Distribution Of Avalanches Research Articles

Study of the optimal configuration for a Gas Electron Multiplier aimed at plasma impurity radiation monitoring

For the purpose of monitoring the level of plasma impurity (especially tungsten) and its distribution reconstruction at tokamaks (ITER in particular), a Soft X-Ray (SXR) tomographic diagnostics based on Gas Electron Multiplier (GEM) detectors with energy discrimination has been extensively considered for a while. Coupled with advanced electronics, GEM detectors offer excellent time and space resolution, as well as a charge spectrum from which the SXR photon spectrum can be deconvolved. In addition, they are less subjected to a neutron damage as compared to standard semiconductor diodes. This contribution highlights the latest studies supporting the development of such diagnostics focusing on laboratory tests to examine: (a) the impact of GEM holes geometry on the properties and distribution of the electron avalanche; (b) the effect of the high rate photon flux on GEM foil performance; and (c) the optimal electric field distribution.

Increasing power-law range in avalanche amplitude and energy distributions.

Power-law-type probability density functions spanning several orders of magnitude are found for different avalanche properties. We propose a methodology to overcome empirical constraints that limit the range of truncated power-law distributions. By considering catalogs of events that cover different observation windows, the maximum likelihood estimation of a global power-law exponent is computed. This methodology is applied to amplitude and energy distributions of acoustic emission avalanches in failure-under-compression experiments of a nanoporous silica glass, finding in some cases global exponents in an unprecedented broad range: 4.5 decades for amplitudes and 9.5 decades for energies. In the latter case, however, strict statistical analysis suggests experimental limitations might alter the power-law behavior.

Crossover from three-dimensional to two-dimensional systems in the nonequilibrium zero-temperature random-field Ising model.

We present extensive numerical studies of the crossover from three-dimensional to two-dimensional systems in the nonequilibrium zero-temperature random-field Ising model with metastable dynamics. Bivariate finite-size scaling hypotheses are presented for systems with sizes L×L×l which explain the size-driven critical crossover from two dimensions (l=const, L→∞) to three dimensions (l∝L→∞). A model of effective critical disorder R_{c}^{eff}(l,L) with a unique fitting parameter and no free parameters in the R_{c}^{eff}(l,L→∞) limit is proposed, together with expressions for the scaling of avalanche distributions bringing important implications for related experimental data analysis, especially in the case of thin three-dimensional systems.

Numerical experiment studies of clogging during the discharge of granular matter in a three-dimensional hopper

For a granular flow in hopper in engineering and experimental applications, it is necessary to guarantee the discharge continuously and steadily. The clogging will easily happen if the outlet size is small enough via formation of the arch above the outlet. The clogging phenomenon is also important for studying traffic or evacuation problems. In previous numerical and experimental study, to expedite the experiments or simulations, the perturbations, such as a jet of pressurized air or the vibration of the wall of the hopper, were induced to break the clogging and restart the flow. But these perturbations are hardly normalized and described in modeling the process. In this paper, we present a series of numerical experiments of clogging in the discharge of particles from a three-dimensional hopper through a circular opening. We employ our discrete element method simulation code for large scale dense granular flow based on the graphic processing unit to expedite this simulation. In contrast to pervious studies, here we study the first clogging after opening the outlet of hopper, thus the above perturbations are avoided. From simulating granular flow in hopper in a wide range of outlet size and cone angle, we obtain the size of distribution of avalanche, which is defined as the number of particles that fall through the opening from the outlet opening to the first clogging. The effects of the outlet size and cone angle of hopper on avalanche size are investigated and discussed. The results show that the previous conclusion of the distribution of possibility of avalanche size is also valid in this study. There is a peak in the distribution of possibility of avalanche size, and the distribution can be divided into two regions, which can be fitted with a power-law and an exponential function respectively. The exponential part can be explained by a possibility model which is suggested by Janda et al. From the fitting we find that it has a critical value for the outlet size above which no clogging will occur and the value in this work (4.75d) is slightly lower than in Zuriguel et al.'s experiment (4.94d). Moreover, there is also a critical value for the cone angle of hopper, which supports the inference in previous study and the value in this paper (77) is closed to the predicted one (75) in To et al.'s work.

