Self-organized criticality in a crack-propagation model of earthquakes

Chen, Kan; Bak, Per; Obukhov, S P

doi:10.1103/physreva.43.625

Cited by 269 publications

(174 citation statements)

References 15 publications

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“…However, for many real systems specific equations describing the detailed evolutions of the systems are not known, and, in addition, the information on which the forecast must be based is typically incomplete. The basic prediction problem is, therefore, an inverse problem in the sense that one wants to use some information such as the time 3 series of events to infer something about the likely configuration of the system which is, in most practical situations, completely inaccessible to measurement.…”

Section: Introductionmentioning

confidence: 99%

“…More generally, self-organizing systems, whether critical or not, typically exhibit scaling over some range of sizes and are thought to evolve so that fluctuations in space and time are intrinsically coupled by an underlying threshold dynamics. There has recently been a considerable effort to use self-organizing systems as simple dynamical models of seismic phenomena, 1,2,3,4 in part due to the clear connection between earthquakes and threshold dynamics. Particular attention has been paid to the robust power-law scaling relation-the Gutenberg-Richter law 5 -relating the frequency of earthquakes to their size.…”

Section: Introductionmentioning

confidence: 99%

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Predictability of self-organizing systems

Pepke

Carlson

1994

Phys. Rev. E

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We study the predictability of large events in self-organizing systems. We focus on a set of models which have been studied as analogs of earthquake faults and fault systems, and apply methods based on techniques which are of current interest in seismology. In all cases we find detectable correlations between precursory smaller events and the large events we aim to forecast. We compare predictions based on different patterns of precursory events and find that for all of the models a new precursor based on the spatial distribution of activity outperforms more traditional measures based on temporal variations in the local activity.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Predictability of self-organizing systems

Pepke

Carlson

1994

Phys. Rev. E

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“…The concept of SOC was first introduced in terms of simple cellular automaton models that could reproduce a 1͞f power spectrum [1]. Indeed the power-law characteristic of SOC has been found in the noisy behavior of some transport processes over vastly different time scales as, for instance, the Barkhausen noise of ferromagnets [2], or the distribution of earthquakes' magnitudes [3].…”

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confidence: 99%

Looking for Self-Organized Critical Behavior in Avalanches of Slightly Cohesive Powders

et al. 2001

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We report results from a statistical analysis of avalanches of cohesive powders in a slowly rotated drum. Interparticle adhesion, which diminishes the effect of inertia and whose magnitude strongly fluctuates in a local scale, makes avalanches in slightly cohesive powders eligible for displaying self-organized criticality. However, the results show that avalanche sizes, time interval between avalanches, and maximum stable angle do not follow a power-law distribution. Otherwise, these parameters scale with powder cohesiveness.

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“…The two main microscopic approaches are discrete dislocation dynamics, accounting for dislocation interactions on different slip planes [8][9][10], and a pinning-depinning model dealing with plasticity on a single slip plane [11,12]. Different meso-scopic continuum models implying partial averaging have also been shown to generate power law statistics of avalanches with realistic exponents [4,13]. Since scale free dislocation activity is expected to be independent of either microscopic or macroscopic details, one can try to maximally simplify the underlying physics while still capturing the observed exponents and even characteristic shape functions [14].…”

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confidence: 99%

Minimal Integer Automaton behind Crystal Plasticity

Salman

Truskinovsky

2011

Phys. Rev. Lett.

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Power law fluctuations and scale free spatial patterns are known to characterize steady state plastic flow in crystalline materials. In this Letter we study the emergence of correlations in a simple Frenkel-Kontorova (FK) type model of 2D plasticity which is largely free of arbitrariness, amenable to analytical study and is capable of generating critical exponents matching experiments. Our main observation concerns the possibility to reduce continuum plasticity to an integer valued automaton revealing inherent discreteness of the plastic flow.At the macroscale one usually assumes that crystalline materials flow plastically when averaged stresses exceed yield thresholds. At the microscale plasticity evolves through a sequence of slow-fast events involving collective pinning and depinning of dislocational structures. Classical engineering theory has been very successful in reproducing the most important plasticity phenomenology such as yield, hardening and shakedown [1], however, a fully quantitative link between the phenomenological theory and the microscopic picture of plasticity remains elusive. The main reason is that the phenomenological approach implies spatial and temporal averaging in the system with poorly understood long range correlations.The presence of such correlations have been confirmed by numerous experiments revealing intermittent character of plastic activity with power law statistics of avalanches and self similar structure of dislocation cell structures [2]. The emergence of power laws suggests that in plasticity the relation between the microscopic and the macroscopic models is more akin to turbulence than to elasticity [3,4]. Similar critical features of stationary nonequilibrium states have been observed in a variety other driven systems with threshold nonlinearity and rate independent dissipation including, for instance, tectonic faults, magnets, and superconductors [5]. The origin of scale free attractors in such systems is a subject of active research, in particular, the problem of classifying the universality classes remains largely open [6]. In this situation finding the minimal representation of each class which is amenable to rigorous analysis is of significant general interest.The experimental evidence of plastic criticality has been corroborated by several numerical models [7]. The two main microscopic approaches are discrete dislocation dynamics, accounting for dislocation interactions on different slip planes [8][9][10], and a pinning-depinning model dealing with plasticity on a single slip plane [11,12]. Different meso-scopic continuum models implying partial averaging have also been shown to generate power law statistics of avalanches with realistic exponents [4,13]. Since scale free dislocation activity is expected to be independent of either microscopic or macroscopic details, one can try to maximally simplify the underlying physics while still capturing the observed exponents and even characteristic shape functions [14]. Presently the only analytically tractable models of pl...

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Self-organized criticality in a crack-propagation model of earthquakes

Cited by 269 publications

References 15 publications

Predictability of self-organizing systems

Predictability of self-organizing systems

Looking for Self-Organized Critical Behavior in Avalanches of Slightly Cohesive Powders

Minimal Integer Automaton behind Crystal Plasticity

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