The breakdown of superconductivity in the presence of magnetic steps

Research output: Contribution to journalArticle

Standard

The breakdown of superconductivity in the presence of magnetic steps. / Assaad, Wafaa.

In: Communications in Contemporary Mathematics, Vol. 23, No. 2, 2050005, 2021.

Research output: Contribution to journalArticle

Harvard

APA

CBE

MLA

Vancouver

Author

RIS

TY - JOUR

T1 - The breakdown of superconductivity in the presence of magnetic steps

AU - Assaad, Wafaa

PY - 2021

Y1 - 2021

N2 - Many earlier works were devoted to the study of the breakdown of superconductivity in type-II superconducting bounded planar domains, submitted to smooth magnetic fields. In the present contribution, we consider a new situation where the applied magnetic field is piecewise-constant, and the discontinuity jump occurs along a smooth curve meeting the boundary transversely. To handle this situation, we perform a detailed spectral analysis of a new effective model. Consequently, we establish the monotonicity of the transition from a superconducting to a normal state. Moreover, we determine the location of superconductivity in the sample just before it disappears completely. Interestingly, the study shows similarities with the case of corner domains subjected to constant fields.

AB - Many earlier works were devoted to the study of the breakdown of superconductivity in type-II superconducting bounded planar domains, submitted to smooth magnetic fields. In the present contribution, we consider a new situation where the applied magnetic field is piecewise-constant, and the discontinuity jump occurs along a smooth curve meeting the boundary transversely. To handle this situation, we perform a detailed spectral analysis of a new effective model. Consequently, we establish the monotonicity of the transition from a superconducting to a normal state. Moreover, we determine the location of superconductivity in the sample just before it disappears completely. Interestingly, the study shows similarities with the case of corner domains subjected to constant fields.

KW - diamagnetic inequality

KW - Ginzburg-Landau equations

KW - magnetic Laplacian

KW - step magnetic fields

U2 - 10.1142/S0219199720500054

DO - 10.1142/S0219199720500054

M3 - Article

AN - SCOPUS:85082045802

VL - 23

JO - Communications in Contemporary Mathematics

JF - Communications in Contemporary Mathematics

SN - 0219-1997

IS - 2

M1 - 2050005

ER -