Localized domain patterns in complex polymers

abstract. Block copolymers are macromolecules that can form variety of
microstructures as a result of incomplete phase separation.  For this
reason, they are natural candidates for controlled nanoscale
self-assembly and possess novel material properties.

This talk focuses on the mathematical issues surrounding density
functional models of dilute diblock copolymer mixtures and their
related gradient flows. Isolated structures emerge in the subcritical
regime (stable to phase segregation) that resemble amphiphilic
bilayers and micelles.  Existence and dynamical properties of these
solutions are discussed. Curve-like two dimensional domains also arise
from one dimensional localized patterns.  There are a rich set of
associated dynamics, such as curve lengthening, buckling, and
side-branching.  Time permitting, a similar set of phenomenon for the
Swift-Hohenberg equation will be discussed.