of Brown's method is presented.Statistical problems in measuring surface ozone and modelling its patternsHutchison, Paul Stewarthttp://hdl.handle.net/10023/137732018-06-07T14:58:44Z1996-01-01T00:00:00ZThe thesis examines ground level air pollution data supplied by ITE Bush, Penicuik, Midlothian, Scotland. There is a brief examination of sulphur dioxide concentration data, but the Thesis is primarily concerned with ozone. The diurnal behaviour of ozone is the major topic, and a new methodology of classification of 'ozone days' is introduced and discussed. In chapter 2, the inverse Gaussian distribution is considered and rejected as a possible alternative to the standard approach of using the lognormal as a model for the frequency distribution of observed sulphur dioxide concentrations. In chapter 3, the behaviour of digital gas pollution analysers is investigated by making use of data obtained from two such machines operating side by side. A time series model of the differences between the readings obtained from the two machines is considered, and possible effects on modelling discussed. In chapter 4, the changes in the diurnal behaviour of ozone over a year are examined. A new approach involving a distortion of the time axis is shown to give diurnal ozone curves more homogeneous properties and have beneficial effects for modelling purposes. Chapter 5 extends the analysis of the diurnal behaviour of ozone begun in chapter 4 by considering individual 'ozone days' and attempting to classify them as one of several typical 'types' of day. The time distortion method introduced in chapter 4 is used, and a new classification methodology is introduced for considering data of this type. The statistical properties of this method are discussed in chapter 6.
1996-01-01T00:00:00ZHutchison, Paul StewartThe thesis examines ground level air pollution data supplied by ITE Bush, Penicuik, Midlothian, Scotland. There is a brief examination of sulphur dioxide concentration data, but the Thesis is primarily concerned with ozone. The diurnal behaviour of ozone is the major topic, and a new methodology of classification of 'ozone days' is introduced and discussed. In chapter 2, the inverse Gaussian distribution is considered and rejected as a possible alternative to the standard approach of using the lognormal as a model for the frequency distribution of observed sulphur dioxide concentrations. In chapter 3, the behaviour of digital gas pollution analysers is investigated by making use of data obtained from two such machines operating side by side. A time series model of the differences between the readings obtained from the two machines is considered, and possible effects on modelling discussed. In chapter 4, the changes in the diurnal behaviour of ozone over a year are examined. A new approach involving a distortion of the time axis is shown to give diurnal ozone curves more homogeneous properties and have beneficial effects for modelling purposes. Chapter 5 extends the analysis of the diurnal behaviour of ozone begun in chapter 4 by considering individual 'ozone days' and attempting to classify them as one of several typical 'types' of day. The time distortion method introduced in chapter 4 is used, and a new classification methodology is introduced for considering data of this type. The statistical properties of this method are discussed in chapter 6.A study of character recognition using geometric moments under conditions of simple and non-simple lossTucker, N. D.http://hdl.handle.net/10023/137682018-06-13T16:08:18Z1974-01-01T00:00:00ZThe theory of Loss Functions Is a fundamental part of Statistical Decision Theory and of Pattern Recognition. However It is a subject which few have studied In detail. This thesis is an attempt to develop a simple character recognition process In which losses may be Implemented when and where necessary. After a brief account of the history of Loss Functions and an Introduction to elementary Decision Theory, some examples have been constructed to demonstrate how various decision boundaries approximate to the optimal boundary and what Increase In loss would be associated with these sub-optimal boundaries. The results show that the Euclidean and Hamming distance discriminants can be sufficiently close approximations that the decision process may be legitimately simplified by the use of these linear boundaries. Geometric moments were adopted for the computer simulation of the recognition process because each moment is closely related to the symmetry and structure of a character, unlike many other features. The theory of Moments is discussed, in particular their geometrical properties. A brief description of the programs used in the simulation follows. Two different data sets were investigated, the first being hand-drawn capitals and the second machine-scanned lower case type script. This latter set was in the form of a message, which presented interesting programming problems in itself. The results from the application of different discriminants to these sets under conditions of simple loss are analysed and the recognition efficiencies are found to vary between about 30% and. 99% depending on the number of moments being used and the type of discriminant. Next certain theoretical problems are studied. The relations between the rejection rate, the error rate and the rejection threshold are discussed both theoretically and practically. Also an attempt is made to predict theoretically the variation of efficiency with the number of moments used in the discrimination. This hypothesis is then tested on the data already calculated and shown to be true within reasonable limits. A discussion of moment ordering by defining their re-solving powers is undertaken and it seems likely that the moments normally used unordered are among the most satisfactory. Finally, some time is devoted towards methods of improving recognition efficiency. Information content is discussed along with the possibilities inherent in the use of digraph and trigraph probabilities. A breakdown of the errors in the recognition system adopted here is presented along with suggestions to improve the technique. The execution time of the different decision mechanisms is then inspected and a refined 2-Stage method is produced. Lastly the various methods by which a decision mechanism might be improved are united under a common loss matrix, formed by a product of matrices each of which represents a particular facet of the recognition problem.
1974-01-01T00:00:00ZTucker, N. D.The theory of Loss Functions Is a fundamental part of Statistical Decision Theory and of Pattern Recognition. However It is a subject which few have studied In detail. This thesis is an attempt to develop a simple character recognition process In which losses may be Implemented when and where necessary. After a brief account of the history of Loss Functions and an Introduction to elementary Decision Theory, some examples have been constructed to demonstrate how various decision boundaries approximate to the optimal boundary and what Increase In loss would be associated with these sub-optimal boundaries. The results show that the Euclidean and Hamming distance discriminants can be sufficiently close approximations that the decision process may be legitimately simplified by the use of these linear boundaries. Geometric moments were adopted for the computer simulation of the recognition process because each moment is closely related to the symmetry and structure of a character, unlike many other features. The theory of Moments is discussed, in particular their geometrical properties. A brief description of the programs used in the simulation follows. Two different data sets were investigated, the first being hand-drawn capitals and the second machine-scanned lower case type script. This latter set was in the form of a message, which presented interesting programming problems in itself. The results from the application of different discriminants to these sets under conditions of simple loss are analysed and the recognition efficiencies are found to vary between about 30% and. 99% depending on the number of moments being used and the type of discriminant. Next certain theoretical problems are studied. The relations between the rejection rate, the error rate and the rejection threshold are discussed both theoretically and practically. Also an attempt is made to predict theoretically the variation of efficiency with the number of moments used in the discrimination. This hypothesis is then tested on the data already calculated and shown to be true within reasonable limits. A discussion of moment ordering by defining their re-solving powers is undertaken and it seems likely that the moments normally used unordered are among the most satisfactory. Finally, some time is devoted towards methods of improving recognition efficiency. Information content is discussed along with the possibilities inherent in the use of digraph and trigraph probabilities. A breakdown of the errors in the recognition system adopted here is presented along with suggestions to improve the technique. The execution time of the different decision mechanisms is then inspected and a refined 2-Stage method is produced. Lastly the various methods by which a decision mechanism might be improved are united under a common loss matrix, formed by a product of matrices each of which represents a particular facet of the recognition problem.A study of the work and methods of Henry Briggs, with special reference to the early history of interpolationWaterson, Andrewhttp://hdl.handle.net/10023/137602018-06-13T23:17:37Z1941-01-01T00:00:00Z1941-01-01T00:00:00ZWaterson, AndrewTransformations in regression, estimation, testing and modellingParker, Imeldahttp://hdl.handle.net/10023/137592018-06-06T23:16:31Z1988-01-01T00:00:00ZTransformation is a powerful tool for model building. In regression the response variable is transformed in order to achieve the usual assumptions of normality, constant variance and additivity of effects. Here the normality assumption is replaced by the Laplace distributional assumption, appropriate when more large errors occur than would be expected if the errors were normally distributed. The parametric model is enlarged to include a transformation parameter and a likelihood procedure is adopted for estimating this parameter simultaneously with other parameters of interest. Diagnostic methods are described for assessing the influence of individual observations on the choice of transformation. Examples are presented. In distribution methodology the independent responses are transformed in order that a distributional assumption is satisfied for the transformed data. Here the interest is in the family of distributions which are not dependent on an unknown shape parameter. The gamma distribution (known order), with special case the exponential distribution, is a member of this family. An information number approach is proposed for transforming a known distribution to the gamma distribution (known order). The approach provides an insight into the large-sample behaviour of the likelihood procedure considered by Draper and Guttman (1968) for investigating transformations of data which allow the transformed observations to follow a gamma distribution. The information number approach is illustrated for three examples end the improvement towards the gamma distribution introduced by transformation is measured numerically and graphically. A graphical procedure is proposed for the general case of investigating transformations of data which allow the transformed observations to follow a distribution dependent on unknown threshold and scale parameters. The procedure is extended to include model testing and estimation for any distribution which with the aid of a power transformation can be put in the simple form of a distribution that is not dependent on an unknown shape parameter. The procedure is based on a ratio, R(y), which is constructed from the power transformation. Also described is a ratio-based technique for estimating the threshold parameter in important parametric models, including the three-parameter Weibull and lognormal distributions. Ratio estimation for the weibull distribution is assessed and compared with the modified maximum likelihood estimation of Cohen and Whitten (1982) in terms of bias and root mean squared error, by means of a simulation study. The methods are illustrated with several examples and extend naturally to singly Type 1 and Type 2 censored data.
1988-01-01T00:00:00ZParker, ImeldaTransformation is a powerful tool for model building. In regression the response variable is transformed in order to achieve the usual assumptions of normality, constant variance and additivity of effects. Here the normality assumption is replaced by the Laplace distributional assumption, appropriate when more large errors occur than would be expected if the errors were normally distributed. The parametric model is enlarged to include a transformation parameter and a likelihood procedure is adopted for estimating this parameter simultaneously with other parameters of interest. Diagnostic methods are described for assessing the influence of individual observations on the choice of transformation. Examples are presented. In distribution methodology the independent responses are transformed in order that a distributional assumption is satisfied for the transformed data. Here the interest is in the family of distributions which are not dependent on an unknown shape parameter. The gamma distribution (known order), with special case the exponential distribution, is a member of this family. An information number approach is proposed for transforming a known distribution to the gamma distribution (known order). The approach provides an insight into the large-sample behaviour of the likelihood procedure considered by Draper and Guttman (1968) for investigating transformations of data which allow the transformed observations to follow a gamma distribution. The information number approach is illustrated for three examples end the improvement towards the gamma distribution introduced by transformation is measured numerically and graphically. A graphical procedure is proposed for the general case of investigating transformations of data which allow the transformed observations to follow a distribution dependent on unknown threshold and scale parameters. The procedure is extended to include model testing and estimation for any distribution which with the aid of a power transformation can be put in the simple form of a distribution that is not dependent on an unknown shape parameter. The procedure is based on a ratio, R(y), which is constructed from the power transformation. Also described is a ratio-based technique for estimating the threshold parameter in important parametric models, including the three-parameter Weibull and lognormal distributions. Ratio estimation for the weibull distribution is assessed and compared with the modified maximum likelihood estimation of Cohen and Whitten (1982) in terms of bias and root mean squared error, by means of a simulation study. The methods are illustrated with several examples and extend naturally to singly Type 1 and Type 2 censored data.Parameterisation-invariant versions of Wald testsLarsen, Pia Veldthttp://hdl.handle.net/10023/137502018-06-06T23:16:57Z1999-01-01T00:00:00ZAlthough Wald tests form one of the major classes of hypothesis tests, they suffer from the well-known major drawback that they are not invariant under reparameterisation. This thesis uses the differential-geometric concept of a yoke to introduce one-parameter families of geometric Wald statistics, which are parameterisation-invariant statistics in the spirit of the traditional Wald statistics. Both the geometric Wald statistics based on the expected likelihood yokes and those based on the observed likelihood yokes are investigated. Bartlett-type adjustments of the geometric Wald statistics are obtained, in order to improve the accuracy of the chi-squared approximations to their distributions under the null hypothesis.
1999-01-01T00:00:00ZLarsen, Pia VeldtAlthough Wald tests form one of the major classes of hypothesis tests, they suffer from the well-known major drawback that they are not invariant under reparameterisation. This thesis uses the differential-geometric concept of a yoke to introduce one-parameter families of geometric Wald statistics, which are parameterisation-invariant statistics in the spirit of the traditional Wald statistics. Both the geometric Wald statistics based on the expected likelihood yokes and those based on the observed likelihood yokes are investigated. Bartlett-type adjustments of the geometric Wald statistics are obtained, in order to improve the accuracy of the chi-squared approximations to their distributions under the null hypothesis.Estimating the parameters in mixtures of circular and spherical distributionsKoutbeiy, Majdi Aminehttp://hdl.handle.net/10023/137482018-06-06T23:16:21Z1990-01-01T00:00:00ZIn this thesis we compare various methods for estimating the unknown parameters in mixtures of circular and spherical distributions. We study the von Mises distribution on the circle and the Fisher distribution on the sphere. We propose a new method of estimation based on the characteristic function and compare it with the classical methods based on maximum likelihood and moments. Thus far these methods have only been successfully applied to distributions on the line. Here we show that the extension to circular and spherical distributions is reasonably straightforward and convergence to the final estimates is fairly rapid. We apply these methods to various simulated and real data sets and show that the results obtained for the mixture of two von Mises distributions are satisfactory but generally depend on the sample size and method of estimation used. However, results obtained for the mixture of two Fisher distributions show that maximum likelihood performs best overall.
1990-01-01T00:00:00ZKoutbeiy, Majdi AmineIn this thesis we compare various methods for estimating the unknown parameters in mixtures of circular and spherical distributions. We study the von Mises distribution on the circle and the Fisher distribution on the sphere. We propose a new method of estimation based on the characteristic function and compare it with the classical methods based on maximum likelihood and moments. Thus far these methods have only been successfully applied to distributions on the line. Here we show that the extension to circular and spherical distributions is reasonably straightforward and convergence to the final estimates is fairly rapid. We apply these methods to various simulated and real data sets and show that the results obtained for the mixture of two von Mises distributions are satisfactory but generally depend on the sample size and method of estimation used. However, results obtained for the mixture of two Fisher distributions show that maximum likelihood performs best overall.Statistical aspects of the population regulation of migrating brown trout "Salmo trutta" in a Lake District streamFryer, Robert Johnhttp://hdl.handle.net/10023/137462018-06-06T23:16:37Z1990-01-01T00:00:00ZStatistical aspects of the population regulation of a migratory brown trout population are investigated. The life cycle of the trout, the study area and the sampling routine are described in Chapter 1. Models of numerical changes in fish populations are reviewed in Chapter 2. Measures that assess the nonlinear behaviour of nonlinear regression models are described in Chapter 3. The additive error Ricker model describes the relationship between the number of 0+ parr in May/June and the number of eggs. The nonlinear behaviour of the model is investigated in Chapter 4. The parameter effects nonlinearity of the model is reduced by a reparameterisation. Chapter 5 investigates the effect of errors in the egg variable on the distributions of the least squares estimators of the additive error and the multiplicative error Ricker models. The errors-in-variables considerably increase the variances of the least squares estimators. Models of the relationships between the numbers of 0+ parr in August/September, the number of 1+ parr, the egg production of a year class and the number of eggs are developed in Chapter 6. These models account for the effect of summer drought on survival. Survival is density dependent during the first summer of the life cycle and density independent thereafter. Standard measures of nonlinearity can seriously underestimate the nonlinear behaviour of piecewise linear change-point models. New measures of nonlinearity appropriate for piecewise linear change-point models are developed in Chapter 7. Chapter 8 develops a model of the growth of brown trout fed on maximum rations as a function of time, body weight and water temperature. Chapter 9 develops a model that relates the survival rate of 0+ parr between May/June and August/September to the length distribution of the trout in May/June. The results of the Thesis are discussed in Chapter 10.
1990-01-01T00:00:00ZFryer, Robert JohnStatistical aspects of the population regulation of a migratory brown trout population are investigated. The life cycle of the trout, the study area and the sampling routine are described in Chapter 1. Models of numerical changes in fish populations are reviewed in Chapter 2. Measures that assess the nonlinear behaviour of nonlinear regression models are described in Chapter 3. The additive error Ricker model describes the relationship between the number of 0+ parr in May/June and the number of eggs. The nonlinear behaviour of the model is investigated in Chapter 4. The parameter effects nonlinearity of the model is reduced by a reparameterisation. Chapter 5 investigates the effect of errors in the egg variable on the distributions of the least squares estimators of the additive error and the multiplicative error Ricker models. The errors-in-variables considerably increase the variances of the least squares estimators. Models of the relationships between the numbers of 0+ parr in August/September, the number of 1+ parr, the egg production of a year class and the number of eggs are developed in Chapter 6. These models account for the effect of summer drought on survival. Survival is density dependent during the first summer of the life cycle and density independent thereafter. Standard measures of nonlinearity can seriously underestimate the nonlinear behaviour of piecewise linear change-point models. New measures of nonlinearity appropriate for piecewise linear change-point models are developed in Chapter 7. Chapter 8 develops a model of the growth of brown trout fed on maximum rations as a function of time, body weight and water temperature. Chapter 9 develops a model that relates the survival rate of 0+ parr between May/June and August/September to the length distribution of the trout in May/June. The results of the Thesis are discussed in Chapter 10.Reliability theory in operational researchAl-Baidhani, Fadil Ajabhttp://hdl.handle.net/10023/137452018-06-06T23:16:24Z1991-01-01T00:00:00ZThis thesis is concerned principally with the problem of estimating the parameters of the Weibull and Beta distributions using several different techniques. These distributions are used in the area of reliability testing and it is important to achieve the best estimates possible of the parameters involved. After considering several accepted methods of estimating the relevant parameters, it is considered that the best method depends on the aim of the analysis, and on the value of the shape parameter 𝛽. For estimating the two-parameter Weibull distribution, it is recommended that Generalized Least Squares (GLS) is the best method to use for values of 𝛽 between 0.5 and 30. However, Maximum Likelihood Estimator (MLE) is a good method for estimating quantiles.
On this basis, the three-parameter Weibull distribution is investigated. The traditional parametrization is compared with a new parametrization developed in this work. By considering parameter effects and intrinsic curvature it is shown that the new parametrization results in a linear effect of the shape parameter. Also it has advantages in quantile estimation because of its ability to provide estimates for a wider range of data sets.
A less frequently used distribution in the field of reliability is the Beta distribution. The lack of frequency of its use is partly due to the difficulty in estimating its parameters. A simple, applicable method is developed here of estimating these parameters. This 'group method' involves estimating the two ends of the distribution. It is shown that this procedure can be used, together with other methods of estimating the two- parameter Beta distribution successfully to estimate the four-parameter Beta distribution.
1991-01-01T00:00:00ZAl-Baidhani, Fadil AjabThis thesis is concerned principally with the problem of estimating the parameters of the Weibull and Beta distributions using several different techniques. These distributions are used in the area of reliability testing and it is important to achieve the best estimates possible of the parameters involved. After considering several accepted methods of estimating the relevant parameters, it is considered that the best method depends on the aim of the analysis, and on the value of the shape parameter 𝛽. For estimating the two-parameter Weibull distribution, it is recommended that Generalized Least Squares (GLS) is the best method to use for values of 𝛽 between 0.5 and 30. However, Maximum Likelihood Estimator (MLE) is a good method for estimating quantiles.
On this basis, the three-parameter Weibull distribution is investigated. The traditional parametrization is compared with a new parametrization developed in this work. By considering parameter effects and intrinsic curvature it is shown that the new parametrization results in a linear effect of the shape parameter. Also it has advantages in quantile estimation because of its ability to provide estimates for a wider range of data sets.
A less frequently used distribution in the field of reliability is the Beta distribution. The lack of frequency of its use is partly due to the difficulty in estimating its parameters. A simple, applicable method is developed here of estimating these parameters. This 'group method' involves estimating the two ends of the distribution. It is shown that this procedure can be used, together with other methods of estimating the two- parameter Beta distribution successfully to estimate the four-parameter Beta distribution.Inference for plant-captureAshbridge, Jonathanhttp://hdl.handle.net/10023/137412018-06-05T23:17:32Z1998-01-01T00:00:00ZWhen investigating the dynamics of an animal population, a primary objective is to obtain reasonable estimates of abundance or population size. This thesis concentrates on the problem of obtaining point estimates of abundance from capture-recapture data and on how such estimation can be improved by using the method of plant-capture. Plant-capture constitutes a natural generalisation of capture-recapture. In a plant-capture study a pre-marked population of known size is added to the target population of unknown size. The capture-recapture experiment is then carried out on the augmented population. Chapter 1 considers the addition of planted individuals to target populations which behave according to the standard capture-recapture model M₀. Chapter 2 investigates an analogous model based on sampling in continuous time. In each of these chapters, distributional results are derived under the assumption that the behaviour of the plants is indistinguishable from that of members of the target population. Maximum likelihood estimators and other new estimators are proposed for each model. The results suggest that the use of plants is beneficial, and furthermore that the new estimators perform more satisfactorily than the maximum likelihood estimators. Chapter 3 introduces, initially in the absence of plants, a new class of estimators, described as coverage adjusted estimators, for the standard capture-recapture model M[sub]h. These new estimators are shown, through simulation and real life data, to compare favourably with estimators that have previously been proposed. Plant-capture versions of these new estimators are then derived and the usefulness of the plants is demonstrated through simulation. Chapter 4 describes how the approach taken in chapter 3 can be modified to produce a new estimator for the analogous continuous time model. This estimator is then shown through simulation to be preferable to estimators that have previously been proposed.
1998-01-01T00:00:00ZAshbridge, JonathanWhen investigating the dynamics of an animal population, a primary objective is to obtain reasonable estimates of abundance or population size. This thesis concentrates on the problem of obtaining point estimates of abundance from capture-recapture data and on how such estimation can be improved by using the method of plant-capture. Plant-capture constitutes a natural generalisation of capture-recapture. In a plant-capture study a pre-marked population of known size is added to the target population of unknown size. The capture-recapture experiment is then carried out on the augmented population. Chapter 1 considers the addition of planted individuals to target populations which behave according to the standard capture-recapture model M₀. Chapter 2 investigates an analogous model based on sampling in continuous time. In each of these chapters, distributional results are derived under the assumption that the behaviour of the plants is indistinguishable from that of members of the target population. Maximum likelihood estimators and other new estimators are proposed for each model. The results suggest that the use of plants is beneficial, and furthermore that the new estimators perform more satisfactorily than the maximum likelihood estimators. Chapter 3 introduces, initially in the absence of plants, a new class of estimators, described as coverage adjusted estimators, for the standard capture-recapture model M[sub]h. These new estimators are shown, through simulation and real life data, to compare favourably with estimators that have previously been proposed. Plant-capture versions of these new estimators are then derived and the usefulness of the plants is demonstrated through simulation. Chapter 4 describes how the approach taken in chapter 3 can be modified to produce a new estimator for the analogous continuous time model. This estimator is then shown through simulation to be preferable to estimators that have previously been proposed.The asymptotic distribution and robustness of the likelihood ratio and score test statisticsEmberson, E. A.http://hdl.handle.net/10023/137382018-06-13T16:14:04Z1995-01-01T00:00:00ZCordeiro & Ferrari (1991) use the asymptotic expansion of Harris (1985) for the moment generating function of the score statistic to produce a generalization of Bartlett adjustment for application to the score statistic. It is shown here that Harris's expansion is not invariant under reparameterization and an invariant expansion is derived using a method based on the expected likelihood yoke. A necessary and sufficient condition for the existence of a generalized Bartlett adjustment for an arbitrary statistic is given in terms of its moment generating function. Generalized Bartlett adjustments to the likelihood ratio and score test statistics are derived in the case where the interest parameter is one-dimensional under the assumption of a mis-specified model, where the true distribution is not assumed to be that under the null hypothesis.
1995-01-01T00:00:00ZEmberson, E. A.Cordeiro & Ferrari (1991) use the asymptotic expansion of Harris (1985) for the moment generating function of the score statistic to produce a generalization of Bartlett adjustment for application to the score statistic. It is shown here that Harris's expansion is not invariant under reparameterization and an invariant expansion is derived using a method based on the expected likelihood yoke. A necessary and sufficient condition for the existence of a generalized Bartlett adjustment for an arbitrary statistic is given in terms of its moment generating function. Generalized Bartlett adjustments to the likelihood ratio and score test statistics are derived in the case where the interest parameter is one-dimensional under the assumption of a mis-specified model, where the true distribution is not assumed to be that under the null hypothesis.On the equivalence of Markov Algorithms and Turing machines and some consequent resultsPapathanassiou, Eleftherioshttp://hdl.handle.net/10023/137362018-06-13T11:57:24Z1979-01-01T00:00:00ZTuring Machines and Markov Algorithms are, and were designed to be, the most powerful devices possible in the field of abstract automata: by their means any and every computable function can be computed.
Because of their equal, indeed maximal, strength, it was naturally assumed that these devices should be equivalent. Nonetheless a formal, exact proof of this universally presumed equivalence was lacking.
The present dissertation rectifies that omission by developing the desired complete, rigorous proof of the equivalence between Turing Machines and Markov Algorithms. The demonstration is being conducted in a constructionist way: for any given Markov Algorithm it is shown that a Turing Machine can be constructed capable of performing exactly what the Algorithm can do and nothing more, and vice versa.
The proof consists in the theoretical construction, given an arbitrary Markov Algorithm, of a Turing Machine behaving in exactly the same way as the Algorithm for all possible inputs; and conversely. Furthermore, the proof is given concrete shape by designing a computer program which can actually carry out the said theoretical constructions.
The equivalence between TM and MA as proven in the first part of our thesis, is being used in the second part for establishing some important consequent results: Thus the equivalence of Deterministic and Nondeterministic MA, of TM and Type 0 Grammars, and of Labelled and Unlabelled MA is concisely shown, and the use of TM as recognizers for type 1 and 3 grammars exclusively is exhibited. It is interesting that, by utilizing the equivalence of TM and MA, it was made possible that the proofs of these latter results be based on primitive principles.
1979-01-01T00:00:00ZPapathanassiou, EleftheriosTuring Machines and Markov Algorithms are, and were designed to be, the most powerful devices possible in the field of abstract automata: by their means any and every computable function can be computed.
Because of their equal, indeed maximal, strength, it was naturally assumed that these devices should be equivalent. Nonetheless a formal, exact proof of this universally presumed equivalence was lacking.
The present dissertation rectifies that omission by developing the desired complete, rigorous proof of the equivalence between Turing Machines and Markov Algorithms. The demonstration is being conducted in a constructionist way: for any given Markov Algorithm it is shown that a Turing Machine can be constructed capable of performing exactly what the Algorithm can do and nothing more, and vice versa.
The proof consists in the theoretical construction, given an arbitrary Markov Algorithm, of a Turing Machine behaving in exactly the same way as the Algorithm for all possible inputs; and conversely. Furthermore, the proof is given concrete shape by designing a computer program which can actually carry out the said theoretical constructions.
The equivalence between TM and MA as proven in the first part of our thesis, is being used in the second part for establishing some important consequent results: Thus the equivalence of Deterministic and Nondeterministic MA, of TM and Type 0 Grammars, and of Labelled and Unlabelled MA is concisely shown, and the use of TM as recognizers for type 1 and 3 grammars exclusively is exhibited. It is interesting that, by utilizing the equivalence of TM and MA, it was made possible that the proofs of these latter results be based on primitive principles.Some contributions to the theory of mathematical programmingSaksena, Chandra P.http://hdl.handle.net/10023/137342018-06-13T11:50:27Z1970-01-01T00:00:00ZAs stated earlier the Simplex Method (or its variations e.g. Dual Simplex Method) has thus far been the most effective and widely used general method for the solution of linear programming problems. The Simplex Method in its various forms starts initially with a basic feasible solution and continues its moves in different iterations within the feasible region till it finds the optimal solution. The only other notable variation of the Simplex Method, namely the Dual Simplex Method, on the other hand, by virtue of the special formulation of the linear programming problem, starts with an in-feasible solution and continues to move in the in-feasible region till it finds the optimal solution at which it enters the feasible region. In other respects both the Simplex and the Dual Simplex Methods follow essentially the same principle for obtaining the optimal solution. The rigorous mathematical features have been widely discussed in the literature [12, 16, 34, 35, 38, 68, 77] and only those formal aspects of this topic which are closely related to the subject of this thesis will be outlined.
The Multiplex Method, though reported in the literature [30, 15, 69, 71, 29, 32], is not so well known and has also not been widely coded on electronic computers. It had earlier been programmed for the English Electric’s Computer ‘DEUCE’ by the author [72] and Ferranti’s ‘MERCURY’ by Ole-John Dahl in 1960 [15]. Later both the above mentioned computers were obsolete and the efforts presently concentrate on coding it for UNIVAC 1100 and IBM 360. The Multiplex Method, as such, has been included in the present thesis and discussed in some detail in chapter 2. The flow diagram and the algorithm for the method is given in section 2.4, chapter 2.
The main body of the thesis consists of developing a new linear programming method which has been called the Bounding Hyperplane Method – Part I. This is explained in detail in chapter 3. The method could initially start with either a basic feasible or in-feasible point and in its subsequent moves it may either alternate between the feasible and the in-feasible regions or get restricted to either of them depending upon the problem. It is applicable as a new phase which we call phase 0 to the Simple Method, particularly in situations where an initial basic feasible point is not available. In such cases it either results in a feasible point at the end of phase 0 or else yields a ‘better’ in-feasible point for phase 1 operations of the Simplex Method. Moreover, it is found that the number of iterations required to reach either the former by the application of phase 0 or the latter by the application of first phase 0 and then phase 1 are, in general, less than those required by following phase 1 alone. This is explained with illustrations in Chapter 6. Even when applied alone the method, in general, yields the optimal solution in fewer iterations as compared with the Simplex Method. This is illustrated with examples in chapter 3.
We also develop and illustrate a powerful but straight-forward method whereby we first find the solution to the equality constraints and (if the former does not yield an inconsistent solution point) then the transformations to the latter are obtained from the equality solution tableau corresponding to the former. This results in reducing the iteration time appreciably for each iteration of the method. It has been called the B.H.P.M. – part II and is discussed in chapter 4.
To estimate the time taken by the B.H.P and the Simplex Method, the two codes (written in Fortran) have been run on a number of problems taken from the literature. The results have been summarised in chapter 7.
Finally, the suggestions for further research towards i. the extensions of the B.H.P.M. to the quadratic programming problem where the function in (1.1.1) is positive semi-definite, and (ii) the accuracy of computations in linear programming, in general, are discussed in sections 8.1 and 8.2 respectively of chapter 8.
1970-01-01T00:00:00ZSaksena, Chandra P.As stated earlier the Simplex Method (or its variations e.g. Dual Simplex Method) has thus far been the most effective and widely used general method for the solution of linear programming problems. The Simplex Method in its various forms starts initially with a basic feasible solution and continues its moves in different iterations within the feasible region till it finds the optimal solution. The only other notable variation of the Simplex Method, namely the Dual Simplex Method, on the other hand, by virtue of the special formulation of the linear programming problem, starts with an in-feasible solution and continues to move in the in-feasible region till it finds the optimal solution at which it enters the feasible region. In other respects both the Simplex and the Dual Simplex Methods follow essentially the same principle for obtaining the optimal solution. The rigorous mathematical features have been widely discussed in the literature [12, 16, 34, 35, 38, 68, 77] and only those formal aspects of this topic which are closely related to the subject of this thesis will be outlined.
The Multiplex Method, though reported in the literature [30, 15, 69, 71, 29, 32], is not so well known and has also not been widely coded on electronic computers. It had earlier been programmed for the English Electric’s Computer ‘DEUCE’ by the author [72] and Ferranti’s ‘MERCURY’ by Ole-John Dahl in 1960 [15]. Later both the above mentioned computers were obsolete and the efforts presently concentrate on coding it for UNIVAC 1100 and IBM 360. The Multiplex Method, as such, has been included in the present thesis and discussed in some detail in chapter 2. The flow diagram and the algorithm for the method is given in section 2.4, chapter 2.
The main body of the thesis consists of developing a new linear programming method which has been called the Bounding Hyperplane Method – Part I. This is explained in detail in chapter 3. The method could initially start with either a basic feasible or in-feasible point and in its subsequent moves it may either alternate between the feasible and the in-feasible regions or get restricted to either of them depending upon the problem. It is applicable as a new phase which we call phase 0 to the Simple Method, particularly in situations where an initial basic feasible point is not available. In such cases it either results in a feasible point at the end of phase 0 or else yields a ‘better’ in-feasible point for phase 1 operations of the Simplex Method. Moreover, it is found that the number of iterations required to reach either the former by the application of phase 0 or the latter by the application of first phase 0 and then phase 1 are, in general, less than those required by following phase 1 alone. This is explained with illustrations in Chapter 6. Even when applied alone the method, in general, yields the optimal solution in fewer iterations as compared with the Simplex Method. This is illustrated with examples in chapter 3.
We also develop and illustrate a powerful but straight-forward method whereby we first find the solution to the equality constraints and (if the former does not yield an inconsistent solution point) then the transformations to the latter are obtained from the equality solution tableau corresponding to the former. This results in reducing the iteration time appreciably for each iteration of the method. It has been called the B.H.P.M. – part II and is discussed in chapter 4.
To estimate the time taken by the B.H.P and the Simplex Method, the two codes (written in Fortran) have been run on a number of problems taken from the literature. The results have been summarised in chapter 7.
Finally, the suggestions for further research towards i. the extensions of the B.H.P.M. to the quadratic programming problem where the function in (1.1.1) is positive semi-definite, and (ii) the accuracy of computations in linear programming, in general, are discussed in sections 8.1 and 8.2 respectively of chapter 8.Involutive automorphisms and real forms of Kac-Moody algebrasClarke, Stefanhttp://hdl.handle.net/10023/137312018-06-11T16:13:03Z1996-01-01T00:00:00ZInvolutive automorphisms of complex affine Kac-Moody algebras (in particular, their conjugacy classes within the group of all automorphisms) and their compact real forms are studied, using the matrix formulation which was developed by Cornwell. The initial study of the a⁽¹⁾ series of affine untwisted Kac-Moody algebras is extended to include the complex affine untwisted Kac-Moody algebras B⁽¹⁾, C⁽¹⁾ and D⁽¹⁾. From the information obtained, explicit bases for real forms of these Kac-Moody algebras are then constructed. A scheme for naming some real forms is suggested. Further work is included which examines the involutive automorphisms and the real forms of A₂⁽²⁾and the algebra G⁽¹⁾₂ (which is based upon an exceptional simple Lie algebra). The work involving the algebra A₂⁽²⁾is part of work towards extending the matrix formulation to twisted Kac-Moody algebras. The analysis also acts as a practical test of this method, and from it we may infer different ways of using the formulation to eventually obtain a complete picture of the conjugacy classes of the involutive automorphisms of all the affine Kac-Moody algebras.
1996-01-01T00:00:00ZClarke, StefanInvolutive automorphisms of complex affine Kac-Moody algebras (in particular, their conjugacy classes within the group of all automorphisms) and their compact real forms are studied, using the matrix formulation which was developed by Cornwell. The initial study of the a⁽¹⁾ series of affine untwisted Kac-Moody algebras is extended to include the complex affine untwisted Kac-Moody algebras B⁽¹⁾, C⁽¹⁾ and D⁽¹⁾. From the information obtained, explicit bases for real forms of these Kac-Moody algebras are then constructed. A scheme for naming some real forms is suggested. Further work is included which examines the involutive automorphisms and the real forms of A₂⁽²⁾and the algebra G⁽¹⁾₂ (which is based upon an exceptional simple Lie algebra). The work involving the algebra A₂⁽²⁾is part of work towards extending the matrix formulation to twisted Kac-Moody algebras. The analysis also acts as a practical test of this method, and from it we may infer different ways of using the formulation to eventually obtain a complete picture of the conjugacy classes of the involutive automorphisms of all the affine Kac-Moody algebras.Subalgebras of free nilpotent and polynilpotent lie algebrasBoral, Melihhttp://hdl.handle.net/10023/137292018-06-11T16:09:40Z1977-01-01T00:00:00ZIn this thesis we study subalgebras in free nilpotent and polynilpotent Lie algebras. Chapter 1 sets up the notation and includes definitions and elementary properties of free and certain reduced free Lie algebras that we use throughout this thesis. We also describe a Hall basis of a free Lie algebra as in [4] and a basis for a free polynilpotent Lie algebra which was developed in [24].
In Chapter 2 we first consider the class of nilpotency of subalbebras of free nilpotent Lie algebras starting with two-generator subalgebras. Then we study those subalgebras in a free nilpotent Lie algebra which, are themselves free nilpotent. We give necessary and sufficient conditions in the case of two-generator subalgebras.
Chapter 3 extends the results obtained in Chapter 2 to the polynilpotent case. First we look at two-generator subalgebras of a free polynilpotent Lie algebra. Then we consider more general subalgebras. Finally we study those subalgebras which are themselves free polynilpotent and give necessary and sufficient conditions for two-generator subalgebras to be free polynilpotent.
In Chapter 4 we first study certain properties of ideals in free, free nilpotent and free polynilpotent Lie algebras and establish the fact that in a free polynilpotent Lie algebra a nonzero ideal which is finitely-generated as a subalgebra must be equal to the whole algebra. Then we consider the quotient Lie algebra of a lower central term of a free Lie algebra by a term of the lower central series of an ideal. We then generalize the results to cover the free nilpotent and free polynilpotent cases. In the last section of Chapter 4 we consider ideals of free nilpotent (and later polynilpotent) Lie algebras as free nilpotent (polynilpotent) subalgebras and establish the fact that in most non-trivial cases such an ideal cannot be free nilpotent (polynilpotent).
In the last chapter we consider the m+k-th term of the lower central series of a free Lie algebra as a subalgebra of the m-th term for m ⩽ k and generalize the results proved in [25]. We give reasons for the failure of these results in the case m > k.
1977-01-01T00:00:00ZBoral, MelihIn this thesis we study subalgebras in free nilpotent and polynilpotent Lie algebras. Chapter 1 sets up the notation and includes definitions and elementary properties of free and certain reduced free Lie algebras that we use throughout this thesis. We also describe a Hall basis of a free Lie algebra as in [4] and a basis for a free polynilpotent Lie algebra which was developed in [24].
In Chapter 2 we first consider the class of nilpotency of subalbebras of free nilpotent Lie algebras starting with two-generator subalgebras. Then we study those subalgebras in a free nilpotent Lie algebra which, are themselves free nilpotent. We give necessary and sufficient conditions in the case of two-generator subalgebras.
Chapter 3 extends the results obtained in Chapter 2 to the polynilpotent case. First we look at two-generator subalgebras of a free polynilpotent Lie algebra. Then we consider more general subalgebras. Finally we study those subalgebras which are themselves free polynilpotent and give necessary and sufficient conditions for two-generator subalgebras to be free polynilpotent.
In Chapter 4 we first study certain properties of ideals in free, free nilpotent and free polynilpotent Lie algebras and establish the fact that in a free polynilpotent Lie algebra a nonzero ideal which is finitely-generated as a subalgebra must be equal to the whole algebra. Then we consider the quotient Lie algebra of a lower central term of a free Lie algebra by a term of the lower central series of an ideal. We then generalize the results to cover the free nilpotent and free polynilpotent cases. In the last section of Chapter 4 we consider ideals of free nilpotent (and later polynilpotent) Lie algebras as free nilpotent (polynilpotent) subalgebras and establish the fact that in most non-trivial cases such an ideal cannot be free nilpotent (polynilpotent).
In the last chapter we consider the m+k-th term of the lower central series of a free Lie algebra as a subalgebra of the m-th term for m ⩽ k and generalize the results proved in [25]. We give reasons for the failure of these results in the case m > k.Finite difference solutions of the Von Mises equationThomson, John Younghttp://hdl.handle.net/10023/137272018-06-11T16:05:48Z1958-01-01T00:00:00ZPrandtl in 1904 discovered that the flow of a fluid over a thin obstacle can be adequately represented by an approximate set of equations, much simpler than the complex Navier-Stokes equations which govern the motion of fluid.
A particularly simple for of these equations, for the two-dimensional steady flow of a fluid past a flat plate, are the Von Mises Boundary layer equations. Unfortunately the Von Mises transformation introduces a singularity at the plate and this discouraged the use of the equations as a means for obtaining numerical solutions of boundary layer problems in incompressible and compressible flow.
In this thesis, we show that this difficulty can be overcome and the Von Mises equations are used as a basis for a finite difference evaluation of the velocity and temperature in the boundary layer adjacent to a flat plate, particular attention being given to conditions near the plate and more especially to the separation point.
In the section on compressible flow, the calculations also yield a check on certain common simplifying assumptions.
1958-01-01T00:00:00ZThomson, John YoungPrandtl in 1904 discovered that the flow of a fluid over a thin obstacle can be adequately represented by an approximate set of equations, much simpler than the complex Navier-Stokes equations which govern the motion of fluid.
A particularly simple for of these equations, for the two-dimensional steady flow of a fluid past a flat plate, are the Von Mises Boundary layer equations. Unfortunately the Von Mises transformation introduces a singularity at the plate and this discouraged the use of the equations as a means for obtaining numerical solutions of boundary layer problems in incompressible and compressible flow.
In this thesis, we show that this difficulty can be overcome and the Von Mises equations are used as a basis for a finite difference evaluation of the velocity and temperature in the boundary layer adjacent to a flat plate, particular attention being given to conditions near the plate and more especially to the separation point.
In the section on compressible flow, the calculations also yield a check on certain common simplifying assumptions.Semigroups of singular endomorphisms of vector spaceDawlings, Robert J. H.http://hdl.handle.net/10023/137252018-06-07T16:14:28Z1980-01-01T00:00:00ZIn 1967, J. A. Erdős showed, using a matrix theory approach that the semigroup Sing[sub]n of singular endomorphisms of an n-dimensional vector space is generated by the set E of idempotent endomorphisms of rank n - 1. This thesis gives an alternative proof using a linear algebra and semigroup theory approach. It is also shown that not all the elements of E are needed to generate Sing[sub]n. Necessary conditions for a subset of E to generate found; these conditions are shown to be sufficient if the vector space is defined over a finite field. In this case, the minimum order of all subsets of E that generate Sing[sub]n is found. The problem of determining the number of subsets of E that generate Sing[sub]n and have this minimum order is considered; it is completely solved when the vector space is two-dimensional. From the proof given by Erdős, it could be deduced that any element of Sing[sub]n could be expressed as the product of, at most, 2n elements of E. It is shown here that this bound may be reduced to n, and that this is best possible. It is also shown that, if E⁺ is the set of all idempotent of Singn, then (E⁺)ⁿ⁻¹ is strictly contained in Sing[sub]n. Finally, it is shown that Erdős's result cannot be extended to the semigroup Sing of continuous singular endomorphisms of a separable Hilbert space. The sub semigroup of Sing generated by the idempotent of Sing is determined and is, clearly, strictly contained in Sing.
1980-01-01T00:00:00ZDawlings, Robert J. H.In 1967, J. A. Erdős showed, using a matrix theory approach that the semigroup Sing[sub]n of singular endomorphisms of an n-dimensional vector space is generated by the set E of idempotent endomorphisms of rank n - 1. This thesis gives an alternative proof using a linear algebra and semigroup theory approach. It is also shown that not all the elements of E are needed to generate Sing[sub]n. Necessary conditions for a subset of E to generate found; these conditions are shown to be sufficient if the vector space is defined over a finite field. In this case, the minimum order of all subsets of E that generate Sing[sub]n is found. The problem of determining the number of subsets of E that generate Sing[sub]n and have this minimum order is considered; it is completely solved when the vector space is two-dimensional. From the proof given by Erdős, it could be deduced that any element of Sing[sub]n could be expressed as the product of, at most, 2n elements of E. It is shown here that this bound may be reduced to n, and that this is best possible. It is also shown that, if E⁺ is the set of all idempotent of Singn, then (E⁺)ⁿ⁻¹ is strictly contained in Sing[sub]n. Finally, it is shown that Erdős's result cannot be extended to the semigroup Sing of continuous singular endomorphisms of a separable Hilbert space. The sub semigroup of Sing generated by the idempotent of Sing is determined and is, clearly, strictly contained in Sing.Formal languages and idempotent semigroupsSezinando, Helena Maria da Encarnaçãohttp://hdl.handle.net/10023/137242018-06-07T16:12:32Z1991-01-01T00:00:00ZThe structure of the lattice 𝗟𝗕 of varieties of idempotent semigroups or bands (as universal algebras) was determined by Birjukov, Fennemore and Gerhard. Wis- math determined the structure of a related lattice: the lattice LBM of varieties of band monoids. In the first two parts we study several questions about these varieties.
In Part I we compute the cardinalities of the Green classes of the free objects in each variety of 𝗟𝗕 [𝗟𝗕𝗠]. These cardinalities constitute a useful piece of information in the study of several questions about these varieties and some of the conclusions obtained here are used in parts II and III.
Part II concerns expansions of bands [band monoids]. More precisely, we compute here the cut-down to generators of the Rhodes expansions of the free objects in the varieties of 𝗟𝗕. We define Rhodes expansion of a monoid, its cut-down to generators and we compute the cut-down to generators of the Rhodes expansions of the free objects in the varieties of 𝗟𝗕𝗠.
In Part III we deal with Eilenberg varieties of band monoids. The last chapter is particularly concerned with the description of the varieties of languages corresponding to these varieties.
1991-01-01T00:00:00ZSezinando, Helena Maria da EncarnaçãoThe structure of the lattice 𝗟𝗕 of varieties of idempotent semigroups or bands (as universal algebras) was determined by Birjukov, Fennemore and Gerhard. Wis- math determined the structure of a related lattice: the lattice LBM of varieties of band monoids. In the first two parts we study several questions about these varieties.
In Part I we compute the cardinalities of the Green classes of the free objects in each variety of 𝗟𝗕 [𝗟𝗕𝗠]. These cardinalities constitute a useful piece of information in the study of several questions about these varieties and some of the conclusions obtained here are used in parts II and III.
Part II concerns expansions of bands [band monoids]. More precisely, we compute here the cut-down to generators of the Rhodes expansions of the free objects in the varieties of 𝗟𝗕. We define Rhodes expansion of a monoid, its cut-down to generators and we compute the cut-down to generators of the Rhodes expansions of the free objects in the varieties of 𝗟𝗕𝗠.
In Part III we deal with Eilenberg varieties of band monoids. The last chapter is particularly concerned with the description of the varieties of languages corresponding to these varieties.Random-walk theory and statistical mechanics of lattice systemsNieto, Alberto Robledohttp://hdl.handle.net/10023/137222018-06-07T16:10:35Z1974-01-01T00:00:00ZIt has been found elsewhere that when approximate relations for the two-particle correlation functions of classical statistical mechanics, such as the Percus-Yevick and the mean-spherical approximations, are applied to the lattice gas models with nearest-neighbour interactions simple expressions are obtained for the total correlation function in terms of the lattice Green's function. Since many of the properties of random walks on a lattice can be described by the lattice Green's function, it follows that these systems, at least when treated under these approximations, may be analysed in terms of the language of random walks.
Here the theory of random walks on lattices is appropriately extended to show that the relationship between the correlation functions and the lattice Green's function is not dependent upon the employment of these approximations, nor to a particular range or form of the potential function. Instead, this relationship is shown to be an alternative form of the Ornstein-Zernike relation between the direct and total correlation functions. The direct correlation function is directly related to the probability of a single step, whereas the total correlation function is given by the first-passage- time probabilities of the random walks. Thermodynamic properties, such as the isothermal compressibility, are also interpreted in terms of random-walk concepts.
The random-walk formulation is then extended to include the study of ordered phases in lattice-gas models and hence order-disorder transitions in these systems. Also, an asymptotic form for the lattice Green's function is derived to illustrate how the form of decay of the total correlation function at large distances depends on the properties of the potential function.
To show that the random-walk interpretation of the Ornstein-Zernike relation is not restricted to lattice systems, we define analogous random-walk functions for continuous space. These lead to a straight-forward generalization of most expressions for discrete space-; the relationship between the continuous-space total correlation and Green's functions has the same form as that for the lattice systems. We also explore the possibility of obtaining random-walk properties of a (lattice or continuous-space) system, not from the existing approximate expressions for the direct correlation function, but instead from a generalised Ornstein-Zernike relation based on a maximum principle of classical statistical mechanics.
Finally, we choose a few specific lattice-gas models to show how the method describes their different properties, such as the behaviour of the total correlation function or that of an order- disorder phase transition.
1974-01-01T00:00:00ZNieto, Alberto RobledoIt has been found elsewhere that when approximate relations for the two-particle correlation functions of classical statistical mechanics, such as the Percus-Yevick and the mean-spherical approximations, are applied to the lattice gas models with nearest-neighbour interactions simple expressions are obtained for the total correlation function in terms of the lattice Green's function. Since many of the properties of random walks on a lattice can be described by the lattice Green's function, it follows that these systems, at least when treated under these approximations, may be analysed in terms of the language of random walks.
Here the theory of random walks on lattices is appropriately extended to show that the relationship between the correlation functions and the lattice Green's function is not dependent upon the employment of these approximations, nor to a particular range or form of the potential function. Instead, this relationship is shown to be an alternative form of the Ornstein-Zernike relation between the direct and total correlation functions. The direct correlation function is directly related to the probability of a single step, whereas the total correlation function is given by the first-passage- time probabilities of the random walks. Thermodynamic properties, such as the isothermal compressibility, are also interpreted in terms of random-walk concepts.
The random-walk formulation is then extended to include the study of ordered phases in lattice-gas models and hence order-disorder transitions in these systems. Also, an asymptotic form for the lattice Green's function is derived to illustrate how the form of decay of the total correlation function at large distances depends on the properties of the potential function.
To show that the random-walk interpretation of the Ornstein-Zernike relation is not restricted to lattice systems, we define analogous random-walk functions for continuous space. These lead to a straight-forward generalization of most expressions for discrete space-; the relationship between the continuous-space total correlation and Green's functions has the same form as that for the lattice systems. We also explore the possibility of obtaining random-walk properties of a (lattice or continuous-space) system, not from the existing approximate expressions for the direct correlation function, but instead from a generalised Ornstein-Zernike relation based on a maximum principle of classical statistical mechanics.
Finally, we choose a few specific lattice-gas models to show how the method describes their different properties, such as the behaviour of the total correlation function or that of an order- disorder phase transition.Contributions to the theory of Ockham algebrasFang, Jiehttp://hdl.handle.net/10023/137202018-06-07T15:06:25Z1997-01-01T00:00:00ZIn the first part of this thesis we consider particular ordered sets (connected and of small height) and determine the cardinality of the corresponding dual MS - algebra and of its set of fixed points.
The remainder of the thesis is devoted to a study of congruences of Ockham algebras and a generalised variety K𝜔 of Ockham algebras that contains all of the Berman varieties K[sub]p,[sub]q. In particular we consider the congruences [sub]i(i = 1, 2,...) defined on an Ockham algebra (L; f) by
(x, y) ∊ [sub]i ⇔ fⁱ(x)= fⁱ(y)
and show that (L; f) ∊ K𝜔 is subdirectly irreducible if and only if the lattice of congruences of L reduces to the chain
𝜔 = 𝝫₀ ≤ 𝝫₁≤ 𝝫₂≤ … ≤𝝫𝜔<𝞲
Where 𝝫𝜔 = ⌵ [sub]i≥0𝝫i. Finally we obtain a characterisation of the finite simple Ockham algebras.
1997-01-01T00:00:00ZFang, JieIn the first part of this thesis we consider particular ordered sets (connected and of small height) and determine the cardinality of the corresponding dual MS - algebra and of its set of fixed points.
The remainder of the thesis is devoted to a study of congruences of Ockham algebras and a generalised variety K𝜔 of Ockham algebras that contains all of the Berman varieties K[sub]p,[sub]q. In particular we consider the congruences [sub]i(i = 1, 2,...) defined on an Ockham algebra (L; f) by
(x, y) ∊ [sub]i ⇔ fⁱ(x)= fⁱ(y)
and show that (L; f) ∊ K𝜔 is subdirectly irreducible if and only if the lattice of congruences of L reduces to the chain
𝜔 = 𝝫₀ ≤ 𝝫₁≤ 𝝫₂≤ … ≤𝝫𝜔<𝞲
Where 𝝫𝜔 = ⌵ [sub]i≥0𝝫i. Finally we obtain a characterisation of the finite simple Ockham algebras.The descent algebras of Coxeter groupsVan WIlligenburg, Stephaniehttp://hdl.handle.net/10023/137132018-06-07T15:04:40Z1997-01-01T00:00:00ZA descent algebra is a subalgebra of the group algebra of a Coxeter group. They were first defined over a field of characteristic zero. In this thesis, the main areas of research to be addressed are;
1. The formulation of a rule for multiplying two elements of descent algebra of the Coxeter groups of type D.
2. The identification of properties exhibited by descent algebras over a field of prime characteristic.
In addressing the first, a framework which exploits the specific properties of Coxeter groups is set up. With this framework, a new justification is given for existing rules for multiplying together two elements in the descent algebras of the Coxeter groups of type A and B. This framework is then used to derive a new multiplication rule for the descent algebra of the Coxeter groups of type D.
To address the second, a descent algebra over a field of prime characteristic, p, is defined. A homomorphism into the algebra of generalised p-modular characters is then described. This homomorphism is then used to obtain the radical, and allows the irreducible modules of the descent algebra to be determined.
Results from the two areas addressed are then exploited to give an explicit description of the radical of the descent algebra of the symmetric groups, over a finite field. In this instance, the nilpotency index of the radical and the irreducible representations are also described. Similarly, the descent algebra of the hyper-octahedral groups, over a finite field, has its radical, nilpotency index, and irreducible representations explicitly determined.
1997-01-01T00:00:00ZVan WIlligenburg, StephanieA descent algebra is a subalgebra of the group algebra of a Coxeter group. They were first defined over a field of characteristic zero. In this thesis, the main areas of research to be addressed are;
1. The formulation of a rule for multiplying two elements of descent algebra of the Coxeter groups of type D.
2. The identification of properties exhibited by descent algebras over a field of prime characteristic.
In addressing the first, a framework which exploits the specific properties of Coxeter groups is set up. With this framework, a new justification is given for existing rules for multiplying together two elements in the descent algebras of the Coxeter groups of type A and B. This framework is then used to derive a new multiplication rule for the descent algebra of the Coxeter groups of type D.
To address the second, a descent algebra over a field of prime characteristic, p, is defined. A homomorphism into the algebra of generalised p-modular characters is then described. This homomorphism is then used to obtain the radical, and allows the irreducible modules of the descent algebra to be determined.
Results from the two areas addressed are then exploited to give an explicit description of the radical of the descent algebra of the symmetric groups, over a finite field. In this instance, the nilpotency index of the radical and the irreducible representations are also described. Similarly, the descent algebra of the hyper-octahedral groups, over a finite field, has its radical, nilpotency index, and irreducible representations explicitly determined.Certain classes of group presentationsVatansever, Bilalhttp://hdl.handle.net/10023/137092018-06-07T15:02:35Z1993-01-01T00:00:00ZIn Chapter two we look at the class
F(n) = <R, S | Rⁿ = Sⁿ = (Rᵃ¹Sᵇ¹)ˣ¹(Rᶜ¹Sᵈ¹)ʸ¹(Rᵃ²Sᵇ²)ˣ² (Rᶜ²Sᵈ²)ʸ² …(RᵃᵐSᵇᵐ)ˣᵐ (RᶜᵐSᵈᵐ)ʸᵐ = 1 >.
For some values of n, a[sub]i , b[sub]i, d[sub]i, x[sub]i, y[sub]i we give results on these groups where we have been able to determine their order, either finite or infinite. In the last section in Chapter two we study two classes of groups generated by A and B and subject to the following relations:
Relations for class 1:
A⁴ = 1, B⁴ = 1, (B(AB)²)⁴ = 1, (B(BA)⁶)⁴ = 1, (B(BA)¹⁴)⁴ = 1, …,
B(BA)⁽²⁽ⁿ⁻¹⁾ᐟ²-2)⁴ = 1
A⁻¹B⁻¹)²⁽ⁿ⁻³⁾ᐟ²B(BA)⁽²⁽ⁿ⁻¹⁾ᐟ²-2)B(BA)⁽²⁽ⁿ⁻³⁾ᐟ²B⁻¹(A⁻¹B⁻¹)²⁽ⁿ⁻¹⁾ᐟ²-2) B⁻¹
A⁻¹B⁻¹)²⁽ⁿ⁺¹⁾ᐟ²-3) A(BA)⁽²⁽ⁿ⁻¹⁾ᐟ²-1)B⁻¹= 1
(BA)²⁽ⁿ⁻¹⁾ᐟ² B⁻¹(A⁻¹B⁻¹)²⁽ⁿ⁻¹⁾ᐟ²-2) B⁻¹(A⁻¹B⁻¹)²⁽ⁿ⁺¹⁾ᐟ²-3) A² =1
Relations for class 2:
A⁴ = 1, B⁴ = 1, (B(AB)²)⁴ = 1, (B(BA)⁶)⁴ = 1, (B(BA)¹⁴)⁴ = 1, …, B(BA)⁽²⁽ⁿᐟ²⁻²⁾)⁴ = 1 , B⁻¹(BA)² ⁽ⁿ⁻²⁾ᐟ²B(BA) ⁽²ⁿᐟ²⁻²⁾ B(A⁻¹B⁻¹)²⁽ⁿ⁻²⁾ᐟ²-1) = 1, (BA) ⁽²ⁿᐟ²+2⁽ⁿ⁻²⁾ᐟ²+2)B(BA) ⁽²ⁿᐟ²-2)B(A⁻¹B⁻¹)²⁽ⁿ⁻²⁾ᐟ²-1)A² =1.
