Renormalized ginzburg-landau energy and location of near boundary vortices

Leonid Berlyand, Volodymyr Rybalko, Nung Kwan Yip

Research output: Contribution to journalArticlepeer-review

Abstract

We consider the location of near boundary vortices which arise in the study of minimizing sequences of Ginzburg-Landau functional with degree boundary condition. As the problem is not well-posed - minimizers do not exist, we consider a regularized problem which corresponds physically to the presence of a superconducting layer at the boundary. The study of this formulation in which minimizers now do exist, is linked to the analysis of a version of renormalized energy. As the layer width decreases to zero, we show that the vortices of any minimizer converge to a point of the boundary with maximum curvature. This appears to be the first such result for complex-valued Ginzburg-Landau type problems.

Original languageEnglish (US)
Pages (from-to)179-196
Number of pages18
JournalNetworks and Heterogeneous Media
Volume7
Issue number1
DOIs
StatePublished - 2012

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Engineering(all)
  • Computer Science Applications
  • Applied Mathematics

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