European Journal of Applied Mathematics

Simplified models of superconducting-normal-superconducting junctions and their numerical approximations 1

Q. DU a1 and J. REMSKI a2p1
a1 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.
a2 Department of Mathematics, Michigan State University, E. Lansing, MI 48823, USA


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.

(Received October 9 1998)
(Revised October 9 1998)

p1 Present address: Department of Mathematics and Statistics, University of Michigan-Dearborn, Dearborn, MI 48128, USA


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