鼓泡床内气固两相流的变尺度格子气模拟

基于格子气自动机的建模思想,建立气固两相流的变尺度格子气模型,用微观层次的气固作用规则描述两相流的宏观行为.二维流场空间被离散成两层不同尺度的正六边形网格,固体颗粒和气体粒子分别在各自的网格上运动;在格子气自动机基本规则基础上设计气固相作用规则和附加演化规则;确定模型宏观物理量的统计计算方法,并根据相似原理建立模型物理量与真实物理量之间的转换关系.用建立的模型对鼓泡床内气固流动行为进行模拟,通过比较发现,变尺度格子气模型的模拟结果与文献中的实验结果和双流体模型的模拟结果吻合较好,且平均相对误差更小,表明建模方法的正确性和模型的有效性.     

Determination of fixed points and shift cycles for nearest neighbor cellular automata

One-dimensional nearest neighbor cellular automata defined over Z₂ are characterized in terms of a set of eight nonadditive basis operators which act on the automaton state space. Every evolution rule for such automata can be expressed as an operator which is a direct sum of the basis operators. This approach allows decomposition of automata rules into additive and nonadditive parts. As a result, it is simple to determine fixed points (those states for which the rule reduces to the identity), and shift cycles (sets of states on which the rule reduces to a shift). Sets of states on which any given nearest neighbor automaton reduces to an identity or a shift are characterized. This allows us to obtain some results on the entropic properties of nonadditive automata, although these are not nearly so complete as results obtained for additive automata.     

Traveling waves and chaotic properties in cellular automata

Traveling wave solutions of cellular automata (CA) with two states and nearest neighbors interaction on one-dimensional (1-D) infinite lattice are computed. Space and time periods and the number of distinct waves have been computed for all representative rules, and each velocity ranging from 2 to 22. This computation shows a difference between spatially extended systems, generating only temporal chaos and those producing as well spatial complexity. In the first case wavelengths are simply related to the velocity of propagation and the dispersivity is an affine function, while in the second case (which coincides with Wolfram class 3), the dispersivity is multiform and its dependence on the velocities is highly random and discontinuous. This property is typical of space-time chaos in CA. (c) 1999 American Institute of Physics.     

Exact results for deterministic cellular automata with additive rules

Deterministic cellular automata (CA) with additive rules are studied by exploiting the properties of circulant matrices on finite fields. Complete state transition diagrams for higher-order and multidimensional CA on finite lattices are analyzed. Conditions on the rules which make them reversible are obtained. It is shown that all state transition diagrams of the CA have identical trees rooted on cycles. General formulae for cycle lengths and multiplicities are given.     

Strategies for using cellular automata to locate constrained layer damping on vibrating structures

It is often hard to optimise constrained layer damping (CLD) for structures more complicated than simple beams and plates as its performance depends on its location, the shape of the applied patch, the mode shapes of the structure and the material properties. This paper considers the use of cellular automata (CA) in conjunction with finite element analysis to obtain an efficient coverage of CLD on structures. The effectiveness of several different sets of local rules governing the CA are compared against each other for a structure with known optimum coverage—namely a plate. The algorithm which attempts to replicate most closely known optimal configurations is considered the most successful. This algorithm is then used to generate an efficient CLD treatment that targets several modes of a curved composite panel. To validate the modelling approaches used, results are also presented of a comparison between theoretical and experimentally obtained modal properties of the damped curved panel.     

Cluster growth in particle-conserving cellular automata

A class of simple two-dimensional cellular automata with particle conservation is proposed for easy simulations of interacting particle systems. The automata are defined by the exchange of states of neighboring cells, depending on the configurations around the cells. By attributing an energy to a configuration of cells, we can select significant rules from the huge number of possible rules and classify them into several groups, based on the analogy with a binary alloy. By numerical calculations, cluster growth is found in two kinds of phases which reveal gas-solid coexistence and liquid droplets. Normalized scaling functions are obtained, and dynamical scaling is examined.     

