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  Finite element analysis on the evolving surfaces

   School of Biological Sciences

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  Prof Andrew Goryachev  Applications accepted all year round  Competition Funded PhD Project (Students Worldwide)

About the Project

A PhD project is available in the group of Andrew Goryachev to develop and/or adapt existing finite element methods for solution of the free boundary problem involving the equations of continuous mechanics on the evolving 3D surface. The project is directly inspired by the whole-cell biomechanics of biological cells. The student will develop finite element methods for simulation of the coupled Navier-Stokes and reaction-diffusion-advection equations on the evolving surface using the approach of tangential differential calculus. The problem will be solved in the thin shell approximation and may be extended to include coupling of the equations on the surface to the equations in the bulk. The project is suitable for graduates with training in applied mathematics, theoretical physics, and numerical methods for partial differential equations.

This project will be open for competition for funding in the autumn 2021 to start in October 2022. Candidates able to secure their own funding can apply at any time. However, all interested candidates are strongly advised to directly contact the supervisor ([Email Address Removed]) before applying.


The Goryachev group works on the interface of mathematical modelling, soft matter physics, and cell biology. The student will receive training in nonlinear dynamical systems, bifurcation theory and stability analysis. The project offers an excellent opportunity to enter modern cutting-edge research on the interface of biological and physical sciences while contributing to publications in the high-profile journals.

Biological Sciences (4) Mathematics (25) Physics (29)


1. Dziuk, G. and Elliot, C. M. Acta Numerica 2013, 22, 289).
2. Kovacs, B. et al. Numer Math 2017, 137, 643
3. A. van Loon, I. Erofeev, I. Maryshev, A. Goryachev, A. Sagasti, Cortical contraction drives the 3D patterning of epithelial cell surfaces, J Cell Biol, 219(3), (2020).

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 About the Project