The groups in the first class turn out to be the cyclic group of order 2 and the groups in the second class turn out to be metabelian groups of order 4. (2ⁿᐟ²-1)² . Moreover the derived group of the groups in the second class is the direct product of two copies of a cyclic group of order (2ⁿᐟ²-1)². In Chapter three we study the groups with a presentation of the form:
<A,B|A⁴ = 1, Bⁿ = 1, AⁱBʲAᵏBᵗ =1
and determine all possibilities with conditions: j+t = 0 and i,k ∊ { + 1, 2 }.
Also in the second section of Chapter three we study the groups with a presentation of the form:
<A,B | A⁴ = 1, Bⁿ =1, AⁱBʲAᵏBᵗA ᵐBᵖ =1>
and determine some of the possibilities with conditions: j = l,t = l,p = -2 and i,k,m ∊ ℤ. In Chapter four we give new efficient presentations for the groups PSL(2,p), where p is an odd prime, p ∊ { 5,7,11,13,17,19,23,29,31,37, 41,43,53,59,79,83,89,109,139,229 }. We give permutation generators for these groups which satisfy our efficient presentation. Also we give new efficient presentations for PSL(2,p), where p is a prime power and p ∊ { 9,25,27,49,169}. Also in Chapter four, permutation generators are given for these groups which satisfy our presentations. In Chapter five we give new efficient presentations for the groups SL(2,p), where p is an odd prime and p ∊ { 5,7,11,13,17,19,23,29,31,41, 43,53,79,89,109,139,229 }. Also we give new efficient presentations for the groups SL(2,p), where p is an prime power and p ∊ { 8,16,25,27,49,169 }. In Chapter six we study the class of groups with the presentation
<a,b |aᵖ =1, bᵐ⁺ᵖa⁻ᵐbᵐa⁻ᵐ =1, (ab)² = 1>
,p an odd number and m ∊ ℤ. For some values of p and m these groups have connections with the groups PSL(2,p). In Chapter 7 we attempt to show the efficiency of PSL(2, ℤ[sub]n ) x PSL(2, ℤ[sub]m). For some values of n and m we give efficient presentation for these groups. In the same chapter we also attempt to show the efficiency of PSL(2, ℤ [sub]p) x PSL(2,32). For some values of p we give an efficient presentation for these groups. In the last section of the thesis we give efficient presentations for the following direct products
(i) PSL(2,5) X PSL(2,3²)
(ii) PSL(2,7) X PSL(2,3²)
(iii) PSL(2,5) X PSL(2,3³)
Also in the last section of the thesis the structure of a perfect group of order 161280 is investigated.
1993-01-01T00:00:00ZVatansever, BilalIn Chapter two we look at the class
F(n) = <R, S | Rⁿ = Sⁿ = (Rᵃ¹Sᵇ¹)ˣ¹(Rᶜ¹Sᵈ¹)ʸ¹(Rᵃ²Sᵇ²)ˣ² (Rᶜ²Sᵈ²)ʸ² …(RᵃᵐSᵇᵐ)ˣᵐ (RᶜᵐSᵈᵐ)ʸᵐ = 1 >.
For some values of n, a[sub]i , b[sub]i, d[sub]i, x[sub]i, y[sub]i we give results on these groups where we have been able to determine their order, either finite or infinite. In the last section in Chapter two we study two classes of groups generated by A and B and subject to the following relations:
Relations for class 1:
A⁴ = 1, B⁴ = 1, (B(AB)²)⁴ = 1, (B(BA)⁶)⁴ = 1, (B(BA)¹⁴)⁴ = 1, …,
B(BA)⁽²⁽ⁿ⁻¹⁾ᐟ²-2)⁴ = 1
A⁻¹B⁻¹)²⁽ⁿ⁻³⁾ᐟ²B(BA)⁽²⁽ⁿ⁻¹⁾ᐟ²-2)B(BA)⁽²⁽ⁿ⁻³⁾ᐟ²B⁻¹(A⁻¹B⁻¹)²⁽ⁿ⁻¹⁾ᐟ²-2) B⁻¹
A⁻¹B⁻¹)²⁽ⁿ⁺¹⁾ᐟ²-3) A(BA)⁽²⁽ⁿ⁻¹⁾ᐟ²-1)B⁻¹= 1
(BA)²⁽ⁿ⁻¹⁾ᐟ² B⁻¹(A⁻¹B⁻¹)²⁽ⁿ⁻¹⁾ᐟ²-2) B⁻¹(A⁻¹B⁻¹)²⁽ⁿ⁺¹⁾ᐟ²-3) A² =1
Relations for class 2:
A⁴ = 1, B⁴ = 1, (B(AB)²)⁴ = 1, (B(BA)⁶)⁴ = 1, (B(BA)¹⁴)⁴ = 1, …, B(BA)⁽²⁽ⁿᐟ²⁻²⁾)⁴ = 1 , B⁻¹(BA)² ⁽ⁿ⁻²⁾ᐟ²B(BA) ⁽²ⁿᐟ²⁻²⁾ B(A⁻¹B⁻¹)²⁽ⁿ⁻²⁾ᐟ²-1) = 1, (BA) ⁽²ⁿᐟ²+2⁽ⁿ⁻²⁾ᐟ²+2)B(BA) ⁽²ⁿᐟ²-2)B(A⁻¹B⁻¹)²⁽ⁿ⁻²⁾ᐟ²-1)A² =1.
The groups in the first class turn out to be the cyclic group of order 2 and the groups in the second class turn out to be metabelian groups of order 4. (2ⁿᐟ²-1)² . Moreover the derived group of the groups in the second class is the direct product of two copies of a cyclic group of order (2ⁿᐟ²-1)². In Chapter three we study the groups with a presentation of the form:
<A,B|A⁴ = 1, Bⁿ = 1, AⁱBʲAᵏBᵗ =1
and determine all possibilities with conditions: j+t = 0 and i,k ∊ { + 1, 2 }.
Also in the second section of Chapter three we study the groups with a presentation of the form:
<A,B | A⁴ = 1, Bⁿ =1, AⁱBʲAᵏBᵗA ᵐBᵖ =1>
and determine some of the possibilities with conditions: j = l,t = l,p = -2 and i,k,m ∊ ℤ. In Chapter four we give new efficient presentations for the groups PSL(2,p), where p is an odd prime, p ∊ { 5,7,11,13,17,19,23,29,31,37, 41,43,53,59,79,83,89,109,139,229 }. We give permutation generators for these groups which satisfy our efficient presentation. Also we give new efficient presentations for PSL(2,p), where p is a prime power and p ∊ { 9,25,27,49,169}. Also in Chapter four, permutation generators are given for these groups which satisfy our presentations. In Chapter five we give new efficient presentations for the groups SL(2,p), where p is an odd prime and p ∊ { 5,7,11,13,17,19,23,29,31,41, 43,53,79,89,109,139,229 }. Also we give new efficient presentations for the groups SL(2,p), where p is an prime power and p ∊ { 8,16,25,27,49,169 }. In Chapter six we study the class of groups with the presentation
<a,b |aᵖ =1, bᵐ⁺ᵖa⁻ᵐbᵐa⁻ᵐ =1, (ab)² = 1>
,p an odd number and m ∊ ℤ. For some values of p and m these groups have connections with the groups PSL(2,p). In Chapter 7 we attempt to show the efficiency of PSL(2, ℤ[sub]n ) x PSL(2, ℤ[sub]m). For some values of n and m we give efficient presentation for these groups. In the same chapter we also attempt to show the efficiency of PSL(2, ℤ [sub]p) x PSL(2,32). For some values of p we give an efficient presentation for these groups. In the last section of the thesis we give efficient presentations for the following direct products
(i) PSL(2,5) X PSL(2,3²)
(ii) PSL(2,7) X PSL(2,3²)
(iii) PSL(2,5) X PSL(2,3³)
Also in the last section of the thesis the structure of a perfect group of order 161280 is investigated.Semigroups with length morphismsSaunders, Bryan Jameshttp://hdl.handle.net/10023/137062018-06-04T23:16:41Z1998-01-01T00:00:00ZThe class of metrical semigroups is defined as the set consisting of those semigroups which can be homomorphically mapped into the semigroup of natural numbers (without zero) under addition.
The finitely generated members of this class are characterised and the infinitely generated case is discussed. A semigroup is called locally metrical if every finitely generated subsemigroup is metrical.
The classical Green's relations are trivial on any metrical semigroup. Generalisations 𝓗+, 𝓛+ and 𝓡+ of the Green's relations are defined and it is shown that for any cancellative metrical semigroup, S, 𝓗 + is " as big as possible " if and only if S is isomorphic to a special type of semidirect product of 𝗡 and a group. Lyndon's characterisation of free groups by length functions is discussed andalink between length functions, metrical semigroups and semigroups embeddable into free semigroups is investigated. Next the maximal locally metrical ideal of a semigroup is discussed, and the class of t-compressible semigroups is defined as the set consisting of those semigroups that have no locally metrical ideal. The class of t-compressible semigroups is seen to contain the classes of regular and simple semigroups. Finally it is shown that a large class of semigroups can be decomposed into a chain of locally metrical ideals together with a t-compressible semigroup.
1998-01-01T00:00:00ZSaunders, Bryan JamesThe class of metrical semigroups is defined as the set consisting of those semigroups which can be homomorphically mapped into the semigroup of natural numbers (without zero) under addition.
The finitely generated members of this class are characterised and the infinitely generated case is discussed. A semigroup is called locally metrical if every finitely generated subsemigroup is metrical.
The classical Green's relations are trivial on any metrical semigroup. Generalisations 𝓗+, 𝓛+ and 𝓡+ of the Green's relations are defined and it is shown that for any cancellative metrical semigroup, S, 𝓗 + is " as big as possible " if and only if S is isomorphic to a special type of semidirect product of 𝗡 and a group. Lyndon's characterisation of free groups by length functions is discussed andalink between length functions, metrical semigroups and semigroups embeddable into free semigroups is investigated. Next the maximal locally metrical ideal of a semigroup is discussed, and the class of t-compressible semigroups is defined as the set consisting of those semigroups that have no locally metrical ideal. The class of t-compressible semigroups is seen to contain the classes of regular and simple semigroups. Finally it is shown that a large class of semigroups can be decomposed into a chain of locally metrical ideals together with a t-compressible semigroup.Infinite transformation semigroupsMarques, Maria Paulahttp://hdl.handle.net/10023/137052018-06-04T23:17:09Z1983-01-01T00:00:00ZIn this thesis some topics in the field of Infinite Transformation Semigroups are investigated.
In 1966 Howie considered the full transformation semigroup 𝓣 (x) on an infinite set x of cardinality m. For each 𝝰 in 𝓣 (x) he defined defect of 𝝰 = def 𝝰 and collapse of 𝝰= C(a) to be the sets X \ X 𝝰 and { 𝓍 ∊ x : (∃∊ x, y ≠ 𝓍) X𝝰 = Y𝝰 }, respectively. Later, in 1981 he introduced the set
S[sub]m̱ = {𝝰 ∊ 𝓣(x): |def 𝝰 | = | c(𝝰) | = | ran 𝝰 | = m, |y 𝝰 [super]-1 | <m,
(∀ y ∊ ran 𝝰) }
which is a subsemigroup of 𝓣 (x) provided the cardinal m is regular. Taking m to be a regular cardinal number, Howie proved that S[sub]m̱ is then a bisimple, idempotent-generated semigroup of depth 4. Next he considered the congruence defined in S[sub]m̱ by
△[sub]m̱ = {(𝝰, β) ∊ S[sub]m̱ x S[sub]m̱ : max (|D(𝝰, β) 𝝰| , | D((𝝰, β) β | ) < m̱ }
where D(𝝰, β) = { 𝓍 ∊ X : 𝓍 𝝰 ≠ 𝓍β } and showed that S[sub]m̱* = S[sub]m̱/ △[sub]m̱ is a bisimple, congruence-free and idempotent-generated semigroup of depth 4.
In this thesis comparable results are obtained for the semigroup P[sub]m̱ which is the top principal factor of the semigroup
𝓠[sub]m̱ = {𝝰 ∊ 𝓣(x): |def 𝝰 | = | c(𝝰) | = m̱}
Here it is no longer necessary to restrict to a regular cardinal m̱. The set S[sub]m̱ considered by Howie fails to be a subsemigroup of 𝓣 (𝓍) if m̱ is not regular. It is shown that in this case <S[sub]m̱ > = O[sub]m̱ . In the case where m̱ = 𝓍₀ (a regular cardinal) it is shown that △[sub]𝓍₀ is the only proper congruence on S[sub]m̱.
Within the symmetric inverse semigroup 𝓣(𝓍), the Baer-Levi semigroup B of type (m̱, m̱) on X is considered and a dual B* found. The products BB* and B*B are investigated and the semigroup Km̱ = <B*B> is described. The top principal factor of Km̱ is denoted by Lm̱ and it is shown that Lm̱ = B*B ⋃ {O}. On the set Lm̱ a congruence δ[sub]m̱, closely analogous to the congruence △[sub]m̱ defined above, is considered, and it is shown that Lm̱ / δ[sub]m̱ is a o-bisimple, inverse and nilpotent-generated semigroup.
Finally, two embedding theorems for inverse semigroups and semigroups in general are presented. The cardinalities of some of the semigroups introduced in this thesis are studied.
1983-01-01T00:00:00ZMarques, Maria PaulaIn this thesis some topics in the field of Infinite Transformation Semigroups are investigated.
In 1966 Howie considered the full transformation semigroup 𝓣 (x) on an infinite set x of cardinality m. For each 𝝰 in 𝓣 (x) he defined defect of 𝝰 = def 𝝰 and collapse of 𝝰= C(a) to be the sets X \ X 𝝰 and { 𝓍 ∊ x : (∃∊ x, y ≠ 𝓍) X𝝰 = Y𝝰 }, respectively. Later, in 1981 he introduced the set
S[sub]m̱ = {𝝰 ∊ 𝓣(x): |def 𝝰 | = | c(𝝰) | = | ran 𝝰 | = m, |y 𝝰 [super]-1 | <m,
(∀ y ∊ ran 𝝰) }
which is a subsemigroup of 𝓣 (x) provided the cardinal m is regular. Taking m to be a regular cardinal number, Howie proved that S[sub]m̱ is then a bisimple, idempotent-generated semigroup of depth 4. Next he considered the congruence defined in S[sub]m̱ by
△[sub]m̱ = {(𝝰, β) ∊ S[sub]m̱ x S[sub]m̱ : max (|D(𝝰, β) 𝝰| , | D((𝝰, β) β | ) < m̱ }
where D(𝝰, β) = { 𝓍 ∊ X : 𝓍 𝝰 ≠ 𝓍β } and showed that S[sub]m̱* = S[sub]m̱/ △[sub]m̱ is a bisimple, congruence-free and idempotent-generated semigroup of depth 4.
In this thesis comparable results are obtained for the semigroup P[sub]m̱ which is the top principal factor of the semigroup
𝓠[sub]m̱ = {𝝰 ∊ 𝓣(x): |def 𝝰 | = | c(𝝰) | = m̱}
Here it is no longer necessary to restrict to a regular cardinal m̱. The set S[sub]m̱ considered by Howie fails to be a subsemigroup of 𝓣 (𝓍) if m̱ is not regular. It is shown that in this case <S[sub]m̱ > = O[sub]m̱ . In the case where m̱ = 𝓍₀ (a regular cardinal) it is shown that △[sub]𝓍₀ is the only proper congruence on S[sub]m̱.
Within the symmetric inverse semigroup 𝓣(𝓍), the Baer-Levi semigroup B of type (m̱, m̱) on X is considered and a dual B* found. The products BB* and B*B are investigated and the semigroup Km̱ = <B*B> is described. The top principal factor of Km̱ is denoted by Lm̱ and it is shown that Lm̱ = B*B ⋃ {O}. On the set Lm̱ a congruence δ[sub]m̱, closely analogous to the congruence △[sub]m̱ defined above, is considered, and it is shown that Lm̱ / δ[sub]m̱ is a o-bisimple, inverse and nilpotent-generated semigroup.
Finally, two embedding theorems for inverse semigroups and semigroups in general are presented. The cardinalities of some of the semigroups introduced in this thesis are studied.Idempotents, nilpotents, rank and order in finite transformation semigroupsGarba, Goje Ubahttp://hdl.handle.net/10023/137032018-06-04T23:16:44Z1992-01-01T00:00:00ZLet E, E₁ denote, respectively, the set of singular idempotents in T[sub]n (the semigroup of all full transformations on a finite set X[sub]n = {1,..., n}) and the set of idempotents of defect 1. For a singular element 𝑎 in Tn, let k(𝑎),k₁ (𝑎) be defined by the properties
𝑎 ∈ Eᵏ⁽ᵃ⁾, 𝑎 ∉ Eᵏ⁽ᵃ⁾⁻¹,
𝑎 ∈ E₁ᵏ¹⁽ᵃ⁾, 𝑎 ∉ E₁ᵏ¹⁽ᵃ⁾⁻¹.
In this Thesis, we obtain results analogous to those of Iwahori (1977), Howie (1980), Saito (1989) and Howie, Lusk and McFadden (1990) concerning the values of k(𝑎) and k₁(𝑎) for the partial transformation semigroup P[sub]n. The analogue of Howie and McFadden's (1990) result on the rank of the semigroup K(n,r) = { 𝑎 ∈ T [sub]n: |im 𝑎 | ≤ r,2 ≤ r ≤ n-1} is also obtained.
The nilpotent-generated subsemigroup of P[sub]n was characterised by Sullivan in 1987. In this work, we have obtained its depth and rank.
Nilpotents in IO[sub]n and PO[sub]n (the semigroup of all partial one-one order-preserving maps, and all partial order-preserving maps) are studied. A characterisation of their nilpotent-generated subsemigroups is obtained. So also are their depth and rank. We have also characterised their nilpotent-generated subsemigroup for the infinite set X = {1,2,...}. The rank of the semigroup L(n,r) = {a ∈ S : |im 𝑎 | ≤r, 1 ≤ r ≤ n - 2} is investigated for S = O[sub]n,PO[sub]n,SPO[sub]n and I[sub]n (where O[sub]n is the semigroup of all order-preserving full transformations, SPO[sub]n the semigroup of all strictly partial order- preserving maps, and In the semigroup of one-one partial transformation).
1992-01-01T00:00:00ZGarba, Goje UbaLet E, E₁ denote, respectively, the set of singular idempotents in T[sub]n (the semigroup of all full transformations on a finite set X[sub]n = {1,..., n}) and the set of idempotents of defect 1. For a singular element 𝑎 in Tn, let k(𝑎),k₁ (𝑎) be defined by the properties
𝑎 ∈ Eᵏ⁽ᵃ⁾, 𝑎 ∉ Eᵏ⁽ᵃ⁾⁻¹,
𝑎 ∈ E₁ᵏ¹⁽ᵃ⁾, 𝑎 ∉ E₁ᵏ¹⁽ᵃ⁾⁻¹.
In this Thesis, we obtain results analogous to those of Iwahori (1977), Howie (1980), Saito (1989) and Howie, Lusk and McFadden (1990) concerning the values of k(𝑎) and k₁(𝑎) for the partial transformation semigroup P[sub]n. The analogue of Howie and McFadden's (1990) result on the rank of the semigroup K(n,r) = { 𝑎 ∈ T [sub]n: |im 𝑎 | ≤ r,2 ≤ r ≤ n-1} is also obtained.
The nilpotent-generated subsemigroup of P[sub]n was characterised by Sullivan in 1987. In this work, we have obtained its depth and rank.
Nilpotents in IO[sub]n and PO[sub]n (the semigroup of all partial one-one order-preserving maps, and all partial order-preserving maps) are studied. A characterisation of their nilpotent-generated subsemigroups is obtained. So also are their depth and rank. We have also characterised their nilpotent-generated subsemigroup for the infinite set X = {1,2,...}. The rank of the semigroup L(n,r) = {a ∈ S : |im 𝑎 | ≤r, 1 ≤ r ≤ n - 2} is investigated for S = O[sub]n,PO[sub]n,SPO[sub]n and I[sub]n (where O[sub]n is the semigroup of all order-preserving full transformations, SPO[sub]n the semigroup of all strictly partial order- preserving maps, and In the semigroup of one-one partial transformation).On a family of semigroup congruencesKopamu, Samuel Joseph Lyambianhttp://hdl.handle.net/10023/136992018-06-04T23:16:46Z1996-01-01T00:00:00ZWe introduce in this thesis a new family of semigroup congruences, and we set out to prove that it is worth studying them for the following very important reasons:
(a) that it provides an alternative way of studying algebraic structures of semigroups, thus shedding new light over semigroup structures already known, and it also provides new information about other structures not formerly understood;
(b) that it is useful for constructing new semigroups, hence producing new and interesting classes of semigroups from known classes; and
(c) that it is useful for classifying semigroups, particularly in describing lattices formed by semigroup species such as varieties, pseudovarieties, existence varieties etc.
This interesting family of congruences is described as follows: for any semigroup S, and any ordered pair (n,m) of non-negative integers, define ⦵(n,m) = {(a,b): uav = ubv, for all ⋿Sn and v ⋿Sm}, and we make the convention that S¹ = S and that S0 denotes the set containing only the empty word. The particular cases ⦵(0,1), ⦵(1,0) and ⦵(0,0) were considered by the author in his M.Sc. thesis (1991). In fact, one can recognise ⦵(1,0) to be the well known kernel of the right regular representation of S. It turns out that if S is reductive (for example, if S is a monoid), then ⦵(i,j) is equal to ⦵(0,0) - the identity relation on S, for every (i,j).
After developing the tools required for the latter part of the thesis in Chapters 0-2, in Chapter 3 we introduce a new class of semigroups - the class of all structurally regular semigroups. Making use of a new Mal'tsev-type product, in Chapters 4,5,6 and 7, we describe the lattices formed by certain varieties of structurally regular semigroups.
Many interesting open problems are posed throughout the thesis, and brief literature reviews are inserted in the text where appropriate.
1996-01-01T00:00:00ZKopamu, Samuel Joseph LyambianWe introduce in this thesis a new family of semigroup congruences, and we set out to prove that it is worth studying them for the following very important reasons:
(a) that it provides an alternative way of studying algebraic structures of semigroups, thus shedding new light over semigroup structures already known, and it also provides new information about other structures not formerly understood;
(b) that it is useful for constructing new semigroups, hence producing new and interesting classes of semigroups from known classes; and
(c) that it is useful for classifying semigroups, particularly in describing lattices formed by semigroup species such as varieties, pseudovarieties, existence varieties etc.
This interesting family of congruences is described as follows: for any semigroup S, and any ordered pair (n,m) of non-negative integers, define ⦵(n,m) = {(a,b): uav = ubv, for all ⋿Sn and v ⋿Sm}, and we make the convention that S¹ = S and that S0 denotes the set containing only the empty word. The particular cases ⦵(0,1), ⦵(1,0) and ⦵(0,0) were considered by the author in his M.Sc. thesis (1991). In fact, one can recognise ⦵(1,0) to be the well known kernel of the right regular representation of S. It turns out that if S is reductive (for example, if S is a monoid), then ⦵(i,j) is equal to ⦵(0,0) - the identity relation on S, for every (i,j).
After developing the tools required for the latter part of the thesis in Chapters 0-2, in Chapter 3 we introduce a new class of semigroups - the class of all structurally regular semigroups. Making use of a new Mal'tsev-type product, in Chapters 4,5,6 and 7, we describe the lattices formed by certain varieties of structurally regular semigroups.
Many interesting open problems are posed throughout the thesis, and brief literature reviews are inserted in the text where appropriate.Numerical preservation of velocity induced invariant regions for reaction-diffusion systems on evolving surfacesFrittelli, MassimoMadzvamuse, AnotidoSgura, IvonneVenkataraman, Chandrasekharhttp://hdl.handle.net/10023/136982018-06-10T23:39:51Z2018-06-01T00:00:00ZWe propose and analyse a finite element method with mass lumping (LESFEM) for the numerical approximation of reaction–diffusion systems (RDSs) on surfaces in ℝ3 that evolve under a given velocity field. A fully-discrete method based on the implicit–explicit (IMEX) Euler time-discretisation is formulated and dilation rates which act as indicators of the surface evolution are introduced. Under the assumption that the mesh preserves the Delaunay regularity under evolution, we prove a sufficient condition, that depends on the dilation rates, for the existence of invariant regions (i) at the spatially discrete level with no restriction on the mesh size and (ii) at the fully-discrete level under a timestep restriction that depends on the kinetics, only. In the specific case of the linear heat equation, we prove a semi- and a fully-discrete maximum principle. For the well-known activator-depleted and Thomas reaction–diffusion models we prove the existence of a family of rectangles in the phase space that are invariant only under specific growth laws. Two numerical examples are provided to computationally demonstrate (i) the discrete maximum principle and optimal convergence for the heat equation on a linearly growing sphere and (ii) the existence of an invariant region for the LESFEM–IMEX Euler discretisation of a RDS on a logistically growing surface.
The authors (MF, AM, IS CV) would like to thank the Isaac Newton Institute for Mathematical Sciences for its hospitality during the programme [Coupling Geometric PDEs with Physics for Cell Morphology, Motility and Pattern Formation] supported by EPSRC Grant Number EP/K032208/1. MF’s and IS’s research work has been performed under the auspices of the Italian National Group for Scientific Calculus (GNCS-INdAM). This work (AM, CV) is partly supported by the EPSRC grant number EP/J016780/1 and the Leverhulme Trust Research Project Grant (RPG-2014-149). AM acknowledges funding from the European Union Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 642866.
2018-06-01T00:00:00ZFrittelli, MassimoMadzvamuse, AnotidoSgura, IvonneVenkataraman, ChandrasekharWe propose and analyse a finite element method with mass lumping (LESFEM) for the numerical approximation of reaction–diffusion systems (RDSs) on surfaces in ℝ3 that evolve under a given velocity field. A fully-discrete method based on the implicit–explicit (IMEX) Euler time-discretisation is formulated and dilation rates which act as indicators of the surface evolution are introduced. Under the assumption that the mesh preserves the Delaunay regularity under evolution, we prove a sufficient condition, that depends on the dilation rates, for the existence of invariant regions (i) at the spatially discrete level with no restriction on the mesh size and (ii) at the fully-discrete level under a timestep restriction that depends on the kinetics, only. In the specific case of the linear heat equation, we prove a semi- and a fully-discrete maximum principle. For the well-known activator-depleted and Thomas reaction–diffusion models we prove the existence of a family of rectangles in the phase space that are invariant only under specific growth laws. Two numerical examples are provided to computationally demonstrate (i) the discrete maximum principle and optimal convergence for the heat equation on a linearly growing sphere and (ii) the existence of an invariant region for the LESFEM–IMEX Euler discretisation of a RDS on a logistically growing surface.Nonstandard quantum groups: twisting constructions and noncommutative differential geometryJacobs, Andrew D.http://hdl.handle.net/10023/136932018-06-04T23:16:55Z1998-01-01T00:00:00ZThe general subject of this thesis is quantum groups. The major original results are obtained in the particular areas of twisting constructions and noncommutative differential geometry.
Chapters 1 and 2 are intended to explain to the reader what are quantum groups. They are written in the form of a series of linked results and definitions. Chapter 1 reviews the theory of Lie algebras and Lie groups, focusing attention in particular on the classical Lie algebras and groups. Though none of the quoted results are due to the author, such a review, aimed specifically at setting up the paradigm which provides essential guidance in the theory of quantum groups, does not seem to have appeared already. In Chapter 2 the elements of the quantum group theory are recalled. Once again, almost none of the results are due to the author, though in Section 2.10, some results concerning the nonstandard Jordanian group are presented, by way of a worked example, which have not been published.
Chapter 3 concerns twisting constructions. We introduce a new class of 2-cocycles defined explicitly on the generators of certain multiparameter standard quantum groups. These allow us, through the process of twisting the familiar standard quantum groups, to generate new as well as previously known examples of non-standard quantum groups. In particular we are able to construct generalisations of both the Cremmer-Gervais deformation of SL(3) and the so called esoteric quantum groups of Fronsdal and Galindo in an explicit and straightforward manner.
In Chapter 4 we consider the differential calculus on Hopf algebras as introduced by Woronowicz. We classify all 4-dimensional first order bicovariant calculi on the Jordanian quantum group GL[sub]h,[sub]g(2) and all 3-dimensional first order bicovariant calculi on the Jordanian quantum group SL[sub]h(2). In both cases we assume that the bicovariant bimodules are generated as left modules by the differentials of the quantum group generators. It is found that there are 3 1-parameter families of 4-dimensional bicovariant first order calculi on GL[sub]h,[sub]g(2) and that there is a single, unique, 3-dimensional bicovariant calculus on SL[sub]h(2). This 3-dimensional calculus may be obtained through a classical-like reduction from any one of the three families of 4-dimensional calculi on GL[sub]h,[sub]g(2). Details of the higher order calculi and also the quantum Lie algebras are presented for all calculi. The quantum Lie algebra obtained from the bicovariant calculus on SL[sub]h(2) is shown to be isomorphic to the quantum Lie algebra we obtain as an ad-submodule within the Jordanian universal enveloping algebra U[sub]h(sl[sub]2(C)) and also through a consideration of the decomposition of the tensor product of two copies of the deformed adjoint module. We also obtain the quantum Killing form for this quantum Lie algebra.
1998-01-01T00:00:00ZJacobs, Andrew D.The general subject of this thesis is quantum groups. The major original results are obtained in the particular areas of twisting constructions and noncommutative differential geometry.
Chapters 1 and 2 are intended to explain to the reader what are quantum groups. They are written in the form of a series of linked results and definitions. Chapter 1 reviews the theory of Lie algebras and Lie groups, focusing attention in particular on the classical Lie algebras and groups. Though none of the quoted results are due to the author, such a review, aimed specifically at setting up the paradigm which provides essential guidance in the theory of quantum groups, does not seem to have appeared already. In Chapter 2 the elements of the quantum group theory are recalled. Once again, almost none of the results are due to the author, though in Section 2.10, some results concerning the nonstandard Jordanian group are presented, by way of a worked example, which have not been published.
Chapter 3 concerns twisting constructions. We introduce a new class of 2-cocycles defined explicitly on the generators of certain multiparameter standard quantum groups. These allow us, through the process of twisting the familiar standard quantum groups, to generate new as well as previously known examples of non-standard quantum groups. In particular we are able to construct generalisations of both the Cremmer-Gervais deformation of SL(3) and the so called esoteric quantum groups of Fronsdal and Galindo in an explicit and straightforward manner.
In Chapter 4 we consider the differential calculus on Hopf algebras as introduced by Woronowicz. We classify all 4-dimensional first order bicovariant calculi on the Jordanian quantum group GL[sub]h,[sub]g(2) and all 3-dimensional first order bicovariant calculi on the Jordanian quantum group SL[sub]h(2). In both cases we assume that the bicovariant bimodules are generated as left modules by the differentials of the quantum group generators. It is found that there are 3 1-parameter families of 4-dimensional bicovariant first order calculi on GL[sub]h,[sub]g(2) and that there is a single, unique, 3-dimensional bicovariant calculus on SL[sub]h(2). This 3-dimensional calculus may be obtained through a classical-like reduction from any one of the three families of 4-dimensional calculi on GL[sub]h,[sub]g(2). Details of the higher order calculi and also the quantum Lie algebras are presented for all calculi. The quantum Lie algebra obtained from the bicovariant calculus on SL[sub]h(2) is shown to be isomorphic to the quantum Lie algebra we obtain as an ad-submodule within the Jordanian universal enveloping algebra U[sub]h(sl[sub]2(C)) and also through a consideration of the decomposition of the tensor product of two copies of the deformed adjoint module. We also obtain the quantum Killing form for this quantum Lie algebra.Computing with simple groups: maximal subgroups and presentationsJamali, Ali-Rezahttp://hdl.handle.net/10023/136922018-06-04T23:17:16Z1989-01-01T00:00:00ZFor the non-abelian simple groups G of order up to 10⁶ , excluding the groups PSL(2,q), q > 9, the presentations in terms of an involution a and an element b of minimal order (with respect to a) such that G=<a,b> are well known. The presentations are complete in the sense that any pair (x,y) of generators of G satisfying x²=yᵐ=1, with m minimal, will satisfy the defining relations of just one presentation in the list. There are 106 such presentations.
Using a computer, we give generators for each maximal subgroup of the groups G. For each presentation of G, the generators of maximal subgroups are given as words in the group generators. Similarly generators for a Sylow p-subgroup of G, for each p, are given. For each group G, we give a representative for each conjugacy class of the group as a word in the group generators.
Minimal presentations for each Sylow p-subgroup of the groups G, and for most of the maximal subgroups of G are constructed. To obtain such presentations, the Schur multipliers of the underlying groups are calculated.
The same tasks are carried out for those groups PSL(2,q) of order less than 10⁶ which are included in the "ATLAS of finite groups". For these groups we consider a presentation on two generators x, y with x²=y³=1.
A finite group G is said to be efficient if it has a presentation on d generators and d+rank(M(G)) relations (for some d) where M(G) is the Schur multiplier of G. We show that the simple groups J₁, PSU(3,5) and M₂₂ are efficient. We also give efficient presentations for the direct products A₅xA₆, A₅xA₆,A₆xA₇ where Ĥ denotes the covering group of H.
1989-01-01T00:00:00ZJamali, Ali-RezaFor the non-abelian simple groups G of order up to 10⁶ , excluding the groups PSL(2,q), q > 9, the presentations in terms of an involution a and an element b of minimal order (with respect to a) such that G=<a,b> are well known. The presentations are complete in the sense that any pair (x,y) of generators of G satisfying x²=yᵐ=1, with m minimal, will satisfy the defining relations of just one presentation in the list. There are 106 such presentations.
Using a computer, we give generators for each maximal subgroup of the groups G. For each presentation of G, the generators of maximal subgroups are given as words in the group generators. Similarly generators for a Sylow p-subgroup of G, for each p, are given. For each group G, we give a representative for each conjugacy class of the group as a word in the group generators.
Minimal presentations for each Sylow p-subgroup of the groups G, and for most of the maximal subgroups of G are constructed. To obtain such presentations, the Schur multipliers of the underlying groups are calculated.
The same tasks are carried out for those groups PSL(2,q) of order less than 10⁶ which are included in the "ATLAS of finite groups". For these groups we consider a presentation on two generators x, y with x²=y³=1.
A finite group G is said to be efficient if it has a presentation on d generators and d+rank(M(G)) relations (for some d) where M(G) is the Schur multiplier of G. We show that the simple groups J₁, PSU(3,5) and M₂₂ are efficient. We also give efficient presentations for the direct products A₅xA₆, A₅xA₆,A₆xA₇ where Ĥ denotes the covering group of H.Semigroup presentationsIbrahim, Mohammed Ali Fayahttp://hdl.handle.net/10023/136892018-06-04T23:17:04Z1997-01-01T00:00:00ZIn this thesis we consider 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 other related results.
After an introduction in Chapter 1, we consider the first problem in Chapter 2, and establish a presentation for the commutative semigroup of integers Zpt. Dually, in Chapter 3 we consider the second problem and study presentations of semigroups related to the direct product of cyclic groups. In Chapter 4 we study presentations of semigroups related to dihedral groups and establish their V-classes structure in Chapter 5. In Chapter 6 we establish some results related to the Schutzenberger group which were suggested by our studies of the semigroup presentations in Chapters 3 and 4. Finally, in Chapter 7 we define and study new classes of semigroups which we call R, L-semi-commutative and semi-commutative semigroups and they were also suggested by our studies of the semigroup presentations in Chapters 3 and 4.
1997-01-01T00:00:00ZIbrahim, Mohammed Ali FayaIn this thesis we consider 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 other related results.
After an introduction in Chapter 1, we consider the first problem in Chapter 2, and establish a presentation for the commutative semigroup of integers Zpt. Dually, in Chapter 3 we consider the second problem and study presentations of semigroups related to the direct product of cyclic groups. In Chapter 4 we study presentations of semigroups related to dihedral groups and establish their V-classes structure in Chapter 5. In Chapter 6 we establish some results related to the Schutzenberger group which were suggested by our studies of the semigroup presentations in Chapters 3 and 4. Finally, in Chapter 7 we define and study new classes of semigroups which we call R, L-semi-commutative and semi-commutative semigroups and they were also suggested by our studies of the semigroup presentations in Chapters 3 and 4.Algorithms for subgroup presentations: computer implementation and applicationsHeggie, Patricia, M.http://hdl.handle.net/10023/136842018-06-04T23:17:03Z1991-01-01T00:00:00ZOne of the main algorithms of computational group theory is the Todd-Coxeter coset enumeration algorithm, which provides a systematic method for finding the index of a subgroup of a finitely presented group. This has been extended in various ways to provide not only the index of a subgroup, but also a presentation for the subgroup. These methods tie in with a technique introduced by Reidemeister in the 1920's and later improved by Schreier, now known as the Reidemeister-Schreier algorithm.
In this thesis we discuss some of these variants of the Todd-Coxeter algorithm and their inter-relation, and also look at existing computer implementations of these different techniques. We then go on to describe a new package for coset methods which incorporates various types of coset enumeration, including modified Todd- Coxeter methods and the Reidemeister-Schreier process. This also has the capability of carrying out Tietze transformation simplification. Statistics obtained from running the new package on a collection of test examples are given, and the various techniques compared.
Finally, we use these algorithms, both theoretically and as computer implementations, to investigate a particular class of finitely presented groups defined by the presentation: < a, b | aⁿ = b² = (ab-1) ß =1, ab² = ba²>. Some interesting results have been discovered about these groups for various values of β and n. For example, if n is odd, the groups turn out to be finite and metabelian, and if β= 3 or β= 4 the derived group has an order which is dependent on the values of n (mod 8) and n (mod 12) respectively.
1991-01-01T00:00:00ZHeggie, Patricia, M.One of the main algorithms of computational group theory is the Todd-Coxeter coset enumeration algorithm, which provides a systematic method for finding the index of a subgroup of a finitely presented group. This has been extended in various ways to provide not only the index of a subgroup, but also a presentation for the subgroup. These methods tie in with a technique introduced by Reidemeister in the 1920's and later improved by Schreier, now known as the Reidemeister-Schreier algorithm.
In this thesis we discuss some of these variants of the Todd-Coxeter algorithm and their inter-relation, and also look at existing computer implementations of these different techniques. We then go on to describe a new package for coset methods which incorporates various types of coset enumeration, including modified Todd- Coxeter methods and the Reidemeister-Schreier process. This also has the capability of carrying out Tietze transformation simplification. Statistics obtained from running the new package on a collection of test examples are given, and the various techniques compared.
Finally, we use these algorithms, both theoretically and as computer implementations, to investigate a particular class of finitely presented groups defined by the presentation: < a, b | aⁿ = b² = (ab-1) ß =1, ab² = ba²>. Some interesting results have been discovered about these groups for various values of β and n. For example, if n is odd, the groups turn out to be finite and metabelian, and if β= 3 or β= 4 the derived group has an order which is dependent on the values of n (mod 8) and n (mod 12) respectively.On the efficiency of finite groupsBrookes, Melaniehttp://hdl.handle.net/10023/136822018-06-04T23:16:49Z1996-01-01T00:00:00ZIn Chapter 2 of this thesis we look at methods for finding efficient presentations of the transitive permutation groups of degree ≤ 12. Chapter 3 gives efficient presentations for certain direct products of groups including PSL(2, P)2 SL(2, p) X SL(2, 8), PSL(2, p) x C2, for prime p ≥ 5 and PSL(2, 25)3. Chapter 4 introduces a new class of inefficient groups and Chapter 5 gives a brief survey of some of the open problems relating to the efficiency of finite groups.
1996-01-01T00:00:00ZBrookes, MelanieIn Chapter 2 of this thesis we look at methods for finding efficient presentations of the transitive permutation groups of degree ≤ 12. Chapter 3 gives efficient presentations for certain direct products of groups including PSL(2, P)2 SL(2, p) X SL(2, 8), PSL(2, p) x C2, for prime p ≥ 5 and PSL(2, 25)3. Chapter 4 introduces a new class of inefficient groups and Chapter 5 gives a brief survey of some of the open problems relating to the efficiency of finite groups.Last call: Passive acoustic monitoring shows continued rapid decline of critically endangered vaquitaThomas, LenJaramillo-legorreta, ArmandoCardenas-Hinojosa, GustavoNieto-Garcia, EdwynaRojas-Bracho, LorenzoVer Hoef, Jay M.Moore, JeffreyTaylor, BarbaraBarlow, JayTregenza, Nicholashttp://hdl.handle.net/10023/135762018-05-29T23:16:21Z2017-11-01T00:00:00ZThe vaquita is a critically endangered species of porpoise. It produces echolocation clicks, making it a good candidate for passive acoustic monitoring. A systematic grid of sensors has been deployed for 3 months annually since 2011; results from 2016 are reported here. Statistical models (to compensate for non-uniform data loss) show an overall decline in the acoustic detection rate between 2015 and 2016 of 49% (95% credible interval 82% decline to 8% increase), and total decline between 2011 and 2016 of over 90%. Assuming the acoustic detection rate is proportional to population size, approximately 30 vaquita (95% credible interval 8–96) remained in November 2016.
Funding: the Mexican Government (through the Mexican Secretaría de Medio Ambiente y Recursos Naturales), especially Minister R. Pacchiano and A. Michel; U.S. Marine Mammal Commission, in particular T. Ragen, R. Lent, and P. Thomas; the World Wildlife Fund (WWF) Mexico, in particular O. Vidal and E. Sanjurjo; Le Equipe Cousteau; The Ocean Foundation; Fonds de Dotation pour la Biodiversité; MAAF Assurances (Save Your Logo); WWF-US; Opel Project Earth; Fideicomiso Fondo para la Biodiversidad; Instituto Nacional de Ecología y Cambio Climático; Comisión Nacional de Áreas Naturales Protegidas; and Directorate of the Reserva de la Biósfera Alto Golfo de California y Delta del Río Colorado.
2017-11-01T00:00:00ZThomas, LenJaramillo-legorreta, ArmandoCardenas-Hinojosa, GustavoNieto-Garcia, EdwynaRojas-Bracho, LorenzoVer Hoef, Jay M.Moore, JeffreyTaylor, BarbaraBarlow, JayTregenza, NicholasThe vaquita is a critically endangered species of porpoise. It produces echolocation clicks, making it a good candidate for passive acoustic monitoring. A systematic grid of sensors has been deployed for 3 months annually since 2011; results from 2016 are reported here. Statistical models (to compensate for non-uniform data loss) show an overall decline in the acoustic detection rate between 2015 and 2016 of 49% (95% credible interval 82% decline to 8% increase), and total decline between 2011 and 2016 of over 90%. Assuming the acoustic detection rate is proportional to population size, approximately 30 vaquita (95% credible interval 8–96) remained in November 2016.Impact of type II spicules in the corona : simulations and synthetic observablesMartínez-Sykora, JuanDe Pontieu, BartDe Moortel, InekeHansteen, ViggoCarlsson, Matshttp://hdl.handle.net/10023/135692018-05-28T23:17:03Z2018-05-02T00:00:00ZThe role of type II spicules in the corona has been a much debated topic in recent years. This paper aims to shed light on the impact of type II spicules in the corona using novel 2.5D radiative MHD simulations including ion-neutral interaction effects with the Bifrost code. We find that the formation of simulated type II spicules, driven by the release of magnetic tension, impacts the corona in various manners. Associated with the formation of spicules, the corona exhibits 1) magneto-acoustic shocks and flows which supply mass to coronal loops, and 2) transversal magnetic waves and electric currents that propagate at Alfvén speeds. The transversal waves and electric currents, generated by the spicule's driver and lasting for many minutes, are dissipated and heat the associated loop. These complex interactions in the corona can be connected with blue shifted secondary components in coronal spectral lines (Red-Blue asymmetries) observed with Hinode/EIS and SOHO/SUMER, as well as the EUV counterpart of type II spicules and propagating coronal disturbances (PCDs) observed with the 171 Å and 193 Å SDO/AIA channels.
We gratefully acknowledge support by NASA grants, NNX16AG90G, NNH15ZDA001N, NNX17AD33G, and NNG09FA40C (IRIS), NSF grant AST1714955. This research has received funding from the UK Science and Technology Facilities Council (Consolidated Grant ST/K000950/1) and the European Union Horizon 2020 research and innovation programme (grant agreement No. 647214). This research was supported by the European Research Council under the European Union's Seventh Framework Programme (FP7/2007-2013) / ERC Grant agreement nr. 291058. We thankfully acknowledge the support of the Research Council of Norway through grant 230938/F50, through its Center of Excellence scheme, project number 262622, and through grants of computing time from the Programme for Supercomputing.
2018-05-02T00:00:00ZMartínez-Sykora, JuanDe Pontieu, BartDe Moortel, InekeHansteen, ViggoCarlsson, MatsThe role of type II spicules in the corona has been a much debated topic in recent years. This paper aims to shed light on the impact of type II spicules in the corona using novel 2.5D radiative MHD simulations including ion-neutral interaction effects with the Bifrost code. We find that the formation of simulated type II spicules, driven by the release of magnetic tension, impacts the corona in various manners. Associated with the formation of spicules, the corona exhibits 1) magneto-acoustic shocks and flows which supply mass to coronal loops, and 2) transversal magnetic waves and electric currents that propagate at Alfvén speeds. The transversal waves and electric currents, generated by the spicule's driver and lasting for many minutes, are dissipated and heat the associated loop. These complex interactions in the corona can be connected with blue shifted secondary components in coronal spectral lines (Red-Blue asymmetries) observed with Hinode/EIS and SOHO/SUMER, as well as the EUV counterpart of type II spicules and propagating coronal disturbances (PCDs) observed with the 171 Å and 193 Å SDO/AIA channels.Application of the Todd-Coxeter coset enumeration algorithmCampbell, C. M. (Colin Matthew)http://hdl.handle.net/10023/135082018-05-23T23:15:58Z1975-01-01T00:00:00ZThis thesis is concerned with a topic in combinatorial group theory and, in particular, with a study of some groups with finite presentations. After preliminary definitions and theorems we describe the Todd-Coxeter coset enumeration algorithm and the modified Todd-Coxeter algorithm which shows that, given a finitely generated subgroup H of finite index in a finitely presented group G, we can find a presentation for H. We then give elementary examples illustrating the algorithms and include a discussion on the computer programmes that are to be used. In the main part of the thesis we investigate two classes of cyclically presented groups. Supposewhere w1 = w is a word in a1,a2,...,an, and wi+1 is obtained from wi by applying the permutation (1 2 ... n) to the suffices of the a's. The first class we investigate are the groups that is the groups G(l,m,n) are groups of type G2 (w). Secondly we investigate the Fibonacci-type groups H(r,n,k,s,h) obtained when, for some integers r,s,h > 1, k > O, the word w is given by Fibonacci groups being the special case given by k = s = h = 1. For both classes we begin by giving some homomorphisms and isomorphisms that may be obtained. We show, using the Todd-Coxeter algorithm when appropriate, that the six groups G(2,2,3), G(2,2,-3), G(-l,-l,4), G(2,3,-2), G(-2,2,-1) and G(-2,3,l) are finite non-metacyclic groups of deficiency zero, having orders 215.33, 28.33, 29.3.5, 23.33.7, 23.3.5.11 amd 23.36 respectively. We also show that the groups G(1-n, 6, n) where n = 1 mod 5 give an infinite series of non-metacyclic groups. We consider the structure of the non-metacyclic groups H(3,6,1,1,1) and H(3,6,5,l,2) both of order 1512, showing that neither is isomorphic to G(2, 3, -2) another non-metacyclic group of order 1512. In a paper on the Fibonacci groups D.L. Johnson, J.W. Wamsley and D. Wright pose two questions relating to the Fibonacci groups for the case r = 1 mod n, namely to find 2-generator 2-relation presentations for them and also their orders. We answer these questions and generalise the results to the class H(r,n,k,s,1) where it is shown that H(r,n,k,s,1) is metacyclic if (i) r = s mod n, (ii) (r,n) = 1, (iii) (r + k - 1, n) - 1, and a 2-generator 2-relation presentation is found for these groups. Further if (iv) (r,s) = 1, then we show that H(r,n,k,s,1) is a finite metacyclic group of order rn - sn. A possible generalisation to the groups H(r,n,k,s,h) is considered. Finally the metacyclic groups H(r,4,1,2,1), r odd are discussed.
1975-01-01T00:00:00ZCampbell, C. M. (Colin Matthew)This thesis is concerned with a topic in combinatorial group theory and, in particular, with a study of some groups with finite presentations. After preliminary definitions and theorems we describe the Todd-Coxeter coset enumeration algorithm and the modified Todd-Coxeter algorithm which shows that, given a finitely generated subgroup H of finite index in a finitely presented group G, we can find a presentation for H. We then give elementary examples illustrating the algorithms and include a discussion on the computer programmes that are to be used. In the main part of the thesis we investigate two classes of cyclically presented groups. Supposewhere w1 = w is a word in a1,a2,...,an, and wi+1 is obtained from wi by applying the permutation (1 2 ... n) to the suffices of the a's. The first class we investigate are the groups that is the groups G(l,m,n) are groups of type G2 (w). Secondly we investigate the Fibonacci-type groups H(r,n,k,s,h) obtained when, for some integers r,s,h > 1, k > O, the word w is given by Fibonacci groups being the special case given by k = s = h = 1. For both classes we begin by giving some homomorphisms and isomorphisms that may be obtained. We show, using the Todd-Coxeter algorithm when appropriate, that the six groups G(2,2,3), G(2,2,-3), G(-l,-l,4), G(2,3,-2), G(-2,2,-1) and G(-2,3,l) are finite non-metacyclic groups of deficiency zero, having orders 215.33, 28.33, 29.3.5, 23.33.7, 23.3.5.11 amd 23.36 respectively. We also show that the groups G(1-n, 6, n) where n = 1 mod 5 give an infinite series of non-metacyclic groups. We consider the structure of the non-metacyclic groups H(3,6,1,1,1) and H(3,6,5,l,2) both of order 1512, showing that neither is isomorphic to G(2, 3, -2) another non-metacyclic group of order 1512. In a paper on the Fibonacci groups D.L. Johnson, J.W. Wamsley and D. Wright pose two questions relating to the Fibonacci groups for the case r = 1 mod n, namely to find 2-generator 2-relation presentations for them and also their orders. We answer these questions and generalise the results to the class H(r,n,k,s,1) where it is shown that H(r,n,k,s,1) is metacyclic if (i) r = s mod n, (ii) (r,n) = 1, (iii) (r + k - 1, n) - 1, and a 2-generator 2-relation presentation is found for these groups. Further if (iv) (r,s) = 1, then we show that H(r,n,k,s,1) is a finite metacyclic group of order rn - sn. A possible generalisation to the groups H(r,n,k,s,h) is considered. Finally the metacyclic groups H(r,4,1,2,1), r odd are discussed.Centralisers and normalisers in symmetric and alternating groupsBilgiç, Huseyinhttp://hdl.handle.net/10023/135072018-05-23T23:15:57Z1998-01-01T00:00:00ZIn this thesis, we analyse the structure of the centraliser of an element and of the normaliser of a cyclic subgroup in both Sn and An. We show that the centraliser in Sn of a permutation can be written as a direct product of centralisers of regular permutations and that the centraliser of a regular permutation is a wreath product. In certain cases we prove that this wreath product splits as a direct product and we analyse the centre of the subgroup. We calculate the centraliser of a general permutation in An and show how this is related to the centralisers of regular permutations. We investigate the normaliser of the cyclic subgroup generated by an element of Sn and show how this is related to the centraliser of the permutation. We calculate the centre of the normaliser and investigate when the normaliser splits as a direct product. We carry out a similar investigation for normalisers of cyclic subgroups of An and investigate the relationship between normalisers in An and Sn. We give presentations for both centralisers and normalisers.
1998-01-01T00:00:00ZBilgiç, HuseyinIn this thesis, we analyse the structure of the centraliser of an element and of the normaliser of a cyclic subgroup in both Sn and An. We show that the centraliser in Sn of a permutation can be written as a direct product of centralisers of regular permutations and that the centraliser of a regular permutation is a wreath product. In certain cases we prove that this wreath product splits as a direct product and we analyse the centre of the subgroup. We calculate the centraliser of a general permutation in An and show how this is related to the centralisers of regular permutations. We investigate the normaliser of the cyclic subgroup generated by an element of Sn and show how this is related to the centraliser of the permutation. We calculate the centre of the normaliser and investigate when the normaliser splits as a direct product. We carry out a similar investigation for normalisers of cyclic subgroups of An and investigate the relationship between normalisers in An and Sn. We give presentations for both centralisers and normalisers.Some applications of computer algebra and interval mathematicsMonsi, Mansor Binhttp://hdl.handle.net/10023/135022018-05-23T23:15:43Z1988-01-01T00:00:00ZThis thesis contains some applications of Computer Algebra to unconstrained optimization and some applications of Interval Mathematics to the problem of simultaneously bounding the simple zeros of polynomials. Chapter 1 contains a brief introduction to Computer Algebra and Interval Mathematics, and several of the fundamental results from Interval Mathematics which are used in Chapters 4 and 5. Chapter 2 contains a survey of those features of the symbol manipulation package ALgLIB[Shew-85] which it is necessary to understand in order to use ALgLIB as explained in Chapter 3. Chapter 3 contains a description of Sisser's method [Sis-82a] for unconstrained minimization and several modifications thereof which are implemented using the pseudo-code of Dennis and Schnabel [DenS-83], and ALgLIB, Chapter 3 also contains numerical results corresponding to Sisser's method and its modifications for 7 examples. Chapter 4 contains a new algorithm PRSS for the simultaneous estimation of polynomial zeros and the corresponding interval form IRSS for simultaneously bounding real polynomial zeros. Comparisons are made with some related existing algorithms. Numerical results of the comparisons are also given in this chapter. Chapter 5 contains an application of an idea due to Neumaier [Neu-85] to the problem of constructing interval versions of point iterative procedures for the estimation of simple zeros of analytic functions. In particular, interval versions of some point iterative procedures for the simultaneous estimation of simple (complex) polynomial zeros are described. Finally, numerical results are given to show the efficiency of the new algorithm.
1988-01-01T00:00:00ZMonsi, Mansor BinThis thesis contains some applications of Computer Algebra to unconstrained optimization and some applications of Interval Mathematics to the problem of simultaneously bounding the simple zeros of polynomials. Chapter 1 contains a brief introduction to Computer Algebra and Interval Mathematics, and several of the fundamental results from Interval Mathematics which are used in Chapters 4 and 5. Chapter 2 contains a survey of those features of the symbol manipulation package ALgLIB[Shew-85] which it is necessary to understand in order to use ALgLIB as explained in Chapter 3. Chapter 3 contains a description of Sisser's method [Sis-82a] for unconstrained minimization and several modifications thereof which are implemented using the pseudo-code of Dennis and Schnabel [DenS-83], and ALgLIB, Chapter 3 also contains numerical results corresponding to Sisser's method and its modifications for 7 examples. Chapter 4 contains a new algorithm PRSS for the simultaneous estimation of polynomial zeros and the corresponding interval form IRSS for simultaneously bounding real polynomial zeros. Comparisons are made with some related existing algorithms. Numerical results of the comparisons are also given in this chapter. Chapter 5 contains an application of an idea due to Neumaier [Neu-85] to the problem of constructing interval versions of point iterative procedures for the estimation of simple zeros of analytic functions. In particular, interval versions of some point iterative procedures for the simultaneous estimation of simple (complex) polynomial zeros are described. Finally, numerical results are given to show the efficiency of the new algorithm.Proof diagrams and term rewriting with applications to computational algebraShand, Duncanhttp://hdl.handle.net/10023/134982018-05-23T23:15:31Z1997-01-01T00:00:00ZIn this thesis lessons learned from the use of computer algebra systems and machine assisted theorem provers are developed in order to give an insight into both the problems and their solutions. Many algorithms in computational algebra and automated deduction (for example Grobner basis computations and Knuth-Bendix completion) tend to produce redundant facts and can contain more than one proof of any particular fact. This thesis introduces proof diagrams in order to compare and contrast the proofs of facts which such procedures generate. Proof diagrams make it possible to analyse the effect of heuristics which can be used to guide implementations of such algorithms. An extended version of an inference system for Knuth-Bendix completion is introduced. It is possible to see that this extension characterises the applicability of critical pair criteria, which are heuristics used in completion. We investigate a number of executions of a completion procedure by analysing the associated proof diagrams. This leads to a better understanding of the heuristics used to control these examples. Derived rales of inference are also investigated in this thesis. This is done in the formalism of proof diagrams. Rewrite rules for proof diagrams are defined: this is motivated by the notion of a transformation tactic in the Nuprl proof development system. A method to automatically extract 'useful' derived inference rales is also discussed. 'Off the shelf' theorem provers, such as the Larch Prover and Otter, are compared to specialised programs from computational group theory. This analysis makes it possible to see where methods from automated deduction can improve on the tools which group theorists currently use. Problems which can be attacked with theorem provers but not with currently used specialised programs are also indicated. Tietze transformations, from group theory, are discussed. This makes it possible to link ideas used in Knuth-Bendix completion programs and group presentation simplification programs. Tietze transformations provide heuristics for more efficient and effective implementations of these programs.
