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
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Fairfax, VA 22030-4444
http://math.gmu.edu/
Tel. 703-993-1460, Fax. 703-993-1491