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1.
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. 相似文献
2.
A. Garber H. Kantz 《The European Physical Journal B - Condensed Matter and Complex Systems》2009,67(3):437-443
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. 相似文献
3.
Luc Oger Chrystèle Annic Daniel Bideau Rongqing Dai Stuart B. Savage 《Journal of statistical physics》1996,82(3-4):1047-1061
Rapid granular flow is diffusive in character. This diffusive nature is important in the generation of constitutive properties such as effective shear and bulk viscosities, effective conductivity of particle fluctuation energy, and self-diffusion coefficients. Experiments were performed in a large air-table apparatus that can sustain up to a few thousand small, light disks just above a horizontal porous plane. Experiments on 2D diffusion processes were performed using this apparatus. Measurements of self-diffusion coefficients and granular temperature in systems having different areal concentrations are in good agreement with predictions based on the kinetic theory and on numerical simulations. 相似文献
4.
Many systems respond to slowly changing external conditions with crackling noise, created by avalanches or pulses with a broad range of sizes. Examples range from Barkhausen noise (BN) in magnets to earthquakes. In this Letter, we discuss the effects of increasing driving rate Omega on the scaling behavior of the avalanche size and duration distributions as well as qualitative effects of Omega on the power spectra. We derive an exponent inequality as a criteria for the relevance of Omega. To illustrate these general results, we use recent experiments on BN as a successful example. 相似文献
5.
N. E. Savitskaya 《JETP Letters》2016,103(3):206-212
The stabilization of avalanches on dynamical networks has been studied. Dynamical networks are networks where the structure of links varies in time owing to the presence of the individual “activity” of each site, which determines the probability of establishing links with other sites per unit time. An interesting case where the times of existence of links in a network are equal to the avalanche development times has been examined. A new mathematical model of a system with the avalanche dynamics has been constructed including changes in the network on which avalanches are developed. A square lattice with a variable structure of links has been considered as a dynamical network within this model. Avalanche processes on it have been simulated using the modified Abelian sandpile model and fixed-energy sandpile model. It has been shown that avalanche processes on the dynamical lattice under study are more stable than a static lattice with respect to the appearance of catastrophic events. In particular, this is manifested in a decrease in the maximum size of an avalanche in the Abelian sandpile model on the dynamical lattice as compared to that on the static lattice. For the fixed-energy sandpile model, it has been shown that, in contrast to the static lattice, where an avalanche process becomes infinite in time, the existence of avalanches finite in time is always possible. 相似文献
6.
We analyze a sequence of short transient sound waves, called "crackles," which are associated with explosive openings of airways during lung inflation. The distribution of time intervals between consecutive crackles Delta(t) shows two regimes of power law behavior. We develop an avalanche model which fits the data over five decades of Delta(t). We find that the regime for large Delta(t) is related to the dynamics of distinct avalanches in a Cayley tree, and the regime for small Delta(t) is determined by the dynamics of crackle propagation within a single avalanche. We also obtain a mean-field solution of the model which provides information about lung inflation. 相似文献
7.
We report experimental measurements of avalanche behavior of thin granular layers on an inclined plane for low volume flow rate. The dynamical properties of avalanches were quantitatively and qualitatively different for smooth glass beads compared to irregular granular materials such as sand. Two scenarios for granular avalanches on an incline are identified, and a theoretical explanation for these different scenarios is developed based on a depth-averaged approach that takes into account the differing rheologies of the granular materials. 相似文献
8.
L. de Arcangelis 《The European physical journal. Special topics》2012,205(1):243-257
Recent experiments have detected a novel form of spontaneous neuronal activity both in vitro and in vivo: neuronal avalanches.
