Avalanche prediction in a self-organized pile of beads

Dilation as a precursor in a continuous granular fault

We analyze the dilation of the system in a cylindrical granular fault consisting of one single layer of disks submitted to both normal pressure and continuous and slow shear, which results in intermittent and sudden energy release events that reproduce the main laws of seismicity. The dilation of the system can be separated into two parts: a smooth increase of dilation, plus sudden changes both contracting and dilating the medium, which are correlated to abrupt jumps -both positive and negative- in the measured resisting torque. We explain the four possible (and existing) general scenarios combining those two variables: dilation jumps and torque jumps, thanks to the assumption of an optimal local angle in the direction of force chains, and each reorganization of the structure as a replacement of the force chain holding most of the applied stress. The average rate of increase of global dilation varies monotonically with the size of the energy release event, making dilation a plausible candidate to predict catastrophic events in such earthquake-like systems.

Acoustic localisation in a two-dimensional granular medium

We focus on localizing the source of acoustic emissions within a compressed two-dimensional granular ensemble of photoelastic disks, having as main information the arrival times of the acoustic signal to 6 sensors located in the boundaries of the system. By estimating, thanks to the photoelasticity of the grains, the wave speed at every point of the structure, we are able to compute the arrival times from every point of the system to the sensors. A comparison between the arrival time differences between every set of computed values to those from the actual measurements allows finding the source of the acoustic emissions.

The scale-invariant, temporal profile of neuronal avalanches in relation to cortical γ-oscillations

Activity cascades are found in many complex systems. In the cortex, they arise in the form of neuronal avalanches that capture ongoing and evoked neuronal activities at many spatial and temporal scales. The scale-invariant nature of avalanches suggests that the brain is in a critical state, yet predictions from critical theory on the temporal unfolding of avalanches have yet to be confirmed in vivo. Here we show in awake nonhuman primates that the temporal profile of avalanches follows a symmetrical, inverted parabola spanning up to hundreds of milliseconds. This parabola constrains how avalanches initiate locally, extend spatially and shrink as they evolve in time. Importantly, parabolas of different durations can be collapsed with a scaling exponent close to 2 supporting critical generational models of neuronal avalanches. Spontaneously emerging, transient γ-oscillations coexist with and modulate these avalanche parabolas thereby providing a temporal segmentation to inherently scale-invariant, critical dynamics. Our results identify avalanches and oscillations as dual principles in the temporal organization of brain activity.

Self-organization of dragon king failures

The mechanisms underlying cascading failures are often modeled via the paradigm of self-organized criticality. Here we introduce a simple network model where nodes self-organize to be either weakly or strongly protected against failure in a manner that captures the trade-off between degradation and reinforcement of nodes inherent in many network systems. If strong nodes cannot fail, any failure is contained to a single, isolated cluster of weak nodes and the model produces power-law distributions of failure sizes. We classify the large, rare events that involve the failure of only a single cluster as "black swans." In contrast, if strong nodes fail once a sufficient fraction of their neighbors fail, then failure can cascade across multiple clusters of weak nodes. If over 99.9% of the nodes fail due to this cluster hopping mechanism, we classify this as a "dragon king," which are massive failures caused by mechanisms distinct from smaller failures. The dragon kings observed are self-organized, existing over a wide range of reinforcement rates and system sizes. We find that once an initial cluster of failing weak nodes is above a critical size, the dragon king mechanism kicks in, leading to piggybacking system-wide failures. We demonstrate that the size of the initial failed weak cluster predicts the likelihood of a dragon king event with high accuracy and we develop a simple control strategy that can dramatically reduce dragon kings and other large failures.

Attenuation of pressure dips underneath piles of spherocylinders

The discrete element method (DEM) was used to simulate the piling of rod-like (elongated sphero-cylindrical) particles, mainly focusing on the effect of particle shape on the structural and force properties of the piles. In this work, rod-like particles of different aspect ratios were discharged on a flat surface to form wedge-shaped piles. The surface properties of the piles were characterized in terms of angle of repose and stress at the bottom of the piles. The results showed that the rise of the angle of repose became slower with the increase of particle aspect ratio. The pressure dip underneath the piles reached the maximum when the particle aspect ratio was around 1.6, beyond which the pressure dip phenomenon became attenuated. Both the pressure dip and the shear stress dip were quantitatively examined. The structure and forces inside the piles were further analyzed to understand the change in pressure dip, indicating that "bridging" or "arching" structures within the piles were the cause of the pressure dip.

