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Numerical analysis of the Fokas method in two and three dimensions
(Department of Applied Mathematics and Theoretical Physics, University of CambridgeUniversity of CambridgeDepartment of Applied Mathematics and Theoretical PhysicsSt Edmund's College, 2016-10-05)
This thesis considers the numerical solution to elliptic boundary value problems (BVPs) in convex domains. Specifically we look at the two-dimensional problem in a polygon, and the three dimensional problem in a polyhedron. ...
Matrix model for non-Abelian quantum Hall states
(American Physical SocietyPhysical Review B, 2016-08-09)
We propose a matrix quantum mechanics for a class of non-Abelian quantum Hall states. The model describes electrons which carry an internal SU($p$) spin. The ground states of the matrix model include spin-singlet generalizations ...
Coupled-channel $\textit{Dπ}$, $\textit{Dη}$ and $\textit{D$_{s}$$\bar K$}$ scattering from lattice QCD
(SpringerJournal of High Energy Physics, 2016-10-04)
We present the first lattice QCD study of coupled-channel $\textit{Dπ}$, $\textit{Dη}$ and $\textit{D$_{s}$$\bar K$}$ scattering in isospin-1/2 in three partial waves. Using distillation, we compute matrices of correlation ...
A new method for isolating turbulent states in transitional stratified plane Couette flow
(Cambridge University PressJournal of Fluid Mechanics, 2016-10-26)
We present a new adaptive control strategy to isolate and stabilize turbulent states in transitional, stably stratified plane Couette flow in which the gravitational acceleration (non-dimensionalized as the bulk Richardson ...
Modelling the effects on building temperatures of phase change materials
(Department of Applied Mathematics and Theoretical Physics, University of CambridgeUniversity of CambridgeDepartment of Applied Mathematics and Theoretical Physics, 2016-11-08)
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 ...
Instability of supersymmetric microstate geometries
(SpringerJournal of High Energy Physics, 2016-10-07)
We investigate the classical stability of supersymmetric, asymptotically flat, microstate geometries with five non-compact dimensions. Such geometries admit an “evanescent ergosurface”: a timelike hypersurface of infinite ...
Robust identification of dynamically distinct regions in stratified turbulence
(Cambridge University PressJournal of Fluid Mechanics, 2016-10-18)
We present a new robust method for identifying three dynamically distinct regions in a stratified turbulent flow, which we characterise as quiescent flow, intermittent layers and turbulent patches. The method uses the ...
Fluid dynamics at the scale of the cell
(Cambridge University PressJournal of Fluid Mechanics, 2016-10-17)
The world of cellular biology provides us with many fascinating fluid dynamical phenomena that lie at the heart of physiology, development, evolution and ecology. Advances in imaging, micromanipulation and microfluidics ...
Learning parametrised regularisation functions via quotient minimisation
(WileyProceedings in Applied Mathematics and Mechanics, 2016-10-25)
We propose a novel strategy for the computation of adaptive regularisation functions. The general strategy consists of minimising the ratio of a parametrised regularisation function; the numerator contains the regulariser ...
Stresslets Induced by Active Swimmers
(American Physical SocietyPhysical Review Letters, 2016-09-30)
Active particles disturb the fluid around them as force dipoles, or stresslets, which govern their collective dynamics. Unlike swimming speeds, the stresslets of active particles are rarely determined due to the lack of a ...