Universal fluctuations and extreme statistics of avalanches near the depinning transition

Quantifying chemomechanical weakening in muscovite mica with a simple micromechanical model

In response to gradual nanoindentation, the surface of muscovite mica deforms by sudden stochastic nanometer-scale displacement bursts. Here, the statistics of these displacement events are interpreted using a statistical model previously used to model earthquakes to understand how chemically reactive environments alter the surface properties of this material. We show that the statistics of nanoindentation displacement bursts in muscovite mica are tuned by chemomechanical weakening in a manner similar to how the statistics of model events are tuned by a mechanical weakening parameter that describes how easily system-spanning cracks can be nucleated. Because the predictions of this model are independent of any surface defects or structural details, these results suggest this simple model can be universally used to describe chemomechanical weakening in many systems prone to slip avalanches on a wide range of spatio-temporal scales.

Uncovering avalanche sources via acceleration measurements

Avalanche sources describe rapid and local events that govern deformation processes in various materials. The fundamental differences between an avalanche source and its associated measured acoustic emission (AE) signal are encoded in the acoustic transfer function, which undesirably modifies the properties of the source. Consequently, information about the physical characteristics of avalanche sources is scarce and its exposure poses a great challenge. We introduce a novel experimental method based on acceleration measurements, which eliminates the effect of the transfer function and distills the avalanche source. Applying this method to deformation twinning in magnesium shows that the amplitudes and characteristic times of avalanche sources are unrelated by a clear physical law. Conversely, the amplitudes and durations of AE signals are related by a power law, which is attributed to the transfer function. Using our method, we identify and compute a new feature of avalanche sources, which is directly linked to the growth rate of the twinned volume. This feature displays a power-law distribution, implying an unpredicted behavior at dynamic criticality. Simultaneously, the characteristic times of avalanche sources possess an intrinsic upper bound, indicating a predicted limit that relates to the underlying physical process of twinning.

Acoustic emissions from spin crossover complexes

Acoustic emission from the compounds [Fe(HB(tz)3)2] and [Fe(Htrz)(trz)2]BF4 was detected during the thermally induced spin transition and is correlated with simultaneously recorded calorimetric signals. We ascribe this phenomenon to elastic waves produced by microstructural and volume changes accompanying the spin transition. Despite the perfect reversibility of the spin state switching (seen by the calorimeter), the acoustic emission activity decreases for successive thermal cycles, revealing thus irreversible microstructural evolution of the samples. The acoustic emission signal amplitude and energy probability distribution functions followed power-law behavior and the characteristic exponents were found to be similar for the two samples both on heating and cooling, indicating the universal character, which is further substantiated by the well scaled average temporal shapes of the avalanches.

Avalanches and Extreme Value Statistics of a Mesoscale Moving Contact Line

We report direct atomic force microscopy measurements of pinning-depinning dynamics of a circular moving contact line (CL) over the rough surface of a micron-sized vertical hanging glass fiber, which intersects a liquid-air interface. The measured capillary force acting on the CL exhibits sawtoothlike fluctuations, with a linear accumulation of force of slope k (stick) followed by a sharp release of force δf, which is proportional to the CL slip length. From a thorough analysis of a large volume of the stick-slip events, we find that the local maximal force F_{c} needed for CL depinning follows the extreme value statistics and the measured δf follows the avalanche dynamics with a power law distribution in good agreement with the Alessandro-Beatrice-Bertotti-Montorsi (ABBM) model. The experiment provides an accurate statistical description of the CL dynamics at mesoscale, which has important implications to a common class of problems involving stick-slip motion in a random defect or roughness landscape.

Statistical laws of stick-slip friction at mesoscale

Friction between two rough solid surfaces often involves local stick-slip events occurring at different locations of the contact interface. If the apparent contact area is large, multiple local slips may take place simultaneously and the total frictional force is a sum of the pinning forces imposed by many asperities on the interface. Here, we report a systematic study of stick-slip friction over a mesoscale contact area using a hanging-beam lateral atomic-force-microscope, which is capable of resolving frictional force fluctuations generated by individual slip events and measuring their statistical properties at the single-slip resolution. The measured probability density functions (PDFs) of the slip length δxs, the maximal force Fc needed to trigger the local slips, and the local force gradient [Formula: see text] of the asperity-induced pinning force field provide a comprehensive statistical description of stick-slip friction that is often associated with the avalanche dynamics at a critical state. In particular, the measured PDF of δxs obeys a power law distribution and the power-law exponent is explained by a new theoretical model for the under-damped spring-block motion under a Brownian-correlated pinning force field. This model provides a long-sought physical mechanism for the avalanche dynamics in stick-slip friction at mesoscale.

