Dissipation and velocity distribution at the shear-driven jamming transition

TL;DR

This study explores how energy dissipation and particle velocity distributions behave at the shear-driven jamming transition in frictionless disks, revealing that dissipation is dominated by a small subset of particles with diverging velocities.

Contribution

It uncovers the role of fastest particles in dissipation and characterizes the velocity distribution tail approaching jamming, highlighting divergence in different velocity measures.

Findings

Dissipation is caused by the fastest particles.

The velocity distribution tail approaches v^{-3} near jamming.

Different velocity measures diverge differently, affecting theoretical models.

Abstract

We investigate energy dissipation and the distribution of particle velocities at the jamming transition for overdamped shear-driven frictionless disks in two dimensions at zero temperature. We find that the dissipation is caused by the fastest particles and that the fraction of particles responsible for the dissipation decreases towards zero as jamming is approached. These particles belong to an algebraic tail of the velocity distribution that approaches $\sim v^{-3}$ as jamming is approached. We further find that different measures of the velocity diverge differently, which means that concepts like "typical velocity" may no longer be used---a finding that should have implications for analytical approaches to shear-driven jamming.