Class Of Cellular Automata Research Articles

A Three Dimensional Modified Cellular Automaton Model for the Prediction of Solidification Microstructures.

A three dimensional modified cellular automaton model (3-D MCA) was developed in order to simulate the evolution of microstructures in solidification of alloys. Different from the classical cellular automata in which only the temperature field was calculated, this model included the solute redistribution both in liquid and solid during solidification. The relationship between the growth velocity of a dendrite tip and the local undercooling, which consists of thermal, constitutional and curvature undercooling terms, was calculated according to the KGT (Kurz-Giovanola-Trivedi) and LKT (Lipton-Kurz-Trivedi) models. The finite volume method, which was coupled with the cellular automaton model, was used to calculate the temperature and solute fields in the calculation domain. The present 3-D MCA model was applied to predict the microstructures, such as the free dendritic growth from an undercooled melt, the competitive dendritic growth in practical casting solidification. Some of the simulated results were compared with those obtained experimentally.

A Modified Cellular Automaton Model for the Simulation of Dendritic Growth in Solidification of Alloys.

A modified cellular automaton model (MCA) was developed in order to simulate the evolution of dendritic microstructures in solidification of alloys. Different from the classical cellular automata in which only the temperature field was calculated, this model also included the solute redistribution both in liquid and solid during solidification. The finite volume method, which was coupled with the cellular automaton model, was used to calculate the temperature and solute fields in the domain. The relationship between the growth velocity of a dendrite tip and the local undercooling was calculated according to the KGT (Kurz–Giovanola– Trivedi) model. The effects of constitutional undercooling and curvature undercooling on the equilibrium interface temperature were also considered in the present model. The MCA model was applied to predict thedendritic microstructures, such as the free dendritic growth from an undercooled melt and competitive dendritic growth in practical casting solidification. The simulated results were compared with those obtained experimentally.

Expansive invertible onesided cellular automata

We study expansive invertible onesided cellular automata (i.e., expansive automorphisms of onesided full shifts) and find severe dynamical and arithmetic constraints which provide partial answers to questions raised by M. Nasu [N2]. We employ the images and bilateral dimension groups, measure multipliers, and constructive combinatorial characterizations for two classes of cellular automata.

Relative diffusion transform and quantum speedup of computations

It is shown that every function computable in time T(n) and space S(n) on a classical one-dimensional cellular automaton can be computed with certainty in time O(T1/2S) and space \(n\sqrt T \) on a quantum computer with relative diffusion transforms (RDTs) on parts of intermediate products of classical computation. However, in the general case, RDTs cannot be implemented by the conventional quantum computer even with oracles for intermediate results. Such a function can be computed only in time O(S4S/2T/T1) on the conventional quantum computer with oracles for the intermediate results of classical computations with time T1.

An empirical method for modelling and simulating some complex macroscopic phenomena by cellular automata

Novel parallel computing models sometime represent a valid alternative to standard differential equation methods in modelling complex phenomena. In particular, Cellular Automata (CA) provide such an alternative approach for some complex natural systems, whose behaviour can be described in terms of local interactions of their constituent parts. This paper illustrates an empirical method applied with interesting results in modelling and simulating some complex macroscopic phenomena. While classical CA are based upon elementary automata, with few states and a simple transition function, in order to deal with macroscopic phenomena it is often necessary to allow a large number of different states a more complicated transition. The notion of substate is introduced in the macroscopic case for decomposing the state of the cell. The values associated to substates can change in time either due to interactions among substates inside the cell (internal transformations) or to local interactions among neighbouring cells. The internal transformations are treated in a way similar to ordinary difference equations. The local interactions among cells can be often treated according to an algorithm for the minimisation of differences, which describes a tendency of conserved quantities to reach an equilibrium distribution. A large class of complex macroscopic phenomena seem to satisfy the applicability conditions of such an empirical method; some of them are briefly reviewed.

