Emergence of rigidity percolation in flowing granular systems

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. Our numerical simulations along with analytical arguments predict a crossover flow rate γ ˙ c ≃ 1 0 − 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 γ ˙ > γ ˙ c .

Short-range correlation of stress chains near solid-to-liquid transition in active monolayers

“…Additionally, contact connectivity percolation [78,79] has critical exponents that are different from those for random percolation [80,81]. Our results also contrast with non-equilibrium, boundary-driven sheared granular systems exhibiting long-range force correlation [36] and delineate the difference between an active matter system, driven by local subsystems with characteristic length ℓ and their collapse after performing a finite size scaling analysis for P(p, ℓ) (b, f) and S(p, ℓ) (d, h). First row (a-d) corresponds to increasing dimensionless cell-cell adhesion ω ~= ω cc /ω cw and the second row (e-h) corresponds to the increasing strength of active traction forces α ~.…”

“…Additionally, contact connectivity percolation [78,79] has critical exponents that are different from those for random percolation [80,81]. Our results also contrast with non-equilibrium, boundary-driven sheared granular systems exhibiting long-range force correlation [36] and delineate the difference between an active matter system, driven by local injection of energy and boundary-driven non-equilibrium systems. In this vein, our study provides a new context to explore potential links between dense active matter and glasses [82–84].…”

“…In such passive systems, the long-range force or stress correlations are attributed to mechanical equilibrium [30][31][32][33]. However, in some non-equilibrium systems, long-range mechanical correlations can also emerge in two seemingly disparate systems: (i) active matter [34], where local energy injection results in the breaking of time-reversal symmetry and detailed balance [35], and (ii) boundary-driven shear of granular systems [36]. Whether a broad framework to understand these two systems exists remains to be established [37].…”