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Nucleation of bulk superconductivity close to critical magnetic fields

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Nucleation of bulk superconductivity close to critical magnetic fields. / Fournais, Søren; Kachmar, Ayman.

I: Advances in Mathematics, Bind 226, Nr. 2, 2011, s. 1213-1258.

Publikation: Bidrag til tidsskrift/Konferencebidrag i tidsskrift /Bidrag til avisTidsskriftartikelForskningpeer review

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Fournais, Søren ; Kachmar, Ayman. / Nucleation of bulk superconductivity close to critical magnetic fields. I: Advances in Mathematics. 2011 ; Bind 226, Nr. 2. s. 1213-1258.

Bibtex

@article{f160d2d0015411e083f5000ea68e967b,
title = "Nucleation of bulk superconductivity close to critical magnetic fields",
abstract = "We consider the two-dimensional Ginzburg–Landau functional with constant applied magnetic field. For applied magnetic fields close to the second critical field HC2 and large Ginzburg–Landau parameter, we provide leading order estimates on the energy of minimizing configurations. We obtain a fine threshold value of the applied magnetic field for which bulk superconductivity contributes to the leading order of the energy. Furthermore, the energy of the bulk is related to that of the Abrikosov problem in a periodic lattice. A key ingredient of the proof is a novel L∞-bound which is of independent interest.",
author = "S{\o}ren Fournais and Ayman Kachmar",
year = "2011",
doi = "10.1016/j.aim.2010.08.004",
language = "English",
volume = "226",
pages = "1213--1258",
journal = "Advances in Mathematics",
issn = "0001-8708",
publisher = "Academic Press",
number = "2",

}

RIS

TY - JOUR

T1 - Nucleation of bulk superconductivity close to critical magnetic fields

AU - Fournais, Søren

AU - Kachmar, Ayman

PY - 2011

Y1 - 2011

N2 - We consider the two-dimensional Ginzburg–Landau functional with constant applied magnetic field. For applied magnetic fields close to the second critical field HC2 and large Ginzburg–Landau parameter, we provide leading order estimates on the energy of minimizing configurations. We obtain a fine threshold value of the applied magnetic field for which bulk superconductivity contributes to the leading order of the energy. Furthermore, the energy of the bulk is related to that of the Abrikosov problem in a periodic lattice. A key ingredient of the proof is a novel L∞-bound which is of independent interest.

AB - We consider the two-dimensional Ginzburg–Landau functional with constant applied magnetic field. For applied magnetic fields close to the second critical field HC2 and large Ginzburg–Landau parameter, we provide leading order estimates on the energy of minimizing configurations. We obtain a fine threshold value of the applied magnetic field for which bulk superconductivity contributes to the leading order of the energy. Furthermore, the energy of the bulk is related to that of the Abrikosov problem in a periodic lattice. A key ingredient of the proof is a novel L∞-bound which is of independent interest.

U2 - 10.1016/j.aim.2010.08.004

DO - 10.1016/j.aim.2010.08.004

M3 - Journal article

VL - 226

SP - 1213

EP - 1258

JO - Advances in Mathematics

JF - Advances in Mathematics

SN - 0001-8708

IS - 2

ER -