Dr N Popovic
Top university
1 year ago
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Bifurcation and pattern formation on the surface of biological cells University of Edinburgh in United Kingdom
Degree Level
PhD
Field of study
Biophysics
Funding
Fully Funded
Deadline
Expired
Country
United Kingdom
University
University of Edinburgh

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About this position
Biological cells dynamically create, maintain, and disassemble cell surface structures that determine their shape and behaviour, such as directed migration. Mathematically, the study of the underlying biophysical mechanisms of intracellular morphogenesis — which includes biochemical reactions, molecular transport, and membrane dynamics, among others — frequently relies on the well-developed machinery of reaction-diffusion equations [1]. These equations can exhibit multiple-scale dynamics, giving rise to rich coherent structures that include travelling waves, excitable pulses, and spiral waves that exhibit complex bifurcations; the latter are frequently not well-understood mathematically [2,3].
In this project, the student will contribute to a rigorous mathematical understanding of bifurcations in systems of reaction-diffusion equations, building on recent advances in the study of pattern-forming models for intracellular morphogenesis.
The project will give the student a solid foundation in the mathematical modelling of intracellular morphogenesis, with a particular focus on dynamical systems techniques, such as normal forms, invariant manifolds, geometric singular perturbation theory.
No previous background on these topics is assumed, though experience in the analytical and numerical solution of ordinary and partial differential equations and some experience in coding is preferable.
If you are interested in applying to this project or have any questions, please contact Prof Andrew Goryachev (Primary supervisor): [email protected] & Dr Nikola Popovic (Second supervisor): [email protected]
Funding details
Fully Funded
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