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Doctoral research

If you are interested in joining our group then there are plenty of possibilities. We currently invite applications to the following opportunities:

1) DPhil in Industrial Mathematics Studentship
These projects are in collaboration with Chris Breward, Jon Chapman and Peter Howell.

We currently have a fully funded studentship, to begin October 2022 in industrial mathematics. The position is open to all applicants, irrespective of nationality/residence. The application form may be found here. The successful candidate will work on one of the following four projects; each of which will involve working with industrial collaborators:

  • Batteries
    Mathematical modelling of batteries provides insight into how to design batteries and their charging/discharging regimes in order to maximise their lifetime. Large scale flow-batteries, used in grid-storage, have two porous electrodes through which an electrolyte is pumped and which are kept electrically apart by a porous separator. The flow is influenced by large gradients in chemical concentration, created by the electrochemical reactions occurring at the electrode surfaces. In this project, we will model the close coupling between fluid flow and electrochemical processes, exploit asymptotic methods and homogenisation to derive simplified models, and use numerical methods to provide comparisons with experiments as well as practical methods for finding optimal designs.

  • Decontamination
    Following exposure of porous structures to hazardous chemical agents, one standard response is to apply cleanser to the outside of the surface and work it into the surface where it reacts with, and neutralises, the agent. In this project, we will build and solve models to explore the lateral spread of agents and optimal ways of cleansing, paying particular attention to the situation where the porous medium is unsaturated. This will involve a mixture of mathematical modelling, asymptotic analysis (including homogenisation theory), and scientific computing, and our aim will be to predict optimal strategies for decontamination.

  • Filtration
    Filtration encompasses a wide range of practical applications, including the separation of blood cells, the purification of water, and the removal of dust by an air-purifier. A common theme among filtration applications is the need to know the behaviour on the small scale (such as a single dust particle sticking to a part of the filter) in order to predict the behaviour on the large scale (such as how often an air-purifier filter should be replaced). In this project, we will use homogenisation theory to connect these two otherwise disparate scales, and analyse the resulting equations using asymptotic analysis and numerical methods to predict and improve filtration performance.

  • Glass
    Glass processing typically involves the flow of a viscous liquid, whose viscosity is a strong function of temperature, in a thin domain. We are particularly interested in modelling situations where the geometry is complicated and unknown in advance and/or where the process may be subject to instabilities. In this project, we will focus on the drawing of thin glass sheets to make screens for TVs, tablets and smartphones. It is known that regions of compression can cause these sheets to buckle, resulting in local ripples in the final product. However, there is currently no good complete theory of viscous sheet buckling that explains how the amplitude of the disturbance saturates, due to weakly nonlinear effects, or how the ripples become "frozen in" as the glass cools.
Less details

2) Microscale coiling and wrapping in nature and technology
More details.

3) Engineering liquid-crystal-based platforms for rapid sensing of biomolecules
More details.

4) DPhil in the Mathematical Institute
More details.