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Finite element analysis on the evolving surfaces

School of Biological Sciences

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Prof Andrew Goryachev No more applications being accepted 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. 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.

The research focus in the Goryachev group ( is on understanding biophysical mechanisms of pattern formation in biological systems via symmetry breaking. Symmetry breaking manifests itself in a variety of dazzling biological phenomena and our aim is to improve their understanding via construction of predictive mechanistic models. We are looking for motivated, enthusiastic young people with the background in physical, life, computational sciences and engineering who are passionate about research.

Several types of competitive scholarships are available for the prospective PhD students at the University of Edinburgh. Depending on the topic, allied faculty from physics, mathematics and informatics departments are available as co-supervisors.

The School of Biological Sciences is committed to Equality & Diversity:

Funding Notes

The “Institution Website” button on this page will take you to our Online Application checklist. Please complete each step and download the checklist which will provide a list of funding options and guide you through the application process.

If you would like us to consider you for one of our scholarships you must apply by 6 January 2021 at the latest.


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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