Critical Scaling of Shearing Rheology at the Jamming Transition of Soft Core Frictionless Disks

TL;DR

This paper uses numerical simulations and critical scaling analysis to investigate the behavior of shear stress and pressure near the jamming transition in a 2D soft-disk model, emphasizing the importance of corrections to scaling.

Contribution

It provides a detailed critical scaling analysis of jamming, highlighting the necessity of including corrections to scaling for accurate characterization.

Findings

Pressure corrections to scaling are smaller than shear stress.

Pressure and shear stress exhibit superlinear behavior above the jamming point.

Critical behavior near jamming is accurately described when corrections to scaling are included.

Abstract

We perform numerical simulations to determine the shear stress and pressure of steady-state shear flow in a soft-disk model in two dimensions at zero temperature in the vicinity of the jamming transition \phi_J. We use critical point scaling analyses to determine the critical behavior at jamming, and we find that it is crucial to include corrections to scaling for a reliable analysis. We find that the relative size of these corrections are much smaller for pressure than for shear stress. We furthermore find a superlinear behavior for pressure and shear stress above \phi_J, both from the scaling analysis and from a direct analysis of pressure data extrapolated to the limit of vanishing shear rate.