Ordering in dense packings
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We examine various models of soft matter, and one model of quasicrystals, focusing on abrupt changes as density is varied. We consider in detail two models, one of granular matter and another of confined wires, showing that the models become ordered as density is increased, with crystalline order observed in the former and nematic order observed in the latter. We associate the phenomenon of random close packing with the onset of crystalline order in our granular model, and we conjecture that crumpled wires should exhibit a nematic transition with increasing compaction. We also consider two other models of granular matter: one which describes dilatancy onset as a second order phase transition, and one which describes random loose packing as a precise, well- defined density. Finally, we examine an equilibrium model of quasicrystals with a first order phase transition to a solid phase without any crystalline order.