Percolation analysis of force networks in anisotropic granular matter
(10.01.2012)Zusammenfassung
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.