Percolation analysis of force networks in anisotropic granular matter

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 (2006 Nature 439 828), we consider a percolation process in which forces smaller than a given threshold f are deleted in the network. For a critical threshold fc ,t he system experiences at ransition 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 a! ected 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 di! erences shown by the computed exponents can be related to the presence of strong directed correlations and mass conservation laws in the model under scrutiny.

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