Jamming in finite systems: stability, anisotropy, fluctuations and scaling

TL;DR

This paper investigates how finite system size influences the properties and stability of jammed sphere packings, revealing effects on isotropy, contact scaling, and elastic response near the jamming transition.

Contribution

It provides a comprehensive numerical analysis of finite-size effects on stability, contact number scaling, and anisotropy in jammed sphere packings.

Findings

Finite size affects the isotropy of jammed packings.

Scaling laws for contact number are modified by system size.

Elastic response exhibits finite-size scaling near jamming.

Abstract

Athermal packings of soft repulsive spheres exhibit a sharp jamming transition in the thermodynamic limit. Upon further compression, various structural and mechanical properties display clean power-law behavior over many decades in pressure. As with any phase transition, the rounding of such behavior in finite systems close to the transition plays an important role in understanding the nature of the transition itself. The situation for jamming is surprisingly rich: the assumption that jammed packings are isotropic is only strictly true in the large-size limit, and finite-size has a profound effect on the very meaning of jamming. Here, we provide a comprehensive numerical study of finite-size effects in sphere packings above the jamming transition, focusing on stability as well as the scaling of the contact number and the elastic response.