Anomalous Scaling Behaviors in a Rice-Pile Model with Two Different Driving Mechanisms

The moment analysis is applied to perform large scale simulations of the rice-pile model. We find that this model shows different scaling behavior depending on the driving mechanism used. With the noisy driving, the rice-pile model violates the finite-size scaling hypothesis, whereas, with fixed driving, it shows well defined avalanche exponents and displays good finite size scaling behavior for the avalanche size and time duration distributions.     

Moment Analysis of a Rice-Pile Model

Large scale simulations of a rice-pile model are performed. We use moment analysis techniques to evaluate critical exponents and data collapse method to verify the obtained results. The moment analysis yields well-defined avalanche exponents, which show that the rice-pile model can be coherently described within a finite size scaling framework. The general picture resulting from our analysis allows us to characterize the large scale behavior of the present model with great accuracy.     

Critical Behaviors in a Stochastic Local Limited One-Dimensional Rice-Pile Model

A stochastic local limited one-dimensional rice-pile model is numerically investigated. The distributions for avalanche sizes have a clear power-law behavior and it displays a simple finite size scaling. We obtain the avalanche exponents τ_s=1.54±0.10, β_s=2.17±0.10 and τ_T=1.80±0.10, β_T=1.46±0.10. This self-organized critical model belongs to the same universality class with the Oslo rice-pile model studied by K. Christensen et al. [Phys. Rev. Lett. 77 (1996) 107], a rice-pile model studied by L.A.N. Amaral et al. [Phys. Rev. E 54 (1996) 4512], and a simple deterministic self-organized critical model studied by M.S. Vieira [Phys. Rev. E 61 (2000) 6056].     

一个含崩塌概率的一维沙堆模型

在一维沙堆模型中加入了崩塌概率,并用元胞自动机的方法进行计算机模拟,发现该模型具有自组织临界性,其临界指数α=1.50±0.02,并且还发现只有当崩塌概率处于0.05~0.98时,系统才体现出自组织临界性.另外,根据该模型的结果,解释了一维米粒堆实验中出现的自组织临界现象.     

Critical Behaviors in a Stochastic Local Limited One-Dimensional Rice-Pile Model

A stochastic local limited one-dimensional rice-pile model is numerically investigated. The distributions for avalanche sizes have a clear power-law behavior and it displays a simple finite size scaling. We obtain the avalanche exponents Ts= 1.54±0.10,βs = 2.17±0.10 and TT = 1.80±0.10, βT =1.46 ± 0.10. This self-organized critical model belongs to the same universality class with the Oslo rice-pile model studied by K. Christensen et al. [Phys. Rev. Lett. 77 （1996） 107], a rice-pile model studied by L.A.N. Amaral et al. [Phys. Rev. E 54 （1996） 4512], and a simple deterministic self-organized critical model studied by M.S. Vieira [Phys. Rev. E 61 （2000） 6056].     

Avalanche dynamics of idealized neuron function in the brain on an uncorrelated random scale-free network

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, T_r. 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.     

Self-organized critical earthquake model with moving boundary

A globally driven self-organized critical model of earthquakes with conservative dynamics has been studied. An open but moving boundary condition has been used so that the origin (epicenter) of every avalanche (earthquake) is at the center of the boundary. As a result, all avalanches grow in equivalent conditions and the avalanche size distribution obeys excellent finite size scaling. Though the recurrence time distribution of the time series of avalanche sizes obeys well both the scaling forms recently observed in analysis of the real data of earthquakes, it is found that the scaling function decays only exponentially in contrast to a generalized gamma distribution observed in the real data analysis. The non-conservative version of the model shows periodicity even with open boundary.     

Time distribution and loss of scaling in granular flow

Two cellular automata models with directed mass flow and internal time scales are studied by numerical simulations. Relaxation rules are a combination of probabilistic critical height (probability of toppling p) and deterministic critical slope processes with internal correlation time t_c equal to the avalanche lifetime, in model A, and ,in model B. In both cases nonuniversal scaling properties of avalanche distributions are found for , where is related to directed percolation threshold in d=3. Distributions of avalanche durations for are studied in detail, exhibiting multifractal scaling behavior in model A, and finite size scaling behavior in model B, and scaling exponents are determined as a function of p. At a phase transition to noncritical steady state occurs. Due to difference in the relaxation mechanisms, avalanche statistics at approaches the parity conserving universality class in model A, and the mean-field universality class in model B. We also estimate roughness exponent at the transition. Received: 29 May 1998 / Revised: 8 September 1998 / Accepted: 10 September 1998     

A sharp transition between a trivial 1D BTW model and self-organized critical rice-pile model

A one-dimensional model of a rice-pile is numerically studied for different driving mechanisms. We found that for a sufficiently large system, there is a sharp transition between the trivial behaviour of a 1D BTW model and self-organized critical (SOC) behaviour. Depending on the driving mechanism, the self-organized critical rice-pile model belongs to two different universality classes. Received 18 December 1998     

