Applied mathematics

Supervisor: Associate Professor Stuart Hawkins

Topic description

The wave field scattered by a particle carries detailed information about the location, shape and material properties of the particle. Advanced algorithms are required to extract this information and use it to reconstruct the particle’s features.

In this project we will construct stochastic reconstructions of particles from acoustic and electromagnetic scattering data using Bayes theorem. A crucial component of the project will be to develop fast surrogate models for the wave scattering using neural networks.

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 Christian Thomas

Topic description

As fluid flows over a surface, it transitions from a smooth laminar state to a chaotic turbulent one. This transition is typically triggered by the growth of small two- and three-dimensional disturbances that arise naturally on aircraft wings and in flows involving rotating bodies.

Recent theoretical and experimental studies have revealed that carefully designed surface roughness can suppress these instability mechanisms and significantly delay the onset of turbulence, offering the potential for major reductions in fuel consumption and greenhouse gas emissions.

Despite these advances, existing theoretical models rely on simplified representations of surface roughness and do not fully capture the complex physics involved.

This project will develop innovative numerical methods to model and optimise laminar flow control using surface roughness, contributing to the design of more efficient and environmentally sustainable fluid systems.

Supervisor: Dr Christian Thomas

Topic description

Hybrid-nanofluids which combine multiple types of nanoparticles suspended in a base fluid, offer the potential to significantly enhance heat transfer in engineering systems such as turbomachinery, electronics cooling and renewable energy technologies. However, current mathematical models are often based on oversimplified single-phase assumptions that fail to capture the true fluid-particle interactions.

This project will develop new physically consistent two-phase models and computational methods to investigate how hybrid-nanofluids influence both heat transfer and flow stability, with the aim of identifying optimal nanoparticle combinations that enhance thermal performance while delaying laminar-turbulent transition and improving efficiency in fluid systems.

Supervisor: Associate Professor Stuart Hawkins

Topic description

Rayleigh-Bloch waves are localised unforced waves that can exist in configurations of particles arranged in an infinite periodic one-dimensional structure. Knowledge of the Rayleigh-Bloch waves in an infinite structure can inform design of finite structures that engineer waves having particular desired characteristics such as energy trapping, with applications including energy capture. I

In this project we will apply state of the art numerical methods to simulate Rayleigh-Bloch waves in infinite and finite structures comprising particles with complex morphology.