The densest packing of spheres, although known for millennia to be a Face-Centered Cubic (FCC) crystal with volume fraction φFCC ~0.74, has only recently been proven mathematically (2014). An equally ancient problem is “Random Close Packing”, 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”. RCP has escaped a noncontroversial definition although many experiments and simulations agree to a value φRCP ~0.64. We have found that a simple model, “Random Organization”, RO, exhibits a dynamical phase transition between absorbing, 'dead', and active states that appears to have RCP as its critical endpoint. Invented to understand a reversible to irreversible transition in sheared colloids, RO finds RCP with emergent properties such as, randomness, isotropy, isostaticity, hyperuniformity and jamming, that were previously put in by hand. It also yields an upper critical dimension of 4, ⇒ the critical behavior is mean field, infinite dimensional, for dimensions 4 → ∞.
In Random Organization, RO, overlapping particles are each given a random displacement < ε. In BRO some repulsive displacements are added. For BRO we find φcMAX ~ 0.64 ~ φRCP, isostatic coordination, Z=6, and a similar radial distribution function as found in several previous RCP experiments and simulations. BRO, an absorbing state model, remains in the Manna (sand-pile) universality class. Such models are hyperuniform at critical, S(q→0) ~qα. For the Manna class, α3D =0.25. At φcMAX, we show that BRO and two other protocols for RCP have very similar S(q) with α3D =0.25. We conjecture that the highest density absorbing state for an isotropic RO or BRO nderstand model, produces an ensemble of configurations that characterizes the state conventionally known as RCP. This characterization requires neither randomness nor jamming which rather become emergent properties. RCP’s identification with a dynamical phase transition provides new insights into disorder, jamming and glass transitions.
