# Salvatore Torquato

**Research Area:**

##### Contact:

#### Torquato Group Website

**Salvatore Torquato**

*Lewis Bernard Professor of Natural Sciences, Professor of Chemistry and the Princeton Institute for the Science and Technology of Materials (PRISM)*

[email protected]

Frick Laboratory, 160

Phone: 609-258-3341

##### Faculty Assistant:

**Nagwan Ali**

[email protected]

Frick Laboratory, 389

609-258-2330

## Research Focus

Research work in the Torquato group is centered in statistical mechanics and soft condensed matter theory. A common theme of the research is the search for unifying and rigorous principles to elucidate a broad range of physical and biological phenomena.

Topics of current interest include novel low-temperature states of matter, packing problems, structure and bulk properties of colloids, liquids, glasses, quasicrystals and crystals, hyperuniform disordered materials, novel photonic materials, discrete geometry, self-assembly theory, disordered heterogeneous materials, optimization in materials science, and modeling the dynamics of tumor growth.

Our group has made fundamental contributions to our understanding of the degree of disorder/order of low-temperature states of matter through the identification of sensitive order metrics. We have made fundamental contributions to packing problems, which enable the modeling of crystals, structural glasses and liquids. This includes pioneering the notion of the “maximally random jammed” state of particle packings, identifying a Kepler-like conjecture for the densest packings of nonspherical particles, and providing strong theoretical evidence that the densest sphere packings in high dimensions: a problem of importance in digital communications. We have devised the premier algorithm to reconstruct microstructures of random media and formulated the first comprehensive cellular automaton model of cancer growth.

We have made seminal contributions to the study of random heterogeneous materials. The group has been at the forefront of “materials by design” and guided self-assembly using optimization techniques, including “inverse” statistical mechanics in which interactions are designed to achieve targeted many-particle configurations. More recently, we have introduced a new exotic state of matter called “disordered hyperuniformity,” which is intermediate between a crystal and liquid. Such materials are endowed with novel physical properties.

## Honors

American Chemical Society Joel Henry Hildebrand Award for Theoretical and Experimental Chemistry of Liquids (2017)

Simons Foundation Fellowship in Theoretical Physics (2012)

Fellow, Society for Industrial & Applied Mathematics (2009)

American Physical Society, David Adler Lectureship Award in Material Physics (2009)

Member, Institute for Advanced Study (2007 – 2008)

Society for Industrial & Applied Mathematics Ralph E. Kleinman Prize (2007)

Fellow, American Physical Society (2004)

Society of Engineering Science William Prager Medal (2004)

Member, Institute for Advanced Study (2003-2004)

Am. Soc. Mechanical Engineers Charles Russ Richards Memorial Award (2002)

Guggenheim Memorial Foundation Fellow (1998)

Member, Institute for Advanced Study (1998-1999)

## Selected Publications

Chen, D.; Jiao, Y.; Torquato, S., “Equilibrium Phase Behavior and Maximally Random Jammed State of Truncated Tetrahedra.” *Journal of Physical Chemistry B ***2014,** *118* (28), 7981-7992.

Guo, E.-Y.; Chawla, N.; Jing, T.; Torquato, S.; Jiao, Y., “Accurate modeling and reconstruction of three-dimensional percolating filamentary microstructures from two-dimensional micrographs via dilation-erosion method.” *Materials Characterization ***2014,** *89*, 33-42.

Jiao, Y.; Lau, T.; Hatzikirou, H.; Meyer-Hermann, M.; Corbo, J. C.; Torquato, S., “Avian photoreceptor patterns represent a disordered hyperuniform solution to a multiscale packing problem.” *Physical Review E ***2014,** *89* (2).

Gabbrielli, R.; Jiao, Y.; Torquato, S., “Dense periodic packings of tori.” *Physical Review E ***2014,** *89* (2).

Martis, S.; Marcotte, E.; Stillinger, F. H.; Torquato, S., “Exotic Ground States of Directional Pair Potentials via Collective-Density Variables.” *Journal of Statistical Physics ***2013,** *150* (3), 414-431.

Marcotte, E.; Stillinger, F. H.; Torquato, S., “Nonequilibrium static growing length scales in supercooled liquids on approaching the glass transition.” *Journal of Chemical Physics ***2013,** *138* (12).