The statistical properties of this activity are typical of critical phenomena, with power laws characterizing the distributions
of avalanche size and duration. A critical behaviour for the spontaneous brain activity has important consequences on stimulated
activity and learning. Very interestingly, these statistical properties can be altered in significant ways in epilepsy and
by pharmacological manipulations. In particular, there can be an increase in the number of large events anticipated by the
power law, referred to herein as dragon-king avalanches. This behaviour, as verified by numerical models, can originate from
a number of different mechanisms. For instance, it is observed experimentally that the emergence of a critical behaviour depends
on the subtle balance between excitatory and inhibitory mechanisms acting in the system. Perturbing this balance, by increasing
either synaptic excitation or the incidence of depolarized neuronal up-states causes frequent dragon-king avalanches. Conversely,
an unbalanced GABAergic inhibition or long periods of low activity in the network give rise to sub-critical behaviour. Moreover,
the existence of power laws, common to other stochastic processes, like earthquakes or solar flares, suggests that correlations
are relevant in these phenomena. The dragon-king avalanches may then also be the expression of pathological correlations leading
to frequent avalanches encompassing all neurons. We will review the statistics of neuronal avalanches in experimental systems.
We then present numerical simulations of a neuronal network model introducing within the self-organized criticality framework
ingredients from the physiology of real neurons, as the refractory period, synaptic plasticity and inhibitory synapses. The
avalanche critical behaviour and the role of dragon-king avalanches will be discussed in relation to different drives, neuronal
states and microscopic mechanisms of charge storage and release in neuronal networks. 相似文献
9.
Strain Avalanches in Microsized Single Crystals:Avalanche Size Predicted by a Continuum Crystal Plasticity Model
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《中国物理快报》2016,(10)
Plastic deformation of small crystals occurs by power-law distributed strain avalanches whose universality is still debated.In this work we introduce a continuum crystal plasticity model for the deformation of microsized single crystals,which is able to reproduce the main experimental observations such as Row intermittency and statistics of strain avalanches.We report exact predictions for scaling exponents and scaling functions associated with random distribution of avalanche sizes.In this way,the developed model provides a routine for a quantitative characterization of the statistical aspects of strain avalanches in microsized single crystals. 相似文献
10.
Y. Louzoun N. M. Shnerb S. Solomon 《The European Physical Journal B - Condensed Matter and Complex Systems》2007,56(2):141-148
The survival of autocatalytic agents in hostile environments depends on their ability to adapt their spatial configuration
to local
fluctuations. A model of diffusive reactants that extract the
advantage of spatio-temporal fluctuations associated with the
stochastic wandering of diffusive catalysts is discussed. Two
arguments are presented for the basic processes behind this
extraordinary behavior. In the first, the local colonies that evolve
around any spatially advantageous region overlap in space-time and
an infinite directed percolation cluster emerges. The second
argument is based on the return probability of a diffusive agent
that is shown to yield finite density of active “oases" with an
exponentially large contribution to the reactant population. The
different range of applicability of these survival lower bounds to
small systems is discussed. 相似文献
11.
12.
C. Ancey 《The European physical journal. Special topics》2012,205(1):117-129
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. 相似文献
13.
Gaël Benabou 《Journal of statistical physics》2005,121(3-4):319-341
In this paper, we are interested in the study of the diffusion of a passive particle with positive mass by a divergence free
velocity field. We consider here the very simple turbulent shear flow case, in which we will prove the superdiffusive behaviour
of the motion for large enough values of the energy spectrum of the velocity field. For small values, the proof of the diffusive
behaviour of the model is also new, and it is shown that this diffusion is strictly greater than the one obtained with a non-massive
particle. One interesting point to insist on is that we are able to obtain explicit hydrodynamic equations without even having
the stationary measure of the studied processes 相似文献
14.
Kraikivski P Lipowsky R Kierfeld J 《The European physical journal. E, Soft matter》2005,16(3):319-340
We study the thermally activated motion of semiflexible polymers in double-well potentials using field-theoretic methods. Shape, energy, and effective diffusion constant of kink excitations are calculated, and their dependence on the bending rigidity of the semiflexible polymer is determined. For symmetric potentials, the kink motion is purely diffusive whereas kink motion becomes directed in the presence of a driving force. We determine the average velocity of the semiflexible polymer based on the kink dynamics. The Kramers escape over the potential barriers proceeds by nucleation and diffusive motion of kink-antikink pairs, the relaxation to the straight configuration by annihilation of kink-antikink pairs. We consider both uniform and point-like driving forces. For the case of point-like forces the polymer crosses the potential barrier only if the force exceeds a critical value. Our results apply to the activated motion of biopolymers such as DNA and actin filaments or of synthetic polyelectrolytes on structured substrates. 相似文献
15.
