DEPARTMENT OF MATHEMATICAL SCIENCES

APPLIED AND COMPUTATIONAL MATHEMATICS SEMINAR

**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

Department of Mathematical Sciences

George Mason University

4400 University Drive, MS 3F2

Fairfax, VA 22030-4444

http://math.gmu.edu/

Tel. 703-993-1460, Fax. 703-993-1491