Modeling the electrical characteristics of periodic dielectric media

The dispersion of the effective permittivities of two inhomogeneous matrix systems with unidirectional fiber inclusions with a square cross section is studied. Interpolation formulas for the effective permittivity as a function of the frequency are obtained, whose range of applicability is determined through physical modeling and comparison with known systems of equations admitting exact solutions. It is established that the effective loss factor exhibits anomalous behavior in the vicinity of the critical concentration of inclusions.