Effective Behavior of Heterogeneous Media

A widespread problem of science and technology is that of determining the macroscopic or large scale behavior of a medium which exhibits microscopic or small scale heterogeneity. Expressing the continuum or macroscopic description of matter in terms of its molecular constituents is a basic problem of this type. Another is the problem of determining the gross behavior of a solid which is composed of small randomly oriented crystallites. A third is the technological problem of describing the overall behavior of composite materials, which are composed of macroscopic layers or fibers of one material imbedded in another material. A fourth example is that of analyzing a nuclear reactor which contains rods of one material regularly arranged in a matrix composed of a second material. A fifth example is the problem of describing the propagation of electromagnetic or acoustic waves through a fluid in turbulent motion. Elliott Montroll has contributed significantly to the solution of such problems by using the methods of statistical mechanics, as well as other methods.