Edwin graduated with an MMath from the University of Oxford in 2019. His mathematical studies included a diverse range of general methods in modelling and dynamic systems as well as stochastic processes in genetics, finance, and biology. In the summer between his Bachelors and his Masters he worked in polar research at the Alfred Wegener Institute in Bremerhaven, Germany where he numerically modelled both the migration of arctic cod and the dependence of chlorophyll-A on the external environment. His Masters’ thesis was on sharp-interface limits of different generalised formulations of the Cahn-Hilliard Equation. Edwin’s main sporting passions are rugby and motorsports and his hobbies include gaming, travelling, and whisky.

Research project title:
Hybrid numerical-asymptotic analysis of snaking bifurcations

Supervisor(s):
Philippe Trinh, Jonathan Dawes

Project description:
There is a great deal of interest in nonlinear differential and difference equations that exhibit homoclinic snaking, in which solution curves of localised patterns ‘snake’ back and forth across a bifurcation diagram in a narrow region of parameter space. These snaking bifurcations arise in many experimental and theoretical contexts, including optics, convection, ferrofluids, Couette flow, buckling problems, neuroscience, and so forth. In recent years, a methodology using beyond-all-orders asymptotics has been developed to describe snaking bifurcations. However, this approach has not yet enjoyed wide adoption on account of the significant technical theory and machinery required. Edwin is making this more accessible by using numerical methods to replace certain analytical steps. This would also enable generalising this method to systems where we cannot solve these steps analytically, as opposed to basic 1D systems and Edwin is generalising the beyond-all-orders analysis to systems with non-smooth nonlinearities.