Recovery of inclusion separations in strongly heterogeneous composites from effective property measurements

摘要: An effective property of a composite material consisting inclusions within host matrix depends on the geometry and connectedness inclusions. This dependence may be quite strong if constituents have highly contrasting properties. Here, we consider inverse problem using data to obtain information microstructure. While previous work has been devoted recovering volume fractions constituents, our focus is their connectedness—a key feature in critical behaviour phase transitions. We solve exactly reduced spectral by bounding fraction an inclusion separation parameter gap self-adjoint operator that composite. present new algorithm based Mobius transformation structure forward bounds whose output set algebraic curves space regions admissible values. These results advance development techniques for characterizing microstructure materials. As example, brine sea ice from measurements its complex permittivity.