Salvatore Torquato is an American theoretical scientist born in Falerna, Italy. His research work has impacted a variety of fields, including physics, chemistry, applied and pure mathematics, materials science, engineering, and biological physics. He is the Lewis Bernard Professor of Natural Sciences in the department of chemistry and Princeton Institute for the Science and Technology of Materials at Princeton University. He has been a senior faculty fellow in the Princeton Center for Theoretical Science, an enterprise dedicated to exploring frontiers across the theoretical natural sciences. He is also an associated faculty member in three departments or programs at Princeton University: physics, applied and computational mathematics, and mechanical and aerospace engineering. On multiple occasions, he was a member of the schools of mathematics and natural sciences at the Institute for Advanced Study, Princeton, New Jersey.
Research accomplishments
Torquato's research work is centered in statistical mechanics and soft condensed matter theory. The impact of his work has also extended into the biological sciences, discrete geometry, and number theory. As of Oct. 2024, his published work has been cited over 55,870 times and his h-index is 122.
Torquato has identified sensitive order metrics pertaining to the randomness of condensed phases of matter. He is also an expert on packing problems, including 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) are counterintuitively disordered, not ordered as in our three-dimensional world. He has devised the premier algorithm to reconstruct microstructures of random media. Torquato formulated the first comprehensive cellular automaton model of cancer growth. He has made contributions to the study of random heterogeneous materials, including writing the treatise on this subject called "Random Heterogeneous Materials." He also works on "materials by design" using optimization techniques, including "inverse" statistical mechanics. In 2003, he introduced a new exotic state of matter called "disordered hyperuniformity", which is intermediate between a crystal and liquid. These states of matter are endowed with novel physical properties. A study in 2019 has uncovered that the prime numbers in certain large intervals possess unanticipated order across length scales and represent the first example of a new class of many-particle systems with pure point diffraction patterns, which are called effectively limit-periodic.
Random heterogeneous media
The work on the theory of random heterogeneous media dates back to the work of James Clerk Maxwell, Lord Rayleigh and Einstein, and has important ramifications in the physical and biological sciences. Random media abound in nature and synthetic situations, and include composites, thin films, colloids, packed beds, foams, microemulsions, blood, bone, animal and plant tissue, sintered materials, and sandstones. The effective transport, mechanical and electromagnetic properties are determined by the ensemble-averaged fields that satisfy the governing partial differential equations. Thus, they depend, in a complex manner, upon the random microstructure of the material via correlation functions, including those that characterize clustering and percolation.
In 1990s, progress in predicting the effective properties had been hampered because of the difficulty involved in characterizing the random microstructures. To resolve this problem, Torquato created a rigorous categorization system of the microstructures and macroscopic properties of widely diverse random heterogeneous media, and his treatise on the matter has been cited over 5,300 times. In an article published in Physical Review X in 2021, Torquato and Jaeuk Kim formulated the first "nonlocal" exact formula for the effective dynamic dielectric constant tensor for general composite microstructures that accounts for multiple scattering of electromagnetic waves to all orders.
In 1997, Ole Sigmund and Torquato wrote a paper on the use of the topology optimization method to design metamaterials with negative thermal expansion or those with zero thermal expansion. They also designed 3D anisotropic porous solids with negative Poisson's ratio to optimize the performance of piezoelectric composites. Torquato and coworkers were the first to show that composites whose interfaces are triply periodic minimal surfaces are optimal for multifunctionality.
Torquato and colleagues created an inverse optimization procedure to reconstruct or construct realizations of disordered many-particle or two-phase systems from lower-order correlation functions. This proved that pair information of a disordered many-particle system is insufficient to uniquely determine a representative configuration and identified more sensitive structural descriptors beyond the standard three-, four-body distribution functions, which is relevant in the study of liquid and glassy states of matter.
In 1986, Torquato formulated a unified theoretical approach to represent exactly a general n-point "canonical" correlation function Hn from which one can obtain and compute any of the various types of correlation functions that determine the bulk properties of liquids, glasses and random media, as well as the generalizations of these correlation functions. The wealth of structural information contained in Hn is far from understood. More recently, Torquato and colleagues are discovering connections of special cases of the Hn to the covering and quantizer problems of discrete geometry as well as to problems in number theory.
