共查询到20条相似文献,搜索用时 31 毫秒
1.
《Physica A》2006,363(2):299-306
We study the distributions of dissipative and nondissipative avalanches separately in the stochastic Zhang (SP-Z) sandpile in two dimension. We find that dissipative and nondissipative avalanches obey simple power laws and do not have the logarithmic correction, while the avalanche distributions in the Abelian Manna model should include a logarithmic correction. We use the moment analysis to determine the numerical critical exponents of dissipative and nondissipative avalanches, respectively, and find that they are different from the corresponding values in the Abelian Manna model. All these indicate that the stochastic Zhang model and the Abelian Manna model belong to distinct universality classes, which imply that the Abelian symmetry breaking changes the scaling behavior of the avalanches in the case of the stochastic sandpile model. 相似文献
2.
We introduce a sandpile model driven by degree on scale-free networks, where the perturbation is triggered at nodes with the same degree. We numerically investigate the avalanche behaviour of sandpile driven by different degrees on scale-free networks. It is observed that the avalanche area has the same behaviour with avalanche size. When the sandpile is driven at nodes with the minimal degree, the avalanches of our model behave similarly to those of the original Bak-Tang-Wiesenfeld (BTW) model on scale-free networks. As the degree of driven nodes increases from the minimal value to the maximal value, the avalanche distribution gradually changes from a clean power law, then a mixture of Poissonian and power laws, finally to a Poisson-like distribution. The average avalanche area is found to increase with the degree of driven nodes so that perturbation triggered on higher-degree nodes will result in broader spreading of avalanche propagation. 相似文献
3.
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. 相似文献
4.
S. L. Ginzburg A. V. Nakin N. E. Savitskaya 《Journal of Experimental and Theoretical Physics》2010,111(3):503-511
The effect of the structure of a complex network on the properties of avalanche dynamical process on it has been analyzed
for the first time. It has been shown that the assortativity (disassortativity) degree, which is a structure characteristic
of the network and is numerically characterized by the assortativity coefficient r, is a control parameter governing the properties of the dynamical process on the network. The structure of individual avalanches
on networks with various r values has been studied. It has been shown that the number of nodes involved in an avalanche is a periodic function of the
time. 相似文献
5.
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
6.
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
7.
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
8.
S. Lübeck N. Rajewsky D.E. Wolf 《The European Physical Journal B - Condensed Matter and Complex Systems》2000,13(4):715-721
The Bak-Tang-Wiesenfeld (BTW) sandpile model is a cellular automaton which has been intensively studied during the last years
as a paradigm for self-organized criticality. In this paper, we reconsider a deterministic version of the BTW model introduced
by Wiesenfeld, Theiler and McNamara, where sand grains are added always to one fixed site on the square lattice. Using the
Abelian sandpile formalism we discuss the static properties of the system. We present numerical evidence that the deterministic model is only
in the BTW universality class if the initial conditions and the geometric form of the boundaries do not respect the full symmetry
of the square lattice.
Received 19 August 1999 相似文献
9.
V. B. Priezzhev 《Journal of statistical physics》1994,74(5-6):955-979
The height probabilities of the two-dimensional Abelian sandpile model are the fractionial numbers of lattice sites having heights 1, 2, 3, 4. A combinatorial method for evaluation of these quantities is proposed. The method is based on mapping the set of allowed sandpile configurations onto the set of spanning trees covering a given lattice. Exact analytical expressions for all probabilities are obtained. 相似文献
10.
Vazquez A Sotolongo-Costa O 《Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics》2000,61(1):944-947
The avalanche statistics in a stochastic sandpile model where toppling takes place with a probability p is investigated. The limiting case p=1 corresponds to the Bak-Tang-Wiesenfeld (BTW) model with a deterministic toppling rule. Based on the moment analysis of the distribution of avalanche sizes we conclude that for 0
相似文献
11.
We study the minimal recurrent configurations of the Abelian sandpile model on the hexagonal lattice referred to the dynamics of a nonconservative sandpile model. The one-to-one correspondence between these configurations and the set of maximally oriented spanning trees on the triangular sublattice is constructed. We derive the correlation functions in minimal recurrent configurations on a quasi-one-dimensional 2 × N lattice, compare them with correlations for ordinary recurrent configurations, and argue for asymptotic equivalence between them. 相似文献
12.
