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Mathematical Physics Seminar

Random Close Packing as a Dynamical Phase Transition

Paul Chaikin – New York University

Location:  zoom
Date & time: Wednesday, 14 July 2021 at 10:45AM - 11:45AM


Wednesday, July 14, 10:45AM (Zoom meeting starts at 10:30)


“Random Close Packing” is an ancient problem. RCP - the densest packing of spheres poured into a jar described in Biblical times (Luke 6:38, KJV) as, “pressed down, and shaken together, and running over” - has escaped a noncontroversial definition although many experiments and simulations agree to a value ?RCP  ~0.64. We have found that a simple model, “Biased Random Organization”, BRO, exhibits a dynamical phase transition between absorbing (non-overlapping) and active states that appears to have RCP as its critical endpoint. In Random Organization, RO, overlapping particles are each given a random displacement < ?. In BRO some fraction of repulsive displacements are added. For 3D BRO we find ?cMAX  ~ 0.64 ~ ?RCP, isostatic coordination, Z=6,  and a similar radial distribution function as found in previous RCP experiments and simulations. BRO, an absorbing state model, remains in the Manna universality class. Such models are hyperuniform at critical, S(q?0) ~q?. For the Manna class, ?3D =0.25. At ?cMAX, we show that BRO other protocols for RCP have very similar S(q) with ?3D =0.25. Characterizing RCP as the highest density ensemble of BRO configurations requires neither randomness, nor hyperuniformity, nor jamming which rather become emergent properties. In 2D BRO yields a rich phase diagram with a dense hexagonal crystal, area fraction ~0.91, as its critical endpoint.

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