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.