Neuronal avalanches: Where temporal complexity and criticality meet.

The model of the current paper is an extension of a previous publication, wherein we have used the leaky integrate-and-fire model on a regular lattice with periodic boundary conditions, and introduced the temporal complexity as a genuine signature of criticality. In that work, the power-law distribution of neural avalanches was a manifestation of supercriticality rather than criticality. Here, however, we show that the continuous solution of the model and replacing the stochastic noise with a Gaussian zero-mean noise leads to the coincidence of power-law display of temporal complexity, and spatiotemporal patterns of neural avalanches at the critical point. We conclude that the source of inconsistency may be a numerical artifact originated by the discrete description of the model which may imply a slow numerical convergence of the avalanche distribution compared to temporal complexity.

Avalanche criticality in thermal-driven martensitic transitions: the asymmetry of the forward and reverse transitions in shape-memory materials**This paper is dedicated to our friend Ekhard Salje in the occasion of his 70th birthday.

Martensitic transitions take place intermittently as a sequence of avalanches which are accompanied by the emission of acoustic waves. The study of this acoustic emission (AE) reveals the scale-free nature of the avalanches. In a number of shape memory materials undergoing a martensitic transition it has been found that, in spite of relatively low hysteresis, the dynamics of forward and reverse transitions are different, which may explain the fact that the AE activity is different in both forward and reverse transitions. The asymmetry could be a consequence of the fact that, while nucleation is required for the transition from the parent to martensitic phase to take place, reverse transition occurs by fast shrinkage of martensitic domains. We have analysed in detail the distribution of avalanches in cooling and heating runs in Fe–Pd and Cu–Zn–Al shape-memory alloys. In the former, the martensitic transition is weakly first order while it shows a significant first order character in the latter. We have found that in Fe–Pd the distributions are power law for the forward and reverse transitions characterized by the same critical exponents. For Cu–Zn–Al the distribution of avalanches is critical in forward transitions but exponentially damped in the reverse transition. It is suggested that this different behaviour could originate from the different dynamic mechanisms in forward and reverse transitions.

Criticality meets learning: Criticality signatures in a self-organizing recurrent neural network.

Many experiments have suggested that the brain operates close to a critical state, based on signatures of criticality such as power-law distributed neuronal avalanches. In neural network models, criticality is a dynamical state that maximizes information processing capacities, e.g. sensitivity to input, dynamical range and storage capacity, which makes it a favorable candidate state for brain function. Although models that self-organize towards a critical state have been proposed, the relation between criticality signatures and learning is still unclear. Here, we investigate signatures of criticality in a self-organizing recurrent neural network (SORN). Investigating criticality in the SORN is of particular interest because it has not been developed to show criticality. Instead, the SORN has been shown to exhibit spatio-temporal pattern learning through a combination of neural plasticity mechanisms and it reproduces a number of biological findings on neural variability and the statistics and fluctuations of synaptic efficacies. We show that, after a transient, the SORN spontaneously self-organizes into a dynamical state that shows criticality signatures comparable to those found in experiments. The plasticity mechanisms are necessary to attain that dynamical state, but not to maintain it. Furthermore, onset of external input transiently changes the slope of the avalanche distributions – matching recent experimental findings. Interestingly, the membrane noise level necessary for the occurrence of the criticality signatures reduces the model’s performance in simple learning tasks. Overall, our work shows that the biologically inspired plasticity and homeostasis mechanisms responsible for the SORN’s spatio-temporal learning abilities can give rise to criticality signatures in its activity when driven by random input, but these break down under the structured input of short repeating sequences.

