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Droplet phases in non-local Ginzburg-Landau models with Coulomb repulsion in two dimensions

ARGOMENTI: Seminari

SEMINARI DI EQUAZIONI DIFFERENZIALI E APPLICAZIONI
Giovedi' 12 novembre alle ore 12.15 in aula 2AB/45 Cyrill Muratov (New Jersey Institute of Technology, Newark) terra' un seminario dal titolo "Droplet phases in non-local Ginzburg-Landau models with Coulomb repulsion in two dimensions".

-Abstract
In this talk I will present an analysis of the behavior of the minimal energy in non-local Ginzburg-Landau models with Coulomb repulsion in two space dimensions near the onset of multi-droplet patterns. As a first step, I will show that under suitable scaling the energy of minimizers becomes asymptotically equal to that of a sharp interface energy with screened Coulomb interaction. I will then show that the minimizers of the corresponding sharp interface energy consist of nearly identical circular droplets of small size separated by large distances. Finally, I will show that in a suitable limit these droplets become uniformly distributed throughout the domain. The analysis allows to obtain precise asymptotic behaviors of the bifurcation threshold, the minimal energy, the droplet radii, and the droplet density in the considered limit.

Rif. int. M. Bardi, A. Cesaroni, M. Novaga

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