At heart I am a parabolic PDE person. Currently, my favourite equations and problems all take this form.

My research program has three main components:

Applied Math Modelling
My work in this area focusses on partial differential equation models for physical systems arising in continuum mechanics. I am particularly interested in asymptotics and simulation for higher-order PDEs and especially in finite time blow-up phenomena. Lately, I have also begun working on problems from image processing.

Relevant papers:




Numerical Analysis
The PDEs I typically study require adaptive numerical methods in time and space. This has lead to work on Parabolic Monge-Ampere equations, r-adaptivity and scaling invariance.

Relevant papers:



Preprints

The following papers are in revision and are available on request.


The following papers have been recently submitted:
  • (In-)Stability of Singular Equivariant Solutions to the Landau-Lifshitz-Gilbert Equation. Joint work with Jan Bouwe van den Berg. Submitted to Communications in Pure and Applied Mathematics (2010).

Industrial Mathematics
I both run and participate in a variety of academic/industrial workshops aimed at bringing high level research tools to bear on industrial problems.
Study groups provide a platform for mathematicians and people working in industry to come together and work on problems in a focussed environment. Students and academics alike get to learn and apply new skills directly to problems of immediate interest and also to develop new connections and possible future industrial collaboration. And, of course, a good time is generally had by all. For a history of the study group concept, go to the source.

Industrial Reports:
(Note: Industrial reports have multiple (possibly 10!) authors.  For brevity these have been omitted here.)


  1. Sodium Flux during Haemodialysis. Proceedings of the OCCAM–Fields–MITACS Biomedical Problem Solving Workshop, 2009.
  2. Proceedings of the 2008 MITACS Industrial Mathematics Summer School. (Editor.)
  3. Proceedings of the 2007 MITACS Industrial Mathematics Summer School. (Editor.)
  4. Proceedings of the 10th PIMS Industrial Problem Solving Workshop. (Editor.)
  5. Cavity formation in loosely packed sandstone. Internal report of the third Schlumberger Mathematical Study Group. (2006)
  6. Modelling the spread of SARS over intercontinental travel routes. Proceedings of the First Fields-MITACS Industrial Math Workshop. (2006)
  7. Mathematical techniques for neuromuscular analysis. Proceedings of the Fifty-Second European Study Group with Industry, 109–127, CWI Syllabi, 55. CWI, Amsterdam, 2006.
  8. Proceedings of the Fifty-Second European Study Group with Industry. Edited by Jan Bouwe van den Berg, Sandjai Bhulai, Joost Hulshof, Ger Koole, Corrie Quant and JF Williams. CWI Syllabi, 55. Centrum voor Wiskunde en Informatica, Amsterdam, 2006. 129 pp. (Editor.)
  9. Droplet breakup in polymeric liquids. Proceedings of the 45th European Study Group with Industry. 2003.
  10. Spider silk spinning. Proceedings of the 46th European Study Group with Industry. 2003.
  11. The Artis Problem. Proceedings of the 42nd European Study Group with Industry. 2002
  12. Magma Design Automation: Component placement on chips; the “holey cheese” problem. Proceedings of the 42nd European Study Group with Industry. 2002.
  13. Modelling crystal growth. Proceedings of the fifth PIMS Industrial Problem Solving Workshop. 2001
  14. Temperatures in cold rooms. Proceedings of the 40th European Study Group with Industry. 2001
  15. Induction heating in oil flow problems. Proceedings of the fourth PIMS Industrial Problem Solving Workshop. (2000)
  16. Thermal modelling in polymer extrusion. Proceedings of the 39th European Study Group with Industry. (2000)
  17. Contaminant transport in a municipal water system. Proceedings of the third PIMS Industrial Problem Solving Workshop. (1999)