On the conductivity of composites with two-dimensional periodic structure

A method is suggested of successive solution of the problem on the conductivity of two-dimensional periodic systems with inclusions of arbitrary shape. The complex potential outside of the inclusions is expressed in terms of the Weierstrass zeta function and its derivatives. The field induced on a separate inclusion is described using the matrix of multipole polarizabilities. The "joining" of potentials is performed at a distance p such that R < p < a, where R is the characteristic dimension (maximum "radius") of the inclusion and a is the half-period of the lattice. The approach suggested enables one to find exact virial expansions for the conductivity of other effective characteristics of similar systems as well. (C) 2001 MAIL "Nauka/Interperiodica".