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Dr N Popovic

Top university

1 year ago

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

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Country

United Kingdom

University

University of Edinburgh

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Keywords

Biophysics
Mathematics
Mathematical Modeling
Computational Physics
Computational Mathematics
Reaction-diffusion Equations
Applied Mathematics
physicss
Biological Sciences
Bioph

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): & Dr Nikola Popovic (Second supervisor):

Funding details

Fully Funded

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