Relaxation times, rheology, and finite size effects for non-Brownian disks in two dimensions

We carry out overdamped simulations in a simple model of jamming-a collection of bidisperse soft core frictionless disks in two dimensions-with the aim to explore the finite size dependence of different quantities, both the relaxation time obtained from the relaxation of the energy and the pressure equivalent of the shear viscosity. The motivation for the paper is the observation [Nishikawa et al., J. Stat. Phys. 182, 37 (2021)] that there are finite size effects in the relaxation time, tau, that give problems in the determination of the critical divergence, and the claim that this is due to a finite size dependence, tau similar to ln N, which makes tau an ill-defined quantity. Beside analyses to determine the relaxation time for the whole system we determine particle relaxation times which allow us to determine both histograms of particle relaxation times and the average particle relaxation times-two quantities that are very useful for the analyses. The starting configurations for the relaxation simulations are of two different kinds-completely random or taken from steady shearing simulations-and we find that the difference between these two cases are bigger than previously noted and that the observed problems in the determination of the critical divergence obtained when starting from random configurations are not present when instead starting the relaxations from shearing configurations. We also argue that the the effect that causes the ln N dependence is not as problematic as asserted. When it comes to the finite size dependence of the pressure equivalent of the shear viscosity we find that our data don't give support for the claimed strong finite size dependence, but also that the finite size dependence is at odds with what one would normally expect for a system with a diverging correlation length, and that this calls for an alternative understanding of the phenomenon of shear-driven jamming.

Automated summary

In this study, overdamped simulations were conducted in a simple model of jamming to explore the finite size dependence of various quantities, including the relaxation time obtained from the relaxation of energy and the pressure equivalent of shear viscosity. The study found that the choice of starting configurations had a significant impact on the determination of critical divergence, and the claimed ln N dependence of the relaxation time was not as problematic as previously thought. Additionally, analyses of particle relaxation times provided useful histograms and averages for further analysis.