研究领域

Statistical mechanics and soft condensed matter theory. Disordered heterogeneous materials/packing problems/colloids/liquids/glasses and crystals. Optimization in materials science and self-assembly theory. Modeling tumor growth.

A common theme of our research work in statistical mechanics and soft condensed matter theory is the search for unifying and rigorous principles to elucidate a broad range of physical phenomena. We have contributed to the following diverse fields: (1) Liquid, Glasses and Crystals; (2) Fundamental Aspects of Statistical Physics; (3) Particle Packings; (4) Self-Assembly Theory: Classical Ground and Excited States; (5) Random Heterogeneous Media; (6) Optimal Design of Materials; and (7) Cancer Modeling. 1. Liquids, Glasses and Crystals We are interested in the applications of statistical mechanics to elucidate our fundamental understanding of the molecular theory of disordered condensed states of matter, such as liquids and glasses. 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. 2. 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. 3. 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. 4. 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. 5. 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. 6. 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. 7. 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.

近期论文

查看导师新发文章 （温馨提示：请注意重名现象，建议点开原文通过作者单位确认）

W. Man, M. Florescu, K. Matsuyama, P. Yadak, G. Nahal, S. Hashemizad, E. Williamson, P. Steinhardt, S. Torquato, and P. Chaikin, Photonic band gap in isotropic hyperuniform disordered solids with low dielectric contrast, Optics Express, 21, 19972 (2013). A. B. Hopkins, F. H. Stillinger, and S. Torquato, Disordered Strictly Jammed Binary Sphere Packings Attain an Anomalously Large Range of Densities, Physical Review E, 88, 022205 (2013). W. Man, M. Florescu, E. P. Williamson, Y. He, S. R. Hashemizad, B. Y. C. Leung, D. R. Liner, S. Torquato, P. Chaikin, and P. Steinhardt, Isotropic Band Gaps and Freeform Waveguides Observed in Hyperuniform Disordered Photonic Solids, Proceedings of the National Academy of Sciences, 110, 15886 (2013). R. A. DiStasio, Jr., é. Marcotte, R. Car, F. H. Stillinger, and S. Torquato, Designer Spin Systems via Inverse Statistical Mechanics, Physical Review B, 88, 134104 (2013). G. Zhang, F. H. Stillinger, and S. Torquato, Probing the Limitations of Isotropic Pair Potentials to Produce Ground-State Structural Extremes via Inverse Statistical Mechanics, Physical Review E, 88, 042309 (2013). G. Zhang and S. Torquato, Precise Algorithm to Generate Random Sequential Addition of Hard Hyperspheres at Saturation, Physical Review E, 88, 053312 (2013). é. Marcotte, R. A. DiStasio, Jr., F. H. Stillinger, and S. Torquato, Designer Spin Systems via Inverse Statistical Mechanics. II. Ground-state Enumeration and Classification, Physical Review B, 88, 184432 (2013). S. Atkinson, F. H. Stillinger, and S. Torquato, Detailed Characterization of Rattlers in Exactly Isostatic, Strictly Jammed Sphere Packings, Physical Review E, 88, 062208 (2013). Y. Kallus, é. Marcotte, and S. Torquato, Jammed Lattice Sphere Packings, Physical Review E, 88, 062151 (2013). R. Gabbrielli, Y. Jiao, and S. Torquato, Dense Periodic Packings of Tori, Physical Review E, 89, 022133 (2014). Y. Jiao, T. Lau, H. Haztzikirou, M. Meyer-Hermann, J. C. Corbo, and S. Torquato, Avian Photoreceptor Patterns Represent a Disordered Hyperuniform Solution to a Multiscale Packing Problem, Physical Review E, 89, 022721 (2014). E. Guo, N. Chawla, T. Jing, S. Torquato, and Y. Jiao, Accurate Modeling and Reconstruction of Three-Dimensional Percolating Filamentary Microstructures from Two-Dimensional Micrographs via Dilation-Erosion Method, Materials Characterization, 89, 33 (2014). D. Chen, Y. Jiao, and S. Torquato, Equilibrium Phase Behavior and Maximally Random Jammed State of Truncated Tetrahedra, Journal of Physical Chemistry B, 118, 7981 (2014). H. Liasneuski, D. Hlushkou, S. Khirevich, A. H?ltzel, U. Tallarek, and S. Torquato, Impact of Microsctructure on the Effective Diffusivity in Random Packings of Hard Spheres, Journal of Applied Physics, 116, 034904 (2014). Y. Kallus and S. Torquato, Marginal Stability in Jammed Packings: Quasicontacts and Weak Contacts, Physical Review E, 90, 022114 (2014). D. Chen, Y. Jiao, and S. Torquato, A Cellular Automaton Model for Tumor Dormancy: Emergence of a Proliferative Switch, PLoS ONE, 9, e109934 (2014). J. Spangenberg, G. W. Scherer, A. B. Hopkins, and S. Torquato, Viscosity of Bimodal Suspensions With Hard Spherical Particles, Journal of Applied Physics, 116, 184902 (2014). M. A. Klatt and S. Torquato, Characterization of Maximally Random Jammed Sphere Packings: Voronoi Correlation Functions, Physical Review E, 90, 052120 (2014). S. Atkinson, F. H. Stillinger, and S. Torquato, Existence of Isostatic, Maximally Random Jammed Monodisperse Hard-Disk Packings, Proceedings of the National Academy of Sciences, 111, 18436 (2014). R. Dreyfus, Y. Xu, T. Still, L. A. Hough, A. G. Yodh, and S. Torquato Diagnosing Hyperuniformity in Two-Dimensional, Disordered, Jammed Packings of Soft Spheres, Physical Review E, 91, 012302 (2015).