Critical behavior in the dielectric properties of random self-similar composites

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Abstract
A theory for the dielectric properties of self-similar composite media is presented, in which inclusions of one component are introduced recursively into a second component. The spectral-representation formalism, which gives a material-independent description of the recursive process, is used. General expressions are derived for critical exponents that describe the behavior of the dc conductivity, the static dielectric constant, and limits of the spectral function near the percolation threshold. The critical exponents depend on the form of the average dielectric function used at each stage of the recursive procedure. The Maxwell-Garnett and Bruggeman forms of this average dielectric function are chosen as examples. Applications of the theory to some dielectric properties of brine-filled porous rocks are discussed.