Universality in the jamming limit for elongated hard particles in one dimension

TL;DR

This paper investigates the thermodynamic and correlation properties of a one-dimensional gas of elongated hard particles, revealing universal behaviors in the high-density jamming limit depending on particle shape.

Contribution

It introduces a universality classification for the jamming behavior of elongated particles in one dimension based on shape-dependent correlation length divergence.

Findings

Correlation length diverges for needle and rectangle shapes at jamming

Universal classes depend on the contact point location relative to the center line

High-density behavior characterized by shape-dependent universality classes

Abstract

We study thermodynamics properties of a one dimensional gas of hard elongated particles. The particle centers are restricted to a line, while they can rotate in two-dimensional space. Correlations between orientations of the objects are studied (by transfer matrix method) as a function of density and aspect ratio. The behavior in the extreme high-density (jamming) limit is described by a few universality classes depending on the object's shape. In particular, there is a diverging correlation length when the contact point of adjacent objects is far from the line along which their centers move, as for needles and rectangles.