We numerically investigate the quenched random directed sandpile models which are local, conservative and Abelian. A local flow balance between the outflow of grains during a single toppling at a site and the total number of grains flowing into the same site plays an important role when all the nearest-neighbouring sites of the above-mentioned site topple for once. The quenched model has the same critical exponents with the Abelian deterministic directed sandpile model when the local flow balance exists, otherwise the critical exponents of this quenched model and the annealed Abelian random directed sandpile model are the same. These results indicate that the presence or absence of this local flow balance determines the universality class of the Abelian directed sandpile model. 相似文献
13.
Anton L 《Physical review letters》2001,86(1):67-70
The time and size distributions of the waves of topplings in the Abelian sandpile model are expressed as the first arrival at the origin distribution for a scale invariant, time-inhomogeneous Fokker-Plank equation. Assuming a linear conjecture for the time inhomogeneity exponent as a function of a loop-erased random walk (LERW) critical exponent, suggested by numerical results, this approach allows one to estimate the lower critical dimension of the model and the exact value of the critical exponent for LERW in three dimensions. The avalanche size distribution in two dimensions is found to be the difference between two closed power laws. 相似文献
14.
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
15.
By an inversion symmetry, we show that in the Abelian sandpile model the probability distribution of dissipating waves of topplings that touch the boundary of the system shows a power-law relationship with critical exponent 5/8 and the probability distribution of those dissipating waves that are also last in an avalanche has an exponent of 1. Our extensive numerical simulations not only support these predictions, but also show that inversion symmetry is useful for the analysis of the two-wave probability distributions. 相似文献
16.
LINMin CHENTian-Lun 《理论物理通讯》2004,42(3):373-378
We introduce the Olami-Feder-Christensen (OFC) model on a square lattice with some “rewired“ longrange connections having the properties of small world networks. We find that our model displays the power-law behavior, and connectivity topologies are very important to model‘s avalanche dynamical behaviors. Our model has some behaviors different from the OFC model on a small world network with “added“ long-range connections in our previous work [LIN Min, ZHAO Xiao-Wei, and CHEN Tian-Lun, Commun. Theor. Phys. (Beijing, China) 41 (2004) 557.]. 相似文献
17.
PAN Gui-Jun ZHANG Duan-Ming SUN Hong-Zhang YIN Yan-Ping 《理论物理通讯》2005,44(3):483-486
We present a stochastic critical slope sandpile model, where the amount of grains that fall in an overturning event is stochastic variable. The model is local, conservative, and Abelian. We apply the moment analysis to evaluate critical exponents and finite size scaling method to consistently test the obtained results. Numerical results show that this model, Oslo model, and one-dimensional Abelian Manna model have the same critical behavior although the three models have different stochastic toppling rules, which provides evidences suggesting that Abelian sandpile models with different stochastic toppling rules are in the same universality class. 相似文献
18.
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
19.
We present a stochastic critical slope sandpile model, where the amount of grains that fall in an overturning event is stochastic variable. The model is local, conservative, and Abelian. We apply the moment analysis to evaluate critical exponents and finite size scaling method to consistently test the obtained results. Numerical results show that this model, Oslo model, and one-dimensional Abelian Manna model have the same critical behavior although the three models have different stochastic toppling rules, which provides evidences suggesting that Abelian sandpile models with different stochastic toppling rules are in the same universality class. 相似文献
20.
K. E. Lee J. W. Lee 《The European Physical Journal B - Condensed Matter and Complex Systems》2006,50(1-2):271-275
We study a simple model for a neuron function in a collective brain
system. The neural network is composed of an uncorrelated
configuration model (UCM) for eliminating the degree correlation
of dynamical processes. The interaction of neurons is assumed to
be isotropic and idealized. These neuron dynamics are similar to
biological evolution in extremal dynamics with locally isotropic
interaction but has a different time scale. The functioning of
neurons takes place as punctuated patterns based on avalanche
dynamics. In our model, the avalanche dynamics of neurons exhibit
self-organized criticality which shows power-law behavior of the
avalanche sizes. For a given network, the avalanche dynamic
behavior is not changed with different degree exponents of
networks, γ≥2.4 and various refractory periods
referred to the memory effect, Tr. Furthermore, the avalanche
size distributions exhibit power-law behavior in a single scaling
region in contrast to other networks. However, return time
distributions displaying spatiotemporal complexity have three
characteristic time scaling regimes Thus, we find that UCM may be
inefficient for holding a memory. 相似文献