1997-01-01T00:00:00ZShand, DuncanIn this thesis lessons learned from the use of computer algebra systems and machine assisted theorem provers are developed in order to give an insight into both the problems and their solutions. Many algorithms in computational algebra and automated deduction (for example Grobner basis computations and Knuth-Bendix completion) tend to produce redundant facts and can contain more than one proof of any particular fact. This thesis introduces proof diagrams in order to compare and contrast the proofs of facts which such procedures generate. Proof diagrams make it possible to analyse the effect of heuristics which can be used to guide implementations of such algorithms. An extended version of an inference system for Knuth-Bendix completion is introduced. It is possible to see that this extension characterises the applicability of critical pair criteria, which are heuristics used in completion. We investigate a number of executions of a completion procedure by analysing the associated proof diagrams. This leads to a better understanding of the heuristics used to control these examples. Derived rales of inference are also investigated in this thesis. This is done in the formalism of proof diagrams. Rewrite rules for proof diagrams are defined: this is motivated by the notion of a transformation tactic in the Nuprl proof development system. A method to automatically extract 'useful' derived inference rales is also discussed. 'Off the shelf' theorem provers, such as the Larch Prover and Otter, are compared to specialised programs from computational group theory. This analysis makes it possible to see where methods from automated deduction can improve on the tools which group theorists currently use. Problems which can be attacked with theorem provers but not with currently used specialised programs are also indicated. Tietze transformations, from group theory, are discussed. This makes it possible to link ideas used in Knuth-Bendix completion programs and group presentation simplification programs. Tietze transformations provide heuristics for more efficient and effective implementations of these programs.Tools and techniques for machine-assisted meta-theoryAdams, Andrew, 1969-http://hdl.handle.net/10023/133822018-05-17T23:17:00Z1997-01-01T00:00:00ZMachine-assisted formal proofs are becoming commonplace in certain fields of mathematics and theoretical computer science. New formal systems and variations on old ones are constantly invented. The meta-theory of such systems, i.e. proofs about the system as opposed to proofs within the system, are mostly done informally with a pen and paper. Yet the meta-theory of deductive systems is an area which would obviously benefit from machine support for formal proof. Is the software currently available sufficiently powerful yet easy enough to use to make machine assistance for formal meta-theory a viable proposition? This thesis presents work done by the author on formalizing proof theory from [DP97a] in various formal systems: SEQUEL [Tar93, Tar97], Isabelle [Pau94] and Coq [BB+96]. SEQUEL and Isabelle were found to be difficult to use for this type of work. In particular, the lack of automated production of induction principles in SEQUEL and Isabelle undermined confidence in the resulting formal proofs. Coq was found to be suitable for the formalisation methodology first chosen: the use of nameless dummy variables (de Bruijn indices) as pioneered in [dB72]. A second approach (inspired by the work of McKinna and Pollack [vBJMR94, MP97]) formalising named variables was also the subject of some initial work, and a comparison of these two approaches is presented. The formalisation was restricted to the implicational fragment of propositional logic. The informal theory has been extended to cover full propositional logic by Dyckhoff and Pinto, and extension of the formalisation using de Bruijn indices would appear to present few difficulties. An overview of other work in this area, in terms of both the tools and formalisation methods, is also presented. The theory formalised differs from other such work in that other formalisations have involved only one calculus. [DP97a] involves the relationships between three different calculi. There is consequently a much greater requirement for equality reasoning in the formalisation. It is concluded that a formalisation of any significance is still difficult, particularly one involving multiple calculi. No tools currently exist that allow for the easy representation of even quite simple systems in a way that fits human intuitions while still allowing for automatic derivation of induction principles. New work on integrating higher order abstract syntax and induction may be the way forward, although such work is still in the early stages.
1997-01-01T00:00:00ZAdams, Andrew, 1969-Machine-assisted formal proofs are becoming commonplace in certain fields of mathematics and theoretical computer science. New formal systems and variations on old ones are constantly invented. The meta-theory of such systems, i.e. proofs about the system as opposed to proofs within the system, are mostly done informally with a pen and paper. Yet the meta-theory of deductive systems is an area which would obviously benefit from machine support for formal proof. Is the software currently available sufficiently powerful yet easy enough to use to make machine assistance for formal meta-theory a viable proposition? This thesis presents work done by the author on formalizing proof theory from [DP97a] in various formal systems: SEQUEL [Tar93, Tar97], Isabelle [Pau94] and Coq [BB+96]. SEQUEL and Isabelle were found to be difficult to use for this type of work. In particular, the lack of automated production of induction principles in SEQUEL and Isabelle undermined confidence in the resulting formal proofs. Coq was found to be suitable for the formalisation methodology first chosen: the use of nameless dummy variables (de Bruijn indices) as pioneered in [dB72]. A second approach (inspired by the work of McKinna and Pollack [vBJMR94, MP97]) formalising named variables was also the subject of some initial work, and a comparison of these two approaches is presented. The formalisation was restricted to the implicational fragment of propositional logic. The informal theory has been extended to cover full propositional logic by Dyckhoff and Pinto, and extension of the formalisation using de Bruijn indices would appear to present few difficulties. An overview of other work in this area, in terms of both the tools and formalisation methods, is also presented. The theory formalised differs from other such work in that other formalisations have involved only one calculus. [DP97a] involves the relationships between three different calculi. There is consequently a much greater requirement for equality reasoning in the formalisation. It is concluded that a formalisation of any significance is still difficult, particularly one involving multiple calculi. No tools currently exist that allow for the easy representation of even quite simple systems in a way that fits human intuitions while still allowing for automatic derivation of induction principles. New work on integrating higher order abstract syntax and induction may be the way forward, although such work is still in the early stages.The Arabic translation of Theodosius's SphaericaMartin, Thomas J.http://hdl.handle.net/10023/133802018-05-17T23:16:41Z1975-01-01T00:00:00ZThe thesis "The Arabic Translation of Theodosius's Sphaerica" is an edition of the Istanbul manuscript Topkapi Seray Ahmet III 3464.2. Included is a comparative apparatus of the Greek and Arabic texts showing possible correspondence between the posited Greek exemplar of the translator and the various Greek manuscript traditions reported by J.L. Heiberg in his critical edition of the text. Further differences are pointed out in the English Trajislation. There is also a glossary of terminology- giving listings from Greek to Arabic and Arabic to Greek. An appendix discussing the execution of the drawings in the Arabic manuscript and their relation to the Greek drawings as reported by Heiberg is also given. Other appendices include a chart representing the convention seemingly adopted by the translator for lettering the drawings, a listing of inconsistent grammatical usage found in the manuscript, parallel passages from the Greek text, the text of the present edition, the versions of al-Maghribi and al-Tusi, and a privately owned manuscript, and finally a list of interlinear sigla found on the first few folios of the manuscript the purpose of which is unclear.
1975-01-01T00:00:00ZMartin, Thomas J.The thesis "The Arabic Translation of Theodosius's Sphaerica" is an edition of the Istanbul manuscript Topkapi Seray Ahmet III 3464.2. Included is a comparative apparatus of the Greek and Arabic texts showing possible correspondence between the posited Greek exemplar of the translator and the various Greek manuscript traditions reported by J.L. Heiberg in his critical edition of the text. Further differences are pointed out in the English Trajislation. There is also a glossary of terminology- giving listings from Greek to Arabic and Arabic to Greek. An appendix discussing the execution of the drawings in the Arabic manuscript and their relation to the Greek drawings as reported by Heiberg is also given. Other appendices include a chart representing the convention seemingly adopted by the translator for lettering the drawings, a listing of inconsistent grammatical usage found in the manuscript, parallel passages from the Greek text, the text of the present edition, the versions of al-Maghribi and al-Tusi, and a privately owned manuscript, and finally a list of interlinear sigla found on the first few folios of the manuscript the purpose of which is unclear.The life and work of Prof. George Chrystal (1851-1911)Yousuf, Mohammadhttp://hdl.handle.net/10023/133792018-05-17T23:16:23Z1990-01-01T00:00:00ZThis thesis is principally concerned with George Chrystal's life and his work, mainly in three directions viz., as an experimentalist, a mathematician, and an educationist. The main object is to bring to light the work of a personality who is representative of many more who are always forgotten. The majority of historians of science consider the works of the giants in science, ignoring totally the contributions made by the less prominent people like Prof. George Chrystal. In fact their contributions serve as one of the most important factors in propagation of scientific knowledge. His main contributions: verification of Ohm's Law experimentally; Non-Euclidean geometry; differential equations; text books on algebra; theory of seiches; institution of leaving certificate examination in Scottish education and many more have been discussed in detail. A survey of Chrystal's general thought is given in so far as it may be gathered from his scattered remarks. The references are mentioned by numerals in the superscript, details of which are given at the end of each chapter. The main text consists of six chapters. There are three appendices at the end,' Appendix 'A' consists of his correspondence with different scientists, most of which is still unpublished. Appendix 'B' contains a bibliography of his contributions in chronological order, and Appendix 'C contains his three Promoter's addresses. Tables and figures are attached at their proper places, including some rarely available photographs.
1990-01-01T00:00:00ZYousuf, MohammadThis thesis is principally concerned with George Chrystal's life and his work, mainly in three directions viz., as an experimentalist, a mathematician, and an educationist. The main object is to bring to light the work of a personality who is representative of many more who are always forgotten. The majority of historians of science consider the works of the giants in science, ignoring totally the contributions made by the less prominent people like Prof. George Chrystal. In fact their contributions serve as one of the most important factors in propagation of scientific knowledge. His main contributions: verification of Ohm's Law experimentally; Non-Euclidean geometry; differential equations; text books on algebra; theory of seiches; institution of leaving certificate examination in Scottish education and many more have been discussed in detail. A survey of Chrystal's general thought is given in so far as it may be gathered from his scattered remarks. The references are mentioned by numerals in the superscript, details of which are given at the end of each chapter. The main text consists of six chapters. There are three appendices at the end,' Appendix 'A' consists of his correspondence with different scientists, most of which is still unpublished. Appendix 'B' contains a bibliography of his contributions in chronological order, and Appendix 'C contains his three Promoter's addresses. Tables and figures are attached at their proper places, including some rarely available photographs.Normalisation techniques in proof theory and category theoryHamza, Taher Tawfik Ahmedhttp://hdl.handle.net/10023/133712018-05-17T23:16:45Z1986-01-01T00:00:00ZThe word problem for the free categories with some structure generated by a category X can be solved using proof-theoretical means. These free categories give a semantics in which derivations of GENTZEN's propositional sequent calculus can be interpreted by means of arrows of those categories. In this thesis we describe, implement and document the cut-elimination and the normalization techniques in proof theory as outlined in SZABO [1978]: we show how these are used in order to solve, mechanically, the word problem for the free categories with structure of : cartesian, bicartesian, distributive bicartesian, cartesian closed, and bicartesian closed. This implementation is extended by a procedure to interpret intuitionistic propositional sequent derivations as arrows of the above categories. Implementation of those techniques has forced us to modify the techniques in various inessential ways. The description and the representation in the syntax of our implementation of the above categories is contained in chapters 1 - 5, where each chapter describes one theory and concludes with examples of the system In use to represent concepts and solve simple word problems from category theory ( of various typos ). Appendix 1 contains some apparent printing errors we have observed in the work done by SZABO. The algorithms used in the proof of the cut-elimination theorems and normalization through chapters 1 - 5 are collected in appendices 2 - 4. Appendices 5 - 8 concern the implementation and its user manual.
1986-01-01T00:00:00ZHamza, Taher Tawfik AhmedThe word problem for the free categories with some structure generated by a category X can be solved using proof-theoretical means. These free categories give a semantics in which derivations of GENTZEN's propositional sequent calculus can be interpreted by means of arrows of those categories. In this thesis we describe, implement and document the cut-elimination and the normalization techniques in proof theory as outlined in SZABO [1978]: we show how these are used in order to solve, mechanically, the word problem for the free categories with structure of : cartesian, bicartesian, distributive bicartesian, cartesian closed, and bicartesian closed. This implementation is extended by a procedure to interpret intuitionistic propositional sequent derivations as arrows of the above categories. Implementation of those techniques has forced us to modify the techniques in various inessential ways. The description and the representation in the syntax of our implementation of the above categories is contained in chapters 1 - 5, where each chapter describes one theory and concludes with examples of the system In use to represent concepts and solve simple word problems from category theory ( of various typos ). Appendix 1 contains some apparent printing errors we have observed in the work done by SZABO. The algorithms used in the proof of the cut-elimination theorems and normalization through chapters 1 - 5 are collected in appendices 2 - 4. Appendices 5 - 8 concern the implementation and its user manual.Parameter identification through mode isolation for reaction-diffusion systems on arbitrary geometriesMurphy, LauraVenkataraman, ChandrasekharMadzvamuse, Anotidahttp://hdl.handle.net/10023/133632018-05-28T10:30:07Z2018-05-03T00:00:00ZWe present a computational framework for isolating spatial patterns arising in the steady states of reaction-diffusion systems. Such systems have been used to model many natural phenomena in areas such as developmental and cancer biology, cell motility and material science. In many of these applications, often one is interested in identifying parameters which will lead to a particular pattern for a given reaction-diffusion model. To attempt to answer this, we compute eigenpairs of the Laplacian on a variety of domains and use linear stability analysis to determine parameter values for the system that will lead to spatially inhomogeneous steady states whose patterns correspond to particular eigenfunctions. This method has previously been used on domains and surfaces where the eigenvalues and eigenfunctions are found analytically in closed form. Our contribution to this methodology is that we numerically compute eigenpairs on arbitrary domains and surfaces. Here we present examples and demonstrate that mode isolation is straightforward especially for low eigenvalues. Additionally we see that the inhomogeneous steady state can be a linear combination of eigenfunctions. Finally we show an example suggesting that pattern formation is robust on similar surfaces in cases that the surface either has or does not have a boundary.
This work (LM) was supported by an EPSRC Doctoral Training Centre Studentship through the University of Sussex. CV and AM acknowledge support from the Leverhulme Trust Research Project Grant (RPG-2014-149) and the EPSRC grant (EP/J016780/1). This research was partly undertaken whilst LM, CV and AM were participants in the Isaac Newton Institute Program, Coupling Geometric PDEs with Physics for Cell Morphology, Motility and Pattern Formation. This work (AM) has received funding from the European Union Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement (No 642866). AM was partially supported by a grant from the Simons Foundation. AM is a Royal Society Wolfson Research Merit Award Holder, generously supported by the Wolfson Foundation. LM acknowledges the support from the University of Sussex ITS for computational purposes.
2018-05-03T00:00:00ZMurphy, LauraVenkataraman, ChandrasekharMadzvamuse, AnotidaWe present a computational framework for isolating spatial patterns arising in the steady states of reaction-diffusion systems. Such systems have been used to model many natural phenomena in areas such as developmental and cancer biology, cell motility and material science. In many of these applications, often one is interested in identifying parameters which will lead to a particular pattern for a given reaction-diffusion model. To attempt to answer this, we compute eigenpairs of the Laplacian on a variety of domains and use linear stability analysis to determine parameter values for the system that will lead to spatially inhomogeneous steady states whose patterns correspond to particular eigenfunctions. This method has previously been used on domains and surfaces where the eigenvalues and eigenfunctions are found analytically in closed form. Our contribution to this methodology is that we numerically compute eigenpairs on arbitrary domains and surfaces. Here we present examples and demonstrate that mode isolation is straightforward especially for low eigenvalues. Additionally we see that the inhomogeneous steady state can be a linear combination of eigenfunctions. Finally we show an example suggesting that pattern formation is robust on similar surfaces in cases that the surface either has or does not have a boundary.Proof search issues in some non-classical logicsHowe, Jacob M.http://hdl.handle.net/10023/133622018-05-17T23:16:19Z1999-01-01T00:00:00ZThis thesis develops techniques and ideas on proof search. Proof search is used with one of two meanings. Proof search can be thought of either as the search for a yes/no answer to a query (theorem proving), or as the search for all proofs of a formula (proof enumeration). This thesis is an investigation into issues in proof search in both these senses for some non-classical logics. Gentzen systems are well suited for use in proof search in both senses. The rules of Gentzen sequent calculi are such that implementations can be directed by the top level syntax of sequents, unlike other logical calculi such as natural deduction. All the calculi for proof search in this thesis are Gentzen sequent calculi. In Chapter 2, permutation of inference rules for Intuitionistic Linear Logic is studied. A focusing calculus, ILLF, in the style of Andreoli ([And92]) is developed. This calculus allows only one proof in each equivalence class of proofs equivalent up to permutations of inferences. The issue here is both theorem proving and proof enumeration. For certain logics, normal natural deductions provide a proof-theoretic semantics. Proof enumeration is then the enumeration of all these deductions. Herbelin's cut- free LJT ([Her95], here called MJ) is a Gentzen system for intuitionistic logic allowing derivations that correspond in a 1-1 way to the normal natural deductions of intuitionistic logic. This calculus is therefore well suited to proof enumeration. Such calculi are called 'permutation-free' calculi. In Chapter 3, MJ is extended to a calculus for an intuitionistic modal logic (due to Curry) called Lax Logic. We call this calculus PFLAX. The proof theory of MJ is extended to PFLAX. Chapter 4 presents work on theorem proving for propositional logics using a history mechanism for loop-checking. This mechanism is a refinement of one developed by Heuerding et al ([HSZ96]). It is applied to two calculi for intuitionistic logic and also to two modal logics; Lax Logic and intuitionistic S4. The calculi for intuitionistic logic are compared both theoretically and experimentally with other decision procedures for the logic. Chapter 5 is a short investigation of embedding intuitionistic logic in Intuitionistic Linear Logic. A new embedding of intuitionistic logic in Intuitionistic Linear Logic is given. For the hereditary Harrop fragment of intuitionistic logic, this embedding induces the calculus MJ for intuitionistic logic. In Chapter 6 a 'permutation-free' calculus is given for Intuitionistic Linear Logic. Again, its proof-theoretic properties are investigated. The calculus is proved to be sound and complete with respect to a proof-theoretic semantics and (weak) cut- elimination is proved. Logic programming can be thought of as proof enumeration in constructive logics. All the proof enumeration calculi in this thesis have been developed with logic programming in mind. We discuss at the appropriate points the relationship between the calculi developed here and logic programming. Appendix A contains presentations of the logical calculi used and Appendix B contains the sets of benchmark formulae used in Chapter 4.
1999-01-01T00:00:00ZHowe, Jacob M.This thesis develops techniques and ideas on proof search. Proof search is used with one of two meanings. Proof search can be thought of either as the search for a yes/no answer to a query (theorem proving), or as the search for all proofs of a formula (proof enumeration). This thesis is an investigation into issues in proof search in both these senses for some non-classical logics. Gentzen systems are well suited for use in proof search in both senses. The rules of Gentzen sequent calculi are such that implementations can be directed by the top level syntax of sequents, unlike other logical calculi such as natural deduction. All the calculi for proof search in this thesis are Gentzen sequent calculi. In Chapter 2, permutation of inference rules for Intuitionistic Linear Logic is studied. A focusing calculus, ILLF, in the style of Andreoli ([And92]) is developed. This calculus allows only one proof in each equivalence class of proofs equivalent up to permutations of inferences. The issue here is both theorem proving and proof enumeration. For certain logics, normal natural deductions provide a proof-theoretic semantics. Proof enumeration is then the enumeration of all these deductions. Herbelin's cut- free LJT ([Her95], here called MJ) is a Gentzen system for intuitionistic logic allowing derivations that correspond in a 1-1 way to the normal natural deductions of intuitionistic logic. This calculus is therefore well suited to proof enumeration. Such calculi are called 'permutation-free' calculi. In Chapter 3, MJ is extended to a calculus for an intuitionistic modal logic (due to Curry) called Lax Logic. We call this calculus PFLAX. The proof theory of MJ is extended to PFLAX. Chapter 4 presents work on theorem proving for propositional logics using a history mechanism for loop-checking. This mechanism is a refinement of one developed by Heuerding et al ([HSZ96]). It is applied to two calculi for intuitionistic logic and also to two modal logics; Lax Logic and intuitionistic S4. The calculi for intuitionistic logic are compared both theoretically and experimentally with other decision procedures for the logic. Chapter 5 is a short investigation of embedding intuitionistic logic in Intuitionistic Linear Logic. A new embedding of intuitionistic logic in Intuitionistic Linear Logic is given. For the hereditary Harrop fragment of intuitionistic logic, this embedding induces the calculus MJ for intuitionistic logic. In Chapter 6 a 'permutation-free' calculus is given for Intuitionistic Linear Logic. Again, its proof-theoretic properties are investigated. The calculus is proved to be sound and complete with respect to a proof-theoretic semantics and (weak) cut- elimination is proved. Logic programming can be thought of as proof enumeration in constructive logics. All the proof enumeration calculi in this thesis have been developed with logic programming in mind. We discuss at the appropriate points the relationship between the calculi developed here and logic programming. Appendix A contains presentations of the logical calculi used and Appendix B contains the sets of benchmark formulae used in Chapter 4.Distance sampling with camera trapsHowe, Eric J.Buckland, Stephen T.Després-Einspenner, Marie-LyneKühl, Hjalmarhttp://hdl.handle.net/10023/133282018-05-13T01:34:46Z2017-11-01T00:00:00Z1. Reliable estimates of animal density and abundance are essential for effective wildlife conservation and management. Camera trapping has proven efficient for sampling multiple species, but statistical estimators of density from camera trapping data for species that cannot be individually identified are still in development. 2. We extend point-transect methods for estimating animal density to accommodate data from camera traps, allowing researchers to exploit existing distance sampling theory and software for designing studies and analyzing data. We tested it by simulation, and used it to estimate densities of Maxwell’s duikers (Philantomba maxwellii) in Taï National Park, Côte d’Ivoire. 3. Densities estimated from simulated data were unbiased when we assumed animals were not available for detection during long periods of rest. Estimated duiker densities were higher than recent estimates from line transect surveys, which are believed to underestimate densities of forest ungulates. 4. We expect these methods to provide an effective means to estimate animal density from camera trapping data and to be applicable in a variety of settings.
We thank the Robert Bosch Foundation, the Max Planck Society, and the University of St Andrews for funding. The data files from which densities of Maxwell's duikers were estimated using Distance software, and data describing start times of videos of Maxwell's duikers, have been archived at the Dryad data repository (https://doi.org/10.5061/dryad.b4c70) (Howe et al. 2017).
2017-11-01T00:00:00ZHowe, Eric J.Buckland, Stephen T.Després-Einspenner, Marie-LyneKühl, Hjalmar1. Reliable estimates of animal density and abundance are essential for effective wildlife conservation and management. Camera trapping has proven efficient for sampling multiple species, but statistical estimators of density from camera trapping data for species that cannot be individually identified are still in development. 2. We extend point-transect methods for estimating animal density to accommodate data from camera traps, allowing researchers to exploit existing distance sampling theory and software for designing studies and analyzing data. We tested it by simulation, and used it to estimate densities of Maxwell’s duikers (Philantomba maxwellii) in Taï National Park, Côte d’Ivoire. 3. Densities estimated from simulated data were unbiased when we assumed animals were not available for detection during long periods of rest. Estimated duiker densities were higher than recent estimates from line transect surveys, which are believed to underestimate densities of forest ungulates. 4. We expect these methods to provide an effective means to estimate animal density from camera trapping data and to be applicable in a variety of settings.Chains of subsemigroupsCameron, Peter J.Gadouleau, MaximilienMitchell, James D.Peresse, Yannhttp://hdl.handle.net/10023/133132018-05-09T23:15:39Z2017-06-01T00:00:00ZWe investigate the maximum length of a chain of subsemigroups in various classes of semigroups, such as the full transformation semigroups, the general linear semigroups, and the semigroups of order-preserving transformations of finite chains. In some cases, we give lower bounds for the total number of subsemigroups of these semigroups. We give general results for finite completely regular and finite inverse semigroups. Wherever possible, we state our results in the greatest generality; in particular, we include infinite semigroups where the result is true for these. The length of a subgroup chain in a group is bounded by the logarithm of the group order. This fails for semigroups, but it is perhaps surprising that there is a lower bound for the length of a subsemigroup chain in the full transformation semigroup which is a constant multiple of the semigroup order.
2017-06-01T00:00:00ZCameron, Peter J.Gadouleau, MaximilienMitchell, James D.Peresse, YannWe investigate the maximum length of a chain of subsemigroups in various classes of semigroups, such as the full transformation semigroups, the general linear semigroups, and the semigroups of order-preserving transformations of finite chains. In some cases, we give lower bounds for the total number of subsemigroups of these semigroups. We give general results for finite completely regular and finite inverse semigroups. Wherever possible, we state our results in the greatest generality; in particular, we include infinite semigroups where the result is true for these. The length of a subgroup chain in a group is bounded by the logarithm of the group order. This fails for semigroups, but it is perhaps surprising that there is a lower bound for the length of a subsemigroup chain in the full transformation semigroup which is a constant multiple of the semigroup order.Imprimitive permutations in primitive groupsAraújo, JoaoAraújo, Joao PedroCameron, Peter JephsonDobson, TedHulpke, AlexanderLopes, Pedrohttp://hdl.handle.net/10023/132822018-05-03T23:15:15Z2017-09-15T00:00:00ZThe goal of this paper is to study primitive groups that are contained in the union of maximal (in the symmetric group) imprimitive groups. The study of types of permutations that appear inside primitive groups goes back to the origins of the theory of permutation groups. However, this is another instance of a situation common in mathematics in which a very natural problem turns out to be extremely difficult. Fortunately, the enormous progresses of the last few decades seem to allow a new momentum on the attack to this problem. In this paper we prove that there are infinite families of primitive groups contained in the union of imprimitive groups and propose a new hierarchy for primitive groups based on that fact. In addition we introduce some algorithms to handle permutations, provide the corresponding GAP implementation, solve some open problems, and propose a large list of open problems.
2017-09-15T00:00:00ZAraújo, JoaoAraújo, Joao PedroCameron, Peter JephsonDobson, TedHulpke, AlexanderLopes, PedroThe goal of this paper is to study primitive groups that are contained in the union of maximal (in the symmetric group) imprimitive groups. The study of types of permutations that appear inside primitive groups goes back to the origins of the theory of permutation groups. However, this is another instance of a situation common in mathematics in which a very natural problem turns out to be extremely difficult. Fortunately, the enormous progresses of the last few decades seem to allow a new momentum on the attack to this problem. In this paper we prove that there are infinite families of primitive groups contained in the union of imprimitive groups and propose a new hierarchy for primitive groups based on that fact. In addition we introduce some algorithms to handle permutations, provide the corresponding GAP implementation, solve some open problems, and propose a large list of open problems.A new technique for observationally derived boundary conditions for space weatherPagano, PaoloMackay, Duncan HendryYeates, Anthony Robinsonhttp://hdl.handle.net/10023/132712018-06-02T23:33:16Z2018-04-17T00:00:00ZContext. In recent years, space weather research has focused on developing modelling techniques to predict the arrival time and properties of coronal mass ejections (CMEs) at the Earth. The aim of this paper is to propose a new modelling technique suitable for the next generation of Space Weather predictive tools that is both efficient and accurate. The aim of the new approach is to provide interplanetary space weather forecasting models with accurate time dependent boundary conditions of erupting magnetic flux ropes in the upper solar corona. Methods. To produce boundary conditions, we couple two different modelling techniques, MHD simulations and a quasi-static non-potential evolution model. Both are applied on a spatial domain that covers the entire solar surface, although they extend over a different radial distance. The non-potential model uses a time series of observed synoptic magnetograms to drive the non-potential quasi-static evolution of the coronal magnetic field. This allows us to follow the formation and loss of equilibrium of magnetic flux ropes. Following this a MHD simulation captures the dynamic evolution of the erupting flux rope, when it is ejected into interplanetary space. Results. The present paper focuses on the MHD simulations that follow the ejection of magnetic flux ropes to 4R⊙. We first propose a technique for specifying the pre-eruptive plasma properties in the corona. Next, time dependent MHD simulations describe the ejection of two magnetic flux ropes, that produce time dependent boundary conditions for the magnetic field and plasma at 4R⊙ that in future may be applied to interplanetary space weather prediction models. Conclusions. In the present paper, we show that the dual use of quasi-static non-potential magnetic field simulations and full time dependent MHD simulations can produce realistic inhomogeneous boundary conditions for space weather forecasting tools. Before a fully operational model can be produced there are a number of technical and scientific challenges that still need to be addressed. Nevertheless, we illustrate that coupling quasi-static and MHD simulations in this way can significantly reduce the computational time required to produce realistic space weather boundary conditions.
This research has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 647214). D.H.M. would like to thank STFC and the Leverhulme Trust for their financial support. ARY was supported by STFC consortium grant ST/N000781/1 to the universities of Dundee and Durham.
2018-04-17T00:00:00ZPagano, PaoloMackay, Duncan HendryYeates, Anthony RobinsonContext. In recent years, space weather research has focused on developing modelling techniques to predict the arrival time and properties of coronal mass ejections (CMEs) at the Earth. The aim of this paper is to propose a new modelling technique suitable for the next generation of Space Weather predictive tools that is both efficient and accurate. The aim of the new approach is to provide interplanetary space weather forecasting models with accurate time dependent boundary conditions of erupting magnetic flux ropes in the upper solar corona. Methods. To produce boundary conditions, we couple two different modelling techniques, MHD simulations and a quasi-static non-potential evolution model. Both are applied on a spatial domain that covers the entire solar surface, although they extend over a different radial distance. The non-potential model uses a time series of observed synoptic magnetograms to drive the non-potential quasi-static evolution of the coronal magnetic field. This allows us to follow the formation and loss of equilibrium of magnetic flux ropes. Following this a MHD simulation captures the dynamic evolution of the erupting flux rope, when it is ejected into interplanetary space. Results. The present paper focuses on the MHD simulations that follow the ejection of magnetic flux ropes to 4R⊙. We first propose a technique for specifying the pre-eruptive plasma properties in the corona. Next, time dependent MHD simulations describe the ejection of two magnetic flux ropes, that produce time dependent boundary conditions for the magnetic field and plasma at 4R⊙ that in future may be applied to interplanetary space weather prediction models. Conclusions. In the present paper, we show that the dual use of quasi-static non-potential magnetic field simulations and full time dependent MHD simulations can produce realistic inhomogeneous boundary conditions for space weather forecasting tools. Before a fully operational model can be produced there are a number of technical and scientific challenges that still need to be addressed. Nevertheless, we illustrate that coupling quasi-static and MHD simulations in this way can significantly reduce the computational time required to produce realistic space weather boundary conditions.On the Hausdorff and packing measures of typical compact metric spacesJurina, S.MacGregor, N.Mitchell, A.Olsen, L.Stylianou, A.http://hdl.handle.net/10023/132682018-05-20T00:35:54Z2018-04-24T00:00:00ZWe study the Hausdorff and packing measures of typical compact metric spaces belonging to the Gromov–Hausdorff space (of all compact metric spaces) equipped with the Gromov–Hausdorff metric.
2018-04-24T00:00:00ZJurina, S.MacGregor, N.Mitchell, A.Olsen, L.Stylianou, A.We study the Hausdorff and packing measures of typical compact metric spaces belonging to the Gromov–Hausdorff space (of all compact metric spaces) equipped with the Gromov–Hausdorff metric.Contribution of phase-mixing of Alfvén waves to coronal heating in multi-harmonic loop oscillationsPagano, PaoloPascoe, David JamesDe Moortel, Inekehttp://hdl.handle.net/10023/132632018-06-16T23:32:33Z2018-04-26T00:00:00ZContext. Kink oscillations of a coronal loop are observed and studied in detail because they provide a unique probe into the structure of coronal loops through MHD seismology and a potential test of coronal heating through the phase-mixing of Alfvén waves . In particular, recent observations show that standing oscill ations of loops often involve also higher harmonics, beside the fundamental mode. The damping of these kink oscillations is explained by mode coupling with Alfvén waves. Aims. We investigate the consequences for wave-based coronal hea ting of higher harmonics and what coronal heating observational signatures we may use to infer the presence of higher harmonic kink oscillations. Methods. We perform a set of non-ideal MHD simulations where the damping of the kink oscillation of a flux tube via mode coupling is modelled. Our MHD simulation parameters are based on the seismological inversion of an observation for which the first three harmonics are detected. We study the phase-mixing of Alfvén waves that leads to the deposition of heat in the system, and we apply the seismological inversion techniques to the MHD simulation output. Results. We find that the heating due to phase-mixing of the Alfvén wave s triggered by the damping of the kink oscillation is relatively small, however we can illustrate i) how the heating location drifts due to the subsequent damping of lower order harmonics. We also address the role of the higher order harmonics and the width of the boundary shell in the energy deposition. Conclusions. We conclude that the coronal heating due to phase-mixing see ms not to provide enough energy to maintain the thermal structure of the solar corona even when multi-harmonics oscillations are included, and these oscillations play an inhibiting role in the development of smaller scale structures.
This research has received funding from the Science and Technology Facilities Council (UK) through the consolidated grant ST/N000609/1 and the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program ( grant agreement No. 647214). This work is supported by the European Research Council under the SeismoSun Research Project No. 321141 (DJP). This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 724326). This work used the DiRAC Data Centric system at Durham University, operated by the Institute for Computational Cosmology on behalf of the STFC DiRAC HPC Facility (www.dirac.ac.uk). This equipment was funded by a BIS National E-infrastructure capital grant ST/K00042X/1, STFC capital grant ST/K00087X/1, DiRAC Operations grant ST/K003267/1 and Durham University. DiRAC is part of the National E-Infrastructure.
2018-04-26T00:00:00ZPagano, PaoloPascoe, David JamesDe Moortel, InekeContext. Kink oscillations of a coronal loop are observed and studied in detail because they provide a unique probe into the structure of coronal loops through MHD seismology and a potential test of coronal heating through the phase-mixing of Alfvén waves . In particular, recent observations show that standing oscill ations of loops often involve also higher harmonics, beside the fundamental mode. The damping of these kink oscillations is explained by mode coupling with Alfvén waves. Aims. We investigate the consequences for wave-based coronal hea ting of higher harmonics and what coronal heating observational signatures we may use to infer the presence of higher harmonic kink oscillations. Methods. We perform a set of non-ideal MHD simulations where the damping of the kink oscillation of a flux tube via mode coupling is modelled. Our MHD simulation parameters are based on the seismological inversion of an observation for which the first three harmonics are detected. We study the phase-mixing of Alfvén waves that leads to the deposition of heat in the system, and we apply the seismological inversion techniques to the MHD simulation output. Results. We find that the heating due to phase-mixing of the Alfvén wave s triggered by the damping of the kink oscillation is relatively small, however we can illustrate i) how the heating location drifts due to the subsequent damping of lower order harmonics. We also address the role of the higher order harmonics and the width of the boundary shell in the energy deposition. Conclusions. We conclude that the coronal heating due to phase-mixing see ms not to provide enough energy to maintain the thermal structure of the solar corona even when multi-harmonics oscillations are included, and these oscillations play an inhibiting role in the development of smaller scale structures.Hetonic quartets in a two-layer quasi-geostrophic flow : V-states and stabilityReinaud, J. N.Sokolovskiy, MikhailCarton, Xavierhttp://hdl.handle.net/10023/132472018-05-28T10:30:11Z2018-05-11T00:00:00ZWe investigate families of finite core vortex quartets in mutual equilibrium in a two- layer quasi-geostrophic flow. The finite core solutions stem from known solutions for discrete (singular) vortex quartets. Two vortices lie in the top layer and two vortices lie in the bottom layer. Two vortices have a positive potential vorticity anomaly while the two others have negative potential vorticity anomaly. The vortex configurations are therefore related to the baroclinic dipoles known in the literature as hetons. Two main branches of solutions exist depending on the arrangement of the vortices: the translating zigzag-shaped hetonic quartets and the rotating zigzag- shaped hetonic quartets. By addressing their linear stability, we show that while the rotating quartets can be unstable over a large range of the parameter space, most translating quartets are stable. This has implications on the longevity of such vortex equilibria in the oceans.
M.A.S. and X.C. were supported by RFBR/CNRS (PRC Grant No. 16-55-150001/1069). M.A.S. was supported also by RFBR (Grant No. 16-05-00121), RSF (Grant No. 14-50-00095, geophysical applications) and MESRF (Grant No. 14.W.03.31.0006, numerical simulation, vortex dynamics).
2018-05-11T00:00:00ZReinaud, J. N.Sokolovskiy, MikhailCarton, XavierWe investigate families of finite core vortex quartets in mutual equilibrium in a two- layer quasi-geostrophic flow. The finite core solutions stem from known solutions for discrete (singular) vortex quartets. Two vortices lie in the top layer and two vortices lie in the bottom layer. Two vortices have a positive potential vorticity anomaly while the two others have negative potential vorticity anomaly. The vortex configurations are therefore related to the baroclinic dipoles known in the literature as hetons. Two main branches of solutions exist depending on the arrangement of the vortices: the translating zigzag-shaped hetonic quartets and the rotating zigzag- shaped hetonic quartets. By addressing their linear stability, we show that while the rotating quartets can be unstable over a large range of the parameter space, most translating quartets are stable. This has implications on the longevity of such vortex equilibria in the oceans.Timing the landmark events in the evolution of clear cell renal cell cancer : TRACERx renalMitchell, Thomas J.Turajlic, SamraRowan, AndrewNicol, DavidFarmery, James H.R.O’Brien, TimMartincorena, InigoTarpey, PatrickAngelopoulos, NicosYates, Lucy R.Butler, Adam P.Raine, KeiranStewart, Grant D.Challacombe, BenFernando, ArchanaLopez, Jose I.Hazell, SteveChandra, AshishChowdhury, SimonRudman, SarahSoultati, AspasiaStamp, GordonFotiadis, NicosPickering, LisaAu, LewisSpain, LaviniaLynch, JoannaStares, MarkTeague, JonMaura, FrancescoWedge, David C.Horswell, StuartChambers, TimLitchfield, KevinXu, HangStewart, AengusElaidi, RezaOudard, StéphaneMcGranahan, NicholasCsabai, IstvanGore, MartinFutreal, P. AndrewLarkin, JamesLynch, Andy G.Szallasi, ZoltanSwanton, CharlesCampbell, Peter J.http://hdl.handle.net/10023/131312018-04-30T23:16:33Z2018-04-19T00:00:00ZClear cell renal cell carcinoma (ccRCC) is characterized by near-universal loss of the short arm of chromosome 3, deleting several tumor suppressor genes. We analyzed whole genomes from 95 biopsies across 33 patients with clear cell renal cell carcinoma. We find hotspots of point mutations in the 5′ UTR of TERT, targeting a MYC-MAX-MAD1 repressor associated with telomere lengthening. The most common structural abnormality generates simultaneous 3p loss and 5q gain (36% patients), typically through chromothripsis. This event occurs in childhood or adolescence, generally as the initiating event that precedes emergence of the tumor’s most recent common ancestor by years to decades. Similar genomic changes drive inherited ccRCC. Modeling differences in age incidence between inherited and sporadic cancers suggests that the number of cells with 3p loss capable of initiating sporadic tumors is no more than a few hundred. Early development of ccRCC follows well-defined evolutionary trajectories, offering opportunity for early intervention.
The work presented in this manuscript was funded by EU FP7 (project PREDICT ID number 259303) and the Wellcome Trust and Cancer Research UK. S.T. is funded by Cancer Research UK (C50947/A18176). S.T., J.L., and M.G. receive funding from the National Institute for Health Research (NIHR) Biomedical Research Centre at the Royal Marsden Hospital and Institute of Cancer Research (A109). J.H.R.F. and A.G.L. were supported by the University of Cambridge, Cancer Research UK (C14303/A17197), and Hutchison Whampoa. K.L. is supported by a UK Medical Research Council Skills Development Fellowship Award. C.S. is funded by Cancer Research UK (TRACERx), the Rosetrees Trust, NovoNordisk Foundation (16584), EU FP7 (projects PREDICT and RESPONSIFY, ID number 259303), the Prostate Cancer Foundation, the Breast Cancer Research Foundation, the European Research Council (THESEUS), and National Institute for Health Research University College London Hospitals Biomedical Research Centre. P.J.C. has a Wellcome Trust Senior Clinical Research Fellowship (WT088340MA).
2018-04-19T00:00:00ZMitchell, Thomas J.Turajlic, SamraRowan, AndrewNicol, DavidFarmery, James H.R.O’Brien, TimMartincorena, InigoTarpey, PatrickAngelopoulos, NicosYates, Lucy R.Butler, Adam P.Raine, KeiranStewart, Grant D.Challacombe, BenFernando, ArchanaLopez, Jose I.Hazell, SteveChandra, AshishChowdhury, SimonRudman, SarahSoultati, AspasiaStamp, GordonFotiadis, NicosPickering, LisaAu, LewisSpain, LaviniaLynch, JoannaStares, MarkTeague, JonMaura, FrancescoWedge, David C.Horswell, StuartChambers, TimLitchfield, KevinXu, HangStewart, AengusElaidi, RezaOudard, StéphaneMcGranahan, NicholasCsabai, IstvanGore, MartinFutreal, P. AndrewLarkin, JamesLynch, Andy G.Szallasi, ZoltanSwanton, CharlesCampbell, Peter J.Clear cell renal cell carcinoma (ccRCC) is characterized by near-universal loss of the short arm of chromosome 3, deleting several tumor suppressor genes. We analyzed whole genomes from 95 biopsies across 33 patients with clear cell renal cell carcinoma. We find hotspots of point mutations in the 5′ UTR of TERT, targeting a MYC-MAX-MAD1 repressor associated with telomere lengthening. The most common structural abnormality generates simultaneous 3p loss and 5q gain (36% patients), typically through chromothripsis. This event occurs in childhood or adolescence, generally as the initiating event that precedes emergence of the tumor’s most recent common ancestor by years to decades. Similar genomic changes drive inherited ccRCC. Modeling differences in age incidence between inherited and sporadic cancers suggests that the number of cells with 3p loss capable of initiating sporadic tumors is no more than a few hundred. Early development of ccRCC follows well-defined evolutionary trajectories, offering opportunity for early intervention.Structured models of cell migration incorporating molecular binding processesDomschke, PiaTrucu, DumitruGerisch, AlfChaplain, Mark Andrew Josephhttp://hdl.handle.net/10023/131272018-04-13T23:16:45Z2017-12-01T00:00:00ZThe dynamic interplay between collective cell movement and the various molecules involved in the accompanying cell signalling mechanisms plays a crucial role in many biological processes including normal tissue development and pathological scenarios such as wound healing and cancer. Information about the various structures embedded within these processes allows a detailed exploration of the binding of molecular species to cell-surface receptors within the evolving cell population. In this paper we establish a general spatio-temporal-structural framework that enables the description of molecular binding to cell membranes coupled with the cell population dynamics. We first provide a general theoretical description for this approach and then illustrate it with three examples arising from cancer invasion.
DT and MAJC gratefully acknowledge the support of the ERC Advanced Investigator Grant 227619, “M5CGS - From Mutations to Metastases: Multiscale Mathematical Modelling of Cancer Growth and Spread”.
2017-12-01T00:00:00ZDomschke, PiaTrucu, DumitruGerisch, AlfChaplain, Mark Andrew JosephThe dynamic interplay between collective cell movement and the various molecules involved in the accompanying cell signalling mechanisms plays a crucial role in many biological processes including normal tissue development and pathological scenarios such as wound healing and cancer. Information about the various structures embedded within these processes allows a detailed exploration of the binding of molecular species to cell-surface receptors within the evolving cell population. In this paper we establish a general spatio-temporal-structural framework that enables the description of molecular binding to cell membranes coupled with the cell population dynamics. We first provide a general theoretical description for this approach and then illustrate it with three examples arising from cancer invasion.Estimation and simulation of foraging trips in land-based marine predatorsMichelot, TheoLangrock, RolandBestley, SophieJonsen, Ian D.Photopoulou, TheoniPatterson, Toby A.http://hdl.handle.net/10023/131142018-06-24T00:41:22Z2017-07-01T00:00:00ZThe behavior of colony-based marine predators is the focus of much research globally. Large telemetry and tracking data sets have been collected for this group of animals, and are accompanied by many empirical studies that seek to segment tracks in some useful way, as well as theoretical studies of optimal foraging strategies. However, relatively few studies have detailed statistical methods for inferring behaviors in central place foraging trips. In this paper we describe an approach based on hidden Markov models, which splits foraging trips into segments labeled as "outbound", "search", "forage", and "inbound". By structuring the hidden Markov model transition matrix appropriately, the model naturally handles the sequence of behaviors within a foraging trip. Additionally, by structuring the model in this way, we are able to develop realistic simulations from the fitted model. We demonstrate our approach on data from southern elephant seals (Mirounga leonina) tagged on Kerguelen Island in the Southern Ocean. We discuss the differences between our 4-state model and the widely used 2-state model, and the advantages and disadvantages of employing a more complex model.
TM and TP received support from IMBER-CLIOTOP and Macquarie University Safety Net Grant 9201401743. SB was supported under an Australia Research Council Super Science Fellowship. IDJ was supported by a Macquarie Vice-Chancellors Innovation Fellowship. TAP was supported by a CSIRO Julius Career Award and the Villum Foundation.
2017-07-01T00:00:00ZMichelot, TheoLangrock, RolandBestley, SophieJonsen, Ian D.Photopoulou, TheoniPatterson, Toby A.The behavior of colony-based marine predators is the focus of much research globally. Large telemetry and tracking data sets have been collected for this group of animals, and are accompanied by many empirical studies that seek to segment tracks in some useful way, as well as theoretical studies of optimal foraging strategies. However, relatively few studies have detailed statistical methods for inferring behaviors in central place foraging trips. In this paper we describe an approach based on hidden Markov models, which splits foraging trips into segments labeled as "outbound", "search", "forage", and "inbound". By structuring the hidden Markov model transition matrix appropriately, the model naturally handles the sequence of behaviors within a foraging trip. Additionally, by structuring the model in this way, we are able to develop realistic simulations from the fitted model. We demonstrate our approach on data from southern elephant seals (Mirounga leonina) tagged on Kerguelen Island in the Southern Ocean. We discuss the differences between our 4-state model and the widely used 2-state model, and the advantages and disadvantages of employing a more complex model.On well quasi-order of graph classes under homomorphic image orderingsHuczynska, S.Ruškuc, N.http://hdl.handle.net/10023/130912018-04-08T23:16:08Z2017-06-01T00:00:00ZIn this paper we consider the question of well quasi-order for classes defined by a single obstruction within the classes of all graphs, digraphs and tournaments, under the homomorphic image ordering (in both its standard and strong forms). The homomorphic image ordering was introduced by the authors in a previous paper and corresponds to the existence of a surjective homomorphism between two structures. We obtain complete characterisations in all cases except for graphs under the strong ordering, where some open questions remain.
2017-06-01T00:00:00ZHuczynska, S.Ruškuc, N.In this paper we consider the question of well quasi-order for classes defined by a single obstruction within the classes of all graphs, digraphs and tournaments, under the homomorphic image ordering (in both its standard and strong forms). The homomorphic image ordering was introduced by the authors in a previous paper and corresponds to the existence of a surjective homomorphism between two structures. We obtain complete characterisations in all cases except for graphs under the strong ordering, where some open questions remain.Coronal energy release by MHD avalanches : continuous drivingReid, JackHood, Alan W.Parnell, Clare ElizabethBrowning, P. K.Cargill, P. (Peter)http://hdl.handle.net/10023/130892018-06-13T15:43:42Z2018-03-23T00:00:00ZPrevious work has confirmed the concept of a magnetohydrodynamic (MHD) avalanche in pre-stressed threads within a coronal loop. We undertook a series of full, three-dimensional MHD simulations in order to create three threads by twisting the magnetic field through boundary motions until an instability ensues. We find that, following the original instability, one unstable thread can disrupt its neighbours with continued driving. A ‘bursty’ heating profile results, with a series of ongoing energy releases, but no evident steady state. For the first time using full MHD, we show that avalanches are a viable mechanism for the storing and release of magnetic energy in the solar corona, as a result of photospheric motions.
Funding: Carnegie Trust for the Universities of Scotland; Science and Technology Facilities Council (grants ST/N000609/1 and ST/P000428/1).
2018-03-23T00:00:00ZReid, JackHood, Alan W.Parnell, Clare ElizabethBrowning, P. K.Cargill, P. (Peter)Previous work has confirmed the concept of a magnetohydrodynamic (MHD) avalanche in pre-stressed threads within a coronal loop. We undertook a series of full, three-dimensional MHD simulations in order to create three threads by twisting the magnetic field through boundary motions until an instability ensues. We find that, following the original instability, one unstable thread can disrupt its neighbours with continued driving. A ‘bursty’ heating profile results, with a series of ongoing energy releases, but no evident steady state. For the first time using full MHD, we show that avalanches are a viable mechanism for the storing and release of magnetic energy in the solar corona, as a result of photospheric motions.Enumerating transformation semigroupsEast, JamesEgri-Nagy, AttilaMitchell, James D.http://hdl.handle.net/10023/130642018-04-04T23:16:42Z2017-08-01T00:00:00ZWe describe general methods for enumerating subsemigroups of finite semigroups and techniques to improve the algorithmic efficiency of the calculations. As a particular application we use our algorithms to enumerate all transformation semigroups up to degree 4. Classification of these semigroups up to conjugacy, isomorphism and anti-isomorphism, by size and rank, provides a solid base for further investigations of transformation semigroups.
This work was partially supported by the NeCTAR Research Cloud, an initiative of the Australian Government’s Super Science scheme and the Education Investment Fund; and by the EU Project BIOMICS (Contract Number CNECT-ICT-318202).
2017-08-01T00:00:00ZEast, JamesEgri-Nagy, AttilaMitchell, James D.We describe general methods for enumerating subsemigroups of finite semigroups and techniques to improve the algorithmic efficiency of the calculations. As a particular application we use our algorithms to enumerate all transformation semigroups up to degree 4. Classification of these semigroups up to conjugacy, isomorphism and anti-isomorphism, by size and rank, provides a solid base for further investigations of transformation semigroups.Evaluating the effect of measurement error in pairs of 3D bearings in point transect sampling estimates of densityMarques, Tiago A.Duarte, PedroPeixe, TelmoMoretti, DavidThomas, Lenhttp://hdl.handle.net/10023/130372018-05-12T23:34:25Z2018-03-27T00:00:00Z2018-03-27T00:00:00ZMarques, Tiago A.Duarte, PedroPeixe, TelmoMoretti, DavidThomas, LenTrace-contrast models for capture-recapture without capture historiesFewster, R. M.Stevenson, B. C.Borchers, D. L.http://hdl.handle.net/10023/130102018-04-16T12:30:07Z2016-05-26T00:00:00ZCapture-recapture studies increasingly rely upon natural tags that allow animals to be identified by features such as coat markings, DNA profiles, acoustic profiles, or spatial locations. These innovations greatly increase the number of capture samples achievable and enable capture-recapture estimation for many inaccessible and elusive species. However, natural features are invariably imperfect as indicators of identity. Drawing on the recently developed Palm likelihood approach to parameter estimation in clustered point processes, we propose a new estimation framework based on comparing pairs of detections, which we term the trace-contrast framework. Importantly, no reconstruction of capture histories is needed. We show that we can achieve accurate, precise, and computationally fast inference. We illustrate the methods with a camera-trap study of a partially marked population of ship rats (Rattus rattus) in New Zealand.
This work was funded by the Royal Society of New Zealand through Marsden Grant 14-UOA-155. Ben Stevenson was supported by EPSRC/NERC Grant EP/1000917/1.
2016-05-26T00:00:00ZFewster, R. M.Stevenson, B. C.Borchers, D. L.Capture-recapture studies increasingly rely upon natural tags that allow animals to be identified by features such as coat markings, DNA profiles, acoustic profiles, or spatial locations. These innovations greatly increase the number of capture samples achievable and enable capture-recapture estimation for many inaccessible and elusive species. However, natural features are invariably imperfect as indicators of identity. Drawing on the recently developed Palm likelihood approach to parameter estimation in clustered point processes, we propose a new estimation framework based on comparing pairs of detections, which we term the trace-contrast framework. Importantly, no reconstruction of capture histories is needed. We show that we can achieve accurate, precise, and computationally fast inference. We illustrate the methods with a camera-trap study of a partially marked population of ship rats (Rattus rattus) in New Zealand.A comparison of inferential methods for highly nonlinear state space models in ecology and epidemiologyFasiolo, MatteoPya, NatalyaWood, Simon N.http://hdl.handle.net/10023/130092018-06-10T23:39:14Z2016-01-01T00:00:00ZHighly nonlinear, chaotic or near chaotic, dynamic models are important in fields such as ecology and epidemiology: for example, pest species and diseases often display highly nonlinear dynamics. However, such models are problematic from the point of view of statistical inference. The defining feature of chaotic and near chaotic systems is extreme sensitivity to small changes in system states and parameters, and this can interfere with inference. There are twomain classes ofmethods for circumventing these difficulties: information reduction approaches, such as Approximate Bayesian Computation or Synthetic Likelihood, and state space methods, such as Particle Markov chain Monte Carlo, Iterated Filtering or Parameter Cascading. The purpose of this article is to compare the methods in order to reach conclusions about how to approach inference with such models in practice. We show that neither class of methods is universally superior to the other. We show that state space methods can suffer multimodality problems in settings with low process noise or model misspecification, leading to bias toward stable dynamics and high process noise. Information reduction methods avoid this problem, but, under the correct model and with sufficient process noise, state space methods lead to substantially sharper inference than information reduction methods. More practically, there are also differences in the tuning requirements of different methods. Our overall conclusion is that model development and checking should probably be performed using an information reduction method with low tuning requirements, while for final inference it is likely to be better to switch to a state space method, checking results against the information reduction approach.
Most of this work was undertaken at the University of Bath, where M.F. was a Ph.D. student, and it was supported in part by EPSRC Grants EP/I000917 and EP/K005251/1.
2016-01-01T00:00:00ZFasiolo, MatteoPya, NatalyaWood, Simon N.Highly nonlinear, chaotic or near chaotic, dynamic models are important in fields such as ecology and epidemiology: for example, pest species and diseases often display highly nonlinear dynamics. However, such models are problematic from the point of view of statistical inference. The defining feature of chaotic and near chaotic systems is extreme sensitivity to small changes in system states and parameters, and this can interfere with inference. There are twomain classes ofmethods for circumventing these difficulties: information reduction approaches, such as Approximate Bayesian Computation or Synthetic Likelihood, and state space methods, such as Particle Markov chain Monte Carlo, Iterated Filtering or Parameter Cascading. The purpose of this article is to compare the methods in order to reach conclusions about how to approach inference with such models in practice. We show that neither class of methods is universally superior to the other. We show that state space methods can suffer multimodality problems in settings with low process noise or model misspecification, leading to bias toward stable dynamics and high process noise. Information reduction methods avoid this problem, but, under the correct model and with sufficient process noise, state space methods lead to substantially sharper inference than information reduction methods. More practically, there are also differences in the tuning requirements of different methods. Our overall conclusion is that model development and checking should probably be performed using an information reduction method with low tuning requirements, while for final inference it is likely to be better to switch to a state space method, checking results against the information reduction approach.Modelling the effects of bacterial cell state and spatial location on tuberculosis treatment : insights from a hybrid multiscale cellular automaton modelBowness, RuthChaplain, Mark A.J.Powathil, Gibin G.Gillespie, Stephen H.http://hdl.handle.net/10023/129832018-06-07T00:30:04Z2018-06-07T00:00:00ZIf improvements are to be made in tuberculosis (TB) treatment, an increased understanding of disease in the lung is needed. Studies have shown that bacteria in a less metabolically active state, associated with the presence of lipid bodies, are less susceptible to antibiotics, and recent results have highlighted the disparity in concentration of different compounds into lesions. Treatment success therefore depends critically on the responses of the individual bacteria that constitute the infection. We propose a hybrid, individual-based approach that analyses spatio-temporal dynamics at the cellular level, linking the behaviour of individual bacteria and host cells with the macroscopic behaviour of the microenvironment. The individual elements (bacteria, macrophages and T cells) are modelled using cellular automaton (CA) rules, and the evolution of oxygen, drugs and chemokine dynamics are incorporated in order to study the effects of the microenvironment in the pathological lesion. We allow bacteria to switch states depending on oxygen concentration, which affects how they respond to treatment. This is the first multiscale model of its type to consider both oxygen-driven phenotypic switching of the Mycobacterium tuberculosis and antibiotic treatment. Using this model, we investigate the role of bacterial cell state and of initial bacterial location on treatment outcome. We demonstrate that when bacteria are located further away from blood vessels, less favourable outcomes are more likely, i.e. longer time before infection is contained/cleared, treatment failure or later relapse. We also show that in cases where bacteria remain at the end of simulations, the organisms tend to be slower-growing and are often located within granulomas, surrounded by caseous material.
This work was supported by the Medical Research Council [grant number MR/P014704/1] and the PreDiCT-TB consortium (IMI Joint undertaking grant agreement number 115337, resources of which are composed of financial contribution from the European Union’s Seventh Framework Programme (FP7/2007-2013) and EFPIA companies’ in kind contribution.
