A Solution of an Inverse Problem of the Theory of Heterophase Media for a Matrix System with Cubic Inclusions in Sites of a Simple Cubic Lattice

摘要

The electromagnetic properties of heterogeneous systems were actively investigated previously [1]. Many models of such systems were suggested to calculate the effective permittivity of mixtures with the known permittivities of components. Works investigating the inverse problem of determining the properties of separate phases based on the properties of the whole sample are much less in number. Solving the inverse problem for the existing models, we have concluded that they can be subdivided into two main groups: 1) models for which the inverse problem can be solved and 2) models for which the inverse problem has not yet been solved. The model of matrix system (the Maxwell–Garnet approximation) [2] belongs to the first group, and the model of statistical mixture (the method of effective medium) [2] belongs to the second group. The model of matrix system with cubic inclusions whose centers form a cubic lattice and whose faces are parallel was suggested by Odelevskii [3].