Modeling Heterogeneous Materials via Two-Point Correlation Functions:   II. Algorithmic Details and Applications
  In the first part of this series of two papers, we proposed a theoretical formalism that enables one to model and categorize heterogeneous materials (media) via two-point correlation functions S2 and introduced an efficient heterogeneous-medium (re)construction algorithm called the "lattice-point" algorithm. Here we discuss the algorithmic details of the lattice-point procedure and an algorithm modification using surface optimization to further speed up the (re)construction process. The importance of the error tolerance, which indicates to what accuracy the media are (re)constructed, is also emphasized and discussed. We apply the algorithm to generate three-dimensional digitized realizations of a Fontainebleau sandstone and a boron carbide/aluminum composite from the two- dimensional tomographic images of their slices through the materials. To ascertain whether the information contained in S2 is sufficient to capture the salient structural features, we compute the two-point cluster functions of the media, which are superior signatures of the micro-structure because they incorporate the connectedness information. We also study the reconstruction of a binary laser-speckle pattern in two dimensions, in which the algorithm fails to reproduce the pattern accurately. We conclude that in general reconstructions using S2 only work well for heterogeneous materials with single-scale structures. However, two-point information via S2 is not sufficient to accurately model multi-scale media. Moreover, we construct realizations of hypothetical materials with desired structural characteristics obtained by manipulating their two-point correlation functions. 
Y. Jiao, F. H. Stillinger and S. Torquato