Subsampling scaling

In real-world applications, observations are often constrained to a small fraction of a system. Such spatial subsampling can be caused by the inaccessibility or the sheer size of the system, and cannot be overcome by longer sampling. Spatial subsampling can strongly bias inferences about a system’s aggregated properties. To overcome the bias, we derive analytically a subsampling scaling framework that is applicable to different observables, including distributions of neuronal avalanches, of number of people infected during an epidemic outbreak, and of node degrees. We demonstrate how to infer the correct distributions of the underlying full system, how to apply it to distinguish critical from subcritical systems, and how to disentangle subsampling and finite size effects. Lastly, we apply subsampling scaling to neuronal avalanche models and to recordings from developing neural networks. We show that only mature, but not young networks follow power-law scaling, indicating self-organization to criticality during development.

Serrated plastic flow behavior and microstructure in a Zr-based bulk metallic glass processed by surface mechanical attrition treatment

The serrated plastic flow, microstructure and residual stress of a Zr33 Cu30 Ni5 Al10 bulk metallic glass (BMG) undergone surface mechanical attrition treatment (SMAT) have been investigated by a combination of compression tests with scanning electron microscopy (SEM), high resolution transmission electron microscopy (HRTEM) and the incremental hole-drilling strain-gage method. It is found that SMAT leads to various microstructural modifications and residual stress distribution in the surface layers of the Zr-based BMG due to the mechanically-induced nanocrystallization and generation of shear bands. As a result, the BMG alloy exhibits a remarkable work-hardening like behavior and significant increase of plastic strain from less than 1 % to 15 %, and its plastic deformation dynamics yields a power-law distribution of shear avalanches. Based upon the analysis of the experimental results, it is indicated that this can be connected to the SMAT-induced microstructural modifications and the resulting residual compressive stress in the Zr-based BMG.

Mean-field avalanches in jammed spheres.

Disordered systems are characterized by the existence of many sample-dependent local-energy minima that cause a step-wise response when the system is perturbed. In this article we use an approach based on elementary probabilistic methods to compute the complete probability distribution of the jumps (static avalanches) in the response of mean-field systems described by replica symmetry breaking; we find a precise condition for having a power-law behavior in the distribution of avalanches caused by small perturbations, and we show that our predictions are in remarkable agreement both with previous results and with what is found in simulations of three-dimensional systems of soft spheres, either at jamming or at slightly higher densities.

Jamming/flowing transition of non-Brownian particles suspended in a iso-density fluid flowing in a 2D rectangular duct

We present the results of an experimental study on the jamming/flowing transition. A suspension of neutrally buoyant large particles flows in an horizontal rectangular duct, where an artificial restriction triggers jamming. We show that the avalanche distribution size is exponential, that is memoryless. We further demonstrate that the avalanche size diverges when the restriction size approaches a critical value and that this divergence is well described by a power law. The parameters (critical opening size and divergence velocity) are compared to literature values and show a strong similarity with others systems. Another result of this paper is the study of the influence of the particle morphology. We show that, for a moderate restriction size, the dead-zone formed right upstream of the restriction is larger for angular particles but, paradoxically, that the avalanche size is larger for polyhedra compared to spheres by at least one order of magnitude.

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.

Single electron multiplication distribution in GEM avalanches

In this paper, measurement results and experimental methodology are presented on the determination of multiplication distributions of avalanches initiated by single electron in GEM foils. The measurement relies on the amplification of photoelectrons by the GEM under study, which is subsequently amplified in an MWPC for signal enhancement and readout. The intrinsic detector resolution, namely the sigma-over-mean ratio of the multiplication distribution is also elaborated. Small gain dependence of the shape of the avalanche response distribution is observed in the range of net effective gain of 15 to 100. The distribution has an exponentially decaying tail at large amplitudes. At small amplitudes, the applied working gas is seen to have a well visible effect on the shape of the multiplication distribution. Equivalently, the working gas has an influence on the intrinsic detector resolution of GEMs via suppression of the low amplitude responses. A sigma-over-mean ratio of 0.75 was reached using a neon based mixture, whereas other gases provided an intrinsic detector resolution closer to 1, meaning a multiplication distribution closer to the low-field limit exponential case.

