Theses  Applied Mathematics and Theoretical Physics
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Source modelling at the dawn of gravitationalwave astronomy
(Department of Applied Mathematics and Theoretical Physics, University of Cambridge, 20161108)The age of gravitationalwave astronomy has begun. Gravitational waves are propagating spacetime perturbations ($\textit{“ripples in the fabric of spacetime”}$) predicted by Einstein’s theory of General Relativity. These ... 
Numerical analysis of the Fokas method in two and three dimensions
(Department of Applied Mathematics and Theoretical Physics, University of Cambridge, 20161005)This thesis considers the numerical solution to elliptic boundary value problems (BVPs) in convex domains. Specifically we look at the twodimensional problem in a polygon, and the three dimensional problem in a polyhedron. ... 
Modelling the effects on building temperatures of phase change materials
(Department of Applied Mathematics and Theoretical Physics, University of Cambridge, 20161108)In this thesis, three problems motivated by the possibility of use of phase change materials in buildings are presented. First, a model for the response of phase change material (PCM) to a varying room temperature is ... 
Generalised nonlinear stability of stratified shear flows: adjointbased optimisation, Koopman modes, and reduced models
(Department of Applied Mathematics and Theoretical Physics, University of Cambridge, 20161004)In this thesis I investigate a number of problems in the nonlinear stability of density stratified plane Couette flow. I begin by describing the history of transient growth phenomena, and in particular the recent application ...