Seminari di Equazioni Differenziali e Applicazioni: Low density phases in a uniformly charged liquid

Mercoledì 21 Gennaio 2015, ore 12:15 - Aula 2AB40 - Matteo Novaga



Mercoledì 21 Gennaio 2015 alle ore 12:15 in aula 2AB40, Matteo Novaga (Università di Pisa) terrà un seminario dal titolo "Low density phases in a uniformly charged liquid".

I will discuss the macroscopic behavior of global energy minimizers in the three-dimensional sharp interface Ohta-Kawasaki model of diblock copolymer melts. I'm 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, I 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. I also show 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. This is a joint project with C. Muratov and H. Knuepfer.

Rif. Int. M. Bardi, C. Marchi, F. Ancona.

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