Bounds on the complex permittivity of a multicomponent material

Abstract Recently D. Bergman introduced a method for obtaining bounds on the effective dielectric constant (or conductivity) of a two-component medium. This method does not rely on a variational principle but instead exploits the properties of the effective parameter as an analytic function of the ratio of the component parameters. Here the method is extended to multicomponent media using techniques of several complex variables. We propose for the first time a series of bounds on the complex dielectric constant of a material of three or more components, as well as rederive the Wiener and Hashin-Shtrikman bounds for real parameters. In addition, we obtain in a simple manner a known infinite sequence of bounds for two-component media.

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