For more information about this meeting, contact Fei Wang, Hope Shaffer, Toan Nguyen, Mark Levi, Victor Nistor, Jinchao Xu, Ludmil Zikatanov.

Title: | Algorithms for anisotropic mean curvature flow of networks. |

Seminar: | Computational and Applied Mathematics Colloquium |

Speaker: | Selim Esedoglu, University of Michigan |

Abstract Link: | http://www.math.lsa.umich.edu/~esedoglu/ |

Abstract: |

ABSTRACT: 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 1989, 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 weighted mean curvature flow of networks, where the surface tension of each interface in the network may be different and may depend on the direction of the normal, is of great interest for applications, but has remained elusive. In fact, previous attempts at even the simpler case where the area of each surface in the network is weighted by a different constant 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, first to unequal but constant surface tensions (joint work with Felix Otto), and then to unequal and anisotropic (normal dependent) surface tensions (joint work with Matt Elsey and Felix Otto). |

### Room Reservation Information

Room Number: | MB106 |

Date: | 10 / 14 / 2013 |

Time: | 02:30pm - 03:30pm |