My research interests fall into three broad categories: nonlinear waves, coagulation processes, and mathematical medicine and biology. Please contact me if you are interested in pursuing a PhD in any of these areas.
Nonlinear Waves
– Travelling Kinks and Breathers in FPU-Klein-Gordon lattices: – I started working on solitons on lattices for my PhD thesis, and have continued, expanding to cover more complex modes and higher-dimensional lattices.
– Breathing of DNA: – this is one application of breathers on lattices, but with Charlie Laughton, we have worked on parameterising stochastic differential equation models using AMBER.
– Fluxons in Josephson Junctions: – collaborative work with Hadi Susanto is focused on understanding a range of nonlinear dynamics relevant to current and potential nanotechnological devices.
– ICMS meeting on Nonlinear Waves and Solitons on Lattices – in April 2011, there was a meeting in honour of Chris Eilbeck on his retirement. Details of speakers, talk titles, abstracts are available here.
Coagulation-fragmentation problems
– Polymer nucleation: – collaborative work with Richard Graham focuses on the effects of flow, stretch, nuclei orientation, etc.
– Origins of Life: – I am interested in modelling the chemical processes which occur during the formation of chiral polymers/crystals, also the information storage of primitive DNA/RNA sequences, and simple metabolic processes by which cell-like structures form.
– Island growth during deposition: – for example in molecular beam epitaxy (MBE), the continuous deposition of atoms on a surface causes islands to form; the size distribution of these islands often follows a self-similar form. I am interested in analysing the large-time asymptotics of this process.
– Generalised nucleation theory: I am interested in analysing a range of techniques, for example asymptotics of the Becker-Doring equations, as well as the Smoluchowski equations, and approximation techniques based on coarse-graining and continuum limits.
Mathematical Medicine and Biology
– mRNA degradation: together with Dr Cornelia de Moor of the School of Pharmacy at Nottingham, I am working on the processes by which the poly-A-tails of mRNAs are eroded, leading to the destruction of mRNA.
– Carbohydrate and Fat metabolism in humans: I am collaborating on the construction of computer simulations of human nutrition and the development of various metabolic conditions such as diabetes and fatty liver disease.
– Carbon metabolism during seed germination: – I work with Mark Hooks (Bangor) on mathematical models of fluxes in and through the peroxysome/glyoxysome.
– Metabolic pathways in ovarian cells: – recent collaborative work with Kevin Sinclair (Biosciences, Nottingham) and Helen Byrne (Oxford) aims to model the methionine cycle.
– Telomere dynamics, and the influence of cell cycle on drug treatment: – the evolution of telomere lengths is a process which can be modelled by discrete dynamical system that can be analysed using asymptotic techniques.
– DNA condensation for gene therapy: – this reduces to a classic toy problem in physics, namely random sequential adsorption (RSA), also known as the parking problem. I am interested in deriving solutions to certain cases using asymptotic limits, and connections with MBE (see above), since both are described by coagulation-fragmentation processes. Earlier work in this area involved Snow Stolnik and Clive Roberts (Pharmaceutical Sciences, Nottingham) and Helen Byrne (Oxford).