  We study the minimizers of a degenerate case of the Ohta-Kawasaki energy,
defined as the sum of the perimeter and a Coulombic nonlocal term. We start by
investigating radially symmetric candidates which give us insights into the
asymptotic behaviors of energy minimizers in the large mass limit. In order to
numerically study the problems that are analytically challenging, we propose a
phase-field reformulation which is shown to Gamma-converge to the original
sharp interface model. Our phase-field simulations and asymptotic results
suggest that the energy minimizers exhibit behaviors similar to the
self-assembly of amphiphiles, including the formation of lipid bilayer
membranes.
