On global minimizers for a variational problem with long-range interactions

Abstract

[Energy-driven pattern formation induced by competing short and longrange interactions is common in many physical systems. In these proceedings we report on certain rigorous asymptotic results concerning global minimizers of a nonlocal perturbation to the well-known Ginzburg-Landau/Cahn-Hilliard free energy. We also discuss two hybrid numerical methods for accessing the ground states of these functionals.]