Diffuse Interfaces and Topology: A Phase-Field Model for Thin Membranes

Applied Analysis Seminar

Meeting Details

For more information about this meeting, contact Kristin Berrigan, Mark Levi, Alexei Novikov, Mykhailo Potomkin, Leonid Berlyand.

Speaker: Stephan Wojtowytsch, Carnegie Mellon University

Abstract: We consider the problem of minimizing Willmore's energy in the class of connected surfaces with prescribed area which are embedded into a bounded domain. The problem is motivated from models in biology for lipid bilayers, in particular inner mitochondrial membranes. From a computational point of view, it may be favorable 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 and numerical evidence of the effectiveness of our method. Time permitting, we will present some analytical results on minimizers in the sharp interface model.

Room Reservation Information

Room Number: 114 McAllister

Date: 01/09/2019

Time: 3:30pm - 4:30pm