2 research outputs found
Sticky grains do not change the universality class of isotropic sandpiles
We revisit the sandpile model with ``sticky'' grains introduced by Mohanty
and Dhar [Phys. Rev. Lett. {\bf 89}, 104303 (2002)] whose scaling properties
were claimed to be in the universality class of directed percolation for both
isotropic and directed models. Simulations in the so-called fixed-energy
ensemble show that this conclusion is not valid for isotropic sandpiles and
that this model shares the same critical properties of other stochastic
sandpiles, such as the Manna model. %as expected from the existence of an extra
%conservation-law, absent in directed percolation. These results are
strengthened by the analysis of the Langevin equations proposed by the same
authors to account for this problem which we show to converge, upon
coarse-graining, to the well-established set of Langevin equations for the
Manna class. Therefore, the presence of a conservation law keeps isotropic
sandpiles, with or without stickiness, away from the directed percolation
class.Comment: 4 pages. 3 Figures. Subm. to PR
Growing networks with local rules: preferential attachment, clustering hierarchy and degree correlations
The linear preferential attachment hypothesis has been shown to be quite
successful to explain the existence of networks with power-law degree
distributions. It is then quite important to determine if this mechanism is the
consequence of a general principle based on local rules. In this work it is
claimed that an effective linear preferential attachment is the natural outcome
of growing network models based on local rules. It is also shown that the local
models offer an explanation to other properties like the clustering hierarchy
and degree correlations recently observed in complex networks. These
conclusions are based on both analytical and numerical results of different
local rules, including some models already proposed in the literature.Comment: 17 pages, 14 figures (to appear in Phys. Rev E