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Sal Torquato

Sal Torquato Classical ground states. Classical ground states are those classical many-particle configurations with minimal potential energy per particle. Typically ground states are crystal structures, but they do not have to be. We are interested in finding interaction potentials that robustly stabilize targeted ground-state configurations, an intriguing inverse problem. Target configurations include non-coventional crystals (e.g., low-coordinated lattices), quasicrystals, and amorphous structures. This is achieved using inverse statistical-mechanical optimization techniques. Colloids are an ideal experimental system to test our ideas because interparticle interactions are tunable. We are also interested in finding interaction potentials that counterintuitively yield disordered ground states. This problem has been attacked using a collective coordinate approach.

Structural Glasses. Roughly speaking, a glass is a material that is out of equlibrium, having the disordered molecular structure of a liquid and the rigidity of a solid. But the underlying physics of the glass transition remains one of the most open fascinating questions in materials science and condensed matter theory. We have used random packings of hard particles (e.g., spheres and ellipsoids) to understand the physics of glasses. In particluar, we have introduced the notion of the maximally random jammed (MRJ), which can be viewed as a "perfect" glass, and rests on devising precise meanings for "randomness" and "jamming." We show that the density of MRJ packings of ellipsoids in three dimensions closely approaches that of the densest lattice packing, which has implications for the existence of a thermodynamically stable glass. Interestingly, MRJ sphere packings possess the same type of density fluctuations as the early Universe.

Disordered heterogeneous materials. Research on heterogeneous materials (e.g., composites, colloids, polymer blends, bone, tissue, wood, and blood) dates back to the work of Maxwell and Einstein, and has important ramifications in the physical and biological sciences. We have developed a unified methodology to characterize quantitatively the microstructure of disordered heterogeneous materials using statistical-mechanical theoretical and computer-simulation techniques. Combining this microstructural information with structure/property relations, we have predicted accurately a variety of transport, electromagnetic and mechanical properties. This unified approach has enabled us to relate seemingly disparate physical properties to one another, e.g., diffusion parameters have been linked to the fluid permeability or to the elastic moduli.

Modeling cancer growth. We have developed a novel cellular automata model, which simulates the three-dimensional proliferative growth of a brain tumor. This model predicts important clinical data over time in agreement with published clinical and experimental data for a tumor growing over three orders of magnitude in radius. Further research has modeled tumors comprised of two separate subpopulations. The likelihood of a small subpopulation emerging from a larger one has been quantified. In addition, the importance of understanding clonal composition in forming medical prognosis has been underscored. Other work is underway to model the dynamics of invasive tumor growth.

For more information:
Sal Torquato's webpage

Selected Publications:

  • S. Torquato, S. Hyun, and A. Donev
    Multifunctional Composites: Optimizing Microstructures for Simultaneous Transport of Heat and Electricity
    Physical Review Letters, 89, 266601 (2002).

  • A. Donev, I. Cisse, D. Sachs, E. A. Variano, F. H. Stillinger, R. Connelly, S. Torquato, and P. M. Chaikin
    Improving the Density of Jammed Disordered Packings using Ellipsoids
    Science, 303, 990-993 (2004).

  • M. Rechtsman, F. H. Stillinger, S. Torquato
    Optimized Interactions for Targeted Self-Assembly: Application to Honeycomb Lattice
    Physical Review Letters, 95, 228301 (2005).

  • A. Donev, F. H. Stillinger and S. Torquato
    Do Binary Hard Disks Exhibit an Ideal Glass Transition?
    Physical Review Letters, 96, 225502 (2006).

  • J. H. Conway and S. Torquato
    Packing, Tiling and Covering with Tetrahedra
    Proceedings of the National Academy of Sciences, 103, 10612 (2006).


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