Browsing Applied Mathematics Theses by Title
Now showing items 726 of 53 starting with C

Continued fractions which correspond to two series expansions and the strong Hamburger moment problem
(University of St Andrews, 1984)  ThesisJust as the denominator polynomials of a Jfraction are orthogonal polynomials with respect to some moment functional, the denominator polynomials of an Mfraction are shown to satisfy a skew orthogonality relation with ... 
The contouradvective semiLagrangian hybrid algorithm approach to weather forecasting and freely propagating inertiagravity waves in the shallowwater system
(University of St Andrews, 20090624)  ThesisThis thesis is aimed at extending the spherical barotropic contouradvective semiLagrangian (CASL) Algorithm, written in 1996 by David Dritschel and Maarten Ambaum, to more complex test cases within the shallowwater ... 
Coupling of the solar wind, magnetosphere and ionosphere by MHD waves
(University of St Andrews, 20101130)  ThesisThe solar wind, magnetosphere and ionosphere are coupled by magnetohydrodynamic waves, and this gives rise to new and often unexpected behaviours that cannot be produced by a single, isolated part of the system. This ... 
Current sheets in the solar corona : formation, fragmentation and heating
(University of St Andrews, 20111130)  ThesisIn this thesis we investigate current sheets in the solar corona. The well known 1D model for the tearing mode instability is presented, before progressing to 2D where we introduce a nonuniform resistivity. The effect ... 
Development and application of a global magnetic field evolution model for the solar corona
(University of St Andrews, 20090624)  ThesisMagnetic ﬁelds are fundamental to the structure and dynamics of the Sun’s corona. Observations show them to be locally complex, with highly sheared and twisted ﬁelds visible in solar ﬁlaments/prominences. The free magnetic ... 
The dynamic topology of the solar corona : mapping the Sun’s three dimensional magnetic skeleton
(University of St Andrews, 20180626)  ThesisObservations of the surface of the Sun reveal multiscaled, mixed magnetic features that carpet the entire solar surface. Not surprisingly, the global magnetic fields extrapolated from these observations are highly ... 
Effect of structuring on coronal loop oscillations
(University of St Andrews, 200706)  ThesisIn this Thesis the theoretical understanding of oscillations in coronal structures is developed. In particular, coronal loops are modelled as magnetic slabs of plasma. The effect of introducing inhomogeneities on the ... 
Electron cyclotron heating and current drive using the electron Bernstein modes
(University of St Andrews, 2007)  ThesisElectron Bernstein waves are a mode of oscillation in a plasma, thought a candidate for providing radiofrequency heating and noninductive current drive in spherical tokamaks. Previous studies of these modes have relied ... 
Equilibrium and dynamics of collisionless current sheets
(University of St Andrews, 20090624)  ThesisIn this thesis examples of translationally invariant onedimensional (1D) VlasovMaxwell (VM) equilibria are investigated. The 1D VM equilibrium equations are equivalent to the motion of a pseudoparticle in a conservative ... 
Equilibrium and stability properties of collisionless current sheet models
(University of St Andrews, 20130628)  ThesisThe work in this thesis focuses primarily on equilibrium and stability properties of collisionless current sheet models, in particular of the forcefree Harris sheet model. A detailed investigation is carried out into ... 
Eruptions and jets in the Sun
(University of St Andrews, 20170623)  ThesisMagnetic flux emergence is a fundamental process in the Sun, during which magnetic fields emerge from the solar interior to the surface, to build up active regions and give onset to spectacular dynamic phenomena, such as ... 
Finite and infinite ergodic theory for linear and conformal dynamical systems
(University of St Andrews, 20111130)  ThesisThe first main topic of this thesis is the thorough analysis of two families of piecewise linear maps on the unit interval, the αLüroth and αFarey maps. Here, α denotes a countably infinite partition of the unit interval ... 
The formation and eruption of magnetic flux ropes in solar and stellar coronae
(University of St Andrews, 20151130)  ThesisFlux ropes are magnetic structures commonly found in the solar corona. They are thought to play an important role in solar flares and coronal mass ejections. Understanding their formation and eruption is of paramount ... 
A highly adaptive three dimensional hybrid vortex method for inviscid flows and helically symmetric vortex equilibria
(University of St Andrews, 20120622)  ThesisThis thesis is concerned with threedimensional vortex dynamics, in particular the modelling of vortex structures in an inviscid context. We are motivated by the open problem of regularity of the inviscid equations, i.e. ... 
Inhomogeneous magnetic fields in the solar atmosphere
(University of St Andrews, 1984)  ThesisThe magnetic field in the solar atmosphere is highly inhomogeneous. In the photosphere, the field is concentrated into intense flux tubes and the coronal magnetic field consists of many loops and regions of open field. ... 
An investigation into the use of balance in operational numerical weather prediction
(University of St Andrews, 2011)  ThesisPresented in this study is a wideranging investigation into the use of properties of balance in an operational numerical weather prediction context. Initially, a joint numerical and observational study is undertaken. ... 
The investigation of quasiseparatrix layers in solar magnetic fields
(University of St Andrews, 20110620)  ThesisThe structure of the magnetic field is often an important factor in many energetic processes in the solar corona. To determine the topology of the magnetic field features such as null points, separatrix surfaces, and ... 
Magnetic flux transport simulations : applications to solar and stellar magnetic fields
(University of St Andrews, 201111)  ThesisMagnetic fields play a key role in a wide variety of phenomena found on the Sun. One such phenomena is the Coronal Mass Ejection (CME) where a large amount of material is ejected from the Sun. CME’s may directly affect ... 
Magnetic skeletons and 3D magnetic reconnection
(University of St Andrews, 20080623)  ThesisThe upper atmosphere of the sun, the solar corona, is approximately 1,000,000K hotter than the surface of the Sun, a property which cannot be explained by the normal processes of heat conduction and radiation. It is now ... 
MHD evolution of magnetic null points to static equilibria
(University of St Andrews, 20110518)  ThesisIn magnetised plasmas, magnetic reconnection is the process of magnetic field merging and recombination through which considerable amounts of magnetic energy may be converted into other forms of energy. Reconnection is a ...