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Low density phases in a uniformly charged liquid


This talk is concerned with the macroscopic behavior of global
energy minimizers in the three-dimensional sharp interface Ohta-Kawasaki
model of diblock copolymer melts. 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 show that the considered energy converges to a function 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, with the energy density approaching that of the minimizers of the
volume constrained problem in the whole space. This suggest that in the
microscopic limit the minimizers should appear as a uniformly distributed
array of droplets which minimize the energy density for the volume
constrained whole space problem.
http://cvgmt.sns.it/seminar/447/
When
Wed Nov 26, 2014 4:30pm – 5:30pm Coordinated Universal Time
Where
Sala Seminari (Dipartimento di Matematica) (map)