a1 Mathematical Institute, University of Oxford, 24–29 St. Giles', Oxford OXI 3LB, UK
a2 Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA
a3 Department of Mathematics, Virginia Tech, Blacksburg, VA 24061, USA
A model for superconductors co-existing with normal materials is presented. The model, which applies to such situations as superconductors containing normal impurities and superconductor/normal material junctions, is based on a generalization of the Ginsburg–Landau model for superconductivity. After presenting the model, it is shown that it reduces to well-known models due to de Gennes for certain superconducting/normal interfaces, and in particular, for Josephson junctions. A provident feature of the modified model is that it can, by itself, account for all of these as well as other physical situations. The results of some preliminary computational experiments using the model are then provided; these include flux pinning by normal impurities and a superconductor/normal/superconductor junction. A side benefit of the modified model is that, through its use, these computational simulations are more easily obtained.
† Supported in part by the Air Force Office of Scientific Research under grant number AFOSR-93–1-0061.