CMU Campus
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/Colloquium/Joint Pitt-CNA Colloquium
Rustum Choksi
McGill University
Title: Geometric Variational Problems with Nonlocal Interactions

Abstract: The liquid drop model, an old problem of Gamov for the shape of atomic nuclei, has recently been rediscovered and studied within the framework of the modern calculus of variations. The problem takes the form of a nonlocal isoperimetric problem (NLIP) on all 3-space with nonlocal interactions of Coulombic type.

I will first discuss the context, the Ohta-Kawasaki theory for self-assembly of diblock copolymers, in which Gamov's problem reappeared, and present the current state of the art for the existence and nonexistence of minimizers. Then I will focus on the analysis of two related variational problems. The first addresses the structure of minimizers of the NLIP in the presence of a confining term. This is joint work with S. Alama, L. Bronsard and I. Topaloglu. The second variant consists of a geometric problem based solely on competing interaction potentials of algebraic type. The problem is directly related to a wide class of self-assembly/aggregation models for interacting particle systems (eg. swarming). This is joint work with A. Burchard and I. Topaloglu.

Pdf File: Choksi.pdf
Date: Thursday, March 30, 2017
Time: 4:30 pm
Location: Wean Hall 7218
Submitted by:  Ian Tice