Particle Packing Problems

Princeton University, Princeton NJ

Investigators

Abstract

Torquato 0804431 The investigator and his colleagues study a variety of packing problems. The following five general areas are explored: (1) identification and characterization of dense packings of nonspherical particles for a wide class shapes in two and three space dimensions; (2) study of sphere packings of maximal density in high Euclidean dimensions; (3) identification of low-density jammed sphere packings in various dimensions; (4) studies of jamming on the unit sphere in arbitrary dimensions; and (5) pursuit of improved order metrics to characterize the degree of randomness in a packing. Important scientific advances and outcomes are likely to emerge from the proposed research. This very multidisciplinary project joins the applied mathematics, statistical and condensed-matter physics, materials science, engineering, and pure mathematics communities. Unifying these different perspectives and goals is a challenging task, but one that offers great rewards to the scientific community in general. Packing problems, such as how densely solid objects fill space, have fascinated people since the dawn of civilization, and continue to intrigue scientists because of their connection to a host of problems that arise in the physical sciences, mathematics, engineering, and biology. While optimal packing problems are intimately related to solid states of condensed matter, disordered sphere packings have been employed to model the glassy state of matter. Sphere packings in high dimensions have relevance in communications theory. The way that viruses package DNA in protein containers is a packing problem. What are the densest packings of spheres in dimension greater than three? What are the densest packings of nonspherical objects in two and three dimensions? Can random packings ever fill space more densely than ordered packings (implying disordered or "glassy" ground states)? Can "randomness" of a packing be quantified in a meaningful and precise manner? A greater understanding of packing problems has implications for the synthesis of novel materials, our ability to efficiently design communications channels to send digital signals over large distances, and the design of new drugs, just to mention a few examples.