Tight Bounds on the Effective Complex Permittivity of Isotropic Composites and Related Problems

摘要: Almost four decades ago, Bergman and Milton independently showed that the isotropic effective electric permittivity of a two-phase composite material with given volume fraction is constrained to lie within lens-shaped regions in complex plane are bounded by two circular arcs. An implication particular significance set limits maximum minimum absorption an at frequency. Here, after giving short summary underlying theory, we show bound corresponding one arcs least almost optimal introducing certain class hierarchical laminates. In regard second arc, tighter can be derived using variational methods. This as it corresponds assemblages doubly coated spheres, which easily approximated more realistic microstructures. We briefly discuss implications for related problems, including bounds on polarizability.