Intermittent granular flow and clogging with internal avalanches

The dynamics of intermittent granular flow through an orifice at the bottom of a granular bin and the associated clogging due to formation of arches blocking the outlet, is studied numerically in two dimensions. When the hole size is less than the grain diameter, only a single grain is removed from the system so that the system self-organizes to a steady state and the distribution of the grain displacements decays as power laws. On the other hand, when hole sizes are within few times of the grain diameter, the outflow distributions are also observed to follow a power law. Received 21 July 1999 and Received in final form 17 September 1999     

Statistics of avalanches in the self-organized criticality state of a Josephson junction

Magnetic flux avalanches in Josephson junctions that include superconductor-insulator-superconductor (SIS) tunnel junctions and are magnetized at temperatures lower than approximately 5 K have been studied in detail. Avalanches are of stochastic character and appear when the magnetic field penetration depth λ into a junction becomes equal to the length a of the Josephson junction with a decrease in the temperature. The statistical properties of such avalanches are presented. The size distribution of the avalanches is a power law with a negative noninteger exponent about unity, indicating the self-organized criticality state. The self-organized criticality state is not observed in Josephson junctions with a superconductor-normal metal-superconductor (SNS) junction.     

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.     

Granular avalanches in fluids

Three regimes of granular avalanches in fluids are put in light depending on the Stokes number St which prescribes the relative importance of grain inertia and fluid viscous effects and on the grain/fluid density ratio r. In gas (r>1 and St>1, e.g., the dry case), the amplitude and time duration of avalanches do not depend on any fluid effect. In liquids (r approximately 1), for decreasing St, the amplitude decreases and the time duration increases, exploring an inertial regime and a viscous regime. These three regimes are described by the analysis of the elementary motion of one grain.     

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.     

From the stress response function (back) to the sand pile “dip”

We relate the pressure dip observed at the bottom of a sand pile prepared by successive avalanches to the stress profile obtained on sheared granular layers in response to a localized vertical overload. We show that, within a simple anisotropic elastic analysis, the skewness and the tilt of the response profile caused by shearing provide a qualitative agreement with the sand pile dip effect. We conclude that the texture anisotropy produced by the avalanches is in essence similar to that induced by a simple shearing --albeit tilted by the angle of repose of the pile. This work also shows that this response function technique could be very well adapted to probe the texture of static granular packing.     

Avalanches in a nonlinear oscillator chain in a periodic potential

We consider the dynamics of a chain of coupled units evolving in a periodic substrate potential. The chain is initially in a flat state and situated in a potential well. A bias force, acting as a weak driving mechanism, is applied at a single unit of the chain. We study the instigation of directed transport in two types of system: (i) a microcanonical situation associated with deterministic and conservative dynamics and (ii) the Langevin dynamics when the system is in contact with a heat bath. Interestingly, for the deterministic and conservative dynamics the directed transport is drastically enhanced compared with its Langevin counterpart. In particular, in the deterministic and conservative regime a self-organised redistribution of energy triggers huge-sized avalanches yielding ultimately accelerated transport of the chain. In contrast, in the thermally-assisted process between avalanches the chain settles always into a pinned metastable state impeding continual accelerated chain motion.     

Avalanche dynamics of magnetic flux in a two-dimensional discrete superconductor

The critical state of a two-dimensional discrete superconductor in an external magnetic field is studied. This state is found to be self-organized in the generalized sense, i.e., is a set of metastable states that transform to each other by means of avalanches. An avalanche is characterized by the penetration of a magnetic flux to the system. The sizes of the occurring avalanches, i.e., changes in the magnetic flux, exhibit the power-law distribution. It is also shown that the size of the avalanche occurring in the critical state and the external magnetic field causing its change are statistically independent quantities.     

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.     

一种颗粒底部压力不趋向饱和的粮仓系统

随着深度的增加竖直圆筒容器中的颗粒物质会把自己的重量逐渐转移到容器的侧墙壁上,使容器底部的压力出现不随筒中颗粒材料高度的增加而增加的饱和现象.但值得注意的是,圆筒中的颗粒柱体并不总是表现为这个称为粮仓效应的力学状态.例如当改变侧墙壁的力学环境使其无法承担颗粒的重量时,柱底部的压力显然将随其高度的增加而线性地增加.本文分析讨论了Janssen模型假设对这类处于静力平衡下,但违反粮仓效应的颗粒系统的行为预测. 关键词： 颗粒物质 粮仓 静摩擦 应力     