Representing stochastic damage evolution in disordered media as a jump Markov process using the fiber bundle model

The damage evolution in quasi-brittle materials is inherently stochastic due to the presence of strong disorder in the form of heterogeneities, voids, and microcracks. The final macroscopic failure is foreshadowed by accumulation of a significant amount of distributed damage that results in precursory events observed as avalanches in experiments and simulations. Simulations on spring lattice models of disordered media have been widely used to understand the collective nature of the quasi-brittle material failure process. In this study, we use the jump Markov process to model stochastic damage evolution, which is informed by the avalanche size distributions for a given material. The jump Markov process is defined based on the probability distributions of the jump sizes, the wait-time between consecutive jumps, and the failure strength. The fiber bundle model is used as an example to obtain the required inputs and test the viability of the proposed approach. The stochasticity and size-dependence of the damage evolution process is inherently captured through the inputs provided for the jump Markov process. The avalanche and strength distributions are used to describe the effect of microscopic information present in the form of disorder, on the macroscopic damage evolution behavior.

Hybrid phase transition into an absorbing state: Percolation and avalanches.

Interdependent networks are more fragile under random attacks than simplex networks, because interlayer dependencies lead to cascading failures and finally to a sudden collapse. This is a hybrid phase transition (HPT), meaning that at the transition point the order parameter has a jump but there are also critical phenomena related to it. Here we study these phenomena on the Erdős-Rényi and the two-dimensional interdependent networks and show that the hybrid percolation transition exhibits two kinds of critical behaviors: divergence of the fluctuations of the order parameter and power-law size distribution of finite avalanches at a transition point. At the transition point global or "infinite" avalanches occur, while the finite ones have a power law size distribution; thus the avalanche statistics also has the nature of a HPT. The exponent β_{m} of the order parameter is 1/2 under general conditions, while the value of the exponent γ_{m} characterizing the fluctuations of the order parameter depends on the system. The critical behavior of the finite avalanches can be described by another set of exponents, β_{a} and γ_{a}. These two critical behaviors are coupled by a scaling law: 1-β_{m}=γ_{a}.

Chaotic state to self-organized critical state transition of serrated flow dynamics during brittle-to-ductile transition in metallic glass

We study serrated flow dynamics during brittle-to-ductile transition induced by tuning the sample aspect ratio in a Zr-based metallic glass. The statistical analysis reveals that the serrated flow dynamics transforms from a chaotic state characterized by Gaussian-distribution serrations corresponding to stick-slip motion of randomly generated and uncorrelated single shear band and brittle behavior, into a self-organized critical state featured by intermittent scale-free distribution of shear avalanches corresponding to a collective motion of multiple shear bands and ductile behavior. The correlation found between serrated flow dynamics and plastic deformation might shed light on the plastic deformation dynamic and mechanism in metallic glasses.

Topographical factors, meteorological variables and human factors in the control of the main snow avalanche events in the Făgăraş Massif (Southern Carpathians - Romanian Carpathians): Case studies

Snow avalanches are a common geomorphic process and natural hazard in the Southern Carpathians (Romanian Carpathians). The spatial distribution of avalanches is controlled by topographical factors, meteorological variables and human factors. This study examines the occurrence of avalanches in two glacial areas in the Fagaras massif, Bâlea (on the northern slope) and Capra (on the southern slope). During the period from 1963 to 2015 a total of 27 serious avalanche accidents were recorded in the months November-June in the Fagaras massif resulting in 76 fatalities and 50 burials/injuries. From these avalanches, we examined five major avalanche accidents: the avalanche of June, 1974 which caused 6 fatalities and 8 burials/injuries; the avalanche of April 17, 1977 which caused 23 fatalities; the avalanche of December 23, 1988 which caused 3 fatalities; the avalanche of December 28, 2002 which caused 4 fatalities and the avalanche of February 20, 2010 which caused one fatality and 2 burials/injuries. Our results indicate a good correlation between some topographical factors. On the other hand, an increase in snowfall and snowstorms in particular are factors responsible for one avalanche event; early snowfall and a sudden increase in temperature are factors responsible for two avalanche events and snowfall and a sudden increase in temperature are factors responsible for one avalanche event. Using the weather scenarios we found high snowstorm frequency in one case, early-season weak layers of faceted crystals and depth hoar in two cases and well above-average total snowfall for one case.

