Applied and Computational Math Seminar: Diffuse Interfaces and Topology: A Phase-Field Model for Willmore's Energy

Speaker: Stephan Wojtowytsch, Carnegie Mellon University
Title: Diffuse Interfaces and Topology: A Phase-Field Model for Willmore's Energy

Abstract: We consider the problem of minimising Willmore's energy in the class of connected surfaces with prescribed area embedded into a bounded domain which is a component of models for lipid bilayers. From a computational point of view, it may be favourable to approximate the curvature energy by a phase field functional. Diffuse Interfaces, can easily separate into multiple components along a gradient flow evolution. This is overcome using a topological penalty term in the functional involving a geodesic distance function. We present here a proof of Gamma-convergence to the sharp interface limit in two and three dimensions and numerical evidence of the effectiveness of our method in two dimensions.

Time: Friday, April 27, 2018, 12:30-1:30pm - JOINT CAGS and Computational and Applied Math Seminar

Place: Exploratory Hall, Room 4106