Title: Why do certain jammed packings of hard particles disobey Maxwell’s rigidity criterion?

Author (Talk): Kyle VanderWerf, Yale University

Abstract:

We correct the common misattribution of Maxwell’s rigidity criterion to contact networks in jammed packings of frictionless nonspherical particles, and develop a more detailed theoretical framework for studying these packings. We construct this framework by the following steps: a) we demonstrate that Maxwell’s criterion applies to a jammed packing if and only if the interparticle contacts can all be modeled as point-point distances, b) we show that “hypostatic” packings of nonspherical particles – packings with fewer contacts than Maxwell’s criterion specifies – are in fact jammed, in the sense that their configurations are stable under sufficiently small perturbations, and c) we explain how certain contacts in these hypostatic packings are able to constrain more than one degree of freedom at once, which allows the packings to be jammed despite seemingly “missing” contacts.