Scaling of Average Avalanche Shapes for Acoustic Emission during Jerky Motion of Single Twin Boundary in Single-Crystalline Ni2MnGa

Temporal average shapes of crackling noise avalanches, U(t) (U is the detected parameter proportional to the interface velocity), have self-similar behavior, and it is expected that by appropriate normalization, they can be scaled together according to a universal scaling function. There are also universal scaling relations between the avalanche parameters (amplitude, A, energy, E, size (area), S, and duration, T), which in the mean field theory (MFT) have the form E∝A3, S∝A2, S∝T2. Recently, it turned out that normalizing the theoretically predicted average U(t) function at a fixed size, U(t)=atexp-bt2 (a and b are non-universal, material-dependent constants) by A and the rising time, R, a universal function can be obtained for acoustic emission (AE) avalanches emitted during interface motions in martensitic transformations, using the relation R~A1-φ too, where φ is a mechanism-dependent constant. It was shown that φ also appears in the scaling relations E~A3-φ and S~A2-φ, in accordance with the enigma for AE, that the above exponents are close to 2 and 1, respectively (in the MFT limit, i.e., with φ= 0, they are 3 and 2, respectively). In this paper, we analyze these properties for acoustic emission measurements carried out during the jerky motion of a single twin boundary in a Ni₅₀Mn_28.5Ga_21.5 single crystal during slow compression. We show that calculating from the above-mentioned relations and normalizing the time axis of the average avalanche shapes with A1-φ, and the voltage axis with A, the averaged avalanche shapes for the fixed area are well scaled together for different size ranges. These have similar universal shapes as those obtained for the intermittent motion of austenite/martensite interfaces in two different shape memory alloys. The averaged shapes for a fixed duration, although they could be acceptably scaled together, showed a strong positive asymmetry (the avalanches decelerate much slower than they accelerate) and thus did not show a shape reminiscent of an inverted parabola, predicted by the MFT. For comparison, the above scaling exponents were also calculated from simultaneously measured magnetic emission data. It was obtained that the φ values are in accordance with theoretical predictions going beyond the MFT, but the AE results for φ are characteristically different from these, supporting that the well-known enigma for AE is related to this deviation.

Clustering Characterization of Acoustic Emission Signals Belonging to Twinning and Dislocation Slip during Plastic Deformation of Polycrystalline Sn

Results of acoustic emission (AE) measurements, carried out during plastic deformation of polycrystalline Sn samples, are analyzed by the adaptive sequential k-means method. The acoustic avalanches, originating from different sources, are separated on the basis of their spectral properties, that is, sorted into clusters, presented both on the so-called feature space (energy-median frequency plot) and on the power spectral density (PSD) curves. We found that one cluster in every measurement belongs to background vibrations, while the remaining ones are clearly attributed to twinning as well as dislocation slips at −30 °C and 25 °C, respectively. Interestingly, fingerprints of the well-known “ringing” of AE signals are present in different weights on the PSD curves. The energy and size distributions of the avalanches, corresponding to twinning and dislocation slips, show a bit different power-law exponents from those obtained earlier by fitting all AE signals without cluster separation. The maximum-likelihood estimation of the avalanche energy (ε) and size (τ) exponents provide ε=1.57±0.05 (at −30 °C) and ε=1.35±0.1 (at 25 °C), as well as τ=1.92±0.05 (at −30 °C) and τ= 1.55±0.1 (at 25 °C). The clustering analysis provides not only a manner to eliminate the background noise, but the characteristic avalanche shapes are also different for the two mechanisms, as it is visible on the PSD curves. Thus, we have illustrated that this clustering analysis is very useful in discriminating between different AE sources and can provide more realistic estimates, for example, for the characteristic exponents as compared to the classical hit-based approach where the exponents reflect an average value, containing hits from the low-frequency mechanical vibrations of the test machine, too.

