We investigate several problems in relativity and particle physics where symmetries play a central role; in all cases geometric properties of Lie groups and their quotients are related to physical effects. The first part ...

The field of nonlinear regression is a long way from reaching a consensus. Once a method decides to explore nonlinear combinations of predictors, a number of questions are raised, such as what nonlinear combinations to ...

Internal gravity waves play a fundamental role in the dynamics of stably stratified regions of the atmosphere and ocean. In addition to the radiation of momentum and energy remote from generation sites, internal waves ...

This thesis considers various aspects of general relativity in more than four spacetime dimensions. Firstly, I review the generalization to higher dimensions of the algebraic classification of the Weyl tensor and the ...

In a magnetized plasma, naturally occurring pressure anisotropies facilitate in- stabilities that are expected to modify the transport properties of the system. In this thesis we examine two such instabilities and, where ...

Materials can flow down a slope in a wide range of geophysical and industrial contexts, including lava flows on volcanoes and thin films on coated surfaces. The aim of my research is to provide quantitative insight into ...

In this dissertation we consider the dynamics of the solar interior, with particular focus on angular momentum balance and magnetic field confinement within the tachocline. In Part I we review current knowledge of the ...

The increasing number of discovered extra-solar planets opens a new opportunity for studies of the formation of planetary systems. Their diversity keeps challenging the long-standing theories which were based on data ...

Modified Fourier expansions present an alternative to more standard algorithms for the approximation of nonperiodic functions in bounded domains. This thesis addresses the theory of such expansions, their effective ...

We consider the stability of black holes within both classical general relativity and the semiclassical thermodynamic description. In particular, we study linearised perturbations and their contribution to the gravitational ...

The ultimate goal of this thesis is to improve our understanding of the cosmology of axions. Axions couple to QCD instantons and these non-perturbative effects are modeled within the framework of the interacting instanton ...

This thesis presents methods for efficient numerical approximation of linear and non-linear systems of highly oscillatory ordinary differential equations. Phenomena of high oscillation is considered a major computational ...

Accretion discs are fluid-dynamical entities which surround many black holes. Observations reveal that these systems exhibit variability on a range of time scales. This thesis investigates phenomena occurring in black-hole ...

This dissertation describes efforts to evaluate a recently proposed continuum model for the dense flow of dry granular materials (Jop, Forterre & Pouliquen, 2006, Nature, 441, 167-192). The model, based upon a generalisation ...

The aims of this thesis are to develop and validate a robust and efficient algorithm for the numerical solution of the equations of General Relativistic Hydrodynamics, to implement the algorithm in a computationally efficient ...

Rayleigh-Taylor instability has been an area of active research in fluid dynamics for the last twenty years, but relatively little attention has been paid to the dynamics of problems where Rayleigh-Taylor instability ...

This thesis: (a) presents the solution of several boundary value problems (BVPs) for the Laplace and the modified Helmholtz equations in the interior of an equilateral triangle; (b) presents the solution of the heat ...