Mathematical models involving partial differential equations (PDEs) are useful for simulating many important physical processes including heat and mass transfer, groundwater flow, pollutant transport and drug delivery. This project will focus on developing new mathematical and computational techniques to solve, approximate and/or analyse PDE models.
Potential project topics include:
- developing new numerical and/or analytical methods for solving PDE models
- building new reduced-order PDE models that are easier to solve, interpret or analyse
- extracting insight into time scales of PDE models, such as the amount of time required to reach steady state
- proposing new methods for parameterising PDE models from experimental data.
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 new mathematical and/or computational techniques
- implement mathematical and/or computational techniques in MATLAB, run simulations and generate results
- document your work and results in written form
- write up and publish your research.
For Honours and VRES projects, Dr Carr will typically lead the write up and publication of the work. See my personal research website for examples of past students projects that I have supervised and examples of co-authored journal articles I have published with VRES, Honours, MPhil and PhD students.
The primary aim of the project will be to produce new mathematical research that can be published in the mathematical/scientific literature.
Skills and experience
Experience in solving differential equations and MATLAB programming is required.
You may be eligible to apply for a research scholarship.
- advection diffusion reaction
- partial differential equations
- applied mathematics
- computational mathematics
Contact the supervisor for more information.