COLLOQUIUM
DEPARTMENT OF MATHEMATICS AND STATISTICS
OAKLAND UNIVERSITY
ROCHESTER, MICHIGAN 48309
Selim Esedoglu
University of Michigan
Threshold dynamics for the mean curvature motion of networks with unequal surface tensions
Threshold
dynamics is an algorithm for moving an interface (e.g. a surface in 3D)
by mean curvature motion. It was proposed by Merriman, Bence, and Osher
in 1992, and also extended to networks of surfaces in the same paper.
This dynamics arises as gradient flow for the sum of the areas of the
surfaces in the network, and plays a prominent role in materials science
applications where it describes the motion of grain boundaries in
polycrystals (such as most metals) under heat treatment.
Further
extension of the algorithm to gradient flow for a weighted energy where
the area of each surface in the network is weighted by possibly
different constants (called surface tensions) is of great interest for
applications, but has remained elusive. In fact, previous attempts at
this turn out to be flawed, mainly due to the difficulty of ensuring
that certain natural angle conditions are satisfied along triple curves
(where three surfaces meet). We describe how to extend threshold
dynamics to this unequal surface tension setting. Joint work with Felix
Otto.
Tuesday, February 26, 2013
3:00– 4:00 P.M.
372 Science and Engineering Building
(Refreshments at 2:30-3:00 PM in the kitchen area adjacent to 368 SEB)