Liquids and glasses
Torquato is an expert in the statistical-mechanical theory of liquid and glassy states of matter. He contributed to the understanding of the venerable hard-sphere model, which has been invoked to study local molecular order, transport phenomena, glass formation, and freezing behavior in liquids. He also did research concerning the theory of water, simple liquids, and general statistical-mechanical theory of condensed states of matter. He has also worked on identifying and applying sensitive correlation functions and descriptors to characterize liquid and glassy structures beyond standard pair statistics. He has also characterized the structure of random media within liquid-state theory.
Torquato and colleagues developed the concept of "order metrics and maps" to characterize the degree of order/disorder in many-particle systems. Such descriptors were initially applied to suggest an alternative to the ill-defined random close packed state of sphere packings. Order metrics have been employed by many investigators to characterize the degree of disorder in simple liquids, water and structural glasses. Torquato along with his co-workers have used order metrics to provide novel insights into the structural, thermodynamical, and dynamical nature of molecular systems, such as Lennard-Jones liquids and glasses, water and disordered ground states of matter, among other examples.
Torquato and Stillinger discovered g2-invariant processes in which a given nonnegative pair correlation g2 function remains invariant over the range of densities 0≤ø≤ø*, where ø* is the maximum achievable density subject to satisfaction of certain necessary conditions on g2.S. Torquato and F. H. Stillinger. Controlling the short-range order and packing densities of many particle systems. J. Phys. Chem. B, 106:8354–8359, 2002. Erratum 106, 11406 (2002).S. Torquato and F. H. Stillinger. Local density fluctuations, hyperuniform systems, and order metrics. Phys. Rev. E, 68:041113, 2003.
During the 2000s, Torquato and his collaborators used inverse statistical-mechanical methodologies to find optimized interaction potentials that lead spontaneously and robustly to a target many-particle configuration, including nanoscale structures, at zero temperature (ground states) and positive temperatures (excited states). Target structures included low coordinated 2D and 3D crystal ground states,M. C. Rechtsman, F. H. Stillinger, and S. Torquato. Optimized interactions for targeted selfassembly: Application to honeycomb lattice. Phys. Rev. Lett., 95:228301, 2005. Erratum, 97, 239901 (2006).S. Torquato. Inverse optimization techniques for targeted self-assembly. Soft Matter, 5:1157–1173, 2009. disordered ground states as well as atomic systems with negative Poisson's ratios over a wide range of temperatures and densities.M. C. Rechtsman, F. H. Stillinger, and S. Torquato. Negative Poisson's ratio materials via isotropic interactions. Phys. Rev. Lett., 101:085501, 2008.
In 2013, Marcotte, Stillinger and Torquato demonstrated that a sensitive signature of the glass transition of atomic liquid models is apparent well before the transition temperature Tc is reached upon supercooling as measured by a length scale determined from the volume integral of the direct correlation function c(r), as defined by the Ornstein-Zernike equation.E. Marcotte, F. H. Stillinger, and S. Torquato. Nonequilibrium static growing length scales in supercooled liquids on approaching the glass transition. J. Chem. Phys., 138:12A508, 2013. This length scale grows appreciably with decreasing temperature.
Perfect glasses
In a paper published in 2016, Zheng, Stillinger and Torquato introduced the notion of a "perfect glass".G. Zhang, F. H. Stillinger, and S. Torquato. The perfect glass paradigm: Disordered hyperuniform glasses down to absolute zero. Sci. Rep., 6:36963, 2016. Such amorphous solids involve many-body interactions that eliminate the possibilities of crystalline and quasicrystalline phases for any state variables, while creating mechanically stable amorphous glasses that are hyperuniform down to absolute zero temperature. Subsequently, it was shown computationally that perfect glasses possess unique disordered classical ground states up to trivial symmetries and hence have vanishing entropy.G. Zhang, F. H. Stillinger, and S. Torquato. Classical many-particle systems with unique disordered ground states. Phys. Rev. E, 96:042146, 2017. This discovery provides singular examples in which entropy and disorder are at odds with one another.
Packing problems
Torquato is an expert on packing problems, such as how densely or randomly nonoverlapping particles can fill a volume. Packing problems are intimately related to condensed phases of matter, including classical ground states, liquids, crystals and glasses. While the preponderance of work before 2000 considered sphere packings, Torquato and his colleagues were early adopters of the study of the densest and disordered jammed packings of nonspherical particles (e.g., ellipsoids, polyhedra, superballs, among other shapes). Since 2000, nonspherical packings have become a more popular object of study