[CvGmt News] seminario

[Matteo Novaga]

segnalo ad eventuali interessati:


Wednesday, November 26, 2014
Ora Inizio: 17:30
Aula: Sala Seminari (Dip. Matematica)
Relatore: Matteo Novaga (Univ. Pisa)

Title: Low density phases in a uniformly charged liquid

Abstract: 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.