Effective Permittivity of a Polycrystalline Dielectric

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Abstract
We use statistical variational principles to determine upper and lower bounds for the effective permittivity of a polycrystalline dielectric. We indicate how to derive bounds containing permittivity correlation functions of arbitrary order, and we obtain explicit expressions for bounds depending on one‐ and two‐point correlation functions and for bounds containing one‐, two‐, and three‐point correlation functions. We prove that for two classes of polycrystal, the effective permittivity may be exactly determined, and we use these exact expressions to show that we have obtained the best possible upper and lower bounds.