Generalizations of the Bruggeman equation and a concept of shape-distributed particle composites

We consider generalizations of the classical symmetrical Bruggeman equation based on the concept of shape-distributed particle systems. The use of the Beta distribution for the particle shape is shown to result in some known as well as unknown equations of the effective medium theory. However, these equations yield no percolation threshold. On the other hand, the use of one- and two-dimensional steplike distributions of spheroidal (ellipsoidal) shapes yields a percolation threshold depending on the distribution parameters. The problem of finding the percolation threshold to fit the systems under consideration, as well as the applicability area of the generalized Bruggeman equation and its relation to the Bergman representation, are discussed.