相关论文: Driving sandpiles to criticality and beyond

To explain the ubiquity of power laws and fractals in nature, Bak, Tang, and Wiesenfeld formulated simple conditions for a system to self-organize into a critical state. Dickman, Mu\~noz, Vespignani, and Zapperi postulated that the…

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…

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 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…

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 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…

We study a nonconservative sandpile model in one dimension, in which, if the height at any site exceeds a threshold value, the site topples by transferring one particle along each bond connecting it to its neighbours. Its height is then set…

We revisit the question whether the critical behavior of sandpile models with sticky grains is in the directed percolation universality class. Our earlier theoretical arguments in favor, supported by evidence from numerical simulations […

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…

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 discuss various critical densities in sandpile models. The stationary density is the average expected height in the stationary state of a finite-volume model; the transition density is the critical point in the infinite-volume…

Recognising changes in collective dynamics in complex systems is essential for predicting potential events and their development. Possessing intrinsic attractors with laws associated with scale invariance, self-organised critical dynamics…

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…

A simple model economy with locally interacting producers and consumers is introduced. When driven by extremal dynamics, the model self-organizes {\em not} to an attractor state, but to an asymptote, on which the economy has a constant rate…

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…

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…

Bak, Tang, and Wiesenfeld developed their theory of self-organized criticality in the late 1980s to explain why many real-life processes exhibit signs of critical behavior despite the absence of a tuning parameter. A decade later, Dickman,…

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…

In this thesis we present few theoretical studies of the models of self-organized criticality. Following a brief introduction of self-organized criticality, we discuss three main problems. The first problem is about growing patterns formed…

Aging in complex systems is studied via the sandpile model. Relaxation of avalanches in sandpiles is observed to depend on the time elapsed since the begining of the relaxation. Levy behavior is observed in the distribution of…