2018-06-07T00:00:00ZBowness, RuthChaplain, Mark A.J.Powathil, Gibin G.Gillespie, Stephen H.If improvements are to be made in tuberculosis (TB) treatment, an increased understanding of disease in the lung is needed. Studies have shown that bacteria in a less metabolically active state, associated with the presence of lipid bodies, are less susceptible to antibiotics, and recent results have highlighted the disparity in concentration of different compounds into lesions. Treatment success therefore depends critically on the responses of the individual bacteria that constitute the infection. We propose a hybrid, individual-based approach that analyses spatio-temporal dynamics at the cellular level, linking the behaviour of individual bacteria and host cells with the macroscopic behaviour of the microenvironment. The individual elements (bacteria, macrophages and T cells) are modelled using cellular automaton (CA) rules, and the evolution of oxygen, drugs and chemokine dynamics are incorporated in order to study the effects of the microenvironment in the pathological lesion. We allow bacteria to switch states depending on oxygen concentration, which affects how they respond to treatment. This is the first multiscale model of its type to consider both oxygen-driven phenotypic switching of the Mycobacterium tuberculosis and antibiotic treatment. Using this model, we investigate the role of bacterial cell state and of initial bacterial location on treatment outcome. We demonstrate that when bacteria are located further away from blood vessels, less favourable outcomes are more likely, i.e. longer time before infection is contained/cleared, treatment failure or later relapse. We also show that in cases where bacteria remain at the end of simulations, the organisms tend to be slower-growing and are often located within granulomas, surrounded by caseous material.Theory and observations of the magnetic field in the solar coronaCarcedo, Laurahttp://hdl.handle.net/10023/129482018-06-14T23:17:02Z2005-01-01T00:00:00ZAlthough the solar corona is one of the most studied areas in solar physics, its activity, such as flares, prominence eruptions and CMEs, is far from understood. Since the solar corona is a low-ß plasma, its structure and dynamics are driven by the magnetic field. The aim of this PhD thesis to study the magnetic field in the solar corona. Unfortunately, high quality direct measurements of the coronal magnetic field are not available and theoretical extrapolation using the observed photospheric magnetic field is required. The thesis is mainly divided in two parts. The first part deals with the comparison between theoretical models of magnetic fields and observed structures in the corona. For any theoretical model, a quantitative method to fit magnetic field lines to observed coronal loops is introduced. This method provides a quantity C that measures how closely a theoretical model can reproduce the observed coronal structures. Using linear force-free field extrapolation, the above field line fitting method is used to study the evolution of an active region. The method is also illustrated when the theoretical magnetic field depends on more than one parameter. The second part of the thesis focuses on the linear force-free field assumption using two different geometric configurations. Firstly a vertical rigid magnetic flux tube is considered. The analytical expression of the magnetic field is obtained as an expansion in terms of Bessel functions. The main properties of this system are discussed and compared with two cylindrically symmetric twist profiles. For the second system, the photosphere is assumed to be an infinite plane. Using translational geometry, the analytical expression of the linear force-free magnetic field that matches a prescribed line of sight magnetic field component is obtained. This solution is compared with the non-linear solution obtained by Roumeliotis (1993).
2005-01-01T00:00:00ZCarcedo, LauraAlthough the solar corona is one of the most studied areas in solar physics, its activity, such as flares, prominence eruptions and CMEs, is far from understood. Since the solar corona is a low-ß plasma, its structure and dynamics are driven by the magnetic field. The aim of this PhD thesis to study the magnetic field in the solar corona. Unfortunately, high quality direct measurements of the coronal magnetic field are not available and theoretical extrapolation using the observed photospheric magnetic field is required. The thesis is mainly divided in two parts. The first part deals with the comparison between theoretical models of magnetic fields and observed structures in the corona. For any theoretical model, a quantitative method to fit magnetic field lines to observed coronal loops is introduced. This method provides a quantity C that measures how closely a theoretical model can reproduce the observed coronal structures. Using linear force-free field extrapolation, the above field line fitting method is used to study the evolution of an active region. The method is also illustrated when the theoretical magnetic field depends on more than one parameter. The second part of the thesis focuses on the linear force-free field assumption using two different geometric configurations. Firstly a vertical rigid magnetic flux tube is considered. The analytical expression of the magnetic field is obtained as an expansion in terms of Bessel functions. The main properties of this system are discussed and compared with two cylindrically symmetric twist profiles. For the second system, the photosphere is assumed to be an infinite plane. Using translational geometry, the analytical expression of the linear force-free magnetic field that matches a prescribed line of sight magnetic field component is obtained. This solution is compared with the non-linear solution obtained by Roumeliotis (1993).Loop oscillations in the coronaJames, Lornahttp://hdl.handle.net/10023/129472018-06-14T23:17:13Z2004-01-01T00:00:00ZMagnetic loops in the Sun's corona have been discovered to oscillate in a variety of modes. The oscillations are observed to exhibit strong damping. A number of theories have been put forward to explain the damping, including resonant absorption and phase mixing. Here we consider the modelling of loop oscillations, paying particular attention to two effects: gravity, and the addition of a chromospheric layer below the corona. We develop an acoustic model of coronal loop oscillations and consider two ways of describing the effects of the gravitational stratification and the chromospheric layers, considering either two media separated by a discontinuous interface or a single medium with a sound speed that varies along the loop. A dispersion relation for the two-layer isothermal atmosphere case is obtained and investigated numerically using a bisection code. On comparison with roots obtained for a single isothermal atmosphere, it was found that the effect of chromospheric footpoints on the period of a mode is slight. However, the effect of gravity was found to be more notable, rising up to a twenty percent change in period when considering the longer observed loops. This result is of especial interest since gravity is often ignored by authors discussing loop oscillations. The case of a linear sound speed has been investigated analytically, obtaining a dispersion relation in terms of Bessel functions. Our results show that the Bessel equation is a possible solution for describing the wave modes.
2004-01-01T00:00:00ZJames, LornaMagnetic loops in the Sun's corona have been discovered to oscillate in a variety of modes. The oscillations are observed to exhibit strong damping. A number of theories have been put forward to explain the damping, including resonant absorption and phase mixing. Here we consider the modelling of loop oscillations, paying particular attention to two effects: gravity, and the addition of a chromospheric layer below the corona. We develop an acoustic model of coronal loop oscillations and consider two ways of describing the effects of the gravitational stratification and the chromospheric layers, considering either two media separated by a discontinuous interface or a single medium with a sound speed that varies along the loop. A dispersion relation for the two-layer isothermal atmosphere case is obtained and investigated numerically using a bisection code. On comparison with roots obtained for a single isothermal atmosphere, it was found that the effect of chromospheric footpoints on the period of a mode is slight. However, the effect of gravity was found to be more notable, rising up to a twenty percent change in period when considering the longer observed loops. This result is of especial interest since gravity is often ignored by authors discussing loop oscillations. The case of a linear sound speed has been investigated analytically, obtaining a dispersion relation in terms of Bessel functions. Our results show that the Bessel equation is a possible solution for describing the wave modes.Magnetic annihilation, null collapse and coronal heatingMellor, Christopherhttp://hdl.handle.net/10023/129462018-06-14T23:17:06Z2004-01-01T00:00:00ZThe problem of how the Sun's corona is heated is of central importance to solar physics research. In this thesis we model three main areas. The first, annihilation, is a feature of non-ideal MHD and focusses on how magnetic field of opposite polarity meets at a null point and annihilates, after having been advected with plasma toward a stagnation point in the plasma flow. Generally, the null point of the field and the stagnation point of the flow are coincident at the origin, but in chapter 2 a simple extension is considered where an asymmetry in the boundary conditions of the field moves the null point away from the origin. Chapter 3 presents a model of reconnective annihilation in three dimensions. It represents flux being advected through the fan plane of a 3D null, and diffusing through a thin diffusion region before being annihilated at the spine line, and uses the method of matched asymptotic expansions to find the solution for small values of the resistivity. The second area of the thesis covers null collapse. This is when the magnetic field in close proximity to a null point is disturbed, causing the field to fold up on itself and collapse. This is a feature of ideal MHD, and causes a strong current to build up, allowing non-ideal effects to become important. When using linearised equations for the collapse problem, we are in fact looking at a linear instability. If this instability initiates a collapse, this is only a valid model until non-linear effects become important. By talking about collapse in chapters 4 and 5 (as it is talked about in the literature), we mean that the linear instability initiates collapse, which in principle, non-linear effects could later stop. Chapter 4 introduces a two-dimensional model for collapse, using the ideal, compressible, linearised MHD equations. It is a general solution in which all spatially linear nulls and their supporting plasma flows and pressure gradients can be checked for susceptibility to collapse under open boundary conditions. Chapter 5 uses the model introduced in chapter 4 to investigate the collapse of three-dimensional, potential nulls (again, spatially linear) for all possible supporting plasma flows and pressure gradients. Using this model, all nulls under consideration are found to collapse and produce large currents, except for a group of 2D O-type nulls supported by highly super-Alfvenic plasma flows. The third area of this thesis involves numerically simulating a model of heating by coronal tectonics (Priest et al, 2002). A simple magnetic field is created and the boundary is driven, also in a simple manner. Current sheets which scale with grid resolution are seen to build up on the quasi-separatrix layers, and there is some evidence of magnetic reconnection.
2004-01-01T00:00:00ZMellor, ChristopherThe problem of how the Sun's corona is heated is of central importance to solar physics research. In this thesis we model three main areas. The first, annihilation, is a feature of non-ideal MHD and focusses on how magnetic field of opposite polarity meets at a null point and annihilates, after having been advected with plasma toward a stagnation point in the plasma flow. Generally, the null point of the field and the stagnation point of the flow are coincident at the origin, but in chapter 2 a simple extension is considered where an asymmetry in the boundary conditions of the field moves the null point away from the origin. Chapter 3 presents a model of reconnective annihilation in three dimensions. It represents flux being advected through the fan plane of a 3D null, and diffusing through a thin diffusion region before being annihilated at the spine line, and uses the method of matched asymptotic expansions to find the solution for small values of the resistivity. The second area of the thesis covers null collapse. This is when the magnetic field in close proximity to a null point is disturbed, causing the field to fold up on itself and collapse. This is a feature of ideal MHD, and causes a strong current to build up, allowing non-ideal effects to become important. When using linearised equations for the collapse problem, we are in fact looking at a linear instability. If this instability initiates a collapse, this is only a valid model until non-linear effects become important. By talking about collapse in chapters 4 and 5 (as it is talked about in the literature), we mean that the linear instability initiates collapse, which in principle, non-linear effects could later stop. Chapter 4 introduces a two-dimensional model for collapse, using the ideal, compressible, linearised MHD equations. It is a general solution in which all spatially linear nulls and their supporting plasma flows and pressure gradients can be checked for susceptibility to collapse under open boundary conditions. Chapter 5 uses the model introduced in chapter 4 to investigate the collapse of three-dimensional, potential nulls (again, spatially linear) for all possible supporting plasma flows and pressure gradients. Using this model, all nulls under consideration are found to collapse and produce large currents, except for a group of 2D O-type nulls supported by highly super-Alfvenic plasma flows. The third area of this thesis involves numerically simulating a model of heating by coronal tectonics (Priest et al, 2002). A simple magnetic field is created and the boundary is driven, also in a simple manner. Current sheets which scale with grid resolution are seen to build up on the quasi-separatrix layers, and there is some evidence of magnetic reconnection.Sir Arthur Eddington and the foundations of modern physicsDurham, Ian T.http://hdl.handle.net/10023/129332018-06-14T23:16:37Z2005-01-01T00:00:00ZIn this dissertation I analyze Sir Arthur Eddington's statistical theory as developed in the first six chapters of his posthumously published Fundamental Theory. In particular I look at the mathematical structure, philosophical implications, and relevancy to modern physics. This analysis is the only one of Fundamental Theory that compares it to modern quantum field theory and is the most comprehensive look at his statistical theory in four decades. Several major insights have been made in this analysis including the fact that he was able to derive Pauli's Exclusion Principle in part from Heisenberg's Uncertainty Principle. In addition the most profound general conclusion of this research is that Fundamental Theory is, in fact, an early quantum field theory, something that has never before been suggested. Contrary to the majority of historical reports and some comments by his contemporaries, this analysis shows that Eddington's later work is neither mystical nor was it that far from mainstream when it was published. My research reveals numerous profoundly deep ideas that were ahead of their time when Fundamental Theory was developed, but that have significant applicability at present. As such this analysis presents several important questions to be considered by modern philosophers of science, physicists, mathematicians, and historians. In addition it sheds new light on Eddington as a scientist and mathematician, in part indicating that his marginalization has been largely unwarranted.
2005-01-01T00:00:00ZDurham, Ian T.In this dissertation I analyze Sir Arthur Eddington's statistical theory as developed in the first six chapters of his posthumously published Fundamental Theory. In particular I look at the mathematical structure, philosophical implications, and relevancy to modern physics. This analysis is the only one of Fundamental Theory that compares it to modern quantum field theory and is the most comprehensive look at his statistical theory in four decades. Several major insights have been made in this analysis including the fact that he was able to derive Pauli's Exclusion Principle in part from Heisenberg's Uncertainty Principle. In addition the most profound general conclusion of this research is that Fundamental Theory is, in fact, an early quantum field theory, something that has never before been suggested. Contrary to the majority of historical reports and some comments by his contemporaries, this analysis shows that Eddington's later work is neither mystical nor was it that far from mainstream when it was published. My research reveals numerous profoundly deep ideas that were ahead of their time when Fundamental Theory was developed, but that have significant applicability at present. As such this analysis presents several important questions to be considered by modern philosophers of science, physicists, mathematicians, and historians. In addition it sheds new light on Eddington as a scientist and mathematician, in part indicating that his marginalization has been largely unwarranted.Photospheric observations of surface and body modes in solar magnetic poresKeys, Peter H.Morton, Richard J.Jess, David B.Verth, GaryGrant, Samuel D.T.Mathioudakis, MihalisMackay, Duncan HendryDoyle, John G.Christian, Damian J.Keenan, Francis P.Erdélyi, Robertushttp://hdl.handle.net/10023/129012018-06-18T11:25:41Z2018-04-10T00:00:00ZOver the past number of years, great strides have been made in identifying the various low-order magnetohydrodynamic wave modes observable in a number of magnetic structures found within the solar atmosphere. However, one aspect of these modes that has remained elusive, until now, is their designation as either surface or body modes. This property has significant implications on how these modes transfer energy from the waveguide to the surrounding plasma. Here, for the first time to our knowledge, we present conclusive, direct evidence of these wave characteristics in numerous pores which were observed to support sausage modes. As well as outlining methods to detect these modes in observations, we make estimates of the energies associated with each mode. We find surface modes more frequently in the data, and also that surface modes appear to carry more energy than those displaying signatures of body modes. We find frequencies in the range of ~2 to 12 mHz with body modes as high as 11 mHz, but we do not find surface modes above 10 mHz. It is expected that the techniques we have applied will help researchers search for surface and body signatures in other modes and in differing structures to those presented here.
P.H.K. and R.J.M. are grateful to the Leverhulme Trust for the award of Early Career Fellowships. D.B.J. wishes to thank the UK Science and Technology Facilities Council (STFC) for the award of an Ernest Rutherford Fellowship alongside a dedicated Research Grant. D.B.J. and S.D.T.G. also wish to thank Invest NI and Randox Laboratories Ltd. for the award of a Research & Development Grant (059RDEN-1) that allowed this work to be undertaken. M.M. and F.P.K. acknowledge support from the STFC Consolidated Grant to Queen's University Belfast. R.E. acknowledges the support received from the Royal Society. Armagh Observatory is funded by the Northern Ireland Department of Communities. 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.
2018-04-10T00:00:00ZKeys, Peter H.Morton, Richard J.Jess, David B.Verth, GaryGrant, Samuel D.T.Mathioudakis, MihalisMackay, Duncan HendryDoyle, John G.Christian, Damian J.Keenan, Francis P.Erdélyi, RobertusOver the past number of years, great strides have been made in identifying the various low-order magnetohydrodynamic wave modes observable in a number of magnetic structures found within the solar atmosphere. However, one aspect of these modes that has remained elusive, until now, is their designation as either surface or body modes. This property has significant implications on how these modes transfer energy from the waveguide to the surrounding plasma. Here, for the first time to our knowledge, we present conclusive, direct evidence of these wave characteristics in numerous pores which were observed to support sausage modes. As well as outlining methods to detect these modes in observations, we make estimates of the energies associated with each mode. We find surface modes more frequently in the data, and also that surface modes appear to carry more energy than those displaying signatures of body modes. We find frequencies in the range of ~2 to 12 mHz with body modes as high as 11 mHz, but we do not find surface modes above 10 mHz. It is expected that the techniques we have applied will help researchers search for surface and body signatures in other modes and in differing structures to those presented here.Comparing methods suitable for monitoring marine mammals in low visibility conditions during seismic surveysVerfuss, Ursula K.Gillespie, DouglasGordon, JonathanMarques, Tiago A.Miller, BriannePlunkett, RachaelTheriault, James A.Tollit, Dominic J.Zitterbart, Daniel P.Hubert, PhilippeThomas, Lenhttp://hdl.handle.net/10023/128982018-03-18T02:30:34Z2018-01-01T00:00:00ZLoud sound emitted during offshore industrial activities can impact marine mammals. Regulations typically prescribe marine mammal monitoring before and/or during these activities to implement mitigation measures that minimise potential acoustic impacts. Using seismic surveys under low visibility conditions as a case study, we review which monitoring methods are suitable and compare their relative strengths and weaknesses. Passive acoustic monitoring has been implemented as either a complementary or alternative method to visual monitoring in low visibility conditions. Other methods such as RADAR, active sonar and thermal infrared have also been tested, but are rarely recommended by regulatory bodies. The efficiency of the monitoring method(s) will depend on the animal behaviour and environmental conditions, however, using a combination of complementary systems generally improves the overall detection performance. We recommend that the performance of monitoring systems, over a range of conditions, is explored in a modelling framework for a variety of species.
Funding: This work was supported by the Joint Industry Programme on E&P Sound and Marine Life - Phase III. TAM was partially supported by CEAUL (funded by FCT - Fundação para a Ciência e a Tecnologia, Portugal, through the project UID/MAT/00006/2013).
2018-01-01T00:00:00ZVerfuss, Ursula K.Gillespie, DouglasGordon, JonathanMarques, Tiago A.Miller, BriannePlunkett, RachaelTheriault, James A.Tollit, Dominic J.Zitterbart, Daniel P.Hubert, PhilippeThomas, LenLoud sound emitted during offshore industrial activities can impact marine mammals. Regulations typically prescribe marine mammal monitoring before and/or during these activities to implement mitigation measures that minimise potential acoustic impacts. Using seismic surveys under low visibility conditions as a case study, we review which monitoring methods are suitable and compare their relative strengths and weaknesses. Passive acoustic monitoring has been implemented as either a complementary or alternative method to visual monitoring in low visibility conditions. Other methods such as RADAR, active sonar and thermal infrared have also been tested, but are rarely recommended by regulatory bodies. The efficiency of the monitoring method(s) will depend on the animal behaviour and environmental conditions, however, using a combination of complementary systems generally improves the overall detection performance. We recommend that the performance of monitoring systems, over a range of conditions, is explored in a modelling framework for a variety of species.Transverse wave induced Kelvin-Helmholtz rolls in spiculesAntolin, PatrickSchmit, DonPereira, Tiago M. D.De Pontieu, BartDe Moortel, Inekehttp://hdl.handle.net/10023/128802018-04-22T00:35:56Z2018-03-23T00:00:00ZIn addition to their jet-like dynamic behaviour, spicules usually exhibit strong transverse speeds, multi-stranded structure and heating from chromospheric to transition region temperatures. In this work we first analyse Hinode & IRIS observations of spicules and find different behaviours in terms of their Doppler velocity evolution and collective motion of their sub-structure. Some have a Doppler shift sign change that is rather fixed along the spicule axis, and lack coherence in the oscillatory motion of strand-like structure, matching rotation models or long wavelength torsional Alfvén waves. Others exhibit a Doppler shift sign change at maximum displacement and coherent motion of their strands, suggesting a collective MHD wave. By comparing with an idealised 3D MHD simulation combined with radiative transfer modelling, we analyse the role of transverse MHD waves and associated instabilities in spicule-like features. We find that Transverse Wave Induced Kelvin-Helmholtz (TWIKH) rolls lead to coherence of strand-like structure in imaging and spectral maps, as seen in some observations. The rapid transverse dynamics and the density and temperature gradients at the spicule boundary lead to ring-shaped Mg II k and Ca II H source functions in the transverse cross-section, potentially allowing IRIS to capture the KHI dynamics. Twists and currents propagate along the spicule at Alfvénic speeds, and the temperature variations within TWIKH rolls produce sudden appearance/disappearance of strands seen in Doppler velocity and in Ca II H intensity. However, only a mild intensity increase in higher temperature lines is obtained, suggesting there is an additional heating mechanism at work in spicules.
This research has received funding from the UK Science and Technology Facilities Council (Consolidated Grant ST/K000950/1) and the European Union Horizon 2020 research and innovation programme (grant agreement No. 647214).
2018-03-23T00:00:00ZAntolin, PatrickSchmit, DonPereira, Tiago M. D.De Pontieu, BartDe Moortel, InekeIn addition to their jet-like dynamic behaviour, spicules usually exhibit strong transverse speeds, multi-stranded structure and heating from chromospheric to transition region temperatures. In this work we first analyse Hinode & IRIS observations of spicules and find different behaviours in terms of their Doppler velocity evolution and collective motion of their sub-structure. Some have a Doppler shift sign change that is rather fixed along the spicule axis, and lack coherence in the oscillatory motion of strand-like structure, matching rotation models or long wavelength torsional Alfvén waves. Others exhibit a Doppler shift sign change at maximum displacement and coherent motion of their strands, suggesting a collective MHD wave. By comparing with an idealised 3D MHD simulation combined with radiative transfer modelling, we analyse the role of transverse MHD waves and associated instabilities in spicule-like features. We find that Transverse Wave Induced Kelvin-Helmholtz (TWIKH) rolls lead to coherence of strand-like structure in imaging and spectral maps, as seen in some observations. The rapid transverse dynamics and the density and temperature gradients at the spicule boundary lead to ring-shaped Mg II k and Ca II H source functions in the transverse cross-section, potentially allowing IRIS to capture the KHI dynamics. Twists and currents propagate along the spicule at Alfvénic speeds, and the temperature variations within TWIKH rolls produce sudden appearance/disappearance of strands seen in Doppler velocity and in Ca II H intensity. However, only a mild intensity increase in higher temperature lines is obtained, suggesting there is an additional heating mechanism at work in spicules.Weak convergence to extremal processes and record events for non-uniformly hyperbolic dynamical systemsHolland, MarkTodd, Mikehttp://hdl.handle.net/10023/128772018-03-31T23:36:16Z2017-09-07T00:00:00ZFor a measure-preserving dynamical system (X, ƒ, μ), we consider the time series of maxima Mn = max{X1,…,Xn} associated to the process Xn = φ (ƒn-1(x)) generated by the dynamical system for some observable φ : Χ → R . Using a point-process approach we establish weak convergence of the process Yn(t) = an(M[nt] - bn) to an extremal Y(t) process for suitable scaling constants an, bn ∈ R . Convergence here takes place in the Skorokhod space D(0, ∞) with the J1 topology. We also establish distributional results for the record times and record values of the corresponding maxima process.
This research was partially supported by the London Mathematics Society (Scheme 4, no. 41126), and both authors thank the Erwin Schroedigner Institute (ESI) in Vienna were part of this work was carried out. MH wishes to thank the Department of Mathematics, University of Houston for hospitality and financial support, and MT thanks Exeter University for their hospitality and support.
2017-09-07T00:00:00ZHolland, MarkTodd, MikeFor a measure-preserving dynamical system (X, ƒ, μ), we consider the time series of maxima Mn = max{X1,…,Xn} associated to the process Xn = φ (ƒn-1(x)) generated by the dynamical system for some observable φ : Χ → R . Using a point-process approach we establish weak convergence of the process Yn(t) = an(M[nt] - bn) to an extremal Y(t) process for suitable scaling constants an, bn ∈ R . Convergence here takes place in the Skorokhod space D(0, ∞) with the J1 topology. We also establish distributional results for the record times and record values of the corresponding maxima process.The cycle polynomial of a permutation groupCameron, Peter J.Semeraro, Jasonhttp://hdl.handle.net/10023/128402018-03-04T02:30:58Z2018-01-25T00:00:00ZThe cycle polynomial of a finite permutation group G is the generating function for the number of elements of G with a given number of cycles.In the first part of the paper, we develop basic properties of this polynomial, and give a number of examples. In the 1970s, Richard Stanley introduced the notion of reciprocity for pairs of combinatorial polynomials. We show that, in a considerable number of cases, there is a polynomial in the reciprocal relation to the cycle polynomial of G; this is the orbital chromatic polynomial of Γ and G, where Γ is a G-invariant graph, introduced by the first author, Jackson and Rudd. We pose the general problem of finding all such reciprocal pairs, and give a number of examples and characterisations: the latter include the cases where Γ is a complete or null graph or a tree. The paper concludes with some comments on other polynomials associated with a permutation group.
2018-01-25T00:00:00ZCameron, Peter J.Semeraro, JasonThe cycle polynomial of a finite permutation group G is the generating function for the number of elements of G with a given number of cycles.In the first part of the paper, we develop basic properties of this polynomial, and give a number of examples. In the 1970s, Richard Stanley introduced the notion of reciprocity for pairs of combinatorial polynomials. We show that, in a considerable number of cases, there is a polynomial in the reciprocal relation to the cycle polynomial of G; this is the orbital chromatic polynomial of Γ and G, where Γ is a G-invariant graph, introduced by the first author, Jackson and Rudd. We pose the general problem of finding all such reciprocal pairs, and give a number of examples and characterisations: the latter include the cases where Γ is a complete or null graph or a tree. The paper concludes with some comments on other polynomials associated with a permutation group.Examining the role of individual movement in promoting coexistence in a spatially explicit prisoner's dilemmaBurgess, Andrew E. F.Lorenzi, TommasoSchofield, Pietà G.Hubbard, Stephen F.Chaplain, Mark A. J.http://hdl.handle.net/10023/128132018-03-01T00:15:25Z2017-04-21T00:00:00ZThe emergence of cooperation is a major conundrum of evolutionary biology. To unravel this evolutionary riddle, several models have been developed within the theoretical framework of spatial game theory, focussing on the interactions between two general classes of player, "cooperators" and "defectors". Generally, explicit movement in the spatial domain is not considered in these models, with strategies moving via imitation or through colonisation of neighbouring sites. We present here a spatially explicit stochastic individual-based model in which pure cooperators and defectors undergo random motion via diffusion and also chemotaxis guided by the gradient of a semiochemical. Individual movement rules are derived from an underlying system of reaction-diffusion-taxis partial differential equations which describes the dynamics of the local number of individuals and the concentration of the semiochemical. Local interactions are governed by the payoff matrix of the classical prisoner's dilemma, and accumulated payoffs are translated into offspring. We investigate the cases of both synchronous and non-synchronous generations. Focussing on an ecological scenario where defectors are parasitic on cooperators, we find that random motion and semiochemical sensing bring about self-generated patterns in which resident cooperators and parasitic defectors can coexist in proportions that fluctuate about non-zero values. Remarkably, coexistence emerges as a genuine consequence of the natural tendency of cooperators to aggregate into clusters, without the need for them to find physical shelter or outrun the parasitic defectors. This provides further evidence that spatial clustering enhances the benefits of mutual cooperation and plays a crucial role in preserving cooperative behaviours.
AEFB gratefully acknowledges the support of an EPSRC CASE PhD studentship.
2017-04-21T00:00:00ZBurgess, Andrew E. F.Lorenzi, TommasoSchofield, Pietà G.Hubbard, Stephen F.Chaplain, Mark A. J.The emergence of cooperation is a major conundrum of evolutionary biology. To unravel this evolutionary riddle, several models have been developed within the theoretical framework of spatial game theory, focussing on the interactions between two general classes of player, "cooperators" and "defectors". Generally, explicit movement in the spatial domain is not considered in these models, with strategies moving via imitation or through colonisation of neighbouring sites. We present here a spatially explicit stochastic individual-based model in which pure cooperators and defectors undergo random motion via diffusion and also chemotaxis guided by the gradient of a semiochemical. Individual movement rules are derived from an underlying system of reaction-diffusion-taxis partial differential equations which describes the dynamics of the local number of individuals and the concentration of the semiochemical. Local interactions are governed by the payoff matrix of the classical prisoner's dilemma, and accumulated payoffs are translated into offspring. We investigate the cases of both synchronous and non-synchronous generations. Focussing on an ecological scenario where defectors are parasitic on cooperators, we find that random motion and semiochemical sensing bring about self-generated patterns in which resident cooperators and parasitic defectors can coexist in proportions that fluctuate about non-zero values. Remarkably, coexistence emerges as a genuine consequence of the natural tendency of cooperators to aggregate into clusters, without the need for them to find physical shelter or outrun the parasitic defectors. This provides further evidence that spatial clustering enhances the benefits of mutual cooperation and plays a crucial role in preserving cooperative behaviours.Affine rigidity and conics at infinityConnelly, RobertGortler, Steven J.Theran, Louishttp://hdl.handle.net/10023/127922018-04-21T23:32:52Z2017-02-26T00:00:00ZWe prove that if a framework of a graph is neighborhood affine rigid in d-dimensions (or has the stronger property of having an equilibrium stress matrix of rank n — d — 1) then it has an affine flex (an affine, but non Euclidean, transform of space that preserves all of the edge lengths) if and only if the framework is ruled on a single quadric. This strengthens and also simplifies a related result by Alfakih. It also allows us to prove that the property of super stability is invariant with respect to projective transforms and also to the coning and slicing operations. Finally this allows us to unify some previous results on the Strong Arnold Property of matrices.
RC is partially supported by NSF grant DMS-1564493. SJG is partially supported by NSF grant DMS-1564473.
2017-02-26T00:00:00ZConnelly, RobertGortler, Steven J.Theran, LouisWe prove that if a framework of a graph is neighborhood affine rigid in d-dimensions (or has the stronger property of having an equilibrium stress matrix of rank n — d — 1) then it has an affine flex (an affine, but non Euclidean, transform of space that preserves all of the edge lengths) if and only if the framework is ruled on a single quadric. This strengthens and also simplifies a related result by Alfakih. It also allows us to prove that the property of super stability is invariant with respect to projective transforms and also to the coning and slicing operations. Finally this allows us to unify some previous results on the Strong Arnold Property of matrices.The coronal monsoon : thermal nonequilibrium revealed by periodic coronal rainAuchère, FrédéricFroment, ClaraSoubrié, ElieAntolin, PatrickOliver, RamonPelouze, Gabrielhttp://hdl.handle.net/10023/127612018-04-08T01:30:48Z2018-02-05T00:00:00ZWe report on the discovery of periodic coronal rain in an off-limb sequence of Solar Dynamics Observatory/Atmospheric Imaging Assembly images. The showers are co-spatial and in phase with periodic (6.6 hr) intensity pulsations of coronal loops of the sort described by Auchère et al. and Froment et al. These new observations make possible a unified description of both phenomena. Coronal rain and periodic intensity pulsations of loops are two manifestations of the same physical process: evaporation/condensation cycles resulting from a state of thermal nonequilibrium. The fluctuations around coronal temperatures produce the intensity pulsations of loops, and rain falls along their legs if thermal runaway cools the periodic condensations down and below transition-region temperatures. This scenario is in line with the predictions of numerical models of quasi-steadily and footpoint heated loops. The presence of coronal rain—albeit non-periodic—in several other structures within the studied field of view implies that this type of heating is at play on a large scale.
P.A. has received funding from the UK Science and Technology Facilities Council (Consolidated Grant ST/K000950/1) and the European Union Horizon 2020 research and innovation programme (grant agreement No. 647214).
2018-02-05T00:00:00ZAuchère, FrédéricFroment, ClaraSoubrié, ElieAntolin, PatrickOliver, RamonPelouze, GabrielWe report on the discovery of periodic coronal rain in an off-limb sequence of Solar Dynamics Observatory/Atmospheric Imaging Assembly images. The showers are co-spatial and in phase with periodic (6.6 hr) intensity pulsations of coronal loops of the sort described by Auchère et al. and Froment et al. These new observations make possible a unified description of both phenomena. Coronal rain and periodic intensity pulsations of loops are two manifestations of the same physical process: evaporation/condensation cycles resulting from a state of thermal nonequilibrium. The fluctuations around coronal temperatures produce the intensity pulsations of loops, and rain falls along their legs if thermal runaway cools the periodic condensations down and below transition-region temperatures. This scenario is in line with the predictions of numerical models of quasi-steadily and footpoint heated loops. The presence of coronal rain—albeit non-periodic—in several other structures within the studied field of view implies that this type of heating is at play on a large scale.Statistical issues in first-in-human studies on BIA 10-2474: neglected comparison of protocol against practiceBird, Sheila M.Bailey, Rosemary A.Grieve, Andrew P.Senn, Stephenhttp://hdl.handle.net/10023/127402018-05-27T00:34:41Z2017-03-15T00:00:00ZBy setting the regulatory-approved protocol for a suite of first-in-human studies on BIA 10-2474 against the subsequent French investigations, we highlight six key design and statistical issues which reinforce recommendations by a Royal Statistical Society Working Party which were made in the aftermath of cytokine release storm in six healthy volunteers in the UK in 2006. The 6 issues are dose determination, availability of pharmacokinetic results, dosing interval, stopping rules, appraisal by safety committee, and clear algorithm required if combining approvals for single and multiple ascending dose studies.
Funding information: European Union's FP7 programme, Grant/Award Number: 602552
2017-03-15T00:00:00ZBird, Sheila M.Bailey, Rosemary A.Grieve, Andrew P.Senn, StephenBy setting the regulatory-approved protocol for a suite of first-in-human studies on BIA 10-2474 against the subsequent French investigations, we highlight six key design and statistical issues which reinforce recommendations by a Royal Statistical Society Working Party which were made in the aftermath of cytokine release storm in six healthy volunteers in the UK in 2006. The 6 issues are dose determination, availability of pharmacokinetic results, dosing interval, stopping rules, appraisal by safety committee, and clear algorithm required if combining approvals for single and multiple ascending dose studies.A multiscale mathematical model of tumour invasive growthPeng, LuTrucu, DumitruLin, PingThompson, AlastairChaplain, Mark A. J.http://hdl.handle.net/10023/127392018-05-13T01:34:32Z2017-03-01T00:00:00ZKnown as one of the hallmarks of cancer (Hanahan and Weinberg in Cell 100:57–70, 2000) cancer cell invasion of human body tissue is a complicated spatio-temporal multiscale process which enables a localised solid tumour to transform into a systemic, metastatic and fatal disease. This process explores and takes advantage of the reciprocal relation that solid tumours establish with the extracellular matrix (ECM) components and other multiple distinct cell types from the surrounding microenvironment. Through the secretion of various proteolytic enzymes such as matrix metalloproteinases or the urokinase plasminogen activator (uPA), the cancer cell population alters the configuration of the surrounding ECM composition and overcomes the physical barriers to ultimately achieve local cancer spread into the surrounding tissue. The active interplay between the tissue-scale tumour dynamics and the molecular mechanics of the involved proteolytic enzymes at the cell scale underlines the biologically multiscale character of invasion and raises the challenge of modelling this process with an appropriate multiscale approach. In this paper, we present a new two-scale moving boundary model of cancer invasion that explores the tissue-scale tumour dynamics in conjunction with the molecular dynamics of the urokinase plasminogen activation system. Building on the multiscale moving boundary method proposed in Trucu et al. (Multiscale Model Simul 11(1):309–335, 2013), the modelling that we propose here allows us to study the changes in tissue-scale tumour morphology caused by the cell-scale uPA microdynamics occurring along the invasive edge of the tumour. Our computational simulation results demonstrate a range of heterogeneous dynamics which are qualitatively similar to the invasive growth patterns observed in a number of different types of cancer, such as the tumour infiltrative growth patterns discussed in Ito et al. (J Gastroenterol 47:1279–1289, 2012).
2017-03-01T00:00:00ZPeng, LuTrucu, DumitruLin, PingThompson, AlastairChaplain, Mark A. J.Known as one of the hallmarks of cancer (Hanahan and Weinberg in Cell 100:57–70, 2000) cancer cell invasion of human body tissue is a complicated spatio-temporal multiscale process which enables a localised solid tumour to transform into a systemic, metastatic and fatal disease. This process explores and takes advantage of the reciprocal relation that solid tumours establish with the extracellular matrix (ECM) components and other multiple distinct cell types from the surrounding microenvironment. Through the secretion of various proteolytic enzymes such as matrix metalloproteinases or the urokinase plasminogen activator (uPA), the cancer cell population alters the configuration of the surrounding ECM composition and overcomes the physical barriers to ultimately achieve local cancer spread into the surrounding tissue. The active interplay between the tissue-scale tumour dynamics and the molecular mechanics of the involved proteolytic enzymes at the cell scale underlines the biologically multiscale character of invasion and raises the challenge of modelling this process with an appropriate multiscale approach. In this paper, we present a new two-scale moving boundary model of cancer invasion that explores the tissue-scale tumour dynamics in conjunction with the molecular dynamics of the urokinase plasminogen activation system. Building on the multiscale moving boundary method proposed in Trucu et al. (Multiscale Model Simul 11(1):309–335, 2013), the modelling that we propose here allows us to study the changes in tissue-scale tumour morphology caused by the cell-scale uPA microdynamics occurring along the invasive edge of the tumour. Our computational simulation results demonstrate a range of heterogeneous dynamics which are qualitatively similar to the invasive growth patterns observed in a number of different types of cancer, such as the tumour infiltrative growth patterns discussed in Ito et al. (J Gastroenterol 47:1279–1289, 2012).Sesqui-arrays, a generalisation of triple arraysBailey, Rosemary AnneCameron, Peter JephsonNilson, Tomashttp://hdl.handle.net/10023/127252018-05-27T00:35:48Z2018-01-01T00:00:00ZA triple array is a rectangular array containing letters, each letter occurring equally often with no repeats in rows or columns, such that the number of letters common to two rows, two columns, or a row and a column are (possibly different) non-zero constants. Deleting the condition on the letters commonto a row and a column gives a double array. We propose the term sesqui-array for such an array when only the condition on pairs ofcolumns is deleted. Thus all triple arrays are sesqui-arrays.In this paper we give three constructions for sesqui-arrays. The first gives (n+1) x n2 arrays on n(n+1) letters for n>1. (Such an array for n=2 was found by Bagchi.) This construction uses Latin squares.The second uses the Sylvester graph, a subgraph of the Hoffman--Singleton graph, to build a good block design for 36 treatments in 42 blocks of size 6, and then uses this in a 7 x 36 sesqui-array for 42 letters. We also give a construction for K x (K-1)(K-2)/2 sesqui-arrays onK(K-1)/2 letters. This construction uses biplanes. It starts with a block of a biplane and produces an array which satisfies the requirements for a sesqui-array except possibly that of having no repeated letters in a row or column. We show that this condition holds if and only if the Hussain chains for the selected block contain no 4-cycles. A sufficient condition for the construction to give a triple array is that each Hussain chain is a union of 3-cycles; but this condition is not necessary, and we give a few further examples. We also discuss the question of which of these arrays provide good designs for experiments.
2018-01-01T00:00:00ZBailey, Rosemary AnneCameron, Peter JephsonNilson, TomasA triple array is a rectangular array containing letters, each letter occurring equally often with no repeats in rows or columns, such that the number of letters common to two rows, two columns, or a row and a column are (possibly different) non-zero constants. Deleting the condition on the letters commonto a row and a column gives a double array. We propose the term sesqui-array for such an array when only the condition on pairs ofcolumns is deleted. Thus all triple arrays are sesqui-arrays.In this paper we give three constructions for sesqui-arrays. The first gives (n+1) x n2 arrays on n(n+1) letters for n>1. (Such an array for n=2 was found by Bagchi.) This construction uses Latin squares.The second uses the Sylvester graph, a subgraph of the Hoffman--Singleton graph, to build a good block design for 36 treatments in 42 blocks of size 6, and then uses this in a 7 x 36 sesqui-array for 42 letters. We also give a construction for K x (K-1)(K-2)/2 sesqui-arrays onK(K-1)/2 letters. This construction uses biplanes. It starts with a block of a biplane and produces an array which satisfies the requirements for a sesqui-array except possibly that of having no repeated letters in a row or column. We show that this condition holds if and only if the Hussain chains for the selected block contain no 4-cycles. A sufficient condition for the construction to give a triple array is that each Hussain chain is a union of 3-cycles; but this condition is not necessary, and we give a few further examples. We also discuss the question of which of these arrays provide good designs for experiments.Penalized nonparametric scalar-on-function regression via principal coordinatesReiss, Philip T.Miller, David L.Wu, Pei ShienHua, Wen Yuhttp://hdl.handle.net/10023/126632018-05-23T09:30:12Z2017-01-01T00:00:00ZA number of classical approaches to nonparametric regression have recently been extended to the case of functional predictors. This article introduces a new method of this type, which extends intermediate-rank penalized smoothing to scalar-on-function regression. In the proposed method, which we call principal coordinate ridge regression, one regresses the response on leading principal coordinates defined by a relevant distance among the functional predictors, while applying a ridge penalty. Our publicly available implementation, based on generalized additive modeling software, allows for fast optimal tuning parameter selection and for extensions to multiple functional predictors, exponential family-valued responses, and mixed-effects models. In an application to signature verification data, principal coordinate ridge regression, with dynamic time warping distance used to define the principal coordinates, is shown to outperform a functional generalized linear model. Supplementary materials for this article are available online.
Philip Reiss, Pei-Shien Wu, and Wen-Yu Hua gratefully acknowledge the support of the U.S. National Institute of Mental Health (grant 1R01MH095836-01A1).
2017-01-01T00:00:00ZReiss, Philip T.Miller, David L.Wu, Pei ShienHua, Wen YuA number of classical approaches to nonparametric regression have recently been extended to the case of functional predictors. This article introduces a new method of this type, which extends intermediate-rank penalized smoothing to scalar-on-function regression. In the proposed method, which we call principal coordinate ridge regression, one regresses the response on leading principal coordinates defined by a relevant distance among the functional predictors, while applying a ridge penalty. Our publicly available implementation, based on generalized additive modeling software, allows for fast optimal tuning parameter selection and for extensions to multiple functional predictors, exponential family-valued responses, and mixed-effects models. In an application to signature verification data, principal coordinate ridge regression, with dynamic time warping distance used to define the principal coordinates, is shown to outperform a functional generalized linear model. Supplementary materials for this article are available online.Slow and fast escape for open intermittent mapsDemers, Mark F.Todd, Mikehttp://hdl.handle.net/10023/126582018-02-04T00:16:06Z2017-04-01T00:00:00ZIf a system mixes too slowly, putting a hole in it can completely destroy the richness of the dynamics. Here we study this instability for a class of intermittent maps with a family of slowly mixing measures. We show that there are three regimes:(1) standard hyperbolic-like behavior where the rate of mixing is faster than the rate of escape through the hole, there is a unique limiting absolutely continuous conditionally invariant measure (accim) and there is a complete thermodynamic description of the dynamics on the survivor set; (2) an intermediate regime, where the rate of mixing and escape through the hole coincide, limiting accims exist, but much of the thermodynamic picture breaks down; (3) a subexponentially mixing regime where the slow mixing means that mass simply accumulates on the parabolic fixed point. We give a complete picture of the transitions and stability properties (in the size of the hole and as we move through the family) in this class of open systems. In particular, we are able to recover a form of stability in the third regime above via the dynamics on the survivor set, even when no limiting accim exists.
MD was partially supported by NSF grant DMS 1362420. This project was started as part of an RiGs grant through ICMS, Scotland.
2017-04-01T00:00:00ZDemers, Mark F.Todd, MikeIf a system mixes too slowly, putting a hole in it can completely destroy the richness of the dynamics. Here we study this instability for a class of intermittent maps with a family of slowly mixing measures. We show that there are three regimes:(1) standard hyperbolic-like behavior where the rate of mixing is faster than the rate of escape through the hole, there is a unique limiting absolutely continuous conditionally invariant measure (accim) and there is a complete thermodynamic description of the dynamics on the survivor set; (2) an intermediate regime, where the rate of mixing and escape through the hole coincide, limiting accims exist, but much of the thermodynamic picture breaks down; (3) a subexponentially mixing regime where the slow mixing means that mass simply accumulates on the parabolic fixed point. We give a complete picture of the transitions and stability properties (in the size of the hole and as we move through the family) in this class of open systems. In particular, we are able to recover a form of stability in the third regime above via the dynamics on the survivor set, even when no limiting accim exists.Module theory : an approach to linear algebraBlyth, T. S. (Thomas Scott)http://hdl.handle.net/10023/126432018-06-05T10:25:50Z2018-01-01T00:00:00ZOriginally published in 1977 by Oxford University Press, with a second edition published in 1990. This is a revised version of the second edition published for the first time in electronic form. This electronic edition is published by the University of St Andrews.
2018-01-01T00:00:00ZBlyth, T. S. (Thomas Scott)Flare particle acceleration in the interaction of twisted coronal flux ropesThrelfall, J.Hood, A. W.Browning, P. K.http://hdl.handle.net/10023/126272018-06-24T00:41:10Z2018-03-20T00:00:00ZAims. The aim of this work is to investigate and characterise non-thermal particle behaviour in a three-dimensional (3D) magnetohydrodynamical (MHD) model of unstable multi-threaded flaring coronal loops. Methods. We have used a numerical scheme which solves the relativistic guiding centre approximation to study the motion of electrons and protons. The scheme uses snapshots from high resolution numerical MHD simulations of coronal loops containing two threads, where a single thread becomes unstable and (in one case) destabilises and merges with an additional thread. Results. The particle responses to the reconnection and fragmentation in MHD simulations of two loop threads are examined in detail. We illustrate the role played by uniform background resistivity and distinguish this from the role of anomalous resistivity using orbits in an MHD simulation where only one thread becomes unstable without destabilising further loop threads. We examine the (scalable) orbit energy gains and final positions recovered at different stages of a second MHD simulation wherein a secondary loop thread is destabilised by (and merges with) the first thread. We compare these results with other theoretical particle acceleration models in the context of observed energetic particle populations during solar flares.
The authors gratefully acknowledge the support of the U.K. Science and Technology Facilities Council. JT and AWH acknowledge the financial support of STFC through the Consolidated grant, ST/N000609/1, to the University of St Andrews. PKB acknowledges STFC support through ST/P000428/1 at the University of Manchester.
2018-03-20T00:00:00ZThrelfall, J.Hood, A. W.Browning, P. K.Aims. The aim of this work is to investigate and characterise non-thermal particle behaviour in a three-dimensional (3D) magnetohydrodynamical (MHD) model of unstable multi-threaded flaring coronal loops. Methods. We have used a numerical scheme which solves the relativistic guiding centre approximation to study the motion of electrons and protons. The scheme uses snapshots from high resolution numerical MHD simulations of coronal loops containing two threads, where a single thread becomes unstable and (in one case) destabilises and merges with an additional thread. Results. The particle responses to the reconnection and fragmentation in MHD simulations of two loop threads are examined in detail. We illustrate the role played by uniform background resistivity and distinguish this from the role of anomalous resistivity using orbits in an MHD simulation where only one thread becomes unstable without destabilising further loop threads. We examine the (scalable) orbit energy gains and final positions recovered at different stages of a second MHD simulation wherein a secondary loop thread is destabilised by (and merges with) the first thread. We compare these results with other theoretical particle acceleration models in the context of observed energetic particle populations during solar flares.The construction of finite soluble factor groups of finitely presented groups and its applicationWegner, Alexanderhttp://hdl.handle.net/10023/126002018-01-25T00:15:56Z1992-01-01T00:00:00ZComputational group theory deals with the design, analysis and computer implementation of algorithms for solving computational problems involving groups, and with the applications of the programs produced to interesting questions in group theory, in other branches of mathematics, and in other areas of science. This thesis describes an implementation of a proposal for a Soluble Quotient Algorithm, i.e. a description of the algorithms used and a report on the findings of an empirical study of the behaviour of the programs, and gives an account of an application of the programs. The programs were used for the construction of soluble groups with interesting properties, e.g. for the construction of soluble groups of large derived length which seem to be candidates for groups having efficient presentations. New finite soluble groups of derived length six with trivial Schur multiplier and efficient presentations are described. The methods for finding efficient presentations proved to be only practicable for groups of moderate order. Therefore, for a given derived length soluble groups of small order are of interest. The minimal soluble groups of derived length less than or equal to six are classified.
1992-01-01T00:00:00ZWegner, AlexanderComputational group theory deals with the design, analysis and computer implementation of algorithms for solving computational problems involving groups, and with the applications of the programs produced to interesting questions in group theory, in other branches of mathematics, and in other areas of science. This thesis describes an implementation of a proposal for a Soluble Quotient Algorithm, i.e. a description of the algorithms used and a report on the findings of an empirical study of the behaviour of the programs, and gives an account of an application of the programs. The programs were used for the construction of soluble groups with interesting properties, e.g. for the construction of soluble groups of large derived length which seem to be candidates for groups having efficient presentations. New finite soluble groups of derived length six with trivial Schur multiplier and efficient presentations are described. The methods for finding efficient presentations proved to be only practicable for groups of moderate order. Therefore, for a given derived length soluble groups of small order are of interest. The minimal soluble groups of derived length less than or equal to six are classified.Aggregation and travelling wave dynamics in a two-population model of cancer cell growth and invasionBitsouni, VasilikiTrucu, DumitruChaplain, Mark Andrew JosephEftimie, Ralucahttp://hdl.handle.net/10023/125952018-03-31T23:40:26Z2018-01-15T00:00:00ZCells adhere to each other and to the extracellular matrix (ECM) through protein molecules on the surface of the cells. The breaking and forming of adhesive bonds, a process critical in cancer invasion and metas- tasis, can be influenced by the mutation of cancer cells. In this paper, we develop a nonlocal mathematical model describing cancer cell invasion and movement as a result of integrin-controlled cell-cell adhesion and cell-matrix adhesion, for two cancer cell populations with different levels of mutation. The partial differential equations for cell dynamics are coupled with ordinary differential equations describing the extracellular matrix (ECM) degradation and the production and decay of integrins. We use this model to investigate the role of cancer mutation on the possibility of cancer clonal competition with alternating dominance, or even competitive exclusion (phenomena observed experimentally). We discuss different possible cell aggregation patterns, as well as travelling wave patterns. In regard to the travelling waves, we investigate the effect of cancer mutation rate on the speed of cancer invasion.
Funding: Engineering and Physical Sciences Research Council (UK) grant numbers EP/L504932/1 (VB), EP/K033689/1 (RE).
2018-01-15T00:00:00ZBitsouni, VasilikiTrucu, DumitruChaplain, Mark Andrew JosephEftimie, RalucaCells adhere to each other and to the extracellular matrix (ECM) through protein molecules on the surface of the cells. The breaking and forming of adhesive bonds, a process critical in cancer invasion and metas- tasis, can be influenced by the mutation of cancer cells. In this paper, we develop a nonlocal mathematical model describing cancer cell invasion and movement as a result of integrin-controlled cell-cell adhesion and cell-matrix adhesion, for two cancer cell populations with different levels of mutation. The partial differential equations for cell dynamics are coupled with ordinary differential equations describing the extracellular matrix (ECM) degradation and the production and decay of integrins. We use this model to investigate the role of cancer mutation on the possibility of cancer clonal competition with alternating dominance, or even competitive exclusion (phenomena observed experimentally). We discuss different possible cell aggregation patterns, as well as travelling wave patterns. In regard to the travelling waves, we investigate the effect of cancer mutation rate on the speed of cancer invasion.Telomerecat : a ploidy-agnostic method for estimating telomere length from whole genome sequencing dataFarmery, JamesSmith, MikeNIHR BioResource - Rare DiseasesLynch, Andyhttp://hdl.handle.net/10023/125912018-02-25T01:33:22Z2018-01-22T00:00:00ZTelomere length is a risk factor in disease and the dynamics of telomere length are crucial to our understanding of cell replication and vitality. The proliferation of whole genome sequencing represents an unprecedented opportunity to glean new insights into telomere biology on a previously unimaginable scale. To this end, a number of approaches for estimating telomere length from whole-genome sequencing data have been proposed. Here we present Telomerecat, a novel approach to the estimation of telomere length. Previous methods have been dependent on the number of telomeres present in a cell being known, which may be problematic when analysing aneuploid cancer data and non-human samples. Telomerecat is designed to be agnostic to the number of telomeres present, making it suited for the purpose of estimating telomere length in cancer studies. Telomerecat also accounts for interstitial telomeric reads and presents a novel approach to dealing with sequencing errors. We show that Telomerecat performs well at telomere length estimation when compared to leading experimental and computational methods. Furthermore, we show that it detects expected patterns in longitudinal data, repeated measurements, and cross-species comparisons. We also apply the method to a cancer cell data, uncovering an interesting relationship with the underlying telomerase genotype.
Funding: Cancer Research UK Programme Grant to Simon Tavaré (C14303/A17197) (JHRF, AGL, MLS); European Commission through the Horizon 2020 project SOUND (Grant Agreement no. 633974) (AGL).
2018-01-22T00:00:00ZFarmery, JamesSmith, MikeNIHR BioResource - Rare DiseasesLynch, AndyTelomere length is a risk factor in disease and the dynamics of telomere length are crucial to our understanding of cell replication and vitality. The proliferation of whole genome sequencing represents an unprecedented opportunity to glean new insights into telomere biology on a previously unimaginable scale. To this end, a number of approaches for estimating telomere length from whole-genome sequencing data have been proposed. Here we present Telomerecat, a novel approach to the estimation of telomere length. Previous methods have been dependent on the number of telomeres present in a cell being known, which may be problematic when analysing aneuploid cancer data and non-human samples. Telomerecat is designed to be agnostic to the number of telomeres present, making it suited for the purpose of estimating telomere length in cancer studies. Telomerecat also accounts for interstitial telomeric reads and presents a novel approach to dealing with sequencing errors. We show that Telomerecat performs well at telomere length estimation when compared to leading experimental and computational methods. Furthermore, we show that it detects expected patterns in longitudinal data, repeated measurements, and cross-species comparisons. We also apply the method to a cancer cell data, uncovering an interesting relationship with the underlying telomerase genotype.Combining radiation with hyperthermia : a multiscale model informed by in vitro experimentsBrüningk, SarahPowathil, GibinZiegenhein, PeterIjaz, JannatRivens, IanNill, S.Chaplain, Mark Andrew JosephOelfke, Uweter Haar, Gailhttp://hdl.handle.net/10023/125902018-05-19T23:33:08Z2018-01-01T00:00:00ZCombined radiotherapy and hyperthermia offer great potential for the successful treatment of radio-resistant tumours through thermo-radiosensitization. Tumour response heterogeneity, due to intrinsic, or micro-environmentally induced factors, may greatly influence treatment outcome, but is difficult to account for using traditional treatment planning approaches. Systems oncology simulation, using mathematical models designed to predict tumour growth and treatment response, provides a powerful tool for analysis and optimization of combined treatments. We present a framework that simulates such combination treatments on a cellular level. This multiscale hybrid cellular automaton simulates large cell populations (up to 107 cells) in vitro, while allowing individual cell-cycle progression, and treatment response by modelling radiation-induced mitotic cell death, and immediate cell kill in response to heating. Based on a calibration using a number of experimental growth, cell cycle and survival datasets for HCT116 cells, model predictions agreed well (R2 > 0.95) with experimental data within the range of (thermal and radiation) doses tested (0–40 CEM43, 0–5 Gy). The proposed framework offers flexibility for modelling multimodality treatment combinations in different scenarios. It may therefore provide an important step towards the modelling of personalized therapies using a virtual patient tumour.
Funding: Cancer Research UK. Research at The Institute of Cancer Research is supported by Cancer Research UK under Programme C33589/A19727. Peter Ziegenhein is supported by Cancer Research UK under Programme C33589/A19908.
2018-01-01T00:00:00ZBrüningk, SarahPowathil, GibinZiegenhein, PeterIjaz, JannatRivens, IanNill, S.Chaplain, Mark Andrew JosephOelfke, Uweter Haar, GailCombined radiotherapy and hyperthermia offer great potential for the successful treatment of radio-resistant tumours through thermo-radiosensitization. Tumour response heterogeneity, due to intrinsic, or micro-environmentally induced factors, may greatly influence treatment outcome, but is difficult to account for using traditional treatment planning approaches. Systems oncology simulation, using mathematical models designed to predict tumour growth and treatment response, provides a powerful tool for analysis and optimization of combined treatments. We present a framework that simulates such combination treatments on a cellular level. This multiscale hybrid cellular automaton simulates large cell populations (up to 107 cells) in vitro, while allowing individual cell-cycle progression, and treatment response by modelling radiation-induced mitotic cell death, and immediate cell kill in response to heating. Based on a calibration using a number of experimental growth, cell cycle and survival datasets for HCT116 cells, model predictions agreed well (R2 > 0.95) with experimental data within the range of (thermal and radiation) doses tested (0–40 CEM43, 0–5 Gy). The proposed framework offers flexibility for modelling multimodality treatment combinations in different scenarios. It may therefore provide an important step towards the modelling of personalized therapies using a virtual patient tumour.Quiescent prominences in the era of ALMA. II. Kinetic temperature diagnosticsGunár, StanislavHeinzel, PetrAnzer, UlrichMackay, Duncan Hendryhttp://hdl.handle.net/10023/125572018-04-11T15:30:06Z2018-01-20T00:00:00ZWe provide the theoretical background for diagnostics of the thermal properties of solar prominences observed by the Atacama Large Millimeter/submillimeter Array (ALMA). To do this, we employ the 3D Whole-Prominence Fine Structure (WPFS) model that produces synthetic ALMA-like observations of a complex simulated prominence. We use synthetic observations derived at two different submillimeter/millimeter (SMM) wavelengths—one at a wavelength at which the simulated prominence is completely optically thin and another at a wavelength at which a significant portion of the simulated prominence is optically thick—as if these were the actual ALMA observations. This allows us to develop a technique for an analysis of the prominence plasma thermal properties from such a pair of simultaneous high-resolution ALMA observations. The 3D WPFS model also provides detailed information about the distribution of the kinetic temperature and the optical thickness along any line of sight. We can thus assess whether the measure of the kinetic temperature derived from observations accurately represents the actual kinetic temperature properties of the observed plasma. We demonstrate here that in a given pixel the optical thickness at the wavelength at which the prominence plasma is optically thick needs to be above unity or even larger to achieve a sufficient accuracy of the derived information about the kinetic temperature of the analyzed plasma. Information about the optical thickness cannot be directly discerned from observations at the SMM wavelengths alone. However, we show that a criterion that can identify those pixels in which the derived kinetic temperature values correspond well to the actual thermal properties in which the observed prominence can be established.
