Macroscopic conductivity of random inhomogeneous media. Calculation methods

摘要: The macroscopic conductivity of nonhomogeneous media such as polycrystals, composites, etc., is discussed. One the major global parameters a randomly inhomogeneous medium (RIM), effective (macroscopic) tensor (ECT), considered. Based on functional analysis ideas, particularly projector and orthogonal reduced field concepts, method for obtaining bounds ECT components developed. A criterion given by which position each iteration solution relative to preceding one determined. It shown that previous model results fall within, are in fact special cases, scheme proposed author. importance auxiliary, zero-fluctuation parameter ?c constructing convergent series quantities interest established. Extended versions Hashin?Shtrikman variational principles Keller's theorem obtained. structural introduced describing an RIM expressed, method, terms n-point probabilities (n-point interactions random local field). piecewise uniform 'polarised' approximation combined with classical energy theorems obtain best achievable within description.