Morphology and effective properties of disordered heterogeneous media

Recent progress that we have made on the problem of determining the effective properties of random heterogeneous media from knowledge of the mophrology is reviewed and extended. A variety of different effective properties are considered, including the elastic moduli and electrical conductivity of composites, time scales associated with diffusion and reaction among traps, and fluid permeability of porous media. We also remak on the importance of microstructure fluctuations in influencing the failure characteristics of composites. The preponderance of work thus far has focused on heterogeneous media that are statistically homogeneous. We propose a model for statistically inhomogeneous two-phase random media (including functionally graded materials) consisting of inhomogeneous fully penetrable spheres that permits one to represnt and evaluate certain n-point correlation functions that statistically characterize the microstructure for this model. Unlike the case of statistically homogeneous media, the microstructure functions depend upon the absolute positions of their arguments. Finally, we describe a novel procedure to reconstruct heterogeneous media from limited knowledge aboiut the microstructure and discuss applications of this technique.