Funding: UK STFC, the Leverhulme Trust, and NASA (D.H.M.)
2018-01-20T00:00:00ZGunár, StanislavHeinzel, PetrAnzer, UlrichMackay, Duncan HendryWe provide the theoretical background for diagnostics of the thermal properties of solar prominences observed by the Atacama Large Millimeter/submillimeter Array (ALMA). To do this, we employ the 3D Whole-Prominence Fine Structure (WPFS) model that produces synthetic ALMA-like observations of a complex simulated prominence. We use synthetic observations derived at two different submillimeter/millimeter (SMM) wavelengths—one at a wavelength at which the simulated prominence is completely optically thin and another at a wavelength at which a significant portion of the simulated prominence is optically thick—as if these were the actual ALMA observations. This allows us to develop a technique for an analysis of the prominence plasma thermal properties from such a pair of simultaneous high-resolution ALMA observations. The 3D WPFS model also provides detailed information about the distribution of the kinetic temperature and the optical thickness along any line of sight. We can thus assess whether the measure of the kinetic temperature derived from observations accurately represents the actual kinetic temperature properties of the observed plasma. We demonstrate here that in a given pixel the optical thickness at the wavelength at which the prominence plasma is optically thick needs to be above unity or even larger to achieve a sufficient accuracy of the derived information about the kinetic temperature of the analyzed plasma. Information about the optical thickness cannot be directly discerned from observations at the SMM wavelengths alone. However, we show that a criterion that can identify those pixels in which the derived kinetic temperature values correspond well to the actual thermal properties in which the observed prominence can be established.Mediterranean mesocarnivores in spatially structured managed landscapes : community organisation in time and spaceCurveira-Santos, GonçaloMarques, Tiago A.Björklund, MatsSantos-Reis, Margaridahttp://hdl.handle.net/10023/124472018-01-11T00:15:44Z2017-01-16T00:00:00ZIn the multi-functional and biodiverse cork oak landscapes of Iberia (Montado), agro-silvo-pastoral practices promote landscape heterogeneity and create intricate habitat and resource availability patterns. We used camera-traps to investigate the temporal and spatial organisation of a mesocarnivore community in a Montado landscape in central Portugal. The target carnivore assemblage was largely dominated by three generalist species – the red fox Vulpes vulpes, the European badger Meles meles and the Egyptian mongoose Herpestes ichneumon – while remaining community members – the common genet Genetta genetta and the feral cat Felis silvestris spp. – exhibited restricted distributions. Interspecific differences in activity rhythms and habitat use were particularly marked among widespread species. Low temporal overlap was reported between the diurnal mongoose and predominantly nocturnal red fox and badger. For the latter two species, contrasting differences in habitat use were associated with anthropogenic-induced environmental heterogeneity. Whereas the red fox used more intensively Montado areas preserving dense shrubby understory and avoided semi-disturbed mosaics of sparse shrubs, the badgers displayed the opposite pattern. Our findings add to previous evidence suggesting that the spatial structure created in highly managed landscapes, particularly the diversity of resulting understory structures, promotes the abundance and spread of generalist mesocarnivore species. These may benefit from the surplus of resource amount (e.g. prey) and the creation of different human-made habitats conditions that provide particular combinations of ecological resources favourable to each species requirements. We concur the common view that maintaining understory heterogeneity in Montado landscapes, menaced by current intensification and extensification trends, is important where carnivore persistence is a relevant conservation goal, but alert for potential effects on carnivore assemblages structuring and impacts for specialist species less tolerant to disturbance.
During the final stage of the study GCS was funded by a doctoral grant from FCT (PD/BD/114037/2015). TAM thanks support by CEAUL (funded by FCT project – UID/MAT/00006/2013).
2017-01-16T00:00:00ZCurveira-Santos, GonçaloMarques, Tiago A.Björklund, MatsSantos-Reis, MargaridaIn the multi-functional and biodiverse cork oak landscapes of Iberia (Montado), agro-silvo-pastoral practices promote landscape heterogeneity and create intricate habitat and resource availability patterns. We used camera-traps to investigate the temporal and spatial organisation of a mesocarnivore community in a Montado landscape in central Portugal. The target carnivore assemblage was largely dominated by three generalist species – the red fox Vulpes vulpes, the European badger Meles meles and the Egyptian mongoose Herpestes ichneumon – while remaining community members – the common genet Genetta genetta and the feral cat Felis silvestris spp. – exhibited restricted distributions. Interspecific differences in activity rhythms and habitat use were particularly marked among widespread species. Low temporal overlap was reported between the diurnal mongoose and predominantly nocturnal red fox and badger. For the latter two species, contrasting differences in habitat use were associated with anthropogenic-induced environmental heterogeneity. Whereas the red fox used more intensively Montado areas preserving dense shrubby understory and avoided semi-disturbed mosaics of sparse shrubs, the badgers displayed the opposite pattern. Our findings add to previous evidence suggesting that the spatial structure created in highly managed landscapes, particularly the diversity of resulting understory structures, promotes the abundance and spread of generalist mesocarnivore species. These may benefit from the surplus of resource amount (e.g. prey) and the creation of different human-made habitats conditions that provide particular combinations of ecological resources favourable to each species requirements. We concur the common view that maintaining understory heterogeneity in Montado landscapes, menaced by current intensification and extensification trends, is important where carnivore persistence is a relevant conservation goal, but alert for potential effects on carnivore assemblages structuring and impacts for specialist species less tolerant to disturbance.The number and distribution of polar bears in the western Barents SeaAars, JonMarques, Tiago A.Lone, KarenAndersen, MagnusWiig, ØysteinFløystad, Ida Marie BardalenHagen, Snorre B.Buckland, Stephen T.http://hdl.handle.net/10023/124402018-06-03T00:39:31Z2017-10-09T00:00:00ZPolar bears have experienced a rapid loss of sea-ice habitat in the Barents Sea. Monitoring this subpopulation focuses on the effects on polar bear demography. In August 2015, we conducted a survey in the Norwegian Arctic to estimate polar bear numbers and reveal population substructure. DNA profiles from biopsy samples and ear tags identified on photographs revealed that about half of the bears in Svalbard, compared to only 4.5% in the pack ice north of the archipelago, were recognized recaptures. The recaptured bears had originally been marked in Svalbard, mostly in spring. The existence of a local Svalbard stock, and another ecotype of bears using the pack ice in autumn with low likelihood of visiting Svalbard, support separate population size estimation for the two areas. Mainly by aerial survey line transect distance sampling methods, we estimated that 264 (95% CI = 199 - 363) bears were in Svalbard, close to 241 bears estimated for August 2004. The pack ice area had an estimated 709 bears (95% CI = 334 - 1026). The pack ice and the total (Svalbard + pack ice, 973 bears, 95% CI = 334 - 1026) both had higher estimates compared to August 2004 (444 and 685 bears, respectively), but the increase was not significant. There is no evidence that the fast reduction of sea-ice habitat in the area has yet led to a reduction in population size. The carrying capacity is likely reduced significantly, but recovery from earlier depletion up to 1973 may still be ongoing.
This study was funded by the Norwegian Ministry of Climate and the Environment. TAM is grateful for partial support by Centro de Estatística e Aplicações da Universidade de Lisboa, funded by the Fundação para a Ciência e a Tecnologia, Portugal, through the project UID/MAT/00006/2013.
2017-10-09T00:00:00ZAars, JonMarques, Tiago A.Lone, KarenAndersen, MagnusWiig, ØysteinFløystad, Ida Marie BardalenHagen, Snorre B.Buckland, Stephen T.Polar bears have experienced a rapid loss of sea-ice habitat in the Barents Sea. Monitoring this subpopulation focuses on the effects on polar bear demography. In August 2015, we conducted a survey in the Norwegian Arctic to estimate polar bear numbers and reveal population substructure. DNA profiles from biopsy samples and ear tags identified on photographs revealed that about half of the bears in Svalbard, compared to only 4.5% in the pack ice north of the archipelago, were recognized recaptures. The recaptured bears had originally been marked in Svalbard, mostly in spring. The existence of a local Svalbard stock, and another ecotype of bears using the pack ice in autumn with low likelihood of visiting Svalbard, support separate population size estimation for the two areas. Mainly by aerial survey line transect distance sampling methods, we estimated that 264 (95% CI = 199 - 363) bears were in Svalbard, close to 241 bears estimated for August 2004. The pack ice area had an estimated 709 bears (95% CI = 334 - 1026). The pack ice and the total (Svalbard + pack ice, 973 bears, 95% CI = 334 - 1026) both had higher estimates compared to August 2004 (444 and 685 bears, respectively), but the increase was not significant. There is no evidence that the fast reduction of sea-ice habitat in the area has yet led to a reduction in population size. The carrying capacity is likely reduced significantly, but recovery from earlier depletion up to 1973 may still be ongoing.Comparison of methods for modelling coronal magnetic fieldsGoldstraw, E. E.Hood, Alan W.Browning, P. K.Cargill, P. (Peter)http://hdl.handle.net/10023/124382018-06-13T15:38:59Z2018-02-26T00:00:00ZAims. Four different approximate approaches used to model the stressing of coronal magnetic fields due to an imposed photospheric motion are compared with each other and the results from a full time-dependent magnetohydrodynamic (MHD) code. The assumptions used for each of the approximate methods are tested by considering large photospheric footpoint displacements. Methods. We consider a simple model problem, comparing the full nonlinear magnetohydrodynamic evolution, determined with the Lare2D numerical code, with four approximate approaches. Two of these,magneto-frictional relaxation and a quasi-1D Grad-Shafranov approach, assume sequences of equilibria, whilst the other two methods, a second-order linearisation of the MHD equations and Reduced MHD, are time-dependent. Results. The relaxation method is very accurate compared to full MHD for force-free equilibria for all footpoint displacements but has significant errors when the plasma β0 is of order unity. The 1D approach gives an extremely accurate description of the equilibria away from the photospheric boundary layers, and agrees well with Lare2D for all parameter values tested. The linearised MHD equations correctly predict the existence of photospheric boundary layers that are present in the full MHD results. As soon as the footpoint displacement becomes a significant fraction of the loop length, the RMHD method fails to model the sequences of equilibria correctly. The full numerical solution is interesting in its own right, and care must be taken for low β0 plasmas if the viscosity is too high.
Funding: STFC through the Consolidated grant ST/N000609/1 (AWH); STFC studentship, ST/I505999/1 (EEG).
2018-02-26T00:00:00ZGoldstraw, E. E.Hood, Alan W.Browning, P. K.Cargill, P. (Peter)Aims. Four different approximate approaches used to model the stressing of coronal magnetic fields due to an imposed photospheric motion are compared with each other and the results from a full time-dependent magnetohydrodynamic (MHD) code. The assumptions used for each of the approximate methods are tested by considering large photospheric footpoint displacements. Methods. We consider a simple model problem, comparing the full nonlinear magnetohydrodynamic evolution, determined with the Lare2D numerical code, with four approximate approaches. Two of these,magneto-frictional relaxation and a quasi-1D Grad-Shafranov approach, assume sequences of equilibria, whilst the other two methods, a second-order linearisation of the MHD equations and Reduced MHD, are time-dependent. Results. The relaxation method is very accurate compared to full MHD for force-free equilibria for all footpoint displacements but has significant errors when the plasma β0 is of order unity. The 1D approach gives an extremely accurate description of the equilibria away from the photospheric boundary layers, and agrees well with Lare2D for all parameter values tested. The linearised MHD equations correctly predict the existence of photospheric boundary layers that are present in the full MHD results. As soon as the footpoint displacement becomes a significant fraction of the loop length, the RMHD method fails to model the sequences of equilibria correctly. The full numerical solution is interesting in its own right, and care must be taken for low β0 plasmas if the viscosity is too high.Point process models for spatio-temporal distance sampling data from a large-scale survey of blue whalesYuan, Y.Bachl, F. E.Lindgren, F.Borchers, David LouisIllian, J. B.Buckland, S. T.Rue, H.Gerrodette, T.http://hdl.handle.net/10023/124272018-04-01T01:30:31Z2017-12-01T00:00:00ZDistance sampling is a widely used method for estimating wildlife population abundance. The fact that conventional distance sampling methods are partly design-based constrains the spatial resolution at which animal density can be estimated using these methods. Estimates are usually obtained at survey stratum level. For an endangered species such as the blue whale, it is desirable to estimate density and abundance at a finer spatial scale than stratum. Temporal variation in the spatial structure is also important. We formulate the process generating distance sampling data as a thinned spatial point process and propose model-based inference using a spatial log-Gaussian Cox process. The method adopts a flexible stochastic partial differential equation (SPDE) approach to model spatial structure in density that is not accounted for by explanatory variables, and integrated nested Laplace approximation (INLA) for Bayesian inference. It allows simultaneous fitting of detection and density models and permits prediction of density at an arbitrarily fine scale. We estimate blue whale density in the Eastern Tropical Pacific Ocean from thirteen shipboard surveys conducted over 22 years. We find that higher blue whale density is associated with colder sea surface temperatures in space, and although there is some positive association between density and mean annual temperature, our estimates are consitent with no trend in density across years. Our analysis also indicates that there is substantial spatially structured variation in density that is not explained by available covariates.
2017-12-01T00:00:00ZYuan, Y.Bachl, F. E.Lindgren, F.Borchers, David LouisIllian, J. B.Buckland, S. T.Rue, H.Gerrodette, T.Distance sampling is a widely used method for estimating wildlife population abundance. The fact that conventional distance sampling methods are partly design-based constrains the spatial resolution at which animal density can be estimated using these methods. Estimates are usually obtained at survey stratum level. For an endangered species such as the blue whale, it is desirable to estimate density and abundance at a finer spatial scale than stratum. Temporal variation in the spatial structure is also important. We formulate the process generating distance sampling data as a thinned spatial point process and propose model-based inference using a spatial log-Gaussian Cox process. The method adopts a flexible stochastic partial differential equation (SPDE) approach to model spatial structure in density that is not accounted for by explanatory variables, and integrated nested Laplace approximation (INLA) for Bayesian inference. It allows simultaneous fitting of detection and density models and permits prediction of density at an arbitrarily fine scale. We estimate blue whale density in the Eastern Tropical Pacific Ocean from thirteen shipboard surveys conducted over 22 years. We find that higher blue whale density is associated with colder sea surface temperatures in space, and although there is some positive association between density and mean annual temperature, our estimates are consitent with no trend in density across years. Our analysis also indicates that there is substantial spatially structured variation in density that is not explained by available covariates.Piecewise uniform potential vorticity pancake shielded vorticesReinaud, Jean Noelhttp://hdl.handle.net/10023/124192018-05-06T00:37:04Z2017-01-01T00:00:00ZShielded vortices consist of a core of potential vorticity of a given sign surrounded (or shielded) by a layer of opposite-signed potential vorticity. Such vortices have specific properties and have been the focus of numerous studies, first in two dimensional geometries (where potential vorticity is just the vertical component of the vorticity vector) and in geophysical applications (mostly in layered models). The present paper focuses on three-dimensional, spheroidal shielded vortices. In particular, we focus on vortical structures whose overall volume-integrated potential vorticity is zero. We restrict attention to vortices of piecewise uniform potential vorticity in the present research. We first revisit the problem within the quasi-geostrophic model, then we extend the results to the non-hydrostatic regime. We show that the stability of the structure depends on the ratio of potential vorticity between the inner core and the outer shield. In particular it depends on the polarity of the core and of the wavenumber of the azimuthal mode perturbed.
2017-01-01T00:00:00ZReinaud, Jean NoelShielded vortices consist of a core of potential vorticity of a given sign surrounded (or shielded) by a layer of opposite-signed potential vorticity. Such vortices have specific properties and have been the focus of numerous studies, first in two dimensional geometries (where potential vorticity is just the vertical component of the vorticity vector) and in geophysical applications (mostly in layered models). The present paper focuses on three-dimensional, spheroidal shielded vortices. In particular, we focus on vortical structures whose overall volume-integrated potential vorticity is zero. We restrict attention to vortices of piecewise uniform potential vorticity in the present research. We first revisit the problem within the quasi-geostrophic model, then we extend the results to the non-hydrostatic regime. We show that the stability of the structure depends on the ratio of potential vorticity between the inner core and the outer shield. In particular it depends on the polarity of the core and of the wavenumber of the azimuthal mode perturbed.Individual, ecological, and anthropogenic inﬂuences on activity budgets of long-ﬁnned pilot whalesIsojunno, S.Sadykova, D.DeRuiter, S.Curé, C.Visser, F.Thomas, L.Miller, P. J. O.Harris, C. M.http://hdl.handle.net/10023/124082018-01-14T01:37:51Z2017-12-01T00:00:00ZTime allocation to different activities and habitats enables individuals to modulate their perceived risks and access to resources, and can reveal important trade-offs between fitness-enhancing activities (e.g., feeding vs. social behavior). Species with long reproductive cycles and high parental investment, such as marine mammals, rely on such behavioral plasticity to cope with rapid environmental change, including anthropogenic stressors. We quantified activity budgets of free-ranging long-finned pilot whales in order to assess individual time trade-offs between foraging and other behaviors in different individual and ecological contexts, and during experimental sound exposures. The experiments included 1-2 and 6-7 kHz naval sonar exposures (a potential anthropogenic stressor), playback of killer whale (a potential predator/competitor) vocalizations, and negative controls. We combined multiple time series data from digital acoustic recording tags (DTAG) as well as group-level social behavior data from visual observations of tagged whales at the surface. The data were classified into near-surface behaviors and dive types (using a hidden Markov model for dive transitions) and aggregated into time budgets. On average, individuals (N=19) spent most of their time (69%) resting and transiting near surface, 21% in shallow dives (depth <40m), and only 10% of their time in deep foraging dives, of which 65% reached a depth 10m from the sea bottom. Individuals in the largest of three body size classes or accompanied by calves tended to spend more time foraging than others. Simultaneous tagging of pairs of individuals showed that up to 50% of the activity budget was synchronized between conspecifics with decreased synchrony during foraging periods. Individuals spent less time foraging when forming larger non-vocal aggregations of individuals in late afternoons, and more time foraging when in the mid-range of water depths (300-400m) available in the study area (50-700m). Individuals reduced foraging time by 83% (29-96%) during their first exposure to sonar, but not during killer whale sound playbacks. A relative increase in foraging during repeat sonar exposures indicated habituation or change in response tactic. We discuss the possible adaptive value of these trade-offs in time allocation to reduce individual conflict while maintaining benefits of group living.
The authors would like to thank sponsors, NL Ministry of Defence, NOR Ministry of Defence, U.S. Office of Naval Research (N00014-08-1-0984, N00014-10-1-0355, N00014-14-1-0390), FR Ministry of Defence (DGA; public market no. 15860052), World Wildlife Fund Norway (9E0682), and French Total Foundation and Bleustein-Blanchet Foundation. The statistical development work was supported by a separate grant from the U.S. Office of Naval Research (N00014-12-1-0204), under the project entitled Multi-study OCean acoustics Human effects Analysis (MOCHA).
2017-12-01T00:00:00ZIsojunno, S.Sadykova, D.DeRuiter, S.Curé, C.Visser, F.Thomas, L.Miller, P. J. O.Harris, C. M.Time allocation to different activities and habitats enables individuals to modulate their perceived risks and access to resources, and can reveal important trade-offs between fitness-enhancing activities (e.g., feeding vs. social behavior). Species with long reproductive cycles and high parental investment, such as marine mammals, rely on such behavioral plasticity to cope with rapid environmental change, including anthropogenic stressors. We quantified activity budgets of free-ranging long-finned pilot whales in order to assess individual time trade-offs between foraging and other behaviors in different individual and ecological contexts, and during experimental sound exposures. The experiments included 1-2 and 6-7 kHz naval sonar exposures (a potential anthropogenic stressor), playback of killer whale (a potential predator/competitor) vocalizations, and negative controls. We combined multiple time series data from digital acoustic recording tags (DTAG) as well as group-level social behavior data from visual observations of tagged whales at the surface. The data were classified into near-surface behaviors and dive types (using a hidden Markov model for dive transitions) and aggregated into time budgets. On average, individuals (N=19) spent most of their time (69%) resting and transiting near surface, 21% in shallow dives (depth <40m), and only 10% of their time in deep foraging dives, of which 65% reached a depth 10m from the sea bottom. Individuals in the largest of three body size classes or accompanied by calves tended to spend more time foraging than others. Simultaneous tagging of pairs of individuals showed that up to 50% of the activity budget was synchronized between conspecifics with decreased synchrony during foraging periods. Individuals spent less time foraging when forming larger non-vocal aggregations of individuals in late afternoons, and more time foraging when in the mid-range of water depths (300-400m) available in the study area (50-700m). Individuals reduced foraging time by 83% (29-96%) during their first exposure to sonar, but not during killer whale sound playbacks. A relative increase in foraging during repeat sonar exposures indicated habituation or change in response tactic. We discuss the possible adaptive value of these trade-offs in time allocation to reduce individual conflict while maintaining benefits of group living.Relations among partitionsBailey, Rosemary Annehttp://hdl.handle.net/10023/124072018-04-14T23:34:28Z2017-01-01T00:00:00ZCombinatorialists often consider a balanced incomplete-block design to consist of a set of points, a set of blocks, and an incidence relation between them which satisfies certain conditions. To a statistician, such a design is a set of experimental units with two partitions, one into blocks and the other into treatments: it is the relation between these two partitions which gives the design its properties. The most common binary relations between partitions that occur in statistics are refinement, orthogonality and balance. When there are more than two partitions, the binary relations may not suffice to give all the properties of the system. I shall survey work in this area, including designs such as double Youden rectangles.
2017-01-01T00:00:00ZBailey, Rosemary AnneCombinatorialists often consider a balanced incomplete-block design to consist of a set of points, a set of blocks, and an incidence relation between them which satisfies certain conditions. To a statistician, such a design is a set of experimental units with two partitions, one into blocks and the other into treatments: it is the relation between these two partitions which gives the design its properties. The most common binary relations between partitions that occur in statistics are refinement, orthogonality and balance. When there are more than two partitions, the binary relations may not suffice to give all the properties of the system. I shall survey work in this area, including designs such as double Youden rectangles.JPEG2000 image compression on solar EUV imagesFischer, CatherineMueller, DanielDe Moortel, Inekehttp://hdl.handle.net/10023/123672018-01-07T03:53:09Z2017-01-01T00:00:00ZFor future solar missions as well as ground-based telescopes, efficient ways to return and process data has become increasingly important. Solar Or-biter, e.g., the next ESA/NASA mission to explore the Sun and the heliosphere,is a deep-space mission, which implies a limited telemetry rate that makes efficient onboard data compression a necessity to achieve the mission science goals.Missions like the Solar Dynamics Observatory (SDO) and future ground-based telescopes such as the Daniel K. Inouye Solar Telescope, on the other hand,face the challenge of making petabyte-sized solar data archives accessible to the solar community. New image compression standards address these challenges by implementing efficient and flexible compression algorithms that can be tailored to user requirements. We analyse solar images from the Atmospheric Imaging Assembly (AIA) instrument onboard SDO to study the effect of lossy JPEG2000(from the Joint Photographic Experts Group 2000) image compression at different bit rates. To assess the quality of compressed images, we use the mean structural similarity (MSSIM) index as well as the widely used peak signal-to noise ratio (PSNR) as metrics and compare the two in the context of solar EUV images. In addition, we perform tests to validate the scientific use of the lossily compressed images by analysing examples of an on-disk and off-limb coronal loop oscillation time series observed by AIA/SDO.
2017-01-01T00:00:00ZFischer, CatherineMueller, DanielDe Moortel, InekeFor future solar missions as well as ground-based telescopes, efficient ways to return and process data has become increasingly important. Solar Or-biter, e.g., the next ESA/NASA mission to explore the Sun and the heliosphere,is a deep-space mission, which implies a limited telemetry rate that makes efficient onboard data compression a necessity to achieve the mission science goals.Missions like the Solar Dynamics Observatory (SDO) and future ground-based telescopes such as the Daniel K. Inouye Solar Telescope, on the other hand,face the challenge of making petabyte-sized solar data archives accessible to the solar community. New image compression standards address these challenges by implementing efficient and flexible compression algorithms that can be tailored to user requirements. We analyse solar images from the Atmospheric Imaging Assembly (AIA) instrument onboard SDO to study the effect of lossy JPEG2000(from the Joint Photographic Experts Group 2000) image compression at different bit rates. To assess the quality of compressed images, we use the mean structural similarity (MSSIM) index as well as the widely used peak signal-to noise ratio (PSNR) as metrics and compare the two in the context of solar EUV images. In addition, we perform tests to validate the scientific use of the lossily compressed images by analysing examples of an on-disk and off-limb coronal loop oscillation time series observed by AIA/SDO.Energy release in driven twisted coronal loopsBareford, Michael RGordovskyy, MykolaBrowning, PhilippaHood, Alan W.http://hdl.handle.net/10023/123052018-06-13T15:44:43Z2016-01-01T00:00:00ZMagnetic reconnection in twisted magnetic flux tubes, representing coronal loops, is investigated. The main goal is to establish the influence of the field geometry and various thermodynamic effects on the stability of twisted flux tubes and on the size and distribution of heated regions. In particular, we aim to investigate to what extent the earlier idealised models, based on the initially cylindrically symmetric flux tubes, are different from more realistic models, including the large-scale curvature, atmospheric stratification, thermal conduction and other effects. In addition, we compare the roles of Ohmic heating and shock heating in energy conversion during magnetic reconnection in twisted loops. The models with straight flux tubes show similar distribution of heated plasma during the reconnection: it initially forms a helical shape, which subsequently becomes very fragmented. The heating in these models is rather uniformly distributed along flux tubes. At the same time, the hot plasma regions in curved loops are asymmetric, and concentrate close to the loop tops. Large-scale curvature has a destabilising in influence: lower twist is needed for instability. Footpoint convergence normally delays instability slightly, although, in some cases converging flux tubes can be less stable. Finally, introducing a stratified atmosphere gives rise to decaying wave propagation, which has destabilising effect.
This work is funded by Science and Technology Facilities Council (UK). This equipment was funded by a BIS National E-Infrastructure capital grant ST/K00042X/1, DiRAC Operations grant ST/K003267/1 and Durham University.
2016-01-01T00:00:00ZBareford, Michael RGordovskyy, MykolaBrowning, PhilippaHood, Alan W.Magnetic reconnection in twisted magnetic flux tubes, representing coronal loops, is investigated. The main goal is to establish the influence of the field geometry and various thermodynamic effects on the stability of twisted flux tubes and on the size and distribution of heated regions. In particular, we aim to investigate to what extent the earlier idealised models, based on the initially cylindrically symmetric flux tubes, are different from more realistic models, including the large-scale curvature, atmospheric stratification, thermal conduction and other effects. In addition, we compare the roles of Ohmic heating and shock heating in energy conversion during magnetic reconnection in twisted loops. The models with straight flux tubes show similar distribution of heated plasma during the reconnection: it initially forms a helical shape, which subsequently becomes very fragmented. The heating in these models is rather uniformly distributed along flux tubes. At the same time, the hot plasma regions in curved loops are asymmetric, and concentrate close to the loop tops. Large-scale curvature has a destabilising in influence: lower twist is needed for instability. Footpoint convergence normally delays instability slightly, although, in some cases converging flux tubes can be less stable. Finally, introducing a stratified atmosphere gives rise to decaying wave propagation, which has destabilising effect.Relaxation methods in compressible flowMitchell, A. R. (Andrew R.)http://hdl.handle.net/10023/122982018-06-05T11:52:50Z1949-01-01T00:00:00Z1949-01-01T00:00:00ZMitchell, A. R. (Andrew R.)The infinite simple group V of Richard J. Thompson : presentations by permutationsBleak, CollinQuick, Martynhttp://hdl.handle.net/10023/122962018-04-01T00:41:44Z2017-01-01T00:00:00ZWe show that one can naturally describe elements of R. Thompson's finitely presented infinite simple group V, known by Thompson to have a presentation with four generators and fourteen relations, as products of permutations analogous to transpositions. This perspective provides an intuitive explanation towards the simplicity of V and also perhaps indicates a reason as to why it was one of the first discovered infinite finitely presented simple groups: it is (in some basic sense) a relative of the finite alternating groups. We find a natural infinite presentation for V as a group generated by these "transpositions," which presentation bears comparison with Dehornoy's infinite presentation and which enables us to develop two small presentations for V: a human-interpretable presentation with three generators and eight relations, and a Tietze-derived presentation with two generators and seven relations.
2017-01-01T00:00:00ZBleak, CollinQuick, MartynWe show that one can naturally describe elements of R. Thompson's finitely presented infinite simple group V, known by Thompson to have a presentation with four generators and fourteen relations, as products of permutations analogous to transpositions. This perspective provides an intuitive explanation towards the simplicity of V and also perhaps indicates a reason as to why it was one of the first discovered infinite finitely presented simple groups: it is (in some basic sense) a relative of the finite alternating groups. We find a natural infinite presentation for V as a group generated by these "transpositions," which presentation bears comparison with Dehornoy's infinite presentation and which enables us to develop two small presentations for V: a human-interpretable presentation with three generators and eight relations, and a Tietze-derived presentation with two generators and seven relations.Study on the tumor-induced angiogenesis using mathematical modelsSuzuki, TakashiMinerva, DhisaNishiyama, KoichiKoshikawa, NaohikoChaplain, Mark Andrew Josephhttp://hdl.handle.net/10023/122562018-01-23T15:30:07Z2018-01-01T00:00:00ZWe studied angiogenesis using mathematical models describing the dynamics of tip cells. We reviewed the basic ideas of angiogenesis models and its numerical simulation technique to produce realistic computer graphics images of sprouting angiogenesis. We examined the classical model of Anderson-Chaplain using fundamental concepts of mass transport and chemical reaction with ECM degradation included. We then constructed two types of numerical schemes, model-faithful and model-driven ones, where new techniques of numerical simulation are introduced, such as transient probability, particle velocity, and Boolean variables.
This work was supported by JSPS KAKENHI 16H06576 and JSPS Core-to-Core Project International Research Network.
2018-01-01T00:00:00ZSuzuki, TakashiMinerva, DhisaNishiyama, KoichiKoshikawa, NaohikoChaplain, Mark Andrew JosephWe studied angiogenesis using mathematical models describing the dynamics of tip cells. We reviewed the basic ideas of angiogenesis models and its numerical simulation technique to produce realistic computer graphics images of sprouting angiogenesis. We examined the classical model of Anderson-Chaplain using fundamental concepts of mass transport and chemical reaction with ECM degradation included. We then constructed two types of numerical schemes, model-faithful and model-driven ones, where new techniques of numerical simulation are introduced, such as transient probability, particle velocity, and Boolean variables.Special subgroups of regular semigroupsBlyth, T. S. (Thomas Scott)Almeida Santos, M. H.http://hdl.handle.net/10023/122312018-06-05T10:26:30Z2017-10-03T00:00:00ZExtending the notions of inverse transversal and associate subgroup, we consider a regular semigroup S with the property that there exists a subsemigroup T which contains, for each x∈S, a unique y such that both xy and yx are idempotent. Such a subsemigroup is necessarily a group which we call a special subgroup. Here we investigate regular semigroups with this property. In particular, we determine when the subset of perfect elements is a subsemigroup and describe its structure in naturally arising situations.
This work was partially supported by the Portuguese Foundation for Science and Technology through the grant UID/MAT/00297/2013 (CMA).
2017-10-03T00:00:00ZBlyth, T. S. (Thomas Scott)Almeida Santos, M. H.Extending the notions of inverse transversal and associate subgroup, we consider a regular semigroup S with the property that there exists a subsemigroup T which contains, for each x∈S, a unique y such that both xy and yx are idempotent. Such a subsemigroup is necessarily a group which we call a special subgroup. Here we investigate regular semigroups with this property. In particular, we determine when the subset of perfect elements is a subsemigroup and describe its structure in naturally arising situations.Regularity of Navier--Stokes flows with bounds for the pressureTran, Chuong V.Yu, Xinweihttp://hdl.handle.net/10023/122302018-01-07T03:50:56Z2017-05-01T00:00:00ZThis study derives regularity criteria for solutions of the Navier–Stokes equations. Let Ω(t) := {x : |u(x, t)| > c ||u||Lr(R3) }, for some r ≥ 3 and constant c independent of t, with measure |Ω|. It is shown that if ||p + P||L3/2(Ω) becomes sufficiently small as |Ω| decreases, then||u||L(r+6)/3(R3) decays and regularity is secured. Here p is the physical pressure and P is a pressure moderator of relatively broad forms. The implications of the results are discussed and regularity criteria in terms of bounds for |p + P| within Ω are deduced.
This paper was presented at the Warwick EPSRC Symposium on PDEs in Fluid Mechanics, September 2016. Part of this research was carried out when CVT was visiting the University of Alberta, whose hospitality is gratefully acknowledged. XY was partially supported by NSERC Discovery grant RES0020476
2017-05-01T00:00:00ZTran, Chuong V.Yu, XinweiThis study derives regularity criteria for solutions of the Navier–Stokes equations. Let Ω(t) := {x : |u(x, t)| > c ||u||Lr(R3) }, for some r ≥ 3 and constant c independent of t, with measure |Ω|. It is shown that if ||p + P||L3/2(Ω) becomes sufficiently small as |Ω| decreases, then||u||L(r+6)/3(R3) decays and regularity is secured. Here p is the physical pressure and P is a pressure moderator of relatively broad forms. The implications of the results are discussed and regularity criteria in terms of bounds for |p + P| within Ω are deduced.Simulating the coronal evolution of AR 11437 using SDO/HMI magnetogramsYardley, Stephanie L.Mackay, Duncan HendryGreen, Lucie M.http://hdl.handle.net/10023/122262018-06-18T11:25:53Z2018-01-10T00:00:00ZThe coronal magnetic field evolution of AR 11437 is simulated by applying the magnetofrictional relaxation technique of Mackay et al. (2011). A sequence of photospheric line-of-sight magnetograms produced by SDO/HMI are used todrive the simulation and continuously evolve the coronal magnetic field of the active region through a series of nonlinear force-free equilibria. The simulation is started during the first stages of the active region emergence so that its full evolution from emergence to decay can be simulated. A comparison of the simulation results with SDO/AIA observations show that many aspects of the active region's observed coronal evolution are reproduced. In particular,it shows the presence of a flux rope, which forms at the same location as sheared coronal loops in the observations. The observations show that eruptions occur on 2012 March 17 at 05:09 UT and 10:45 UT and on 2012 March 20 at14:31 UT. The simulation reproduces the first and third eruption, with the simulated flux rope erupting roughly 1 and10 hours before the observed ejections, respectively. A parameter study is conducted where the boundary and initial conditions are varied along with the physical effects of Ohmic diffusion, hyperdiffusion and an additional injection of helicity. When comparing the simulations, the evolution of the magnetic field, free magnetic energy, relative helicity and flux rope eruption timings do not change significantly. This indicates that the key element in reproducing the coronal evolution of AR 11437 is the use of line-of-sight magnetograms to drive the evolution of the coronal magnetic field.
Funding: STFC via the Consolidated Grant SMC1/YST025 (SLY), STFC and the Levehulme Trust (DHM).
2018-01-10T00:00:00ZYardley, Stephanie L.Mackay, Duncan HendryGreen, Lucie M.The coronal magnetic field evolution of AR 11437 is simulated by applying the magnetofrictional relaxation technique of Mackay et al. (2011). A sequence of photospheric line-of-sight magnetograms produced by SDO/HMI are used todrive the simulation and continuously evolve the coronal magnetic field of the active region through a series of nonlinear force-free equilibria. The simulation is started during the first stages of the active region emergence so that its full evolution from emergence to decay can be simulated. A comparison of the simulation results with SDO/AIA observations show that many aspects of the active region's observed coronal evolution are reproduced. In particular,it shows the presence of a flux rope, which forms at the same location as sheared coronal loops in the observations. The observations show that eruptions occur on 2012 March 17 at 05:09 UT and 10:45 UT and on 2012 March 20 at14:31 UT. The simulation reproduces the first and third eruption, with the simulated flux rope erupting roughly 1 and10 hours before the observed ejections, respectively. A parameter study is conducted where the boundary and initial conditions are varied along with the physical effects of Ohmic diffusion, hyperdiffusion and an additional injection of helicity. When comparing the simulations, the evolution of the magnetic field, free magnetic energy, relative helicity and flux rope eruption timings do not change significantly. This indicates that the key element in reproducing the coronal evolution of AR 11437 is the use of line-of-sight magnetograms to drive the evolution of the coronal magnetic field.Lumped finite elements for reaction-cross-diffusion systems on stationary surfacesFrittelli, MassimoMadzvamuse, AnotidaSgura, IvonneVenkataraman, Chandrasekharhttp://hdl.handle.net/10023/121822018-01-07T04:04:17Z2017-12-15T00:00:00ZWe consider a lumped surface finite element method (LSFEM) for the spatial approximation of reaction-diffusion equations on closed compact surfaces in R3 in the presence of cross-diffusion. We provide a fully-discrete scheme by applying the implicit-explicit (IMEX) Euler method. We provide sufficient conditions for the existence of polytopal invariant regions for the numerical solution after spatial and full discretisations. Furthermore, we prove optimal error bounds for the semi- and fully-discrete methods, that is the convergence rates are quadratic in the meshsize and linear in the timestep. To support our theoretical findings, we provide two numerical tests. The first test confirms that in the absence of lumping numerical solutions violate the invariant region leading to blow-up due to the nature of the kinetics. The second experiment is an example of Turing pattern formation in the presence of cross-diffusion on the sphere.
All the authors (AM, IS, CV, MF) thank the Isaac Newton Institute for Mathematical Sciences for its hospitality during the programme (Coupling Geometric PDEs with Physics for Cell Morphology, Motility and Pattern Formation; EPSRC EP/K032208/1). This work (AM) has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 642866. AM and CV acknowledge support from the Engineering and Physical Sciences Research Council (EP/J016780/1) on Modelling, analysis and simulation of spatial patterning on evolving biological surfaces and the Leverhulme Trust Research Project Grant (RPG-2014-149) on Unravelling new mathematics for 3D cell migration. AM was partially supported by a fellowship from the Simons Foundation. AM is a Royal Society Wolfson Research Merit Award Holder, generously funded by the Wolfson Foundation.
2017-12-15T00:00:00ZFrittelli, MassimoMadzvamuse, AnotidaSgura, IvonneVenkataraman, ChandrasekharWe consider a lumped surface finite element method (LSFEM) for the spatial approximation of reaction-diffusion equations on closed compact surfaces in R3 in the presence of cross-diffusion. We provide a fully-discrete scheme by applying the implicit-explicit (IMEX) Euler method. We provide sufficient conditions for the existence of polytopal invariant regions for the numerical solution after spatial and full discretisations. Furthermore, we prove optimal error bounds for the semi- and fully-discrete methods, that is the convergence rates are quadratic in the meshsize and linear in the timestep. To support our theoretical findings, we provide two numerical tests. The first test confirms that in the absence of lumping numerical solutions violate the invariant region leading to blow-up due to the nature of the kinetics. The second experiment is an example of Turing pattern formation in the presence of cross-diffusion on the sphere.Return times at periodic points in random dynamicsHaydn, NicolaiTodd, Michael Johnhttp://hdl.handle.net/10023/121362018-01-07T02:55:26Z2017-01-01T00:00:00ZWe prove a quenched limiting law for random measures on subshifts at periodic points. We consider a family of measures {µω}ω∈Ω, where the ‘driving space’ Ω is equipped with a probability measure which is invariant under a transformation θ. We assume that the fibred measures µω satisfy a generalised invariance property and are ψ-mixing. We then show that for almost every ω the return times to cylinders An at periodic points are in the limit compound Poisson distributed for a parameter ϑ which is given by the escape rate at the periodic point.
2017-01-01T00:00:00ZHaydn, NicolaiTodd, Michael JohnWe prove a quenched limiting law for random measures on subshifts at periodic points. We consider a family of measures {µω}ω∈Ω, where the ‘driving space’ Ω is equipped with a probability measure which is invariant under a transformation θ. We assume that the fibred measures µω satisfy a generalised invariance property and are ψ-mixing. We then show that for almost every ω the return times to cylinders An at periodic points are in the limit compound Poisson distributed for a parameter ϑ which is given by the escape rate at the periodic point.Primary education in Vietnam and pupil online engagementNguyen, QuynhNaguib, RaoufDas, AshishPapathomas, MichailVallar, EdgarWickramasinghe, NilminiSantos, Gil NonatoGalvez, Maria CeciliaNguyen, Viethttp://hdl.handle.net/10023/121072018-01-21T01:35:46Z2018-01-08T00:00:00ZPurpose This paper focuses on exploring the disparities in social awareness and use of the Internet between urban and rural school children in the North of Vietnam. Approach A total of 525 pupils, aged 9 to 11 years old, randomly selected from 7 urban and rural schools, who are Internet users, participated in the study and consented to responding to a questionnaire adapted from an equivalent European Union (EU) study. A comparative statistical analysis of the responses was then carried out, using IBM SPSS v21, which consisted of a descriptive analysis, an identification of personal self-development opportunities, as well as issues related to pupils’ digital prowess and knowledge of Internet use, and Internet safety, including parental engagement in their offspring’s online activities. Findings The study highlights the fact that children from both the urban and rural regions of the North of Vietnam mostly access the Internet from home, but with more children in the urbanized areas accessing it at school than their rural counterparts. Although children from the rural areas scored lower on all the Internet indicators, such as digital access and online personal experience and awareness, there was no disparity in awareness of Internet risks between the two sub-samples. It is noteworthy that there was no statistically significant gender difference towards online activities that support self-development. In relation to safe Internet usage, children are likely to seek advice from their parents, rather than through teachers or friends. However, they are not yet provided with an effective safety net while exposing themselves to the digital world.
2018-01-08T00:00:00ZNguyen, QuynhNaguib, RaoufDas, AshishPapathomas, MichailVallar, EdgarWickramasinghe, NilminiSantos, Gil NonatoGalvez, Maria CeciliaNguyen, VietPurpose This paper focuses on exploring the disparities in social awareness and use of the Internet between urban and rural school children in the North of Vietnam. Approach A total of 525 pupils, aged 9 to 11 years old, randomly selected from 7 urban and rural schools, who are Internet users, participated in the study and consented to responding to a questionnaire adapted from an equivalent European Union (EU) study. A comparative statistical analysis of the responses was then carried out, using IBM SPSS v21, which consisted of a descriptive analysis, an identification of personal self-development opportunities, as well as issues related to pupils’ digital prowess and knowledge of Internet use, and Internet safety, including parental engagement in their offspring’s online activities. Findings The study highlights the fact that children from both the urban and rural regions of the North of Vietnam mostly access the Internet from home, but with more children in the urbanized areas accessing it at school than their rural counterparts. Although children from the rural areas scored lower on all the Internet indicators, such as digital access and online personal experience and awareness, there was no disparity in awareness of Internet risks between the two sub-samples. It is noteworthy that there was no statistically significant gender difference towards online activities that support self-development. In relation to safe Internet usage, children are likely to seek advice from their parents, rather than through teachers or friends. However, they are not yet provided with an effective safety net while exposing themselves to the digital world.Modelling the spatial dynamics of non-state terrorism : world study, 2002-2013Python, Andréhttp://hdl.handle.net/10023/120672017-12-07T16:07:43Z2017-12-07T00:00:00ZTo this day, terrorism perpetrated by non-state actors persists as a worldwide threat, as exemplified by the recent lethal attacks in Paris, London, Brussels, and the ongoing massacres perpetrated by the Islamic State in Iraq, Syria and neighbouring countries. In response, states deploy various counterterrorism policies, the costs of which could be reduced through more efficient preventive measures. The literature has not applied statistical models able to account for complex spatio-temporal dependencies, despite their potential for explaining and preventing non-state terrorism at the sub-national level. In an effort to address this shortcoming, this thesis employs Bayesian hierarchical models, where the spatial random field is represented by a stochastic partial differential equation. The results show that lethal terrorist attacks perpetrated by non-state actors tend to be concentrated in areas located within failed states from which they may diffuse locally, towards neighbouring areas. At the sub-national level, the propensity of attacks to be lethal and the frequency of lethal attacks appear to be driven by antagonistic mechanisms. Attacks are more likely to be lethal far away from large cities, at higher altitudes, in less economically developed areas, and in locations with higher ethnic diversity. In contrast, the frequency of lethal attacks tends to be higher in more economically developed areas, close to large cities, and within democratic countries.
2017-12-07T00:00:00ZPython, AndréTo this day, terrorism perpetrated by non-state actors persists as a worldwide threat, as exemplified by the recent lethal attacks in Paris, London, Brussels, and the ongoing massacres perpetrated by the Islamic State in Iraq, Syria and neighbouring countries. In response, states deploy various counterterrorism policies, the costs of which could be reduced through more efficient preventive measures. The literature has not applied statistical models able to account for complex spatio-temporal dependencies, despite their potential for explaining and preventing non-state terrorism at the sub-national level. In an effort to address this shortcoming, this thesis employs Bayesian hierarchical models, where the spatial random field is represented by a stochastic partial differential equation. The results show that lethal terrorist attacks perpetrated by non-state actors tend to be concentrated in areas located within failed states from which they may diffuse locally, towards neighbouring areas. At the sub-national level, the propensity of attacks to be lethal and the frequency of lethal attacks appear to be driven by antagonistic mechanisms. Attacks are more likely to be lethal far away from large cities, at higher altitudes, in less economically developed areas, and in locations with higher ethnic diversity. In contrast, the frequency of lethal attacks tends to be higher in more economically developed areas, close to large cities, and within democratic countries.Above the noise : the search for periodicities in the inner heliosphereThrelfall, James WilliamDe Moortel, InekeConlon, Thomas Michaelhttp://hdl.handle.net/10023/120542018-02-25T01:33:17Z2017-11-01T00:00:00ZRemote sensing of coronal and heliospheric periodicities can provide vital insight into the local conditions and dynamics of the solar atmosphere. We seek to trace long (one hour or longer) periodic oscillatory signatures (previously identified above the limb in the corona by, e.g., Telloni et al., 2013, Astrophys. J., 767, 138) from their origin at the solar surface out into the heliosphere. To do this, we combine on-disk measurements taken by the Atmospheric Imaging Assembly (AIA) onboard the Solar Dynamics Observatory (SDO) and concurrent extreme ultra-violet (EUV) and coronagraph data from one of the Solar Terrestrial Relations Observatory (STEREO) spacecraft to study the evolution of two active regions in the vicinity of an equatorial coronal hole over several days in early 2011. Fourier and wavelet analysis of signals are performed. Applying white-noise-based confidence levels to the power spectra associated with detrended intensity time series yields detections of oscillatory signatures with periods from 6 − 13 hours in both AIA and STEREO data. As was found by Telloni et al. (2013), these signatures are aligned with local magnetic structures. However, typical spectral power densities all vary substantially as a function of period, indicating spectra dominated by red (rather than white) noise. Contrary to the white-noise-based results, applying global confidence levels based on a generic background noise model (allowing a combination of white noise, red noise, and transients following Auch`ere et al., 2016, Astrophys. J., 825, 110) without detrending the time series, uncovers only sporadic, spatially uncorrelated evidence of periodic signatures in either instrument. Automating this method to individual pixels in the STEREO/COR coronagraph field of view is non-trivial.
2017-11-01T00:00:00ZThrelfall, James WilliamDe Moortel, InekeConlon, Thomas MichaelRemote sensing of coronal and heliospheric periodicities can provide vital insight into the local conditions and dynamics of the solar atmosphere. We seek to trace long (one hour or longer) periodic oscillatory signatures (previously identified above the limb in the corona by, e.g., Telloni et al., 2013, Astrophys. J., 767, 138) from their origin at the solar surface out into the heliosphere. To do this, we combine on-disk measurements taken by the Atmospheric Imaging Assembly (AIA) onboard the Solar Dynamics Observatory (SDO) and concurrent extreme ultra-violet (EUV) and coronagraph data from one of the Solar Terrestrial Relations Observatory (STEREO) spacecraft to study the evolution of two active regions in the vicinity of an equatorial coronal hole over several days in early 2011. Fourier and wavelet analysis of signals are performed. Applying white-noise-based confidence levels to the power spectra associated with detrended intensity time series yields detections of oscillatory signatures with periods from 6 − 13 hours in both AIA and STEREO data. As was found by Telloni et al. (2013), these signatures are aligned with local magnetic structures. However, typical spectral power densities all vary substantially as a function of period, indicating spectra dominated by red (rather than white) noise. Contrary to the white-noise-based results, applying global confidence levels based on a generic background noise model (allowing a combination of white noise, red noise, and transients following Auch`ere et al., 2016, Astrophys. J., 825, 110) without detrending the time series, uncovers only sporadic, spatially uncorrelated evidence of periodic signatures in either instrument. Automating this method to individual pixels in the STEREO/COR coronagraph field of view is non-trivial.Vortex scaling ranges in two-dimensional turbulenceBurgess, B. H.Dritschel, D. G.Scott, R. K.http://hdl.handle.net/10023/120292018-06-01T16:30:04Z2017-11-01T00:00:00ZWe survey the role of coherent vortices in two-dimensional turbulence, including formation mechanisms, implications for classical similarity and inertial range theories, and characteristics of the vortex populations. We review early work on the spatial and temporal scaling properties of vortices in freely evolving turbulence and more recent developments, including a spatiotemporal scaling theory for vortices in the forced inverse energy cascade. We emphasize that Kraichnan-Batchelor similarity theories and vortex scaling theories are best viewed as complementary and together provide a more complete description of two-dimensional turbulence. In particular, similarity theory has a continued role in describing the weak filamentary sea between the vortices. Moreover, we locate both classical inertial and vortex scaling ranges within the broader framework of scaling in far-from-equilibrium systems, which generically exhibit multiple fixed point solutions with distinct scaling behaviour. We describe how stationary transport in a range of scales comoving with the dilatation of flow features, as measured by the growth in vortex area, constrains the vortex number density in both freely evolving and forced two-dimensional turbulence. The new theories for coherent vortices reveal previously hidden nontrivial scaling, point to new dynamical understanding, and provide a novel exciting window into two-dimensional turbulence.
2017-11-01T00:00:00ZBurgess, B. H.Dritschel, D. G.Scott, R. K.We survey the role of coherent vortices in two-dimensional turbulence, including formation mechanisms, implications for classical similarity and inertial range theories, and characteristics of the vortex populations. We review early work on the spatial and temporal scaling properties of vortices in freely evolving turbulence and more recent developments, including a spatiotemporal scaling theory for vortices in the forced inverse energy cascade. We emphasize that Kraichnan-Batchelor similarity theories and vortex scaling theories are best viewed as complementary and together provide a more complete description of two-dimensional turbulence. In particular, similarity theory has a continued role in describing the weak filamentary sea between the vortices. Moreover, we locate both classical inertial and vortex scaling ranges within the broader framework of scaling in far-from-equilibrium systems, which generically exhibit multiple fixed point solutions with distinct scaling behaviour. We describe how stationary transport in a range of scales comoving with the dilatation of flow features, as measured by the growth in vortex area, constrains the vortex number density in both freely evolving and forced two-dimensional turbulence. The new theories for coherent vortices reveal previously hidden nontrivial scaling, point to new dynamical understanding, and provide a novel exciting window into two-dimensional turbulence.Counting subwords and other results related to the generalised star-height problem for regular languagesBourne, Thomashttp://hdl.handle.net/10023/120242017-11-08T00:16:17Z2017-12-07T00:00:00ZThe Generalised Star-Height Problem is an open question in the field of formal language theory that concerns a measure of complexity on the class of regular languages; specifically, it asks whether or not there exists an algorithm to determine the generalised star-height of a given regular language. Rather surprisingly, it is not yet known whether there exists a regular language of generalised star-height greater than one.
Motivated by a theorem of Thérien, we first take a combinatorial approach to the problem and consider the languages in which every word features a fixed contiguous subword an exact number of times. We show that these languages are all of generalised star-height zero. Similarly, we consider the languages in which every word features a fixed contiguous subword a prescribed number of times modulo a fixed number and show that these languages are all of generalised star-height at most one.
Using these combinatorial results, we initiate work on identifying the generalised star-height of the languages that are recognised by finite semigroups. To do this, we establish the generalised star-height of languages recognised by Rees zero-matrix semigroups over nilpotent groups of classes zero and one before considering Rees zero-matrix semigroups over monogenic semigroups.
Finally, we explore the generalised star-height of languages recognised by finite groups of a given order. We do this through the use of finite state automata and 'count arrows' to examine semidirect products of the form 𝐴 ⋊ ℤ[sub]𝑟, where 𝐴 is an abelian group and ℤ[sub]𝑟 is the cyclic group of order 𝑟.
2017-12-07T00:00:00ZBourne, ThomasThe Generalised Star-Height Problem is an open question in the field of formal language theory that concerns a measure of complexity on the class of regular languages; specifically, it asks whether or not there exists an algorithm to determine the generalised star-height of a given regular language. Rather surprisingly, it is not yet known whether there exists a regular language of generalised star-height greater than one.
Motivated by a theorem of Thérien, we first take a combinatorial approach to the problem and consider the languages in which every word features a fixed contiguous subword an exact number of times. We show that these languages are all of generalised star-height zero. Similarly, we consider the languages in which every word features a fixed contiguous subword a prescribed number of times modulo a fixed number and show that these languages are all of generalised star-height at most one.
Using these combinatorial results, we initiate work on identifying the generalised star-height of the languages that are recognised by finite semigroups. To do this, we establish the generalised star-height of languages recognised by Rees zero-matrix semigroups over nilpotent groups of classes zero and one before considering Rees zero-matrix semigroups over monogenic semigroups.
Finally, we explore the generalised star-height of languages recognised by finite groups of a given order. We do this through the use of finite state automata and 'count arrows' to examine semidirect products of the form 𝐴 ⋊ ℤ[sub]𝑟, where 𝐴 is an abelian group and ℤ[sub]𝑟 is the cyclic group of order 𝑟.Preserving invariance properties of reaction-diffusion systems on stationary surfacesFrittelli, MassimoMadzvamuse, AnotideSgura, IvonneVenkataraman, Chandrasekharhttp://hdl.handle.net/10023/120212018-04-07T23:35:04Z2017-10-27T00:00:00ZWe propose and analyse a lumped surface finite element method for the numerical approximation of reaction–diffusion systems on stationary compact surfaces in ℝ3. The proposed method preserves the invariant regions of the continuous problem under discretization and, in the special case of scalar equations, it preserves the maximum principle. On the application of a fully discrete scheme using the implicit–explicit Euler method in time, we prove that invariant regions of the continuous problem are preserved (i) at the spatially discrete level with no restriction on the meshsize and (ii) at the fully discrete level under a timestep restriction. We further prove optimal error bounds for the semidiscrete and fully discrete methods, that is, the convergence rates are quadratic in the meshsize and linear in the timestep. Numerical experiments are provided to support the theoretical findings. We provide examples in which, in the absence of lumping, the numerical solution violates the invariant region leading to blow-up.
This work (AM, CV) is partly supported by the EPSRC grant number EP/J016780/1 and the Leverhulme Trust Research Project Grant (RPG-2014-149). The authors (MF, AM, IS CV) would like to thank the Isaac Newton Institute for Mathematical Sciences for its hospitality during the programme [Coupling Geometric PDEs with Physics for Cell Morphology, Motility and Pattern Formation] supported by EPSRC Grant Number EP/K032208/1. AM acknowledges funding from the European Union Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 642866 and was partially supported by a grant from the Simons Foundation. AM is a Royal Society Wolfson Research Merit Award Holder funded generously by the Wolfson Foundation.
