DEPARTMENT OF MATHEMATICAL SCIENCES

APPLIED AND COMPUTATIONAL MATHEMATICS SEMINAR

**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