Mathematical models of advection diffusion reaction processes are fundamental to many applied disciplines including physics, biology, ecology and medicine. This project will focus on developing mathematical and computational techniques for continuum (PDE) and/or stochastic (random walk) models of advection diffusion reaction.
Potential project topics include:
- building new simplified models that are easier to implement, interpret and analyse
- extracting new mathematical insights into advection diffusion reaction processes
- proposing new methods for parameterising models from data
- developing new numerical and/or analytical methods for solving PDE models.
All project topics can be tailored to either a PhD, Master of Philosophy (MPhil), Honours or Vacation Research Experience Scheme (VRES) project.
You can expect to:
- meet regularly with Dr Carr
- receive regular feedback on your work
- develop your skills and knowledge in applied and computational mathematics
- work closely with Dr Carr to develop mathematical and computational techniques
- implement mathematical and computational techniques in MATLAB, run simulations and generate results
- document your work and results in written form
- (potentially) publish your research in the scientific/mathematical literature.
See Dr Carr's personal research website for examples of past students projects that he has supervised and examples of co-authored journal articles he has published with VRES, Honours, MPhil and PhD students.
The primary aims of the project are to generate:
- novel mathematical knowledge
- code for advection diffusion reaction problems.
Skills and experience
Experience with differential equations and MATLAB programming is required.
You may be eligible to apply for a research scholarship.
- advection diffusion reaction
- differential equations
- random walks
- applied mathematics
- computational mathematics
Contact the supervisor for more information.