Emergence of Rigidity Percolation in Flowing Granular Systems

TL;DR

This study reveals how flow rate influences force chain percolation in granular media, showing a transition from standard rigidity percolation to a flow-dependent universality class with varying critical exponents.

Contribution

It introduces the concept of flow-induced long-range correlations affecting force percolation, with a predicted crossover flow rate and a spectrum of critical exponents.

Findings

Existence of a crossover flow rate $ extstyle ilde{ ext{γ}}_c \\simeq 10^{-5}$ separating regimes.

Below $ ilde{ ext{γ}}_c$, standard rigidity percolation applies.

Above $ ilde{ ext{γ}}_c$, critical exponents vary with flow rate.

Abstract

Jammed granular media and glasses exhibit spatial long-range correlations as a result of mechanical equilibrium. However, the existence of such correlations in the flowing matter, where the mechanical equilibrium is unattainable, has remained elusive. Here, we investigate this problem in the context of the percolation of interparticle forces in flowing granular media. We find that the flow rate introduces an effective long-range correlation, which plays the role of a relevant perturbation giving rise to a spectrum of varying exponents on a critical line as a function of the flow rate. Remarkably, our numerical simulations along with analytical arguments predict a crossover flow rate $\dot{\gamma}_c \simeq 10^{-5}$ below which the effect of induced disorder is weak and the universality of the force chain structure is shown to be given by the standard rigidity percolation. We also find a power-law behavior for the critical exponents with the flow rate $\dot{\gamma}>\dot{\gamma}_c$.