Abstract
We consider a random two-phase medium which represents a matrix containing an array of allowed to overlap spherical inclusions with random radii. A statistical theory of transport phenomena in the medium, on the example of heat propagation, is constructed by means of the functional (Volterra-Wiener) series approach. The functional series for the temperature is rendered virial in the sense that its truncation after the p-tuple term yields results for all multipoint correlation functions of the temperature field that are asymptotically correct to the order np, where n is the mean number of spheres per unit volume. The case p=2 is considered in detail and the needed kernels of the factorial series are found to the order n2. In this way not only the effective conductivity, but also the full statistical solution, i.e., all needed correlation functions, can be expressed in a closed form, correct to the said order.
Published Version
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