Teaching
Lecture courses
Possible undergraduate or honours projects

Networks of coupled oscillators
Many biological systems are structured as a network. Examples range
from microscopic systems such as genes and cells, to macroscopic
systems such as fireflies or even an applauding audience at a
concert. Of paramount importance is the topography of such a network, ie how
the nodes, let's say the fireflies, are connected and how they
couple. Can they only see their nearest neighbours, or all of
them. Are some fireflies brighter than others, and how would that
affect the overall behaviour of a whole swarm of fireflies? For
example, the famous 'only 6 degrees of separation'law for the
connectivity of human relationships is important in this context.
In this project we aim to understand the influence of the topography
of such a network. Question such as: How should a network be
constructed to allow for maximal synchronization will be
addressed. This project requires new creative ideas and good
programming skills.

Dispersive regularization of fluid systems
It is the aim of this project to develop innovative numerical methods
to integrate evolution equations which support shock solutions. Shock
solutions arise as generic solutions in incompressible fluid dynamics
and rarefied gas dynamics. We will develop models and techniques which
approximate the essential dynamics on a coarse grid in such a way that
the price is not paid by sacrificing the preservation of conservation
laws of the underlying equations. The project will do this for the so
called shallowwater equations.
Prior knowledge of Matlab and a symbolic software package such as
mathematica or Maple is desirable.

Critical pulse propagation in excitable media
Many systems in biology and chemistry are so called excitable
media. Examples are nerve fibres and heart tissue. Excitable media can
support wavetrains and spiral waves. Propagation failure of
wavetrain is often associated with clinical conditions such as atrial
fibrillation in cardiology. The proposed project investigates
propagation failure in 1D using a novel perturbation technique. This
work is both of analytical and of computational nature. The proposed
work will look at issues of propagation failure which have so far not
been explored.
This project requires sound analytical and programming skills.

Cardiac alternans
Cardiac alternans is the phenomenon where a short heartbeat duration
is followed by a long one, followed by a short one and so forth. It is
widely believed that these alternans are the precursors of fatal
cardiac failures such as atrial fibrillation. This project  aimed at
students interested in mathematical biology  will investigate
different models of the heart, and study the possibility of alternans
within these models. Questions such as ``Are alternans a real
instability, and on which physiological time scale does the possible
instability evolve?'', or ``Is this a stable phenomenon?'' will be
investigated.
This project is mainly computational, although in the case of quick
progress, we can build an analytical toymodel which captures all the
effects observed during the numerical simulations.
Summer and Graduate schools