Moment analysis of the probability distribution of different sandpile models

Lübeck, S.

doi:10.1103/physreve.61.204

Cited by 80 publications

(99 citation statements)

References 30 publications

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“…The value of τ s for φ = 2 −12 is same as that of previously reported for DSM on RL (φ = 0) [35,40]. Note that the value of τ s of the BTW model (Dhar abelian sandpile model [26]) was also reported to be ≈ 1.11 though in the L → ∞ limit it is expected to be ≈ 1.29 [41][42][43]. There- fore the BTW type sandpile dynamics on RL remains unperturbed when performed on a lattice with additional N φ = 512 shortcuts corresponding to φ = 2 −12 on a lattice of size L = 1024.…”

Section: Probability Distributions and Conditional Expectation Valsupporting

confidence: 84%

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

Bhaumik

Santra

2013

Phys. Rev. E

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A dissipative sandpile model (DSM) is constructed and studied on small world networks (SWN). SWNs are generated adding extra links between two arbitrary sites of a two dimensional square lattice with different shortcut densities φ. Three different regimes are identified as 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 usual Bak, Tang, Weisenfeld (BTW) type correlated scaling whereas in the RN regime it is characterized by the mean field (MF) scaling. On SWN, both the scaling behaviors are found to coexist. Small compact avalanches below certain characteristic size sc are found to belong to the BTW universality class whereas large, sparse avalanches above sc are found to belong to the MF universality class. A scaling theory for the coexistence of two scaling forms on SWN is developed and numerically verified. Though finite size scaling (FSS) is not valid for DSM on RL as well as on SWN, it is found to be valid on RN for the same model. FSS on RN is appeared to be an outcome of super diffusive sand transport and uncorrelated toppling waves.

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Section: Probability Distributions and Conditional Expectation Valsupporting

confidence: 84%

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

Bhaumik

Santra

2013

Phys. Rev. E

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“…In order to gain a better understanding of this general behavior, we have also looked at some other SOC models in this regard. Our preliminary results in the case of Manna model, which obeys FSS, show that the scaling exponent γ maintains a constant value close to 0.5 [31,33,34]. Such observation, as well as the similarities between the behavior of waves and type-α avalanches, makes us believe that the constancy of the γ exponent indicates that the scaling behavior of the corresponding relaxation process follows a simple power law behavior.…”

Section: Scaling Of Cpdf For Different Types Of Avalanchessupporting

confidence: 53%

Scaling and complex avalanche dynamics in the Abelian sandpile model

Abdolvand

Montakhab

2010

Eur. Phys. J. B

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We study the two-dimensional Abelian Sandpile Model on a square lattice of linear size L. We introduce the notion of avalanche's fine structure and compare the behavior of avalanches and waves of toppling. We show that according to the degree of complexity in the fine structure of avalanches, which is a direct consequence of the intricate superposition of the boundaries of successive waves, avalanches fall into two different categories. We propose scaling ansätz for these avalanche types and verify them numerically. We find that while the first type of avalanches has a simple scaling behavior, the second (complex) type is characterized by an avalanche-size dependent scaling exponent. This provides a framework within which one can understand the failure of a consistent scaling behavior in this model.

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“…However, numerical simulations using an extended set of critical exponents showed that deterministic and stochastic models exhibit different scaling properties and thus belong to different universality classes [26,27,28]. Further support for this result was obtained using multifractal analysis [29], moment analysis [30] as well as studies of sandpile models as closed systems [31,32,33]. The crossover between the two classes was also studied [34].…”

Section: Introductionmentioning

confidence: 82%

Sandpile models and random walkers on finite lattices

Shilo

Biham

2003

Phys. Rev. E

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Abelian sandpile models, both deterministic, such as the Bak, Tang, Wiesenfeld (BTW) model [P. Bak, C. Tang and K. Wiesenfeld, Phys. Rev. Lett. 59, 381 (1987) L. The first few moments of this distribution are evaluated numerically and their dependence on the system size is examined. The sandpile models are conservative in the sense that grains are conserved in the bulk and can leave the system only through the boundaries. It is shown that the conservation law provides an interesting connection between sandpile models and random walk models. Using this connection, it is shown that the average avalanche sizes, n L , for the BTW and the Manna models are equal to each other, and both are equal to the average path-length of a random walker starting from a random initial site on the same lattice of size L. This is in spite of the fact that sandpile models with deterministic (BTW) and stochastic (Manna) toppling rules exhibit different critical exponents, indicating that they belong to different universality classes.

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Moment analysis of the probability distribution of different sandpile models

Cited by 80 publications

References 30 publications

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

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

Scaling and complex avalanche dynamics in the Abelian sandpile model

Sandpile models and random walkers on finite lattices

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