A branched transport limit of the Ginzburg-Landau functional

Sergio Conti, Michael Goldman, Felix Otto, Sylvia Serfaty

Research output: Contribution to journalArticle

Abstract

We study the Ginzburg-Landau model of type-I superconductors in the regime of small external magnetic fields. We show that, in an appropriate asymptotic regime, flux patterns are described by a simplified branched transportation functional. We derive the simplified functional from the full Ginzburg-Landau model rigorously via -convergence. The detailed analysis of the limiting procedure and the study of the limiting functional lead to a precise understanding of the multiple scales contained in the model.

LanguageEnglish (US)
Pages317-375
Number of pages59
JournalJournal de l'Ecole Polytechnique - Mathematiques
Volume5
DOIs
StatePublished - Jan 1 2018

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Ginzburg-Landau Functional
Ginzburg-Landau Model
Limiting
Multiple Scales
Superconductor
External Field
Magnetic Field
Model

Keywords

  • Branched transportation
  • Gamma convergence
  • Ginzburg-Landau
  • Pattern formation
  • Type-I superconductors

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

A branched transport limit of the Ginzburg-Landau functional. / Conti, Sergio; Goldman, Michael; Otto, Felix; Serfaty, Sylvia.

In: Journal de l'Ecole Polytechnique - Mathematiques, Vol. 5, 01.01.2018, p. 317-375.

Research output: Contribution to journalArticle

Conti, Sergio ; Goldman, Michael ; Otto, Felix ; Serfaty, Sylvia. / A branched transport limit of the Ginzburg-Landau functional. In: Journal de l'Ecole Polytechnique - Mathematiques. 2018 ; Vol. 5. pp. 317-375.
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