Generic Sandpile Models Have Directed Percolation Exponents

We study sandpile models with stochastic toppling rules and having sticky grains so that with a non-zero probability no toppling occurs, even if the local height of pile exceeds the threshold value. Dissipation is introduced by adding a small probability of particle loss at each toppling. Generically, for models with a preferred direction, the avalanche exponents are those of critical directed percolation clusters. For undirected models, avalanche exponents are those of directed percolation clusters in one higher dimension.Comment: 4 pages, 4 figures, minor change

The origin of power-law distributions in self-organized criticality

The origin of power-law distributions in self-organized criticality is investigated by treating the variation of the number of active sites in the system as a stochastic process. An avalanche is then regarded as a first-return random walk process in a one-dimensional lattice. Power law distributions of the lifetime and spatial size are found when the random walk is unbiased with equal probability to move in opposite directions. This shows that power-law distributions in self-organized criticality may be caused by the balance of competitive interactions. At the mean time, the mean spatial size for avalanches with the same lifetime is found to increase in a power law with the lifetime.Comment: 4 pages in RevTeX, 3 eps figures. To appear in J.Phys.G. To appear in J. Phys.

Finite driving rate and anisotropy effects in landslide modeling

In order to characterize landslide frequency-size distributions and individuate hazard scenarios and their possible precursors, we investigate a cellular automaton where the effects of a finite driving rate and the anisotropy are taken into account. The model is able to reproduce observed features of landslide events, such as power-law distributions, as experimentally reported. We analyze the key role of the driving rate and show that, as it is increased, a crossover from power-law to non power-law behaviors occurs. Finally, a systematic investigation of the model on varying its anisotropy factors is performed and the full diagram of its dynamical behaviors is presented.Comment: 8 pages, 9 figure

Self-Organized Criticality model for Brain Plasticity

Networks of living neurons exhibit an avalanche mode of activity, experimentally found in organotypic cultures. Here we present a model based on self-organized criticality and taking into account brain plasticity, which is able to reproduce the spectrum of electroencephalograms (EEG). The model consists in an electrical network with threshold firing and activity-dependent synapse strenghts. The system exhibits an avalanche activity power law distributed. The analysis of the power spectra of the electrical signal reproduces very robustly the power law behaviour with the exponent 0.8, experimentally measured in EEG spectra. The same value of the exponent is found on small-world lattices and for leaky neurons, indicating that universality holds for a wide class of brain models.Comment: 4 pages, 3 figure

Scaling in a Nonconservative Earthquake Model of Self-Organised Criticality

We numerically investigate the Olami-Feder-Christensen model for earthquakes in order to characterise its scaling behaviour. We show that ordinary finite size scaling in the model is violated due to global, system wide events. Nevertheless we find that subsystems of linear dimension small compared to the overall system size obey finite (subsystem) size scaling, with universal critical coefficients, for the earthquake events localised within the subsystem. We provide evidence, moreover, that large earthquakes responsible for breaking finite size scaling are initiated predominantly near the boundary.Comment: 6 pages, 6 figures, to be published in Phys. Rev. E; references sorted correctl

Corrections to scaling in the forest-fire model

We present a systematic study of corrections to scaling in the self-organized critical forest-fire model. The analysis of the steady-state condition for the density of trees allows us to pinpoint the presence of these corrections, which take the form of subdominant exponents modifying the standard finite-size scaling form. Applying an extended version of the moment analysis technique, we find the scaling region of the model and compute the first non-trivial corrections to scaling.Comment: RevTeX, 7 pages, 7 eps figure

Universal Fluctuations in Correlated Systems

The probability density function (PDF) of a global measure in a large class of highly correlated systems has been suggested to be of the same functional form. Here, we identify the analytical form of the PDF of one such measure, the order parameter in the low temperature phase of the 2D-XY model. We demonstrate that this function describes the fluctuations of global quantities in other correlated, equilibrium and non-equilibrium systems. These include a coupled rotor model, Ising and percolation models, models of forest fires, sand-piles, avalanches and granular media in a self organized critical state. We discuss the relationship with both Gaussian and extremal statistics.Comment: 4 pages, 2 figure

A Two-Threshold Model for Scaling Laws of Non-Interacting Snow Avalanches

The sizes of snow slab failure that trigger snow avalanches are power-law distributed. Such a power-law probability distribution function has also been proposed to characterize different landslide types. In order to understand this scaling for gravity driven systems, we introduce a two-threshold 2-d cellular automaton, in which failure occurs irreversibly. Taking snow slab avalanches as a model system, we find that the sizes of the largest avalanches just preceeding the lattice system breakdown are power law distributed. By tuning the maximum value of the ratio of the two failure thresholds our model reproduces the range of power law exponents observed for land-, rock- or snow avalanches. We suggest this control parameter represents the material cohesion anisotropy.Comment: accepted PR

Transitions in non-conserving models of Self-Organized Criticality

We investigate a random--neighbours version of the two dimensional non-conserving earthquake model of Olami, Feder and Christensen [Phys. Rev. Lett. {\bf 68}, 1244 (1992)]. We show both analytically and numerically that criticality can be expected even in the presence of dissipation. As the critical level of conservation, $\alpha_c$, is approached, the cut--off of the avalanche size distribution scales as $\xi\sim(\alpha_c-\alpha)^{-3/2}$. The transition from non-SOC to SOC behaviour is controlled by the average branching ratio $\sigma$ of an avalanche, which can thus be regarded as an order parameter of the system. The relevance of the results are discussed in connection to the nearest-neighbours OFC model (in particular we analyse the relevance of synchronization in the latter).Comment: 8 pages in latex format; 5 figures available upon reques

1/f noise from correlations between avalanches in self-organized criticality

We show that large, slowly driven systems can evolve to a self-organized critical state where long range temporal correlations between bursts or avalanches produce low frequency $1/f^{\alpha}$ noise. The avalanches can occur instantaneously in the external time scale of the slow drive, and their event statistics are described by power law distributions. A specific example of this behavior is provided by numerical simulations of a deterministic ``sandpile'' model.Comment: Completely revised version: 4 pages (revtex), 3 eps figure