PhD Studentships: Nonlinear Problems Related to Traction Force Microscopy

PhD studentship in the Analysis and Numerical Analysis of Partial Differential Equations 

Type of award

Postgraduate Research

PhD project

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

Traction force microscopy (TFM) involves estimating forces exerted by cells indirectly from deformations of the medium upon which the cells exert force. Crucial to this is the formulation of a, typically nonlinear, constitutive law relating force generation to medium deformation as well as the formulation of a well-posed inverse problem to recover forces from the observed deformation. Another challenge arises in the numerical approximation of the inverse problem which mandates the solution of the forward model. This is well understood in the linear case but much less studied for nonlinear models.

This project seeks to develop a framework for the formulation of well-posed inverse problems related to TFM. We will focus on energetic models for the mechanics of the medium which involve appropriate notions of convexity (e.g. polyconvexity, quasiconvexity) such that the forward problem is well-posed but which allow for enough generality to be applicable. We will also develop, analyse and implement numerical methods for the approximation of the inverse problem. The project is suitable for students interested in some, or all, of the following areas: analysis of PDE, continuum modelling, finite element methods, numerical analysis and mathematical biology.

Amount

• Fully-paid tuition fees for three and a half years at the home or international 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

03/05/2024

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 no MPS/2024/KOU

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 Koumatos at k.koumatos@sussex.ac.uk or Dr Venkataraman at c.venkataraman@sussex.ac.uk

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