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

Document Type

Article

Publication Date

7-29-2010

Abstract

We establish the behavior of the energy of minimizers of non-local Ginzburg-Landau energies with Coulomb repulsion in two space dimensions near the onset of multi-droplet patterns. Under suitable scaling of the background charge density with vanishing surface tension the non-local Ginzburg-Landau energy becomes asymptotically equivalent to a sharp interface energy with screened Coulomb interaction. Near the onset the minimizers of the sharp interface energy consist of nearly identical circular droplets of small size separated by large distances. In the limit the droplets become uniformly distributed throughout the domain. The precise asymptotic limits of the bifurcation threshold, the minimal energy, the droplet radii, and the droplet density are obtained. © 2010 Springer-Verlag.

Identifier

77955556283 (Scopus)

Publication Title

Communications in Mathematical Physics

External Full Text Location

https://doi.org/10.1007/s00220-010-1094-8

e-ISSN

14320916

ISSN

00103616

First Page

45

Last Page

87

Issue

1

Volume

299

Grant

0908279

Fund Ref

National Science Foundation

This document is currently not available here.

Share

COinS