Distribution Of Avalanches Research Articles

Failure process of fiber bundles with random misalignment

We investigate the failure process of fiber bundles with structural disorder represented by the random misalignment of fibers. The strength of fibers is assumed to be constant so that misalignment is the only source of disorder, which results in a heterogeneous load distribution over fibers. We show by analytical calculations and computer simulations that increasing the amount of structural disorder a transition occurs from a perfectly brittle behavior with abrupt global failure to a quasibrittle phase where failure is preceded by breaking avalanches. The size distribution of avalanches follows a power-law functional form with a complex dependence of the exponent on the amount of disorder. In the vicinity of the critical point the avalanche exponent is 3/2; however, with increasing disorder a crossover emerges to a higher exponent 5/2. We show analytically that the mechanical behavior of the bundle of misaligned fiber with no strength disorder can be mapped to an equal load sharing fiber bundle of perfectly aligned fibers with properly selected strength disorder. Published by the American Physical Society 2024

Hysteretic response to different modes of ramping an external field in sparse and dense Ising spin glasses

We consider the hysteretic behavior of Ising spin glasses at T=0 for various modes of driving. Previous studies mostly focused on an infinitely slow speed Ḣ by which the external field H was ramped to trigger avalanches of spin flips by starting with destabilizing a single spin while few have focused on the effect of different driving methods. First, we show that this conventional protocol imposes a system size dependence. Then, we numerically analyze the response of Ising spin glasses at rates Ḣ that are fixed as well, to elucidate the differences in the response. Specifically, we compare three different modes of ramping (Ḣ=c/N, Ḣ=c/N, and Ḣ=c for constant c) for two types of spin glass systems of size N, representing dense networks by the Sherrington–Kirkpatrick model and sparse networks by the lattice spin glass in d=3 dimensions known as the Edwards Anderson model. Depending on the mode of ramping, we find that the response of each system, in form of spin-flip avalanches and other observables, can vary considerably. In particular, in the N-independent mode applied to the lattice spin glass, which is closest to experimental reality, we observe a percolation transition with a broad avalanche distribution between phases of localized and system-spanning responses. We explore implications for combinatorial optimization problems pertaining to sparse systems.

Scale‐Dependent Processes and Runout in Bidisperse Granular Flows: Insights From Laboratory Experiments and Implications for Rock/Debris Avalanches

AbstractThe bidispersity observed in the particle‐size distribution of rock avalanches and volcanic debris avalanches (rock/debris avalanches) has been proposed as a factor contributing to their long runout. This has been supported by small‐scale analog experimental studies, which observe that a small proportion of fine particles mixed with coarser particles enhances granular avalanche runout. However, the mechanisms enabling this phenomenon and their resemblance to rock/debris avalanches have not been directly evaluated. Here, binary mixture granular avalanche experiments are employed to constrain the processes and conditions under which bidispersity enhances the runout of granular avalanches in experiments. Structure‐from‐motion photogrammetry is used to measure center of mass displacement and assess energy dissipation. Subsequently, this study evaluates the dynamic scaling and flow regimes in the lab and field to assess whether the runout‐enhancing mechanism is applicable to rock/debris avalanches. In small‐scale experiments, the granular mass propagates under a collisional regime, enabling kinetic sieving and size segregation. Fine particles migrate to the base where they reduce frictional areas between coarse particles and the substrate and encourage rolling. The reduced energy dissipation increases the kinetic energy conversion and avalanche mobility. However, rock/debris avalanches are unlikely to acquire a purely collisional regime; instead, they propagate under a frictional regime. The size segregation which is essential for the process observed at the lab‐scale is prohibited by the frictional regime, as evident by the sedimentology of rock/debris avalanche deposits. The proposal of bidispersity as a runout‐enhancing mechanism overlooks that scale‐dependent behaviors of natural events are often omitted in small‐scale experiments.

Avalanche properties at the yielding transition: from externally deformed glasses to active systems.

We investigated the yielding phenomenon in the quasistatic limit using numerical simulations of soft particles. Two different deformation scenarios, simple shear (passive) and self-random force (active), and two interaction potentials were used. Our approach reveals that the exponents describing the avalanche distribution are universal within the margin of error, showing consistency between the passive and active systems. This indicates that any differences observed in the flow curves may have resulted from a dynamic effect on the avalanche propagation mechanism. The evolution time required to reach a steady state differs significantly between active and passive scenarios under similar conditions. However, we demonstrated that plastic avalanches under athermal quasistatic simulation dynamics display a similar scaling relationship between avalanche size and relaxation time, which cannot explain the different flow curves.

