共查询到20条相似文献,搜索用时 15 毫秒
1.
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
2.
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
3.
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
4.
Landslides, forest fires, and earthquakes: examples of self-organized critical behavior 总被引:6,自引:0,他引:6
Per Bak conceived self-organized criticality as an explanation for the behavior of the sandpile model. Subsequently, many cellular automata models were found to exhibit similar behavior. Two examples are the forest-fire and slider-block models. Each of these models can be associated with a serious natural hazard: the sandpile model with landslides, the forest-fire model with actual forest fires, and the slider-block model with earthquakes. We examine the noncumulative frequency–area statistics for each natural hazard, and show that each has a robust power-law (fractal) distribution. We propose an inverse-cascade model as a general explanation for the power-law frequency–area statistics of the three cellular-automata models and their ‘associated’ natural hazards. 相似文献
5.
We study the rotor router model and two deterministic sandpile models. For the rotor router model in ℤ
d
, Levine and Peres proved that the limiting shape of the growth cluster is a sphere. For the other two models, only bounds
in dimension 2 are known. A unified approach for these models with a new parameter h (the initial number of particles at each site), allows to prove a number of new limiting shape results in any dimension d≥1.
For the rotor router model, the limiting shape is a sphere for all values of h. For one of the sandpile models, and h=2d−2 (the maximal value), the limiting shape is a cube. For both sandpile models, the limiting shape is a sphere in the limit
h→−∞. Finally, we prove that the rotor router shape contains a diamond. 相似文献
6.
Eugene R. Speer 《Journal of statistical physics》1993,71(1-2):61-74
In the Abelian sandpile models introduced by Dhar, long-time behavior is determined by an invariant measure supported uniformly on a set of implicitly defined recurrent configurations of the system. Dhar proposed a simple procedure, theburning algorithm, as a possible test of whether a configuration is recurrent, and later with Majumdar verified the correctness of this test when the toppling rules of the sandpile are symmetric. We observe that the test is not valid in general and give a new algorithm which yields a test correct for all sandpiles; we also obtain necessary and sufficient conditions for the validity of the original test. The results are applied to a family of deterministic one-dimensional sandpile models originally studied by Lee, Liang, and Tzeng. 相似文献
7.
Anomalous scaling in the Zhang model 总被引:2,自引:0,他引:2
R. Pastor-Satorras A. Vespignani 《The European Physical Journal B - Condensed Matter and Complex Systems》2000,18(2):197-200
We apply the moment analysis technique to analyze large scale simulations of the Zhang sandpile model. We find that this model
shows different scaling behavior depending on the update mechanism used. With the standard parallel updating, the Zhang model
violates the finite-size scaling hypothesis, and it also appears to be incompatible with the more general multifractal scaling
form. This makes impossible its affiliation to any one of the known universality classes of sandpile models. With sequential
updating, it shows scaling for the size and area distribution. The introduction of stochasticity into the toppling rules of
the parallel Zhang model leads to a scaling behavior compatible with the Manna universality class.
Received 8 August 2000 and Received in final form 4 October 2000 相似文献
8.
将离散单元法应用到三维堆积过程的模拟计算,探讨了滑动摩擦及滚动摩擦对堆积形成的影响,得到了颗粒堆内部的应力分布规律,发现颗粒堆的形态是由滑动摩擦和滚动摩擦共同决定的,在堆内颗粒间的作用力基本呈树状结构.在模拟得到的颗粒堆中出现了应力分布奇异现象,在堆积角较大的情况下,颗粒堆与地面间作用力的最大值常发生在距堆底中心不远的环状区域,而并非发生在堆底的中心;在堆积角相对较小时颗粒堆与地面间作用力的最大值较容易发生在堆底的中心.对于一个颗粒堆,具体会发生哪种受力情况具有一定的偶然性.
关键词:
堆积
离散单元法
计算颗粒力学 相似文献
9.
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
10.
