Jammed disks in narrow channel: criticality and ordering tendencies

TL;DR

This paper models jammed disk configurations in a narrow channel using configurational statistics, revealing a critical point where different jammed states with varying heterogeneity emerge.

Contribution

It introduces a novel statistical framework for analyzing jammed states in a confined disk system, identifying a critical point with path-dependent macrostate properties.

Findings

Existence of a critical point in the control variable space.

Jammed states exhibit heterogeneity or uniform domains depending on approach.

Volume and entropy characterize the macrostate configurations.

Abstract

A system of identical disks is confined to a narrow channel, closed off at one end by a stopper and at the other end by a piston. All surfaces are hard and frictionless. A uniform gravitational field is directed parallel to the plane of the disks and perpendicular to the axis of the channel. We employ a method of configurational statistics that interprets jammed states as configurations of floating particles with structure. The particles interlink according to set rules. The two jammed microstates with smallest volume act as pseudo-vacuum. The placement of particles is subject to a generalized Pauli principle. Jammed macrostates are generated by random agitations and specified by two control variables. One is a measure of the intensity of random agitations at given pressure. The other is a measure of the change in gravitational potential energy in units of compression work when one particle is excited. In this two-dimensional space of variables there exists a critical point. The jammed macrostate realized at the critical point depends on the path of approach. We describe all jammed macrostates by volume and entropy. Both are functions of the average population densities of particles. Approaching the critical point in an extended space of control variables generates two types of jammed macrostates: states with random heterogeneities in mass density and states with domains of uniform mass density.