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We perform numerical simulations of the sandpile model for non-vanishing driving fields $h$ and dissipation rates $\epsilon$. Unlike simulations performed in the slow driving limit, the unique time scale present in our system allows us to…

Statistical Mechanics · Physics 2009-10-31 A. Barrat , A. Vespignani , S. Zapperi

Similar evolutionary variational inequalities appear as convenient formulations for continuous quasistationary models for sandpile growth, formation of a network of lakes and rivers, magnetization of type-II superconductors, and…

Soft Condensed Matter · Physics 2009-11-10 Leonid Prigozhin

Kinetic equations, which explicitly take into account the branching nature of sandpile avalanches, are derived. The dynamics of the sandpile model is described by the generating functions of a branching process. Having used the results…

Condensed Matter · Physics 2009-10-28 E. V. Ivashkevich

Sand pile models are dynamical systems describing the evolution from $N$ stacked grains to a stable configuration. It uses local rules to depict grain moves and iterate it until reaching a fixed configuration from which no rule can be…

Discrete Mathematics · Computer Science 2013-04-19 Kevin Perrot , Eric Rémila

We introduce and study a new directed sandpile model with threshold dynamics and stochastic toppling rules. We show that particle conservation law and the directed percolation-like local evolution of avalanches lead to the formation of a…

Statistical Mechanics · Physics 2009-10-30 Bosiljka Tadić , Deepak Dhar

The paper develops one-parametric family of the sand-piles dealing with the grains' local losses on the fixed amount. The family exhibits the crossover between the models with deterministic and stochastic relaxation. The mean height of the…

Statistical Mechanics · Physics 2009-11-11 A. B. Shapoval , M. G. Shnirman

We show that tilting a model sandpile that has dynamic disorder leads to bistability and hysteresis at the angle of repose. Also the distribution of {\it local slopes} shows an interesting dependence on the amount of tilt - weakly tilted…

Soft Condensed Matter · Physics 2009-10-31 Anita Mehta , G. C. Barker

We consider the Bak-Tang-Wiesenfeld sandpile model on square lattices in different dimensions (D>=6). A finite size scaling analysis of the avalanche probability distributions yields the values of the distribution exponents, the dynamical…

Condensed Matter · Physics 2009-10-30 S. Lubeck , K. D. Usadel

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

This paper considers a sandpile model subjected to a sinusoidal external drive with the time period $T$. We develop a theoretical model for the Green function in a large $T$ limit, which predicts that the avalanches are anisotropic and…

Statistical Mechanics · Physics 2023-07-12 J. Cheraghalizadeh , M. A. Seifi MirJafarlou , M. N. Najafi

We present and analyze a model of an evolving sandpile surface in (2 + 1) dimensions where the dynamics of mobile grains ({\rho}(x, t)) and immobile clusters (h(x, t)) are coupled. Our coupling models the situation where the sandpile is…

Statistical Mechanics · Physics 2012-06-26 Bandan Chakrabortty , Anita Mehta

The divisible sandpile starts with i.i.d. random variables ("masses") at the vertices of an infinite, vertex-transitive graph, and redistributes mass by a local toppling rule in an attempt to make all masses at most 1. The process…

Probability · Mathematics 2016-06-29 Lionel Levine , Mathav Murugan , Yuval Peres , Baris Evren Ugurcan

We investigate the sandpile model with Yukawa-type interactions, whose effective range is tuned by an external parameter $R$. Our results reveal that at specific values of $R$, the system exhibits giant avalanches that span the system,…

Statistical Mechanics · Physics 2025-09-18 Abbas Shoja-Daliklidash , Morteza Nattagh Najafi

In the single-source sandpile model, a number $N$ grains of sand are positioned at a central vertex on the 2-dimensional grid $\mathbb{Z}^2$. We study the stabilisation of this configuration for a stochastic sandpile model based on a…

Probability · Mathematics 2022-08-23 Thomas Selig , Haoyue Zhu

Sandpiles form one of the largest class of models displaying a critical stationary state. Despite a few decades of research, a comprehensive and systematic rigorous characterisation of their spatial and, even more, time dependent properties…

Statistical Mechanics · Physics 2025-12-23 Valentin Lallemant

In the stochastic sandpile model on a graph, particles interact pairwise as follows: if two particles occupy the same vertex, they must each take an independent random walk step with some probability $0<p<1$ of not moving. These…

Probability · Mathematics 2022-04-27 Andrew Melchionna

The surface of conservative coupled sandpiles in the self-organized cooperative critical state is found to exhibit intermittency in both time and space. The spatiotemporal intermittent structure is also found to be a multifractal. The…

Adaptation and Self-Organizing Systems · Physics 2015-09-01 Lei Liu , Fei Hu

Sand pile models are dynamical systems describing the evolution from $N$ stacked grains to a stable configuration. It uses local rules to depict grain moves and iterate it until reaching a fixed configuration from which no rule can be…

Discrete Mathematics · Computer Science 2013-02-19 Kévin Perrot , Eric Rémila

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

Multiple avalanches, initiated by simultaneously toppling neighbouring sites, are studied in three different directed sandpile models. It is argued that, while the single avalanche exponents are different for the three models, a suitably…

Statistical Mechanics · Physics 2011-05-13 R. Rajesh