Marcotte, E.; Stillinger, F. H.; Torquato, S., “Communication: Designed diamond ground state via optimized isotropic monotonic pair potentials.” *Journal of Chemical Physics ***2013,** *138* (6).

Man, W.; Florescu, M.; Williamson, E. P.; He, Y.; Hashemizad, S. R.; Leung, B. Y. C.; Liner, D. R.; Torquato, S.; Chaikin, P. M.; Steinhardt, P. J., “Isotropic band gaps and freeform waveguides observed in hyperuniform disordered photonic solids.” *Proceedings of the National Academy of Sciences of the United States of America ***2013,** *110* (40), 15886-15891.

Xie, R.; Long, G. G.; Weigand, S. J.; Moss, S. C.; Carvalho, T.; Roorda, S.; Hejna, M.; Torquato, S.; Steinhardt, P. J., “Hyperuniformity in amorphous silicon based on the measurement of the infinite-wavelength limit of the structure factor.” *Proceedings of the National Academy of Sciences of the United States of America ***2013,** *110* (33), 13250-13254.

Marcotte, E.; DiStasio, R. A., Jr.; Stillinger, F. H.; Torquato, S., “Designer spin systems via inverse statistical mechanics. II. Ground-state enumeration and classification.” *Physical Review B ***2013,** *88* (18).

DiStasio, R. A., Jr.; Marcotte, E.; Car, R.; Stillinger, F. H.; Torquato, S., “Designer spin systems via inverse statistical mechanics.” *Physical Review B ***2013,** *88* (13).

Kallus, Y.; Marcotte, E.; Torquato, S., “Jammed lattice sphere packings.” *Physical Review E ***2013,** *88* (6).

Atkinson, S.; Stillinger, F. H.; Torquato, S., “Detailed characterization of rattlers in exactly isostatic, strictly jammed sphere packings.” *Physical Review E ***2013,** *88* (6).

Zhang, G.; Torquato, S., “Precise algorithm to generate random sequential addition of hard hyperspheres at saturation.” *Physical Review E ***2013,** *88* (5).

Zhang, G.; Stillinger, F. H.; Torquato, S., “Probing the limitations of isotropic pair potentials to produce ground-state structural extremes via inverse statistical mechanics.” *Physical Review E ***2013,** *88* (4).

Hopkins, A. B.; Stillinger, F. H.; Torquato, S., “Disordered strictly jammed binary sphere packings attain an anomalously large range of densities.” *Physical Review E ***2013,** *88* (2).

Hejna, M.; Steinhardt, P. J.; Torquato, S., “Nearly hyperuniform network models of amorphous silicon.” *Physical Review B ***2013,** *87* (24).

Florescu, M.; Steinhardt, P. J.; Torquato, S., “Optical cavities and waveguides in hyperuniform disordered photonic solids.” *Physical Review B ***2013,** *87* (16).

Marcotte, E.; Torquato, S., “Efficient linear programming algorithm to generate the densest lattice sphere packings.” *Physical Review E ***2013,** *87* (6).

Jiao, Y.; Torquato, S., “Evolution and morphology of microenvironment-enhanced malignancy of three-dimensional invasive solid tumors.” *Physical Review E ***2013,** *87* (5).

Torquato, S.; Jiao, Y., “Effect of dimensionality on the percolation thresholds of various d-dimensional lattices.” *Physical Review E ***2013,** *87* (3).

Torquato, S.; Jiao, Y., “Effect of dimensionality on the percolation threshold of overlapping nonspherical hyperparticles.” *Physical Review E ***2013,** *87* (2).

Man, W.; Florescu, M.; Matsuyama, K.; Yadak, P.; Nahal, G.; Hashemizad, S.; Williamson, E.; Steinhardt, P.; Torquato, S.; Chaikin, P., “Photonic band gap in isotropic hyperuniform disordered solids with low dielectric contrast.” *Optics Express ***2013,** *21* (17), 19972-19981.

Gabbrielli, R.; Jiao, Y.; Torquato, S., “Families of tessellations of space by elementary polyhedra via retessellations of face-centered-cubic and related tilings.” *Physical Review E ***2012,** *86* (4).

Atkinson, S.; Jiao, Y.; Torquato, S., “Maximally dense packings of two-dimensional convex and concave noncircular particles.” *Physical Review E ***2012,** *86* (3).