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 ...

Much of the recent progress in cosmology has come from studying the power spectrum of the cosmic microwave background (CMB). The latest results from the Planck satellite confirmed that the inflationary paradigm with the ...

The subject matter of this dissertation is the design, analysis and practical implementation of a new numerical method to approximate the eigenvalues and eigenfunctions of regular Sturm–Liouville problems, given in Liouville’s ...

We study aspects of the quantum mechanics of nonlinear $\sigma$-models with superconformal invariance. The connection between the differential geometry of the target manifold and symmetries of the quantum mechanics is ...

The focus of this thesis is variational image restoration techniques that involve novel non-smooth first-order gradient regularisers: Total Variation (TV) regularisation in image and data space for reconstruction of thin ...

We investigate the spin dynamics of polariton condensates spatially separated from and effectively confined by the pumping exciton reservoir. We obtain a strong correlation between the ellipticity of the non-resonant optical ...

Digital signatures are widely used in modern communication to guarantee authenticity and transferability of messages. The security of currently used classical schemes relies on computational assumptions. We present a quantum ...

We calculate reduced B(E2) electromagnetic transition strengths for light nuclei of mass numbers B = 8,12,16,20,24, and 32 within the Skyrme model. We find that the predicted transition strengths are of the correct order ...

We present results from Monte Carlo calculations investigating the properties of the homogeneous, spin-balanced unitary Fermi gas in three dimensions. The temperature is varied across the superfluid transition allowing us ...

Shannon’s entropy power inequality (EPI) can be viewed as a statement of concavity of an entropic function of a continuous random variable under a scaled addition rule: f(√a X + √1 − a Y) ≥ a f(X) + (1 − a)f(Y) ∀ a ∈ [0, ...

The accuracy of existing impedance boundary conditions is investigated, and new impedance boundary conditions are derived, for lined ducts with inviscid shear flow. The accuracy of the Ingard–Myers boundary condition is ...

Cilia and flagella often exhibit synchronized behavior; this includes phase-locking, as seen in Chlamydomonas, and metachronal wave formation in the respiratory cilia of higher organisms. Since the observations by Gray and ...

These lecture notes and example problems are based on a course given at the University of Cambridge in Part III of the Mathematical Tripos. Fluid dynamics is involved in a very wide range of astrophysical phenomena, ...

The role of slow-mode magnetohydrodynamic (MHD) shocks in magnetic reconnection is of great importance for energy conversion and transport, but in many astrophysical plasmas the plasma is not fully ionised. In this paper, ...

This paper describes how measurements of the movement of identifiable features at the edge of a turbulent plume can be interpreted to determine the properties of the mean flow and consequently, using plume theory, can be ...

An analytical model for asymmetric rolling is presented, which includes asymmetry in roll friction, roll size and roll speed, for a rigid, perfectly-plastic thin sheet deformed with Coulomb friction. This model is solved ...