DEPARTMENT OF MATHEMATICAL SCIENCES

APPLIED AND COMPUTATIONAL MATHEMATICS SEMINAR

**Speaker:**David Shirokoff, New Jersey Institute of Technology

**Title: ***
A simple, efficient and accurate method for computing the
order-disorder phase transition in double well energy functionals
*

**Abstract:**
A wide variety of materials 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 non-convex nature of the functionals
makes the computation and verification of global minimizers much more
difficult. Here the verification of the global minimizers is important
for understanding the material phase diagram. In this talk I will
focus on mass-constrained global minimizers for a class of double well
energy functionals: including Ohta-Kawasaki and phase-field crystals.
I will derive sufficient conditions to show that a candidate minimizer
is a global minimizer, and using convex relaxations coupled with
numerical methods find bounds on the liquid to solid phase transition
curve. I will then extend the discussion to non-constant states to
show that for thin rectangles, a one dimensional structure is the
global minimizer.

**Time:** Friday, March 6, 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