Denouement of the Energy-Amplitude and Size-Amplitude Enigma for Acoustic-Emission Investigations of Materials

There are many systems producing crackling noise (avalanches) in materials. Temporal shapes of avalanches, U(t) (U is the detected voltage signal, t is the time), have self-similar behaviour and the normalized U(t) function (e.g., dividing both the values of U and t by S^1/2, where S is the avalanche area), averaged for fixed S, should be the same, independently of the type of materials or avalanche mechanisms. However, there are experimental evidences that the temporal shapes of avalanches do not scale completely in a universal way. The self-similarity also leads to universal power-law-scaling relations, e.g., between the energy, E, and the peak amplitude, A_m, or between S and A_m. There are well-known enigmas, where the above exponents in acoustic emission measurements are rather close to 2 and 1, respectively, instead of E~Am3 and S~Am2, obtained from the mean field theory, MFT. We show, using a theoretically predicted averaged function for the fixed avalanche area, U(t)=atexp(−bt2) (where a and b are non-universal, material-dependent constants), that the scaling exponents can be different from the MFT values. Normalizing U by A_m and t by t_m (the time belonging to the A_m: rise time), we obtain tm~Am1−φ (the MFT values can be obtained only if φ would be zero). Here, φ is expected to be material-independent and to be the same for the same mechanism. Using experimental results on martensitic transformations in two different shape-memory single-crystals, φ = 0.8 ± 0.1 was obtained (φ is the same for both alloys). Thus, dividing U by A_m as well as t by Am1−φ (~t_m) leads to the same common, normalized temporal shape for different, fixed values of S. This normalization can also be used in general for other experimental results (not only for acoustic emission), which provide information about jerky noises in materials.

Mild-to-wild plastic transition is governed by athermal screw dislocation slip in bcc Nb

Plastic deformation in crystals is mediated by the motion of line defects known as dislocations. For decades, dislocation activity has been treated as a homogeneous, smooth continuous process. However, it is now recognized that plasticity can be determined by long-range correlated and intermittent collective dislocation processes, known as avalanches. Here we demonstrate in body-centered cubic Nb how the long-range and scale-free dynamics at room temperature are progressively quenched out with decreasing temperature, eventually revealing intermittency with a characteristic length scale that approaches the Burgers vector itself. Plasticity is shown to be bimodal across the studied temperature regime, with conventional thermally-activated smooth plastic flow (‘mild’) coexisting with sporadic bursts (‘wild’) controlled by athermal screw dislocation activity, thereby violating the classical notion of temperature-dependent screw dislocation motion at low temperatures. An abrupt increase of the athermal avalanche component is identified at the critical temperature of the material. Our results indicate that plasticity at any scale can be understood in terms of the coexistence of these mild and wild modes of deformation, which could help design better alloys by suppressing one of the two modes in desired temperature windows.

Recent studies have recognized that plasticity in metals can be controlled by dislocation avalanches. Here the authors examine temperature-dependent microplasticity in bcc Nb and reveal the dominance of athermal screw dislocation activity during intermittent slip.

Change of Acoustic Emission Characteristics during Temperature Induced Transition from Twinning to Dislocation Slip under Compression in Polycrystalline Sn

In this study, acoustic emission (AE) measurements on polycrystalline tin as a function of temperature at different driving rates under compression were carried out. It is shown that there is a definite difference between the acoustic emission characteristics belonging to twinning (low temperatures) as well as to dislocation slip (high temperatures). The stress averaged values of the exponents of the energy probability density functions decreased from ε = 1.45 ± 0.05 (-60 °C) to ε = 1.20 ± 0.15 (50 °C) at a driving rate of ε=0.15 s-1, and the total acoustic energy decreased by three orders of magnitude with increasing temperature. In addition, the exponent γ in the scaling relation S_AE~D_AE^γ (S_AE is the area and D_AE is the duration) also shows similar temperature dependence (changing from γ = 1.78 ± 0.08 to γ = 1.35 ± 0.05), illustrating that the avalanche statistics belong to two different microscopic deformation mechanisms. The power law scaling relations were also analyzed, taking into account that the detected signal is always the convolution of the source signal and the transfer function of the system. It was obtained that approximate values of the power exponents can be obtained from the parts of the above functions, belonging to large values of parameters. At short duration times, the attenuation effect of the AE detection system dominates the time dependence, from which the characteristic attenuation time, τ_a, was determined as τ_a ≅ 70 μs.

