Calculating the duration of time required for a diffusive process to end is a classical problem in mathematics, engineering, biology and economics. The concept of mean exit time is widely used to study transport phenomena in biology, such as calculating the duration of time required for a protein created in a cell nucleus to reach the cell membrane. While many exact calculations of mean exit time are known for simple geometries and homogeneous media, exact solutions are rare for complicated geometries or heterogeneous media.
In this project we will adapt techniques from groundwater flow modelling to construct, visualise and interpret exact solutions for the mean exit time in a range of complicated geometries.
- Construct stochastic random walk simulations of diffusion in complex geometries and with variable material coefficients.
- Adapt exact solutions from the Analytic element modelling literature to develop new solutions of Poisson's equation in complex geometries and with variable material coefficients.
- Compare stochastic and analytical results.
- New stochastic simulation algorithms.
- New exact expressions for the solution of Poisson's equation in complex geometries, and with variable material coefficients.
- Publish the outcomes in the applied mathematics/mathematical biology literature.
Skills and experience
The student should have:
- a strong programming background
- completed undergraduate subjects in ordinary differential equations (MXB225).
Contact Professor Matthew Simpson for more information.