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SAS

Seminar

Turing patterns on growing surfaces

Venkataraman, C (University of Warwick)
Thursday 15 March 2012, 11:00-11:20

Satellite

Abstract

We investigate models for biological pattern formation via reaction-diffusion systems posed on continuously evolving surfaces. The nonlinear reaction kinetics inherent in the models and the evolution of the spatial domain mean that analytical solutions are generally unavailable and numerical simulations are necessary. In the first part of the talk, we examine the feasibility of reaction-diffusion systems to model the process of parr mark pattern formation on the skin surface of the Amago trout. By simulating a reaction-diffusion system on growing surfaces of differing mean curvature, we show that the geometry of the surface, specifically the surface curvature, plays a central role in the patterns generated by a reaction-diffusion mechanism. We conclude that the curvilinear geometry that characterises fish skin should be taken into account in future modelling endeavours. In the second part of the talk, we investigate a model for cell motility and chemotaxis. Our model consists of a surface reaction-diffusion system that models cell polarisation coupled to a geometric evolution equation for the position of the cell membrane. We derive a numerical method based on surface finite elements for the approximation of the model and we present numerical results for the migration of two and three dimensional cells.

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