Universal fluctuations and extreme statistics of avalanches near the depinning transition

LeBlanc, Michael; Angheluta, Luiza; Dahmen, Karin A.; Goldenfeld, Nigel

doi:10.1103/physreve.87.022126

Cited by 61 publications

(83 citation statements)

References 58 publications

(122 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Note that this result was obtained independently in Refs. [58,59] by completely different methods. It can also be obtained by integrating the propagator (136) overu f from 0 to ∞.…”

Section: Subavalanche Durations In the Standard Abbm Modelmentioning

confidence: 99%

Statistics of avalanches with relaxation and Barkhausen noise: A solvable model

2013

View full text Add to dashboard Cite

We study a generalization of the Alessandro-Beatrice-Bertotti-Montorsi (ABBM) model of a particle in a Brownian force landscape, including retardation effects. We show that under monotonous driving the particle moves forward at all times, as it does in absence of retardation (Middleton's theorem). This remarkable property allows us to develop an analytical treatment. The model with an exponentially decaying memory kernel is realized in Barkhausen experiments with eddy-current relaxation and has previously been shown numerically to account for the experimentally observed asymmetry of Barkhausen pulse shapes. We elucidate another qualitatively new feature: the breakup of each avalanche of the standard ABBM model into a cluster of subavalanches, sharply delimited for slow relaxation under quasistatic driving. These conditions are typical for earthquake dynamics. With relaxation and aftershock clustering, the present model includes important ingredients for an effective description of earthquakes. We analyze quantitatively the limits of slow and fast relaxation for stationary driving with velocity v>0. The v-dependent power-law exponent for small velocities, and the critical driving velocity at which the particle velocity never vanishes, are modified. We also analyze nonstationary avalanches following a step in the driving magnetic field. Analytically, we obtain the mean avalanche shape at fixed size, the duration distribution of the first subavalanche, and the time dependence of the mean velocity. We propose to study these observables in experiments, allowing a direct measurement of the shape of the memory kernel and tracing eddy current relaxation in Barkhausen noise.

show abstract

“…Note that this result was obtained independently in Refs. [58,59] by completely different methods. It can also be obtained by integrating the propagator (136) overu f from 0 to ∞.…”

Section: Subavalanche Durations In the Standard Abbm Modelmentioning

confidence: 99%

Statistics of avalanches with relaxation and Barkhausen noise: A solvable model

2013

View full text Add to dashboard Cite

show abstract

“…where v 0 ∼ S m /δt, with S m the minimum avalanche size and δt the minimum avalanche duration [27]. v 0 may be thought of as the size of the initial "kick" starting an avalanche.…”

Section: Appendix: Derivation Of the Merged Avalanche Distributionmentioning

confidence: 99%

“…3 will go undetected by the standard methods. If we assume the avalanches are drawn from the distribution predicted by MFT [27],…”

Section: A One Avalanche Per Time Step (T S T I and T A T I )mentioning

confidence: 99%

See 1 more Smart Citation

Avalanche statistics from data with low time resolution

et al. 2016

Self Cite

View full text Add to dashboard Cite

Extracting avalanche distributions from experimental microplasticity data can be hampered by limited time resolution. We compute the effects of low time resolution on avalanche size distributions and give quantitative criteria for diagnosing and circumventing problems associated with low time resolution. We show that traditional analysis of data obtained at low acquisition rates can lead to avalanche size distributions with incorrect power-law exponents or no power-law scaling at all. Furthermore, we demonstrate that it can lead to apparent data collapses with incorrect power-law and cutoff exponents. We propose new methods to analyze low-resolution stress-time series that can recover the size distribution of the underlying avalanches even when the resolution is so low that naive analysis methods give incorrect results. We test these methods on both downsampled simulation data from a simple model and downsampled bulk metallic glass compression data and find that the methods recover the correct critical exponents.

show abstract

“…Questions related to the statistics of the first maximum, X max = M 1,N have emerged in various areas of physics ranging from disordered systems [19][20][21] and fluctuating interfaces [22][23][24][25][26] to stochastic processes [27], random matrices [28] and many others. While the statistics of the extremum X max is important another natural question is: is this extremal value isolated, i.e., far away from the others, or is there many other events close to them?…”

Section: Introductionmentioning

confidence: 99%

Exact Record and Order Statistics of Random Walks via First-Passage Ideas

Schehr

Majumdar

2014

First-Passage Phenomena and Their Applications

View full text Add to dashboard Cite

While records and order statistics of independent and identically distributed (i.i.d.) random variables X1, · · · , XN are fully understood, much less is known for strongly correlated random variables, which is often the situation encountered in statistical physics. Recently, it was shown, in a series of works, that one-dimensional random walk (RW) is an interesting laboratory where the influence of strong correlations on records and order statistics can be studied in detail. We review here recent exact results which have been obtained for these questions about RW, using techniques borrowed from the study of first-passage problems. We also present a brief review of the well known (and not so well known) results for records and order statistics of i.i.d. variables.

show abstract

Universal fluctuations and extreme statistics of avalanches near the depinning transition

Cited by 61 publications

References 58 publications

Statistics of avalanches with relaxation and Barkhausen noise: A solvable model

Statistics of avalanches with relaxation and Barkhausen noise: A solvable model

Avalanche statistics from data with low time resolution

Exact Record and Order Statistics of Random Walks via First-Passage Ideas

Contact Info

Product

Resources

About