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E. Cherkaev
University of Utah
Inverse homogenization and indirect evaluation of effective properties of a mixture
The talk discusses indirect evaluation of the effective thermal conductivity of
a mixture of two different materials from measured complex permittivity of the
same mixture. The method is based on deriving information about the microstructure of the composite from its effective properties; we call this approach the inverse homogenization. The structural information is contained in the spectral measure in an integral representation of the effective complex permittivity. We reconstruct this spectral measure from effective measurements and use it to estimate other effective properties of the same material. We show that the identification problem for the spectral function has unique solution, however the problem is extremely ill-posed. Several techniques for stabilizing the solution are discussed.
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