Related papers: E-pile model of self-organized criticality
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…
Criticality in the cortex emerges from the seemingly random interaction of microscopic components and produces higher cognitive functions at mesoscopic and macroscopic scales. Random graphs and percolation theory provide natural means to…
When a finite volume of etching solution is in contact with a disordered solid, complex dynamics of the solid-solution interface develop. If the etchant is consumed in the chemical reaction, the dynamics stop spontaneously on a self-similar…
I review the concept of self-organized criticality, wherein dissipative systems naturally drive themselves to a critical state with important phenomena occurring over a wide range of length and time scales. Several exact results are…
The dynamics of an elastic interface profile h(x,t) under a driving force increasing at rate c, a restored force -epsilon h, and disorder is investigated. Using perturbation theory and functional renormalization group the phase diagram and…
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…
Avalanches in sandpiles are represented throughout a process of percolation in a Bethe lattice with a feedback mechanism. The results indicate that the frequency spectrum and probability distribution of avalanches resemble more to…
Percolation is one of the simplest and nicest models in probability theory/statistical mechanics which exhibits critical phenomena. Dynamical percolation is a model where a simple time dynamics is added to the (ordinary) percolation model.…
We study a model of ``organized'' criticality, where a single avalanche propagates through an \textit{a priori} static (i.e., organized) sandpile configuration. The latter is chosen according to an i.i.d. distribution from a Borel…
A percolation model is presented, with computer simulations for illustrations, to show how the sales of a new product may penetrate the consumer market. We review the traditional approach in the marketing literature, which is based on…
A self-organized model with social percolation process is proposed to describe the propagations of information for different trading ways across a social system and the automatic formation of various groups within market traders. Based on…
Self-organized criticality has been proposed to be a universal mechanism for the emergence of scale-free dynamics in many complex systems, and possibly in the brain. While such scale-free patterns were identified experimentally in many…
We study two driven dynamical systems with conserved energy. The two automata contain the basic dynamical rules of the Bak, Tang and Wiesenfeld sandpile model. In addition a global constraint on the energy contained in the lattice is…
We propose a simple "evolutionary" sandpile model exhibiting self-organised criticality and exactly $1/f$-noise (i.e. the critical exponent is equal to $-1$) and observe emergent phenomena of the same type self-organised criticality on the…
Self-organized criticality is a dynamical system property where, without external tuning, a system naturally evolves towards its critical state, characterized by scale-invariant patterns and power-law distributions. In this paper, we…
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…
Probabilistic cellular automata are prototypes of non equilibrium critical phenomena. This class of models includes among others the directed percolation problem (Domany Kinzel model) and the dynamical Ising model. The critical properties…
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…
A novel mechanism for the generation of self-organized criticality (SOC) is discussed in terms of the coupled-vibration model where the total system is forced under the uniform expansion of the Hubble type. This system shows a robust SOC…
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…