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Packing problems, such as how densely solid objects occupy 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 and materials science. While optimal packing problems are intimately related to ground states of condensed matter, disordered "jammed" sphere packings have been employed to model the glassy state of matter. Sphere packings in high dimensions have relevance in communications theory. Discrete geometers have a longstanding interest in packing problems. There are many open questions. What are the best packings of spheres in dimension greater than three? Can upper and lower bounds on the maximal densities aid in identifying the optimal arrangements in high dimensions? What are the densest packings of nonspherical objects in two and three dimensions? What is the precise connection between symmetry and optimal packings? Can random packings ever occupy space more densely than ordered packings? Can "randomness" be quantified in a meaningful and precise manner? Can the rigorous study of the hard-sphere model shed light on disorder/order phase transitions? Can the study of minimum energy configurations of interacting particles give insight into fundamental aspects of optimal packings? Examples of the cross-fertilization between the physical sciences and mathematics on packing problems abound. The aim of the workshop is to continue to foster the interchange of ideas between different fields by bringing together a diverse group of physicists, chemists, and mathematicians who work on packing problems.
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Many of the most intriguing problems in solid and fluid mechanics involve systems in which key physical parameters are very large (or small), or in which unusual geometries constrain the behavior of systems in surprising ways. Thus, in granular systems the rigidity of the particles is in marked contrast to their softness at a macroscopic level. In some soft biological systems of recent physics interest, the macroscopic elastic properties are both non-linear and tunable in ways that can shed new light on solid/continuum mechanics. In fluid mechanics, free boundary problems such as drop snap-off and related phenomena combine familiar hydrodynamic phenomena in counter-intuitive (and often aesthetically pleasing) ways. This workshop will cover this timely subject, which can fairly be termed"extreme mechanics."
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