Speaker:David Shirokoff, NJIT
Title: Convex relaxations in material science and approximate global minimizers

Abstract: A wide range of material systems exhibit energy driven pattern formation governed by an underlying non-convex energy functional. Although numerically finding and verifying local minima to these functionals is relatively straight-forward, the computation and verification of global minimizers is much more difficult. Here the verification of global minimizers is often important in understanding the material phase diagram, especially at low temperatures. In this talk I will examine two separate model functionals: those arising in non-local pairwise interaction problems, and those containing a double-well potential. In the case of the pairwise interaction problems I will present an efficient systematic approach for the computation of approximate global minimizers based on a new convex relaxation and recovery technique. The approach is sometimes exact, and also provides a numerical recovery guarantee for the approximate minimizer that is often within a few percent of the global minimum. For the double-well functionals, I will derive sufficient conditions to show that a candidate minimizer is a global minimizer, and present a numerical method for estimating the order-disorder transition (ODT) curve.

Time: Friday, September 25, 2015, 1:30-2:30 p.m.

Place: Exploratory Hall, Room 4106

Department of Mathematical Sciences
George Mason University
4400 University Drive, MS 3F2
Fairfax, VA 22030-4444
http://math.gmu.edu/
Tel. 703-993-1460, Fax. 703-993-1491