I started my career as an Applied Mathematician working in a research laboratory dedicated to solving problems in the mining industry. Subsequent to completing my Ph.D. in 1987, I have focussed my research efforts on challenging mathematical problems that come from industry. This practical industrial experience has led to a continuing fascination with the rich and interesting problems that can be solved using mathematics.
My research has focussed primarily on the following application areas (starting with the most recent): Numerical and analytic models of hydraulic fracture propagation; rock fracture processes around mining excavations, control of molecular motion; reactive flows in porous media; analysis of diffusion models with localized reactions. The techniques that have been used in these problems have involved the tools of modern Applied Mathematics such as Functional Analysis, Numerical Analysis, Asymptotic Analysis, and Bifurcation Theory.
Fracture around Mining Excavations
Reactive Flow and Free Boundary Problems
Diffusion Models with Localized Reactions