Ordering According to Size of Disks in a Narrow Channel

TL;DR

This paper provides an exact statistical analysis of jammed configurations of mixed-size disks in a narrow channel, revealing how jamming protocols influence size segregation and mixing.

Contribution

It introduces a novel tile-based approach to characterize jammed states and analyzes size segregation driven by steric forces in granular matter.

Findings

Identifies regimes that promote or suppress size mixing.

Shows broken symmetry leads to size segregation or alternation.

Provides exact formulas for jammed macrostate properties.

Abstract

A long and narrow channel confines disks of two sizes. The disks are randomly agitated in a widened channel under moderate pressure, then jammed according to a tunable protocol. We present exact results that characterize jammed macrostates (volume, entropy, jamming patterns). The analysis divides jammed disk sequences into overlapping tiles out of which statistically interacting quasiparticles are constructed. The fractions of small and large disks are controlled by a chemical potential adapted to configurational statistics of granular matter. The results show regimes for the energy parameters (determined by the jamming protocol) that either enhance or suppress the mixing of disk sizes. Size segregation or size alternation driven by steric forces alone are manifestations of a broken symmetry.