Signature of Transition between Granular Solid and Fluid: Rate-Dependent Stick Slips in Steady Shearing

Despite extensive studies on either smooth granular-fluid flow or the solidlike deformation at the slow limit, the change between these two extremes remains largely unexplored. By systematically investigating the fluctuations of tightly packed grains under steady shearing, we identify a transition zone with prominent stick-slip avalanches. We establish a state diagram, and propose a new dimensionless shear rate based on the speed dependence of interparticle friction and particle size. With fluid-immersed particles confined in a fixed volume and forced to "flow" at viscous numbers J decades below reported values, we answer how a granular system can transition to the regime sustained by solid-to-solid friction that goes beyond existing paradigms based on suspension rheology.

Local Probe Comparison of Ferroelectric Switching Event Statistics in the Creep and Depinning Regimes in Pb(Zr_{0.2}Ti_{0.8})O_{3} Thin Films

Ferroelectric materials provide a useful model system to explore the jerky, highly nonlinear dynamics of elastic interfaces in disordered media. The distribution of nanoscale switching event sizes is studied in two Pb(Zr_{0.2}Ti_{0.8})O_{3} thin films with different disorder landscapes using piezoresponse force microscopy. While the switching event statistics show the expected power-law scaling, significant variations in the value of the scaling exponent τ are seen, possibly as a consequence of the different intrinsic disorder landscapes in the samples and of further alterations under high tip bias applied during domain writing. Importantly, higher exponent values (1.98-2.87) are observed when crackling statistics are acquired only for events occurring in the creep regime. The exponents are systematically lowered when all events across both creep and depinning regimes are considered-the first time such a distinction is made in studies of ferroelectric materials. These results show that distinguishing the two regimes is of crucial importance, significantly affecting the exponent value and potentially leading to incorrect assignment of universality class.

The duration-energy-size enigma for acoustic emission

Acoustic emission (AE) measurements of avalanches in different systems, such as domain movements in ferroics or the collapse of voids in porous materials, cannot be compared with model predictions without a detailed analysis of the AE process. In particular, most AE experiments scale the avalanche energy E, maximum amplitude Amax and duration D as E ~ A_max^x and A_max ~ D^χ with x = 2 and a poorly defined power law distribution for the duration. In contrast, simple mean field theory (MFT) predicts that x = 3 and χ = 2. The disagreement is due to details of the AE measurements: the initial acoustic strain signal of an avalanche is modified by the propagation of the acoustic wave, which is then measured by the detector. We demonstrate, by simple model simulations, that typical avalanches follow the observed AE results with x = 2 and ‘half-moon’ shapes for the cross-correlation. Furthermore, the size S of an avalanche does not always scale as the square of the maximum AE avalanche amplitude A_max as predicted by MFT but scales linearly S ~ A_max. We propose that the AE rise time reflects the atomistic avalanche time profile better than the duration of the AE signal.

Asymmetric Damage Avalanche Shape in Quasibrittle Materials and Subavalanche (Aftershock) Clusters

Crackling dynamics is characterized by a release of incoming energy through intermittent avalanches. The shape, i.e., the internal temporal structure of these avalanches, gives insightful information about the physical processes involved. It was experimentally shown recently that progressive damage toward compressive failure of quasibrittle materials can be mapped onto the universality class of interface depinning when considering scaling relationships between the global characteristics of the microcracking avalanches. Here we show, for three concrete materials and from a detailed analysis of the acoustic emission waveforms generated by microcracking events, that the shape of these damage avalanches is strongly asymmetric, characterized by a very slow decay. This remarkable asymmetry, at odds with mean-field depinning predictions, could be explained, in these quasibrittle materials, by retardation effects induced by enhanced viscoelastic processes within a fracture process zone generated by the damage avalanche as it progresses. It is associated with clusters of subavalanches, or aftershocks, within the main avalanche.

