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Geometrical properties of avalanches in self-organized critical models of solar flares.

We investigate the geometrical properties of avalanches in self-organized critical models of solar flares. Traditionally, such models differ from the classical sandpile model in their formulation of stability criteria in terms of the curvature of the nodal field, and belong to a distinct universality class. With a view toward comparing these properties to those inferred from spatially and temporally resolved flare observations, we consider the properties of avalanche peak snapshots, time-integrated avalanches in two and three dimensions, and the two-dimensional projections of the latter. The nature of the relationship between the avalanching volume and its projected area is an issue of particular interest in the solar flare context. Using our simulation results we investigate this relationship, and demonstrate that proper accounting of the fractal nature of avalanches can bring into agreement hitherto discrepant results of observational analyses based on simple, nonfractal geometries for the flaring volume.

Journal Article↗

Cohesion-induced deepening transition of avalanches.

A directed avalanche model with a control parameter is introduced to describe the transition between cohesive and noncohesive granular material. The underlying dynamics of the process can be mapped to interface growth model. In that representation, a continuous phase transition separates the rough phase and the flat phase. In the avalanche formulation, this corresponds to a transition from deep to shallow avalanches. The scaling exponents of the avalanches indeed follow those of the underlying interface growth in both phases and at the transition point. However, the mass hyperscaling relation is broken at the transition point due to the fractal nature of the avalanche and a hierarchy of critical directed percolation processes.

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Kinetic description of avalanching systems.

Avalanching systems are treated analytically using the renormalization group (in the self-organized-criticality regime) or mean-field approximation, respectively. The latter describes the state in terms of the mean number of active and passive sites, without addressing the inhomogeneity in their distribution. This paper goes one step further by proposing a kinetic description of avalanching systems making use of the distribution function for clusters of active sites. We illustrate an application of the kinetic formalism to a model proposed for the description of the avalanching processes in the reconnecting current sheet of the Earth's magnetosphere. A description of avalanching systems is proposed that makes use of the distribution function for clusters of active sites. A general kinetic equation is derived that describes the temporal evolution of the distribution function, in terms of growth and shrinking probabilities. The distribution of clusters is derived for the stationary regime, for a quite general class of avalanching systems or arbitrary dimensionality. The approach, including the probability calculation, is illustrated by an application of the kinetic description to the recently proposed burning model.

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Electronic portal imaging with an avalanche-multiplication-based video camera.

The aim of this study is to investigate the degree to which the imaging quality of an existing (video-based) electronic portal imaging device (EPID) system may be improved by using an avalanche-multiplication-based video camera (called the avalanche-gain method). Due to avalanche multiplication in the target of the video camera tube, the new camera can be made up to several hundred times more sensitive than a camera using a conventional video (e.g., Saticon) tube. As a result, the camera noise which limits the performance of current video-based EPIDs should be overwhelmed and made negligible. The detective quantum efficiency (DQE) of an EPID using the avalanche-gain method has been measured with 6 MV and 18 MV beams obtained using a linear accelerator. It is shown that the camera noise is indeed much smaller than quantum noise and that the DQE of the system is significantly increased compared to conventional video-based EPIDs. Variation of DQE of the avalanche-gain video portal system with a change of demagnification was also investigated. It has been shown that the improvement of optical coupling has less effect in this system than that in a conventional video-based EPID system.

Humans↗

GPS signal reception under snow cover: a pilot study establishing the potential usefulness of GPS in avalanche search and rescue operations.

