Supervisors
- Position
- Senior Lecturer
- Division / Faculty
- Faculty of Science
Overview
Mathematical models of particle transport are fundamental to many applied disciplines including physics, biology, ecology and medicine. Particle transport is typically modelled using either a stochastic model, where probability rules govern the motion of individual particles, or a continuum model, where partial differential equations govern the concentration of particles in space and time. This project aims to use analytical and numerical techniques from applied and computational mathematics to address one or both of the following questions:
- what is the average time for a particle to exit a specified region?
- what proportion of particles remain after a certain amount of time?
The project can be tailored to either a Master of Philosophy (MPhil), Honours or Vacation Research Experience Scheme (VRES) project. See Dr Carr's personal research website for examples of past student projects that he has supervised.
Research activities
You can expect to:
- meet regularly with Dr Carr
- solve problems using pen and paper
- implement code in MATLAB, run simulations and generate results
- document your work and results in written form
- receive regular feedback on your work
- (potentially) publish your research as a co-authored journal article in the scientific/mathematical literature.
Outcomes
This project provides you with the opportunity to:
- experience mathematical research
- expand your skills and knowledge in applied and computational mathematics
- improve your MATLAB programming skills
- develop your mathematical writing and communication skills
- investigate your potential for pursuing further research (e.g. MPhil/Honours for VRES applicants and PhD for MPhil/Honours applicants).
Skills and experience
Some experience with MATLAB programming and differential equations is required. No previous experience in probability or statistical modelling is required.
Scholarships
You may be eligible to apply for a research scholarship.
Explore our research scholarships
Keywords
- differential equations
- random walks
- applied mathematics
- computational mathematics
- advection diffusion reaction
Contact
Contact the supervisor for more information.