Related papers: Sandpile models in the large
We study the scaling properties of avalanche activity in the two-dimensional Abelian sandpile model. Instead of the conventional avalanche size distribution, we analyze the site activity distribution, which measures how often a site…
We introduce the sandpile model on multiplex networks with more than one type of edge and investigate its scaling and dynamical behaviors. We find that the introduction of multiplexity does not alter the scaling behavior of avalanche…
Statistical mechanical systems at and near their points of phase transition are expected to exhibit rich, fractal-like behaviour that is independent of the small-scale details of the system but depends strongly on the dimension in which the…
Catalogues of galaxies, clusters of galaxies and superclusters - sources of information to study the large-scale structure of the Universe are reviewed. The power spectrum of density perturbations, and the correlation function are discussed…
We study sandpile models with stochastic toppling rules and having sticky grains so that with a non-zero probability no toppling occurs, even if the local height of pile exceeds the threshold value. Dissipation is introduced by adding a…
An interesting feature of growth in animals is that different parts of the body grow at approximately the same rate. This property is called proportionate growth. In this paper, we review our recent work on patterns formed by adding $N$…
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…
The paper contributes to building algebraic foundations of self-organized criticality answering a previously unsolved question about the limiting structure of the extended sandpile group as well as relating it to another limit at the level…
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…
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,…
Can the concept of self-organized criticality, exemplified by models such as the sandpile model, be described within the framework of continuous phase transitions? In this paper, we provide extensive numerical evidence supporting an…
We consider near-critical two-dimensional statistical systems at phase coexistence on the half plane with boundary conditions leading to the formation of a droplet separating coexisting phases. General low-energy properties of…
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…
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…
The geometrical structure is among the most fundamental ingredients in understanding complex systems. Is there any systematic approach in defining structures quantitatively, rather than illustratively? If yes, what are the basic principles…
We elaborate on Abelian complex scalar models, which are dictated by natural actions (all couplings are of order one), at fixed and large global $U(1)$ charge in an arbitrary number of dimensions. The ground state $| \upsilon\rangle$ is…
The Abelian sandpile growth model is a diffusion process for configurations of chips placed on vertices of the integer lattice $\mathbb{Z}^d$, in which sites with at least 2d chips {\em topple}, distributing 1 chip to each of their…
The hypothesis of self-organized criticality explains the existence of long-range `space-time' correlations, observed inseparably in many natural dynamical systems. A simple link between these correlations is yet unclear, particularly in…
The abelian sandpile model is a simple combinatorial model for critical behaviour which has the "abelian property" that the order in which we make moves does not change the final outcome of the game. This might seem to restrict the model's…
In this paper we rigorously construct a finite volume representation for the height-one field of the Abelian sandpile model and the degree field of the uniform spanning tree in terms of the fermionic Gaussian free field. This representation…