The University of Sydney is welcoming applications for a Postdoctoral Research Associate (Level A) in Dynamical Systems to work on the project "A Novel Geometric Approach to Shocks in Reaction-Nonlinear Diffusion Models" which has recently been funded by the ARC (Australian Research Council). Reaction-nonlinear diffusion models play a vital role in the study of cell migration and population dynamics. However, the presence of aggregation, or backward diffusion, leads to the formation of shock waves - distinct, sharp interfaces between different populations of densities of cells - and the breakdown of the model.
The aim of this project is to develop new geometric methods to explain the formation and temporal evolution of shock waves in regularised reaction-nonlinear diffusion models and devise innovative tools in singular perturbation theory and stability analysis that will identify key parameters in the creation of shock waves, as well as their dynamic behaviour.
This is an opportunity to conduct research in a collaborative research team. You will be based at the School of Mathematics and Statistics at the University of Sydney and supervised by CIs Marangell and Wechselberger and interact with additional nodes at the University of South Australia (CI Hajek), and Queensland University of Technology (CI van Heijster).
The successful applicant will initiate and construct numerical algorithms for multiple scale problems which are necessary for the existence analysis and develop a numerical toolbox for the stability analysis of regularised reaction-nonlinear diffusion problems.
The role will require carrying out scientific research and preparing and presenting scientific results in papers and conferences, co-supervising undergraduate and graduate research students, assisting in the recruitment of research students and continuously working towards attracting new funding. Additionally, you will help to coordinate the research of different researchers.
For more information and to apply, click here.