Research Thesis Topic
Modelling Nonlinear Reactions and Forcing in Sub-Diffusive Systems
In recent years numerous physical and biological systems have been reported in which the diffusion rates of species cannot be characterized by the single parameter of the diffusion constant. Instead, the (anomalous) diffusion is characterized by a scaling parameter as well as a diffusion coefficient and the mean square displacement of diffusing species scales as a nonlinear power law in time. The case of subdiffusion is particularly prevalent in biological systems and is generic in media with obstacles or binding sites.
Anomalous subdiffusion can be modelled mesocopically using Continuous-Time Random Walks (CTRWs) and macroscopically by fractional subdiffusion equations. CTRWs are more general random walk where a waiting time and step length are chosen from probability densities.
A fundamental question that, has arisen in recent years, is how to incorporate reaction terms correctly when the particles involved are undergoing anomalous subdiffusion. Models derived by simply adding reaction terms to the fractional variant of the diffusion equation lead to physically unrealistic negative predictions. A number of alternative fractional reaction diffusion equations instead have been proposed. However only the case of linear reactions have been verified by the use of Monte Carlo (CTRWs) simulations. The general case of nonlinear reactions remains untested by simulation.
This project will involve the development of simulation software to simulate the mesoscopic process using CTRWs. This will also include the modelling of reactions due to particle interaction.
- Computational Engineering and Science Research Centre
- School of Agricultural, Computational and Environmental Sciences
- Applied Mathematics
- Mathematical Physics
- Numerical and Computational Mathematics
Please review the admission requirements for the academic program associated with this Thesis Topic