Shocks Generate Crossover Behavior in Lattice Avalanches (original) (raw)
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Avalanches in Out of Equilibrium Systems: Statistical Analysis of Experiments and Simulations
2015
Instead of a linear and smooth evolution, many physical system react to external stimuli in avalanche dynamics. When an out of equilibrium system governed by disorder is externally driven the evolution of internal variables is local and non-homogeneous. This process is a collective behaviour adiabatically quick known as avalanches. Avalanche dynamics are associated to the transformation of spatial domains in different scales: from microscopic, to large catastrophic events such as earthquakes or solar flares. Avalanche dynamics is also involved in interdisiplinar topics such as the return prices of stock markets, the signalling in neuron networks or the biological evolution. Many avalanche dynamics are characterised by scale invariance, trademark of criticality. The physics in a so-called critical point are the same in all observational scales. Some avalanche dynamics share empirical laws and can define Universality Classes, reducing the complexity of systems to simpler mathematical ...
On the interpretation of "off the edge" avalanches
2004
We establish both experimentally and theoretically the relation between off the edge and internal avalanches in a sandpile model, a central issue in the interpretation of most experiments in these systems. In BTW simulations and also in the experiments the size distributions of internal avalanches show power laws and critical exponents related with the dimension of the system. We show that, in a SOC scenario, the distributions of off the edge avalanches do not show power laws but follow scaling relations with critical exponents different from their analogous for the internal avalanche distributions. PACS numbers: 45.70.Ht, 05.65.+b Since Bak, Tang and Wiesenfeld (BTW) developed in 1987 the ideas of self-organized criticality (SOC)[1, 2], a great amount of research in phenomena as diverse as earthquakes, superconducting vortex dynamics, stock markets, and ecology [3, 4, 5, 6] has been carried out. A sandpile illustrates this concept: the slow addition of grains onto a flat surface provokes the growth of a pile with slopes around a critical angle adjusted through an avalanche mechanism. According to SOC, the avalanches should not show any characteristic size or frequency, and the distributions of avalanche sizes and durations are robust relative to variations of external parameters; i.e., the system self-organizes. The result is that the pile will show robust power law distributions of avalanche size and duration, "1/f " power spectra, and finite-size scaling of the distribution of internal avalanches, measured as the movements of the grains within the totality of the system.
Bubbling and Large-Scale Structures in Avalanche Dynamics
Physical Review Letters, 2000
Using a simple lattice model for granular media, we present a scenario of self-organization that we term self-organized structuring where the steady state has several unusual features: (1) large scale space and/or time inhomogeneities and (2) the occurrence of a non-trivial peaked distribution of large events which propagate like "bubbles" and have a well-defined frequency of occurrence. We discuss the applicability of such a scenario for other models introduced in the framework of self-organized criticality.
Two-Threshold Model for Scaling Laws of Noninteracting Snow Avalanches
Physical Review Letters, 2004
The sizes of snow slab failure that trigger snow avalanches are power-law distributed. Such a power-law probability distribution function has also been proposed to characterize different landslide types. In order to understand this scaling for gravity driven systems, we introduce a two-threshold 2-d cellular automaton, in which failure occurs irreversibly. Taking snow slab avalanches as a model system, we find that the sizes of the largest avalanches just preceeding the lattice system breakdown are power law distributed. By tuning the maximum value of the ratio of the two failure thresholds our model reproduces the range of power law exponents observed for land-, rock-or snow avalanches. We suggest this control parameter represents the material cohesion anisotropy.
Chaos, Solitons & Fractals, 2020
Relaxational processes in many complex systems often occur in the form of avalanches resulting from internal cascades from across the system scale. Here, we probe the space, time, and magnitude signatures of avalanching behavior using a network of temporally-directed links subject to a spatial distance criterion between events in the entire catalog. We apply this method onto three systems with avalanchelike characteristics: (i) highly controllable scaled experiments , particularly that of a slowly-driven pile of granular material in a quasi-two-dimensional setup with open edges; (ii) the sandpile, a numerical model of nearest-neighbor interactions in a grid; and (iii) substantially complete empirical data on earthquakes from southern California. Apart from the recovery of the fat-tailed statistics of event sizes, we recover similar power-laws in the spatial and temporal aspects of the networks of these representative systems, hinting at possible common underlying generative mechanisms governing them. By consolidating the results from experiments, numerical models, and empirical data, we can gain a better understanding of these highly nonlinear processes in nature.
Finite-size scaling of critical avalanches
Physical Review E
We examine probability distribution for avalanche sizes observed in self-organized critical systems. While a power-law distribution with a cutoff because of finite system size is typical behavior, a systematic investigation reveals that it may decrease on increasing the system size at a fixed avalanche size. We implement the scaling method and identify scaling functions. The data collapse ensures a correct estimation of the critical exponents and distinguishes two exponents related to avalanche size and system size. Our simple analysis provides striking implications. While the exact value for avalanches size exponent remains elusive for the prototype sandpile on a square lattice, we suggest the exponent should be 1. The simulation results represent that the distribution shows a logarithmic system size dependence, consistent with the normalization condition. We also argue that for train or Oslo sandpile model with bulk drive, the avalanche size exponent is slightly less than 1 that is significantly different from the previous estimate 1.11.
Scale Invariant Avalanches: A Critical Confusion
2011
The "Self-organized criticality" (SOC), introduced in 1987 by Bak, Tang and Wiesenfeld, was an attempt to explain the 1/f noise, but it rapidly evolved towards a more ambitious scope: explaining scale invariant avalanches. In two decades, phenomena as diverse as earthquakes, granular piles, snow avalanches, solar flares, superconducting vortices, sub-critical fracture, evolution, and even stock market crashes have been reported to evolve through scale invariant avalanches. The theory, based on the key axiom that a critical state is an attractor of the dynamics, presented an exponent close to -1 (in two dimensions) for the power-law distribution of avalanche sizes. However, the majority of real phenomena classified as SOC present smaller exponents, i.e., larger absolute values of negative exponents, a situation that has provoked a lot of confusion in the field of scale invariant avalanches. The main goal of this chapter is to shed light on this issue. The essential role of ...
Correlations in avalanche critical points
Physical Review E, 2009
Avalanche dynamics and related power law statistics are ubiquitous in nature, arising in phenomena like earthquakes, forest fires and solar flares. Very interestingly, an analogous behavior is associated with many condensed matter systems, like ferromagnets and martensites. Bearing it in mind, we study the prototypical 3D RFIM at T = 0. We find a finite correlation between waiting intervals between avalanches and the previous avalanche size. This correlation is not found in other models for avalanches, such as the standard BTW model, but it is experimentally found in earthquakes and in forest fires. Our study suggests that this effect occurs in critical points which are at the end of an athermal first-order transition line separating two behaviors: one with high activity from another with low activity.
Finite-size effects of avalanche dynamics
2002
In the last decade, a considerable number of publications have been dedicated to the occurrence of power-law behavior in systems involving interacting threshold elements driven by slow external input. The dynamics accounts for phenomena occurring in such diverse systems as piles of granular matter 1, earthquakes 2, the game of life 3, friction 4, and sound generated in the lung during breathing 5.