Coupling of the effective properties of a random mixture through the reconstructed spectral representation

The spectral representation of the effective complex permittivity of a two-component composite medium is used to develop an approach to coupling of various effective properties of a random mixture. The spectral function contains all information about the microstructure, hence providing a coupling link between the various effective properties of the same composite material. It is demonstrated that the representation can be reconstructed from measurements of one effective property and used then to evaluate other properties of the same material. The reconstruction problem is very ill-posed and requires regularization. Several numerical examples of reconstruction of the spectral function from broadband measurements of the effective complex permittivity and the measurements of the effective thermal conductivity are shown. The approach can be used for indirect estimation of the thermal conductivity (or other properties) of the medium from broadband measurements of the effective complex permittivity. r 2003 Elsevier B.V. All rights reserved.