Reorganization of a granular medium around a localized transformation

Physical and chemical transformation processes in reactive granular media involve the reorganization of the structure. In this paper, we study experimentally the rearrangements of a two-dimensional (2D) granular packing undergoing a localized transformation. We track the position and evolution of all the disks that constitute the granular packing when either a large intruder shrinks in size or is pulled out of the granular structure. In the two situations the displacements at long time are similar to 2D quasistatic silo flows whereas the short-time dynamic is heterogeneous in both space and time. We observe an avalanchelike behavior with power-law distributed events uncorrelated in time. In addition, the instantaneous evolutions of the local solid fraction exhibit self-similar distributions. The averages and the standard deviations of the solid fraction variations can be rescaled, suggesting a single mechanism of rearrangement.

Avalanche structural rearrangement through cracking-healing in weakly stressed cold dusty plasma liquids

We experimentally investigate the spatiotemporal dynamical behaviors of the avalanche structural rearrangement through micro-cracking-healing in weakly stressed cold dusty plasma liquids, and the kinetic origins for their different spatial and temporal classifications. The crystalline ordered domains can be cracked or temporarily sustain and transfer the weak stress to remote regions for cracking-healing. It is found that cracking sites form a fractal network with cluster size following power law distribution in the xyt space. The histograms of the persistent times for sustaining regional ordered and disordered structure, the temporal cracking burst width, and quiescent time between two bursts all follow power law decays with fast descending tails. Cracking can be classified into a single temporal burst with simple line like spatial patterns and the successive cracking fluctuation with densely packed cracking clusters. For an ordered region, whether the Burgers vectors of the incoming dislocations from the boundary allow direct dislocation reduction is the key for the above two classifications through cracking a large ordered domain into medium scale corotating ordered domains or small patches. The low regional structural order at the end of a cracking burst can be regarded as an alarm for predicting the short quiescent period before the next cracking burst.

Granular chaos and mixing: Whirled in a grain of sand

In this paper, we overview examples of chaos in granular flows. We begin by reviewing several remarkable behaviors that have intrigued researchers over the past few decades, and we then focus on three areas in which chaos plays an intrinsic role in granular behavior. First, we discuss pattern formation in vibrated beds, which we show is a direct result of chaotic scattering combined with dynamical dissipation. Next, we consider stick-slip motion, which involves chaotic scattering on the micro-scale, and which results in complex and as yet unexplained peculiarities on the macro-scale. Finally, we examine granular mixing, which we show combines micro-scale chaotic scattering and macro-scale stick-slip motion into behaviors that are well described by dynamical systems tools, such as iterative mappings.

Fluctuations of particle motion in granular avalanches - from the microscopic to the macroscopic scales

In this study, we have investigated the fluctuations of particle motion, i.e. the non-affine motion, during the avalanche process, discovering a rich dynamic from the microscopic to the macroscopic scales. We find that there is a strong correlation between the magnitude of the velocity fluctuation and the velocity magnitude in the spatial and temporal domains. The possible connection between this finding and the theory of the shear transformation zones is discussed based on the direct measurement of the T1 events. In addition, the velocity magnitude of the system and the stress fluctuations of the system are strongly temporally correlated. Our finding will pose challenges to the development of more rigorous theories to describe avalanche dynamics based on the microscopic approach. Moreover, our finding presents a plausible mechanism of particle entrainment in a simple system.

Spatiotemporal chaotic unjamming and jamming in granular avalanches

We have investigated the spatiotemporal chaotic dynamics of unjamming and jamming of particles in a model experiment – a rotating drum partially filled with bidisperse disks to create avalanches. The magnitudes of the first Lyapunov vector δu(t) and velocity v(t) of particles are directly measured for the first time to yield insights into their spatial correlation C_δu,v, which is on statistical average slightly larger near the unjamming than the value near the jamming transition. These results are consistent with the recent work of Banigan et al (Nature Phys. 2013), and it is for the first time to validate their theoretical models in a real scenario. v(t) shows rich dynamics: it grows exponentially for unstable particles and keeps increasing despite stochastic interactions; after the maximum, it decays with large fluctuations. Hence the spatiotemporal chaotic dynamics of avalanche particles are entangled, causing temporal correlations of macroscopic quantities of the system. We propose a simple model for these observations.

