B.S., Mechanical Engineering, Syracuse

University, 1975

M.S., Mechanical Engineering, State University

of New York at Stony Brook, 1977

Ph.D., Mechanical Engineering, State University of New York at

Stony Brook, 1981

*Room: 160, Frick Chemistry Laboratory
Phone: (609) 258-3341
E-mail: torquato@electron.princeton.edu*

- Simons Fellowship in Theoretical Physics, 2012
- Fellow, Society for Industrial & Applied Mathematics, 2009
- David Adler Lectureship Award in Material Physics, American Physical Society, 2009
- Ralph E. Kleinman Prize, Society for Industrial & Applied Mathematics, 2007
- Fellow, American Physical Society, 2004
- William Prager Medal, Society of Engineering Science, 2004
- Member, Institute for Advanced Study, 2003-04
- Charles Russ Richards Memorial Award, American Society of Mechanical Engineers, 2002
- Guggenheim Fellow, John Simon Guggenheim Memorial Foundation, 1998
- Gustus L. Larson Memorial Award, American Society of Mechanical Engineers, 1994
- Fellow, American Society of Mechanical Engineers, 1993

- Associated Faculty, Department of Mechanical and Aerospace Engineering
- Associated Faculty, Department of Chemical Engineering
- Associated Faculty, Program in Applied and Computational Mathematics
- Associated Faculty, Department of Physics
- Senior Faculty Fellow, Princeton Center for Theoretical Sciences

**Liquids, Glasses, Quasicrystals and Crystals**

We are interested in the applications of statistical mechanics to elucidate our fundamental understanding of the molecular theory of noncrystalline condensed states of matter, such as liquids, glasses, and quasicrystals. We have made seminal contributions to our understanding of the well-known hard-sphere model, which has been invoked to study local molecular order, transport phenomena, glass formation, and freezing behavior in liquids. Other notable research advances concern the theory of water, simple liquids, and general statistical-mechanical theory of condensed states of matter. We have recently become interested in crystal structures and their symmetries.**Fundamental Problems in Statistical Physics**

We have pioneered the “reconstruction” and “realizability” problems of statistical mechanics and their solutions, g2-invariant processes”, and our basic understanding and characterization of point processes. Often theoretical and computational optimization techniques are employed. Seminal theoretical results were obtained for “hyperuniform” systems, i.e., point patterns that do not possess infinite-wavelength density fluctuations. Such point distributions have connections to integrable quantum systems and number theory. We have used the hyperuniformity concept to view crystals, quasicrystals and special disordered structures in a unified manner.**Particle Packings**

Packing problems, such as how densely or randomly objects can fill a volume, are among the most ancient and persistent problems in mathematics and science. Packing problems are intimately related to condensed phases of matter, including classical ground states, liquids and glasses. Despite its long history, there are many fundamental conundrums concerning packings of spheres that has remained elusive, including the nature of random packings and whether such packings can ever be denser than ordered packings, especially in high spatial dimensions. The latter problem has direct relevance in communications theory. We have recently been interested in the densest packings of nonspherical particle shapes, including ellipsoids, superballs, and polyhedra.**Self-Assembly Theory: Classical Ground and Excited States**

While classical ground states are readily produced by slowly freezing liquids in experiments and computer simulations, our theoretical understanding of them is far from complete. There are many open and fascinating questions. For example, to what extent can we control classi- cal ground states? Can ground states ever be disordered? We are leading a program to shed light on these fundamental aspects of classical ground states and their corresponding excited states using the tools and machinery of statistical mechanics. We have recently devised inverse statistical-mechanical methodologies to find optimized interaction potentials that lead sponta- neously and robustly to unusual target many-particle configurations, including low-coordinated crystal ground states and disordered ground states. One can regard such approaches as “tar- geted” self-assembly. The particular experimental systems that could achieve the optimally designed interactions include colloids and polymers, since their interactions can be tuned.**Random Heterogeneous Media**

Random heterogeneous media abound in nature and synthetic situations, and include compos- ites, thin films, colloids, packed beds, foams, microemulsions, blood, bone, animal and plant tissue, sintered materials, and sandstones. This area dates back to the work of Maxwell, Lord Rayleigh and Einstein, and has important ramifications in the physical and biological sciences. The effective properties are determined by the ensemble-averaged fields that satisfy the gov- erning partial differential equations. The properties depend, in a complex manner, upon the random microstructure of the material via various n-point statistical correlation functions, in- cluding those that characterize percolation and clustering. Two decades ago, rigorous progress in predicting the effective properties had been hampered because of the difficulty involved in characterizing the random microstructures. We broke this impasse using statistical-mechanical techniques.**Optimal Design of Materials**

A holy grail of materials science is to have exquisite knowledge of structure/property relations to design material microstructures with desired properties and performance characteristics. We have been at the forefront of this exciting area. Specifically, we have posed this task as an optimization problem in which an objective function involving a set of physical properties is extremized subject to constraints. The resulting optimal microstructures are often surprising in nature. Combining such modeling techniques with novel synthesis and fabrication methodologies may make optimal design of real materials a reality in the future.**Cancer Modeling**

The aim of the project is to show that we can model the growth (proliferation and invasion) of brain tumors using concepts from statistical physics, materials science and dynamical systems, as well as data from novel oncological experiments. We expect the work not only to increase our understanding of tumorigenesis, but to provide insight into novel ways to treat malignant brain tumors. This work will now be done in conjunction with the new Princeton Physical Sciences-Oncology Center.

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