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Both the deterministic and stochastic sandpile models are studied on the percolation backbone, a random fractal, generated on a square lattice in $2$-dimensions. In spite of the underline random structure of the backbone, the deterministic…

Statistical Mechanics · Physics 2020-05-20 Himangsu Bhaumik , S. B. Santra

We derive the steady state properties of a general directed ``sandpile'' model in one dimension. Using a central limit theorem for dependent random variables we find the precise conditions for the model to belong to the universality class…

Statistical Mechanics · Physics 2009-11-11 M A Stapleton , K Christensen

We revisit the question whether the critical behavior of sandpile models with sticky grains is in the directed percolation universality class. Our earlier theoretical arguments in favor, supported by evidence from numerical simulations […

Statistical Mechanics · Physics 2010-09-03 P. K. Mohanty , Deepak Dhar

We present results of large scale numerical simulations of the Bak, Tang and Wiesenfeld sandpile model. We analyze the critical behavior of the model in Euclidean dimensions $2\leq d\leq 6$. We consider a dissipative generalization of the…

Statistical Mechanics · Physics 2009-10-31 Alessandro Chessa , Enzo Marinari , Alessandro Vespignani , Stefano Zapperi

Statistics of waves of topplings in the Sandpile model is analysed both analytically and numerically. It is shown that the probability distribution of dissipating waves of topplings that touch the boundary of the system obeys power-law with…

Statistical Mechanics · Physics 2009-10-31 Chin-Kun Hu , E. V. Ivashkevich , Chai-Yu Lin , V. B. Priezzhev

Consider the Abelian sandpile measure on $\mathbb{Z}^d$, $d \ge 2$, obtained as the $L \to \infty$ limit of the stationary distribution of the sandpile on $[-L,L]^d \cap \mathbb{Z}^d$. When adding a grain of sand at the origin, some region,…

Probability · Mathematics 2017-09-29 Sandeep Bhupatiraju , Jack Hanson , Antal A. Járai

We study diffusion of particles in large-scale simulations of one-dimensional stochastic sandpiles, in both the restricted and unrestricted versions. The results indicate that the diffusion constant scales in the same manner as the activity…

Statistical Mechanics · Physics 2015-05-13 S. D. da Cunha , Ronaldo R. Vidigal , L. R. da Silva , Ronald Dickman

We study the stochastic sandpile model on $\mathbb{Z}^d$ and demonstrate that the critical density is strictly less than one in all dimensions. This generalizes a previous result by Hoffman, Hu, Richey, and Rizzolo (2022), which was limited…

Probability · Mathematics 2025-03-19 Concetta Campailla , Nicolas Forien , Lorenzo Taggi

We study numerically the dynamical properties of the BTW model on a square lattice for various dimensions. The aim of this investigation is to determine the value of the upper critical dimension where the avalanche distributions are…

Statistical Mechanics · Physics 2009-10-31 Sven Lubeck

Rotational constraint representing a local external bias generally has non-trivial effect on the critical behavior of lattice statistical models in equilibrium critical phenomena. In order to study the effect of rotational bias in a out of…

Soft Condensed Matter · Physics 2009-11-13 S. B. Santra , S. Ranjita Chanu , D. Deb

The existing estimation of the upper critical dimension of the Abelian Sandpile Model is based on a qualitative consideration of avalanches as self-avoiding branching processes. We find an exact representation of an avalanche as a sequence…

Statistical Mechanics · Physics 2007-05-23 V. B. Priezzhev

We study a nonconservative sandpile model in one dimension, in which, if the height at any site exceeds a threshold value, the site topples by transferring one particle along each bond connecting it to its neighbours. Its height is then set…

Condensed Matter · Physics 2016-08-31 Agha Afsar Ali

The avalanche statistics in a stochastic sandpile model where toppling takes place with a probability p is investigated. The limiting case p=1 corresponds to the Bak-Tang-Wiesenfeld (BTW) model with deterministic toppling rule. Based on the…

Condensed Matter · Physics 2007-05-23 Alexei Vazquez , O. Sotolongo-Costa

We introduce a family of abelian sandpile models with two parameters $n, m \in {\bf N}$ defined on finite lattices on $d$-dimensional torus. Sites with $2dn+m$ or more grains of sand are unstable and topple, and in each toppling $m$ grains…

Mathematical Physics · Physics 2015-09-02 Makoto Katori

We investigate sandpile models where the updating of unstable columns is done according to a stochastic rule. We examine the effect of introducing nonlocal relaxation mechanisms. We find that the models self-organize into critical states…

Statistical Mechanics · Physics 2009-10-30 L. A. N. Amaral , K. B. Lauritsen

A single sandpile model with quenched random toppling matrices captures the crucial features of different models of self-organized criticality. With symmetric matrices avalanche statistics falls in the multiscaling BTW universality class.…

Statistical Mechanics · Physics 2009-11-10 R. Karmakar , S. S. Manna , A. L. Stella

We study fixed density sandpiles in which the number of particles transferred to a neighbor on relaxing an active site is determined stochastically by a parameter $p$. Using an argument, the critical density at which an active-absorbing…

Statistical Mechanics · Physics 2009-11-10 Kavita Jain

We introduce and study numerically a directed two-dimensional sandpile automaton with probabilistic toppling (probability parameter p) which provides a good laboratory to study both self-organized criticality and the far-from-equilibrium…

Condensed Matter · Physics 2009-10-28 S. Luebeck , B. Tadic , K. D. Usadel

We study numerically scaling properties of the distribution of cumulative energy dissipated in an avalanche and the dynamic phase transition in a stochastic directed cellular automaton [B. Tadi\'c and D. Dhar, Phys. Rev. Lett. {\bf 79},…

Statistical Mechanics · Physics 2009-10-31 Bosiljka Tadic

A new classification of sandpile models into universality classes is presented. On the basis of extensive numerical simulations, in which we measure an extended set of exponents, the Manna two state model [S. S. Manna, J. Phys. A 24, L363…

Statistical Mechanics · Physics 2009-10-31 A. Ben-Hur , O. Biham