Optimal bounds on field fluctuations for random composites: Three dimensional problems

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The electric field fluctuation inside a two-phase anisotropic composite is studied when the composite sample is subjected to a constant applied electric field. Upper and lower bounds on the covariance tensor of the electric field are found in terms of the effective dielectric properties of the composite. The lower bounds are shown to be optimal for two well known families of microgeometries. Lower bounds on the covariance tensor are found when only the phase volume fractions and the two-point correlation function are available. For statistically isotropic composites optimal lower bounds are derived when only the phase volume fractions are known. © 2001 American Institute of Physics.

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Journal of Applied Physics

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