Burst predicting neurons survive an in vitro glutamate injury model of cerebral ischemia.

Neuronal activity in vitro exhibits network bursts characterized by brief periods of increased spike rates. Recent work shows that a subpopulation of neurons reliably predicts the occurrence of network bursts. Here, we examined the role of burst predictors in cultures undergoing an in vitro model of cerebral ischemia. Dissociated primary cortical neurons were plated on multielectrode arrays and spontaneous activity was recorded at 17 days in vitro (DIV). This activity was characterized by neuronal avalanches where burst statistics followed a power law. We identified burst predictors as channels that consistently fired immediately prior to network bursts. The timing of these predictors relative to bursts followed a skewed distribution that differed sharply from a null model based on branching ratio. A portion of cultures were subjected to an excitotoxic insult (DIV 18). Propidium iodine and fluorescence imaging confirmed cell death in these cultures. While the insult did not alter the distribution of avalanches, it resulted in alterations in overall spike rates. Burst predictors, however, maintained baseline levels of activity. The resilience of burst predictors following excitotoxic insult suggests a key role of these units in maintaining network activity following injury, with implications for the selective effects of ischemia in the brain.

Strain hardening and dislocation avalanches in micrometer-sized dimensions

Present experiments and computational simulations furnish a fundamental background to the understanding of plastic flow across sample sizes. It is shown that self-organized criticality (SOC) governs the size distribution of dislocation avalanches in micrometer-sized sample dimensions. Onset of SOC denotes inception of a dislocation network so that dislocation avalanches occur at constant criticality level irrespectively of the applied stress. In these microcrystals, we find that the ratio between the characteristic sample dimension and the mean free path traveled by the mobile dislocations, D/Leff, rules the onset of strain hardening. This index simultaneously accounts for the role of loading orientation and dislocation density upon microscale plasticity. It is shown that strain-hardening emerges for D/Leff>2, where surface dislocation annihilations are inconsequential to network development and the flow stress scales with dislocation density. This regime naturally evolves toward bulk plasticity at increasing sample sizes. Conversely, strain hardening is suppressed when confining sample dimensions dominate plastic flow for D/Leff<1.5. Confining microscale plasticity is characterized by a significant increase in the size of dislocation avalanches under a stagnant dislocation network.

Active microrheology in active matter systems: Mobility, intermittency, and avalanches

We examine the mobility and velocity fluctuations of a driven particle moving through an active matter bath of self-mobile disks for varied density or area coverage and varied activity. We show that the driven particle mobility can exhibit nonmonotonic behavior that is correlated with distinct changes in the spatiotemporal structures that arise in the active media. We demonstrate that the probe particle velocity distributions exhibit specific features in the different dynamic regimes and identify an activity-induced uniform crystallization that occurs for moderate activity levels and is distinct from the previously observed higher activity cluster phase. The velocity distribution in the cluster phase has telegraph noise characteristics produced when the probe particle moves alternately through high-mobility areas that are in the gas state and low-mobility areas that are in the dense phase. For higher densities and large activities, the system enters what we characterize as an active jamming regime. Here the probe particle moves in intermittent jumps or avalanches that have power-law-distributed sizes that are similar to the avalanche distributions observed for nonactive disk systems near the jamming transition.