### GEORGE MASON
UNIVERSITY

DEPARTMENT OF MATHEMATICAL
SCIENCES

APPLIED AND COMPUTATIONAL MATHEMATICS SEMINAR

**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