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The Distribution of Superconductivity Near a Magnetic Barrier

  • Wafaa Assaad
  • Ayman Kachmar
  • Mikael Persson-SundqvistEmail author
Open Access
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Abstract

We consider the Ginzburg–Landau functional, defined on a two-dimensional simply connected domain with smooth boundary, in the situation when the applied magnetic field is piecewise constant with a jump discontinuity along a smooth curve. In the regime of large Ginzburg–Landau parameter and strong magnetic field, we study the concentration of the minimizing configurations along this discontinuity by computing the energy of the minimizers and their weak limit in the sense of distributions.

Notes

Acknowledgements

We would like to thank Jacob Christiansen for his insightful comments on the manuscript and Virginie Bonnaillie-Noël for the numerical computations and Fig. 5. We would also like to acknowledge the constructive reviews by the anonymous referees, which led to substantial improvements of this manuscript. The research of the second author was partially supported by a grant from the Lebanese University.

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© The Author(s) 2019

OpenAccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Department of MathematicsLund UniversityLundSweden
  2. 2.Department of MathematicsLebanese UniversityNabatiehLebanon

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