J. A. Ahmed S. B. Santra 《The European Physical Journal B - Condensed Matter and Complex Systems》2010,76(1):13-20
Lattice statistical models of equilibrium critical phenomena
generally obey finite size scaling (FSS) ansatz. However, the
critical behavior of the prototypical BTW sandpile model
demonstrating self-organized criticality at out of equilibrium is
described by a peculiar multiscaling behaviour. FSS hypothesis is
verified here on two versions (RSM1 and RSM2) of a rotational
sandpile model (RSM) with broken mirror symmetry. In these models,
sand grains flow only in the forward direction and in a specific
rotational direction from an active site after toppling. The
toppling rules are such that RSM1 will have less randomness whereas
RSM2 will have more randomness with respect to RSM. RSM1 is expected
to be more closer to BTW whereas RSM2 is expected to be more closer
to Manna’s stochastic model. Both RSM1 and RSM2 are found to belong
to the same universality class of RSM. The scaling functions of
RSM1 and RSM2 are also found to obey usual FSS hypothesis at out of
equilibrium instead of multiscaling as in BTW. 相似文献
11.
Reduction in b-values before a large earthquake is a very popular topic for discussion. This study proposes an alternative sandpile model being able to demonstrate reduction in scaling exponents before large events through adaptable long-range connections. The distant connection between two separated cells was introduced in the sandpile model. We found that our modified long-range connective sandpile (LRCS) system repeatedly approaches and retreats from a critical state. When a large avalanche occurs in the LRCS model, accumulated energy dramatically dissipates and the system simultaneously retreats from criticality. The system quickly approaches the critical state accompanied by the increase in the slopes of the power-law frequency-size distributions of events. Afterwards, and most interestingly, the power-law slope declines before the next large event. The precursory b-value reduction before large earthquakes observed from earthquake catalogues closely mimics the evolution in power-law slopes for the frequency-size distributions of events derived in the LRCS models. Our paper, thus, provides a new explanation for declined b-values before large earthquakes. 相似文献
12.
The relationships between the Hurst exponent H and the power-law scaling exponent B in a new modification of sandpile models, i.e. the long-range connective sandpile (LRCS) models, exhibit a strong dependence upon the system size L. As L decreases, the LRCS model can demonstrate a transition from the negative to positive correlations between H- and B-values. While the negative and null correlations are associated with the fractional Gaussian noise and generalized Cauchy processes, respectively, the regime with the positive correlation between the Hurst and power-law scaling exponents may suggest an unknown, interesting class of the stochastic processes. 相似文献
13.
We elucidate a long-standing puzzle about the nonequilibrium universality classes describing self-organized criticality in sandpile models. We show that depinning transitions of linear interfaces in random media and absorbing phase transitions (with a conserved nondiffusive field) are two equivalent languages to describe sandpile criticality. This is so despite the fact that local roughening properties can be radically different in the two pictures, as explained here. Experimental implications of our work as well as promising paths for future theoretical investigations are also discussed. 相似文献
14.
Lubeck S 《Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics》2000,61(1):204-209
We reconsider the moment analysis of the Bak-Tang-Wiesenfeld and the stochastic sandpile model introduced by Manna [J. Phys. A 24, L363 (1991)] in two and three dimensions. In contrast to recently performed investigations our analysis reveals that the models are characterized by different scaling behavior, i.e., they belong to different universality classes. 相似文献
15.
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
16.
A single sandpile model with quenched random toppling matrices captures the crucial features of different models of self-organized criticality. With symmetric matrices avalanche statistics falls in the multiscaling Bak-Tang-Wiesenfeld universality class. In the asymmetric case the simple scaling of the Manna model is observed. The presence or absence of a precise toppling balance between the amount of sand released by a toppling site and the total quantity the same site receives when all its neighbors topple once determines the appropriate universality class. 相似文献
17.
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
18.
Sandpile-based models have successfully shed light on key features of nonlinear relaxational processes in nature, particularly the occurrence of fat-tailed magnitude distributions and exponential return times, from simple local stress redistributions. In this work, we extend the existing sandpile paradigm into an inter-sandpile cascade, wherein the avalanches emanating from a uniformly-driven sandpile (first layer) is used to trigger the next (second layer), and so on, in a successive fashion. Statistical characterizations reveal that avalanche size distributions evolve from a power-law p(S)≈S−1.3 for the first layer to gamma distributions p(S)≈Sαexp(−S/S0) for layers far away from the uniformly driven sandpile. The resulting avalanche size statistics is found to be associated with the corresponding waiting time distribution, as explained in an accompanying analytic formulation. Interestingly, both the numerical and analytic models show good agreement with actual inventories of non-uniformly driven events in nature. 相似文献
19.
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
20.
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