Reconstructing random media

We formulate a procedure to reconstruct the structure of general random heterogeneous media from limited morphological information by extending the methodology of Rintoul and Torquato [J. Colloid Interface Sci. 186, 467 (1997)] developed for dispersions. The procedure has the advantages that it is simple to implement and generally applicable to multidimensional, multiphase, and anisotropic structures. Furthermore, an extremely useful feature is that it can incorporate any type and number of correlation functions in order to provide as much morphological information as is necessary for accurate reconstruction. We consider a variety of one- and two-dimensional reconstructions, including periodic and random arrays of rods, various distribution of disks, Debye random media, and a Fontainebleau sandstone sample. We also use our algorithm to construct heterogeneous media from specified hypothetical correlation functions, including an exponentially damped, oscillating function as well as physically unrealizable ones.