Date: Friday, March 18, 2016
Location: 1084 East Hall (3:00 PM to 4:00 PM)
Title: Nonlocal energies defined via attractive-repulsive interaction potentials
Abstract: A variety of physical and biological interaction - from self-assembly of nano particles to collective behavior of many-agent systems such as biological swarming - can be modeled via a nonlocal energy. Depending on the choice of the interaction kernel, the asymptotic states of these physical and biological systems can be characterized as minimizers of such energies via a gradient flow connection. In this talk, first, I will present on a joint project with Katy Craig where we show that regularization of singular attractive-repulsive kernels allows us to restore convexity and differentiability; hence enables us to understand the minimizers and the gradient flows of these energies. Next, I will consider the minimization of these energies over sets. Although this nonlocal shape optimization problem poses additional challenges I will discuss the existence/nonexistence of minimizers on certain parameter regimes and present on recent results joint with Almut Burchard and Rustum Choksi.
Files:
Speaker: Ihsan Topaloglu
Institution: McMaster University
Event Organizer: Manuel Gnann mvgnann@umich.edu
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