Speaker:Xiaofeng Ren, Mathematics, George Washington University
Title: Droplet solutions of a 2D free boundary problem from diblock copolymer morphology
Abstract: The Ohta-Kawasaki density functional theory of diblock copolymers gives rise to a nonlocal free boundary problem. In a proper parameter range an equilibrium pattern of many droplets is proved to exist in a general planar domain. A sub-range is identified where the multiple droplet pattern is stable. Each droplet is close to a round disc. The boundaries of the droplets satisfy an equation that involves the curvature of the boundary and a quantity that depends nonlocally on the whole pattern. The locations of the droplets are determined via a Green's function of the domain. In constructing the droplet pattern we overcome three obstacles: interface oscillation, droplet coarsening, and droplet translation.
Time: Friday, February 22, 2007, 1:30-2:30 p.m.Place: Research I, Room 301
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