Related papers: Power-law and log-normal avalanche size statistics…
We study the correlations between avalanches in the depinning dynamics of elastic interfaces driven on a random substrate. In the mean field theory (the Brownian force model), it is known that the avalanches are uncorrelated. Here we obtain…
Statistical fluctuations of the light emitted from amplifying random media are studied theoretically and numerically. The characteristic scales of the diffusive motion of light lead to Gaussian or power-law (Levy) distributed fluctuations…
We study size and growth distributions of products and business firms in the context of a given industry. Firm size growth is analyzed in terms of two basic mechanisms, i.e. the increase of the number of new elementary business units and…
Avalanche statistics of various threshold activated dynamical systems are known to depend on the magnitude of the drive, or stress, on the system. Such dependencies exist for earthquake size distributions, in sheared granular avalanches,…
Many-body stochastic processes with weighted multiplicative interactions are investigated analytically and numerically. An interaction rate between particles with quantities $x, y$ is controlled by a homogeneous symmetric kernel $K(x, y)…
The aim of this study is to investigate a wave dynamics and size scaling of avalanches which were created by the mathematical model {[}J. \v{C}ern\'ak Phys. Rev. E \textbf{65}, 046141 (2002)]. Numerical simulations were carried out on a two…
Critical states are sometimes identified experimentally through power-law statistics or universal scaling functions. We show here that such features naturally emerge from networks in self-sustained irregular regimes away from criticality.…
We study the onset of bulk avalanches and boundary outflow in the Bak Tang Wiesenfeld (BTW) model and in the stochastic BTW models by computer simulation. We also study the dependency of these two onset times on system sizes. We observe…
The average avalanche size can be calculated exactly in a number of models of self-organised criticality (SOC). While the calculation is straight-forward in one dimension, it is more involved in higher dimensions and further complicated by…
We revisit the problem of influencing the sex ratio of a population by subjecting reproduction of each family to some stopping rule. As an easy consequence of the strong law of large numbers, no such modification is possible in the sense…
Martensites subjected to quasistatic deformation are known to exhibit power law distributed acoustic emission in a broad range of scales, however, the origin of the observed scaling behavior and the mechanism of self-organization towards…
We consider random rectangles in $\mathbb{R}^2$ that are distributed according to a Poisson random measure, i.e., independently and uniformly scattered in the plane. The distributions of the length and the width of the rectangles are…
We study the minimum-energy configuration of a d-dimensional elastic interface in a random potential tied to a harmonic spring. As a function of the spring position, the center of mass of the interface changes in discrete jumps, also called…
Many astronomical phenomena, including Fast Radio Bursts and Soft Gamma Repeaters, consist of brief, separated, seemingly aperiodic events. The intervals between these events vary randomly, but there are epochs of greater activity, with…
In a critically self--organized model of punctuated equilibrium, boundaries determine peculiar scaling of the size distribution of evolutionary avalanches. This is derived by an inhomogeneous generalization of standard branching processes,…
Elastic systems, such as magnetic domain walls, density waves, contact lines, and cracks, are all pinned by substrate disorder. When driven, they move via successive jumps called avalanches, with power law distributions of size, duration…
We investigate the complex spatio-temporal dynamics in avalanche driven surface growth by means of scaling theory. We study local activity statistics, avalanche kinetics, and temporal correlations in the global interface velocity, obtaining…
A length dependence of the effective mobility in the form of a power law, B ~ L^(1-1/alpha) is observed in dispersive transport in amorphous substances, with 0 < \alpha < 1. We deduce this behavior as a simple consequence of the statistical…
Self-organized critical states are found in many natural systems, from earthquakes to forest fires, they have also been observed in neural systems, particularly, in neuronal cultures. However, the presence of critical states in the awake…
The strength and stability properties of hierarchical load bearing networks and their strengthened variants have been discussed in recent work. Here, we study the avalanche time distributions on these load bearing networks. The avalanche…