Dynamical approach to the jamming problem

TL;DR

This paper introduces a dynamical model called Biased Random Organization (BRO) that reproduces Random Close Packing configurations across multiple dimensions, revealing critical behavior and universality class associations.

Contribution

The study proposes BRO as a universal dynamical model for RCP, demonstrating its critical properties and universality class across dimensions 2 to 5.

Findings

BRO produces RCP configurations in dimensions 3-5

BRO belongs to the Manna universality class of phase transitions

RCP's upper-critical dimension is consistent with d=4

Abstract

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 $d_{uc} = 4$.