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 shallow-water 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 wave-trains and spiral waves. Propagation failure of wave-train 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 heart-beat 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 toy-model which captures all the effects observed during the numerical simulations.

Summer and Graduate schools

Les Houches School of Physics: Physics and Mathematics of Turbulent Flows at Different Scales, Les Houches, France (25 Febuary - 1 March 2019)
Summer Research Program on Dynamics of Complex Systems, ICTS, Bangalore, India (23 May - 6 June 2016)
5th ICE-EM/AMSI Summer School, University of Sydney (15 January - 9 February 2007)
Graduate School "PHYSBIO: Non-equilibrium in Physics and in Biology", St Etienne de Tineé, France (13 August - 18 October 2006)