Role of composition in fracture behavior of two-phase solids.

In a two-phase solid, we examine the growth of a preexisting macroscopic crack based on simulations of a random spring network model. We find that the enhancement in toughness, as well as strength, is strongly dependent on the ratio of elastic moduli as well as on the relative proportion of the phases. We find that the mechanism that leads to enhancement in toughness is not the same as that for enhancement in strength; however, the overall enhancement is similar in mode I and mixed-mode loading. Based on the crack paths, and the spread of the fracture process zone, we identify the type of fracture to transition from nucleation type, for close to single-phase compositions, whether hard or soft, to avalanche type for more mixed compositions. We also show that the associated avalanche distributions exhibit power-law statistics with different exponents for each phase. The significance of variations in the avalanche exponents with the relative proportion of phases and possible connections to the fracture types are discussed in detail.

Mechanical excitation and marginal triggering during avalanches in sheared amorphous solids.

We study plastic strain during individual avalanches in overdamped particle-scale molecular dynamics (MD) and mesoscale elastoplastic models (EPM) for amorphous solids sheared in the athermal quasistatic limit. We show that the spatial correlations in plastic activity exhibit a short length scale that grows as t^{3/4} in MD and ballistically in EPM, which is generated by mechanical excitation of nearby sites not necessarily close to their stability thresholds, and a longer lengthscale that grows diffusively for both models and is associated with remote marginally stable sites. These similarities in spatial correlations explain why simple EPMs accurately capture the size distribution of avalanches observed in MD, though the temporal profiles and dynamical critical exponents are quite different.

Dimensional crossover in driving-rate induced criticality on the hysteresis-loop of disordered ferromagnetic systems

We study the effect of finite driving rate on the nonequilibrium hysteresis-loop criticality with the systems’ nonequilateral geometry constraints allowing the dimensional crossover from three-dimensional to two-dimensional disordered ferromagnetic systems . For each system’s thickness, the disorder is fixed above the critical line for adiabatic driving, such that the emergent critical behaviors are solely attributed to the increased driving rates of the external field.We demonstrate it by computing the pertaining magnetizations and coercive fields, changes in avalanche distributions and shapes, and correlation functions of spin-flip events where the pace of the field increments are varied in a broad range. Our results reveal that the driving field rate profoundly affects system evolution attaining three distinct regimes of the induced criticality at the proper thickness-dependent rate values. In particular, these regimes are characterized by the occurrence of non-spanning avalanches (slow driving), the first appearance of spanning avalanches (intermediate regime), and being overwhelmed by system-spanning avalanches (fast driving regime) for a given thickness. Our results will bring some critical insights to the theoretical and experimental studies on the field-driven nonequilateral systems both for conceptual reasons and the versatility of their applications..

Finite driving rate effects in the nonequilibrium athermal random field Ising model of thin systems

Thin disordered ferromagnetic systems driven by varying magnetic field represent a challenge from theoretical, experimental and technological perspective. Understanding their temporal evolution under the mutual influence of finite driving rate with which the external magnetic field changes, geometry of the sample, and the amount of disorder is a complex task. It is studied here within the framework of the nonequilibrium athermal random field Ising model which has a dynamical behavior suitable for this kind of analysis both in statistical physics and physics of magnetism. Our results, obtained by means of numerical simulations performed at a discrete time scale of the model in a wide range of driving rates and domains of disorder, unveil the rate sensitivity exhibited by the response signal and the underlying avalanche distributions, correlation functions of spin-flip events, average avalanche shapes and the values of coercive field. Due to the rate-imposed spreading of multiple avalanches during the same/partially shared intervals of time, the pertaining effective exponents turn out to be rate-dependent as well. Our findings provide new insights on some features of field driven nonequilateral systems that could be applicable for investigations of a variety of thin systems driven at finite driving rates.

Inferring the stability of concentrated emulsions from droplet configuration information

When droplets are tightly packed in a 2D microchannel, coalescence of a pair of droplets can trigger an avalanche of coalescence events that propagate through the entire emulsion. This propagation is found to be stochastic, i.e. every coalescence event does not necessarily trigger another. To study how the local probabilistic propagation affects the dynamics of the avalanche, as a whole, a stochastic agent based model is used. Taking as input, i) how the droplets are packed (configuration) and ii) a measure of local probabilistic propagation (experimentally derived; function of fluid and other system parameters), the model predicts the expected size distribution of avalanches. In this article, we investigate how droplet configuration affects the avalanche dynamics. We find the mean size of these avalanches to depend non-trivially on how droplets are packed together. Large variations in the avalanche dynamics are observed when droplet packing are different, even when the other system properties (number of droplets, fluid properties, channel geometry, etc.) are kept constant. Bidisperse emulsions show less variation in the dynamics and they are surprisingly more stable than monodisperse emulsions. To get a systems-level understanding of how a given droplet-configuration either facilitates or impedes the propagation of an avalanche, we employ a graph-theoretic analysis, where emulsions are expressed as graphs. We find that the properties of the underlying graph, namely the mean degree and the algebraic connectivity, are well correlated with the observed avalanche dynamics. We exploit this dependence to derive a data-based model that predicts the expected avalanche sizes from the properties of the graph.

