Center for                           Nonlinear Analysis CNA Home People Seminars Publications Workshops and Conferences CNA Working Groups CNA Comments Form Summer Schools Summer Undergraduate Institute PIRE Cooperation Graduate Topics Courses SIAM Chapter Seminar Positions Contact 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 \$-nRecording (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.pdfDate: Tuesday, October 15, 2013Time: 1:30 pmLocation: WeH 7218Submitted by:  David Kinderlehrer