Protocol dependence of the jamming transition

TL;DR

This paper develops a theoretical framework to understand how different preparation protocols affect the jamming transition in frictionless particle systems, predicting protocol-dependent jamming probabilities and strain thresholds with numerical validation.

Contribution

It introduces a predictive model for protocol dependence in jamming, linking packing-generation methods to jamming probabilities and strain-induced jamming behavior.

Findings

Jammed packings can be generated by multiple protocols.

The probability of jamming depends on the protocol used.

Predicted shear strain for jamming matches numerical simulations.

Abstract

We propose a theoretical framework for predicting the protocol dependence of the jamming transition for frictionless spherical particles that interact via purely repulsive contact forces. We study isostatic jammed disk packings obtained via two protocols: isotropic compression and simple shear. We show that for frictionless systems, all jammed packings can be obtained via either protocol. However, the probability to obtain a particular jammed packing depends on the packing-generation protocol. We predict the average shear strain required to induce jamming in initially unjammed packings from the measured probability to jam at packing fraction $\phi$ from isotropic compression. We compare our predictions to results from numerical simulations of jamming and find quantitative agreement. We also show that the packing fraction range, over which strain-induced jamming occurs, tends to zero in the large system limit for frictionless packings with overdamped dynamics.