For references, see our list of publications.

Heterogeneous Materials: This area dates back to the work of Maxwell and Einstein, and has important ramifications in many fields, including composite materials, rheology, geophysics, polymer physics, statistical physics, chemical physics, colloid science, oil exploration, biotechnology, and photographic science. Until recently, rigorous progress in this field has been hampered because of the difficulty involved in characterizing the complex random microstructure. We have developed a general and unified methodology to quantitatively characterize the microstructure of disordered heterogeneous materials using statistical-mechanical theoretical [26,29,66] as well as computer-simulation techniques [64,112,114]. Using this microstructural information in conjunction with structure/property relations that we have developed [15,20,27,39,51,84,115], predictions of a variety of transport, electromagnetic and mechanical properties for heterogeneous materials have been made with heretofore unattained accuracy. This unified approach has enabled us to relate seemingly disparate physical properties to one another (i.e., cross-property relations), e.g., diffusion parameters have been linked to the fluid permeability [62,85] or to the elastic moduli [101,118,120,147]. A new book entitled "Random Heterogeneous Materials: Microstructure and Macroscopic Properties", has recently been published by Prof. Torquato.

Optimal Design of Composites: It is desired to design at will composite materials with optimum properties (e.g., thermally-insulating, high-strength, low-weight composites)[128,139]. The time and cost involved to attack this problem by performing direct measurements on each material sample, for all possible spatial arrangements of the particles, size and orientation of the particles, and volume fractions, would be prohibitive. The optimization methodology that we have developed provides a means of optimally designing new composites with minimal cost and time. For example, we have discovered composite structures that have exotic properties, such as negative thermal expansion [128,129]. Recently, we determined that the hydrophone performance of piezoelectric/polymer matrix composites can be greatly enhanced by using matrix materials that have negative Poisson's ratios [138,149]. Based on this design, we have fabricated such exotic materials using stereolithography techniques.

Liquids and Amorphous Solids: Our research in this area seeks to ascertain the distribution functions that characterize the molecular structure as well as the equilibrium and non-equilibrium behavior of such states of matter. We have been able to represent and compute certain nearest-neighbor distribution functions for models of such systems [56,110,111]. These quantities are of fundamental importance in understanding the mobility of electrons in simple insulating fluids and in determining the random close-packed state of spheres, to mention a few examples. In another work, we carried out large-scale molecular dynamics simulations of systems of dense hard spheres along the disordered, metastable branch of the phase diagram [127,129]. By quantifying the degree of local order, we were the first to determine a necessary condition to obtain a truly random system, enabling us to compute the pressure carefully along the entire metastable branch. Contrary to conventional wisdom, we found no evidence of a thermodynamic glass transition and that after long times the system crystallizes for all densities above the melting point.

Percolation Theory: We have made contributions to the field of continuum (off-lattice) percolation using theoretical [38,43,108,126] as well as computer-simulation techniques [44,50,61,69,143]. For example, we introduced and quantified the so-called two-point cluster function which turns out to be an excellent microstructural ``signature" or ``fingerprint" of the system [38]. Elsewhere we devised an especially accurate algorithm to obtain the pair-connectedness function: a quantity of fundamental interest [44]. We showed that the usual periodic boundary conditions employed in simulations become deficient as one approaches the percolation threshold and introduced so-called ``free boundary conditions'' (over central and replicating cells) to correct this problem.

Tomography and Image Science: We have been at the forefront of the use of x-ray tomographic techniques to obtain three-dimensional digitized images of composite and porous media [123,124]. By storing the digitized images on a computer workstation, we have analyzed the microstructure and subsequently estimated the macroscopic properties of interest using the aforementioned unified methodology. This work has enabled us to extract important topological information that otherwise cannot be obtained from standard techniques that yield two-dimensional images of cross-sections of the material.

Return to our Home Page