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On the transition to the normal phase for superconductors surrounded by normal conductors

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On the transition to the normal phase for superconductors surrounded by normal conductors. / Fournais, Søren; Kachmar, Ayman.

I: Journal of Differential Equations, Bind 247, Nr. 6, 2009, s. 1637-1672.

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

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Fournais, Søren ; Kachmar, Ayman. / On the transition to the normal phase for superconductors surrounded by normal conductors. I: Journal of Differential Equations. 2009 ; Bind 247, Nr. 6. s. 1637-1672.

Bibtex

@article{83f3de20e74511dd8f9a000ea68e967b,
title = "On the transition to the normal phase for superconductors surrounded by normal conductors",
abstract = "For a cylindrical superconductor surrounded by a normal material, we discuss transition to the normal phase of stable, locally stable and critical configurations. Associated with those phase transitions, we define critical magnetic fields and we provide a sufficient condition for which those critical fields coincide. In particular, when the conductivity ratio of the superconducting and the normal material is large, we show that the aforementioned critical magnetic fields coincide, thereby proving that the transition to the normal phase is sharp. One key-ingredient in the paper is the analysis of an elliptic boundary value problem involving {\textquoteleft}transmission{\textquoteright} boundary conditions. Another key-ingredient involves a monotonicity result (with respect to the magnetic field strength) of the first eigenvalue of a magnetic Schr{\"o}dinger operator with discontinuous coefficients.",
author = "S{\o}ren Fournais and Ayman Kachmar",
year = "2009",
doi = "10.1016/j.jde.2009.04.012",
language = "English",
volume = "247",
pages = "1637--1672",
journal = "Journal of Differential Equations",
issn = "0022-0396",
publisher = "Academic Press",
number = "6",

}

RIS

TY - JOUR

T1 - On the transition to the normal phase for superconductors surrounded by normal conductors

AU - Fournais, Søren

AU - Kachmar, Ayman

PY - 2009

Y1 - 2009

N2 - For a cylindrical superconductor surrounded by a normal material, we discuss transition to the normal phase of stable, locally stable and critical configurations. Associated with those phase transitions, we define critical magnetic fields and we provide a sufficient condition for which those critical fields coincide. In particular, when the conductivity ratio of the superconducting and the normal material is large, we show that the aforementioned critical magnetic fields coincide, thereby proving that the transition to the normal phase is sharp. One key-ingredient in the paper is the analysis of an elliptic boundary value problem involving ‘transmission’ boundary conditions. Another key-ingredient involves a monotonicity result (with respect to the magnetic field strength) of the first eigenvalue of a magnetic Schrödinger operator with discontinuous coefficients.

AB - For a cylindrical superconductor surrounded by a normal material, we discuss transition to the normal phase of stable, locally stable and critical configurations. Associated with those phase transitions, we define critical magnetic fields and we provide a sufficient condition for which those critical fields coincide. In particular, when the conductivity ratio of the superconducting and the normal material is large, we show that the aforementioned critical magnetic fields coincide, thereby proving that the transition to the normal phase is sharp. One key-ingredient in the paper is the analysis of an elliptic boundary value problem involving ‘transmission’ boundary conditions. Another key-ingredient involves a monotonicity result (with respect to the magnetic field strength) of the first eigenvalue of a magnetic Schrödinger operator with discontinuous coefficients.

U2 - 10.1016/j.jde.2009.04.012

DO - 10.1016/j.jde.2009.04.012

M3 - Journal article

VL - 247

SP - 1637

EP - 1672

JO - Journal of Differential Equations

JF - Journal of Differential Equations

SN - 0022-0396

IS - 6

ER -