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CNA Seminar
Ihsan Topaloglu
McGill University
Title: Minimization of an Energy Defined via an Attractive-Repulsive Interaction Potential

Abstract: Recently, aggregation models given by the active transport equation of the form $\rho_t - \nabla \cdot (\rho(\nabla K \ast \rho)) = 0$, where $\rho$ denotes the density of aggregation and $K$ is an interaction potential, have received much attention. This PDE is, indeed, the gradient flow of the energy $E[\rho]=\iint_{\mathbb{R}^n\times\mathbb{R}^n} K(x-y)\rho(x)\rho(y)dxdy$ with respect to the Wasserstein metric. These models have a wide range of applications including biological swarms, granular media and self-assembly of nanoparticles.

In this talk I will concentrate on the energy $E$ defined via interaction potentials of the form $K(|x|)=|x|^q/q - |x|^p/p$ in the parameter regime $-n
Recording (avi): http://mm.math.cmu.edu/recordings/cna/CNA-IhsanTopalogluTape-Oct-15-2013.avi
Recording (mp4): http://mm.math.cmu.edu/recordings/cna/CNA-IhsanTopalogluTape-Oct-15-2013.mp4
Pdf File: Topaloglu_CNA_Seminar.pdf
Date: Tuesday, October 15, 2013
Time: 1:30 pm
Location: WeH 7218
Submitted by:  David Kinderlehrer