Dynamical approach to the jamming problem

A simple dynamical model, Biased Random Organization, BRO, appears to produce configurations known as Random Close Packing (RCP) as BRO's densest critical point in dimension \(d=3\). We conjecture that BRO likewise produces RCP in any dimension; if so, then RCP does not exist in \(d=1-2\) (where BRO dynamics lead to crystalline order). In \(d=3-5\), BRO produces isostatic configurations and previously estimated RCP volume fractions 0.64, 0.46, and 0.30, respectively. For all investigated dimensions (\(d=2-5\)), we find that BRO belongs to the Manna universality class of dynamical phase transitions by measuring critical exponents associated with the steady-state activity and the long-range density fluctuations. Additionally, BRO's distribution of near-contacts (gaps) displays behavior consistent with the infinite-dimensional theoretical treatment of RCP when \(d \ge 4\). The association of BRO's densest critical configurations with Random Close Packing implies that RCP's upper-critical dimension is consistent with the Manna class \(d_{uc} = 4\).