Semester 2, Week 3: Prof Oliver Jensen, University of Manchester

Academic webpage

Title: Multicellular Calculus

Abstract: The disordered and granular nature of multicellular tissues endows them with exotic mechanical properties and presents challenges to continuum modelling frameworks.  To address this, many researchers use the vertex model as a convenient computational tool with which to simulate epithelia, the cell layers that coat developing embryos or provide protective barriers within the body.  Based on very simple constitutive assumptions, the vertex model connects the shape of individual cells to their mechanical environment.  To facilitate analysis of the model, we have developed tools of discrete calculus using a blend of mimetic finite differences and exterior calculus.  Using this machinery, I will explain how puncturing a cell monolayer excites a discrete harmonic vector field that captures some features of a simulated laser-ablation experiment.  This approach illustrates how some familiar continuum modelling techniques may be adapted to describe disordered microstructured materials, without relying on smoothness or regularity conditions

Location: Maths Lecture Theatre B