2017-10-27T00:00:00ZFrittelli, MassimoMadzvamuse, AnotideSgura, IvonneVenkataraman, ChandrasekharWe propose and analyse a lumped surface finite element method for the numerical approximation of reaction–diffusion systems on stationary compact surfaces in ℝ3. The proposed method preserves the invariant regions of the continuous problem under discretization and, in the special case of scalar equations, it preserves the maximum principle. On the application of a fully discrete scheme using the implicit–explicit Euler method in time, we prove that invariant regions of the continuous problem are preserved (i) at the spatially discrete level with no restriction on the meshsize and (ii) at the fully discrete level under a timestep restriction. We further prove optimal error bounds for the semidiscrete and fully discrete methods, that is, the convergence rates are quadratic in the meshsize and linear in the timestep. Numerical experiments are provided to support the theoretical findings. We provide examples in which, in the absence of lumping, the numerical solution violates the invariant region leading to blow-up.Modelling complex dependencies inherent in spatial and spatio-temporal point pattern dataJones-Todd, Charlotte Mhttp://hdl.handle.net/10023/120092017-12-06T13:42:42Z2017-06-23T00:00:00ZPoint processes are mechanisms that beget point patterns. Realisations of point processes are observed in many contexts, for example, locations of stars in the sky, or locations of trees in a forest. Inferring the mechanisms that drive point processes relies on the development of models that appropriately account for the dependencies inherent in the data. Fitting models that adequately capture the complex dependency structures in either space, time, or both is often problematic. This is commonly due to—but not restricted to—the intractability of the likelihood function, or computational burden of the required numerical operations.
This thesis primarily focuses on developing point process models with some hierarchical structure, and specifically where this is a latent structure that may be considered as one of the following: (i) some unobserved construct assumed to be generating the observed structure, or (ii) some stochastic process describing the structure of the point pattern. Model fitting procedures utilised in this thesis include either (i) approximate-likelihood techniques to circumvent intractable likelihoods, (ii) stochastic partial differential equations to model continuous spatial latent structures, or (iii) improving computational speed in numerical approximations by exploiting automatic differentiation.
Moreover, this thesis extends classic point process models by considering multivariate dependencies. This is achieved through considering a general class of joint point process model, which utilise shared stochastic structures. These structures account for the dependencies inherent in multivariate point process data. These models are applied to data originating from various scientific fields; in particular, applications are considered in ecology, medicine, and geology. In addition, point process models that account for the second order behaviour of these assumed stochastic structures are also considered.
2017-06-23T00:00:00ZJones-Todd, Charlotte MPoint processes are mechanisms that beget point patterns. Realisations of point processes are observed in many contexts, for example, locations of stars in the sky, or locations of trees in a forest. Inferring the mechanisms that drive point processes relies on the development of models that appropriately account for the dependencies inherent in the data. Fitting models that adequately capture the complex dependency structures in either space, time, or both is often problematic. This is commonly due to—but not restricted to—the intractability of the likelihood function, or computational burden of the required numerical operations.
This thesis primarily focuses on developing point process models with some hierarchical structure, and specifically where this is a latent structure that may be considered as one of the following: (i) some unobserved construct assumed to be generating the observed structure, or (ii) some stochastic process describing the structure of the point pattern. Model fitting procedures utilised in this thesis include either (i) approximate-likelihood techniques to circumvent intractable likelihoods, (ii) stochastic partial differential equations to model continuous spatial latent structures, or (iii) improving computational speed in numerical approximations by exploiting automatic differentiation.
Moreover, this thesis extends classic point process models by considering multivariate dependencies. This is achieved through considering a general class of joint point process model, which utilise shared stochastic structures. These structures account for the dependencies inherent in multivariate point process data. These models are applied to data originating from various scientific fields; in particular, applications are considered in ecology, medicine, and geology. In addition, point process models that account for the second order behaviour of these assumed stochastic structures are also considered.Bifurcations and chaotic dynamics in a tumour-immune-virus systemEftimie, R.Macnamara, C. K.Dushoff, JonathanBramson, J. L.Earn, D. J. D.http://hdl.handle.net/10023/119992018-01-07T03:54:34Z2016-12-07T00:00:00ZDespite mounting evidence that oncolytic viruses can be effective in treating cancer, understanding the details of the interactions between tumour cells, oncolytic viruses and immune cells that could lead to tumour control or tumour escape is still an open problem. Mathematical modelling of cancer oncolytic therapies has been used to investigate the biological mechanisms behind the observed temporal patterns of tumour growth. However, many models exhibit very complex dynamics, which renders them difficult to investigate. In this case, bifurcation diagrams could enable the visualisation of model dynamics by identifying (in the parameter space) the particular transition points between different behaviours. Here, we describe and investigate two simple mathematical models for oncolytic virus cancer therapy, with constant and immunity-dependent carrying capacity. While both models can exhibit complex dynamics, namely fixed points, periodic orbits and chaotic behaviours, only the model with immunity-dependent carrying capacity can exhibit them for biologically realistic situations, i.e., before the tumour grows too large and the experiment is terminated. Moreover, with the help of the bifurcation diagrams we uncover two unexpected behaviours in virus-tumour dynamics: (i) for short virus half-life, the tumour size seems to be too small to be detected, while for long virus half-life the tumour grows to larger sizes that can be detected; (ii) some model parameters have opposite effects on the transient and asymptotic dynamics of the tumour.
2016-12-07T00:00:00ZEftimie, R.Macnamara, C. K.Dushoff, JonathanBramson, J. L.Earn, D. J. D.Despite mounting evidence that oncolytic viruses can be effective in treating cancer, understanding the details of the interactions between tumour cells, oncolytic viruses and immune cells that could lead to tumour control or tumour escape is still an open problem. Mathematical modelling of cancer oncolytic therapies has been used to investigate the biological mechanisms behind the observed temporal patterns of tumour growth. However, many models exhibit very complex dynamics, which renders them difficult to investigate. In this case, bifurcation diagrams could enable the visualisation of model dynamics by identifying (in the parameter space) the particular transition points between different behaviours. Here, we describe and investigate two simple mathematical models for oncolytic virus cancer therapy, with constant and immunity-dependent carrying capacity. While both models can exhibit complex dynamics, namely fixed points, periodic orbits and chaotic behaviours, only the model with immunity-dependent carrying capacity can exhibit them for biologically realistic situations, i.e., before the tumour grows too large and the experiment is terminated. Moreover, with the help of the bifurcation diagrams we uncover two unexpected behaviours in virus-tumour dynamics: (i) for short virus half-life, the tumour size seems to be too small to be detected, while for long virus half-life the tumour grows to larger sizes that can be detected; (ii) some model parameters have opposite effects on the transient and asymptotic dynamics of the tumour.Inhomogeneous self-similar sets with overlapsBaker, SimonFraser, Jonathan M.Máthé, Andráshttp://hdl.handle.net/10023/119952018-03-18T01:39:01Z2017-05-04T00:00:00ZIt is known that if the underlying iterated function system satisfies the open set condition, then the upper box dimension of an inhomogeneous self-similar set is the maximum of the upper box dimensions of the homogeneous counterpart and the condensation set. First, we prove that this 'expected formula' does not hold in general if there are overlaps in the construction. We demonstrate this via two different types of counterexample: the first is a family of overlapping inhomogeneous self-similar sets based upon Bernoulli convolutions; and the second applies in higher dimensions and makes use of a spectral gap property that holds for certain subgroups of SO(d) for d≥3. We also obtain new upper bounds for the upper box dimension of an inhomogeneous self-similar set which hold in general. Moreover, our counterexamples demonstrate that these bounds are optimal. In the final section we show that if the weak separation property is satisfied, that is, the overlaps are controllable, then the 'expected formula' does hold.
2017-05-04T00:00:00ZBaker, SimonFraser, Jonathan M.Máthé, AndrásIt is known that if the underlying iterated function system satisfies the open set condition, then the upper box dimension of an inhomogeneous self-similar set is the maximum of the upper box dimensions of the homogeneous counterpart and the condensation set. First, we prove that this 'expected formula' does not hold in general if there are overlaps in the construction. We demonstrate this via two different types of counterexample: the first is a family of overlapping inhomogeneous self-similar sets based upon Bernoulli convolutions; and the second applies in higher dimensions and makes use of a spectral gap property that holds for certain subgroups of SO(d) for d≥3. We also obtain new upper bounds for the upper box dimension of an inhomogeneous self-similar set which hold in general. Moreover, our counterexamples demonstrate that these bounds are optimal. In the final section we show that if the weak separation property is satisfied, that is, the overlaps are controllable, then the 'expected formula' does hold.On interfaces between cell populations with different mobilitiesLorenzi, TommasoLorz, AlexanderPerthame, Benoithttp://hdl.handle.net/10023/119802018-05-27T00:33:47Z2017-03-01T00:00:00ZPartial differential equations describing the dynamics of cell population densities from a fluid mechanical perspective can model the growth of avascular tumours. In this framework, we consider a system of equations that describes the interaction between a population of dividing cells and a population of non-dividing cells. The two cell populations are characterised by different mobilities. We present the results of numerical simulations displaying two-dimensional spherical waves with sharp interfaces between dividing and non-dividing cells. Furthermore, we numerically observe how different ratios between the mobilities change the morphology of the interfaces, and lead to the emergence of finger-like patterns of invasion above a threshold. Motivated by these simulations, we study the existence of one-dimensional travelling wave solutions.
2017-03-01T00:00:00ZLorenzi, TommasoLorz, AlexanderPerthame, BenoitPartial differential equations describing the dynamics of cell population densities from a fluid mechanical perspective can model the growth of avascular tumours. In this framework, we consider a system of equations that describes the interaction between a population of dividing cells and a population of non-dividing cells. The two cell populations are characterised by different mobilities. We present the results of numerical simulations displaying two-dimensional spherical waves with sharp interfaces between dividing and non-dividing cells. Furthermore, we numerically observe how different ratios between the mobilities change the morphology of the interfaces, and lead to the emergence of finger-like patterns of invasion above a threshold. Motivated by these simulations, we study the existence of one-dimensional travelling wave solutions.Arithmetic patches, weak tangents, and dimensionFraser, Jonathan MacDonaldYu, Hanhttp://hdl.handle.net/10023/119782018-06-07T12:30:09Z2018-02-01T00:00:00ZWe investigate the relationships between several classical notions in arithmetic combinatorics and geometry including the presence (or lack of) arithmetic progressions (or patches in dimensions at least 2), the structure of tangent sets, and the Assouad dimension. We begin by extending a recent result of Dyatlov and Zahl by showing that a set cannot contain arbitrarily large arithmetic progressions (patches) if it has Assouad dimension strictly smaller than the ambient spatial dimension. Seeking a partial converse, we go on to prove that having Assouad dimension equal to the ambient spatial dimension is equivalent to having weak tangents with non-empty interior and to ‘asymptotically’ containing arbitrarily large arithmetic patches. We present some applications of our results concerning sets of integers, which include a weak solution to the Erdös–Turán conjecture on arithmetic progressions.
The first named author is supported by a Leverhulme Trust Research Fellowship (RF-2016-500) and the second named author is supported by a PhD scholarship provided bythe School of Mathematics in the University of St Andrews
2018-02-01T00:00:00ZFraser, Jonathan MacDonaldYu, HanWe investigate the relationships between several classical notions in arithmetic combinatorics and geometry including the presence (or lack of) arithmetic progressions (or patches in dimensions at least 2), the structure of tangent sets, and the Assouad dimension. We begin by extending a recent result of Dyatlov and Zahl by showing that a set cannot contain arbitrarily large arithmetic progressions (patches) if it has Assouad dimension strictly smaller than the ambient spatial dimension. Seeking a partial converse, we go on to prove that having Assouad dimension equal to the ambient spatial dimension is equivalent to having weak tangents with non-empty interior and to ‘asymptotically’ containing arbitrarily large arithmetic patches. We present some applications of our results concerning sets of integers, which include a weak solution to the Erdös–Turán conjecture on arithmetic progressions.A path reconstruction method integrating dead-reckoning and position fixes applied to humpback whalesWensveen, Paul J.Thomas, LenMiller, Patrick J Ohttp://hdl.handle.net/10023/119762018-04-08T00:42:41Z2015-09-21T00:00:00ZBACKGROUND: Detailed information about animal location and movement is often crucial in studies of natural behaviour and how animals respond to anthropogenic activities. Dead-reckoning can be used to infer such detailed information, but without additional positional data this method results in uncertainty that grows with time. Combining dead-reckoning with new Fastloc-GPS technology should provide good opportunities for reconstructing georeferenced fine-scale tracks, and should be particularly useful for marine animals that spend most of their time under water. We developed a computationally efficient, Bayesian state-space modelling technique to estimate humpback whale locations through time, integrating dead-reckoning using on-animal sensors with measurements of whale locations using on-animal Fastloc-GPS and visual observations. Positional observation models were based upon error measurements made during calibrations. RESULTS: High-resolution 3-dimensional movement tracks were produced for 13 whales using a simple process model in which errors caused by water current movements, non-location sensor errors, and other dead-reckoning errors were accumulated into a combined error term. Positional uncertainty quantified by the track reconstruction model was much greater for tracks with visual positions and few or no GPS positions, indicating a strong benefit to using Fastloc-GPS for track reconstruction. Compared to tracks derived only from position fixes, the inclusion of dead-reckoning data greatly improved the level of detail in the reconstructed tracks of humpback whales. Using cross-validation, a clear improvement in the predictability of out-of-set Fastloc-GPS data was observed compared to more conventional track reconstruction methods. Fastloc-GPS observation errors during calibrations were found to vary by number of GPS satellites received and by orthogonal dimension analysed; visual observation errors varied most by distance to the whale. CONCLUSIONS: By systematically accounting for the observation errors in the position fixes, our model provides a quantitative estimate of location uncertainty that can be appropriately incorporated into analyses of animal movement. This generic method has potential application for a wide range of marine animal species and data recording systems.
PW received a PhD studentship with matched funding from The Netherlands Ministry of Defence (administered by TNO) and the UK Natural Environment Research Council (NE/J500276/1). The 3S2 project was funded by the US Office of Naval Research (N00014-10-1-0355), the Norwegian Ministry of Defence, and The Netherlands Ministry of Defence. Part of this work was supported by the Multi-study Ocean acoustics Human effects Analysis (MOCHA) project funded by the US Office of Naval Research (N00014-12-1-0204).
2015-09-21T00:00:00ZWensveen, Paul J.Thomas, LenMiller, Patrick J OBACKGROUND: Detailed information about animal location and movement is often crucial in studies of natural behaviour and how animals respond to anthropogenic activities. Dead-reckoning can be used to infer such detailed information, but without additional positional data this method results in uncertainty that grows with time. Combining dead-reckoning with new Fastloc-GPS technology should provide good opportunities for reconstructing georeferenced fine-scale tracks, and should be particularly useful for marine animals that spend most of their time under water. We developed a computationally efficient, Bayesian state-space modelling technique to estimate humpback whale locations through time, integrating dead-reckoning using on-animal sensors with measurements of whale locations using on-animal Fastloc-GPS and visual observations. Positional observation models were based upon error measurements made during calibrations. RESULTS: High-resolution 3-dimensional movement tracks were produced for 13 whales using a simple process model in which errors caused by water current movements, non-location sensor errors, and other dead-reckoning errors were accumulated into a combined error term. Positional uncertainty quantified by the track reconstruction model was much greater for tracks with visual positions and few or no GPS positions, indicating a strong benefit to using Fastloc-GPS for track reconstruction. Compared to tracks derived only from position fixes, the inclusion of dead-reckoning data greatly improved the level of detail in the reconstructed tracks of humpback whales. Using cross-validation, a clear improvement in the predictability of out-of-set Fastloc-GPS data was observed compared to more conventional track reconstruction methods. Fastloc-GPS observation errors during calibrations were found to vary by number of GPS satellites received and by orthogonal dimension analysed; visual observation errors varied most by distance to the whale. CONCLUSIONS: By systematically accounting for the observation errors in the position fixes, our model provides a quantitative estimate of location uncertainty that can be appropriately incorporated into analyses of animal movement. This generic method has potential application for a wide range of marine animal species and data recording systems.The interaction of two surface vortices near a topographic slope in a stratified oceande Marez, CharlyCarton, XavierMorvan, MathieuReinaud, Jean Noelhttp://hdl.handle.net/10023/119722018-06-23T23:32:14Z2017-12-01T00:00:00ZWe study the influence of bottom topography on the interaction of two identical vortices in a two-layer, quasi-geostrophic model. The two vortices have piecewise-uniform potential vorticity, and are lying in the upper layer of the model. The topography is a smooth bottom slope. For two cyclones, topography modifies the merger critical distance and the merger efficiency: the topographic wave and vortices can advect the two cyclones along the shelf when they are initially far from it, or towards the shelf when they are initially closer to it. They can also advect the two cyclones towards each other, and thus favour merger. The topographic wave and vortices exert a deformation on these cyclones, which filament. Regimes of partial vortex merger or of vortex splitting are then observed. The interaction of the vorticity poles in the two layers are analysed to explain the evolution of the two upper layer cyclones. For taller topography, two new regimes appear: vortex drift and splitting, and filamentation and asymmetric merger. They are due to the hetonic coupling of lower layer vorticity with the upper vortices, or to the strong shear that the former exert on the latter. The interaction of two anticyclones shows regimes of co-rotation or merger, but specifically, it leads to the drift of the two vortices away from the slope, via a hetonic coupling with opposite signed vorticity in the lower layer. This vorticity originates in the breaking of the topographic wave. The analysis of passive tracer evolution confirms the inshore or offshore drift of the fluid, the formation of tracer fronts along filaments and its mixing in regions of vortex merger. The trajectories of particles indicates how the fluid initially in the vortices is finally partitioned.
2017-12-01T00:00:00Zde Marez, CharlyCarton, XavierMorvan, MathieuReinaud, Jean NoelWe study the influence of bottom topography on the interaction of two identical vortices in a two-layer, quasi-geostrophic model. The two vortices have piecewise-uniform potential vorticity, and are lying in the upper layer of the model. The topography is a smooth bottom slope. For two cyclones, topography modifies the merger critical distance and the merger efficiency: the topographic wave and vortices can advect the two cyclones along the shelf when they are initially far from it, or towards the shelf when they are initially closer to it. They can also advect the two cyclones towards each other, and thus favour merger. The topographic wave and vortices exert a deformation on these cyclones, which filament. Regimes of partial vortex merger or of vortex splitting are then observed. The interaction of the vorticity poles in the two layers are analysed to explain the evolution of the two upper layer cyclones. For taller topography, two new regimes appear: vortex drift and splitting, and filamentation and asymmetric merger. They are due to the hetonic coupling of lower layer vorticity with the upper vortices, or to the strong shear that the former exert on the latter. The interaction of two anticyclones shows regimes of co-rotation or merger, but specifically, it leads to the drift of the two vortices away from the slope, via a hetonic coupling with opposite signed vorticity in the lower layer. This vorticity originates in the breaking of the topographic wave. The analysis of passive tracer evolution confirms the inshore or offshore drift of the fluid, the formation of tracer fronts along filaments and its mixing in regions of vortex merger. The trajectories of particles indicates how the fluid initially in the vortices is finally partitioned.New aspects of particle acceleration in collapsing magnetic trapsEradat Oskoui, Solmazhttp://hdl.handle.net/10023/119542017-12-21T00:16:18Z2014-01-01T00:00:00ZCollapsing magnetic traps (CMTs) have been suggested as one of the mechanisms that could contribute to particle energisation in solar flares. The basic idea behind CMTs is that charged particles will be trapped on the magnetic field lines below the reconnection region of a flare. This thesis discusses a number of important new aspects in particle energisation processes in CMTs, based on the model by Giuliani et al. (2005). In particular, we extend previous studies of particle acceleration in this CMT model to the relativistic regime and compare our results obtained using relativistic guiding centre theory with results obtained using the non-relativistic guiding centre theory. The similarities and differences found are discussed. We then present a detailed study of the question, what leads to the trapping or escape of particle orbits from CMTs. The answer to this question is investigated by using results from the non-relativistic orbit calculations with guiding centre theory and a number of simple models for particle energy gain in CMTs. We find that there is a critical pitch angle dividing trapped particle orbits from the escaping particle orbits and that this critical pitch angle does not coincide with the initial loss cone angle. Furthermore, we also present a calculation of the time evolution of an anisotropic pressure tensor and of the plasma density under the assumptions that they evolve in line with our kinematic MHD CMT model and that the pressure tensor satisfies the double-adiabatic Chew-Goldburger-Low (CGL) theory.
Finally, we make a first step to introduce Coulomb scattering by a Maxwellian background plasma into our guiding centre equations by changing them into a set of stochastic differential equations. We study the influence of a static background plasma onto selected particle orbits by pitch angle scattering and energy losses, and look at its effect on the particle energy and the trapping conditions.
2014-01-01T00:00:00ZEradat Oskoui, SolmazCollapsing magnetic traps (CMTs) have been suggested as one of the mechanisms that could contribute to particle energisation in solar flares. The basic idea behind CMTs is that charged particles will be trapped on the magnetic field lines below the reconnection region of a flare. This thesis discusses a number of important new aspects in particle energisation processes in CMTs, based on the model by Giuliani et al. (2005). In particular, we extend previous studies of particle acceleration in this CMT model to the relativistic regime and compare our results obtained using relativistic guiding centre theory with results obtained using the non-relativistic guiding centre theory. The similarities and differences found are discussed. We then present a detailed study of the question, what leads to the trapping or escape of particle orbits from CMTs. The answer to this question is investigated by using results from the non-relativistic orbit calculations with guiding centre theory and a number of simple models for particle energy gain in CMTs. We find that there is a critical pitch angle dividing trapped particle orbits from the escaping particle orbits and that this critical pitch angle does not coincide with the initial loss cone angle. Furthermore, we also present a calculation of the time evolution of an anisotropic pressure tensor and of the plasma density under the assumptions that they evolve in line with our kinematic MHD CMT model and that the pressure tensor satisfies the double-adiabatic Chew-Goldburger-Low (CGL) theory.
Finally, we make a first step to introduce Coulomb scattering by a Maxwellian background plasma into our guiding centre equations by changing them into a set of stochastic differential equations. We study the influence of a static background plasma onto selected particle orbits by pitch angle scattering and energy losses, and look at its effect on the particle energy and the trapping conditions.Spatial distribution of citizen science casuistic observations for different taxonomic groupsTiago, PatríciaCeia-Hasse, AnaMarques, Tiago A.Capinha, CésarPereira, Henrique M.http://hdl.handle.net/10023/119332018-01-07T04:06:26Z2017-10-16T00:00:00ZOpportunistic citizen science databases are becoming an important way of gathering information on species distributions. These data are temporally and spatially dispersed and could have limitations regarding biases in the distribution of the observations in space and/or time. In this work, we test the influence of landscape variables in the distribution of citizen science observations for eight taxonomic groups. We use data collected through a Portuguese citizen science database (biodiversity4all.org). We use a zero-inflated negative binomial regression to model the distribution of observations as a function of a set of variables representing the landscape features plausibly influencing the spatial distribution of the records. Results suggest that the density of paths is the most important variable, having a statistically significant positive relationship with number of observations for seven of the eight taxa considered. Wetland coverage was also identified as having a significant, positive relationship, for birds, amphibians and reptiles, and mammals. Our results highlight that the distribution of species observations, in citizen science projects, is spatially biased. Higher frequency of observations is driven largely by accessibility and by the presence of water bodies. We conclude that efforts are required to increase the spatial evenness of sampling effort from volunteers.
PT acknowledges support from the Portuguese Foundation for Science and Technology (FCT/MCTES) (SFRH/BD/89543/2012). ACH acknowledges support from the Portuguese Foundation for Science and Technology (FCT/MCTES) (UID/BIA/50027/2013) and from FEDER through the Operational Programme for Competitiveness Factors – COMPETE (POCI-01-0145-FEDER-006821). TAM thanks partial support by CEAUL (funded by FCT - Fundação para a Ciência e a Tecnologia, Portugal, through the project UID/MAT/00006/2013). CC acknowledges support from the Portuguese Foundation for Science and Technology (FCT) FCT for funds to GHTM - UID/Multi/04413/2013. We thank all volunteers who participate in BioDiversity4All project.
2017-10-16T00:00:00ZTiago, PatríciaCeia-Hasse, AnaMarques, Tiago A.Capinha, CésarPereira, Henrique M.Opportunistic citizen science databases are becoming an important way of gathering information on species distributions. These data are temporally and spatially dispersed and could have limitations regarding biases in the distribution of the observations in space and/or time. In this work, we test the influence of landscape variables in the distribution of citizen science observations for eight taxonomic groups. We use data collected through a Portuguese citizen science database (biodiversity4all.org). We use a zero-inflated negative binomial regression to model the distribution of observations as a function of a set of variables representing the landscape features plausibly influencing the spatial distribution of the records. Results suggest that the density of paths is the most important variable, having a statistically significant positive relationship with number of observations for seven of the eight taxa considered. Wetland coverage was also identified as having a significant, positive relationship, for birds, amphibians and reptiles, and mammals. Our results highlight that the distribution of species observations, in citizen science projects, is spatially biased. Higher frequency of observations is driven largely by accessibility and by the presence of water bodies. We conclude that efforts are required to increase the spatial evenness of sampling effort from volunteers.DESNT : a poor prognosis category of human prostate cancerLuca, Bogdan-AlexandruBrewer, Daniel S.Edwards, Dylan R.Edwards, SandraWhitaker, Hayley C.Merson, SueDennis, NeningCooper, Rosalin A.Hazell, StevenWarren, Anne Y.Eeles, RosalindLynch, Andy G.Ross-Adams, HelenLamb, Alastair D.Neal, David E.Sethia, KrishnaMills, Robert D.Ball, Richard Y.Curley, HelenClark, JeremyMoulton, VincentCooper, Colin S.http://hdl.handle.net/10023/119222018-05-13T01:35:10Z2017-03-06T00:00:00ZBackground : A critical problem in the clinical management of prostate cancer is that it is highly heterogeneous. Accurate prediction of individual cancer behaviour is therefore not achievable at the time of diagnosis leading to substantial overtreatment. It remains an enigma that, in contrast to breast cancer, unsupervised analyses of global expression profiles have not currently defined robust categories of prostate cancer with distinct clinical outcomes. Objective: To devise a novel classification framework for human prostate cancer based on unsupervised mathematical approaches. Design, setting, and participants: Our analyses are based on the hypothesis that previous attempts to classify prostate cancer have been unsuccessful because individual samples of prostate cancer frequently have heterogeneous compositions. To address this issue, we applied an unsupervised Bayesian procedure called Latent Process Decomposition to four independent prostate cancer transcriptome datasets obtained using samples from prostatectomy patients and containing between 78 and 182 participants. Outcome measurements and statistical analysis: Biochemical failure was assessed using log-rank analysis and Cox regression analysis. Results and limitations: Application of Latent Process Decomposition identified a common process in all four independent datasets examined. Cancers assigned to this process (designated DESNT cancers) are characterized by low expression of a core set of 45 genes, many encoding proteins involved in the cytoskeleton machinery, ion transport, and cell adhesion. For the three datasets with linked prostate-specific antigen failure data following prostatectomy, patients with DESNT cancer exhibited poor outcome relative to other patients (p = 2.65 × 10−5, p = 4.28 × 10−5, and p = 2.98 × 10−8). When these three datasets were combined the independent predictive value of DESNT membership was p = 1.61 × 10−7 compared with p = 1.00 × 10−5 for Gleason sum. A limitation of the study is that only prediction of prostate-specific antigen failure was examined. Conclusions: Our results demonstrate the existence of a novel poor prognosis category of human prostate cancer and will assist in the targeting of therapy, helping avoid treatment-associated morbidity in men with indolent disease. Patient Summary: Prostate cancer, unlike breast cancer, does not have a robust classification framework. We propose that this failure has occurred because prostate cancer samples selected for analysis frequently have heterozygous compositions (individual samples are made up of many different parts that each have different characteristics). Applying a mathematical approach that can overcome this problem we identify a novel poor prognosis category of human prostate cancer called DESNT.
his work was funded by the Bob Champion Cancer Trust, The Masonic Charitable Foundation successor to The Grand Charity, The King Family, and The University of East Anglia. We acknowledge support from Movember, from Prostate Cancer UK, Callum Barton, and from The Andy Ripley Memorial Fund. We would like to acknowledge the support of the National Institute for Health Research which funds the Cambridge Bio-medical Research Centre, Cambridge UK.
2017-03-06T00:00:00ZLuca, Bogdan-AlexandruBrewer, Daniel S.Edwards, Dylan R.Edwards, SandraWhitaker, Hayley C.Merson, SueDennis, NeningCooper, Rosalin A.Hazell, StevenWarren, Anne Y.Eeles, RosalindLynch, Andy G.Ross-Adams, HelenLamb, Alastair D.Neal, David E.Sethia, KrishnaMills, Robert D.Ball, Richard Y.Curley, HelenClark, JeremyMoulton, VincentCooper, Colin S.Background : A critical problem in the clinical management of prostate cancer is that it is highly heterogeneous. Accurate prediction of individual cancer behaviour is therefore not achievable at the time of diagnosis leading to substantial overtreatment. It remains an enigma that, in contrast to breast cancer, unsupervised analyses of global expression profiles have not currently defined robust categories of prostate cancer with distinct clinical outcomes. Objective: To devise a novel classification framework for human prostate cancer based on unsupervised mathematical approaches. Design, setting, and participants: Our analyses are based on the hypothesis that previous attempts to classify prostate cancer have been unsuccessful because individual samples of prostate cancer frequently have heterogeneous compositions. To address this issue, we applied an unsupervised Bayesian procedure called Latent Process Decomposition to four independent prostate cancer transcriptome datasets obtained using samples from prostatectomy patients and containing between 78 and 182 participants. Outcome measurements and statistical analysis: Biochemical failure was assessed using log-rank analysis and Cox regression analysis. Results and limitations: Application of Latent Process Decomposition identified a common process in all four independent datasets examined. Cancers assigned to this process (designated DESNT cancers) are characterized by low expression of a core set of 45 genes, many encoding proteins involved in the cytoskeleton machinery, ion transport, and cell adhesion. For the three datasets with linked prostate-specific antigen failure data following prostatectomy, patients with DESNT cancer exhibited poor outcome relative to other patients (p = 2.65 × 10−5, p = 4.28 × 10−5, and p = 2.98 × 10−8). When these three datasets were combined the independent predictive value of DESNT membership was p = 1.61 × 10−7 compared with p = 1.00 × 10−5 for Gleason sum. A limitation of the study is that only prediction of prostate-specific antigen failure was examined. Conclusions: Our results demonstrate the existence of a novel poor prognosis category of human prostate cancer and will assist in the targeting of therapy, helping avoid treatment-associated morbidity in men with indolent disease. Patient Summary: Prostate cancer, unlike breast cancer, does not have a robust classification framework. We propose that this failure has occurred because prostate cancer samples selected for analysis frequently have heterozygous compositions (individual samples are made up of many different parts that each have different characteristics). Applying a mathematical approach that can overcome this problem we identify a novel poor prognosis category of human prostate cancer called DESNT.Theory of one-dimensional Vlasov-Maxwell equilibria: with applications to collisionless current sheets and flux tubesAllanson, Oliver Douglashttp://hdl.handle.net/10023/119162017-10-25T23:17:32Z2017-12-07T00:00:00ZVlasov-Maxwell equilibria are characterised by the self-consistent descriptions of the steady-states of collisionless plasmas in particle phase-space, and balanced macroscopic forces. We study the theory of Vlasov-Maxwell equilibria in one spatial dimension, as well as its application to current sheet and flux tube models.
The ‘inverse problem’ is that of determining a Vlasov-Maxwell equilibrium distribution function self-consistent with a given magnetic field. We develop the theory of inversion using expansions in Hermite polynomial functions of the canonical momenta. Sufficient conditions for the convergence of a Hermite expansion are found, given a pressure tensor. For large classes of DFs, we prove that non-negativity of the distribution function is contingent on the magnetisation
of the plasma, and make conjectures for all classes.
The inverse problem is considered for nonlinear ‘force-free Harris sheets’. By applying the Hermite method, we construct new models that can describe sub-unity values of the plasma beta (βpl) for the first time. Whilst analytical convergence is proven for all βpl, numerical convergence is attained for βpl = 0.85, and then βpl = 0.05 after a ‘re-gauging’ process.
We consider the properties that a pressure tensor must satisfy to be consistent with ‘asymmetric Harris sheets’, and construct new examples. It is possible to analytically solve the inverse problem in some cases, but others must be tackled numerically. We present new exact Vlasov-Maxwell equilibria for asymmetric current sheets, which can be written as a sum of shifted Maxwellian distributions. This is ideal for implementations in particle-in-cell simulations.
We study the correspondence between the microscopic and macroscopic descriptions of equilibrium in cylindrical geometry, and then attempt to find Vlasov-Maxwell equilibria for the nonlinear force-free ‘Gold-Hoyle’ model. However, it is necessary to include a background field, which can be arbitrarily weak if desired. The equilibrium can be electrically non-neutral, depending on the bulk flows.
2017-12-07T00:00:00ZAllanson, Oliver DouglasVlasov-Maxwell equilibria are characterised by the self-consistent descriptions of the steady-states of collisionless plasmas in particle phase-space, and balanced macroscopic forces. We study the theory of Vlasov-Maxwell equilibria in one spatial dimension, as well as its application to current sheet and flux tube models.
The ‘inverse problem’ is that of determining a Vlasov-Maxwell equilibrium distribution function self-consistent with a given magnetic field. We develop the theory of inversion using expansions in Hermite polynomial functions of the canonical momenta. Sufficient conditions for the convergence of a Hermite expansion are found, given a pressure tensor. For large classes of DFs, we prove that non-negativity of the distribution function is contingent on the magnetisation
of the plasma, and make conjectures for all classes.
The inverse problem is considered for nonlinear ‘force-free Harris sheets’. By applying the Hermite method, we construct new models that can describe sub-unity values of the plasma beta (βpl) for the first time. Whilst analytical convergence is proven for all βpl, numerical convergence is attained for βpl = 0.85, and then βpl = 0.05 after a ‘re-gauging’ process.
We consider the properties that a pressure tensor must satisfy to be consistent with ‘asymmetric Harris sheets’, and construct new examples. It is possible to analytically solve the inverse problem in some cases, but others must be tackled numerically. We present new exact Vlasov-Maxwell equilibria for asymmetric current sheets, which can be written as a sum of shifted Maxwellian distributions. This is ideal for implementations in particle-in-cell simulations.
We study the correspondence between the microscopic and macroscopic descriptions of equilibrium in cylindrical geometry, and then attempt to find Vlasov-Maxwell equilibria for the nonlinear force-free ‘Gold-Hoyle’ model. However, it is necessary to include a background field, which can be arbitrarily weak if desired. The equilibrium can be electrically non-neutral, depending on the bulk flows.Global warming and ocean stratification : a potential result of large extraterrestrial impactsJoshi, Manojvon Glasow, RolandSmith, Robin S.Paxton, Charles G. M.Maycock, Amanda C.Lunt, Daniel J.Loptson, ClaireMarkwick, Paulhttp://hdl.handle.net/10023/119152018-01-19T00:31:56Z2017-04-28T00:00:00ZThe prevailing paradigm for the climatic effects of large asteroid or comet impacts is a reduction in sunlight and significant short-term cooling caused by atmospheric aerosol loading. Here we show, using global climate model experiments, that the large increases in stratospheric water vapor that can occur upon impact with the ocean cause radiative forcings of over +20 W m−2 in the case of 10 km sized bolides. The result of such a positive forcing is rapid climatic warming, increased upper ocean stratification, and potentially disruption of upper ocean ecosystems. Since two thirds of the world's surface is ocean, we suggest that some bolide impacts may actually warm climate overall. For impacts producing both stratospheric water vapor and aerosol loading, radiative forcing by water vapor can reduce or even cancel out aerosol-induced cooling, potentially causing 1–2 decades of increased temperatures in both the upper ocean and on the land surface. Such a response, which depends on the ratio of aerosol to water vapor radiative forcing, is distinct from many previous scenarios for the climatic effects of large bolide impacts, which mostly account for cooling from aerosol loading. Finally, we discuss how water vapor forcing from bolide impacts may have contributed to two well-known phenomena: extinction across the Cretaceous/Paleogene boundary and the deglaciation of the Neoproterozoic snowball Earth.
We acknowledge the support of resources provided by UK National Centre for Atmospheric Science (NCAS), the High Performance Computing Cluster supported by the Research and Specialist Computing Support service at the University of East Anglia, UK Natural Environment Research Council (NERC), grants "CPE" (NE/K014757/1), and "Paleopolar" (NE/I005722/1). Data can be obtained from MJ on request. ACM acknowledges support from an AXA Postdoctoral Fellowship and the ERC ACCI grant Project No 267760, and NERC grant NE/M018199/1.
2017-04-28T00:00:00ZJoshi, Manojvon Glasow, RolandSmith, Robin S.Paxton, Charles G. M.Maycock, Amanda C.Lunt, Daniel J.Loptson, ClaireMarkwick, PaulThe prevailing paradigm for the climatic effects of large asteroid or comet impacts is a reduction in sunlight and significant short-term cooling caused by atmospheric aerosol loading. Here we show, using global climate model experiments, that the large increases in stratospheric water vapor that can occur upon impact with the ocean cause radiative forcings of over +20 W m−2 in the case of 10 km sized bolides. The result of such a positive forcing is rapid climatic warming, increased upper ocean stratification, and potentially disruption of upper ocean ecosystems. Since two thirds of the world's surface is ocean, we suggest that some bolide impacts may actually warm climate overall. For impacts producing both stratospheric water vapor and aerosol loading, radiative forcing by water vapor can reduce or even cancel out aerosol-induced cooling, potentially causing 1–2 decades of increased temperatures in both the upper ocean and on the land surface. Such a response, which depends on the ratio of aerosol to water vapor radiative forcing, is distinct from many previous scenarios for the climatic effects of large bolide impacts, which mostly account for cooling from aerosol loading. Finally, we discuss how water vapor forcing from bolide impacts may have contributed to two well-known phenomena: extinction across the Cretaceous/Paleogene boundary and the deglaciation of the Neoproterozoic snowball Earth.Can substorm particle acceleration be applied to solar flares?Birn, JoachimBattaglia, MarinaFletcher, LyndsayHesse, MichaelNeukirch, Thomashttp://hdl.handle.net/10023/119122018-01-07T04:05:56Z2017-10-20T00:00:00ZUsing test particle studies in the electromagnetic fields of three-dimensional magnetohydrodynamic (MHD) simulations of magnetic reconnection, we study the energization of charged particles in the context of the standard two-ribbon flare picture in analogy to the standard magnetospheric substorm paradigm. In particular, we investigate the effects of the collapsing field ("collapsing magnetic trap") below a reconnection site, which has been demonstrated to be the major acceleration mechanism that causes energetic particle acceleration and injections observed in Earth's magnetotail associated with substorms and other impulsive events. We contrast an initially force-free, high-shear field (low beta) with low and moderate shear, finite-pressure (high-beta) arcade structures, where beta represents the ratio between gas (plasma) and magnetic pressure. We demonstrate that the energization affects large numbers of particles, but the acceleration is modest in the presence of a significant shear field. Without incorporating loss mechanisms, the effect on particles at different energies is similar, akin to adiabatic heating, and thus is not a likely mechanism to generate a power-law tail onto a (heated or not heated) Maxwellian velocity distribution.
2017-10-20T00:00:00ZBirn, JoachimBattaglia, MarinaFletcher, LyndsayHesse, MichaelNeukirch, ThomasUsing test particle studies in the electromagnetic fields of three-dimensional magnetohydrodynamic (MHD) simulations of magnetic reconnection, we study the energization of charged particles in the context of the standard two-ribbon flare picture in analogy to the standard magnetospheric substorm paradigm. In particular, we investigate the effects of the collapsing field ("collapsing magnetic trap") below a reconnection site, which has been demonstrated to be the major acceleration mechanism that causes energetic particle acceleration and injections observed in Earth's magnetotail associated with substorms and other impulsive events. We contrast an initially force-free, high-shear field (low beta) with low and moderate shear, finite-pressure (high-beta) arcade structures, where beta represents the ratio between gas (plasma) and magnetic pressure. We demonstrate that the energization affects large numbers of particles, but the acceleration is modest in the presence of a significant shear field. Without incorporating loss mechanisms, the effect on particles at different energies is similar, akin to adiabatic heating, and thus is not a likely mechanism to generate a power-law tail onto a (heated or not heated) Maxwellian velocity distribution.Correlation estimation using components of Japanese candlesticksPopov, Valentin Minahttp://hdl.handle.net/10023/119012018-01-07T03:36:48Z2016-01-01T00:00:00ZUsing the wick's difference from the classical Japanese candlestick representation of daily open, high, low, close prices brings efficiency when estimating the correlation in a bivariate Brownian motion. An interpretation of the correlation estimator in Rogers and Zhou (2008) in the light of wicks' difference allows us to suggest modifications, which lead to an increased efficiency and robustness against the baseline model. An empirical study on four major financial markets confirms the advantages of the modified estimator.
2016-01-01T00:00:00ZPopov, Valentin MinaUsing the wick's difference from the classical Japanese candlestick representation of daily open, high, low, close prices brings efficiency when estimating the correlation in a bivariate Brownian motion. An interpretation of the correlation estimator in Rogers and Zhou (2008) in the light of wicks' difference allows us to suggest modifications, which lead to an increased efficiency and robustness against the baseline model. An empirical study on four major financial markets confirms the advantages of the modified estimator.Collisionless current sheet equilibriaNeukirch, ThomasWilson, FionaAllanson, Oliver Douglashttp://hdl.handle.net/10023/118902018-02-11T01:35:57Z2018-01-01T00:00:00ZCurrent sheets are important for the structure and dynamics of many plasma systems. In space and astrophysical plasmas they play a crucial role in activity processes, for example by facilitating the release of magnetic energy via processes such as magnetic reconnection. In this contribution we will focus on collisionless plasma systems. A sensible first step in any investigation of physical processes involving current sheets is to find appropriate equilibrium solutions. The theory of collisionless plasma equilibria is well established, but over the past few years there has been a renewed interest in finding equilibrium distribution functions for collisionless current sheets with particular properties, for example for cases where the current density is parallel to the magnetic field (force-free current sheets). This interest is due to a combination of scientific curiosity and potential applications to space and astrophysical plasmas. In this paper we will give an overview of some of the recent developments, discuss their potential applications and address a number of open questions.
The authors acknowledge financial support by the UK Science and Technology Facilities Council Consolidated Grants ST/K000950/1 and and ST/N000609/1, as well as Doctoral Training Grant ST/K502327/1. OA also acknowledges support by the UK Natural Environment Research Council Grant NE/P017274/1.
2018-01-01T00:00:00ZNeukirch, ThomasWilson, FionaAllanson, Oliver DouglasCurrent sheets are important for the structure and dynamics of many plasma systems. In space and astrophysical plasmas they play a crucial role in activity processes, for example by facilitating the release of magnetic energy via processes such as magnetic reconnection. In this contribution we will focus on collisionless plasma systems. A sensible first step in any investigation of physical processes involving current sheets is to find appropriate equilibrium solutions. The theory of collisionless plasma equilibria is well established, but over the past few years there has been a renewed interest in finding equilibrium distribution functions for collisionless current sheets with particular properties, for example for cases where the current density is parallel to the magnetic field (force-free current sheets). This interest is due to a combination of scientific curiosity and potential applications to space and astrophysical plasmas. In this paper we will give an overview of some of the recent developments, discuss their potential applications and address a number of open questions.Parallel algorithms for computing finite semigroupsJonusas, JuliusMitchell, J. D.Pfeiffer, M.http://hdl.handle.net/10023/118792018-04-14T23:33:40Z2017-06-19T00:00:00ZIn this paper, we present two algorithms based on the Froidure-Pin Algorithm for computing a finite semigroup. If U is any semigroup, and A be a subset of U, then we denote by ⟨A⟩ the least subsemigroup of U containing A. If B is any other subset of U, then, roughly speaking, the first algorithm we present describes how to use any information about ⟨A⟩, that has been found using the Froidure-Pin Algorithm, to compute the semigroup ⟨A, B⟩. More precisely, we describe the data structure for a finite semigroup S given by Froidure and Pin, and how to obtain such a data structure for ⟨A, B⟩ from that for ⟨A⟩. The second algorithm is a lock-free concurrent version of the Froidure-Pin Algorithm. As was the case with the original algorithm of Froidure and Pin, the algorithms presented here produce the left and right Cayley graphs, a confluent terminating rewriting system, and a reduced word of the rewriting system for every element of the semigroup they output.
2017-06-19T00:00:00ZJonusas, JuliusMitchell, J. D.Pfeiffer, M.In this paper, we present two algorithms based on the Froidure-Pin Algorithm for computing a finite semigroup. If U is any semigroup, and A be a subset of U, then we denote by ⟨A⟩ the least subsemigroup of U containing A. If B is any other subset of U, then, roughly speaking, the first algorithm we present describes how to use any information about ⟨A⟩, that has been found using the Froidure-Pin Algorithm, to compute the semigroup ⟨A, B⟩. More precisely, we describe the data structure for a finite semigroup S given by Froidure and Pin, and how to obtain such a data structure for ⟨A, B⟩ from that for ⟨A⟩. The second algorithm is a lock-free concurrent version of the Froidure-Pin Algorithm. As was the case with the original algorithm of Froidure and Pin, the algorithms presented here produce the left and right Cayley graphs, a confluent terminating rewriting system, and a reduced word of the rewriting system for every element of the semigroup they output.Vertical structure of tropospheric winds on gas giantsScott, R. K.Dunkerton, T. J.http://hdl.handle.net/10023/118502018-03-04T01:40:48Z2017-04-16T00:00:00ZZonal mean zonal velocity profiles from cloud-tracking observations on Jupiter and Saturn are used to infer latitudinal variations of potential temperature consistent with a shear stable potential vorticity distribution. Immediately below the cloud tops, density stratification is weaker on the poleward and stronger on the equatorward flanks of midlatitude jets, while at greater depth the opposite relation holds. Thermal wind balance then yields the associated vertical shears of midlatitude jets in an altitude range bounded above by the cloud-tops and bounded below by the level where the latitudinal gradient of static stability changes sign. The inferred vertical shear below the cloud tops is consistent with existing thermal profiling of the upper troposphere.The sense of the associated mean meridional circulation in the upper troposphere is discussed and expected magnitudes are given based on existing estimates of the radiative timescale on each planet.
Support for this work was generously provided by the National Science Foundation.
2017-04-16T00:00:00ZScott, R. K.Dunkerton, T. J.Zonal mean zonal velocity profiles from cloud-tracking observations on Jupiter and Saturn are used to infer latitudinal variations of potential temperature consistent with a shear stable potential vorticity distribution. Immediately below the cloud tops, density stratification is weaker on the poleward and stronger on the equatorward flanks of midlatitude jets, while at greater depth the opposite relation holds. Thermal wind balance then yields the associated vertical shears of midlatitude jets in an altitude range bounded above by the cloud-tops and bounded below by the level where the latitudinal gradient of static stability changes sign. The inferred vertical shear below the cloud tops is consistent with existing thermal profiling of the upper troposphere.The sense of the associated mean meridional circulation in the upper troposphere is discussed and expected magnitudes are given based on existing estimates of the radiative timescale on each planet.On the Fourier analytic structure of the Brownian graphFraser, Jonathan MacDonaldSahlsten, Tuomashttp://hdl.handle.net/10023/118462018-01-07T04:05:32Z2018-01-01T00:00:00ZIn a previous article (Int. Math. Res. Not. 2014:10 (2014), 2730–2745) T. Orponen and the authors proved that the Fourier dimension of the graph of any real-valued function on R is bounded above by 1. This partially answered a question of Kahane (1993) by showing that the graph of the Wiener process Wt (Brownian motion) is almost surely not a Salem set. In this article we complement this result by showing that the Fourier dimension of the graph of Wt is almost surely 1. In the proof we introduce a method based on Itô calculus to estimate Fourier transforms by reformulating the question in the language of Itô drift-diffusion processes and combine it with the classical work of Kahane on Brownian images.
2018-01-01T00:00:00ZFraser, Jonathan MacDonaldSahlsten, TuomasIn a previous article (Int. Math. Res. Not. 2014:10 (2014), 2730–2745) T. Orponen and the authors proved that the Fourier dimension of the graph of any real-valued function on R is bounded above by 1. This partially answered a question of Kahane (1993) by showing that the graph of the Wiener process Wt (Brownian motion) is almost surely not a Salem set. In this article we complement this result by showing that the Fourier dimension of the graph of Wt is almost surely 1. In the proof we introduce a method based on Itô calculus to estimate Fourier transforms by reformulating the question in the language of Itô drift-diffusion processes and combine it with the classical work of Kahane on Brownian images.Notes on a semigroup related to the dicyclic group QnSorouhesh, Mohammad R.Campbell, Colin M.http://hdl.handle.net/10023/118372018-01-07T04:05:20Z2017-09-21T00:00:00ZWe consider certain properties of the semigroup S defined by the Presentation S = 〈a,b : a2ⁿ⁻¹ = 1,b2 = a2ⁿ⁻², ba = ab2ⁿ⁻¹-1〉, (n ≥ 3).
2017-09-21T00:00:00ZSorouhesh, Mohammad R.Campbell, Colin M.We consider certain properties of the semigroup S defined by the Presentation S = 〈a,b : a2ⁿ⁻¹ = 1,b2 = a2ⁿ⁻², ba = ab2ⁿ⁻¹-1〉, (n ≥ 3).Root sets of polynomials and power series with finite choice of coefficientsBaker, SimonYu, Hanhttp://hdl.handle.net/10023/118222018-03-07T17:30:06Z2018-03-01T00:00:00ZGiven H⊆C two natural objects to study are the set of zeros of polynomials with coefficients in H, {z∈C:∃k>0,∃(an)∈Hk+1,∑n=0kanzn=0}, and the set of zeros of a power series with coefficients in H, {z∈C:∃(an)∈HN,∑n=0∞anzn=0}. In this paper, we consider the case where each element of H has modulus 1. The main result of this paper states that for any r∈(1/2,1), if H is 2cos−1(5−4|r|24)-dense in S1, then the set of zeros of polynomials with coefficients in H is dense in {z∈C:|z|∈[r,r−1]}, and the set of zeros of power series with coefficients in H contains the annulus {z∈C:|z|∈[r,1)}. These two statements demonstrate quantitatively how the set of polynomial zeros/power series zeros fill out the natural annulus containing them as H becomes progressively more dense.
The first author is supported by the EPSRC Grant EP/M001903/1. The second author is supported by a PhD scholarship provided by the School of Mathematics in the University of St Andrews.
2018-03-01T00:00:00ZBaker, SimonYu, HanGiven H⊆C two natural objects to study are the set of zeros of polynomials with coefficients in H, {z∈C:∃k>0,∃(an)∈Hk+1,∑n=0kanzn=0}, and the set of zeros of a power series with coefficients in H, {z∈C:∃(an)∈HN,∑n=0∞anzn=0}. In this paper, we consider the case where each element of H has modulus 1. The main result of this paper states that for any r∈(1/2,1), if H is 2cos−1(5−4|r|24)-dense in S1, then the set of zeros of polynomials with coefficients in H is dense in {z∈C:|z|∈[r,r−1]}, and the set of zeros of power series with coefficients in H contains the annulus {z∈C:|z|∈[r,1)}. These two statements demonstrate quantitatively how the set of polynomial zeros/power series zeros fill out the natural annulus containing them as H becomes progressively more dense.Appraising the relevance of DNA copy number loss and gain in prostate cancer using whole genome DNA sequence dataCamacho, NiedzicaVan Loo, PeterEdwards, SandraKay, Jonathan D.Matthews, LucyHaase, KerstinClark, JeremyDennis, NeningThomas, SarahKremeyer, BarbaraZamora, JorgeButler, Adam P.Gundem, GunesMerson, SueLuxton, HayleyHawkins, SteveGhori, MohammedMarsden, LukeLambert, AdamKaraszi, KatalinPelvender, GillMassie, Charlie E.Kote-Jarai, ZSofiaRaine, KeiranJones, DavidHowat, William J.Hazell, StevenLivni, NaomiFisher, CyrilOgden, ChristopherKumar, PardeepThompson, AlanNicol, DavidMayer, ErikDudderidge, TimYu, YongweiZhang, HongweiShah, Nimish C.Gnanapragasam, Vincent J.Group, The CRUK-ICGC ProstateIsaacs, WilliamVisakorpi, TapioHamdy, FreddieBerney, DanVerrill, ClareWarren, Anne Y.Wedge, David C.Lynch, Andrew G.Foster, Christopher S.Lu, Yong JieBova, G. StevenWhitaker, Hayley C.McDermott, UltanNeal, David E.Eeles, RosalindCooper, Colin S.Brewer, Daniel S.http://hdl.handle.net/10023/118122018-05-27T00:35:32Z2017-09-25T00:00:00ZA variety of models have been proposed to explain regions of recurrent somatic copy number alteration (SCNA) in human cancer. Our study employs Whole Genome DNA Sequence (WGS) data from tumor samples (n = 103) to comprehensively assess the role of the Knudson two hit genetic model in SCNA generation in prostate cancer. 64 recurrent regions of loss and gain were detected, of which 28 were novel, including regions of loss with more than 15% frequency at Chr4p15.2-p15.1 (15.53%), Chr6q27 (16.50%) and Chr18q12.3 (17.48%). Comprehensive mutation screens of genes, lincRNA encoding sequences, control regions and conserved domains within SCNAs demonstrated that a two-hit genetic model was supported in only a minor proportion of recurrent SCNA losses examined (15/40). We found that recurrent breakpoints and regions of inversion often occur within Knudson model SCNAs, leading to the identification of ZNF292 as a target gene for the deletion at 6q14.3-q15 and NKX3.1 as a two-hit target at 8p21.3-p21.2. The importance of alterations of lincRNA sequences was illustrated by the identification of a novel mutational hotspot at the KCCAT42, FENDRR, CAT1886 and STCAT2 loci at the 16q23.1-q24.3 loss. Our data confirm that the burden of SCNAs is predictive of biochemical recurrence, define nine individual regions that are associated with relapse, and highlight the possible importance of ion channel and G-protein coupled-receptor (GPCR) pathways in cancer development. We concluded that a two-hit genetic model accounts for about one third of SCNA indicating that mechanisms, such haploinsufficiency and epigenetic inactivation, account for the remaining SCNA losses.
We acknowledge support from Cancer Research UK (C5047/A22530, C309/A11566, C368/A6743, A368/A7990, C14303/A17197) and the Dallaglio Foundation. We also acknowledge support from the National Institute of Health Research (NIHR) (The Biomedical Research Centre at The Institute of Cancer Research & The Royal Marsden NHS Foundation Trust and the project "Prostate Cancer: Mechanisms of Progression and Treatment (PROMPT)" [G0500966/75466]). We thank the Wellcome Trust, Bob Champion Cancer Trust, The Orchid Cancer appeal, The RoseTrees Trust, The North West Cancer Research Fund, Big C, The King family, and The Masonic Charitable Foundation for funding. This research is supported by the Francis Crick Institute which receives its core funding from Cancer Research UK (FC001202), the UK Medical Research Council (FC001202), and the Wellcome Trust (FC001202).
2017-09-25T00:00:00ZCamacho, NiedzicaVan Loo, PeterEdwards, SandraKay, Jonathan D.Matthews, LucyHaase, KerstinClark, JeremyDennis, NeningThomas, SarahKremeyer, BarbaraZamora, JorgeButler, Adam P.Gundem, GunesMerson, SueLuxton, HayleyHawkins, SteveGhori, MohammedMarsden, LukeLambert, AdamKaraszi, KatalinPelvender, GillMassie, Charlie E.Kote-Jarai, ZSofiaRaine, KeiranJones, DavidHowat, William J.Hazell, StevenLivni, NaomiFisher, CyrilOgden, ChristopherKumar, PardeepThompson, AlanNicol, DavidMayer, ErikDudderidge, TimYu, YongweiZhang, HongweiShah, Nimish C.Gnanapragasam, Vincent J.Group, The CRUK-ICGC ProstateIsaacs, WilliamVisakorpi, TapioHamdy, FreddieBerney, DanVerrill, ClareWarren, Anne Y.Wedge, David C.Lynch, Andrew G.Foster, Christopher S.Lu, Yong JieBova, G. StevenWhitaker, Hayley C.McDermott, UltanNeal, David E.Eeles, RosalindCooper, Colin S.Brewer, Daniel S.A variety of models have been proposed to explain regions of recurrent somatic copy number alteration (SCNA) in human cancer. Our study employs Whole Genome DNA Sequence (WGS) data from tumor samples (n = 103) to comprehensively assess the role of the Knudson two hit genetic model in SCNA generation in prostate cancer. 64 recurrent regions of loss and gain were detected, of which 28 were novel, including regions of loss with more than 15% frequency at Chr4p15.2-p15.1 (15.53%), Chr6q27 (16.50%) and Chr18q12.3 (17.48%). Comprehensive mutation screens of genes, lincRNA encoding sequences, control regions and conserved domains within SCNAs demonstrated that a two-hit genetic model was supported in only a minor proportion of recurrent SCNA losses examined (15/40). We found that recurrent breakpoints and regions of inversion often occur within Knudson model SCNAs, leading to the identification of ZNF292 as a target gene for the deletion at 6q14.3-q15 and NKX3.1 as a two-hit target at 8p21.3-p21.2. The importance of alterations of lincRNA sequences was illustrated by the identification of a novel mutational hotspot at the KCCAT42, FENDRR, CAT1886 and STCAT2 loci at the 16q23.1-q24.3 loss. Our data confirm that the burden of SCNAs is predictive of biochemical recurrence, define nine individual regions that are associated with relapse, and highlight the possible importance of ion channel and G-protein coupled-receptor (GPCR) pathways in cancer development. We concluded that a two-hit genetic model accounts for about one third of SCNA indicating that mechanisms, such haploinsufficiency and epigenetic inactivation, account for the remaining SCNA losses.On the star-height of subword counting languages and their relationship to Rees zero-matrix semigroupsBourne, TomRuškuc, Nikhttp://hdl.handle.net/10023/118112018-01-07T03:49:18Z2016-11-15T00:00:00ZGiven a word w over a finite alphabet, we consider, in three special cases, the generalised star-height of the languages in which w occurs as a contiguous subword (factor) an exact number of times and of the languages in which w occurs as a contiguous subword modulo a fixed number, and prove that in each case it is at most one. We use these combinatorial results to show that any language recognised by a Rees (zero-)matrix semigroup over an abelian group is of generalised star-height at most one.
