Postgraduate research topics in applied mathematics
Thinking of doing a PhD or research degree in applied mathematics? Here are some suggested topics.
Alternatively, you may have your own topic ideas you'd like to explore. In that case, talk to staff with related interests about developing a proposal.
Supervisors: Dr Catherine Penington and Dr Justin Tzou
Topic Description:
Cells in real biological tissue exist in a crowded environment of other cells and extra-cellular matrix. Many mathematical models and experiments in a lab only include one type of cell to investigate how quickly the cells spread out and invade other tissue. This project will use partial differential equations and probabilistic individual agent models, both existing and newly developed as part of the project, to model and better understand how more representative and complex interactions with the environment affect the spread of cells in real biological tissue. There will (hopefully) be opportunities to work with experimental data on melanoma cells. A background in applied maths is important, but the biology can be learnt as part of the project and is not a prerequisite.
Supervisor: Dr Justin Tzou
Topic Description:
The study of pattern formation in reaction-diffusion systems, which model phenomena such as animal coat markings and patterned vegetation, uses various analytic and numerical methods for analyzing partial differential equations. Many such patterns can exhibit sharp gradients or large deviations from the steady state. The technical difficulties caused by these characteristics have constrained their study to domains with simple geometries, such as disks and spheres. As a result, the effect of curvature on the dynamics and stability of patterns is not yet fully understood. This project will use finite difference, asymptotic, and local analytic methods to formally characterise how localised patterns behave on surfaces of non-constant curvature. The work may involve external collaboration(s).
Supervisor: Dr Christian Thomas
Topic Description:
As fluid flows over a surface, it transitions from a smooth laminar state to a turbulent one. This process is often excited by small two- and three-dimensional disturbances that occur naturally on the wings of aircraft and in applications involving a rotating body. Recent theoretical and experimental results have shown that the right sort of surface roughness can suppress the onset of these disturbances and delay transition, potentially leading to significant reductions in fuel usage and greenhouse gas emissions. However, current theoretical models for surface roughness are based on an approximation of the surface conditions. This project will develop new innovative numerical methods for optimising laminar flow control via surface roughness.