Metastability and Access to the Ground State in a Class of
Variational Models for Self-assembly
Rustum Choksi, McGill University
Abstract: Self-assembly, a process whereby a
disordered system of pre-existing components form an organized
structure or pattern, is both ubiquitous in nature and important
for the synthesis of many designer materials. Focusing on
metastability and access to the ground state, we will address a
class of non-convex variational models consisting of
regularizations to a double-well potential. This class has a
rich and complex energy landscape, and includes the
Ohta-Kawasaki functional, a nonlocal perturbation of
Coulombic-type to the well-known Ginzburg-Landau/Cahn-Hilliard
free energy.
We explore a simple strategy for assessing whether or not a
particular computed metastable state is a global minimizer; the
method is based upon finding a "suitable" global quadratic lower
bound to the free energy. Finally, we address periodicity
of the ground state for Ohta-Kawasaki, both from the perspective
of quadratic lower bounds and from general energy estimates.