A phase field model for thin elastic structures with topological constraint

Date

Jun 1, 2017

Time

3:15 PM - 4:15 PM

Speaker

Prof. Dr. Patrick Dondl

Affiliation

Universität Freiburg, Abt. für Angewandte Mathematik

Series

TUD Mathematik Oberseminar Analysis

Language

en

Main Topic

Mathematik

Other Topics

Mathematik

Host

Prof. Dr. S. Neukamm

Description

With applications in the area of biological membranes in mind, we consider the problem of minimizing Willmore’s energy among the class of closed, connected surfaces with given surface area that are confined to a fixed container. Based on a phase field model for Willmore’s energy originally introduced by de Giorgi, we develop a technique to incorporate the connectedness constraint into a diffuse interface model of elastic membranes. Our approach uses a geodesic distance function associated to the phase field to discern different connected components of the support of the limiting mass measure. We obtain both a suitable compactness property for finite energy sequences as well as a Gamma-convergence result. Furthermore, we present computational evidence for the effectiveness of our technique. The main argument in our proof is based on a new, natural notion of convergence to describe phase fields in three dimensions.

Links

• Oberseminar Analysis

Last modified: May 4, 2017, 3:31:10 PM