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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