PhD Scholarship in the Area of Lie Symmetry Analysis in Regularised Nonlinear Diffusion Problems
- PhD Scholarship in the area of Lie symmetry analysis in regularised nonlinear diffusion problems
- The scholarship is open to commencing domestic and international applicants.
- The scholarship will provide a living allowance at the RTP rate for 3 years.
About this scholarship
The University of South Australia is welcoming applications for a PhD position in Applied Mathematics 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.
The successful applicant will be trained in the area of Lie symmetry analysis and its various extensions to generalised and conditional symmetries. The candidate will use these techniques to investigate the types of analytic solutions that may be found following different regularisation procedures and use this knowledge to shed light on various biological applications in which shocks may be observed.
This is an opportunity to conduct research in a collaborative research team. You will be based at the University of South Australia supervised by CI Hajek and interact with additional nodes at the University of Sydney (CIs Marangell and Wechselberger), and Queensland University of Technology (CI van Heijster).
The scholarship is open to commencing domestic and international applicants.
Applicants should have completed an Honours degree and have a strong background in mathematics. Knowledge in one or more of the following areas would be helpful: differential equations, PDEs, symmetry analysis, dynamical systems, group theory.
Applicants must meet the entry criteria for the award of a Doctor of Philosophy at the University of South Australia.
The scholarship will provide a living allowance at the RTP rate for 3 years.
Some funding is available for conference travel and for collaborative visits to the other project nodes.
How to apply and closing date
This scholarship will remain open for applications until filled.
Interested candidates should submit their CV, cover letter and academic transcripts to Dr Bronwyn Hajek at Bronwyn.Hajek@unisa.edu.au and following the initial endorsement by the supervisor, applicants will go through the UniSA online application process.