Renormalized ginzburg-landau energy and location of near boundary vortices

Leonid Berlyand, Volodymyr Rybalko, Nung Kwan Yip

Research output: Contribution to journalArticle

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 - Dec 18 2012

Fingerprint

Ginzburg-Landau
Minimizer
Vortex
Vortex flow
Energy
Ginzburg-Landau Functional
Minimizing Sequences
Boundary conditions
Curvature
Converge
Decrease
Formulation
Zero

All Science Journal Classification (ASJC) codes

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

Cite this

Berlyand, Leonid ; Rybalko, Volodymyr ; Yip, Nung Kwan. / Renormalized ginzburg-landau energy and location of near boundary vortices. In: Networks and Heterogeneous Media. 2012 ; Vol. 7, No. 1. pp. 179-196.
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Renormalized ginzburg-landau energy and location of near boundary vortices. / Berlyand, Leonid; Rybalko, Volodymyr; Yip, Nung Kwan.

In: Networks and Heterogeneous Media, Vol. 7, No. 1, 18.12.2012, p. 179-196.

Research output: Contribution to journalArticle

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