Jammed disks of two sizes in a narrow channel

TL;DR

This paper presents an exact solution to a granular matter model with two-sized disks in a narrow channel, analyzing jamming states, entropy, and critical phenomena related to volume and agitation.

Contribution

It introduces a novel exactly solvable model of jammed disks with two sizes, characterizing microstates via statistically interacting particles and exploring critical behavior.

Findings

Jammed microstates are characterized by two-disk tiles.

Configurational entropy shows a critical point as a function of excess volume.

Jamming depends on expansion work, gravitational potential, and agitation.

Abstract

A granular-matter model is exactly solved, where disks of two sizes and weights in alternating sequence are confined to a narrow channel. The axis of the channel is horizontal and its plane vertical. Disk sizes and channel width are such that under jamming no disks remain loose and all disks touch one wall. Jammed microstates are characterized via statistically interacting particles constructed out of two-disk tiles. Jammed macrostates depend on measures of expansion work, gravitational potential energy, and intensity of random agitations before jamming. The dependence of configurational entropy on excess volume exhibits a critical point.