Simon Malham Home Page

Dr Simon J.A. Malham

Room No. : CM T.21
Address :    Mathematics Department
                    Heriot-Watt University
                    Edinburgh EH14 4AS
                    Scotland
Telephone No. : +44 131 451 3254
Fax No. : +44 131 451 3249
E-Mail Address : simonm[at]ma.hw.ac.uk

Research

The Navier-Stokes equations and turbulent flows. Do solutions of the Navier-Stokes equations develop a singularity in finite time? Since Leray suggested these singular solutions may signify the onset of turbulence in a real fluid flow, it is also an interesting engineering issue. This remains an important open problem and is currently one of the millenium prize problems set by the Clay Institute and worth a million dollars (see the criteria devised by Charles Fefferman).
Reaction-diffusion phenomena:

Travelling waves;
Autocatalysis;
Combustion.

Computational spectral theory:

Shooting and matching, Evans function;
Geometric/Lie group integration;
Grassmannian and Riccati numerical methods;
Multi-dimensional stability.

Stochastic differential equations:

Strong approximation;
Lie group integration;
Hopf algebra structure;
Implicit methods;
Positivity preservation;
Linear-quadratic optimal control.

If you would like to know more or are interested in doing a PhD, email me: simonm [at] ma.hw.ac.uk.

Publications

Bartuccelli, M.V., Gibbon, J.D. and Malham, S.J.A. 1993, Lattice methods and the pressure field for solutions of the Navier-Stokes equations (pdf), Nonlinearity 6(1), pp. 79-92.
Bartuccelli, M.V., Doering, C.R., Gibbon, J.D. and Malham, S.J.A. 1993, Length scales in solutions of the Navier-Stokes equations (pdf), Nonlinearity 6(4), pp. 549-568.
Malham, S. and Xin, J. 1998, Global solutions to a reactive Boussinesq system with front data on an infinite domain (pdf), Comm. Math. Phys. 193(2), pp. 287-316.
Balmforth, N.J., Craster, R.V. and Malham, S.J.A. 1999, Unsteady fronts in an autocatalytic system (pdf), Proc. R. Soc. Lond. A 455, pp. 1401-1433.
Malham, S.J.A. and Oliver, M. 2000, Accelerating fronts in autocatalysis (pdf) , Proc. R. Soc. Lond. A 456, pp. 1609-1624.
Ford, R., Malham, S.J.A. and Oliver, M. 2002, A new model for shallow water in the low Rossby-number limit (pdf) , JFM 450, pp. 287-296.
Aparicio, N.D., Malham, S.J.A. and Oliver, M. 2005, Numerical evaluation of the Evans function by Magnus integration (pdf), BIT 45, pp. 219-258.
Lord, G., Malham, S.J.A. and Wiese, A. 2008, Efficient strong integrators for linear stochastic systems (arxiv link), SIAM J. on Numerical Analysis 46(6) (2008), pp. 2892-2919.
Malham, S. and Niesen, J., Evaluating the Evans function: order reduction in numerical methods (arxiv link), Math. Comp. 77 (2008), pp. 159-179.
Malham, S.J.A. and Wiese, A., Stochastic Lie group integrators (arxiv link), SIAM J. Sci. Comput. 30 (2) (2008), pp. 597-617.
Ledoux, V., Malham, S.J.A. and Thummler, V., Grassmannian spectral shooting (arxiv link), Math. Comp., published electronically Jan 2010.
Malham, S.J.A. and Wiese, A. 2009, Positive stochastic volatility simulation (arxiv link), under revision.
Ledoux, V., Malham, S.J.A., Niesen, J. and Thummler, V., Computing stability of multi-dimensional travelling waves (arxiv link), SIAM J. on Applied Dynamical Systems 8(1) (2009), pp. 480-507.
Malham, S.J.A. and Wiese, A., Stochastic expansions and Hopf algebras (arxiv link), Proc. R. Soc. A 465 (2009), pp. 3729-3749. doi:10.1098/rspa.2009.0203

Unpublished reviews/notes/thesis

Miscellaneous

Last updated: 8th February 2010. simonm [at] ma.hw.ac.uk

Back to the Mathematics Department's Homepage.

Dr Simon J.A. Malham

Research

Publications

Unpublished reviews/notes/thesis

Thesis

Reviews

Lecture notes

Miscellaneous