含崩塌概率的一维沙堆模型的自组织临界性

提出了一个含崩塌概率的一维沙堆模型，并用元胞自动机方法对该模型进行计算机模拟. 结果表明在崩塌概率p从0到1的变化过程中存在两个临界点p₁和p₂. 当p₁2时模型具有自组织临界行为，并且系统在从平凡行为到自组织临界行为之间有一个快速的转变. 当模型具有自组织临界性时，这种自组织临界行为具有普适性，两个临界指数分别是1.50±0.02和1.58±0.15. 该模型能够较好地解释一维米粒堆实验中出现的自组织临界现象 关键词： 自组织临界性 BTW模型 崩塌概率     

Self-organized Criticality in an Earthquake Model on Random Network

A simplified Olami-Feder-Christensen model on a random network has been studied. We propose a new toppling rule — when there is an unstable site toppling, the energy of the site is redistributed to its nearest neighbors randomly not averagely. The simulation results indicate that the model displays self-organized criticality when the system is conservative, and the avalanche size probability distribution of the system obeys finite size scaling. When the system is nonconservative, the model does not display scaling behavior. Simulation results of our model with different nearest neighbors q is also compared, which indicates that the spatial topology does not alter the critical behavior of the system.     

A Kind of Neural Network Model Displaying Self-Organized Criticality

Based on the LISSOM model and the OFC earthquake model, we introduce a selforganized neural network model, in which the distribution of the avalanche sizes (unstable neurons) shows power-law behavior. In addition, we analyze the influence of various factors of the model on the power-law behavior of the avalanche size distribution.     

Power-law statistics of synchronous transition in inhibitory neuronal networks

We investigate the relationship between the synchronous transition and the power law behavior in spiking networks which are composed of inhibitory neurons and balanced by dc current. In the region of the synchronous transition, the avalanche size and duration distribution obey a power law distribution. We demonstrate the robustness of the power law for event sizes at different parameters and multiple time scales. Importantly, the exponent of the event size and duration distribution can satisfy the critical scaling relation. By changing the network structure parameters in the parameter region of transition, quasicriticality is observed, that is, critical exponents depart away from the criticality while still hold approximately to a dynamical scaling relation. The results suggest that power law statistics can emerge in networks composed of inhibitory neurons when the networks are balanced by external driving signal.     

Driving rate effects on crackling noise

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.     

Scaling and complex avalanche dynamics in the Abelian sandpile model

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.     

On self-organised criticality in one dimension

In critical phenomena, many of the characteristic features encountered in higher dimensions such as scaling, data collapse and associated critical exponents are also present in one dimension. Likewise for systems displaying self-organised criticality. We show that the one-dimensional Bak–Tang–Wiesenfeld sandpile model, although trivial, does indeed fall into the general framework of self-organised criticality. We also investigate the Oslo ricepile model, driven by adding slope units at the boundary or in the bulk. We determine the critical exponents by measuring the scaling of the kth moment of the avalanche size probability with system size. The avalanche size exponent depends on the type of drive but the avalanche dimension remains constant.     

Crack avalanches in the three-dimensional random fuse model

We analyze the scaling of avalanche precursors in the three-dimensional random fuse model by numerical simulations. We find that both the integrated and non-integrated avalanche size distributions are in good agreement with the results of the global load sharing fiber bundle model, which represents the mean-field limit of the model.     

Critical Behaviors in a Stochastic One-Dimensional Sand-Pile Model

A one-dimensional sand-pile model (Manna model), which has a stochastic redistribution process, is studied both in discrete and continuous manners. The system evolves into a critical state after a transient period. A detailed analysis of the probability distribution of the avalanche size and duration is numerically investigated. Interestingly,contrary to the deterministic one-dimensional sand-pile model, where multifractal analysis works well, the analysis based on simple finite-size scaling is suited to fitting the data on the distribution of the avalanche size and duration. The exponents characterizing these probability distributions are measured. Scaling relations of these scaling exponents and their universality class are discussed.     

Criticality in Two-Variable Earthquake Model on a Random Graph

A two-variable earthquake model on a quenched random graph is established here. It can be seen as a generalization of the OFC models. We numerically study the critical behavior of the model when the system is nonconservative: the result indicates that the model exhibits self-organized criticality deep within the nonconservative regime. The probability distribution for avalanche size obeys finite size scaling. We compare our model with the model introduced by Stefano Lise and Maya Paczuski [Phys. Rev. Lett. 88 (2002) 228301], it is proved that they are not in the same universality class.     

Critical Behaviors in a Stochastic One-Dimensional Sand-Pile Model

A one-dimensional sand-pile model （Manna model）, which has a stochastic redistribution process, is studied both in discrete and continuous manners. The system evolves into a critical state after a transient period. A detailed analysis of the probability distribution of the avalanche size and duration is numerically investigated. Interestingly,contrary to the deterministic one-dimensional sand-pile model, where multifractal analysis works well, the analysis based on simple finite-size scaling is suited to fitting the data on the distribution of the avalanche size and duration. The exponents characterizing these probability distributions are measured. Scaling relations of these scaling exponents and their universality class are discussed.