Overview
Topic status: We're looking for students to study this topic.
Reaction-diffusion models have traditionally been used to describe cell population phenomena with great success. Although appropriate from a mechanistic point of view for populations of low density, such models are proving to be inadequate when attempting to mathematically describe dense aggregates of cells, such as tissues. In such cases where cell-cell contacts dominate, advective processes depicting chemotaxis and haptotaxis need to be included. In this project you will explore nonlinear advection-diffusion-reaction models in one space dimension where diffusion is considered small. Such models typically hold the potential to develop travelling waves with shock fronts; however predicting exactly where and when such shocks develop is not a fully developed science. Defining the advection-diffusion-reaction models in relation to an invariant folded manifold allows us to interpret the shock-fronted travelling waves as discontinuous jumps from one branch of the manifold to another. Exploring the phase space of these phenomena and extending the classical theory associated with relaxation oscillators and canards, will contribute to putting the modelling of dense cell populations on a new theoretical foundation.
- Study level
- PhD
- Supervisors
- QUT
- Organisational unit
Science and Engineering Faculty
- Research area
- Contact
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Please contact the supervisor.
Professor Graeme Pettet