Avalanches are one of the major threats to life in high-mountain terrain and account every year for approximately 150 accidents causing injury or death in the United States alone. Every year avalanches cause significant property damages and a death toll of approximately 15 people in the United States. The specific characteristic of the avalanche accident is the extreme importance of getting to the buried victim as soon as, possible to improve survival. Approximately 40% of all buried victims survive 1 hour, and only about 20% survive 2 hours. Newer studies from Europe indicate that the initial survival probability is 92% at 15 minutes, 30% at 35 minutes, 27% at 90 minutes, and finally drops to 3% at 130 minutes. Unless prompt and efficient search and rescue are ensured, the prospect of buried victims is rather grim. Many tools have been used in the past to aid in retrieving buried victims including the avalanche cord, probing techniques, and in more recent time, the use of electronic beacon devices that allow search teams to locate the buried victim. The advent of satellite navigational aids (GPS, GLONASS) makes it possible to determine one's position with remarkable accuracy. We studied the degree to which the GPS satellite signal could penetrate through snow and be received by a commercially available GPS receiver. This information may lead to the development of an additional tool for precise and quick localization of buried victims in avalanche accidents and thus may substantially improve their survival by shortening the search time at the accident site. In this study we used a Motorola Traxar six-channel GPS receiver with amplifier unit connected to an antenna by means of a shielded coaxial cable. The antenna was buried under incremental covers of compact snow, and the reception of the GPS signal was measured at each burial depth: 5 cm, 15 cm, 25 cm, 35 cm, 45 cm, 55 cm, 1 m, and 1.5 m. The variables that were measured included signal quality, number of satellites received by the receiver, and their respective signal strength. A reference reading was taken from the GPS receiver above the testing site before measurements under snow cover were started. The satellite signals were received with good quality and precise readings up to a burial depth of 1 m. Under 1.5 m of snow the receiver was able to lock on only one satellite, making a positional reading impossible. The reception of the GPS signals under snow cover is possible and warrants further study directed toward the development of a search and rescue device using this technology.

Asphyxia↗

[Avalanche emergencies. Review of the current situation].

In North America and Europe around 140 persons die every year due to avalanches, approximately 35 in North America, 100 in the European Alps, and 5 in other parts of Europe. Most of the victims are skiers and snowboarders. This article outlines the specific pathophysiology of avalanche burials, such as hypoxia, hypercapnia, and hypothermia and also other factors which influence survival. Strategies to minimize the mortality due to avalanches and the on-site treatment of buried persons are discussed. Finally, possibilities to reduce the number of avalanche deaths are pointed out.

Avalanches↗

Hypoxia and hypercapnia during respiration into an artificial air pocket in snow: implications for avalanche survival.

Snow avalanche case reports have documented the survival of skiers apparently without permanent hypoxic sequelae, after prolonged complete burial despite there being only a small air pocket on extrication. We investigated the underlying pathophysiological changes in a prospective, randomised 2 x 2 crossover study in 12 volunteers (28 tests) breathing into an artificial air pocket (1- or 2-l volume) in snow. Peripheral SpO(2), ETCO(2), arterialised capillary blood variables, air pocket O(2) and CO(2), snow density, and snow conditions at the inner surface of the air pocket were determined. SpO(2) decreased from a median of 99% (93-100%) to 88% (71-94%; P<0.001) within 4 min of breathing into the air pocket; the reduction was greater at 1 l, than 2 l, volume air pocket (P=0.013, intention to treat P=0.003) and correlated to snow density (r=0.50, P=0.021, partial correlation coefficient). ETCO(2) rose simultaneously from median 5.07 kPa (3.47-6.93 kPa) to 6.8 kPa (5.87-8.27 kPa; P<0.001), with consequent respiratory acidosis. Despite premature interruption due to hypoxia (SpO(2)</=75%) in 17 of 28 tests (61%), a respiratory steady state prevailed in five tests until protocol completion (30 min). We conclude that the degree of hypoxia following avalanche burial is dependent on air pocket volume, snow density and unknown individual personal characteristics, yet long-term survival is possible with only a small air pocket. Hence, the definition of an air pocket, "any space surrounding mouth and nose with the proviso of free air passages" is validated as the main criterion for triage and management of avalanche victims. Our experimental model will facilitate evaluating the interrelation between volume and inner surface area of an air pocket for survival of avalanche victims, whilst the present findings have laid the basis for future investigation of possible interactions between hypoxia, hypercapnia, and hypothermia (triple H syndrome) in snow burial.

Accidents↗

Single p-type/intrinsic/n-type silicon nanowires as nanoscale avalanche photodetectors.

