Dissipative Sandpile Model Research Articles

A self-organized critical model and multifractal analysis for earthquakes in Central Alborz, Iran

This paper is devoted to a phenomenological study of the earthquakes in central Alborz, Iran. Using three observational quantities, namely the weight function, the quality factor, and the velocity model in this region, we develop a modified dissipative sandpile model which captures the main features of the system, especially the average activity field over the region of study. The model is based on external stimuli, the location of which is chosen (I) randomly, (II) on the faults, (III) on the low active points, (IV) on the moderately active points, and (V) on the highly active points in the region. We uncover some universal behaviors depending slightly on the method of external stimuli. A multi-fractal detrended fluctuation analysis is exploited to extract the spectrum of the Hurst exponent of the time series obtained by each of these schemes. Although the average Hurst exponent depends slightly on the method of stimuli, we numerically show that in all cases it is lower than 0.5, reflecting the anti-correlated nature of the system. The lowest average Hurst exponent is found to be associated with the case (V), in such a way that the more active the stimulated sites are, the lower the average Hurst exponent is obtained, i.e. the large earthquakes are more anticorrelated. Moreover, we find that the activity field achieved in this study provide information about the depth and topography of the basement, and also the area that can potentially be the location of the future large events. We successfully determine a high activity zone on the Mosha Fault, where the mainshock occurred on May 7th, 2020 (M_W 4.9).

Critical properties of a dissipative sandpile model on small-world networks

A dissipative sandpile model is constructed and studied on small-world networks (SWNs). SWNs are generated by adding extra links between two arbitrary sites of a two-dimensional square lattice with different shortcut densities ϕ. Three regimes are identified: regular lattice (RL) for ϕ≲2(-12), SWN for 2(-12)<ϕ<0.1, and random network (RN) for ϕ≥0.1. In the RL regime, the sandpile dynamics is characterized by the usual Bak, Tang, and Weisenfeld (BTW)-type correlated scaling, whereas in the RN regime it is characterized by mean-field scaling. On SWNs, both scaling behaviors are found to coexist. Small compact avalanches below a certain characteristic size s(c) are found to belong to the BTW universality class, whereas large, sparse avalanches above s(c) are found to belong to the mean-field universality class. A scaling theory for the coexistence of two scaling forms on a SWN is developed and numerically verified. Though finite-size scaling is not valid for the dissipative sandpile model on RLs or on SWNs, it is found to be valid on RNs for the same model. Finite-size scaling on RNs appears to be an outcome of super diffusive sand transport and uncorrelated toppling waves.

Dissipative sandpile models with universal exponents

We consider a dissipative variant of the stochastic-Abelian sandpile model on a two-dimensional lattice. The boundaries are closed and the dissipation is due to the fact that each toppled grain is removed from the lattice with probability epsilon. It is shown that the scaling properties of this model are in the universality class of the stochastic-Abelian models with conservative dynamics and open boundaries. In particular, the dissipation rate epsilon can be adjusted according to a suitable function epsilon = f(L), such that the avalanche size distribution will coincide with that of the conservative model on a finite lattice of size L.

Crossover component in non critical dissipative sandpile models

The effect of bulk dissipation on non critical sandpile models is studied using both multifractal and finite size scaling analyses. We show numerically that the local limited (LL) model exhibits a crossover from multifractal to self-similar behavior as the control parameters $h_{ext}$ and $\epsilon$ turn towards their critical values, i.e. $h_{ext} \to 0^+ $ and $\epsilon \to \epsilon_c$. The critical exponents are not universal and exhibit a continuous variation with $\epsilon$. On the other hand, the finite size effects for the local unlimited (LU), non local limited (NLL), and non local unlimited (NLU) models are well described by the multifractal analysis for all values of dissipation rate $\epsilon$. The space-time avalanche structure is studied in order to give a deeper understanding of the finite size effects and the origin of the crossover behavior. This result is confirmed by the calculation of the susceptibility.

Critical states in a dissipative sandpile model

A directed dissipative sandpile model is studied in two dimensions. Numerical results indicate that the long time steady states of this model are critical when grains are dropped only at the top, or everywhere. The critical behavior is mean-field-like. We discuss the role of infinite avalanches of dissipative models in periodic systems in determining the critical behavior of same models in open systems.

Self-organised criticality in some dissipative sandpile models

We investigate here self-organised criticality (SOC) in two-dimensional dissipative sandpile models without the local conservation law. Both dissipative cellular automata and dissipative coupled map lattice models with open boundary conditions are considered. There appears to be no evidence for the existence of SOC in the former models. In 2he CML models, scale-invariant avalanches are observed to occur for some specific local dynamical rules. This suggests that the occurrence of SOC depends, at least in part, on the nature of the dissipative dynamics.