Diffusion and Velocity Auto-Correlation in Shearing Granular Media

TL;DR

This study uses numerical simulations to analyze particle diffusion and velocity auto-correlation in sheared granular media at the jamming point, revealing new relationships between exponents and identifying a fundamental decay exponent.

Contribution

It establishes a relation between the diffusion exponent and jamming transition exponents, and introduces a new fundamental exponent for velocity auto-correlation decay.

Findings

Diffusion constant scales with shear rate as D∼γ̇^{q_D} with q_D<1

Velocity auto-correlation governed by two processes with different time scales

Identifies a new exponent λ characterizing algebraic decay of correlations

Abstract

We perform numerical simulations to examine particle diffusion at steady shear in a model granular material in two dimensions at the jamming density and zero temperature. We confirm findings by others that the diffusion constant depends on shear rate as $D\sim\dot\gamma^{q_D}$ with $q_D<1$, and set out to determine a relation between $q_D$ and other exponents that characterize the jamming transition. We then examine the the velocity auto-correlation function, note that it is governed by two processes with different time scales, and identify a new fundamental exponent, $\lambda$, that characterizes an algebraic decay of correlations with time.