We report the controlled synthesis of axial modulation-doped p-type/intrinsic/n-type (p-i-n) silicon nanowires with uniform diameters and single-crystal structures. The p-i-n nanowires were grown in three sequential steps: in the presence of diborane for the p-type region, in the absence of chemical dopant sources for the middle segment, and in the presence of phosphine for the n-type region. The p-i-n nanowires were structurally characterized by transmission electron microscopy, and the spatially resolved electrical properties of individual nanowires were determined by electrostatic force and scanning gate microscopies. Temperature-dependent current-voltage measurements recorded from individual p-i-n devices show an increase in the breakdown voltage with temperature, characteristic of band-to-band impact ionization, or avalanche breakdown. Spatially resolved photocurrent measurements show that the largest photocurrent is generated at the intrinsic region located between the electrode contacts, with multiplication factors in excess of ca. 30, and demonstrate that single p-i-n nanowires function as avalanche photodiodes. Electron- and hole-initiated avalanche gain measurements performed by localized photoexcitation of the p-type and n-type regions yield multiplication factors of ca. 100 and 20, respectively. These results demonstrate the significant potential of single p-i-n nanowires as nanoscale avalanche photodetectors and open possible opportunities for studying impact ionization of electrons and holes within quasi-one-dimensional semiconductor systems.

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Monte Carlo calibration of avalanches described as Coulomb fluid flows.

The idea that snow avalanches might behave as granular flows, and thus be described as Coulomb fluid flows, came up very early in the scientific study of avalanches, but it is not until recently that field evidence has been provided that demonstrates the reliability of this idea. This paper aims to specify the bulk frictional behaviour of snow avalanches by seeking a universal friction law. Since the bulk friction coefficient cannot be measured directly in the field, the friction coefficient must be calibrated by adjusting the model outputs to closely match the recorded data. Field data are readily available but are of poor quality and accuracy. We used Bayesian inference techniques to specify the model uncertainty relative to data uncertainty and to robustly and efficiently solve the inverse problem. A sample of 173 events taken from seven paths in the French Alps was used. The first analysis showed that the friction coefficient behaved as a random variable with a smooth and bell-shaped empirical distribution function. Evidence was provided that the friction coefficient varied with the avalanche volume, but any attempt to adjust a one-to-one relationship relating friction to volume produced residual errors that could be as large as three times the maximum uncertainty of field data. A tentative universal friction law is proposed: the friction coefficient is a random variable, the distribution of which can be approximated by a normal distribution with a volume-dependent mean.

Complex Mixtures↗

Evolution of avalanche conducting states in electrorheological liquids.

Charge transport in electrorheological fluids is studied experimentally under strongly nonequilibrium conditions. By injecting an electrical current into a suspension of conducting nanoparticles we are able to initiate a process of self-organization which leads, in certain cases, to formation of a stable pattern which consists of continuous conducting chains of particles. The evolution of the dissipative state in such a system is a complex process. It starts as an avalanche process characterized by nucleation, growth, and thermal destruction of such dissipative elements as continuous conducting chains of particles as well as electroconvective vortices. A power-law distribution of avalanche sizes and durations, observed at this stage of the evolution, indicates that the system is in a self-organized critical state. A sharp transition into an avalanche-free state with a stable pattern of conducting chains is observed when the power dissipated in the fluid reaches its maximum. We propose a simple evolution model which obeys the maximum power condition and also shows a power-law distribution of the avalanche sizes.

Journal Article↗

Analytic results for scaling function and moments for a different type of avalanche in the bak-sneppen evolution model

Starting from the master equation for the hierarchical structure of avalanches of a different kind within the frame of the Bak-Sneppen evolution model, we derive the exact formula of the scaling function describing the probability distribution of avalanches. The scaling function displays features required by the scaling ansatz and verified by simulations. Using the scaling function we investigate the avalanche moment, denoted by (Delta&fmacr;). It is found that for any non-negative integer k, (Delta&fmacr;) diverges as Delta&fmacr;(-k), which gives an infinite group of exact critical exponents. Simulation outcomes of avalanche moments with k=1,2,3, are found to be consistent with the corresponding analytical results.

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Fracture mechanics of snow avalanches.

Dense snow avalanches are analyzed by modeling the snow slab as an elastic and brittle plate, attached by static friction to the underlying ground. The grade of heterogeneity in the local fracture (slip) thresholds, and the ratio of the average substrate slip threshold to the average slab fracture threshold, are the decisive parameters for avalanche dynamics. For a strong pack of snow there appears a stable precursor of local slips when the frictional contacts are weakened (equivalent to rising temperature), which eventually trigger a catastrophic crack growth that suddenly releases the entire slab. In the opposite limit of very high slip thresholds, the slab simply melts when the temperature is increased. In the intermediate regime, and for a homogeneous slab, the model display features typical of real snow avalanches. The model also suggests an explanation to why avalanches are impossible to forecast reliably based on precursor observations. This explanation may as well be applicable to other catastrophic rupture phenomena such as earthquakes.