Avalanche gain and its effect on energy resolution in GEM-based detectors

We present avalanche gain and associated resolution measurements recorded with a 4He:CO2 (70:30) gas mixture and pure SF6, a Negative Ion (NI) gas. SF6 is of particular interest to the directional dark matter detection community, as its low thermal diffusion helps to retain recoil ionization track features over long drift lengths. With the aid of a general form of the reduced first Townsend coefficient (RFTC), multiple GEM-based detector data sets are used to study the high-gain behavior of the 4He:CO2 gas mixture. The high-gain data is well described purely in terms of the reduced electric field strength and the number of GEMs, and the robust relationship between the RFTC and the average, reduced, electric field strength across the GEMs is emphasized. The associated (pulse-height) resolution measurements are used to discuss the variance of the avalanche distribution and to describe and estimate the lower limits of energy resolution one should expect to measure using a simple relationship with the RFTC. In the end, a description of avalanche gain, its effect on energy resolution, and the contributing experimental parameters in GEM-based detectors is developed over a broad parameter space for further use.

Correlation Between Avalanches and Emitted Energies During Fracture With a Variable Stress Release Range

We observe the failure process of a fiber bundle model with a variable stress release range, γ, and higher the value of γ, lower the stress release range. By tuning γ from low to high, it is possible to go from the mean-field (MF) limit of the model to the local load-sharing (LLS) limit where local stress concentration plays a crucial role. In the MF limit, individual avalanches (number of fibers breaking in going from one stable state to the next, s) and the corresponding energies E emitted during those avalanches have one-to-one linear correlation. This results in the same size distributions for both avalanches (P(s)) and energy bursts (Q(E)): a scale-free distribution with a universal exponent value of −5/2. With increasing γ, the model enters the LLS limit beyond some γc. In this limit, due to the presence of local stress concentrations around a damaged region, such correlation C(γ) between s and E decreases, i.e., a smaller avalanche can emit a large amount of energy or a large avalanche may emit a small amount of energy. The nature of the decrease in the correlation between s and E depends highly on the dimension of the bundle. In this work, we study the decrease in the correlation between avalanche size and the corresponding energy bursts with an increase in the load redistribution localization in the fiber bundle model in one and two dimensions. Additionally, we note that the energy size distribution remains scale-free for all values of γ, whereas the avalanche size distribution becomes exponential for γ > γc.

Optimization of GEM-based detector readout electrode structure for SXR imaging of tokamak plasma

The paper presents an optimization of a readout structure of the GEM-based detector designed for X-ray imaging for DTT tokamak in the energy range of 2–15 keV. The readout electrode of approximately 100 cm2 surface is composed of hexagonal pixels connected in a way that allows reducing the actual number of signal pixels (electronics channels). At the same time, based on time coincidence analysis, it makes possible to unambiguously identify the position of the recorded X-ray photon. For the input spectrum, the Detective Quantum Efficiency (DQE) of the detector was calculated using the Geant4 program and the spatial distributions of electron avalanches at the readout electrode were simulated using the Garfield++ program. These were conducted for a given energy range of radiation and a statistical distribution consistent with the shape of the spectrum considering the DQE of the detector. As a result, the size of a single hexagonal pixel was proposed to capture the position of the recorded radiation quanta in an optimal and effective way.

Mean field fracture in disordered solids: Statistics of fluctuations

Power law distributed fluctuations are known to accompany terminal failure in disordered brittle solids. The associated intermittent scale-free behavior is of interest from the fundamental point of view as it emerges universally from an intricate interplay of threshold-type nonlinearity, quenched disorder, and long-range interactions. We use the simplest mean-field description of such systems to show that they can be expected to undergo a transition between brittle and quasi-brittle (ductile) responses. While the former is characterized by a power law distribution of avalanches, in the latter, the statistics of avalanches is predominantly Gaussian. The realization of a particular regime depends on the variance of disorder and the effective rigidity represented by a combination of elastic moduli. We argue that the robust criticality, as in the cases of earthquakes and collapsing porous materials, indicates the self-tuning of the system towards the boundary separating brittle and ductile regimes.

