A branched transport limit of the Ginzburg-Landau functional

Sergio Conti; Michael Goldman; Felix Otto; Sylvia Serfaty

doi:10.5802/jep.72

A branched transport limit of the Ginzburg-Landau functional

Sergio Conti, Michael Goldman, Felix Otto, Sylvia Serfaty

Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English (US)
Pages (from-to)	317-375
Number of pages	59
Journal	Journal de l'Ecole Polytechnique - Mathematiques
Volume	5
DOIs	https://doi.org/10.5802/jep.72
State	Published - 2018

Keywords

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

ASJC Scopus subject areas

General Mathematics

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10.5802/jep.72

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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.",

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AU - Goldman, Michael

AU - Otto, Felix

AU - Serfaty, Sylvia

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PY - 2018

Y1 - 2018

N2 - 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.

AB - 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.

KW - Branched transportation

KW - Gamma convergence

KW - Ginzburg-Landau

KW - Pattern formation

KW - Type-I superconductors

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A branched transport limit of the Ginzburg-Landau functional

Abstract

Keywords

ASJC Scopus subject areas

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