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Analyticity of the effective dielectric constant

When waves propagate in a medium in which the microstructure is much smaller than the wavelength, the waves behave almost as if they were propagating in a homogeneous medium characterized by effective moduli. In this lecture I will discuss and prove the analytic properties of the effective moduli as a function of the component moduli in a two or multicomponent composite. The analyticity properties have important ramifications. They provide a justification for the correspondence principle, and enable one to place bounds on the effective moduli. These bounds hold for all conceivable microstructures.

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Department of Mathematics
University of Utah
155 South 1400 East; Room 233
Salt Lake City, UT 84112