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    Ordering in dense packings

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    ARISTOFF-DISSERTATION.pdf (3.165Mb)
    Date
    2011-05
    Author
    Aristoff, David Gregory
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    Abstract
    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.
    Department
    Mathematics
    Description
    text
    Subject
    Statistical mechanics
    Phase transition
    Sphere packing
    Soft matter
    Crystalline
    Granular matter
    Quasicrystals
    URI
    http://hdl.handle.net/2152/ETD-UT-2011-05-2800
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    © The University of Texas at Austin