Composites made from two linear dielectric materials are considered. It is assumed that only the volume fraction and two point correlation function of each dielectric material is known. For this case new optimal lower bounds on all moments of the electric field intensity inside each phase are obtained. An optimal lower bound on the maximum field intensity inside the composite is obtained. All of these bounds are shown to be attained by the electric field inside a suitably oriented space filling confocal ellipsoidal assemblage. The bounds provide a new opportunity for the assessment of local field behavior in terms of a statistical description of the microstructure.
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