On interevent time distributions of avalanche dynamics

Physical systems characterized by stick-slip dynamics often display avalanches. Regardless of the diversity of their microscopic structure, these systems are governed by a power-law distribution of avalanche size and duration. Here we focus on the interevent times between avalanches and show that, unlike their distributions of size and duration, the interevent time distributions are able to distinguish different mechanical states of the system. We use experiments on granular systems and numerical simulations of emulsions to show that systems having the same probability distribution for avalanche size and duration can have different interevent time distributions. Remarkably, these interevent time distributions look similar to those for earthquakes and, if different from an exponential, are indirect evidence of non trivial space-time correlations among avalanches. Our results therefore indicate that interevent time statistics are essential to characterise the dynamics of avalanches.

Compressive Failure as a Critical Transition: Experimental Evidence and Mapping onto the Universality Class of Depinning

Acoustic emission (AE) measurements performed during the compressive loading of concrete samples with three different microstructures (aggregate sizes and porosity) and four sample sizes revealed that failure is preceded by an acceleration of the rate of fracturing events, power law distributions of AE energies and durations near failure, and a divergence of the fracturing correlation length and time towards failure. This argues for an interpretation of compressive failure of disordered materials as a critical transition between an intact and a failed state. The associated critical exponents were found to be independent of sample size and microstructural disorder and close to mean-field depinning values. Although compressive failure differs from classical depinning in several respects, including the nature of the elastic redistribution kernel, an analogy between the two processes allows deriving (finite-) sizing effects on strength that match our extensive data set. This critical interpretation of failure may have also important consequences in terms of natural hazards forecasting, such as volcanic eruptions, landslides, or cliff collapses.

Avalanches and extreme value statistics in interfacial crackling dynamics

We study the avalanche and extreme statistics of the global velocity of a crack front, propagating slowly along a weak heterogeneous interface of a transparent polymethyl methacrylate block. The different loading conditions used (imposed constant velocity or creep relaxation) lead to a broad range of average crack front velocities. Our high-resolution and large dataset allows one to characterize in detail the observed intermittent crackling dynamics. We specifically measure the size S, the duration D, as well as the maximum amplitude [Formula: see text] of the global avalanches, defined as bursts in the interfacial crack global velocity time series. Those quantities characterizing the crackling dynamics follow robust power-law distributions, with scaling exponents in agreement with the values predicted and obtained in numerical simulations of the critical depinning of a long-range elastic string, slowly driven in a random medium. Nevertheless, our experimental results also set the limit of such model which cannot reproduce the power-law distribution of the maximum amplitudes of avalanches of a given duration reminiscent of the underlying fat-tail statistics of the local crack front velocities.This article is part of the theme issue 'Statistical physics of fracture and earthquakes'.

Avalanches and scaling collapse in the large-N Kuramoto model

We study avalanches in the Kuramoto model, defined as excursions of the order parameter due to ephemeral episodes of synchronization. We present scaling collapses of the avalanche sizes, durations, heights, and temporal profiles, extracting scaling exponents, exponent relations, and scaling functions that are shown to be consistent with the scaling behavior of the power spectrum, a quantity independent of our particular definition of an avalanche. A comprehensive scaling picture of the noise in the subcritical finite-N Kuramoto model is developed, linking this undriven system to a larger class of driven avalanching systems.

Analysis of crackling noise using the maximum-likelihood method: Power-law mixing and exponential damping

Crackling noise can be initiated by competing or coexisting mechanisms. These mechanisms can combine to generate an approximate scale invariant distribution that contains two or more contributions. The overall distribution function can be analyzed, to a good approximation, using maximum-likelihood methods and assuming that it follows a power law although with nonuniversal exponents depending on a varying lower cutoff. We propose that such distributions are rather common and originate from a simple superposition of crackling noise distributions or exponential damping.

Strain intermittency due to avalanches in ferroelastic and porous materials

The avalanche statistics in porous materials and ferroelastic domain wall systems has been studied for slowly increasing compressive uniaxial stress with stress rates between 0.2 and 17 kPa s^-1. Velocity peaks [Formula: see text] are calculated from the measured strain drops and used to determine the corresponding Energy distributions [Formula: see text]. Power law distributions [Formula: see text] have been obtained over 4-6 decades. For most of the porous materials and domain wall systems an exponent [Formula: see text] was obtained in good agreement with mean-field theory of the interface pinning transition. For charcoal, shale and calcareous schist we found significant deviations of the exponents from mean-field values in agreement with recent acoustic emission experiments.

