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CNA Seminar/Colloquium/Joint Pitt-CNA Colloquium
Ihsan Topaloglu
Virginia Commonwealth University
Title: Droplet phase in a nonlocal isoperimetric problem under confinement

Abstract: In this talk I will consider the small volume-fraction asymptotic limit of a nonlocal isoperimetric functional with a confinement term. This functional is derived as the sharp interface limit of a variational model for self-assembly of diblock copolymers under confinement by nanoparticle inclusion. By considering confinement densities which are spatially variable and attain a nondegenerate maximum, I will present a two-stage asymptotic analysis in the sense of Γ-convergence wherein a separation of length scales is captured due to the competition between the nonlocal repulsive and confining attractive effects in the energy. The results will also relate to existence and non-existence of minimizers of a recently well-studied nonlocal isoperimetric functional which appears in the liquid drop model. This is a joint work with S. Alama, L. Bronsard, and R. Choksi.

Recording: http://mm.math.cmu.edu/recordings/cna/Ihsan_Topaloglu_small.mp4
Date: Tuesday, December 6, 2016
Time: 1:30 pm
Location: Wean Hall 7218
Submitted by:  Ian Tice