Revealing the structure of a granular medium through ballistic sound propagation

We study the propagation of sound through a bidimensional granular medium consisting of photoelastic disks, which are packed into different crystalline and disordered structures. Acoustic sensors placed at the boundaries of the system capture the acoustic signal produced by a local and well-controlled mechanical excitation. By compressing the system, we find that the speed of the ballistic part of the acoustic wave behaves as a power law of the applied force with both exponent and prefactor sensitive to the internal geometry of the contact network. This information, which we are able to link to the force-deformation relation of single grains under different contact geometries, provides enough information to reveal the structure of the granular medium.

Correlating structural order with structural rearrangement in dusty plasma liquids: can structural rearrangement be predicted by static structural information?

Whether the static microstructural order information is strongly correlated with the subsequent structural rearrangement (SR) and their predicting power for SR are investigated experimentally in the quenched dusty plasma liquid with microheterogeneities. The poor local structural order is found to be a good alarm to identify the soft spot and predict the short term SR. For the site with good structural order, the persistent time for sustaining the structural memory until SR has a large mean value but a broad distribution. The deviation of the local structural order from that averaged over nearest neighbors serves as a good second alarm to further sort out the short time SR sites. It has the similar sorting power to that using the temporal fluctuation of the local structural order over a small time interval.

Electrostatic precursors to granular slip events

It has been known for over a century that electrical signals are produced by material failure, for example during crack formation of crystals and glasses, or stick-slip motion of liquid mercury on glass. We describe here new experiments revealing that slip events in cohesive powders also produce electrical signals, and remarkably these signals can appear significantly in advance of slip events. We have confirmed this effect in two different experimental systems and using two common powdered materials, and in a third experiment we have demonstrated that similar voltage signals are produced by crack-like defects in several powdered materials.

Predictability of the coherent-noise model and its applications

We study the threshold distribution function of the coherent-noise model for the case of infinite number of agents. This function is piecewise constant with a finite number of steps n. The latter exhibits a 1/f behavior as a function of the order of occurrence of an avalanche and hence versus natural time. An analytic expression of the expectation value E(S) for the size S of the next avalanche is obtained and used for the prediction of the next avalanche. Apart from E(S), the number of steps n can also serve for this purpose. This enables the construction of a similar prediction scheme which can be applied to real earthquake aftershock data.

Catastrophic regime in the discharge of a granular pile

We present a molecular-dynamics study of discharges in a granular pile evincing a catastrophic regime depending on the outlet size. The avalanche size distribution function suggests a phase transition where the height of the remaining pile is taken as the order parameter. Our results indicate that there is a critical outlet size beyond which discharges become catastrophic and the initial pile is split in two minor piles. As the system size increases, finite-size analysis indicates that the critical orifice width converges to a finite value.

Controlling self-organized criticality in sandpile models

We introduce an external control to reduce the size of avalanches in some sandpile models exhibiting self-organized criticality. This rather intuitive approach seems to be missing in the vast literature on such systems. The control action, which amounts to triggering avalanches in sites that are near to become critical, reduces the probability of very large events, so that energy dissipation occurs most locally. The control is applied to a directed Abelian sandpile model driven by both uncorrelated and correlated depositions. The latter is essential to design an efficient and simple control heuristic, but has only small influence in the uncontrolled avalanche probability distribution. The proposed control seeks a trade-off between control cost and large event risk. Preliminary results hint that the proposed control works also for an undirected sandpile model.

Predicting extreme avalanches in self-organized critical sandpiles

In a finite-size Abelian sandpile model, extreme avalanches are repelling each other. Taking a time series of the avalanche size and using a decision variable derived from that, we predict the occurrence of a particularly large avalanche in the next time step. The larger the magnitude of these target avalanches, the better is their predictability. The predictability which is based on a finite-size effect, is discussed as a function of the system size.