Stochastic DEs
With
Jiri Horak (University of Cologne)
and Mark Peletier (Eindhoven,NL)
we have been investigating the isotropic cylinder and role of a
mountain pass solution.
Notes on simple compilation of matlab to run as standalone
Much of my recent work has looked at the role of noise in systems and
how this can be simulated and methods for reducing uncertainty and
hence obtain better predictions.
I am intersted in the numerical solution of stochastic differential
equations. I am developing new numerical methods based on exponential
integrators.
Porous Media
With Prof Sebastian Geiger in IPE I am developing efficient solvers
for 3D flow in heterogeneous porous media.
These model potential ground water contamination,
underground reservoirs, subsurface storage. These lead to
We are examining multilevel MC methods, upscaling, and modelling with
stochastic forcing and random fields.
Neuronal Dynamics
Computational models are being increasingly used
to gain insight into the behaviour and information processing abilities
of neurons. We are interested in models of single
neurons, coupled neuron dynamics as well as neural field models.
Editor of
Stochastic Methods in Neuroscience. Looking at reactions and
movements of vesicules, reaction with snap25 and syntaxin.
Buckling Cylinders
Work on buckling cylinders in primarily driven by the need for light strong
structures (such as silos, rockets, aircraft)
and the desire to understand how these structures fail.
As anyone who has crushed a can knows - cylinders are very strong but
then buckle suddenly with a great release of energy.
I am looking at the buckling of thin cylinders under axial compression,
and the numerical solution of the von Karman-Donnell
equations with a quantitative comparison between experimental and
numerical results. For further details click on the buckled cylinder.
With Alan
Champneys (Eng Maths, Bristol),
Giles Hunt (Mech Eng, Bath),
Mark Peletier (Eindhoven,NL) we examined the
isotropic cylinder and the maxwell load.
Computational PDEs
The direct approximation of global attractors and the convergence of
discrete inertial manifolds and global attractors.
Numerical solution of partial differential equations, specifically in
the context of dynamical systems. In particular the long-time
dynamical behaviour and the process through which chaos (or
unpredictability) appears in dynamical systems and investigating how
it may be reasonably approximated numerically.
In recent work have looked at Epsilon-Entropy, a measure of
complexity, in the limit of unbounded domains. This is joint work with
Jacques Rougemont on
EPSRC
grant GR/R29949/01.
Differential equations, dynamical systems, scientific computing,
numerical analysis,
numerical
continuation, computational neuroscience, numerics for
stochastic (partial) differential equations.
