Related papers: Directed Abelian sandpile with multiple downward n…
We check the universality properties of the two-dimensional Abelian sandpile model by computing some of its properties on the honeycomb lattice. Exact expressions for unit height correlation functions in presence of boundaries and for…
We prove a necessary and sufficient condition for an Abelian Sandpile Model (ASM) to be avalanche-finite, namely: all unstable states of the system can be brought back to stability in finite number of topplings. The method is also…
We consider the Bak-Tang-Wiesenfeld sandpile model on a two-dimensional square lattice of lattice sizes up to L=4096. A detailed analysis of the probability distribution of the size, area, duration and radius of the avalanches will be…
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…
We study the patterns formed by adding $N$ sand-grains at a single site on an initial periodic background in the Abelian sandpile models, and relaxing the configuration. When the heights at all sites in the initial background are low…
The Abelian Sandpile Model, seen as a deterministic lattice automaton, on two-dimensional periodic graphs generates complex regular patterns displaying (fractal) self-similarity. In particular, on a variety of lattices and initial…
We investigate a set of directed sandpile models on the Apollonian network, which are inspired on the work by Dhar and Ramaswamy (PRL \textbf{63}, 1659 (1989)) for Euclidian lattices. They are characterized by a single parameter $q$, that…
We introduce a sandpile model where, at each unstable site, all grains are transferred randomly to downstream neighbors. The model is local and conservative, but not Abelian. This does not appear to change the universality class for the…
We investigate the avalanche dynamics of the abelian sandpile model on arbitrarily large balls of the expanded cactus graph (the Cayley graph of the free product $\mathbb{Z}_3 * \mathbb{Z}_2$). We follow the approach of Dhar and Majumdar…
We insert some asymmetries in the continuous Abelian sandpile models, such as directedness and ellipticity. We analyze probability distribution of different heights and also find the field theory corresponding to the models. Also we find…
We study a directed stochastic sandpile model of Self-Organized Criticality, which exhibits recurrent, multiple topplings, putting it in a separate universality class from the exactly solved model of Dhar and Ramaswamy. We show that in the…
We study critical properties of the continuous Abelian sandpile model with anisotropies in toppling rules that produce ordered patterns on it. Also we consider the continuous directed sandpile model perturbed by a weak quenched randomness…
We revisit the calculation of height correlations in the two-dimensional Abelian sandpile model by taking advantage of a technique developed recently by Kenyon and Wilson. The formalism requires to equip the usual graph Laplacian,…
The abelian sandpile model in two dimensions does not show the type of critical behavior familar from equilibrium systems. Rather, the properties of the stationary state follow from the condition that an avalanche started at a distance r…
We study here a variant of the Abelian Sandpile Model, where the playground is a cylinder of width $w$ and of circumference c. When c << w, we describe a phenomenon which has not been observed in other geometries: the probability…
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…
We perform large scale numerical simulations of a directed version of the two-state stochastic sandpile model. Numerical results show that this stochastic model defines a new universality class with respect to the Abelian directed sandpile.…
We show that the patterns in the Abelian sandpile are stable. The proof combines the structure theory for the patterns with the regularity machinery for non-divergence form elliptic equations. The stability results allows one to improve…
Since the work of Creutz, identifying the group identities for the Abelian Sandpile Model (ASM) on a given lattice is a puzzling issue: on rectangular portions of Z^2 complex quasi-self-similar structures arise. We study the ASM on the…
We use a discrete-time formulation to study the asymmetric avalanche process [Phys. Rev. Lett. vol. 87, 084301 (2001)] on a finite ring and obtain an exact expression for the average avalanche size of particles as a function of toppling…