Mathematics and Statistics Colloquium

Date: Friday, March 7
Time: 3:30 pm
Location: Arts Building Room 206, 9 Campus Dr., Saskatoon

Free and open to the public

About this event

Bulk-surface PDEs: Modelling, Analysis, Simulations and Applications

A talk by Dr. Anotida Madzvamuse (DPhil), Department of Mathematics, University of British Columbia

In this talk, I will present a new mathematical formalism of a coupled system of bulk-surface partial differential equations (semilinear parabolic type) for describing molecular interactions (active and inactive Rho GTPases) taking place in the cytosol and the cortex (where the cortex is assumed to be a sharp surface). The model couples Laplace (in the cytosol) and Laplace-Beltrami (on the surface) operators. The first result is the generalization of Turing diffusion-driven instability for bulk-surface reaction-diffusion equations. Theoretical implications of these generalized conditions will be explored and pattern generation exhibited on various 3-dimensional domains and surfaces will be presented. As an application, I will present the bulk-surface wave pinning model, and show how this framework captures more faithfully the physical representing of the molecular interactions between active and inactive Rho GTPAses through a minimalistic model. To support theoretical findings, the bulk-surface finite element method is employed to numerically solve the coupled system of bulk-surface PDEs. If time permits, I will demonstrate how this numerical method captures the inherent theoretical properties of the bulk-surface wave pinning model.

The Colloquium Committee gratefully acknowledges that our colloquium series is supported in part by the Pacific Institute for the Mathematical Sciences.

Info: colloquium@math.usask.ca

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