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Simplified models of superconducting-normal-superconducting junctions and their numerical approximations

Published online by Cambridge University Press:  01 February 1999

Q. DU  and
J. REMSKI
Q. DU
Affiliation:
Department of Mathematics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong and Department of Mathematics, Iowa State University, Ames, IA 50011, USA.
J. REMSKI
Affiliation:
Department of Mathematics, Michigan State University, E. Lansing, MI 48823, USA Present address: Department of Mathematics and Statistics, University of Michigan-Dearborn, Dearborn, MI 48128, USA
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Abstract

When a thin layer of normal (non-superconducting) material is placed between layers of superconducting material, a superconducting-normal-superconducting junction is formed. This paper considers a model for the junction based on the Ginzburg–Landau equations as the thickness of the normal layer tends to zero. The model is first derived formally by averaging the unknown variables in the normal layer. Rigorous convergence is then established, as well as an estimate for the order of convergence. Numerical results are shown for one-dimensional junctions.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 10 , Issue 1 , February 1999 , pp. 1 - 25
Copyright
1999 Cambridge University Press

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Footnotes

The research was supported in part by a NSF grant MS-9500718 and a grant from HKRGC.