Title: Random Close Packing as a Dynamical Phase Transition: Jamming, Hyperuniformity and Photonics
Abstract: “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 volume fraction φRCP ~0.64. We have found that a simple model, “Biased Random Organization”, developed to explain a reversible/irreversible transition of driven particles at low Reynolds # has RCP as its critical endpoint. Further it predicts that RCP is hyperuniform with suppression of long range density fluctuations that can lead to isotropic photonic bandgaps in disordered materials. Characterizing RCP as the highest density ensemble of BRO configurations requires neither randomness, nor hyperuniformity, nor jamming which rather become emergent properties.