The effect of finite driving rate on avalanche distributions

We study distributions of spin avalanches in the three-dimensional nonequilibrium zero temperature random field Ising model driven by external magnetic field that is increased at constant rate. Our results show that avalanche distributions are affected by the driving regime and although the avalanche properties (e.g. size) remain power-law distributed above critical disorder, the scaling exponents vary with the driving rate. For slow driving, the integral distributions of nonspanning avalanches are almost the same as in the adiabatic and quasi-static driving regime and therefore described by constant values of power-law exponents. Owing to temporal overlapping and merging of avalanches, these distributions become markedly different with the increased driving rate which causes an increase of exponent values in the range of moderate driving rates and their saturation for fast driving. The integral distributions of all avalanches behave similarly but without the saturation of exponents for fast driving. Our results, based on extensive numerical simulations, could be relevant for studies of variety of systems in finite driving regime, particularly those with experimental realizations that are not easily attainable.

Criticality-Driven Evolution of Adaptable Morphologies of Voxel-Based Soft-Robots.

The paradigm of voxel-based soft robots has allowed to shift the complexity from the control algorithm to the robot morphology itself. The bodies of voxel-based soft robots are extremely versatile and more adaptable than the one of traditional robots, since they consist of many simple components that can be freely assembled. Nonetheless, it is still not clear which are the factors responsible for the adaptability of the morphology, which we define as the ability to cope with tasks requiring different skills. In this work, we propose a task-agnostic approach for automatically designing adaptable soft robotic morphologies in simulation, based on the concept of criticality. Criticality is a property belonging to dynamical systems close to a phase transition between the ordered and the chaotic regime. Our hypotheses are that 1) morphologies can be optimized for exhibiting critical dynamics and 2) robots with those morphologies are not worse, on a set of different tasks, than robots with handcrafted morphologies. We introduce a measure of criticality in the context of voxel-based soft robots which is based on the concept of avalanche analysis, often used to assess criticality in biological and artificial neural networks. We let the robot morphologies evolve toward criticality by measuring how close is their avalanche distribution to a power law distribution. We then validate the impact of this approach on the actual adaptability by measuring the resulting robots performance on three different tasks designed to require different skills. The validation results confirm that criticality is indeed a good indicator for the adaptability of a soft robotic morphology, and therefore a promising approach for guiding the design of more adaptive voxel-based soft robots.

Neural field theory of neural avalanche exponents.

The power-law exponents of observed size and lifetime distributions of near-critical neural avalanches are calculated from neural field theory using diagrammatic methods. This brings neural avalanches within the ambit of neural field theory, which has also previously explained near-critical 1/f spectra and many other observed features of neural activity. This strengthens the case for near-criticality of the brain and opens the way for these other phenomena to be interrelated with avalanches and their dynamics.

Clusters and avalanches of fibre breaks in a model of an impregnated unidirectional fibre bundle under tension

Development of clusters and avalanches of damage events is a key characteristic in statistical physics of structures susceptible to a catastrophic failure. This paper applies the concepts of such descriptions to the process of fibre breakage under tension in an impregnated fibre bundle model (IFBM). The following parameters are analysed: (1) susceptibility (damage caused by change in loading); (2) spatial clustering of breaks and its interdependency with avalanches; (3) the size distribution of fibre break clusters and avalanches; (4) fractal dimensions; and (5) correlation lengths of breaks. A systematic workflow and algorithms for this analysis are presented and applied for two realisations of a random fibre placement of carbon fibre/epoxy bundles with fibre volume fractions of 50% and 60%. For these two realisations: (1) the susceptibility divergence near the failure point is affected by the finite-size effect, being nearly constant for the last ~1/20th of strain life; this behaviour can be considered as a failure predictor; (2) the morphology of the break system is a spatially distributed multi-defect occurrence with the dimensionality of 3 for all breaks together and weak planarity demonstrated only by the largest clusters near failure; (3) the exponents of the cluster-size and avalanche-size power law distributions reached 2.5–3 for both statistics near the bundle failure, which may constitute an imminent failure indicator. Damage evolution of the carbon/epoxy IFBM up to the final failure is found to be short-correlated (with correlation length of the order of one fibre break stress redistribution zone) in the absence of collective long-range defect interactions. During the catastrophic avalanche, the spatially distributed morphology of breaks is gradually reorganized into a translaminar fracture mode.