2016-11-15T00:00:00ZBourne, TomRuškuc, NikGiven a word w over a finite alphabet, we consider, in three special cases, the generalised star-height of the languages in which w occurs as a contiguous subword (factor) an exact number of times and of the languages in which w occurs as a contiguous subword modulo a fixed number, and prove that in each case it is at most one. We use these combinatorial results to show that any language recognised by a Rees (zero-)matrix semigroup over an abelian group is of generalised star-height at most one.Vortex merger near a topographic slope in a homogeneous rotating fluidCarton, XavierMorvan, MathieuReinaud, Jean NoelSokolovskiy, MikhailL'Hégaret, PierreVic, Clémenthttp://hdl.handle.net/10023/117792018-06-03T00:39:14Z2017-10-01T00:00:00ZThe effect of a bottom slope on the merger of two identical Rankine vortices is investigated in a two dimensional, quasi-geostrophic, incompressible fluid. When two cyclones initially lie parallel to the slope, and more than two vortex diameters away from the slope, the critical merger distance is unchanged. When the cyclones are closer to the slope, they can merge at larger distances, but they lose more mass into filaments, thus weakening the efficiency of merger. Several effects account for this: the topographic Rossby wave advects the cyclones, reduces their mutual distance and deforms them. This along shelf wave breaks into filaments and into secondary vortices which shear out the initial cyclones. The global motion of fluid towards the shallow domain and the erosion of the two cyclones are confirmed by the evolution of particles seeded both in the cyclone sand near the topographic slope. The addition of tracer to the flow indicates that diffusion is ballistic at early times. For two anticyclones, merger is also facilitated because one vortex is ejected offshore towards the other, via coupling with a topographic cyclone. Again two anticyclones can merge at large distance but they are eroded in the process. Finally, for taller topographies, the critical merger distance is again increased and the topographic influence can scatter or completely erode one of the two initial cyclones. Conclusions are drawn on possible improvements of the model configuration for an application to the ocean.
This work is a contribution to the PHYSINDIEN research program. It was supported by CNRS-RFBR contract PRC 1069/16-55-150001.
2017-10-01T00:00:00ZCarton, XavierMorvan, MathieuReinaud, Jean NoelSokolovskiy, MikhailL'Hégaret, PierreVic, ClémentThe effect of a bottom slope on the merger of two identical Rankine vortices is investigated in a two dimensional, quasi-geostrophic, incompressible fluid. When two cyclones initially lie parallel to the slope, and more than two vortex diameters away from the slope, the critical merger distance is unchanged. When the cyclones are closer to the slope, they can merge at larger distances, but they lose more mass into filaments, thus weakening the efficiency of merger. Several effects account for this: the topographic Rossby wave advects the cyclones, reduces their mutual distance and deforms them. This along shelf wave breaks into filaments and into secondary vortices which shear out the initial cyclones. The global motion of fluid towards the shallow domain and the erosion of the two cyclones are confirmed by the evolution of particles seeded both in the cyclone sand near the topographic slope. The addition of tracer to the flow indicates that diffusion is ballistic at early times. For two anticyclones, merger is also facilitated because one vortex is ejected offshore towards the other, via coupling with a topographic cyclone. Again two anticyclones can merge at large distance but they are eroded in the process. Finally, for taller topographies, the critical merger distance is again increased and the topographic influence can scatter or completely erode one of the two initial cyclones. Conclusions are drawn on possible improvements of the model configuration for an application to the ocean.Emergence of spatial patterns in a mathematical model for the co-culture dynamics of epithelial-like and mesenchymal-like cellsDelitala, MarcelloLorenzi, Tommasohttp://hdl.handle.net/10023/117752018-01-07T03:43:54Z2017-02-01T00:00:00ZAccumulating evidence indicates that the interaction between epithelial and mesenchymal cells plays a pivotal role in cancer development and metastasis formation. Here we propose an integro-differential model for the co-culture dynamics of epithelial-like and mesenchymal-like cells. Our model takes into account the effects of chemotaxis, adhesive interactions between epithelial-like cells, proliferation and competition for nutrients. We present a sample of numerical results which display the emergence of spots, stripes and honeycomb patterns, depending on parameters and initial data. These simulations also suggest that epithelial-like and mesenchymal-like cells can segregate when there is little competition for nutrients. Furthermore, our computational results provide a possible explanation for how the concerted action between epithelial-cell adhesion and mesenchymal-cell spreading can precipitate the formation of ring-like structures, which resemble the fibrous capsules frequently observed in hepatic tumours.
2017-02-01T00:00:00ZDelitala, MarcelloLorenzi, TommasoAccumulating evidence indicates that the interaction between epithelial and mesenchymal cells plays a pivotal role in cancer development and metastasis formation. Here we propose an integro-differential model for the co-culture dynamics of epithelial-like and mesenchymal-like cells. Our model takes into account the effects of chemotaxis, adhesive interactions between epithelial-like cells, proliferation and competition for nutrients. We present a sample of numerical results which display the emergence of spots, stripes and honeycomb patterns, depending on parameters and initial data. These simulations also suggest that epithelial-like and mesenchymal-like cells can segregate when there is little competition for nutrients. Furthermore, our computational results provide a possible explanation for how the concerted action between epithelial-cell adhesion and mesenchymal-cell spreading can precipitate the formation of ring-like structures, which resemble the fibrous capsules frequently observed in hepatic tumours.Spatio-temporal models of synthetic genetic oscillatorsMacnamara, Cicely K.Chaplain, Mark A. J.http://hdl.handle.net/10023/117742018-05-06T00:35:05Z2017-02-01T00:00:00ZSignal transduction pathways play a major role in many important aspects of cellular function e.g. cell division, apoptosis. One important class of signal transduction pathways is gene regulatory networks (GRNs). In many GRNs, proteins bind to gene sites in the nucleus thereby altering the transcription rate. Such proteins are known as transcription factors. If the binding reduces the transcription rate there is a negative feedback leading to oscillatory behaviour in mRNA and protein levels, both spatially (e.g. by observing fluorescently labelled molecules in single cells) and temporally (e.g. by observing protein/mRNA levels over time). Recent computational modelling has demonstrated that spatial movement of the molecules is a vital component of GRNs and may cause the oscillations. These numerical findings have subsequently been proved rigorously i.e. the diffusion coefficient of the protein/mRNA acts as a bifurcation parameter and gives rise to a Hopf bifurcation. In this paper we first present a model of the canonical GRN (the Hes1 protein) and show the effect of varying the spatial location of gene and protein production sites on the oscillations. We then extend the approach to examine spatio-temporal models of synthetic gene regulatory networks e.g. n-gene repressilators and activator-repressor systems.
2017-02-01T00:00:00ZMacnamara, Cicely K.Chaplain, Mark A. J.Signal transduction pathways play a major role in many important aspects of cellular function e.g. cell division, apoptosis. One important class of signal transduction pathways is gene regulatory networks (GRNs). In many GRNs, proteins bind to gene sites in the nucleus thereby altering the transcription rate. Such proteins are known as transcription factors. If the binding reduces the transcription rate there is a negative feedback leading to oscillatory behaviour in mRNA and protein levels, both spatially (e.g. by observing fluorescently labelled molecules in single cells) and temporally (e.g. by observing protein/mRNA levels over time). Recent computational modelling has demonstrated that spatial movement of the molecules is a vital component of GRNs and may cause the oscillations. These numerical findings have subsequently been proved rigorously i.e. the diffusion coefficient of the protein/mRNA acts as a bifurcation parameter and gives rise to a Hopf bifurcation. In this paper we first present a model of the canonical GRN (the Hes1 protein) and show the effect of varying the spatial location of gene and protein production sites on the oscillations. We then extend the approach to examine spatio-temporal models of synthetic gene regulatory networks e.g. n-gene repressilators and activator-repressor systems.The eruption of a small-scale emerging flux rope as the driver of an M-class flare and of a coronal mass ejectionYan, X. L.Jiang, C. W.Xue, Z. K.Wang, J. C.Priest, E. R.Yang, L. H.Kong, D. F.Cao, W. D.Ji, H. S.http://hdl.handle.net/10023/117612018-06-24T00:40:43Z2017-08-10T00:00:00ZSolar flares and coronal mass ejections are the most powerful explosions in the Sun. They are major sources of potentially destructive space weather conditions. However, the possible causes of their initiation remain controversial. Using high-resolution data observed by the New Solar Telescope of Big Bear Solar Observatory, supplemented by Solar Dynamics Observatory observations, we present unusual observations of a small-scale emerging flux rope near a large sunspot, whose eruption produced an M-class flare and a coronal mass ejection. The presence of the small-scale flux rope was indicated by static nonlinear force-free field extrapolation as well as data-driven magnetohydrodynamics modeling of the dynamic evolution of the coronal three-dimensional magnetic field. During the emergence of the flux rope, rotation of satellite sunspots at the footpoints of the flux rope was observed. Meanwhile, the Lorentz force, magnetic energy, vertical current, and transverse fields were increasing during this phase. The free energy from the magnetic flux emergence and twisting magnetic fields is sufficient to power the M-class flare. These observations present, for the first time, the complete process, from the emergence of the small-scale flux rope, to the production of solar eruptions.
This work is sponsored by the National Science Foundation of China (NSFC) under the grant numbers 11373066, 11603071, 11503080, 11633008, 11533008, by the Key Laboratory of Solar Activity of CAS under numbers KLSA201603, KLSA201508, by the Yunnan Science Foundation of China under number 2013FB086, CAS "Light of West China" Program, by the Youth Innovation Promotion Association CAS (No.2011056), and the national basic research program of China (973 program, 2011CB811400). The BBSO operation is supported by NJIT, US NSF AGS-1250818, and NASA NNX13AG14G grants, and the NST operation is partly supported by the Korea Astronomy and Space Science Institute and Seoul National University and by the strategic priority research program of CAS with Grant No. XDB09000000.
2017-08-10T00:00:00ZYan, X. L.Jiang, C. W.Xue, Z. K.Wang, J. C.Priest, E. R.Yang, L. H.Kong, D. F.Cao, W. D.Ji, H. S.Solar flares and coronal mass ejections are the most powerful explosions in the Sun. They are major sources of potentially destructive space weather conditions. However, the possible causes of their initiation remain controversial. Using high-resolution data observed by the New Solar Telescope of Big Bear Solar Observatory, supplemented by Solar Dynamics Observatory observations, we present unusual observations of a small-scale emerging flux rope near a large sunspot, whose eruption produced an M-class flare and a coronal mass ejection. The presence of the small-scale flux rope was indicated by static nonlinear force-free field extrapolation as well as data-driven magnetohydrodynamics modeling of the dynamic evolution of the coronal three-dimensional magnetic field. During the emergence of the flux rope, rotation of satellite sunspots at the footpoints of the flux rope was observed. Meanwhile, the Lorentz force, magnetic energy, vertical current, and transverse fields were increasing during this phase. The free energy from the magnetic flux emergence and twisting magnetic fields is sufficient to power the M-class flare. These observations present, for the first time, the complete process, from the emergence of the small-scale flux rope, to the production of solar eruptions.Open population maximum likelihood spatial capture-recaptureGlennie, RichardBorchers, David LouisMurchie, MatthewHarmsen, BartFoster, Rebeccahttp://hdl.handle.net/10023/117582018-06-16T23:32:12Z2017-09-04T00:00:00ZOpen population capture-recapture models are widely used to estimate population demographics and abundance over time. Bayesian methods exist to incorporate open population modelling with spatial capture-recapture, allowing for estimation ofthe effective area sampled and population density. Here, open population spatial capture-recapture, both Cormack-Jolly-Seber and Jolly-Seber models, is formulated as a hidden Markov model, allowing inference by maximum likelihood. The method is applied to a twelve-year survey of male jaguars (Panthera onca) in the Cockscomb Wildlife Sanctuary Basin, Belize, to estimate the apparent survival and population abundance over time. The hidden Markov model approach is compared with Bayesian data augmentation, demonstrating it to be substantially more efficient. A simulation study shows maximum likelihood inference to be negligibly biased for small sample sizes and recapture rates.
2017-09-04T00:00:00ZGlennie, RichardBorchers, David LouisMurchie, MatthewHarmsen, BartFoster, RebeccaOpen population capture-recapture models are widely used to estimate population demographics and abundance over time. Bayesian methods exist to incorporate open population modelling with spatial capture-recapture, allowing for estimation ofthe effective area sampled and population density. Here, open population spatial capture-recapture, both Cormack-Jolly-Seber and Jolly-Seber models, is formulated as a hidden Markov model, allowing inference by maximum likelihood. The method is applied to a twelve-year survey of male jaguars (Panthera onca) in the Cockscomb Wildlife Sanctuary Basin, Belize, to estimate the apparent survival and population abundance over time. The hidden Markov model approach is compared with Bayesian data augmentation, demonstrating it to be substantially more efficient. A simulation study shows maximum likelihood inference to be negligibly biased for small sample sizes and recapture rates.Incorporating animal movement into distance samplingGlennie, RichardBuckland, Stephen TerrenceLangrock, RolandGerrodette, TimBallance, LisaChivers, SusanScott, MichaelPerrin, Williamhttp://hdl.handle.net/10023/117572018-06-02T23:33:02Z2017-09-08T00:00:00ZDistance sampling is a popular statistical method to estimate the density of wild animal populations. Conventional distance sampling represents animals as fixed points in space that are detected with an unknown probability that depends on the distance between the observer and the animal. Animal movement, responsive or non-responsive to the observer, can cause substantial bias in density estimation. Methods to correct for responsive animal movement exist, but none account for non-responsive movement independent of the observer. Here, an explicit animal movement model is incorporated into distance sampling, combining distance sampling survey data with independently obtained animal telemetry data.A detection probability that depends on the entire unobserved path the animal travels is derived in continuous space-time. The intractable integration overall possible animal paths is approximated by a hidden Markov model. A simulation study shows the method to be negligibly biased (less than 5%) in scenarios where conventional distance sampling overestimates abundance by up to 100%.The method is applied to a line transect survey of spotted dolphins (Stenella attenuata attenuata) in the eastern tropical Pacific.
2017-09-08T00:00:00ZGlennie, RichardBuckland, Stephen TerrenceLangrock, RolandGerrodette, TimBallance, LisaChivers, SusanScott, MichaelPerrin, WilliamDistance sampling is a popular statistical method to estimate the density of wild animal populations. Conventional distance sampling represents animals as fixed points in space that are detected with an unknown probability that depends on the distance between the observer and the animal. Animal movement, responsive or non-responsive to the observer, can cause substantial bias in density estimation. Methods to correct for responsive animal movement exist, but none account for non-responsive movement independent of the observer. Here, an explicit animal movement model is incorporated into distance sampling, combining distance sampling survey data with independently obtained animal telemetry data.A detection probability that depends on the entire unobserved path the animal travels is derived in continuous space-time. The intractable integration overall possible animal paths is approximated by a hidden Markov model. A simulation study shows the method to be negligibly biased (less than 5%) in scenarios where conventional distance sampling overestimates abundance by up to 100%.The method is applied to a line transect survey of spotted dolphins (Stenella attenuata attenuata) in the eastern tropical Pacific.Title redactedSharifi Far, Servehhttp://hdl.handle.net/10023/117392017-09-25T14:47:04Z2017-12-07T00:00:00Z2017-12-07T00:00:00ZSharifi Far, ServehInteraction between a surface quasi-geostrophic buoyancy filament and an internal vortexReinaud, Jean NoelDritschel, David GerardCarton, Xavierhttp://hdl.handle.net/10023/117272018-05-20T00:34:05Z2016-09-23T00:00:00ZThis paper focuses on the nonlinear interaction between a surface quasi-geostrophic buoyancy filament and an internal vortex. We first revisit the stability of an isolated buoyancy filament. The buoyancy profile considered is continuous and leads to a continuous velocity field, albeit one with infinite shear just outside its edge. The stability properties of an isolated filament help to interpret the unsteady interaction with a sub-surface (internal) vortex studied next. We find that, in all cases, the filament breaks into billows, analogous in form to those occurring in Kelvin-Helmholtz shear instability. For intense buoyancy filaments, the vortex itself may undergo strong deformations, including being split into several pieces. Generally, the nonlinear interaction causes both the filament and the vortex to lose their respective ‘self’-energies to the energy of interaction. The flow evolution depends sensitively on whether the vertical vorticity of the filament and the vortex have the same or opposite signs — termed “cooperative” and “adverse” shear respectively. In cooperative shear, the filament rolls up into a coherent surface eddy above a vortex initially placed below it, whereas in adverse shear, buoyancy is expelled above the vortex. Although sufficiently great shear induced by the buoyancy filament may split the vortex in both cases, adverse shear is significantly more destructive.
2016-09-23T00:00:00ZReinaud, Jean NoelDritschel, David GerardCarton, XavierThis paper focuses on the nonlinear interaction between a surface quasi-geostrophic buoyancy filament and an internal vortex. We first revisit the stability of an isolated buoyancy filament. The buoyancy profile considered is continuous and leads to a continuous velocity field, albeit one with infinite shear just outside its edge. The stability properties of an isolated filament help to interpret the unsteady interaction with a sub-surface (internal) vortex studied next. We find that, in all cases, the filament breaks into billows, analogous in form to those occurring in Kelvin-Helmholtz shear instability. For intense buoyancy filaments, the vortex itself may undergo strong deformations, including being split into several pieces. Generally, the nonlinear interaction causes both the filament and the vortex to lose their respective ‘self’-energies to the energy of interaction. The flow evolution depends sensitively on whether the vertical vorticity of the filament and the vortex have the same or opposite signs — termed “cooperative” and “adverse” shear respectively. In cooperative shear, the filament rolls up into a coherent surface eddy above a vortex initially placed below it, whereas in adverse shear, buoyancy is expelled above the vortex. Although sufficiently great shear induced by the buoyancy filament may split the vortex in both cases, adverse shear is significantly more destructive.Particle acceleration with anomalous pitch angle scattering in 2D magnetohydrodynamic reconnection simulationsBorissov, AlexeiKontar, EduardThrelfall, James WilliamNeukirch, Thomashttp://hdl.handle.net/10023/117142018-01-07T04:03:59Z2017-09-01T00:00:00ZThe conversion of magnetic energy into other forms (such as plasma heating, bulk plasma flows, and non-thermal particles) during solar flares is one of the outstanding open problems in solar physics. It is generally accepted that magnetic reconnection plays a crucialrole in these conversion processes. In order to achieve the rapid energy release required in solar flares, an anomalous resistivity, which is orders of magnitude higher than the Spitzer resistivity, is often used in magnetohydrodynamic (MHD) simulations of reconnection in the corona. The origin of Spitzer resistivity is based on Coulomb scattering, which becomes negligible at the high energies achieved by accelerated particles. As a result, simulations of particle acceleration in reconnection events are often performed in the absence of any interaction between accelerated particles and any background plasma. This need not be the case for scattering associated with anomalous resistivity caused by turbulence within solar flares, as the higher resistivity implies an elevated scattering rate. We present results of test particle calculations, with and without pitch angle scattering, subject to fields derived from MHD simulations of two-dimensional (2D) X-point reconnection. Scattering rates proportional to the ratio of the anomalous resistivity to the local Spitzer resistivity, as well as at fixed values, are considered. Pitch angle scattering, which is independent of the anomalous resistivity, causes higher maximum energies in comparison to those obtained without scattering. Scattering rates which are dependent on the local anomalous resistivity tend to produce fewer highly energised particles due to weaker scattering in the separatrices, even though scattering in the current sheet may be stronger when compared to resistivity-independent scattering. Strong scattering also causes an increase in the number of particles exiting the computational box in the reconnection outflow region, as opposed to along the separatrices as is the case in the absence of scattering.
A.B. would like to thank the University of St Andrews for financial support from the 7th Century Scholarship and the Scottish Government for support from the Saltire Scholarship. E.P.K.’s work is partially supported by a STFC consolidated grant ST/L000741/1. J.T. and T.N. gratefully acknowledge the support of the UK STFC (consolidated grant SN/N000609/1).
2017-09-01T00:00:00ZBorissov, AlexeiKontar, EduardThrelfall, James WilliamNeukirch, ThomasThe conversion of magnetic energy into other forms (such as plasma heating, bulk plasma flows, and non-thermal particles) during solar flares is one of the outstanding open problems in solar physics. It is generally accepted that magnetic reconnection plays a crucialrole in these conversion processes. In order to achieve the rapid energy release required in solar flares, an anomalous resistivity, which is orders of magnitude higher than the Spitzer resistivity, is often used in magnetohydrodynamic (MHD) simulations of reconnection in the corona. The origin of Spitzer resistivity is based on Coulomb scattering, which becomes negligible at the high energies achieved by accelerated particles. As a result, simulations of particle acceleration in reconnection events are often performed in the absence of any interaction between accelerated particles and any background plasma. This need not be the case for scattering associated with anomalous resistivity caused by turbulence within solar flares, as the higher resistivity implies an elevated scattering rate. We present results of test particle calculations, with and without pitch angle scattering, subject to fields derived from MHD simulations of two-dimensional (2D) X-point reconnection. Scattering rates proportional to the ratio of the anomalous resistivity to the local Spitzer resistivity, as well as at fixed values, are considered. Pitch angle scattering, which is independent of the anomalous resistivity, causes higher maximum energies in comparison to those obtained without scattering. Scattering rates which are dependent on the local anomalous resistivity tend to produce fewer highly energised particles due to weaker scattering in the separatrices, even though scattering in the current sheet may be stronger when compared to resistivity-independent scattering. Strong scattering also causes an increase in the number of particles exiting the computational box in the reconnection outflow region, as opposed to along the separatrices as is the case in the absence of scattering.Spatio-temporal variation in click production rates of beaked whales : implications for passive acoustic density estimationWarren, Victoria E.Marques, Tiago A.Harris, DanielleThomas, LenTyack, Peter L.Aguilar de Soto, NatachaHickmott, Leigh S.Johnson, Mark P.http://hdl.handle.net/10023/117122018-06-03T00:38:38Z2017-03-01T00:00:00ZPassive acoustic monitoring has become an increasingly prevalent tool for estimating density of marine mammals, such as beaked whales, which vocalize often but are difficult to survey visually. Counts of acoustic cues (e.g., vocalizations), when corrected for detection probability, can be translated into animal density estimates by applying an individual cue production rate multiplier. It is essential to understand variation in these rates to avoid biased estimates. The most direct way to measure cue production rate is with animal-mounted acoustic recorders. This study utilized data from sound recording tags deployed on Blainville's (Mesoplodon densirostris, 19 deployments) and Cuvier's (Ziphius cavirostris, 16 deployments) beaked whales, in two locations per species, to explore spatial and temporal variation in click production rates. No spatial or temporal variation was detected within the average click production rate of Blainville's beaked whales when calculated over dive cycles (including silent periods between dives); however, spatial variation was detected when averaged only over vocal periods. Cuvier's beaked whales exhibited significant spatial and temporal variation in click production rates within vocal periods and when silent periods were included. This evidence of variation emphasizes the need to utilize appropriate cue production rates when estimating density from passive acoustic data.
T.A.M. was funded under Grant No. N000141010382 from the Office of Naval Research (LATTE project) and thanks support by CEAUL (funded by FCT - Fundação para a Ciência e a Tecnologia, Portugal, through the project UID/MAT/00006/2013). M.P.J. was funded by a Marie Curie Career Integration Grant and M.P.J. and P.L.T. were funded by MASTS (The Marine Alliance for Science and Technology for Scotland, a research pooling initiative funded by the Scottish Funding Council under grant HR09011 and contributing institutions). L.S.H. thanks the BRS Bahamas team that helped collect the Bahamas data, and A. Bocconcelli. D.H. and L.T. were funded by the Office of Naval Research (Award No. N00014-14-1-0394). N.A.S. was funded by an EU-Horizon 2020 Marie Slodowska Curie fellowship (project ECOSOUND). DTAG data in the Canary Islands were collected with funds from the U.S. Office of Naval Research and Fundación Biodiversidad (EU project LIFE INDEMARES) with permit from the Canary Islands and Spanish governments.
2017-03-01T00:00:00ZWarren, Victoria E.Marques, Tiago A.Harris, DanielleThomas, LenTyack, Peter L.Aguilar de Soto, NatachaHickmott, Leigh S.Johnson, Mark P.Passive acoustic monitoring has become an increasingly prevalent tool for estimating density of marine mammals, such as beaked whales, which vocalize often but are difficult to survey visually. Counts of acoustic cues (e.g., vocalizations), when corrected for detection probability, can be translated into animal density estimates by applying an individual cue production rate multiplier. It is essential to understand variation in these rates to avoid biased estimates. The most direct way to measure cue production rate is with animal-mounted acoustic recorders. This study utilized data from sound recording tags deployed on Blainville's (Mesoplodon densirostris, 19 deployments) and Cuvier's (Ziphius cavirostris, 16 deployments) beaked whales, in two locations per species, to explore spatial and temporal variation in click production rates. No spatial or temporal variation was detected within the average click production rate of Blainville's beaked whales when calculated over dive cycles (including silent periods between dives); however, spatial variation was detected when averaged only over vocal periods. Cuvier's beaked whales exhibited significant spatial and temporal variation in click production rates within vocal periods and when silent periods were included. This evidence of variation emphasizes the need to utilize appropriate cue production rates when estimating density from passive acoustic data.The theoretical foundation of 3D Alfvén resonances : time dependent solutionsElsden, T.Wright, A. N.http://hdl.handle.net/10023/117062018-03-04T01:40:48Z2017-03-01T00:00:00ZWe present results from a 3D numerical simulation which investigates the coupling of fast and Alfvén magnetohydrodynamic (MHD) waves in a nonuniform dipole equilibrium. This represents the time dependent extension of the normal mode (∝ exp(−iωt)) analysis of Wright and Elsden [2016], and provides a theoretical basis for understanding 3D Alfvén resonances. Wright and Elsden [2016] show that these are fundamentally different to resonances in 1D and 2D. We demonstrate the temporal behaviour of the Alfvén resonance, which is formed within the ‘Resonant Zone’; a channel of the domain where a family of solutions exists such that the natural Alfvén frequency matches the fast mode frequency. At early times, phase mixing leads to the production of prominent ridges in the energy density, whose shape is determined by the Alfvén speed profile and the chosen background magnetic field geometry. These off resonant ridges decay in time, leaving only a main 3D resonant sheet in the steady state. We show that the width of the 3D resonance in time and in space can be accurately estimated by adapting previous analytical estimates from 1D theory. We further provide an analytical estimate for the resonance amplitude in 3D, based upon extending 2D theory.
Both authors were funded in part by STFC (through Consolidated Grant ST/N000609/1) and The Leverhulme Trust (through Research Grant RPG-2016-071).
2017-03-01T00:00:00ZElsden, T.Wright, A. N.We present results from a 3D numerical simulation which investigates the coupling of fast and Alfvén magnetohydrodynamic (MHD) waves in a nonuniform dipole equilibrium. This represents the time dependent extension of the normal mode (∝ exp(−iωt)) analysis of Wright and Elsden [2016], and provides a theoretical basis for understanding 3D Alfvén resonances. Wright and Elsden [2016] show that these are fundamentally different to resonances in 1D and 2D. We demonstrate the temporal behaviour of the Alfvén resonance, which is formed within the ‘Resonant Zone’; a channel of the domain where a family of solutions exists such that the natural Alfvén frequency matches the fast mode frequency. At early times, phase mixing leads to the production of prominent ridges in the energy density, whose shape is determined by the Alfvén speed profile and the chosen background magnetic field geometry. These off resonant ridges decay in time, leaving only a main 3D resonant sheet in the steady state. We show that the width of the 3D resonance in time and in space can be accurately estimated by adapting previous analytical estimates from 1D theory. We further provide an analytical estimate for the resonance amplitude in 3D, based upon extending 2D theory.Fine-scale harbour seal usage for informed marine spatial planningJones, Esther LaneSparling, Carol ElizabethMcConnell, Bernie JMorris, ChristopherSmout, Sophie Carolinehttp://hdl.handle.net/10023/116952018-01-07T03:57:40Z2017-09-14T00:00:00ZHigh-resolution species distribution maps are required for marine spatial planning, consenting, and licensing to assess interactions between anthropogenic activities and ecosystems. This approach can inform conservation measures for protected species and facilitate commercial developments needed for economic growth. A case study centred on Orkney, UK, is an area where concern for a declining harbour seal population has led to constraints being placed on tidal energy generation developments. Telemetry data from 54 animals tagged between 2003 and 2015 were combined with terrestrial counts from 2008 to 2015 to produce density estimation maps. Predictive habitat models using GAM-GEEs provided robust predictions in areas where telemetry data were absent, and were combined with density estimation maps. Harbour seal usage maps with confidence intervals were produced around Orkney and the North coast of Scotland. The selected habitat model showed that distance from haul out, proportion of sand in seabed sediment, and peak flow of tidal current were important predictors of space-use. Fine-scale usage maps can be used in consenting and licensing of anthropogenic developments to determine local abundance. When quantifying anthropogenic impacts through changes to species distributions, usage maps could be spatially explicitly linked to individual-based models to inform predicted movement and behaviour.
The work was funded through Scottish Government MSQ0174 contract CR/2014/11; CREEM, University of St Andrews; the National Capability fund from the Natural Environment Research Council to the Sea Mammal Research Unit (grant no. SMRU1001); and MASTS pooling initiative, which is funded by the Scottish Funding Council (grant reference HR09011).
2017-09-14T00:00:00ZJones, Esther LaneSparling, Carol ElizabethMcConnell, Bernie JMorris, ChristopherSmout, Sophie CarolineHigh-resolution species distribution maps are required for marine spatial planning, consenting, and licensing to assess interactions between anthropogenic activities and ecosystems. This approach can inform conservation measures for protected species and facilitate commercial developments needed for economic growth. A case study centred on Orkney, UK, is an area where concern for a declining harbour seal population has led to constraints being placed on tidal energy generation developments. Telemetry data from 54 animals tagged between 2003 and 2015 were combined with terrestrial counts from 2008 to 2015 to produce density estimation maps. Predictive habitat models using GAM-GEEs provided robust predictions in areas where telemetry data were absent, and were combined with density estimation maps. Harbour seal usage maps with confidence intervals were produced around Orkney and the North coast of Scotland. The selected habitat model showed that distance from haul out, proportion of sand in seabed sediment, and peak flow of tidal current were important predictors of space-use. Fine-scale usage maps can be used in consenting and licensing of anthropogenic developments to determine local abundance. When quantifying anthropogenic impacts through changes to species distributions, usage maps could be spatially explicitly linked to individual-based models to inform predicted movement and behaviour.Synthetic lethality between androgen receptor signalling and the PARP pathway in prostate cancerAsim, MohammadTarish, FirasZecchini, Heather ISanjiv, KumarGelali, EleniMassie, Charles EBaridi, AjoebWarren, Anne YZhao, WanfengOgris, ChristophMcDuffus, Leigh-AnneMascalchi, PatriceShaw, GregDev, HarveerWadhwa, KaranWijnhoven, PaulForment, Josep VLyons, Scott RLynch, Andy GO'Neill, CormacZecchini, Vincent RRennie, Paul SBaniahmad, AriaTavaré, SimonMills, Ian GGalanty, YaronCrosetto, NicolaSchultz, NiklasNeal, DavidHelleday, Thomashttp://hdl.handle.net/10023/116802018-06-24T00:40:41Z2017-08-29T00:00:00ZEmerging data demonstrate homologous recombination (HR) defects in castration-resistant prostate cancers, rendering these tumours sensitive to PARP inhibition. Here we demonstrate a direct requirement for the androgen receptor (AR) to maintain HR gene expression and HR activity in prostate cancer. We show that PARP-mediated repair pathways are upregulated in prostate cancer following androgen-deprivation therapy (ADT). Furthermore, upregulation of PARP activity is essential for the survival of prostate cancer cells and we demonstrate a synthetic lethality between ADT and PARP inhibition in vivo. Our data suggest that ADT can functionally impair HR prior to the development of castration resistance and that, this potentially could be exploited therapeutically using PARP inhibitors in combination with androgen-deprivation therapy upfront in advanced or high-risk prostate cancer.Tumours with homologous recombination (HR) defects become sensitive to PARPi. Here, the authors show that androgen receptor (AR) regulates HR and AR inhibition activates the PARP pathway in vivo, thus inhibition of both AR and PARP is required for effective treatment of high risk prostate cancer.
This study was supported by the National Cancer Research Institute (National Institute of Health Research (NIHR) Collaborative Study: ‘Prostate Cancer: Mechanisms of Progression and Treatment (PROMPT)” (grant G0500966/75466). This work was funded by a Cancer Research UK program grant (D.N.), the Swedish Research Council (T.H.), AFA insurance (T.H.), Swedish Cancer Society (T.H.), the Swedish Pain Relief Foundation (T.H.), the Torsten and Ragnar Söderberg Foundation (T.H.), AstraZeneca (T.H.) Centre for Clinical Research (CKF) (F.T.), the Västmanland Research Foundation for Cancer in Vasteras (F.T.), the Henning and Ida Persson Research Foundation (F.T.).
2017-08-29T00:00:00ZAsim, MohammadTarish, FirasZecchini, Heather ISanjiv, KumarGelali, EleniMassie, Charles EBaridi, AjoebWarren, Anne YZhao, WanfengOgris, ChristophMcDuffus, Leigh-AnneMascalchi, PatriceShaw, GregDev, HarveerWadhwa, KaranWijnhoven, PaulForment, Josep VLyons, Scott RLynch, Andy GO'Neill, CormacZecchini, Vincent RRennie, Paul SBaniahmad, AriaTavaré, SimonMills, Ian GGalanty, YaronCrosetto, NicolaSchultz, NiklasNeal, DavidHelleday, ThomasEmerging data demonstrate homologous recombination (HR) defects in castration-resistant prostate cancers, rendering these tumours sensitive to PARP inhibition. Here we demonstrate a direct requirement for the androgen receptor (AR) to maintain HR gene expression and HR activity in prostate cancer. We show that PARP-mediated repair pathways are upregulated in prostate cancer following androgen-deprivation therapy (ADT). Furthermore, upregulation of PARP activity is essential for the survival of prostate cancer cells and we demonstrate a synthetic lethality between ADT and PARP inhibition in vivo. Our data suggest that ADT can functionally impair HR prior to the development of castration resistance and that, this potentially could be exploited therapeutically using PARP inhibitors in combination with androgen-deprivation therapy upfront in advanced or high-risk prostate cancer.Tumours with homologous recombination (HR) defects become sensitive to PARPi. Here, the authors show that androgen receptor (AR) regulates HR and AR inhibition activates the PARP pathway in vivo, thus inhibition of both AR and PARP is required for effective treatment of high risk prostate cancer.Wave of chaos in a spatial eco-epidemiological system : generating realistic patterns of patchiness in rabbit-lynx dynamicsUpadhyay, RanjitRoy, ParimitaVenkataraman, C.Madzvamuse, Anotidahttp://hdl.handle.net/10023/116662018-01-07T03:47:54Z2016-11-01T00:00:00ZIn the present paper, we propose and analyse an eco-epidemiological model with diffusion to study the dynamics of rabbit populations which are consumed by lynx populations. Existence, boundedness, stability and bifurcation analyses of solutions for the proposed rabbit-lynx model are performed. Results show that in the presence of diffusion the model has the potential of exhibiting Turing instability. Numerical results (finite difference and finite element methods) reveal the existence of the wave of chaos and this appears to be a dominant mode of disease dispersal. We also show the mechanism of spatiotemporal pattern formation resulting from the Hopf bifurcation analysis, which can be a potential candidate for understanding the complex spatiotemporal dynamics of eco-epidemiological systems. Implications of the asymptotic transmission rate on disease eradication among rabbit population which in turn enhances the survival of Iberian lynx are discussed.
AM and CV would like to acknowledge support from the Engineering and Physical Sciences Research Council grant (EP/J016780/1) and the Leverhulme Trust Research Project Grant (RPG-2014-149).
2016-11-01T00:00:00ZUpadhyay, RanjitRoy, ParimitaVenkataraman, C.Madzvamuse, AnotidaIn the present paper, we propose and analyse an eco-epidemiological model with diffusion to study the dynamics of rabbit populations which are consumed by lynx populations. Existence, boundedness, stability and bifurcation analyses of solutions for the proposed rabbit-lynx model are performed. Results show that in the presence of diffusion the model has the potential of exhibiting Turing instability. Numerical results (finite difference and finite element methods) reveal the existence of the wave of chaos and this appears to be a dominant mode of disease dispersal. We also show the mechanism of spatiotemporal pattern formation resulting from the Hopf bifurcation analysis, which can be a potential candidate for understanding the complex spatiotemporal dynamics of eco-epidemiological systems. Implications of the asymptotic transmission rate on disease eradication among rabbit population which in turn enhances the survival of Iberian lynx are discussed.On the energetics of a two-layer baroclinic flowJougla, ThibaultDritschel, David Gerardhttp://hdl.handle.net/10023/116372018-01-07T03:56:59Z2017-04-01T00:00:00ZThe formation, evolution and co-existence of jets and vortices in turbulent planetary atmospheres is examined using a two-layer quasi-geostrophic β -channel shallow-water model. The study in particular focuses on the vertical structure of jets. Following Panetta & Held (J. Atmos. Sci., vol. 45 (22), 1988, pp. 3354–3365), a vertical shear arising from latitudinal heating variations is imposed on the flow and maintained by thermal damping. Idealised convection between the upper and lower layers is implemented by adding cyclonic/anti-cyclonic pairs, called hetons, to the flow, though the qualitative flow evolution is evidently not sensitive to this or other small-scale stochastic forcing. A very wide range of simulations have been conducted. A characteristic simulation which exhibits alternation between two different phases, quiescent and turbulent, is examined in detail. We study the energy transfers between different components and modes, and find the classical picture of barotropic/baroclinic energy transfers to be too simplistic. We also discuss the dependence on thermal damping and on the imposed vertical shear. Both have a strong influence on the flow evolution. Thermal damping is a major factor affecting the stability of the flow while vertical shear controls the number of jets in the domain, qualitatively through the Rhines scale LRh = √U/β.
2017-04-01T00:00:00ZJougla, ThibaultDritschel, David GerardThe formation, evolution and co-existence of jets and vortices in turbulent planetary atmospheres is examined using a two-layer quasi-geostrophic β -channel shallow-water model. The study in particular focuses on the vertical structure of jets. Following Panetta & Held (J. Atmos. Sci., vol. 45 (22), 1988, pp. 3354–3365), a vertical shear arising from latitudinal heating variations is imposed on the flow and maintained by thermal damping. Idealised convection between the upper and lower layers is implemented by adding cyclonic/anti-cyclonic pairs, called hetons, to the flow, though the qualitative flow evolution is evidently not sensitive to this or other small-scale stochastic forcing. A very wide range of simulations have been conducted. A characteristic simulation which exhibits alternation between two different phases, quiescent and turbulent, is examined in detail. We study the energy transfers between different components and modes, and find the classical picture of barotropic/baroclinic energy transfers to be too simplistic. We also discuss the dependence on thermal damping and on the imposed vertical shear. Both have a strong influence on the flow evolution. Thermal damping is a major factor affecting the stability of the flow while vertical shear controls the number of jets in the domain, qualitatively through the Rhines scale LRh = √U/β.Self-similar sets: projections, sections and percolationFalconer, Kenneth JohnJin, Xionghttp://hdl.handle.net/10023/116292018-01-07T03:13:34Z2017-01-01T00:00:00ZWe survey some recent results on the dimension of orthogonal projections of self-similar sets and of random subsets obtained by percolation on self-similar sets. In particular we highlight conditions when the dimension of the projections takes the generic value for all, or very nearly all, projections. We then describe a method for deriving dimensional properties of sections of deterministic self-similar sets by utilising projection properties of random percolation subsets.
2017-01-01T00:00:00ZFalconer, Kenneth JohnJin, XiongWe survey some recent results on the dimension of orthogonal projections of self-similar sets and of random subsets obtained by percolation on self-similar sets. In particular we highlight conditions when the dimension of the projections takes the generic value for all, or very nearly all, projections. We then describe a method for deriving dimensional properties of sections of deterministic self-similar sets by utilising projection properties of random percolation subsets.Exact Vlasov-Maxwell equilibria for asymmetric current sheetsAllanson, O.Wilson, F.Neukirch, T.Liu, Yi-HsinHodgson, J. D. B.http://hdl.handle.net/10023/116262018-01-07T04:04:19Z2017-09-16T00:00:00ZThe NASA Magnetospheric Multiscale mission has made in-situ diffusion region and kinetic-scale resolution measurements of asymmetric magnetic reconnection for the first time [Burch et al., 2016], in the Earth’s magnetopause. The principal theoretical tool currently used to model collisionless asymmetric reconnection is particle-in-cell simulations. Many particle-in-cell simulations of asymmetric collisionless reconnection start from an asymmetric Harris-type magnetic field, but with distribution functions that are not exact equilibrium solutions of the Vlasov equation. We present new and exact equilibrium solutions of the Vlasov-Maxwell system that are self-consistent with one-dimensional asymmetric current sheets, with an asymmetric Harris-type magnetic field profile, plus a constant non-zero guide field. The distribution functions can be represented as a combination of four shifted Maxwellian distribution functions. This equilibrium describes a magnetic field configuration with more freedom than the previously known exact solution [Alpers, 1969], and has different bulk flow properties.
Funding: Science and Technology Facilities Council Consolidated Grant Nos. ST/K000950/1 and ST/N000609/1 (O.A., T.N., J.D.B.H.and F.W.), the Science and Technology Facilities Council Doctoral Training Grant No. ST/K502327/1 (O.A. and J.D.B.H), the Natural Environment Research Council Grant No. NE/P017274/1 (Rad-Sat) (O.A.)
2017-09-16T00:00:00ZAllanson, O.Wilson, F.Neukirch, T.Liu, Yi-HsinHodgson, J. D. B.The NASA Magnetospheric Multiscale mission has made in-situ diffusion region and kinetic-scale resolution measurements of asymmetric magnetic reconnection for the first time [Burch et al., 2016], in the Earth’s magnetopause. The principal theoretical tool currently used to model collisionless asymmetric reconnection is particle-in-cell simulations. Many particle-in-cell simulations of asymmetric collisionless reconnection start from an asymmetric Harris-type magnetic field, but with distribution functions that are not exact equilibrium solutions of the Vlasov equation. We present new and exact equilibrium solutions of the Vlasov-Maxwell system that are self-consistent with one-dimensional asymmetric current sheets, with an asymmetric Harris-type magnetic field profile, plus a constant non-zero guide field. The distribution functions can be represented as a combination of four shifted Maxwellian distribution functions. This equilibrium describes a magnetic field configuration with more freedom than the previously known exact solution [Alpers, 1969], and has different bulk flow properties.Spatial variation in boundary conditions can govern selection and location of eyespots in butterfly wingsVenkataraman, ChandrasekharSekimura, Toshiohttp://hdl.handle.net/10023/116182018-02-11T01:36:19Z2017-01-01T00:00:00ZDespite being the subject of widespread study, many aspects of the development of eyespot patterns in butterfly wings remain poorly understood. In this work, we examine, through numerical simulations, a mathematical model for eyespot focus point formation in which a reaction-diffusion system is assumed to play the role of the patterning mechanism. In the model, changes in the boundary conditions at the veins at the proximal boundary alone are capable of determining whether or not an eyespot focus forms in a given wing cell and the eventual position of focus points within the wing cell. Furthermore, an auxiliary surface reaction diffusion system posed along the entire proximal boundary of the wing cells is proposed as the mechanism that generates the necessary changes in the proximal boundary profiles. In order to illustrate the robustness of the model, we perform simulations on a curved wing geometry that is somewhat closer to a biological realistic domain than the rectangular wing cells previously considered, and we also illustrate the ability of the model to reproduce experimental results on artificial selection of eyespots.
2017-01-01T00:00:00ZVenkataraman, ChandrasekharSekimura, ToshioDespite being the subject of widespread study, many aspects of the development of eyespot patterns in butterfly wings remain poorly understood. In this work, we examine, through numerical simulations, a mathematical model for eyespot focus point formation in which a reaction-diffusion system is assumed to play the role of the patterning mechanism. In the model, changes in the boundary conditions at the veins at the proximal boundary alone are capable of determining whether or not an eyespot focus forms in a given wing cell and the eventual position of focus points within the wing cell. Furthermore, an auxiliary surface reaction diffusion system posed along the entire proximal boundary of the wing cells is proposed as the mechanism that generates the necessary changes in the proximal boundary profiles. In order to illustrate the robustness of the model, we perform simulations on a curved wing geometry that is somewhat closer to a biological realistic domain than the rectangular wing cells previously considered, and we also illustrate the ability of the model to reproduce experimental results on artificial selection of eyespots.Force-free collisionless current sheet models with non-uniform temperature and density profilesWilson, FionaNeukirch, ThomasAllanson, Oliver Douglashttp://hdl.handle.net/10023/116142018-01-07T04:04:03Z2017-08-17T00:00:00ZWe present a class of one-dimensional, strictly neutral, Vlasov-Maxwell equilibrium distribution functions for force-free current sheets, with magnetic fields defined in terms of Jacobian elliptic functions, extending the results of Abraham-Shrauner48 to allow for non-uniform density and temperature pro les. To achieve this, we use an approach previously applied to the force-free Harris sheet by Kolotkov et al.49. In one limit of the parameters, we recover the model of Kolotkov et al.49, while another limit gives a linear force-free field. We discuss conditions on the parameters such that the distribution functions are always positive, and give expressions for the pressure, density, temperature and bulk- ow velocities of the equilibrium, discussing differences from previous models. We also present some illustrative plots of the distribution function in velocity space.
The authors acknowledge the support of the Science and Technology Facilities Council via the consolidated grants ST/K000950/1 and ST/N000609/1 and the doctoral training grant ST/K502327/1 (O. A.), and the Natural Environment Research Council via grant no. NE/P017274/1 (Rad-Sat) (O. A.). F. W. and T. N. would also like to thank the University of St Andrews for general financial support
2017-08-17T00:00:00ZWilson, FionaNeukirch, ThomasAllanson, Oliver DouglasWe present a class of one-dimensional, strictly neutral, Vlasov-Maxwell equilibrium distribution functions for force-free current sheets, with magnetic fields defined in terms of Jacobian elliptic functions, extending the results of Abraham-Shrauner48 to allow for non-uniform density and temperature pro les. To achieve this, we use an approach previously applied to the force-free Harris sheet by Kolotkov et al.49. In one limit of the parameters, we recover the model of Kolotkov et al.49, while another limit gives a linear force-free field. We discuss conditions on the parameters such that the distribution functions are always positive, and give expressions for the pressure, density, temperature and bulk- ow velocities of the equilibrium, discussing differences from previous models. We also present some illustrative plots of the distribution function in velocity space.Inference from randomized (factorial) experimentsBailey, Rosemary Annehttp://hdl.handle.net/10023/116062018-04-06T12:30:11Z2017-01-01T00:00:00ZThis is a contribution to the discussion of the interesting paper by Ding [Statist. Sci. 32 (2017) 331–345], which contrasts approaches attributed to Neyman and Fisher. I believe that Fisher’s usual assumption was unit-treatment additivity, rather than the “sharp null hypothesis” attributed to him. Fisher also developed the notion of interaction in factorial experiments. His explanation leads directly to the concept of marginality, which is essential for the interpretation of data from any factorial experiment.
2017-01-01T00:00:00ZBailey, Rosemary AnneThis is a contribution to the discussion of the interesting paper by Ding [Statist. Sci. 32 (2017) 331–345], which contrasts approaches attributed to Neyman and Fisher. I believe that Fisher’s usual assumption was unit-treatment additivity, rather than the “sharp null hypothesis” attributed to him. Fisher also developed the notion of interaction in factorial experiments. His explanation leads directly to the concept of marginality, which is essential for the interpretation of data from any factorial experiment.Near-complete external difference familiesDavis, James A.Huczynska, SophieMullen, Gary L.http://hdl.handle.net/10023/115762018-04-08T00:42:42Z2017-09-01T00:00:00ZWe introduce and explore near-complete external difference families, a partitioning of the nonidentity elements of a group so that each nonidentity element is expressible as a difference of elements from distinct subsets a fixed number of times. We show that the existence of such an object implies the existence of a near-resolvable design. We provide examples and general constructions of these objects, some of which lead to new parameter families of near-resolvable designs on a non-prime-power number of points. Our constructions employ cyclotomy, partial difference sets, and Galois rings.
2017-09-01T00:00:00ZDavis, James A.Huczynska, SophieMullen, Gary L.We introduce and explore near-complete external difference families, a partitioning of the nonidentity elements of a group so that each nonidentity element is expressible as a difference of elements from distinct subsets a fixed number of times. We show that the existence of such an object implies the existence of a near-resolvable design. We provide examples and general constructions of these objects, some of which lead to new parameter families of near-resolvable designs on a non-prime-power number of points. Our constructions employ cyclotomy, partial difference sets, and Galois rings.Genomic evolution of breast cancer metastasis and relapseYates, Lucy R.Knappskog, StianWedge, DavidFarmery, James H. R.Gonzalez, SantiagoMartincorena, InigoAlexandrov, Ludmil B.Van Loo, PeterHaugland, Hans KristianLilleng, Peer KaareGundem, GunesGerstung, MoritzPappaemmanuil, ElliGazinska, PatrycjaBhosle, Shriram GJones, DavidRaine, KeiranMudie, LauraLatimer, CalliSawyer, ElinorDesmedt, ChristineSotiriou, ChristosStratton, Michael R.Sieuwerts, Anieta M.Lynch, Andy G.Martens, John W.Richardson, Andrea L.Tutt, AndrewLønning, Per EysteinCampbell, Peter J.http://hdl.handle.net/10023/115532018-06-24T00:40:39Z2017-08-14T00:00:00ZPatterns of genomic evolution between primary and metastatic breast cancer have not been studied in large numbers, despite patients with metastatic breast cancer having dismal survival. We sequenced whole genomes or a panel of 365 genes on 299 samples from 170 patients with locally relapsed or metastatic breast cancer. Several lines of analysis indicate that clones seeding metastasis or relapse disseminate late from primary tumors, but continue to acquire mutations, mostly accessing the same mutational processes active in the primary tumor. Most distant metastases acquired driver mutations not seen in the primary tumor, drawing from a wider repertoire of cancer genes than early drivers. These include a number of clinically actionable alterations and mutations inactivating SWI-SNF and JAK2-STAT3 pathways.
A.G.L. and J.H.R.F. were supported by a Cancer Research UK Program Grant to Simon Tavaré (C14303/A17197).
2017-08-14T00:00:00ZYates, Lucy R.Knappskog, StianWedge, DavidFarmery, James H. R.Gonzalez, SantiagoMartincorena, InigoAlexandrov, Ludmil B.Van Loo, PeterHaugland, Hans KristianLilleng, Peer KaareGundem, GunesGerstung, MoritzPappaemmanuil, ElliGazinska, PatrycjaBhosle, Shriram GJones, DavidRaine, KeiranMudie, LauraLatimer, CalliSawyer, ElinorDesmedt, ChristineSotiriou, ChristosStratton, Michael R.Sieuwerts, Anieta M.Lynch, Andy G.Martens, John W.Richardson, Andrea L.Tutt, AndrewLønning, Per EysteinCampbell, Peter J.Patterns of genomic evolution between primary and metastatic breast cancer have not been studied in large numbers, despite patients with metastatic breast cancer having dismal survival. We sequenced whole genomes or a panel of 365 genes on 299 samples from 170 patients with locally relapsed or metastatic breast cancer. Several lines of analysis indicate that clones seeding metastasis or relapse disseminate late from primary tumors, but continue to acquire mutations, mostly accessing the same mutational processes active in the primary tumor. Most distant metastases acquired driver mutations not seen in the primary tumor, drawing from a wider repertoire of cancer genes than early drivers. These include a number of clinically actionable alterations and mutations inactivating SWI-SNF and JAK2-STAT3 pathways.Underwater ambient noise in a baleen whale migratory habitat off the AzoresRomagosa, MiriamCascão, IrmaMerchant, Nathan D.Lammers, Marc O.Giacomello, EvaMarques, Tiago A.Silva, Mónica A.http://hdl.handle.net/10023/115452018-01-07T04:05:05Z2017-04-25T00:00:00ZAssessment of underwater noise is of particular interest given the increase in noise-generating human activities and the potential negative effects on marine mammals which depend on sound for many vital processes. The Azores archipelago is an important migratory and feeding habitat for blue (Balaenoptera musculus), fin (Balaenoptera physalus) and sei whales (Balaenoptera borealis) en route to summering grounds in northern Atlantic waters. High levels of low frequency noise in this area could displace whales or interfere with foraging behavior, impacting energy intake during a critical stage of their annual cycle. In this study, bottom-mounted Ecological Acoustic Recorders were deployed at three Azorean seamounts (Condor, Açores and Gigante) to measure temporal variations in background noise levels and ship noise in the 18-1,000 Hz frequency band, used by baleen whales to emit and receive sounds. Monthly average noise levels ranged from 90.3 dB re 1 μPa (Açores seamount) to 103.1 dB re 1 μPa (Condor seamount) and local ship noise was present up to 13% of the recording time in Condor. At this location, average contribution of local boat noise to background noise levels is almost 10 dB higher than wind contribution, which might temporally affect detection ranges for baleen whale calls and difficult communication at long ranges. Given the low time percentatge with noise levels above 120 dB re 1μPa found here (3.3 % at Condor), we woud expect limited behavioural responses to ships from baleen whales. Sound pressure levels measured in the Azores are lower than those reported for the Mediterranean basin and the Strait of Gibraltar. However, the currently unknown effects of baleen whale vocalization masking and the increasing presence of boats at the monitored sites underline the need for continuous monitoring to understand any long-term impacts on whales.
TM is a member of CEA/UL (Funded by FCT- Fundação para a Ciência e a Tecnologia, Portugal, through the project UID/MAT/00006/2013).
2017-04-25T00:00:00ZRomagosa, MiriamCascão, IrmaMerchant, Nathan D.Lammers, Marc O.Giacomello, EvaMarques, Tiago A.Silva, Mónica A.Assessment of underwater noise is of particular interest given the increase in noise-generating human activities and the potential negative effects on marine mammals which depend on sound for many vital processes. The Azores archipelago is an important migratory and feeding habitat for blue (Balaenoptera musculus), fin (Balaenoptera physalus) and sei whales (Balaenoptera borealis) en route to summering grounds in northern Atlantic waters. High levels of low frequency noise in this area could displace whales or interfere with foraging behavior, impacting energy intake during a critical stage of their annual cycle. In this study, bottom-mounted Ecological Acoustic Recorders were deployed at three Azorean seamounts (Condor, Açores and Gigante) to measure temporal variations in background noise levels and ship noise in the 18-1,000 Hz frequency band, used by baleen whales to emit and receive sounds. Monthly average noise levels ranged from 90.3 dB re 1 μPa (Açores seamount) to 103.1 dB re 1 μPa (Condor seamount) and local ship noise was present up to 13% of the recording time in Condor. At this location, average contribution of local boat noise to background noise levels is almost 10 dB higher than wind contribution, which might temporally affect detection ranges for baleen whale calls and difficult communication at long ranges. Given the low time percentatge with noise levels above 120 dB re 1μPa found here (3.3 % at Condor), we woud expect limited behavioural responses to ships from baleen whales. Sound pressure levels measured in the Azores are lower than those reported for the Mediterranean basin and the Strait of Gibraltar. However, the currently unknown effects of baleen whale vocalization masking and the increasing presence of boats at the monitored sites underline the need for continuous monitoring to understand any long-term impacts on whales.Erwin Schrödinger and quantum wave mechanicsO'Connor, John J. (John Joseph)Robertson, Edmund F.http://hdl.handle.net/10023/115432018-06-11T08:20:12Z2017-08-22T00:00:00ZThe fathers of matrix quantum mechanics believed that the quantum particles are unanschaulich (unvisualizable) and that quantum particles pop into existence only when we measure them. Challenging the orthodoxy, in 1926 Erwin Schrödinger developed his wave equation that describes the quantum particles as a packet of quantum probability amplitudes evolving in space and time. Thus, Schrödinger visualized the unvisualizable and lifted the veil that has been obscuring the wonders of the quantum world.
