Properties of two-phase ``cell materials''

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Abstract
``Symmetric cell materials'' and ``asymmetric cell materials'' were defined by Miller in connection with the physical properties (such as the effective dielectric constant) of two‐phase solid mixtures. It is shown here that while the ``symmetric cell material'' is self‐consistent, the ``asymmetric cell material'' is not: The postulated three‐point probabilities do not add up to the correct one‐point probabilities. A self‐consistent generalization of the ``symmetric cell material'', based on the requirement that a certain integral must reduce to an integral over a finite region, is developed, and one construction procedure for producing such a material is described.