Scaling of slip avalanches in sheared amorphous materials based on large-scale atomistic simulations

Atomistic simulations of binary amorphous systems with over 4 million atoms are performed. Systems of two interatomic potentials of the Lennard-Jones type, LJ12-6 and LJ9-6, are simulated. The athermal quasistatic shearing protocol is adopted, where the shear strain is applied in a stepwise fashion with each step followed by energy minimization. For each avalanche event, the shear stress drop (Δσ), the hydrostatic pressure drop (Δσ_{h}), and the potential energy drop (ΔE) are computed. It is found that, with the avalanche size increasing, the three become proportional to each other asymptotically. The probability distributions of avalanche sizes are obtained and values of scaling exponents fitted. In particular, the distributions follow a power law, P(ΔU)∼ΔU^{-τ}, where ΔU is a measure of avalanche sizes defined based on shear stress drops. The exponent τ is 1.25±0.1 for the LJ12-6 systems, and 1.15±0.1 for the LJ9-6 systems. The value of τ for the LJ12-6 systems is consistent with that from an earlier atomistic simulation study by Robbins et al. [Phys. Rev. Lett. 109, 105703 (2012)]PRLTAO0031-900710.1103/PhysRevLett.109.105703, but the fitted values of other scaling exponents differ, which may be because the shearing protocol used here differs from that in their study.

Avalanche statistics from data with low time resolution

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.

Statistical Evaluation of Waveform Collapse Reveals Scale-Free Properties of Neuronal Avalanches

Neural avalanches are a prominent form of brain activity characterized by network-wide bursts whose statistics follow a power-law distribution with a slope near 3/2. Recent work suggests that avalanches of different durations can be rescaled and thus collapsed together. This collapse mirrors work in statistical physics where it is proposed to form a signature of systems evolving in a critical state. However, no rigorous statistical test has been proposed to examine the degree to which neuronal avalanches collapse together. Here, we describe a statistical test based on functional data analysis, where raw avalanches are first smoothed with a Fourier basis, then rescaled using a time-warping function. Finally, an F ratio test combined with a bootstrap permutation is employed to determine if avalanches collapse together in a statistically reliable fashion. To illustrate this approach, we recorded avalanches from cortical cultures on multielectrode arrays as in previous work. Analyses show that avalanches of various durations can be collapsed together in a statistically robust fashion. However, a principal components analysis revealed that the offset of avalanches resulted in marked variance in the time-warping function, thus arguing for limitations to the strict fractal nature of avalanche dynamics. We compared these results with those obtained from cultures treated with an AMPA/NMDA receptor antagonist (APV/DNQX), which yield a power-law of avalanche durations with a slope greater than 3/2. When collapsed together, these avalanches showed marked misalignments both at onset and offset time-points. In sum, the proposed statistical evaluation suggests the presence of scale-free avalanche waveforms and constitutes an avenue for examining critical dynamics in neuronal systems.

Probabilistic model of waiting times between large failures in sheared media

Using a probabilistic approximation of a mean-field mechanistic model of sheared systems, we analytically calculate the statistical properties of large failures under slow shear loading. For general shear F(t), the distribution of waiting times between large system-spanning failures is a generalized exponential distribution, ρ_{T}(t)=λ(F(t))P(F(t))exp[-∫_{0}^{t}dτλ(F(τ))P(F(τ))], where λ(F(t)) is the rate of small event occurrences at stress F(t) and P(F(t)) is the probability that a small event triggers a large failure. We study the behavior of this distribution as a function of fault properties, such as heterogeneity or shear rate. Because the probabilistic model accommodates any stress loading F(t), it is particularly useful for modeling experiments designed to understand how different forms of shear loading or stress perturbations impact the waiting-time statistics of large failures. As examples, we study how periodic perturbations or fluctuations on top of a linear shear stress increase impact the waiting-time distribution.

