Interfacial patterns in systems with long-range interactions of Coulomb type

This talk will present an overview of modeling, microstructure, and
fluctuation phenomena in systems with competing short-range attractive
interactions and long-range repulsive interactions of Coulomb
type. Due to the fundamental character of Coulomb interaction, these
systems arise in a wide range of applications, from polyelectrolytes and
diblock copolymers to hight-$T_c$ superconductors. We consider the
situation in which the long-range interaction is a singular
perturbation and introduce an interfacial reduction for the energetics on
an infinite domain. This reduction allows one to study existence and
stability of localized and periodic patterns in the appropriate singular
limits, as well as the effect of thermal fluctuations.