Landslides on sandpiles: Some moment relations in one dimension

Several relations between the structure of stable recurrent states and the statistics of avalanches in a one-dimensional sandpile automaton are derived and numerically verified. In particular, it is shown that the average avalanche size is determined by the second rather than the first moment of the distribution of trough distances. The two moments scale differently with system size, which implies multiscaling for the distribution. Moreover, the scaling of edge events (avalanches which fall off the pile) is shown to differ from that of bulk events (avalanches which remain on the pile).     

Characteristic length scale of avalanches in propagating interfaces

A new method for evaluating a characteristic length scale of avalanches in propagating interfaces is presented. The method was applied to propagation of crystalline Al interface into amorphous Al:Ge binary crystal. The results are in agreement with results from direct measurements of the avalanches’ size.     

Equivalence of the train model of earthquake and boundary driven Edwards-Wilkinson interface

A discretized version of the Burridge-Knopoff train model with (non-linear friction force replaced by) random pinning is studied in one and two dimensions. A scale free distribution of avalanches and the Omori law type behaviour for after-shocks are obtained. The avalanche dynamics of this model becomes precisely similar (identical exponent values) to the Edwards-Wilkinson (EW) model of interface propagation. It also allows the complimentary observation of depinning velocity growth (with exponent value identical with that for EW model) in this train model and Omori law behaviour of after-shock (depinning) avalanches in the EW model.     

Characterizing the Flowability of a Powder Using the Concepts of Fractal Geometry and Chaos Theory

Avalanching powder is a non-linear system which falls within a branch of the modern science known as deterministic chaos. The pattern of events generated by an avalanching powder can be described using the concepts of fractal geometry. The basic theory of these new techniques for characterizing the flowability of a powder by avalanching studies is outlined. Two different instruments: a ramp for flow studies and a rotating disc for studying avalanches are described. Data characterizing the effect of particle size, humidity, and flowagents on the flowability of powders is presented. The usefulness of angle of repose measurements is discussed.     

Signal Processing and Analysis Applied to Powder Behavior in a Rotating Drum

Previous studies of the flow of granular materials in a rotating drum have described the observed time sequences of angle of repose or time to avalanche. The time between avalanches approach has been incorporated into a commercially available powder flow analysis tool. In the present study, the time to avalanche analysis was complemented with a Fourier Transform power spectrum and phase space analysis of the angle of repose time series and avalanche size variability determination. The avalanche size variability approach was found to most readily differentiate between the flow properties of powders across material types. A model was constructed to provide an explanation for the utility of this method.     

Are there “dragon-kings” events (i.e. genuine outliers) among extreme avalanches?

Predicting the occurrence and spatial extent of extreme avalanches is a longstanding issue. Using field data pooled from various sites within the same mountain range, authors showed that the avalanche size distribution can be described using either an extreme value distribution or a thick-tailed distribution, which implies that although they are much larger than common avalanches, extreme avalanches belong to the same population of events as “small” avalanches. Yet, when looking at historical records of catastrophic avalanches, archives reveal that a few avalanches had features that made them “extra-ordinary.” Applying avalanche-dynamics or statistical models to simulate these past events runs into considerable difficulty since the model parameters or the statical properties are very different from the values usually set to model extreme avalanches. Were these events genuine outliers (also called “dragon-kings”)? What were their distinctive features? This paper reviews some of the concepts in use to model extreme events, gives examples of processes that were at play in extreme avalanches, and shows that the concept of dragon-king avalanches is of particular relevance to describing some extreme avalanches.     

Self-organized criticality in a nutshell

In order to gain insight into the nature of self-organized criticality (SOC), we present a minimal model exhibiting this phenomenon. In this analytically solvable model, the state of the system is fully described by a single-integer variable. The system organizes in its critical state without external tuning. We derive analytically the probability distribution of durations of disturbances propagating through the system. As required by SOC, this distribution is scale invariant and follows a power law over several orders of magnitude. Our solution also reproduces the exponential tail of the distribution due to finite size effects. Moreover, we show that large avalanches are suppressed when stabilizing the system in its critical state. Interestingly, avalanches are affected in a similar way when driving the system away from the critical state. With this model, we have reduced SOC dynamics to a leveling process as described by Ehrenfest's famous flea model.     