Stick-slip behavior in a continuum-granular experiment

We report moment distribution results from a laboratory experiment, similar in character to an isolated strike-slip earthquake fault, consisting of sheared elastic plates separated by a narrow gap filled with a two-dimensional granular medium. Local measurement of strain displacements of the plates at 203 spatial points located adjacent to the gap allows direct determination of the event moments and their spatial and temporal distributions. We show that events consist of spatially coherent, larger motions and spatially extended (noncoherent), smaller events. The noncoherent events have a probability distribution of event moment consistent with an M(-3/2) power law scaling with Poisson-distributed recurrence times. Coherent events have a log-normal moment distribution and mean temporal recurrence. As the applied normal pressure increases, there are more coherent events and their log-normal distribution broadens and shifts to larger average moment.

Moving line model and avalanche statistics of Bingham fluid flow in porous media

In this article, we propose a simple model to understand the critical behavior of path opening during flow of a yield stress fluid in porous media as numerically observed by Chevalier and Talon (2015). This model can be mapped to the problem of a contact line moving in an heterogeneous field. Close to the critical point, this line presents an avalanche dynamic where the front advances by a succession of waiting time and large burst events. These burst events are then related to the non-flowing (i.e. unyielded) areas. Remarkably, the statistics of these areas reproduce the same properties as in the direct numerical simulations. Furthermore, even if our exponents seem to be close to the mean field universal exponents, we report an unusual bump in the distribution which depends on the disorder. Finally, we identify a scaling invariance of the cluster spatial shape that is well fit, to first order, by a self-affine parabola.

From mild to wild fluctuations in crystal plasticity

Macroscopic crystal plasticity is classically viewed as an outcome of uncorrelated dislocation motions producing Gaussian fluctuations. An apparently conflicting picture emerged in recent years emphasizing highly correlated dislocation dynamics characterized by power-law distributed fluctuations. We use acoustic emission measurements in crystals with different symmetries to show that intermittent and continuous visions of plastic flow are not incompatible. We demonstrate the existence of crossover regimes where strongly intermittent events coexist with a Gaussian quasiequilibrium background and propose a simple theoretical framework compatible with these observations.

Independence of slip velocities on applied stress in small crystals

Directly tracing the spatiotemporal dynamics of intermittent plasticity at the micro- and nanoscale reveals that the obtained slip dynamics are independent of applied stress over a range of up to ∼400 MPa, as well as being independent of plastic strain. Whilst this insensitivity to applied stress is unexpected for dislocation plasticity, the stress integrated statistical properties of both the slip size magnitude and the slip velocity follow known theoretical predictions for dislocation plasticity. Based on these findings, a link between the crystallographic slip velocities and an underlying dislocation avalanche velocity is proposed. Supporting dislocation dynamics simulations exhibit a similar regime during microplastic flow, where the mean dislocation velocity is insensitive to the applied stress. Combining both experimental and modeling observations, the results are discussed in a framework that firmly places the plasticity of nano- and micropillars in the microplastic regime of bulk crystals.

Bulk metallic glasses deform via slip avalanches

For the first time in metallic glasses, we extract both the exponents and scaling functions that describe the nature, statistics, and dynamics of slip events during slow deformation, according to a simple mean field model. We model the slips as avalanches of rearrangements of atoms in coupled shear transformation zones (STZs). Using high temporal resolution measurements, we find the predicted, different statistics and dynamics for small and large slips thereby excluding self-organized criticality. The agreement between model and data across numerous independent measures provides evidence for slip avalanches of STZs as the elementary mechanism of inhomogeneous deformation in metallic glasses.

Analysis of spanning avalanches in the two-dimensional nonequilibrium zero-temperature random-field Ising model

We present a numerical analysis of spanning avalanches in a two-dimensional (2D) nonequilibrium zero-temperature random field Ising model. Finite-size scaling analysis, performed for distribution of the average number of spanning avalanches per single run, spanning avalanche size distribution, average size of spanning avalanche, and contribution of spanning avalanches to magnetization jump, is augmented by analysis of spanning field (i.e., field triggering spanning avalanche), which enabled us to collapse averaged magnetization curves below critical disorder. Our study, based on extensive simulations of sufficiently large systems, reveals the dominant role of subcritical 2D-spanning avalanches in model behavior below and at the critical disorder. Other types of avalanches influence finite systems, but their contribution for large systems remains small or vanish.

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

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.