Research Interests

My work focusses on developing and analysing mathematical models of physical processes arising in practical problems and interpreting the results into their original context. The majority of my work takes place on the interface between mathematics, industry and other sciences, namely; physics, chemistry, engineering and biology.

Areas of application that I have worked on/am working in, include; (i) lithium-ion batteries; (ii) organic and hybrid (particularly perovskite) solar cells; (iii) signal propogation in axons, and; (iv) fluid flow in glass manufacture.

Working in these areas I have naturally developed keen interests in the following arenas of mathematics: (a) differential (and integro-differential) equations; (b) asymptotic/perturbation methods; (c) numerical methods/scientific computation; (d) continuum mechanics (both solid and fluid); (e) free boundary problems; (f) homogenisation and upscaling in multiscale systems, and; (g) Monte Carlo simulation.