Amir Abdolvand Afshin Montakhab 《The European Physical Journal B - Condensed Matter and Complex Systems》2010,76(1):21-30
We study the two-dimensional Abelian Sandpile Model on a squarelattice of linear size L. We introduce the notion of avalanche’sfine structure and compare the behavior of avalanches and waves oftoppling. We show that according to the degree of complexity inthe fine structure of avalanches, which is a direct consequence ofthe intricate superposition of the boundaries of successive waves,avalanches fall into two different categories. We propose scalingansätz for these avalanche types and verify them numerically.We find that while the first type of avalanches (α) has a simplescaling behavior, the second complex type (β) is characterized by anavalanche-size dependent scaling exponent. In particular, we define an exponent γto characterize the conditional probability distribution functions for these typesof avalanches and show that γ α = 0.42, while 0.7 ≤ γ β ≤ 1.0depending on the avalanche size. This distinction provides aframework within which one can understand the lack of aconsistent scaling behavior in this model, and directly addresses thelong-standing puzzle of finite-size scaling in the Abelian sandpile model. 相似文献
16.
H. S. Yamada K. S. Ikeda 《The European Physical Journal B - Condensed Matter and Complex Systems》2012,85(1):41
This paper concerns the time-reversal characteristics of intrinsic normal diffusion in quantum systems. Time-reversible properties
are quantified by the time-reversal test; the system evolved in the forward direction for a certain period is time-reversed
for the same period after applying a small perturbation at the reversal time, and the separation between the time-reversed
perturbed and unperturbed states is measured as a function of perturbation strength, which characterizes sensitivity of the
time reversed system to the perturbation and is called the time-reversal characteristic. Time-reversal characteristics are
investigated for various quantum systems, namely, classically chaotic quantum systems and disordered systems including various
stochastic diffusion system. When the system is normally diffusive, there exists a fundamental quantum unit of perturbation,
and all the models exhibit a universal scaling behavior in the time-reversal dynamics as well as in the time-reversal characteristics,
which leads us to a basic understanding of the nature of quantum irreversibility. 相似文献
17.
Joachim Krug 《Journal of statistical physics》1992,66(5-6):1635-1641
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). 相似文献
18.
ZHANG Duan-Ming SUN Fan YU Bo-Ming PAN Gui-Jun YIN Yah-Ping LI Rui SU Xiang-Ying 《理论物理通讯》2006,46(2):261-264
We consider the earthquake model on a random graph. A detailed analysis of the probability distribution of the size of the avalanches will be given. The model with different inhomogeneities is studied in order to compare the critical behavior of different systems. The results indicate that with the increase of the inhomogeneities, the avalanche exponents reduce, i.e., the different numbers of defects cause different critical behaviors of the system. This is virtually ascribed to the dynamical perturbation. 相似文献
19.
We consider the earthquake model on a random graph. A detailed analysis of the probability distribution of the size of the avalanches will be given. The model with different inhomogeneities is studied in order to compare the critical behavior of different systems. The results indicate that with the increase of the inhomogeneities, the avalanche exponents reduce, i.e., the different numbers of defects cause different critical behaviors of the system. This is virtually ascribed to the dynamical perturbation. 相似文献
20.
A Brownian motor with Gaussian short-range correlated spatial disorder and time-delayed feedback is investigated. The effects of disorder intensity, correlation strength and delay time on the transport properties of an overdamped periodic ratchet are discussed for different driving force. For small driving force, the disorder intensity can induce a peak in the drift motion and a linear increasing function in diffusion motion. For large driving force, the disorder intensity can suppress the drift motion but enhance the diffusion motion. For both small and large driving forces, the correlation strength of the spatial disorder can enhance the drift motion but suppress the diffusion motion. While the delay time can reduce the drift motion to a small value and enhance the diffusion motion to a large value. The drift motion increases as the driving force increases. However, the diffusion motion is either decreases or only increases slightly when the driving force increases. 相似文献