The theory of conductivity of ternary composite films with a two-sublattice structure

A general method is suggested for solving problems on the conductivity and other effective characteristics of two-dimensional ternary two-sublattice models 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 electric field induced on a separate inclusion is described using the matrix of multipole polarizabilities, for which the symmetry relation is found. The suggested approach enables one to find exact virial expansions for the basic electrophysical characteristics of such systems.