Laboratory singing sand avalanches

Some desert sand dunes have the peculiar ability to emit a loud sound up to 110 dB, with a well-defined frequency: this phenomenon, known since early travelers (Darwin, Marco Polo, etc.), has been called the song of dunes. But only in late 19th century scientific observations were made, showing three important characteristics of singing dunes: first, not all dunes sing, but all the singing dunes are composed of dry and well-sorted sand; second, this sound occurs spontaneously during avalanches on a slip face; third this is not the only way to produce sound with this sand.More recent field observations have shown that during avalanches, the sound frequency does not depend on the dune size or shape, but on the grain diameter only, and scales as the square root of g/d - with g the gravity and d the diameter of the grains - explaining why all the singing dunes in the same vicinity sing at the same frequency.We have been able to reproduce these singing avalanches in laboratory on a hard plate, which made possible to study them more accurately than on the field. Signals of accelerometers at the flowing surface of the avalanche are compared to signals of microphones placed above, and it evidences a very strong vibration of the flowing layer at the same frequency as on the field, responsible for the emission of sound.Moreover, other characteristics of the booming dunes are reproduced and analyzed, such as a threshold under which no sound is produced, or beats in the sound that appears when the flow is too large. Finally, the size of the coherence zones emitting sound has been measured and discussed.     

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.     

Finite-size effects on the statistics of extreme events in the BTW model

The BTW Abelian sandpile model is a prominent example of systems showing self-organised criticality (SOC) in the infinite size limit. We study finite-size effects with special focus on the statistics of extreme events, i.e., of particularly large avalanches. Not only the avalanche size probability distribution, but also the mutual independence of large avalanches in the critical state is affected by finite-size effects. Instead of a Poissonian recurrencetime distribution, in the finite system we find a repulsion of extreme events that depends on the avalanche size and not on the respective probability. The dependence of these effects on the system size is investigated and some data collapse is found. Our results imply that SOC is an unsuitable mechanism for the explanation of extreme events which occur in clusters.     

Crossover behavior in burst avalanches: signature of imminent failure

The statistics of damage avalanches during a failure process typically follows a power law. When these avalanches are recorded only near the point at which the system fails catastrophically, one finds that the power law has an exponent which is different from that one finds if the recording of events starts away from the vicinity of catastrophic failure. We demonstrate this analytically for bundles of many fibers, with statistically distributed breakdown thresholds for the individual fibers and where the load is uniformly distributed among the surviving fibers. In this case the distribution D(Delta) of the avalanches (Delta) follows the power law Delta-xi with xi=3/2 near catastrophic failure and xi=5/2 away from it. We also study numerically square networks of electrical fuses and find xi=2.0 near catastrophic failure and xi=3.0 away from it. We propose that this crossover in xi may be used as a signal of imminent failure.     

From a grain to avalanches: on the physics of granular surface flows

Granular surface flows have still to be fully modelled. Analysing the motion of a single grain can already help us to understand the physical origin of several characteristic angles (starting, stopping, jumping angles). Then looking at layers of grains allows the inference of the velocity profile inside the flowing layer, and the physical origin of the flow depth selection. Then these results can be plugged into a general model of mass and momentum conservation integrated vertically (St-Venant). This model can be tested on stationary flows, but also on transients, such as avalanches. To cite this article: S. Douady et al., C. R. Physique 3 (2002) 177–186.     

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.     

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.     

Large scale structures, symmetry, and universality in sandpiles

We introduce a sandpile model where, at each unstable site, all grains are transferred randomly to downstream neighbors. The model is local and conservative, but not Abelian. This does not appear to change the universality class for the avalanches in the self-organized critical state. It does, however, introduce long-range spatial correlations within the metastable states. For the transverse direction d(perpendicular)>0, we find a fractal network of occupied sites, whose density vanishes as a power law with distance into the sandpile.     

Influence of the modulating interfacial state on Sr2FeMoO6 powder magnetoresistance properties

In this paper, we studied the effects of the modulating interfacial state, which was introduced by mechanical ball milling, on the magnetoresistance (MR) properties of Sr₂FeMoO₆ polycrystalline material. The X-ray diffraction analysis showed that the crystal structure of Sr₂FeMoO₆ polycrystalline material was not changed in the process of ball milling, but the SrMoO₄ impurity phase was introduced at grain boundaries, and its quantity increased with the milling time. The results of resistance measurements at different temperatures indicated that ball milling had a very important influence on the MR properties. At due to the enhancement of the tunneling among adjacent grains by introducing the insulating SrMoO₄ phase at grain boundaries, the MR was enhanced with increasing the milling time. However, at the MR decreased rapidly with the increase in milling time. This phenomenon was mainly caused by the inelastic hopping of electrons through the localized states introduced at grain boundaries.