Effective properties of periodic tubular structures

A method is described to calculate effective tensor properties of a periodic array of two-phase dielectric tubes embedded in a host matrix. The method uses Weierstrass’ quasiperodic functions for representation of the potential that considerably facilitates the problem and allows us to find an exact expression for the effective tensor. For weakly interacting tubes we obtain Maxwell-like approximation of the effective parameter which is in very good agreement with experimental results in considered examples.