Percolation analysis of force networks in anisotropic granular matter

TL;DR

This paper investigates the percolation transition of force networks in an anisotropic granular model, revealing unique critical exponents influenced by anisotropy, correlations, and conservation laws through extensive numerical simulations.

Contribution

It introduces a finite-size scaling analysis for directed percolation in an anisotropic granular model, highlighting how anisotropy affects critical exponents and transition behavior.

Findings

Percolation transition is strongly affected by anisotropy.

Critical exponents differ from isotropic and standard directed percolation.

Strong directed correlations and mass conservation influence the transition.

Abstract

We study the percolation properties of force networks in an anisotropic model for granular packings, the so-called q-model. Following the original recipe of Ostojic et al. [Nature 439, 828 (2006)], we consider a percolation process in which forces smaller than a given threshold f are deleted in the network. For a critical threshold f_c, the system experiences a transition akin to percolation. We determine the point of this transition and its characteristic critical exponents applying a finite-size scaling analysis that takes explicitly into account the directed nature of the q-model. By means of extensive numerical simulations, we show that this percolation transition is strongly affected by the anisotropic nature of the model, yielding characteristic exponents which are neither those found in isotropic granular systems nor those in the directed version of standard percolation. The differences shown by the computed exponents can be related to the presence of strong directed correlations and mass conservation laws in the model under scrutiny.