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Avalanche structure in a running sandpile model.

The probability distribution function of the avalanche size in the sandpile model does not verify strict self-similarity under changes of the sandpile size. Here we show the existence of avalanches with different space-time structure, and each type of avalanche has a different scaling with the sandpile size. This is the main cause of the lack of self-similarity of the probability distribution function of the avalanche sizes, although the boundary effects can also play a role.

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Development of correlations in the dynamics of wet granular avalanches.

A detailed characterization of avalanche dynamics of wet granular media in a rotating drum apparatus is presented. The results confirm the existence of the three wetness regimes observed previously: the granular, the correlated, and the viscoplastic regime. These regimes show qualitatively different dynamic behaviors that are reflected in all the investigated quantities. We discuss the effect of interstitial liquid on the characteristic angles of the material and on the avalanche size distribution. These data also reveal logarithmic aging and allow us to map out the phase diagram of the dynamic behavior as a function of liquid content and flow rate. Via quantitative measurements of the flow velocity and the granular flux during avalanches, we characterize avalanche types unique to wet media. We also explore the details of viscoplastic flow (observed at the highest liquid contents) in which there are lasting contacts during flow, leading to coherence across the entire sample. This coherence leads to a velocity independent flow depth at high rotation rates and robust pattern formation in the granular surface.

Journal Article↗

Avalanche exponents and corrections to scaling for a stochastic sandpile.

We study distributions of dissipative and nondissipative avalanches in Manna's stochastic sandpile, in one and two dimensions. Our results lead to the following conclusions: (1) avalanche distributions, in general, do not follow simple power laws, but rather have the form P(s) approximately s(-tau(s))(ln s)(gamma)f(s/s(c)), with f a cutoff function; (2) the exponents for sizes of dissipative avalanches in two dimensions differ markedly from the corresponding values for the Bak-Tang-Wiesenfeld (BTW) model, implying that the BTW and Manna models belong to distinct universality classes; (3) dissipative avalanche distributions obey finite-size scaling, unlike in the BTW model.

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Culling avalanches in bootstrap percolation.

We study the culling avalanches which occur after the "death" of a single randomly chosen site in a network where sites are unstable, and are culled, if they have coordination less than an integer parameter m. Avalanche distributions are presented for triangular and cubic lattices for values of m where the associated bootstrap transitions are either first or second order. In second order cases, the culling avalanche distribution is found to be exponential, while in first order cases it follows a power law. We present an exact relation between culling avalanches and conventional bootstrap percolation and show that a relation proposed by Manna [Physica A 261, 351 (1998)] can be a good approximation for strongly first order bootstrap transitions but not for continuous bootstrap transitions.

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Crossover behavior in failure avalanches.

Composite materials, with statistically distributed thresholds for breakdown of individual elements, are considered. During the failure process of such materials under external stress (load or voltage), avalanches consisting of simultaneous rupture of several elements occur, with a distribution D(Delta) of the magnitude Delta of such avalanches. The distribution is typically a power law D(Delta) proportional to Delta (-xi). For the systems we study here, a crossover behavior is seen between two power laws, with a small exponent xi in the vicinity of complete breakdown and a larger exponent xi for failures away from the breakdown point. We demonstrate this analytically for bundles of many fibers where the load is uniformly distributed among the surviving fibers. In this case xi=3/2 near the breakdown point and xi=5/2 away from it. The latter is known to be the generic behavior. This crossover is a signal of imminent catastrophic failure of the material. Near the breakdown point, avalanche statistics show nontrivial finite size scaling. We observe similar crossover behavior in a network of electric fuses, and find xi=2 near the catastrophic failure and xi=3 away from it. For this fuse model power dissipation avalanches show a similar crossover near breakdown.

Journal Article↗

Looking for self-organized critical behavior in avalanches of slightly cohesive powders.

We report results from a statistical analysis of avalanches of cohesive powders in a slowly rotated drum. Interparticle adhesion, which diminishes the effect of inertia and whose magnitude strongly fluctuates in a local scale, makes avalanches in slightly cohesive powders eligible for displaying self-organized criticality. However, the results show that avalanche sizes, time interval between avalanches, and maximum stable angle do not follow a power-law distribution. Otherwise, these parameters scale with powder cohesiveness.

Journal Article↗