English
Related papers

Related papers: Patterned and Disordered Continuous Abelian Sandpi…

200 papers

A sandpile model with stochastic toppling rule is studied. The control parameters and the phase diagram are determined through a MF approach, the subcritical and critical regions are analyzed. The model is found to have some similarities…

Condensed Matter · Physics 2009-10-31 Alexei Vazquez , Oscar Sotolongo-Costa

This contribution is a review of the deep and powerful connection between the large scale properties of critical systems and their description in terms of a field theory. Although largely applicable to many other models, the details of this…

Statistical Mechanics · Physics 2023-08-25 Philippe Ruelle

We define two general classes of nonabelian sandpile models on directed trees (or arborescences) as models of nonequilibrium statistical phenomena. These models have the property that sand grains can enter only through specified reservoirs,…

Probability · Mathematics 2015-03-17 Arvind Ayyer , Anne Schilling , Benjamin Steinberg , Nicolas M. Thiery

A new sandpile model is studied in which bonds of the system are inhibited for activity after a certain number of transmission of grains. This condition impels an unstable sand column to distribute grains only to those neighbours which have…

Statistical Mechanics · Physics 2009-10-30 S. S. Manna , D. Giri

We show that deterministic systems with strong nonlinearities seem to be more appropriate to model sandpiles than stochastic systems or deterministic systems in which discontinuities are the only nonlinearity. In particular, we are able to…

Statistical Mechanics · Physics 2009-11-10 Maria de Sousa Vieira

We numerically study the directed version of the fixed energy sandpile. On a closed square lattice, the dynamical evolution of a fixed density of sand grains is studied. The activity of the system shows a continuous phase transition around…

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

We study the Abelian sandpile model (ASM), a process where grains of sand are placed on a graph's vertices. When the number of grains on a vertex is at least its degree, one grain is distributed to each neighboring vertex. This model has…

Probability · Mathematics 2019-01-18 Samantha Fairchild , Ilse Haim , Rafael G. Setra , Robert S. Strichartz , Travis Westura

With a toppling rule which generates metastable sites, we explore the properties of a gradient-driven sandpile that is minimally perturbed at one boundary. In two dimensions we find that the transport of grains takes place along deep…

Statistical Mechanics · Physics 2009-11-07 Lucian Anton , Hendrik B. Geyer

Adding grains at a single site on a flat substrate in the Abelian sandpile models produce beautiful complex patterns. We study in detail the pattern produced by adding grains on a two-dimensional square lattice with directed edges (each…

Statistical Mechanics · Physics 2010-10-01 Deepak Dhar , Tridib Sadhu , Samarth Chandra

We introduce an external control to reduce the size of avalanches in some sandpile models exhibiting self organized criticality. This rather intuitive approach seems to be missing in the vast literature on such systems. The control action,…

Computational Physics · Physics 2015-06-16 Daniel O. Cajueiro , Roberto F. S. Andrade

We study a model of ``organized'' criticality, where a single avalanche propagates through an \textit{a priori} static (i.e., organized) sandpile configuration. The latter is chosen according to an i.i.d. distribution from a Borel…

Probability · Mathematics 2007-05-23 Marek Biskup , Philippe Blanchard , Lincoln Chayes , Daniel Gandolfo , Tyll Krueger

In this paper we derive the scaling fields in $c=-2$ conformal field theory associated with weakly allowed clusters in abelian sandpile model and show a direct relation between the two models.

Statistical Mechanics · Physics 2009-11-10 S. Moghimi-Araghi , M. A. Rajabpour , S. Rouhani

We introduce a one-dimensional sandpile model which incorporates particle inertia. The inertial dynamics are governed by a new parameter which, as it passes through a threshold value, alters the toppling dynamics in such a way that the…

Condensed Matter · Physics 2009-10-28 D. A. Head , G. J. Rodgers

We review the status of the two-dimensional Abelian sandpile model as a strong candidate to provide a lattice realization of logarithmic conformal invariance with central charge c=-2. Evidence supporting this view is collected from various…

High Energy Physics - Theory · Physics 2015-06-15 Philippe Ruelle

We consider the abelian stochastic sandpile model. In this model, a site is deemed unstable when it contains more than one particle. Each unstable site, independently, is toppled at rate $1$, sending two of its particles to neighbouring…

Probability · Mathematics 2021-03-17 Moumanti Podder , Leonardo T. Rolla

We prove that the Abelian sandpile model on a random binary and binomial tree, as introduced in \cite{rrs}, is not critical for all branching probabilities $p<1$; by estimating the tail of the annealed survival time of a random walk on the…

Probability · Mathematics 2019-10-31 Frank Redig , Wioletta M. Ruszel , Ellen Saada

In the sandpile model, vertices of a graph are allocated grains of sand. At each unit of time, a grain is added to a randomly chosen vertex. If that causes its number of grains to exceed its degree, that vertex is called unstable, and…

Combinatorics · Mathematics 2024-09-19 Thomas Selig , Haoyue Zhu

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

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

Self-Organized Criticality is the emergence of long-ranged spatio-temporal correlations in non-equilibrium steady states of slowly driven systems without fine tuning of any control parameter. Sandpiles were proposed as prototypical examples…

Soft Condensed Matter · Physics 2007-05-23 S. S. Manna