Related papers: Self-organized criticality via stochastic partial …

Spatial self-similarity is a hallmark of critical phenomena. We study the dynamic process of percolation, in which bonds are incrementally added to an initially empty lattice until the system becomes fully occupied. By tracking the gap --…

We consider the Bernoulli percolation model in a finite box and we introduce an automatic control of the percolation probability, which is a function of the percolation configuration. For a suitable choice of this automatic control, the…

Using a simple lattice model for granular media, we present a scenario of self-organization that we term self-organized structuring where the steady state has several unusual features: (1) large scale space and/or time inhomogeneities and…

We employ the eigen microstate approach to explore the self-organized criticality (SOC) in two celebrated sandpile models, namely, the BTW model and the Manna model. In both models, phase transitions from the absorbing-state to the critical…

We argue that atmospheric cascades can be regarded as example of the self-organized criticality and studied by using Levy flights and nonextensive approach. It allows us to understand the scale-invariant energy fluctuations inside cascades…

A new model of self-organized criticality is proposed. An algebra of operators is introduced which is similar to that used for the Abelian sandpile model. The structure of the configurational space is determined and the number of recurrent…

The Bak-Tang-Wiesenfeld sandpile model provdes a simple and elegant system with which to demonstate self-organized criticality. This model has rather remarkable mathematical properties first elucidated by Dhar. I demonstrate some of these…

We present a unified dynamical mean-field theory for stochastic self-organized critical models. We use a single site approximation and we include the details of different models by using effective parameters and constraints. We identify the…

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…

The existence of true scale-invariance in slowly driven models of self-organized criticality without a conservation law, as forest-fires or earthquake automata, is scrutinized in this paper. By using three different levels of description -…

A simple random-neighbor SOC model that combines properties of the Bak-Sneppen and the relaxation oscillators (slip-stick) models is introduced. The analysis in terms of branching processes is transparent and gives insight about the…

Some stochastic systems are particularly interesting as they exhibit critical behavior without fine-tuning of a parameter, a phenomenon called self-organized criticality. In the context of driven-dissipative steady states, one of the main…

In the prototype sandpile model of self-organized criticality time series obtained by decomposing avalanches into waves of toppling show intermittent fluctuations. The q-th moments of wave size differences possess local multiscaling and…

Atmospheric flows exhibit selfsimilar fluctuations on all scales(space-time) ranging from climate(kilometers/years) to turbulence(millimeters/seconds) manifested as fractal geometry to the global cloud cover pattern concomitant with inverse…

This study deals with continuous limits of interacting one-dimensional diffusive systems, arising from stochastic distortions of discrete curves with various kinds of coding representations. These systems are essentially of a…

The master equation describing non-equilibrium one-dimensional problems like diffusion limited reactions or critical dynamics of classical spin systems can be written as a Schr\"odinger equation in which the wave function is the probability…

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 derive an integration by parts formula for functionals of determinantal processes on compact sets, completing the arguments of [4]. This is used to show the existence of a configuration-valued diffusion process which is non-colliding and…

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…

We study here the Bak and Sneppen model, a prototype model for the study of Self-Organized Criticality. In this model several species interact and undergo extinction with a power law distribution of activity bursts. Species are defined…