Current Research Interests and Activity
Topics in Asymptotic Analysis, Industrial and Applied Mathematical Modelling
- Complex fluids with memory
Asymptotic and numerical solutions of viscoelastic fluids. These are fluids that behave as both liquids and solids.
Particular interest in behaviour near singularities arising in re-entrant corner geometries, wedge flows and stick-slip regimes.
Applications in polymer, food, petroleum and minerals industries, inkjet printing, nanotechnology, smart materials and intelligent gels.
Collaborators: Institute of Non-Newtonian Fluid Mechanics including Prof Ken Walters (FRS), Aberystwyth. Dr T. Hagen,
Department of Mathematics, Univerity of Memphis, USA.
Right: David Boger illustrating his class of constant viscosity
non-Newtonian Boger fluids with fundamental applications to the environment, economy, society (triple bottom line).
Videos showing the bizzare properties of these types of fluids.
- High order nonlinear evolutionary PDEs
Fourth, sixth and tenth order Cahn-Hilliard and thin film type equations (semi-linear and degenerate quasi-linear PDEs). Investigation of self-similar blow-up
and spreading solutions.
Collaborators: Prof Victor Galaktionov, Bath. Dr Pablo Alvarez-Caudevilla, Carlos III University, Madrid.
- Free boundary problems
Engineering applications: heat and mass transfer, semiconductor fabrication (silicon oxidation
and device isolation techniques), concrete carbonation.
Collaborators academic: Prof J.R. King, School of Mathematics, University of Nottingham. Dr A. Muntean,
TU Eindhoven, Netherlands.
Collaborators industrial: Dr A. Nejim, Silvaco, Cambridge. (Past contacts include Prof C. Hill
and Dr S. Jones, GEC-Marconi Materials Technology, Caswell, Northampton.)
Finance: Pricing of American style options/derivatives. Fractal identification in pricing data.
Collaborators: Prof R.A. Kuske, Department of Mathematics, University of British Columbia, Canada.
Prof J.B. Keller, Department of Mathematics, University of Stanford, USA. Prof D Hobson, Warwick.