The probability distributions of several avalanche quantities of the Bak–Tang–Wiesenfeld sandpile in two dimensions display multifractal scaling. This explains why this prototype model remained extremely problematic and controversial for such a long time after its introduction. Other models,...

These notes are intended to provide a pedagogical introduction to the abelian sandpile model of self-organized criticality, and its related models. The abelian group, the algebra of particle addition operators, the burning test for recurrent states, equivalence to the spanning trees problem are...

A weighted Olami, Feder, and Christensen (OFC) model, improving the redistribution rule of the original model, has been introduced. It can be seen as a generalization of the OFC model and exhibits Self-organized criticality (SOC) behavior, too. The stress evolution process has been accelerated...

The statistics of acoustic emission (AE) from as diverse processes as volcanic activity (Stromboli, Italy) and martensitic transformations driven by thermal cycles, is shown to verify the paradigm of self-organized criticality. However, catastrophic event predictability both in laboratory (the...

We analyze a model of biological evolution recently introduced in the literature and show that punctuated equilibrium and power-law behavior arise because of the differential structural stability of the mapping between genotype and phenotype that characterizes the model. Structural stability is...

The scaling properties of waves of topplings of the sandpile model on a fractal lattice are investigated. The exponent describing the asymptotics of the distribution of last waves in an avalanche is found. Predictions for scaling exponents in the forward and backward conditional probabilities...

This study examines the dynamics of two-phase drainage with experiments of air invasion into a translucent water-saturated porous medium, at low injection speeds. Air displaces the water by irregular bursts of motion, suddenly invading small portions of the medium. These periods of activity,...

In a recent experiment with rice piles [V. Frette et al., Nature 379 (1996) 49] it was observed that the distribution of avalanches presents a power-law behavior for elongated rice, while avalanches for round rice present a characteristic length. These experiments showed that granular piles may...

Universality and scaling for systems driven to criticality by a tuning parameter has been well studied. However, there are very few corresponding studies for the models of self-organized criticality, e.g., the Bak, Tang, and Wiesenfeld (BTW) sandpile model. It is well known that every avalanche...

The sun provides an explosive, heavenly example of self-organized criticality. Sudden bursts of intense radiation emanate from rapid rearrangements of the magnetic field network in the corona. Avalanches are triggered by loops of flux that reconnect or snap into lower-energy configurations when...