Scale invariance and intermittency in a creep-slip model of earthquake faults

The dynamics of a generalization of the one-dimensional, spatially discretized Burridge-Knopoff model (slider-block model) is investigated numerically. Plastic deformation of the fault interface is considered in addition to rigid sliding (creep-slip model). The event-size distribution exhibits scale invariance (beta=1.5), as does the power spectral density of the intermittent time series of the spatially averaged sliding rate (sigma=1.3). A diffusive cellular automaton model that reproduces the algebraic correlations in the event-size distribution in the presence of dissipation is proposed.     

Self-organized criticality in a block lattice model of the brittle crust

An earthquake model is introduced, in which the brittle crust is treated as a two-dimensional system of many blocks divided by faults, and the mechanical behavior of the faults is described by the Burridge-Knopoff stick-slip model. The coherent system naturally evolves into a self-organized critical state. Some universal scaling laws of seismicity, such as the Gutenberg-Richter law with the b value in agreement with the observational result and the fractal feature of fault patterns, are reproduced. Some ambiguity in simple cellular automata models is also solved.     

An Algorithm-Independent Definition of Damage Spreading—Application to Directed Percolation

We present a general definition of damage spreading in a pair of models. Using this general framework, one can define damage spreading in an objective manner that does not depend on the particular dynamic procedure that is being used. The formalism can be used for any spin-model or cellular automaton, with sequential or parallel update rules. At this point we present its application to the Domany–Kinzel cellular automaton in one dimension, this being the simplest model in which damage spreading has been found and studied extensively. We show that the active phase of this model consists of three subphases characterized by different damage-spreading properties.     

From quantum cellular automata to quantum lattice gases

A natural architecture for nanoscale quantum computation is that of a quantum cellular automaton. Motivated by this observation, we begin an investigation of exactly unitary cellular automata. After proving that there can be no nontrivial, homogeneous, local, unitary, scalar cellular automaton in one dimension, we weaken the homogeneity condition and show that there are nontrivial, exactly unitary, partitioning cellular automata. We find a one-parameter family of evolution rules which are best interpreted as those for a one-particle quantum automaton. This model is naturally reformulated as a two component cellular automaton which we demonstrate to limit to the Dirac equation. We describe two generalizations of this automaton, the second, of which, to multiple interacting particles, is the correct definition of a quantum lattice gas.     

A Cellular Automaton Model for Two-Lane Traffic

We present some long time limit properties of a cellular automaton that models traffic of cars on a (infinite) two-lane road. This model, called TL184, is a natural generalization of the cellular automaton classified as 184 by Wolfram (to be abbreviated by CA184) and studied before as a model for one-lane traffic. TL184 models cars' motions on each lane by particles that interact via the CA184 rules, and cars' lane changes by a possibility for particles to flip from one CA184 to another. We calculate the infinite-time limit of the particle current in TL184, starting from a translation invariant measure, and use this result to show how the possibility of lane changes may enhance the current of cars in TL184 compared to that in a corresponding model of two non-interacting one-lane roads. We provide examples which demonstrate that even though the rules that regulate lane changes are completely symmetric, the system does not evolve to an equipartition of cars among both lanes from a given initially asymmetric distribution; moreover, the asymptotic car velocities and currents may be different on different lanes. We also show that, for a particular class of initial distributions, the asymptotic car density on a lane may be a non-monotonic function of the initial car density on this lane. Finally, we derive the current-density relation for an extended continuous-time version of TL184 with asymmetric lane-changing rules.     

A Cellular Automaton Model for Heterogeneous and Incosistent Driver Behavior in Urban Traffic

In this paper a cellular automaton model is proposed to describe driver behavior at a single-lane urban roundabout. Driver behavior has been considered as heterogeneous and inconsistent. Most traffic papers in the literature just discussed heterogeneous driver behavior, to our best knowledge. Two truncated Gaussian distributions are used to model heterogeneous and inconsistent driver behavior, respectively. The physical meanings of two truncated distributions are indicated. This method may help enhance a better understanding of driver behavior at roundabout traffic, and even possibly provide references for roundabout design and management.     

