Progress In Electromagnetics Research
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By M. Y. Koledintseva, R. E. DuBroff, and R. W. Schwartz

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An analytical model of an effective permittivity of a composite taking into account statistically distributed orientations of inclusions in the form of prolate spheroids will be presented. In particular, this paper considers the normal Gaussian distribution for either zenith angle, or azimuth angle, or for both angles describing the orientation of inclusions. The model is an extension of the Maxwell Garnett (MG) mixing rule for multiphase mixtures. The resulting complex permittivity is a tensor in the general case. The formulation presented shows that the parameters of the distribution law for orientation of inclusions affect the frequency characteristics of the composites, and that it is possible to engineer the desirable frequency characteristics, if the distribution law is controlled.

M. Y. Koledintseva, R. E. DuBroff, and R. W. Schwartz, "Maxwell garnett rule for dielectric mixtures with statistically distributed orientations of inclusions," Progress In Electromagnetics Research, Vol. 99, 131-148, 2009.

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