2017-08-22T00:00:00ZO'Connor, John J. (John Joseph)Robertson, Edmund F.The fathers of matrix quantum mechanics believed that the quantum particles are unanschaulich (unvisualizable) and that quantum particles pop into existence only when we measure them. Challenging the orthodoxy, in 1926 Erwin Schrödinger developed his wave equation that describes the quantum particles as a packet of quantum probability amplitudes evolving in space and time. Thus, Schrödinger visualized the unvisualizable and lifted the veil that has been obscuring the wonders of the quantum world.The stability of Mars' annular polar vortexSeviour, WilliamWaugh, DarrynScott, Richard Kirknesshttp://hdl.handle.net/10023/115412018-02-11T01:35:06Z2017-05-01T00:00:00ZThe Martian polar atmosphere is known to have a persistent local minimum in potential vorticity (PV) near the winter pole, with a region of high PV encircling it. This finding is surprising since an isolated band of PV is barotropically unstable, a result going back to Rayleigh. Here we investigate the stability of a Mars-like annular vortex using numerical integrations of the rotating shallow water equations. We show how the mode of instability and its growth rate depends upon the latitude and width of the annulus. By introducing thermal relaxation towards an annular equilibrium profile with a time scale similar to that of the instability, we are able to simulate a persistent annular vortex with similar characteristics as that observed in the Martian atmosphere. This time scale, typically 0.5-2 sols, is similar to radiative relaxation time scales for Mars’ polar atmosphere. We also demonstrate that the persistence of an annular vortex is robust to topographic forcing, as long as it is below a certain amplitude. We hence propose that the persistence of this barotropically unstable annular vortex is permitted due to the combination of short radiative relaxation time scales and relatively weak topographic forcing in the Martian polar atmosphere.
This research was partially supported by a NASA grant from the Mars Fundamental Research Program (NNX14AG53G).
2017-05-01T00:00:00ZSeviour, WilliamWaugh, DarrynScott, Richard KirknessThe Martian polar atmosphere is known to have a persistent local minimum in potential vorticity (PV) near the winter pole, with a region of high PV encircling it. This finding is surprising since an isolated band of PV is barotropically unstable, a result going back to Rayleigh. Here we investigate the stability of a Mars-like annular vortex using numerical integrations of the rotating shallow water equations. We show how the mode of instability and its growth rate depends upon the latitude and width of the annulus. By introducing thermal relaxation towards an annular equilibrium profile with a time scale similar to that of the instability, we are able to simulate a persistent annular vortex with similar characteristics as that observed in the Martian atmosphere. This time scale, typically 0.5-2 sols, is similar to radiative relaxation time scales for Mars’ polar atmosphere. We also demonstrate that the persistence of an annular vortex is robust to topographic forcing, as long as it is below a certain amplitude. We hence propose that the persistence of this barotropically unstable annular vortex is permitted due to the combination of short radiative relaxation time scales and relatively weak topographic forcing in the Martian polar atmosphere.Measuring temporal trends in biodiversityBuckland, S. T.Yuan, Y.Marcon, Erichttp://hdl.handle.net/10023/115342018-06-03T00:36:30Z2017-10-01T00:00:00ZIn 2002, nearly 200 nations signed up to the 2010 target of the Convention for Biological Diversity, ‘to significantly reduce the rate of biodiversity loss by 2010’. In order to assess whether the target was met, it became necessary to quantify temporal trends in measures of diversity. This resulted in a marked shift in focus for biodiversity measurement. We explore the developments in measuring biodiversity that were prompted by the 2010 target. We consider measures based on species proportions, and also explain why a geometric mean of relative abundance estimates was preferred to such measures for assessing progress towards the target. We look at the use of diversity profiles, and consider how species similarity can be incorporated into diversity measures. We also discuss measures of turnover that can be used to quantify shifts in community composition arising for example from climate change.
Yuan was part-funded by EPSRC/NERC Grant EP/1000917/1 and Marcon by ANR-10-LABX-25-01.
2017-10-01T00:00:00ZBuckland, S. T.Yuan, Y.Marcon, EricIn 2002, nearly 200 nations signed up to the 2010 target of the Convention for Biological Diversity, ‘to significantly reduce the rate of biodiversity loss by 2010’. In order to assess whether the target was met, it became necessary to quantify temporal trends in measures of diversity. This resulted in a marked shift in focus for biodiversity measurement. We explore the developments in measuring biodiversity that were prompted by the 2010 target. We consider measures based on species proportions, and also explain why a geometric mean of relative abundance estimates was preferred to such measures for assessing progress towards the target. We look at the use of diversity profiles, and consider how species similarity can be incorporated into diversity measures. We also discuss measures of turnover that can be used to quantify shifts in community composition arising for example from climate change.Editing Cavendish : Maxwell and The Electrical Researches of Henry CavendishFalconer, Isobelhttp://hdl.handle.net/10023/115312018-03-31T23:42:49Z2017-01-01T00:00:00ZDuring the last five years of his life, 1874-79, James Clerk Maxwell was absorbed in editing the electrical researches of Henry Cavendish, performed 100 years earlier. This endeavour is often assumed to be a work of duty to the Cavendish family, and an unfortunate waste of Maxwell's time. By looking at the history of Cavendish's papers, and the editorial choices that Maxwell made, this paper questions this assumption, considering the importance of Cavendish's experiments in Maxwell's electrical programme, and the implications that he may have derived for developing a doctrine of experimental method.
2017-01-01T00:00:00ZFalconer, IsobelDuring the last five years of his life, 1874-79, James Clerk Maxwell was absorbed in editing the electrical researches of Henry Cavendish, performed 100 years earlier. This endeavour is often assumed to be a work of duty to the Cavendish family, and an unfortunate waste of Maxwell's time. By looking at the history of Cavendish's papers, and the editorial choices that Maxwell made, this paper questions this assumption, considering the importance of Cavendish's experiments in Maxwell's electrical programme, and the implications that he may have derived for developing a doctrine of experimental method.Synchronization and separation in the Johnson schemesAljohani, MohammedBamberg, JohnCameron, Peter Jephsonhttp://hdl.handle.net/10023/115252018-05-13T01:35:11Z2018-02-09T00:00:00ZRecently Peter Keevash solved asymptotically the existence question for Steiner systems by showing that S(t,k,n) exists whenever the necessary divisibility conditions on the parameters are satisfied and n is sufficiently large in terms of k and t. The purpose of this paper is to make a conjecture which if true would be a significant extension of Keevash's theorem, and to give some theoretical and computational evidence for the conjecture. We phrase the conjecture in terms of the notions (which we define here) of synchronization and separation for association schemes. These definitions are based on those for permutation groups which grow out of the theory of synchronization in finite automata. In this theory, two classes of permutation groups (called synchronizing and separating) lying between primitive and 2-homogeneous are defined. A big open question is how the permutation group induced by Sn on k-subsets of {1,...,n} fits in this hierarchy; our conjecture would give a solution to this problem for n large in terms of k.
2018-02-09T00:00:00ZAljohani, MohammedBamberg, JohnCameron, Peter JephsonRecently Peter Keevash solved asymptotically the existence question for Steiner systems by showing that S(t,k,n) exists whenever the necessary divisibility conditions on the parameters are satisfied and n is sufficiently large in terms of k and t. The purpose of this paper is to make a conjecture which if true would be a significant extension of Keevash's theorem, and to give some theoretical and computational evidence for the conjecture. We phrase the conjecture in terms of the notions (which we define here) of synchronization and separation for association schemes. These definitions are based on those for permutation groups which grow out of the theory of synchronization in finite automata. In this theory, two classes of permutation groups (called synchronizing and separating) lying between primitive and 2-homogeneous are defined. A big open question is how the permutation group induced by Sn on k-subsets of {1,...,n} fits in this hierarchy; our conjecture would give a solution to this problem for n large in terms of k.Multimodality imaging and mathematical modelling of drug delivery to glioblastomasBoujelben, AhmedWatson, MichaelMcDougall, StevenYen, Yi-FenGerstner, ElizabethCatana, CiprianDeisboeck, ThomasBatchelor, TracyBoas, DavidRosen, BruceKalpathy-Cramer, JayashreeChaplain, Mark Andrew Josephhttp://hdl.handle.net/10023/115132018-05-06T00:35:44Z2016-10-06T00:00:00ZPatients diagnosed with glioblastoma, an aggressive brain tumour, have a poor prognosis, with a median overall survival of less than 15 months. Vasculature within these tumours is typically abnormal, with increased tortuosity, dilation and disorganization and they typically exhibit a disrupted blood brain barrier. Although it has been hypothesized that the “normalization” of the vasculature resulting from anti-angiogenic therapies could improve drug delivery through improved blood flow, there is also evidence that suggests that the restoration of blood brain barrier integrity might limit the delivery of therapeutic agents and hence their effectiveness. In this paper we apply mathematical models of blood flow, vascular permeability and diffusion within the tumour microenvironment to investigate the effect of these competing factors on drug delivery. Preliminary results from the modelling indicate that all three physiological parameters investigated – flow rate, vessel permeability, and tissue diffusion coefficient – interact nonlinearly to produce the observed average drug concentration in the microenvironment.
MAJC would like to thank the Isaac Newton Institute for Mathematical Sciences for its hospitality during the programme “Coupling Geometric PDEs with Physics for Cell Morphology, Motility and Pattern Formation” supported by EPSRC Grant Number EP/K032208/1.
2016-10-06T00:00:00ZBoujelben, AhmedWatson, MichaelMcDougall, StevenYen, Yi-FenGerstner, ElizabethCatana, CiprianDeisboeck, ThomasBatchelor, TracyBoas, DavidRosen, BruceKalpathy-Cramer, JayashreeChaplain, Mark Andrew JosephPatients diagnosed with glioblastoma, an aggressive brain tumour, have a poor prognosis, with a median overall survival of less than 15 months. Vasculature within these tumours is typically abnormal, with increased tortuosity, dilation and disorganization and they typically exhibit a disrupted blood brain barrier. Although it has been hypothesized that the “normalization” of the vasculature resulting from anti-angiogenic therapies could improve drug delivery through improved blood flow, there is also evidence that suggests that the restoration of blood brain barrier integrity might limit the delivery of therapeutic agents and hence their effectiveness. In this paper we apply mathematical models of blood flow, vascular permeability and diffusion within the tumour microenvironment to investigate the effect of these competing factors on drug delivery. Preliminary results from the modelling indicate that all three physiological parameters investigated – flow rate, vessel permeability, and tissue diffusion coefficient – interact nonlinearly to produce the observed average drug concentration in the microenvironment.Pressure moderation and effective pressure in Navier-Stokes flowsTran, Chuong VanYu, Xinweihttp://hdl.handle.net/10023/114992018-06-24T00:38:07Z2016-08-17T00:00:00ZWe study the Cauchy problem of the Navier–Stokes equations by both semi-analytic and classical energy methods. The former approach provides a physical picture of how viscous effects may or may not be able to suppress singularity development. In the latter approach, we examine the pressure term that drives the dynamics of the velocity norms ||u||Lq , for q ≥ 3. A key idea behind this investigation is due to the fact that the pressure p in this term is determined upto a function of both space and |u|, say Ƥ(x, |u|), which may assume relatively broad forms. This allows us to use Ƥ as a pressure moderator in the evolution equation for ||u||Lq , whereby optimal regularity criteria can be sought by varying Ƥ within its admissible classes. New regularity criteria are derived with and without making use of the moderator. The results obtained in the absence of the moderator feature some improvement over existing criteria in the literature. Several criteria are derived in terms of the moderated (effective) pressure p+Ƥ. A simple moderation scheme and the plausibility of the present approach to the problem of Navier–Stokes regularity are discussed.
2016-08-17T00:00:00ZTran, Chuong VanYu, XinweiWe study the Cauchy problem of the Navier–Stokes equations by both semi-analytic and classical energy methods. The former approach provides a physical picture of how viscous effects may or may not be able to suppress singularity development. In the latter approach, we examine the pressure term that drives the dynamics of the velocity norms ||u||Lq , for q ≥ 3. A key idea behind this investigation is due to the fact that the pressure p in this term is determined upto a function of both space and |u|, say Ƥ(x, |u|), which may assume relatively broad forms. This allows us to use Ƥ as a pressure moderator in the evolution equation for ||u||Lq , whereby optimal regularity criteria can be sought by varying Ƥ within its admissible classes. New regularity criteria are derived with and without making use of the moderator. The results obtained in the absence of the moderator feature some improvement over existing criteria in the literature. Several criteria are derived in terms of the moderated (effective) pressure p+Ƥ. A simple moderation scheme and the plausibility of the present approach to the problem of Navier–Stokes regularity are discussed.Authentication and characterisation of a new oesophageal adenocarcinoma cell line : MFD-1Garcia, EdwinHayden, AnnetteBirts, CharlesBritton, EdwardCowie, AndrewPickard, KarenMellone, MassimilianoChoh, ClarisaDerouet, MathieuDuriez, PatrickNoble, FergusWhite, Michael J.Primrose, John N.Strefford, Jonathan C.Rose-Zerilli, MatthewThomas, Gareth J.Ang, YengSharrocks, Andrew D.Fitzgerald, Rebecca C.Underwood, Timothy J.Lynch, Andy G.http://hdl.handle.net/10023/114872018-04-15T00:38:32Z2016-09-07T00:00:00ZNew biological tools are required to understand the functional significance of genetic events revealed by whole genome sequencing (WGS) studies in oesophageal adenocarcinoma (OAC). The MFD-1 cell line was isolated from a 55-year-old male with OAC without recombinant-DNA transformation. Somatic genetic variations from MFD-1, tumour, normal oesophagus, and leucocytes were analysed with SNP6. WGS was performed in tumour and leucocytes. RNAseq was performed in MFD-1, and two classic OAC cell lines FLO1 and OE33. Transposase-accessible chromatin sequencing (ATAC-seq) was performed in MFD-1, OE33, and non-neoplastic HET1A cells. Functional studies were performed. MFD-1 had a high SNP genotype concordance with matched germline/tumour. Parental tumour and MFD-1 carried four somatically acquired mutations in three recurrent mutated genes in OAC: TP53, ABCB1 and SEMA5A, not present in FLO-1 or OE33. MFD-1 displayed high expression of epithelial and glandular markers and a unique fingerprint of open chromatin. MFD-1 was tumorigenic in SCID mouse and proliferative and invasive in 3D cultures. The clinical utility of whole genome sequencing projects will be delivered using accurate model systems to develop molecular-phenotype therapeutics. We have described the first such system to arise from the oesophageal International Cancer Genome Consortium project.
2016-09-07T00:00:00ZGarcia, EdwinHayden, AnnetteBirts, CharlesBritton, EdwardCowie, AndrewPickard, KarenMellone, MassimilianoChoh, ClarisaDerouet, MathieuDuriez, PatrickNoble, FergusWhite, Michael J.Primrose, John N.Strefford, Jonathan C.Rose-Zerilli, MatthewThomas, Gareth J.Ang, YengSharrocks, Andrew D.Fitzgerald, Rebecca C.Underwood, Timothy J.Lynch, Andy G.New biological tools are required to understand the functional significance of genetic events revealed by whole genome sequencing (WGS) studies in oesophageal adenocarcinoma (OAC). The MFD-1 cell line was isolated from a 55-year-old male with OAC without recombinant-DNA transformation. Somatic genetic variations from MFD-1, tumour, normal oesophagus, and leucocytes were analysed with SNP6. WGS was performed in tumour and leucocytes. RNAseq was performed in MFD-1, and two classic OAC cell lines FLO1 and OE33. Transposase-accessible chromatin sequencing (ATAC-seq) was performed in MFD-1, OE33, and non-neoplastic HET1A cells. Functional studies were performed. MFD-1 had a high SNP genotype concordance with matched germline/tumour. Parental tumour and MFD-1 carried four somatically acquired mutations in three recurrent mutated genes in OAC: TP53, ABCB1 and SEMA5A, not present in FLO-1 or OE33. MFD-1 displayed high expression of epithelial and glandular markers and a unique fingerprint of open chromatin. MFD-1 was tumorigenic in SCID mouse and proliferative and invasive in 3D cultures. The clinical utility of whole genome sequencing projects will be delivered using accurate model systems to develop molecular-phenotype therapeutics. We have described the first such system to arise from the oesophageal International Cancer Genome Consortium project.Mutational signatures of ionizing radiation in second malignanciesBehjati, SamGundem, GunesWedge, David C.Roberts, Nicola D.Tarpey, Patrick S.Cooke, Susanna L.Van Loo, PeterAlexandrov, Ludmil B.Ramakrishna, ManasaDavies, HelenNik-Zainal, SerenaHardy, ClaireLatimer, CalliRaine, Keiran M.Stebbings, LucyMenzies, AndyJones, DavidShepherd, RebeccaButler, Adam P.Teague, Jon W.Jorgensen, MetteKhatri, BhavishaPillay, NischalanShlien, AdamFutreal, P. AndrewBadie, ChristopheMcDermott, UltanBova, G. StevenRichardson, Andrea L.Flanagan, Adrienne M.Stratton, Michael R.Campbell, Peter J.Lynch, Andrew G.http://hdl.handle.net/10023/114842018-06-10T23:39:08Z2016-09-12T00:00:00ZIonizing radiation is a potent carcinogen, inducing cancer through DNA damage. The signatures of mutations arising in human tissues following in vivo exposure to ionizing radiation have not been documented. Here, we searched for signatures of ionizing radiation in 12 radiation-associated second malignancies of different tumour types. Two signatures of somatic mutation characterize ionizing radiation exposure irrespective of tumour type. Compared with 319 radiation-naive tumours, radiation-associated tumours carry a median extra 201 deletions genome-wide, sized 1-100 base pairs often with microhomology at the junction. Unlike deletions of radiation-naive tumours, these show no variation in density across the genome or correlation with sequence context, replication timing or chromatin structure. Furthermore, we observe a significant increase in balanced inversions in radiation-associated tumours. Both small deletions and inversions generate driver mutations. Thus, ionizing radiation generates distinctive mutational signatures that explain its carcinogenic potential.
Sequencing data have been deposited at the European Genome-Phenome Archive (EGA, http://www.ebi.ac.uk/ega/), which is hosted by the European Bioinformatics Institute; accession numbers EGAS00001000138; EGAS00001000147; EGAS00001000195.
2016-09-12T00:00:00ZBehjati, SamGundem, GunesWedge, David C.Roberts, Nicola D.Tarpey, Patrick S.Cooke, Susanna L.Van Loo, PeterAlexandrov, Ludmil B.Ramakrishna, ManasaDavies, HelenNik-Zainal, SerenaHardy, ClaireLatimer, CalliRaine, Keiran M.Stebbings, LucyMenzies, AndyJones, DavidShepherd, RebeccaButler, Adam P.Teague, Jon W.Jorgensen, MetteKhatri, BhavishaPillay, NischalanShlien, AdamFutreal, P. AndrewBadie, ChristopheMcDermott, UltanBova, G. StevenRichardson, Andrea L.Flanagan, Adrienne M.Stratton, Michael R.Campbell, Peter J.Lynch, Andrew G.Ionizing radiation is a potent carcinogen, inducing cancer through DNA damage. The signatures of mutations arising in human tissues following in vivo exposure to ionizing radiation have not been documented. Here, we searched for signatures of ionizing radiation in 12 radiation-associated second malignancies of different tumour types. Two signatures of somatic mutation characterize ionizing radiation exposure irrespective of tumour type. Compared with 319 radiation-naive tumours, radiation-associated tumours carry a median extra 201 deletions genome-wide, sized 1-100 base pairs often with microhomology at the junction. Unlike deletions of radiation-naive tumours, these show no variation in density across the genome or correlation with sequence context, replication timing or chromatin structure. Furthermore, we observe a significant increase in balanced inversions in radiation-associated tumours. Both small deletions and inversions generate driver mutations. Thus, ionizing radiation generates distinctive mutational signatures that explain its carcinogenic potential.Whole-genome sequencing of nine esophageal adenocarcinoma cell linesContino, GianmarcoEldridge, Matthew D.Secrier, MariaBower, LawrenceElliott, Rachael FelsWeaver, JamieLynch, Andy G.Edwards, Paul A.W.Fitzgerald, Rebecca C.http://hdl.handle.net/10023/114802018-04-15T00:38:31Z2016-06-10T00:00:00ZEsophageal adenocarcinoma (EAC) is highly mutated and molecularly heterogeneous. The number of cell lines available for study is limited and their genome has been only partially characterized. The availability of an accurate annotation of their mutational landscape is crucial for accurate experimental design and correct interpretation of genotype-phenotype findings. We performed high coverage, paired end whole genome sequencing on eight EAC cell lines-ESO26, ESO51, FLO-1, JH-EsoAd1, OACM5.1 C, OACP4 C, OE33, SK-GT-4-all verified against original patient material, and one esophageal high grade dysplasia cell line, CP-D. We have made available the aligned sequence data and report single nucleotide variants (SNVs), small insertions and deletions (indels), and copy number alterations, identified by comparison with the human reference genome and known single nucleotide polymorphisms (SNPs). We compare these putative mutations to mutations found in primary tissue EAC samples, to inform the use of these cell lines as a model of EAC.
This work was funded by an MRC Programme Grant to R.C.F. and a Cancer Research UK grant to PAWE. The pipeline for mutation calling is funded by Cancer Research UK as part of the International Cancer Genome Consortium. G.C. is a National Institute for Health Research Lecturer as part of a NIHR professorship grant to R.C.F. AGL is supported by a Cancer Research UK programme grant (C14303/A20406) to Simon Tavaré and the European Commission through the Horizon 2020 project SOUND (Grant Agreement no. 633974).
2016-06-10T00:00:00ZContino, GianmarcoEldridge, Matthew D.Secrier, MariaBower, LawrenceElliott, Rachael FelsWeaver, JamieLynch, Andy G.Edwards, Paul A.W.Fitzgerald, Rebecca C.Esophageal adenocarcinoma (EAC) is highly mutated and molecularly heterogeneous. The number of cell lines available for study is limited and their genome has been only partially characterized. The availability of an accurate annotation of their mutational landscape is crucial for accurate experimental design and correct interpretation of genotype-phenotype findings. We performed high coverage, paired end whole genome sequencing on eight EAC cell lines-ESO26, ESO51, FLO-1, JH-EsoAd1, OACM5.1 C, OACP4 C, OE33, SK-GT-4-all verified against original patient material, and one esophageal high grade dysplasia cell line, CP-D. We have made available the aligned sequence data and report single nucleotide variants (SNVs), small insertions and deletions (indels), and copy number alterations, identified by comparison with the human reference genome and known single nucleotide polymorphisms (SNPs). We compare these putative mutations to mutations found in primary tissue EAC samples, to inform the use of these cell lines as a model of EAC.Decomposition of mutational context signatures using quadratic programming methodsLynch, Andy G.http://hdl.handle.net/10023/114792018-01-07T04:04:48Z2016-06-07T00:00:00ZMethods for inferring signatures of mutational contexts from large cancer sequencing data sets are invaluable for biological research, but impractical for clinical application where we require tools that decompose the context data for an individual into signatures. One such method has recently been published using an iterative linear modelling approach. A natural alternative places the problem within a quadratic programming framework and is presented here, where it is seen to offer advantages of speed and accuracy.
AGL was supported in this work by a Cancer Research UK programme grant [C14303/A20406] to Simon Tavaré. AGL acknowledges the support of the University of Cambridge, Cancer Research UK and Hutchison Whampoa Limited. Whole-genome sequencing of oesophageal adenocarcinoma was part of the oesophageal International Cancer Genome Consortium (ICGC) project. The oesophageal ICGC project was funded through a programme and infrastructure grant to Rebecca Fitzgerald as part of the OCCAMS collaboration.
2016-06-07T00:00:00ZLynch, Andy G.Methods for inferring signatures of mutational contexts from large cancer sequencing data sets are invaluable for biological research, but impractical for clinical application where we require tools that decompose the context data for an individual into signatures. One such method has recently been published using an iterative linear modelling approach. A natural alternative places the problem within a quadratic programming framework and is presented here, where it is seen to offer advantages of speed and accuracy.A tumor DNA complex aberration index is an independent predictor of survival in breast and ovarian cancerVollan, Hans Kristian MoenRueda, Oscar M.Chin, Suet-FeungCurtis, ChristinaTurashuili, GulisaShah, SohrabLingjaerde, Ole ChristianYuan, YinyinNg, Charlotte K.Dunning, Mark J.Dicks, EdProvenzano, ElenaSammut, StephenMcKinney, StevenEllis, Ian O.Pinder, SarahPurushotham, ArnieMurphy, Leigh C.Kristensen, Vessela N.Brenton, James D.Pharoah, Paul D. P.Borresen-Dale, Anne-LiseAparicio, SamuelCaldas, CarlosLynch, Andyhttp://hdl.handle.net/10023/114782018-01-07T04:04:47Z2015-01-01T00:00:00ZComplex focal chromosomal rearrangements in cancer genomes, also called "firestorms", can be scored from DNA copy number data. The complex arm-wise aberration index (CAAI) is a score that captures DNA copy number alterations that appear as focal complex events in tumors, and has potential prognostic value in breast cancer. This study aimed to validate this DNA-based prognostic index in breast cancer and test for the first time its potential prognostic value in ovarian cancer. Copy number alteration (CNA) data from 1950 breast carcinomas (METABRIC cohort) and 508 high-grade serous ovarian carcinomas (TCGA dataset) were analyzed. Cases were classified as CAAI positive if at least one complex focal event was scored. Complex alterations were frequently localized on chromosome 8p (n = 159), 17q (n = 176) and 11q (n = 251). CAAI events on 11q were most frequent in estrogen receptor positive (ER+) cases and on 17q in estrogen receptor negative (ER) cases. We found only a modest correlation between CAAI and the overall rate of genomic instability (GII) and number of breakpoints (r = 0.27 and r = 0.42, p <0.001). Breast cancer specific survival (BCSS), overall survival (OS) and ovarian cancer progression free survival (PUS) were used as clinical end points in Cox proportional hazard model survival analyses. CAAI positive breast cancers (43%) had higher mortality: hazard ratio (HR) of 1.94 (95%CI, 1.62-2.32) for BCSS, and of 1.49 (95%CI, 1.30-1.71) for OS. Representations of the 70-gene and the 21-gene predictors were compared with CAAI in multivariable models and CAAI was independently significant with a Cox adjusted HR of 1.56 (95%CI, 1.23-1.99) for ER+ and 1.55 (95%CI, 1.11-2.18) for ER disease. None of the expression-based predictors were prognostic in the ER subset. We found that a model including CAM and the two expression-based prognostic signatures outperformed a model including the 21-gene and 70-gene signatures but excluding CAAL Inclusion of CAAI in the clinical prognostication tool PREDICT significantly improved its performance. CAAI positive ovarian cancers (52%) also had worse prognosis: HRs of 1.3 (95%CI, 1.1-1.7) for PFS and 1.3 (95%CI, 1.1-1.6) for OS. This study validates CAM as an independent predictor of survival in both ER+ and ER breast cancer and reveals a significant prognostic value for CAAI in high-grade serous ovarian cancer. (C) 2014 The Authors. Published by Elsevier B.V. on behalf of Federation of European Biochemical Societies. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/).
2015-01-01T00:00:00ZVollan, Hans Kristian MoenRueda, Oscar M.Chin, Suet-FeungCurtis, ChristinaTurashuili, GulisaShah, SohrabLingjaerde, Ole ChristianYuan, YinyinNg, Charlotte K.Dunning, Mark J.Dicks, EdProvenzano, ElenaSammut, StephenMcKinney, StevenEllis, Ian O.Pinder, SarahPurushotham, ArnieMurphy, Leigh C.Kristensen, Vessela N.Brenton, James D.Pharoah, Paul D. P.Borresen-Dale, Anne-LiseAparicio, SamuelCaldas, CarlosLynch, AndyComplex focal chromosomal rearrangements in cancer genomes, also called "firestorms", can be scored from DNA copy number data. The complex arm-wise aberration index (CAAI) is a score that captures DNA copy number alterations that appear as focal complex events in tumors, and has potential prognostic value in breast cancer. This study aimed to validate this DNA-based prognostic index in breast cancer and test for the first time its potential prognostic value in ovarian cancer. Copy number alteration (CNA) data from 1950 breast carcinomas (METABRIC cohort) and 508 high-grade serous ovarian carcinomas (TCGA dataset) were analyzed. Cases were classified as CAAI positive if at least one complex focal event was scored. Complex alterations were frequently localized on chromosome 8p (n = 159), 17q (n = 176) and 11q (n = 251). CAAI events on 11q were most frequent in estrogen receptor positive (ER+) cases and on 17q in estrogen receptor negative (ER) cases. We found only a modest correlation between CAAI and the overall rate of genomic instability (GII) and number of breakpoints (r = 0.27 and r = 0.42, p <0.001). Breast cancer specific survival (BCSS), overall survival (OS) and ovarian cancer progression free survival (PUS) were used as clinical end points in Cox proportional hazard model survival analyses. CAAI positive breast cancers (43%) had higher mortality: hazard ratio (HR) of 1.94 (95%CI, 1.62-2.32) for BCSS, and of 1.49 (95%CI, 1.30-1.71) for OS. Representations of the 70-gene and the 21-gene predictors were compared with CAAI in multivariable models and CAAI was independently significant with a Cox adjusted HR of 1.56 (95%CI, 1.23-1.99) for ER+ and 1.55 (95%CI, 1.11-2.18) for ER disease. None of the expression-based predictors were prognostic in the ER subset. We found that a model including CAM and the two expression-based prognostic signatures outperformed a model including the 21-gene and 70-gene signatures but excluding CAAL Inclusion of CAAI in the clinical prognostication tool PREDICT significantly improved its performance. CAAI positive ovarian cancers (52%) also had worse prognosis: HRs of 1.3 (95%CI, 1.1-1.7) for PFS and 1.3 (95%CI, 1.1-1.6) for OS. This study validates CAM as an independent predictor of survival in both ER+ and ER breast cancer and reveals a significant prognostic value for CAAI in high-grade serous ovarian cancer. (C) 2014 The Authors. Published by Elsevier B.V. on behalf of Federation of European Biochemical Societies. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/).Phenotype specific analyses reveal distinct regulatory mechanism for chronically activated p53Kirschner, KristinaSamarajiwa, Shamith A.Cairns, Jonathan M.Menon, SurajPérez-Mancera, Pedro A.Tomimatsu, KosukeBermejo-Rodriguez, CaminoIto, YokoChandra, TamirNarita, MasakoLyons, Scott K.Lynch, Andy G.Kimura, HiroshiOhbayashi, TetsuyaTavaré, SimonNarita, Masashihttp://hdl.handle.net/10023/114752018-05-27T00:35:25Z2015-03-19T00:00:00ZThe downstream functions of the DNA binding tumor suppressor p53 vary depending on the cellular context, and persistent p53 activation has recently been implicated in tumor suppression and senescence. However, genome-wide information about p53-target gene regulation has been derived mostly from acute genotoxic conditions. Using ChIP-seq and expression data, we have found distinct p53 binding profiles between acutely activated (through DNA damage) and chronically activated (in senescent or pro-apoptotic conditions) p53. Compared to the classical ‘acute’ p53 binding profile, ‘chronic’ p53 peaks were closely associated with CpG-islands. Furthermore, the chronic CpG-island binding of p53 conferred distinct expression patterns between senescent and pro-apoptotic conditions. Using the p53 targets seen in the chronic conditions together with external high-throughput datasets, we have built p53 networks that revealed extensive self-regulatory ‘p53 hubs’ where p53 and many p53 targets can physically interact with each other. Integrating these results with public clinical datasets identified the cancer-associated lipogenic enzyme, SCD, which we found to be directly repressed by p53 through the CpG-island promoter, providing a mechanistic link between p53 and the ‘lipogenic phenotype’, a hallmark of cancer. Our data reveal distinct phenotype associations of chronic p53 targets that underlie specific gene regulatory mechanisms.
This work was supported by the University of Cambridge; Cancer Research UK (C14303/A17197); Hutchison Whampoa. In addition, MasasN and TO were supported by the Human Frontier Science Program (RGY0078/2010); HK was supported by MEXT KAKENHI (Grant Numbers 25116005 and 26291071); KT was supported by the Japan Society for the Promotion of Science (24–8563).
2015-03-19T00:00:00ZKirschner, KristinaSamarajiwa, Shamith A.Cairns, Jonathan M.Menon, SurajPérez-Mancera, Pedro A.Tomimatsu, KosukeBermejo-Rodriguez, CaminoIto, YokoChandra, TamirNarita, MasakoLyons, Scott K.Lynch, Andy G.Kimura, HiroshiOhbayashi, TetsuyaTavaré, SimonNarita, MasashiThe downstream functions of the DNA binding tumor suppressor p53 vary depending on the cellular context, and persistent p53 activation has recently been implicated in tumor suppression and senescence. However, genome-wide information about p53-target gene regulation has been derived mostly from acute genotoxic conditions. Using ChIP-seq and expression data, we have found distinct p53 binding profiles between acutely activated (through DNA damage) and chronically activated (in senescent or pro-apoptotic conditions) p53. Compared to the classical ‘acute’ p53 binding profile, ‘chronic’ p53 peaks were closely associated with CpG-islands. Furthermore, the chronic CpG-island binding of p53 conferred distinct expression patterns between senescent and pro-apoptotic conditions. Using the p53 targets seen in the chronic conditions together with external high-throughput datasets, we have built p53 networks that revealed extensive self-regulatory ‘p53 hubs’ where p53 and many p53 targets can physically interact with each other. Integrating these results with public clinical datasets identified the cancer-associated lipogenic enzyme, SCD, which we found to be directly repressed by p53 through the CpG-island promoter, providing a mechanistic link between p53 and the ‘lipogenic phenotype’, a hallmark of cancer. Our data reveal distinct phenotype associations of chronic p53 targets that underlie specific gene regulatory mechanisms.Frequent somatic transfer of mitochondrial DNA into the nuclear genome of human cancer cellsJu, Young SeokTubio, Jose M.C.Mifsud, WilliamFu, BeiyuanDavies, Helen R.Ramakrishna, ManasaLi, YilongYates, LucyGundem, GunesTarpey, Patrick S.Behjati, SamPapaemmanuil, ElliMartin, SanchaFullam, AnthonyGerstung, MoritzNangalia, JyotiGreen, Anthony R.Caldas, CarlosBorg, ÅkeTutt, AndrewMichael Lee, Ming TaVan'T Veer, Laura J.Tan, Benita K.T.Aparicio, SamuelSpan, Paul N.Martens, John W.M.Knappskog, StianVincent-Salomon, AnneBørresen-Dale, Anne LiseEyfjörd, Jórunn ErlaFlanagan, Adrienne M.Foster, ChristopherNeal, David E.Cooper, ColinEeles, RosalindLakhani, Sunil R.Desmedt, ChristineThomas, GillesRichardson, Andrea L.Purdie, Colin A.Thompson, Alastair M.McDermott, UltanYang, FengtangNik-Zainal, SerenaCampbell, Peter J.Stratton, Michael R.Lynch, Andyhttp://hdl.handle.net/10023/114742018-03-11T01:37:39Z2015-06-01T00:00:00ZMitochondrial genomes are separated from the nuclear genome for most of the cell cycle by the nuclear double membrane, intervening cytoplasm, and the mitochondrial double membrane. Despite these physical barriers, we show that somatically acquired mitochondrial-nuclear genome fusion sequences are present in cancer cells. Most occur in conjunction with intranuclear genomic rearrangements, and the features of the fusion fragments indicate that nonhomologous end joining and/or replication-dependent DNA double-strand break repair are the dominant mechanisms involved. Remarkably, mitochondrial-nuclear genome fusions occur at a similar rate per base pair of DNA as interchromosomal nuclear rearrangements, indicating the presence of a high frequency of contact between mitochondrial and nuclear DNA in some somatic cells. Transmission of mitochondrial DNA to the nuclear genome occurs in neoplastically transformed cells, but we do not exclude the possibility that some mitochondrial-nuclear DNA fusions observed in cancer occurred years earlier in normal somatic cells.
2015-06-01T00:00:00ZJu, Young SeokTubio, Jose M.C.Mifsud, WilliamFu, BeiyuanDavies, Helen R.Ramakrishna, ManasaLi, YilongYates, LucyGundem, GunesTarpey, Patrick S.Behjati, SamPapaemmanuil, ElliMartin, SanchaFullam, AnthonyGerstung, MoritzNangalia, JyotiGreen, Anthony R.Caldas, CarlosBorg, ÅkeTutt, AndrewMichael Lee, Ming TaVan'T Veer, Laura J.Tan, Benita K.T.Aparicio, SamuelSpan, Paul N.Martens, John W.M.Knappskog, StianVincent-Salomon, AnneBørresen-Dale, Anne LiseEyfjörd, Jórunn ErlaFlanagan, Adrienne M.Foster, ChristopherNeal, David E.Cooper, ColinEeles, RosalindLakhani, Sunil R.Desmedt, ChristineThomas, GillesRichardson, Andrea L.Purdie, Colin A.Thompson, Alastair M.McDermott, UltanYang, FengtangNik-Zainal, SerenaCampbell, Peter J.Stratton, Michael R.Lynch, AndyMitochondrial genomes are separated from the nuclear genome for most of the cell cycle by the nuclear double membrane, intervening cytoplasm, and the mitochondrial double membrane. Despite these physical barriers, we show that somatically acquired mitochondrial-nuclear genome fusion sequences are present in cancer cells. Most occur in conjunction with intranuclear genomic rearrangements, and the features of the fusion fragments indicate that nonhomologous end joining and/or replication-dependent DNA double-strand break repair are the dominant mechanisms involved. Remarkably, mitochondrial-nuclear genome fusions occur at a similar rate per base pair of DNA as interchromosomal nuclear rearrangements, indicating the presence of a high frequency of contact between mitochondrial and nuclear DNA in some somatic cells. Transmission of mitochondrial DNA to the nuclear genome occurs in neoplastically transformed cells, but we do not exclude the possibility that some mitochondrial-nuclear DNA fusions observed in cancer occurred years earlier in normal somatic cells.Mobile element insertions are frequent in oesophageal adenocarcinomas and can mislead paired-end sequencing analysisPaterson, Anna L.Weaver, Jamie M. J.Eldridge, Matthew D.Tavare, SimonFitzgerald, Rebecca C.Edwards, Paul A. W.Lynch, Andyhttp://hdl.handle.net/10023/114732018-06-10T23:39:08Z2015-07-10T00:00:00ZBackground: Mobile elements are active in the human genome, both in the germline and cancers, where they can mutate driver genes. Results: While analysing whole genome paired-end sequencing of oesophageal adenocarcinomas to find genomic rearrangements, we identified three ways in which new mobile element insertions appear in the data, resembling translocation or insertion junctions: inserts where unique sequence has been transduced by an L1 (Long interspersed element 1) mobile element; novel inserts that are confidently, but often incorrectly, mapped by alignment software to L1s or polyA tracts in the reference sequence; and a combination of these two ways, where different sequences within one insert are mapped to different loci. We identified nine unique sequences that were transduced by neighbouring L1s, both L1s in the reference genome and L1s not present in the reference. Many of the resulting inserts were small fragments that include little or no recognisable mobile element sequence. We found 6 loci in the reference genome to which sequence reads from inserts were frequently mapped, probably erroneously, by alignment software: these were either L1 sequence or particularly long polyA runs. Inserts identified from such apparent rearrangement junctions averaged 16 inserts/tumour, range 0-153 insertions in 43 tumours. However, many inserts would not be detected by mapping the sequences to the reference genome, because they do not include sufficient mappable sequence. To estimate total somatic inserts we searched for polyA sequences that were not present in the matched normal or other normals from the same tumour batch, and were not associated with known polymorphisms. Samples of these candidate inserts were verified by sequencing across them or manual inspection of surrounding reads: at least 85 % were somatic and resembled L1-mediated events, most including L1Hs sequence. Approximately 100 such inserts were detected per tumour on average (range zero to approximately 700). Conclusions: Somatic mobile elements insertions are abundant in these tumours, with over 75 % of cases having a number of novel inserts detected. The inserts create a variety of problems for the interpretation of paired-end sequencing data.
Funding was primarily from Cancer Research UK program grants to RCF and ST (C14478/A15874 and C14303/A17197), with additional support awarded to RCF from UK Medical Research Council, NHS National Institute for Health Research (NIHR), the Experimental Cancer Medicine Centre Network and the NIHR Cambridge Biomedical Research Centre, and Cancer Research UK Project grant C1023/A14545 to PAWE. JMJW was funded by a Wellcome Trust Translational Medicine and Therapeutics grant.
2015-07-10T00:00:00ZPaterson, Anna L.Weaver, Jamie M. J.Eldridge, Matthew D.Tavare, SimonFitzgerald, Rebecca C.Edwards, Paul A. W.Lynch, AndyBackground: Mobile elements are active in the human genome, both in the germline and cancers, where they can mutate driver genes. Results: While analysing whole genome paired-end sequencing of oesophageal adenocarcinomas to find genomic rearrangements, we identified three ways in which new mobile element insertions appear in the data, resembling translocation or insertion junctions: inserts where unique sequence has been transduced by an L1 (Long interspersed element 1) mobile element; novel inserts that are confidently, but often incorrectly, mapped by alignment software to L1s or polyA tracts in the reference sequence; and a combination of these two ways, where different sequences within one insert are mapped to different loci. We identified nine unique sequences that were transduced by neighbouring L1s, both L1s in the reference genome and L1s not present in the reference. Many of the resulting inserts were small fragments that include little or no recognisable mobile element sequence. We found 6 loci in the reference genome to which sequence reads from inserts were frequently mapped, probably erroneously, by alignment software: these were either L1 sequence or particularly long polyA runs. Inserts identified from such apparent rearrangement junctions averaged 16 inserts/tumour, range 0-153 insertions in 43 tumours. However, many inserts would not be detected by mapping the sequences to the reference genome, because they do not include sufficient mappable sequence. To estimate total somatic inserts we searched for polyA sequences that were not present in the matched normal or other normals from the same tumour batch, and were not associated with known polymorphisms. Samples of these candidate inserts were verified by sequencing across them or manual inspection of surrounding reads: at least 85 % were somatic and resembled L1-mediated events, most including L1Hs sequence. Approximately 100 such inserts were detected per tumour on average (range zero to approximately 700). Conclusions: Somatic mobile elements insertions are abundant in these tumours, with over 75 % of cases having a number of novel inserts detected. The inserts create a variety of problems for the interpretation of paired-end sequencing data.Mining human prostate cancer datasets : the “camcAPP” shiny appDunning, Mark J.Vowler, Sarah L.Lalonde, EmilieRoss-Adams, HelenBoutros, PaulMills, Ian G.Lynch, Andy G.Lamb, Alastair D.http://hdl.handle.net/10023/114722018-06-03T00:39:08Z2017-03-01T00:00:00ZFunding: Core CRUK funding: MD, AGL, ADL. Academy of Medical Sciences Clinical Lecturer Starter Grant SGCL11 (prinicipal funder of this work): ADL.
2017-03-01T00:00:00ZDunning, Mark J.Vowler, Sarah L.Lalonde, EmilieRoss-Adams, HelenBoutros, PaulMills, Ian G.Lynch, Andy G.Lamb, Alastair D.HES5 silencing is an early and recurrent change in prostate tumourigenesisMassie, Charles E.Spiteri, InmaculadaRoss-Adams, HelenLuxton, HayleyKay, JonathanWhitaker, Hayley C.Dunning, Mark J.Lamb, Alastair D.Ramos-Montoya, AntonioBrewer, Daniel S.Cooper, Colin S.Eeles, RosalindWarren, Anne Y.Tavaré, SimonNeal, David E.Lynch, Andy G.UK Prostate ICGC Grouphttp://hdl.handle.net/10023/114712018-03-04T02:30:31Z2015-04-01T00:00:00ZProstate cancer is the most common cancer in men, resulting in over 10 000 deaths/year in the UK. Sequencing and copy number analysis of primary tumours has revealed heterogeneity within tumours and an absence of recurrent founder mutations, consistent with non-genetic disease initiating events. Using methylation profiling in a series of multifocal prostate tumours, we identify promoter methylation of the transcription factor HES5 as an early event in prostate tumourigenesis. We confirm that this epigenetic alteration occurs in 86-97% of cases in two independent prostate cancer cohorts (n=49 and n=39 tumour-normal pairs). Treatment of prostate cancer cells with the demethylating agent 5-aza-2′-deoxycytidine increased HES5 expression and downregulated its transcriptional target HES6, consistent with functional silencing of the HES5 gene in prostate cancer. Finally, we identify and test a transcriptional module involving the AR, ERG, HES1 and HES6 and propose a model for the impact of HES5 silencing on tumourigenesis as a starting point for future functional studies.
The ICGC Prostate UK Group is funded by Cancer Research UK Grant C5047/A14835, by the Dallaglio Foundation, and by The Wellcome Trust. The Human Research Tissue Bank is supported by the NIHR Cambridge Biomedical Research Centre.
2015-04-01T00:00:00ZMassie, Charles E.Spiteri, InmaculadaRoss-Adams, HelenLuxton, HayleyKay, JonathanWhitaker, Hayley C.Dunning, Mark J.Lamb, Alastair D.Ramos-Montoya, AntonioBrewer, Daniel S.Cooper, Colin S.Eeles, RosalindWarren, Anne Y.Tavaré, SimonNeal, David E.Lynch, Andy G.UK Prostate ICGC GroupProstate cancer is the most common cancer in men, resulting in over 10 000 deaths/year in the UK. Sequencing and copy number analysis of primary tumours has revealed heterogeneity within tumours and an absence of recurrent founder mutations, consistent with non-genetic disease initiating events. Using methylation profiling in a series of multifocal prostate tumours, we identify promoter methylation of the transcription factor HES5 as an early event in prostate tumourigenesis. We confirm that this epigenetic alteration occurs in 86-97% of cases in two independent prostate cancer cohorts (n=49 and n=39 tumour-normal pairs). Treatment of prostate cancer cells with the demethylating agent 5-aza-2′-deoxycytidine increased HES5 expression and downregulated its transcriptional target HES6, consistent with functional silencing of the HES5 gene in prostate cancer. Finally, we identify and test a transcriptional module involving the AR, ERG, HES1 and HES6 and propose a model for the impact of HES5 silencing on tumourigenesis as a starting point for future functional studies.Seals and shipping : quantifying population risk and individual exposure to vessel noiseJones, Esther L.Hastie, Gordon D.Smout, SophieOnoufriou, JosephMerchant, Nathan D.Brookes, Kate L.Thompson, Davidhttp://hdl.handle.net/10023/114592018-01-08T14:30:11Z2017-12-01T00:00:00Z1. Vessels can have acute and chronic impacts on marine species. The rate of increase in commercial shipping is accelerating, and there is a need to quantify and potentially manage the risk of these impacts. 2. Usage maps characterising densities of grey and harbour seals and ships around the British Isles were used to produce risk maps of seal co-occurrence with shipping traffic. Acoustic exposure to individual harbour seals was modelled in a study area using contemporaneous movement data from 28 animals fitted with UHF global positioning satellite telemetry tags and automatic identification system data from all ships during 2014 and 2015. Data from four acoustic recorders were used to validate sound exposure predictions. 3. Across the British Isles, rates of co-occurrence were highest within 50 km of the coast, close to seal haul-outs. Areas identified with high risk of exposure included 11 Special Areas of Conservation (SAC; from a possible 25). Risk to harbour seal populations was highest, affecting half of all SACs associated with the species. 4. Predicted cumulative sound exposure level, cSELs(Mpw), over all seals was 176·8 dB re 1 μPa2 s (95% CI 163·3–190·4), ranging from 170·2 dB re 1μPa2 s (95% CI 168·4–171·9) to 189·3 dB re 1 μPa2 s (95% CI 172·6–206·0) for individuals. This represented an increase in 28·3 dB re 1 μPa2 s over measured ambient noise. For 20 of 28 animals in the study, 95% CI for cSELs(Mpw) had upper bounds above levels known to induce temporary threshold shift. Predictions of broadband received sound pressure levels were underestimated on average by 0·7 dB re 1 μPa (±3·3). 5. Synthesis and applications. We present a framework to allow shipping noise, an important marine anthropogenic stressor, to be explicitly incorporated into spatial planning. Potentially sensitive areas are identified through quantifying risk to marine species of exposure to shipping traffic, and individual noise exposure is predicted with associated uncertainty in an area with varying rates of co-occurrence. The detailed approach taken here facilitates spatial planning with regard to underwater noise within areas protected through the Habitats Directive, and could be used to provide evidence for further designations. This framework may have utility in assessing whether underwater noise levels are at Good Environmental Status under the Marine Strategy Framework Directive.
The work was funded under Scottish Government grant MMSS/001/11 and contract CR/2014/04, and supported by National Capability funding from NERC to SMRU (grant no. SMRU1001). Seal at-sea usage maps, location data for individual seals, locations and source levels for vessels, and SPLs from monitoring data used for acoustic validations are available from the Pure repository, https://doi.org/10.17630/89ac9345-240a-41bb-8f53-b3f14bb114c0.
2017-12-01T00:00:00ZJones, Esther L.Hastie, Gordon D.Smout, SophieOnoufriou, JosephMerchant, Nathan D.Brookes, Kate L.Thompson, David1. Vessels can have acute and chronic impacts on marine species. The rate of increase in commercial shipping is accelerating, and there is a need to quantify and potentially manage the risk of these impacts. 2. Usage maps characterising densities of grey and harbour seals and ships around the British Isles were used to produce risk maps of seal co-occurrence with shipping traffic. Acoustic exposure to individual harbour seals was modelled in a study area using contemporaneous movement data from 28 animals fitted with UHF global positioning satellite telemetry tags and automatic identification system data from all ships during 2014 and 2015. Data from four acoustic recorders were used to validate sound exposure predictions. 3. Across the British Isles, rates of co-occurrence were highest within 50 km of the coast, close to seal haul-outs. Areas identified with high risk of exposure included 11 Special Areas of Conservation (SAC; from a possible 25). Risk to harbour seal populations was highest, affecting half of all SACs associated with the species. 4. Predicted cumulative sound exposure level, cSELs(Mpw), over all seals was 176·8 dB re 1 μPa2 s (95% CI 163·3–190·4), ranging from 170·2 dB re 1μPa2 s (95% CI 168·4–171·9) to 189·3 dB re 1 μPa2 s (95% CI 172·6–206·0) for individuals. This represented an increase in 28·3 dB re 1 μPa2 s over measured ambient noise. For 20 of 28 animals in the study, 95% CI for cSELs(Mpw) had upper bounds above levels known to induce temporary threshold shift. Predictions of broadband received sound pressure levels were underestimated on average by 0·7 dB re 1 μPa (±3·3). 5. Synthesis and applications. We present a framework to allow shipping noise, an important marine anthropogenic stressor, to be explicitly incorporated into spatial planning. Potentially sensitive areas are identified through quantifying risk to marine species of exposure to shipping traffic, and individual noise exposure is predicted with associated uncertainty in an area with varying rates of co-occurrence. The detailed approach taken here facilitates spatial planning with regard to underwater noise within areas protected through the Habitats Directive, and could be used to provide evidence for further designations. This framework may have utility in assessing whether underwater noise levels are at Good Environmental Status under the Marine Strategy Framework Directive.multiSNV : a probabilistic approach for improving detection of somatic point mutations from multiple related tumour samplesJosephidou, MalvinaLynch, Andy G.Tavaré, Simonhttp://hdl.handle.net/10023/114472018-01-07T04:04:34Z2015-05-19T00:00:00ZSomatic variant analysis of a tumour sample and its matched normal has been widely used in cancer research to distinguish germline polymorphisms from somatic mutations. However, due to the extensive intratumour heterogeneity of cancer, sequencing data from a single tumour sample may greatly underestimate the overall mutational landscape. In recent studies, multiple spatially or temporally separated tumour samples from the same patient were sequenced to identify the regional distribution of somatic mutations and study intratumour heterogeneity. There are a number of tools to perform somatic variant calling from matched tumour-normal next-generation sequencing (NGS) data; however none of these allow joint analysis of multiple same-patient samples. We discuss the benefits and challenges of multisample somatic variant calling and present multiSNV, a software package for calling single nucleotide variants (SNVs) using NGS data from multiple same-patient samples. Instead of performing multiple pairwise analyses of a single tumour sample and a matched normal, multiSNV jointly considers all available samples under a Bayesian framework to increase sensitivity of calling shared SNVs. By leveraging information from all available samples, multiSNV is able to detect rare mutations with variant allele frequencies down to 3% from whole-exome sequencing experiments.
Funding: Cancer Research UK grant C14303/A17197. Funding for open access charge: University of Cambridge.
2015-05-19T00:00:00ZJosephidou, MalvinaLynch, Andy G.Tavaré, SimonSomatic variant analysis of a tumour sample and its matched normal has been widely used in cancer research to distinguish germline polymorphisms from somatic mutations. However, due to the extensive intratumour heterogeneity of cancer, sequencing data from a single tumour sample may greatly underestimate the overall mutational landscape. In recent studies, multiple spatially or temporally separated tumour samples from the same patient were sequenced to identify the regional distribution of somatic mutations and study intratumour heterogeneity. There are a number of tools to perform somatic variant calling from matched tumour-normal next-generation sequencing (NGS) data; however none of these allow joint analysis of multiple same-patient samples. We discuss the benefits and challenges of multisample somatic variant calling and present multiSNV, a software package for calling single nucleotide variants (SNVs) using NGS data from multiple same-patient samples. Instead of performing multiple pairwise analyses of a single tumour sample and a matched normal, multiSNV jointly considers all available samples under a Bayesian framework to increase sensitivity of calling shared SNVs. By leveraging information from all available samples, multiSNV is able to detect rare mutations with variant allele frequencies down to 3% from whole-exome sequencing experiments.5-hydroxymethylcytosine marks promoters in colon that resist DNA hypermethylation in cancerUribe-Lewis, SantiagoStark, RoryCarroll, ThomasDunning, Mark J.Bachman, MartinIto, YokoStojic, LovorkaHalim, SilviaVowler, Sarah L.Lynch, Andy G.Delatte, Benjaminde Bony, Eric J.Colin, LaurenceDefrance, MatthieuKrueger, FelixSilva, Ana Luisaten Hoopen, RogierIbrahim, Ashraf E.K.Fuks, FrançoisMurrell, Adelehttp://hdl.handle.net/10023/114462018-06-10T23:39:07Z2015-04-01T00:00:00ZBackground : The discovery of cytosine hydroxymethylation (5hmC) as a mechanism that potentially controls DNA methylation changes typical of neoplasia prompted us to investigate its behaviour in colon cancer. 5hmC is globally reduced in proliferating cells such as colon tumours and the gut crypt progenitors, from which tumours can arise. Results : Here, we show that colorectal tumours and cancer cells express Ten-Eleven-Translocation (TET) transcripts at levels similar to normal tissues. Genome-wide analyses show that promoters marked by 5hmC in normal tissue, and those identified as TET2 targets in colorectal cancer cells, are resistant to methylation gain in cancer. In vitro studies of TET2 in cancer cells confirm that these promoters are resistant to methylation gain independently of sustained TET2 expression. We also find that a considerable number of the methylation gain-resistant promoters marked by 5hmC in normal colon overlap with those that are marked with poised bivalent histone modifications in embryonic stem cells. Conclusions : Together our results indicate that promoters that acquire 5hmC upon normal colon differentiation are innately resistant to neoplastic hypermethylation by mechanisms that do not require high levels of 5hmC in tumours. Our study highlights the potential of cytosine modifications as biomarkers of cancerous cell proliferation.
The authors would like to acknowledge the support of The University of Cambridge, Cancer Research UK (CRUK SEB-Institute Group Award A ref10182; CRUK Senior fellowship C10112/A11388 to AEKI) and Hutchison Whampoa Limited. The Human Research Tissue Bank is supported by the NIHR Cambridge Biomedical Research Centre. FF is a ULB Professor funded by grants from the F.N.R.S. and Télévie, the IUAP P7/03 programme, the ARC (AUWB-2010-2015 ULB-No 7), the WB Health program and the Fonds Gaston Ithier. Data access: http://www.ncbi.nlm.nih.gov/geo/query/acc.cgi?token=jpwzvsowiyuamzs&acc=GSE47592
2015-04-01T00:00:00ZUribe-Lewis, SantiagoStark, RoryCarroll, ThomasDunning, Mark J.Bachman, MartinIto, YokoStojic, LovorkaHalim, SilviaVowler, Sarah L.Lynch, Andy G.Delatte, Benjaminde Bony, Eric J.Colin, LaurenceDefrance, MatthieuKrueger, FelixSilva, Ana Luisaten Hoopen, RogierIbrahim, Ashraf E.K.Fuks, FrançoisMurrell, AdeleBackground : The discovery of cytosine hydroxymethylation (5hmC) as a mechanism that potentially controls DNA methylation changes typical of neoplasia prompted us to investigate its behaviour in colon cancer. 5hmC is globally reduced in proliferating cells such as colon tumours and the gut crypt progenitors, from which tumours can arise. Results : Here, we show that colorectal tumours and cancer cells express Ten-Eleven-Translocation (TET) transcripts at levels similar to normal tissues. Genome-wide analyses show that promoters marked by 5hmC in normal tissue, and those identified as TET2 targets in colorectal cancer cells, are resistant to methylation gain in cancer. In vitro studies of TET2 in cancer cells confirm that these promoters are resistant to methylation gain independently of sustained TET2 expression. We also find that a considerable number of the methylation gain-resistant promoters marked by 5hmC in normal colon overlap with those that are marked with poised bivalent histone modifications in embryonic stem cells. Conclusions : Together our results indicate that promoters that acquire 5hmC upon normal colon differentiation are innately resistant to neoplastic hypermethylation by mechanisms that do not require high levels of 5hmC in tumours. Our study highlights the potential of cytosine modifications as biomarkers of cancerous cell proliferation.Epigenetic and oncogenic regulation of SLC16A7 (MCT2) results in protein over-expression, impacting on signalling and cellular phenotypes in prostate cancerPértega-Gomes, NelmaVizcaino, Jose R.Felisbino, SergioWarren, Anne Y.Shaw, GregKay, JonathanWhitaker, HayleyLynch, Andy G.Fryer, Lee