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Theoretical derivation of bounds for complex permittivity in composite materials, suggesting implications for material design.
A generalization of the bounds obtained by Wiener, Hashin and Shtrikman, and others is derived for complex permittivities. Provided the scale of inhomogeneities in the composite is sufficiently small compared with the wavelength of the applied radiation, the permittivity of the composite is found to lie within a simply constructed region of complex plane. The appropriate region depends on what is known about the composite material. We show that in many cases the region is the most restrictive which can be given, using limited information about the structure of the composite.
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Graeme W. Milton (1981) studied this question.
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