A Cellular Automaton Model for Heterogeneous and Incosistent Driver Behavior in Urban Traffic

In this paper a cellular automaton model is proposed to describe driver behavior at a single-lane urban roundabout. Driver behavior has been considered as heterogeneous and inconsistent. Most traffic papers in the literature just discussed heterogeneous driver behavior, to our best knowledge. Two truncated Gaussian distributions are used to model heterogeneous and inconsistent driver behavior, respectively. The physical meanings of two truncated distributions are indicated. This method may help enhance a better understanding of driver behavior at roundabout traffic, and even possibly provide references for roundabout design and management.     

一种考虑速度随机慢化概率动态演化的交通流元胞自动机模型

在NS模型的基础上,利用司机的记忆效应和当前交通环境动态地调整随机慢化概率,从而得到一个改进的交通流元胞自动机模型.数值实验表明,该模型可以很好地刻画司机记忆效应对交通流的影响,记忆效应的引入可以提高平均速度和流量. 关键词： 交通流 元胞自动机模型 记忆效应 随机慢化概率     

Equivalence of the train model of earthquake and boundary driven Edwards-Wilkinson interface

A discretized version of the Burridge-Knopoff train model with (non-linear friction force replaced by) random pinning is studied in one and two dimensions. A scale free distribution of avalanches and the Omori law type behaviour for after-shocks are obtained. The avalanche dynamics of this model becomes precisely similar (identical exponent values) to the Edwards-Wilkinson (EW) model of interface propagation. It also allows the complimentary observation of depinning velocity growth (with exponent value identical with that for EW model) in this train model and Omori law behaviour of after-shock (depinning) avalanches in the EW model.     

A damage model based on failure threshold weakening

A variety of studies have modeled the physics of material deformation and damage as examples of generalized phase transitions, involving either critical phenomena or spinodal nucleation. Here we study a model for frictional sliding with long-range interactions and recurrent damage that is parameterized by a process of damage and partial healing during sliding. We introduce a failure threshold weakening parameter into the cellular automaton slider-block model which allows blocks to fail at a reduced failure threshold for all subsequent failures during an event. We show that a critical point is reached beyond which the probability of a system-wide event scales with this weakening parameter. We provide a mapping to the percolation transition, and show that the values of the scaling exponents approach the values for mean-field percolation (spinodal nucleation) as lattice size L is increased for fixed R. We also examine the effect of the weakening parameter on the frequency-magnitude scaling relationship and the ergodic behavior of the model.     

基于元胞自动机模型的上匝道合流处交替通行控制的研究

上海市高架道路的上匝道合流处率先实施了交替通行的控制策略.以Fukui和Ishibashi提出的FI元胞自动机交通流模型为基础，对实施该策略前后的上匝道合流处分别建立合理的交通流模型，并对交通流进行了数值模拟和分析.结果表明：当高架路主线和上匝道的来流车辆较多时，交替通行控制可以大大改善高架道路交通；当交通流稀疏时，实施控制前后交通流状况基本不发生变化. 关键词： 元胞自动机模型 上匝道合流处 交替通行控制 数值模拟     

Self-organized criticality with and without conservation

The self-organized sandpile models lose criticality if dissipation is introduced. Recently Christensen et al. have shown that dissipative automata based on the Burridge-Knopoff earthquake model exhibit critical behavior. Criticality is qualitatively different for the cases with and without conservation: A new characteristic length appears for the dissipative case which diverges slower than the system size. For all dissipative models we have found a characteristic frequency in the power spectrum of the released energy, which is absent for the conservative case. The exponents describing criticality change continuously as a function of the strength of dissipation and crossover phenomena occur in the vicinity of conservation. Disorder is irrelevant if conservation is present while it destroys criticality in the dissipative case.     

Scaling and critical phenomena in a cellular automaton slider-block model for earthquakes

The dynamics of a general class of two-dimensional cellular automaton slider-block models of earthquake faults is studied as a function of the failure rules that determine slip and the nature of the failure threshold. Scaling properties of clusters of failed sites imply the existence of a mean-field spinodal line in systems with spatially random failure thresholds, whereas spatially uniform failure thresholds produce behavior reminiscent of self-organized critical behavior. This model can describe several classes of faults, ranging from those that only exhibit creep to those that produce large events.     

The critical properties of the agent-based model with environmental–economic interactions

The steady-state and nonequilibrium properties of the model of environmental–economic interactions are studied. The interacting heterogeneous agents are simulated on the platform of the emission dynamics of cellular automaton. The model possesses the discontinuous transition between the safe and catastrophic ecology. Right at the critical line, the broad-scale power-law distributions of emission rates have been identified. Their relationship to Zipf's law and models of self-organized criticality is discussed.     

