# Applied Mathematician specialising in aspects of fluid dynamics and mathematical modelling

## About Me

I am a Bristol based applied mathematician who has worked in a variety of different areas in mathematical modelling including supersonic flow (specificity examining Mach reflection), stress waves in solids, fire dynamics and currently plasma physics and electrohydrodynamics where I am investigating interfacial waves between perfect insulators and perfect conductors. I have been examining the waves due to topography and a moving pressure distribution which lead on to examining the existence of solitary waves. The plasma physics I am working on is modelling the what happens when firing a beam of electrons into a charge neutral plasma and seeing how the beam and plasma interact. From a mathematical point of view the electrohydrodynamic waves are a free boundary problem with Elliptic partial differential equations.  The work in plasma physics involves hyperbolic partial differential equations and may or may not involve free or moving boundaries.

My MPhil these was done at Manchester University under the supervision of Prof Anatoly Ruban (Now at Imperial College in the maths department) on the phenomenon of Mach reflection, my work overturned some of the major ideas about the shape of the Mach stem near the the von Neumann condition. You can read my thesis here. It has an introduction to oblique shock waves and Mach reflection and can be read by anyone with an understanding of vector analysis and asymptotic analysis. My numerical codes which I used as part of my research are available, I have written programs to calculate shock polars, von Neumann points, detachment points for shock in air, I have also written a code that computes a shock polar for an arbitrary equation of state (with some assumptions) and I have a rudimentary 2D CFD code for air flow.

I have recently completed a PhD in applied mathematics specializing in linear and nonlinear free surface flows in electrohydrodynamics – that is combining the phenomenon of electric fields with standard fluid flow seeing just how the electric field affects the waves produced. The thesis was purely theoretical and it was a matter of combining Maxwells’s equations with the Navier-Stokes equations. The type of fluids which I was examining were incompressible, irrotational, inviscid and perfectly insulating/conducting with a forcing term – either a moving pressure distribution or some topography. This lead to the case of potential flow. I derived generalized versions of the KdV and KP equations. I also applied the idea that a horizontal electric field can overcome the Rayleigh-Taylor instability to examine some hanging flows, this work is on my Publications page.

I am currently examing the the weakly viscous case where the viscosity is small by using the visco-potential approach to obtain some insights on real fluids.

I have been given a visiting lecturer position at University College London.

My LinkedIn profile.