R436 Level 4
Glasgow G12 8QW
Physics, Geometry and Analysis meet in the realm of nano-scale material science, generating novel multiple-scale partial differential equations (PDE) which pose new and significant mathematical challenge. My research is focused on the identification of those problems which require the application of new mathematical ideas to material science (EPSRC Annual Review of Mathematics 2010, http://www.epsrc.ac.uk/pubs/reports/Pages/internationalreviews.aspx)
Some areas of current interest include
i) The analysis and computation of Geometric PDE arising from the non-equilibrium thermo-mechanics of interfacial phase boundaries,
ii) Morphometric prediction for evolving networks, such as faceted surfaces, polycrystals and foams.
I also have a distinct strand of research in applied analysis, and in particular the theory of PDE that arise from continuum physics; e.g., priori estimates in thermoviscoelasticity/compressible Navier-Stokes.