Low density phases in a uniformly charged liquid with homogeneous
neutralizing background
Cyril Muratov, NJIT
Abstract:
This talk is concerned with the macroscopic behavior of global
energy minimizers in the three-dimensional sharp interface
unscreened Ohta-Kawasaki model of diblock copolymer melts. This
model is also referred to as the nuclear liquid drop model in the
studies of the structure of highly compressed nuclear matter found
in the crust of neutron stars, and, more broadly, is a paradigm for
energy-driven pattern forming systems in which spatial order arises
as a result of the competition of short-range attractive and
long-range repulsive forces. We are interested in the large volume
behavior of minimizers in the low volume fraction regime, in which
one expects the formation of a periodic lattice of small droplets of
the minority phase in a sea of the majority phase. Under periodic
boundary conditions, we prove that the considered energy Γ-converges
to an energy functional of the limit “homogenized” measure
associated with the minority phase consisting of a local linear term
and a non-local quadratic term mediated by the Coulomb kernel. As a
consequence, asymptotically the mass of the minority phase in a
minimizer spreads evenly across the domain. We also prove that the
energy density distributes uniformly across the domain as well, and
that minimizers appear as a uniformly distributed array of droplets,
most of which minimize the energy density for the volume constrained
whole space problem. This is joint work with H. Knuepfer and M.
Novaga.