Mapping avalanches with satellites – evaluation of performance and completeness

Abstract. The spatial distribution and size of avalanches are essential parameters for avalanche warning, avalanche documentation, mitigation measure design and hazard zonation. Despite its importance, this information is incomplete today and only available for limited areas and limited time periods. Manual avalanche mapping from satellite imagery has recently been applied to reduce this gap achieving promising results. However, their reliability and completeness have not yet been verified satisfactorily. In our study we attempt a full validation of the completeness of visually detected and mapped avalanches from optical SPOT 6, Sentinel-2 and radar Sentinel-1 imagery. We examine manually mapped avalanches from two avalanche periods in 2018 and 2019 for an area of approximately 180 km2 around Davos, Switzerland, relying on ground- and helicopter-based photographs as ground truth. For the quality assessment, we investigate the probability of detection (POD) and the positive predictive value (PPV). Additionally, we relate our results to conditions which potentially influence avalanche detection in the satellite imagery. We statistically confirm the high potential of SPOT for comprehensive avalanche mapping for selected periods (POD = 0.74, PPV = 0.88) as well as the reliability of Sentinel-1 (POD = 0.27, PPV = 0.87) for which the POD is reduced because mainly larger avalanches are mapped. Furthermore, we found that Sentinel-2 is unsuitable for the mapping of most avalanches due to its spatial resolution (POD = 0.06, PPV = 0.81). Because we could apply the same reference avalanche events for all three satellite mappings, our validation results are robust and comparable. We demonstrate that satellite-based avalanche mapping has the potential to fill the existing avalanche documentation gap over large areas, making alpine regions safer.

Scaling of causal neural avalanches in a neutral model

Neural avalanches are collective firings of neurons that exhibit emergent scale-free behavior. Understanding the nature and distribution of these avalanches is an important element in understanding how the brain functions. We study a model of neural avalanches for which the dynamics are governed by neutral theory. The neural avalanches are defined using causal connections between the firing neurons. We analyze the scaling of causal neural avalanches as the critical point is approached from the absorbing phase. By using cluster analysis tools from percolation theory, we characterize the critical properties of the neural avalanches. We identify the tuning parameters consistent with experiments. The scaling hypothesis provides a unified explanation of the power laws which characterize the critical point. The critical exponents characterizing the avalanche distributions and divergence of the response functions are consistent with the predictions of the scaling hypothesis. We use a universal scaling function for the avalanche profile to find that the firing rates for avalanches of different durations show data collapse after appropriate rescaling. We also find data collapse for the avalanche distribution functions, which is stronger evidence of criticality than just the existence of power laws. Critical slowing-down and power law relaxation of avalanches is observed as the system is tuned to its critical point. We discuss how our results motivate future empirical studies of criticality in the brain.

Emergence of Log-Normal Type Distributions in Avalanche Processes in Living Systems: A Network Model

Actin is the major cytoskeletal protein of mammal cells that forms microfilaments organized into higher-order structures by a dynamic assembly-disassembly mechanism with cross-linkers. These networks provide the cells with mechanical support, and allow cells to change their shape, migrate, divide and develop a mechanical communication with their environment. The quick adaptation of these networks upon stretch or compression is important for cell survival in real situations. Using atomic force microscopy to poke living cells with sharp tips, we revealed that they respond to a local and quick shear through a cascade of random and abrupt ruptures of their cytoskeleton, suggesting that they behave as a quasi-rigid random network of intertwined filaments. Surprisingly, the distribution of the strength and the size of these rupture events did not follow power-law statistics but log-normal statistics, suggesting that the mechanics of living cells would not fit into self-organized critical systems. We propose a random Gilbert network to model a cell cytoskeleton, identifying the network nodes as the actin filaments, and its links as the actin cross-linkers. We study mainly two versions of avalanches. First, we do not include the fractional visco-elasticity of living cells, assuming that the ruptures are instantaneous, and we observe three avalanche regimes, 1) a regime where avalanches are rapidly interrupted, and their size follows a distribution decaying faster than a power-law; 2) an explosive regime with avalanches of large size where the whole network is damaged and 3) an intermediate regime where the avalanche distribution goes from a power-law, at the critical point, to a distribution containing both 1) and (ii). Then, we introduce a time varying breaking probability, to include the fractional visco-elasticity of living cells, and recover an approximated log-normal distribution of avalanche sizes, similar to those observed in experiments. Our simulations show that the log-normal statistics requires two simple ingredients: a random network without characteristic length scale, and a breaking rule capturing the broadly observed visco-elasticity of living cells. This work paves the way for future applications to large populations of non-linear individual elements (brain, heart, epidemics, … ) where similar log-normal statistics have also been observed.