Reversibility of 1D Cellular Automata with Periodic Boundary over Finite Fields $\pmb{ {\mathbb{Z}}}_{p}$

The reversibility problem for linear cellular automata with null boundary defined by a rule matrix in the form of a pentadiagonal matrix was studied recently over the binary field ℤ₂ (del Rey and Rodriguez Sánchez in Appl. Math. Comput., 2011, doi:). In this paper, we study one-dimensional linear cellular automata with periodic boundary conditions over any finite field ℤ _p . For any given p≥2, we show that the reversibility problem can be reduced to solving a recurrence relation depending on the number of cells and the coefficients of the local rules defining the one-dimensional linear cellular automata. More specifically, for any given values (from any fixed field ℤ _p ) of the coefficients of the local rules, we outline a computer algorithm determining the recurrence relation which can be solved by testing reversibility of the cellular automaton for some finite number of cells. As an example, we give the full criteria for the reversibility of the one-dimensional linear cellular automata over the fields ℤ₂ and ℤ₃.     

一种基于元胞自动机的自适应网络病毒传播模型

自适应网络是节点动力学和网络动力学相互作用和反馈的演化网络. 基于元胞自动机建立自适应网络中易感-感染-易感(susceptible-infected-susceptible)的病毒传播模型,研究节点为了规避病毒传播所采取的多种网络重连规则对病毒传播及网络统计特征的影响. 结果表明:自适应网络中的重连规则可以有效减缓病毒传播速度,降低病毒传播规模;随机重连规则使得网络统计特征趋于随机网络;基于元胞自动机建立的传播模型清晰地表达了病毒在传播过程中的双稳态现象. 关键词： 自适应网络 传播动力学 网络动力学 元胞自动机     

Intriguing properties of global structure in some classes of finite cellular automata

The simplest one-dimensional cellular automata introduced recently by Wolfram are analyzed. Particularly, the finite cellular automata with two special evolution rules are studied. Non-trivial correspondence in global structure is found between the state transition diagrams under the two rules: correspondence of cycle structure, basin volume of each cycle and structure of transient trees etc. Origin of the correspondence is explored on the basis of local properties of the evolution rules. It is shown that this correspondence becomes exact in the thermodynamic limit.     

一种基于误差快速扩散元胞自动机的加密技术

构造了一个具有较大密钥空间的新型一维元胞自动机. 在该元胞自动机中,密钥为采用移位映射的伪随机序列及受控扰动项,避免了数据膨胀,元胞自动机具有随机性触发规则. 该元胞自动机一次处理信息量大,避免了复杂的计算过程. 所生成的流密码在理论上被证明了具有理想的随机性与雪崩效应,误差扩散速度快. 实证分析研究表明,流密码不仅在全局上、而且在局部上都具有良好的随机性能,通过测试长度为24000的流密码在400次迭代产生的数据表明,经χ²检验,在显著性水平为5%时,频数检验通过率超 关键词： 保密通信 元胞自动机 伪随机序列     

Application of a cellular automaton for the evolution of etched nuclear tracks

In the present work, it is demonstrated the first application of cellular automata to the growing of etched nuclear tracks. The simplest case in which conical etched tracks are gradually formed is presented, as well as a general case of time varying etching rate V_t. It is demonstrated that the cellular automata elements consist in an image pattern of the latent nuclear track input cells, 16 rules for updating states, the Moore neighborhood and an algorithm of four states.     

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.     

Enumeration of limit cycles in noncylindrical cellular automata

Recently a method has been developed by Jen to enumerate limit cycles in cellular automata (CA) with periodic boundary conditions. This involves operations on a connectivity matrix whose elements are related to the invariance of a site in a particular neighborhood to application of the CA rule. We extend this method to the case of fixed boundary conditions, of interest in simulations. In this case, translational invariance is lost, and the enumeration procedure is much more tedious than with periodic boundary conditions. We show examples for a fixed-point, a period-two, and a period-three enumeration in considerable detail, and give results-in agreement with simulations—for the number of fixed points and period-two cycles in selected two-state, nearest-neighbor CA rules.     

Synchronization of cellular automaton pairs

The phenomenon of synchronization in pairs of cellular automata coupled in a driver-replica mode is studied. Necessary and sufficient conditions for synchronization in linear cellular automaton pairs are given. The couplings that make a pair synchronize are determined for all linear elementary cellular automata. (c) 1998 American Institute of Physics.     

