PhD Studentship in the numerical analysis of PDEs on surfaces with applications to biomembranes – University of Sussex

This is a project in the broad area of applied and numerical analysis for geometrical partial differential equations with applications to cell biology.

The shape taken by biological cells as well as a variety of cellular functions are known to be regulated by the interplay between proteins on the cell membrane as well as the curvature of the membrane. It is widely accepted within the literature that the stationary state of lipid membranes are given by minimisers of the Canham-Helfrich energy. This energy depends on geometric quantities, as such, analysis is rather difficult. Over recent years, more tractable energies have been derived which approximate this energy for membranes ‘near’ to critical points [1,2]. With these energies, some analysis and numerical analysis [3,4] is possible.

This project seeks to develop the numerical analysis related to these approximating energies, as well as to consider optimal control problems which consider proteins embedded within, or attached to, the membrane. The project would be suitable for a student interested in some, or all, of the following areas: geometric PDEs, PDEs on surfaces, finite element methods, numerical analysis and mathematical biology.

·      C.M. Elliott, C. Gräser, G. Hobbs, R. Kornhuber, and M.-W. Wolf. A variational approach to particles in lipid membranes. Archive for Rational Mechanics and Analysis, 2016.

·      C.M. Elliott, H. Fritz, and G. Hobbs. Small deformations of Helfrich energy minimising surfaces with applications to biomembranes. Mathematical Models and Methods in Applied Sciences, 2017

·      C.M. Elliott, L. Hatcher, and B. Stinner. On the sharp interface limit of a phase field model for near spherical two phase biomembranes. Interfaces and Free Boundaries, 2022

·      C.M. Elliott and P.J. Herbert. Second order splitting of a class of fourth order PDEs with point constraints. Mathematics of Computation, 2020

Amount

·      Fully-paid tuition fees for three and a half years at the home fee status.

·      A tax-free bursary for living costs for three and a half years (£18,622 per annum in 2023/24).

·      Additional financial support is provided to cover short-term and long-term

travel.

·      If you are not a UK national, nor an EU national with UK settled/pre-settled

status, you will need to apply for a student study visa before admission.

Eligibility

Applicants must hold, or expect to hold, at least a UK upper second class degree (or non-UK equivalent qualification) in Physics/Mathematics, or a closely-related area, or else a lower second class degree followed by a relevant Master’s degree.

This award is open to UK and International students

Deadline

1^st June 2024

How to apply

Apply through the University of Sussex on-line system.

https://www.sussex.ac.uk/study/phd/apply/log-into-account

Select the PhD in Physics/Mathematics, with an entry date of September 2024.

In the Finance & Fees section, state that you wish to be considered for studentship MPS/2024/HER

We advise early application as the position will be filled as soon as a suitable applicant can be found.

Due to the high volume of applications received, you may only hear from us if your application is successful.

Contact us

If you have practical questions about the progress of your on-line application or your eligibility, contact mps-pgrsupport@sussex.ac.uk

For academic questions about the project, contact Dr Philip Herbert at p.herbert@sussex.ac.uk.