Cellular automaton fluids 1: Basic theory

Continuum equations are derived for the large-scale behavior of a class of cellular automaton models for fluids. The cellular automata are discrete analogues of molecular dynamics, in which particles with discrete velocities populate the links of a fixed array of sites. Kinetic equations for microscopic particle distributions are constructed. Hydrodynamic equations are then derived using the Chapman-Enskog expansion. Slightly modified Navier-Stokes equations are obtained in two and three dimensions with certain lattices. Viscosities and other transport coefficients are calculated using the Boltzmann transport equation approximation. Some corrections to the equations of motion for cellular automaton fluids beyond the Navier-Stokes order are given.     

高速车随机延迟逐步加速交通流元胞自动机模型

提出介于Nagel-Schreckenberg(NS)模型和Fukui-Ishibashi(FI)模型之间的一种新的一维交通流元胞自动机模型. 此模型采用NS模型中的车辆逐步加速方式,和FI模型中的仅最大速车可随机减速的车辆延迟方式.证明新模型的基本图,即车流渐近稳态的平均速度与道路上的车辆密度之间的函数关系与FI模型的完全相同.这也就是说,只允许最高速车辆可发生延迟的FI交通流模型,如果将其突然无限制加速方式(车辆可在一个时步内从零速加速到最高速限M或车头距离所允许的最大速度),改变为车辆的逐步有限加速 关键词： 交通流 元胞自动机模型 相变基本图 Nagel-Schreckenberg模型 Fukui-Ishibashi模型     

A new cellular automaton for signal controlled traffic flow based on driving behaviors

The complexity of signal controlled traffic largely stems from the various driving behaviors developed in response to the traffic signal. However, the existing models take a few driving behaviors into account and consequently the traffic dynamics has not been completely explored. Therefore, a new cellular automaton model, which incorporates the driving behaviors typically manifesting during the different stages when the vehicles are moving toward a traffic light, is proposed in this paper. Numerical simulations have demonstrated that the proposed model can produce the spontaneous traffic breakdown and the dissolution of the over-saturated traffic phenomena. Furthermore, the simulation results indicate that the slow-to-start behavior and the inch-forward behavior can foster the traffic breakdown. Particularly, it has been discovered that the over-saturated traffic can be revised to be an under-saturated state when the slow-down behavior is activated after the spontaneous breakdown. Finally, the contributions of the driving behaviors on the traffic breakdown have been examined.     

成对行为对行人疏散动力学的影响研究

熟悉的行人之间经常存在着聚集运动的整体跟随行为现象.为了研究这种行为对疏散过程的影响,考虑了行人的并排成对、前后成对、混合成对三种方式,建立了一个新的元胞自动机模型,研究了三种成对方式对双出口房间内行人疏散过程的影响,并分析、讨论了不同参数下成对方式之间的差异. 关键词： 行人流 元胞自动机 成对疏散 计算机模拟     

决定论性逐步加速交通流模型的渐近稳态行为

研究Nagel-Schreckenberg(NS)交通流元胞自动机模型在不考虑车辆随机延迟情况下的决定论性模型的基本图,即渐近稳态的车流平均速度作为车辆密度的函数关系．证明决定论性NS模型,在车流的自组织作用下,其渐近稳态的基本图,与决定论性Fukui-Ishibashi(FI)交通流模型的基本图完全相同．这个结果表明,若把FI交通流模型中的车辆突然加速方式（即车辆速度可以在仅仅一个时步内加速到其最高速限M或前方空距所允许的最大速度）,改变为车辆逐步加速方式（车辆速度在每一时步中最多仅能增加一个速度单位）,则车辆的自组织相互作用,并不会改变其车流的长时间渐近稳态行为． 关键词：     

An isotropic cellular automaton for excitable media

We propose a new cellular automaton (CA) model, which reproduces isotropic time-evolution patterns observed in the Belousov-Zhabotinsky reaction. Although several CA models have been proposed exhibiting isotropic patterns of the reaction, most of them need complicated rules and a large number of neighboring cells. Our model can produce isotropic patterns from a simple probabilistic rule among a few (4 or 8) neighboring cells.