Related papers: Energy avalanches in a rice-pile model
Self-organized criticality can be translated into the language of absorbing state phase transitions. Most models for which this analogy is established have been investigated for their absorbing state characteristics. In this article, we…
Power-law type probability density functions spanning several orders of magnitude are found for different avalanche properties. We propose a methodology to overcome empirical constrains that limit the power-law range for the distributions…
The origin of power-law distributions in self-organized criticality is investigated by treating the variation of the number of active sites in the system as a stochastic process. An avalanche is then regarded as a first-return random walk…
In [Braz. J. Phys. 30, 27 (2000)] Dickman et al. suggested that self-organized criticality can be produced by coupling the activity of an absorbing state model to a dissipation mechanism and adding an external drive. We analyzed the…
Avalanche-like plastic bursts in crystalline materials follow power law statistics, but the scaling exponents and cutoff parameters vary widely in the literature ($\alpha$ ranging from 1 to 2.2), hindering predictive modeling. Since…
We propose a one-dimensional rice-pile model which connects the 1D BTW sandpile model (Phys. Rev. A 38, 364 (1988)) and the Oslo rice-pile model (Phys. Rev. lett. 77, 107 (1997)) in a continuous manner. We found that for a sufficiently…
The statistics of burst avalanche sizes $n$ during failure processes in a fiber bundle follows a power law, $D(n)\sim n^{-\xi}$, for large avalanches. The exponent $\xi$ depends upon how the avalanches are provoked. While it is known that…
The statistics of natural catastrophes contains very counter-intuitive results. Using earthquakes as a working example, we show that the energy radiated by such events follows a power-law or Pareto distribution. This means, in theory, that…
The discrete height abelian sandpile model was introduced by Bak, Tang & Wiesenfeld and Dhar as an example for the concept of self-organized criticality. When the model is modified to allow grains to disappear on each toppling, it is called…
The temporal fluctuation of the average slope of a ricepile model is investigated. It is found that the power spectrum $S(f)$ scales as $1/f^{\alpha}$ with $\alpha\approx 1.3$ when grains of rice are added only to one end of the pile. If…
We study the abelian sandpile model on a random binary tree. Using a transfer matrix approach introduced by Dhar & Majumdar, we prove exponential decay of correlations, and in a small supercritical region (i.e., where the branching process…
We investigate an extremal dynamics model of evolution with a variable number of units. Due to addition and removal of the units, the topology of the network evolves and the network splits into several clusters. The activity is mostly…
We explore the connection between self-organized criticality and phase transitions in models with absorbing states. Sandpile models are found to exhibit criticality only when a pair of relevant parameters - dissipation epsilon and driving…
We investigate sandpile models where the updating of unstable columns is done according to a stochastic rule. We examine the effect of introducing nonlocal relaxation mechanisms. We find that the models self-organize into critical states…
We introduce a toy model displaying the avalanche dynamics of failure in scale-free networks. In the model, the network growth is based on the Barab\'asi and Albert model and each node is assigned a capacity or tolerance, which is constant…
We review limiting models for fracture in bundles of fibers, with statistically distributed thresholds for breakdown of individual fibers. During the breakdown process, avalanches consisting of simultaneous rupture of several fibers occur,…
We consider an interacting particle system $(\eta_t)_{t\geq 0}$ with values in $\{0,1\}^{\mathbb{Z}}$, in which each vacant site becomes occupied with rate 1, while each connected component of occupied sites become vacant with rate equal to…
Two cellular automata models with directed mass flow and internal time scales are studied by numerical simulations. Relaxation rules are a combination of probabilistic critical height (probability of toppling $p$) and deterministic critical…
Temporal autocorrelation functions for avalanches in the Bak-Sneppen model display aging behavior similar to glassy systems. Numerical simulations show that they decay as power laws with two distinct regimes separated by a time scale which…
Plasticity of two-dimensional discrete dislocation systems is studied. It is shown, that at some threshold stress level the response becomes stress-rate dependent. Below this stress level the stress-plastic strain relation exhibits…