Levich Institute Seminar Announcement, 11/07/2006

Tuesday, 11/07/2006
2:00 PM
Steinman Hall, Room #312
(Chemical Engineering Conference Room)

Professor Salvatore Torquato
Princeton University
Department of Chemistry and Princeton Institute for the Science and Technology of Materials


"Optimal Particle Packings: Problems for the Ages"

ABSTRACT


Dense particle packings have fascinated people since the dawn of civilization and the fascination persists. I discuss why the venerable 50-year old notion of ``random close packing" (RCP) of spheres (the putative ``random" analog of Kepler's conjecture) is mathematically ill-defined. To replace this traditional notion, we introduce a new concept called the maximally random jammed (MRJ) state, which can be made precise. This state can viewed as a ``perfect" glass, and rests on devising precise meanings for ``jamming" and ``randomness," which I describe. We have defined three hierarchical categories of jamming, which relates to the mechanical stability of the packing, and a linear program that enables us to test a particle packing for any of the jamming categories. We show that the density of MRJ packings of ellipsoids in three dimensions closely approaches that of the densest lattice packing. This has interesting implications for the existence of a thermodynamically stable glass. Moreover, we have discovered a periodic ellipsoid packing with the highest known density and one in which the ellipsoids are not highly eccentric in shape. Finally, we provide strong evidence that the densest sphere packings in high Euclidean dimensions might be disordered, implying the existence of disordered (rather than periodic) ground states of matter. This leads to a lower bound on the maximal density of sphere packings in high dimensions that putatively provides the first exponential improvement on the 100-year-old lower bound due to Minkowski.

BRIEF ACADEMIC/EMPLOYMENT BACKGROUND:
  • Professor, Chemistry, Princeton Center for Theoretical Physics (Senior Fellow), and Princeton Institute for the Science and Technology of Materials (Associated Faculty in Physics, Program in Applied and Computational Mathematics, Department of Mechanical ∓ Aerospace Engineering, and Department of Chemical Engineering), Princeton University, July 1992 to present.
  • Professor, Departments of Mechanical and Aerospace Engineering and of Chemical Engineering, North Carolina State University, July 1991 to June, 1992.
  • Visiting Professor, Courant Institute of Mathematical Sciences, New York University, and Engineering and Applied Sciences, Yale University, September 1990 - June 1991.
  • Associate Professor, Departments of Mechanical and Aerospace Engineering and of Chemical Engineering, North Carolina State University, July 1985 - August 1990.
  • Assistant Professor, Departments of Mechanical and Aerospace Engineering and of Chemical Engineering, North Carolina State University, July 1982 to June 1985. Joint appointment with Chemical Engineering began January 1984.
  • Assistant Professor, Department of Mechanical Engineering, General Motors Institute, Flint, Michigan, January 1981 - June 1982.
  • Ph.D. (M.E.) State University of New York at Stony Brook, December 1980

CURRENT RESEARCH INTERESTS:

Statistical Mechanics of Liquids and Glasses, Transport and Mechanical Properties of Heterogeneous Materials, Colloids, Materials Optimization, Granular Media, Biological Materials, Percolation Theory, Image Science, Cancer Growth