Related papers: Conserved sandpile with a variable height restrict…
The notion of Self-organized criticality (SOC) had been conceived to interpret the spontaneous emergence of long range correlations in nature. Since then many different models had been introduced to study SOC. All of them have few common…
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…
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 perform large-scale simulations of directed sandpile models with both deterministic and stochastic toppling rules. Our results show the existence of two distinct universality classes. We also provide numerical simulations of directed…
We study the steady state of the abelian sandpile models with stochastic toppling rules. The particle addition operators commute with each other, but in general these operators need not be diagonalizable. We use their abelian algebra to…
We consider the motion of a discrete random surface interacting by exclusion with a random wall. The heights of the wall at the sites of $\Z^d$ are i.i.d.\ random variables. Fixed the wall configuration, the dynamics is given by the serial…
We study the Zhang model of sandpile on a one dimensional chain of length $L$, where a random amount of energy is added at a randomly chosen site at each time step. We show that in spite of this randomness in the input energy, the…
We define a new version of sandpile model which is very similar to Abelian Sandpile Model (ASM), but the height variables are continuous ones. With the toppling rule we define in our model, we show that the model can be mapped to ASM, so…
Capillary forces significantly affect the stability of sandpiles. We analyze the stability of sandpiles with such forces, and find that the critical angle is unchanged in the limit of an infinitely large system; however, this angle is…
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…
We derive the first four terms in a series for the order paramater (the stationary activity density rho) in the supercritical regime of a one-dimensional stochastic sandpile; in the two-dimensional case the first three terms are reported.…
Motivated by the dissipative abelian sandpile model, we analyze the trajectories of a one-dimensional random walk in a landscape of soft traps. These traps, placed at increasing distances from each other, correspond to dissipative sites in…
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 consider random rectangles in $\mathbb{R}^2$ that are distributed according to a Poisson random measure, i.e., independently and uniformly scattered in the plane. The distributions of the length and the width of the rectangles are…
We give a non-trivial upper bound for the critical density when stabilizing i.i.d. distributed sandpiles on the lattice $\mathbb{Z}^2$. We also determine the asymptotic spectral gap, asymptotic mixing time and prove a cutoff phenomenon for…
We derive a general formulation of the self-organized branching process by considering sandpile dynamics in an evolving population characterized by "birth" (excitation) and "death" (de-excitation) of active sites ($z=1$). New active sites…
The divisible sandpile model is a fixed-energy continuous counterpart of the Abelian sandpile model. We start with a random initial configuration and redistribute mass deterministically. Under certain conditions the sandpile will stabilize.…
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…
Due to intermittency and conservation, the Abelian sandpile in 2D obeys multifractal, rather than finite size scaling. In the thermodynamic limit, a vanishingly small fraction of large avalanches dominates the statistics and a constant gap…
Taking the two-dimensional Ising model for example, short-time behavior of critical dynamics with a conserved order parameter is investigated by Monte Carlo simulations. Scaling behavior is observed, but the dynamic exponent $z$ is updating…