The results of numerical investigation of the Brownian motion in a two-dimensional potential field formed under the coupling of phase transitions at the conditions of the criticality induced by white noise are presented. The suggested system of stochastic equations at the white noise intensity...

A study has been made on the statistics of fluctuations in a spatially distributed system, which describes the interaction of nonequilibrium phase transitions. It is shown that at a certain intensity of external white noise acting on phase transitions, the time and spatial spectra of...

We report an experiment on a granular packing: a box filled with glass beads is tilted very slowly up to the maximum angle of stability where a big avalanche is produced. During the build-up period many rearrangements occur on the free surface of the packing. Digital imaging was used to study...

The Barkhausen jumps or avalanches in magnetic domain-walls motion between successive pinned configurations, due the competition among magnetic external driving force and substrum quenched disorder, appear in bulk materials and thin films. We introduce a model based in rules for the domain wall...

We investigate a one-dimensional rice-pile model. We show that the distribution of dissipated potential energy decays as a power law with an exponent α = 1.53. The system thus provides a one-dimensional example of self-organized criticality. Different driving conditions are examined in order to...

In a model of self-organized criticality unstable sites discharge to just one of their neighbours. For constant discharge ratio α and for a certain range of values of the input energy, avalanches are simple branchless Pólya random walks, and their scaling properties can be derived exactly. If...

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...

The avalanche dynamics in the Bak–Sneppen mechanism of self-organized criticality (SOC) is discussed. Rigorous arguments reveal the emergent history dependence that dominates the intermittent activity. In numerical studies the emergent SOC state shows glassy features, such as aging and an...