Avalanches and Self-Organized Criticality in superconductors

We review the use of superconductors as a playground for the experimental study of front roughening and avalanches. Using the magneto-optical technique, the spatial distribution of the vortex density in the sample is monitored as a function of time. The roughness and growth exponents corresponding to the vortex `landscape' are determined and compared to the exponents that characterize the avalanches in the framework of Self-Organized Criticality. For those situations where a thermo-magnetic instability arises, an analytical non-linear and non-local model is discussed, which is found to be consistent to great detail with the experimental results. On anisotropic substrates, the anisotropy regularizes the avalanches.     

Effect of the link lifetime in a dynamical lattice on the properties of the avalanche processes on it

The properties of the avalanche processes that develop on a dynamical lattice, the structure of links in which changes due to a specific characteristic of each lattice node, namely, its “activity,” which determines the probability of connection of a certain node with neighboring nodes in one step of lattice evolution. The statistics of the sizes of the avalanches appearing in the lattice system is studied as a function of the node activity and the link lifetime (the lifetime of the links formed in the system). It is analytically and numerically shows that the type of avalanche dynamics in the system changes as a function of these parameters. The following three regimes can take place in the system: (1) avalanches of any sizes, from small to catastrophic, can appear, which is reflected in the power-law behavior of the probability density function of the appearance of avalanches of certain sizes; (2) avalanches of a certain average size mainly appear in the system, and the probability density is close to that of a normal distribution; and (3) transient regime, where the probability density function of the appearance of avalanches of certain sizes is close to an exponential function. These results open up the possibilities of controlling the behavior of a complex system; in particular, they can be used to prevent catastrophic avalanches by changing the link lifetime and the average node activity.     

Numerical simulation of corona discharge in N2

A numerical study of a negative corona discharge in nitrogen in a point-plane gap using a Monte Carlo method is presented. The simulation provides a detailed structure of avalanches, propagation of successive avalanches and ion distribution can be discerned. The development of electron avalanches is due to ionization and photoionization in the high-field region, while the quenching of the avalanches is due to the low electric field near the plane electrode. Also the accumulation of electrons and positive ions are displayed in detail. The space charge field distortion is studied.     

Universal phenomenon of self-organized criticality in magnetic flux dynamics

Magnetization curves of square arrays of Josephson junctions of two basic types were investigated: superconductor–insulator–superconductor (SIS) and superconductor–normal metal–superconductor (SNS).

Magnetic flux avalanches were observed in SIS arrays. A statistical analysis of flux avalanches showed that their size distribution can be described by a power law with a crossover where the exponent n varies from −1.2 for small avalanches to −3.5 for the large ones. Such a behavior of avalanches is interpreted as the self-organized criticality (SOC) manifestation. In SNS arrays, the flux avalanches were not observed, but a considerable asymmetry of a hysteresis curve was revealed.     

A reproducible test to characterise the triboelectric charging of powders during their pneumatic transport

Although several investigations had been carried out to explore the triboelectrification of powders, only few data are available on the experimental procedures and set-ups required to obtain reliable data. The present study deals with the development of a pneumatic test to characterise the tribocharging of fine powders. An experimental device was set up allowing on-line monitoring of the charge of both particles and transport pipes. Experiments were carried out using two types of powder (fine sugar and PVC) coupled with two types of pipe materials (Teflon and nylon). Results showed the extreme importance of the control of the relative humidity, the initial charge of particles and the charge dissipation of the walls to obtain pertinent data. Furthermore, the results showed that solids loadings higher than 1 (kg of solids/kg of air) are not proper to achieve reliable measurements. However, at very dilute solids loading (～0.001) the time evolutions of the electrostatic charge and the mass of the powder follow similar trends so that the tribocharging becomes independent of the solids mass flowrate. This allows accurate assessment of the tribocharging of cohesive powders for which a regular flow cannot be guaranteed.     

