Asymptotic study of transverse conductivity in superconducting multifilamentary composites

This paper deals with superconducting multifilamentary composites with periodic structure in the presence of a weak electromagnetic field. We study the magnetic induction and establish an approximation result when the period is small (in the framework of homogenization theory). Then we determine some physical constants of an “equivalent” homogeneous conductor, and thus transverse conductivity can be obtained. For various proportions of superconductor, we compute both the values of transverse conductivity proposed by different physicists and the mathematical value obtained in this paper (we use finite elements and an overrelaxation method); we compare them between themselves and with recent experimental results; we note that our results are in very good agreement with Carr's formula and with the experimental measures of Davoust.