Opinion evolution based on cellular automata rules in small world networks

In this paper,we apply cellular automata rules,which can be given by a truth table,to human memory.We design each memory as a tracking survey mode that keeps the most recent three opinions.Each cellular automata rule,as a personal mechanism,gives the final ruling in one time period based on the data stored in one’s memory.The key focus of the paper is to research the evolution of people’s attitudes to the same question.Based on a great deal of empirical observations from computer simulations,all the rules can be classified into 20 groups.We highlight the fact that the phenomenon shown by some rules belonging to the same group will be altered within several steps by other rules in different groups.It is truly amazing that,compared with the last hundreds of presidential voting in America,the eras of important events in America’s history coincide with the simulation results obtained by our model.     

直管道中绕平板平面流动的格子气仿真

本文首先根据U.Frisch等人所提出的格子气FHPⅡ模型的要点,建立了该模型的完备的微观动力学(碰撞规则)。在此基础上,对一种CVD问题的简单模型进行了格子气仿真。文中介绍了边界条件和初条件的处理,以及在微机上实现仿真的分段算法。     

基于复合符号混沌的伪随机数生成器及加密技术

提出了复合符号混沌序列的概念;并以符号动力学的揉序列为基础,将已知的伪随机数与揉序列规则下的短序列复合后得到新的符号混沌序列,再转换成二进制序列,从而得到长度随迭代次数成几何级数增加的伪随机序列(PRN).理论与实证分析都表明这是一个有效的伪随机生成器.为应用到图像的加解密技术中,建立了一个新型元胞自动机.该元胞自动机能有效地避免数据膨胀,加密效率高,并能产生显著的"雪崩效应",提高了加密技术的安全性. 关键词： 复合符号混沌序列 符号动力学 伪随机序列 元胞自动机     

Linear cellular automata and recurring sequences in finite fields

A one-dimensional linear cellular automaton with periodic boundary conditions consists of a lattice of sites on a cylinder evolving according to a linear local interaction rule. Limit cycles for such a system are studied as sets of strings on which the rule acts as a shift of sizes/h; i.e., each string in the limit cycle cyclically shifts bys sites inh iterations of the rule. For any given rule, the size of the shift varies with the cylinder sizen. The analysis of shifts establishes an equivalence between the strings of values appearing in limit cycles for these automata, and linear recurring sequences in finite fields. Specifically, it is shown that a string appears in a limit cycle for a linear automaton rule on a cylinder sizen iff its values satisfy a linear recurrence relation defined by the shift value for thatn. The rich body of results on recurring sequences and finite fields can then be used to obtain detailed information on periodic behavior for these systems. Topics considered here include the inverse problem of identifying the set of linear automata rules for which a given string appears in a limit cycle, and the structure under operations (such as addition and complementation) of sets of limit cycle strings.     

Cellular automaton model for traffic flow based on safe driving policies and human reactions

This paper proposes a new single-lane cellular automaton model for traffic flow. The model takes into account normal drivers’ spacing policies and transportation engineering practices to guarantee that microscopic vehicle behavior is more in line with vehicular movement in the real world. As a result, drivers’ reactions are based on a safety analysis that determines the most appropriate action for a vehicle to take. Hence, the model introduces a new set of simple rules to change the speed of vehicles that incorporates three important thresholds required by the follower vehicle to accelerate, slow down or maintain its speed. Thus, the space gap, relative speed and limited acceleration/deceleration capabilities are introduced into simulations. Simulation results obtained from a system with periodic conditions show that the model can smooth the speed drop when vehicles approach the upstream front of the traffic jam. Therefore, the model avoids unrealistic deceleration behavior found in most previous cellular automata models. Besides, the model is also capable of reproducing most empirical findings including the three states of traffic flow, the backward speed of the downstream front of the traffic jam, and different congested traffic patterns induced by a system with open boundary conditions with an on-ramp. Moreover, the new model preserves the computational simplicity of the cellular automata models.     

Outer-totalistic cellular automata on graphs

We present an intuitive formalism for implementing cellular automata on arbitrary topologies. By that means, we identify a symmetry operation in the class of elementary cellular automata. Moreover, we determine the subset of topologically sensitive elementary cellular automata and find that the overall number of complex patterns decreases under increasing neighborhood size in regular graphs. As exemplary applications, we apply the formalism to complex networks and compare the potential of scale-free graphs and metabolic networks to generate complex dynamics.