Driftgeschwindigkeiten von Ionen und Elektronen in Argon und Wasserstoff

Short light sparks release 10 nsec pulses of 10⁵ electrons each which initiate electron avalanches in high-purity argon and hydrogen. The transit times of the avalanches are measured and thus the drift velocities of ions and electrons derived. — There is general agreement with available results of other authors.     

Diffusion dominated dynamics of avalanching systems

A surprisingly large number of systems in nature are thought to be governed by internal dynamics which causes avalanches of various sizes. In such systems energy, which is delivered from outside, is redistributed as a result of the occurrence of localized avalanches. Starting an avalanche requires that some threshold condition be satisfied. Random driving (energy input) brings the system into a strongly inhomogeneous state, so that the probability of triggering an avalanche in a large part of the system is small. In most physical systems energy redistribution may occur due to diffusive processes without avalanches. Diffusion also makes the system more uniform, making large avalanche triggering more probable. The observed behavior of a such system may crucially depend on the competition between diffusion and driving. In this paper, the effects of diffusive processes are investigated using a dissipative, isotropic one-dimensional model, in which avalanches can propagate in both directions. It is shown that the system behavior changes progressively as the diffusion rate increases. In the absence of diffusion, many small avalanches are triggered. Increasing the diffusion rate gradually suppresses these small avalanches and leads to the development of large, quasi-periodic bursts.     

A branching process model for sand avalanches

An analytically solvable model for sand avalanches of noninteracting grains of sand, based on the Chapman-Kolmogorov equations, is presented. For a single avalanche, distributions of lifetimes, sizes of overflows and avalanches, and correlation functions are calculated. Some of these are exponentials, some are power laws. Spatially homogeneous distributions of avalanches are also studied. Computer simulations of avalanches of interacting grains of sand are compared to the solutions to the Chapman-Kolmogorov equations. We find that within the range of parameters explored in the simulation, the approximation of noninteracting grains of sand is a good one.     

Strain Avalanches in Microsized Single Crystals:A Theoretical Study of the Relation between the Avalanche Size and Duration

Single crystal micropillars deform via a sequence of discrete strain avalanches,observed as displacement jumps or stress drops.Here we develop a simple crystal plasticity model to provide a quantitative expression of the relation between avalanche duration and avalanche size.It is found that the avalanche durations in scale with the averaged avalanche sizes only hold for those larger magnitudes.We show that the theoretical predictions are capable of capturing the essential aspects of scaling behaviors from micro-compression tests.     

Criticality in a simple model for brain functioning

We introduce a simple model for a set of interacting idealized neurons. The model presents a self-organized state in which avalanches of all sizes are observed and activity is detected in the whole extension of the simulated system without a typical length scale. The basic elements of the model are endowed with the main features of a neuron function. On this basis it is speculated that the collective system that they form, i.e., the brain, could display self-organized criticality in some situations.     

Superfluid Avalanches in Nuclepore: Constrained versus Free-Boundary Experiments and Simulations

Superfluid 4He exhibits hysteretic behavior in the percolated nanoporous material Nuclepore during the filling and draining of pores due to capillary condensation, and one observes avalanches during the pore draining. We observe that the size and frequency of the avalanches depend upon whether the fluid flow off the substrate during draining is impeded or unimpeded. We simulate the draining of superfluid 4He from Nuclepore with and without a perturbation of the pore menisci and find results similar to the results seen in the experiments in the presence or the absence of flow inhibition.     

Preparation of well-adhered γ-Al2O3 washcoat on metallic wire mesh monoliths by electrophoretic deposition

Washcoat deposited on metallic wire mesh monoliths was prepared using γ-alumina powders by electrophoretic deposition under a relatively low electric voltage. The microstructure, phase structure and adhesion of washcoat were investigated by SEM, XRD, ultrasonic vibration and thermal shock. The results showed that the loading and adhesion of washcoat were affected obviously by the properties of suspension, such as the zeta potential and the amount of adding binders. A small quantity of aluminum isopropoxide could promote the cohesive affinity of washcoat in thermal shock. The adhesion of washcoat in ultrasonic vibration could be reinforced by increasing calcined temperature and adding a certain aluminum particles. It was also found that the washcoat immersed metal nitrate has excellent vibration-resistant ability.