Class of Cellular Automata for the Formation of Surface Aggregates

A class of cellular automata is constructed on the basis of a set of simple rules: virtual particles obeying a full exclusion principle are subject to probabilistic dynamics with nonlocal (attractive and repulsive) interactions, and with momentum transfer memory effects. Boundary conditions can be periodic or can be set to simulate open systems, with various geometries. This model system possesses the essential elements to simulate the formation of surface aggregates. A specific application is presented for the formation and the dynamics of islands of hydroxyl groups in the catalytic reduction of NO on a Pt surface. The comparison between the simulation results and the experimental observations by Field Ion Microscopy suggests possible mechanisms for the so-far unexplained formation and dynamics of hydroxyl islands during the NO reduction processes.

Self-organized Criticality in Spatial Evolutionary Game Theory

Self-organized criticality is an important framework for understanding the emergence of scale-free natural phenomena. Cellular automata provide simple interesting models in which to study self-organized criticality. We consider the dynamics of a new class of cellular automata which are constructed as natural spatial extensions of evolutionary game theory. This construction yields a discrete one-parameter family of cellular automata. We show that there is a range of parameter values for which this system exhibits complex dynamics with long range correlations between states in both time and space. In this region the dynamics evolve to a self-organized critical state in which structures exist on all time and length scales, and the relevant statistical measures have power law behaviour.

Geometrical automata for two phase flow simulation

An automaton is an entity defined by a mathematical state which changes following iterative rules representing the interaction with the neighborhood. A model of automata for two-phase flow simulation consisting in a field of disks which are allowed to change their radii and move in a plane is presented. The model is more general than the classical cellular automata in two respects: (1) the grid of cellular automata is dismissed in favor of a trajectory generator; and (2) the rules of interaction involve parameters intended to represent some of the most relevant variables governing the actual physical interactions between phases. Computational experiments show that the algorithm captures the essential physics underlying two-phase flow problems such as bubbly-slug pattern transition and void fraction development along tubes. A comparison with experimental data of void fraction profiles is presented, showing excellent agreement.

MANY-DIMENSIONAL LORENTZ CELLULAR AUTOMATA AND TURING MACHINES

We study the class of cellular automata that generalizes the Lorentz lattice gases in statistical mechanics, the models of industrious ants in the theory of an artificial life and the so-called Tur-mites (many-dimensional Turing machines). We prove that on the square lattice ℤd, d = 2, the existence of a bounded orbit of a particle (ant, machine) determines all nondegenerate local scattering rules (states of a machine). For higher dimensional (d ≥ 3) cubic lattices we show that under some natural conditions all possible bounded orbits (vortices) can live only in some “vortex sheets” that have a dimension strictly less than d.

THE KOLMOGOROV METRIC AND A GENERALIZATION ON A CLASSIFICATION OF CELLULAR AUTOMATA

This paper introduces and applies a new metric, on the space of bi-infinite strings (sequences), to the linear cellular automata classification approach of R. Gilman. The metric presented herein is a generalization of the metric used in the classification work of Gilman and it is shown that those original classification results also hold with this generalized metric.

Symmetry in self-correcting cellular automata

We study a class of cellular automata that are capable of correcting finite configurations of errors within a finite amount of time. Subject to certain natural conditions, we determine the geometric symmetries such automata may possess. In three dimensions the answer is particularly simple: such an automaton may be invariant under all proper rotations that leave the underlying lattice invariant, but it cannot be invariant under the inversion that takes each configuration into its mirror image.

Cellular automata for nanometer-scale computation

Cellular automata have recently been proposed as an architecture for dense, locally-interacting arrays of submicron devices. However, because conventional von Neumann cellular automata do not correctly reflect the long-range behavior of typical inter-device interactions, they do not provide a suitable theoretical model for the proposed device arrays. In this paper we define replica cellular automata, a class of cellular automata that can be generated from lattice-gas cellular automata. We show that for inter-device interactions that have a well-defined screening length D, replica cellular automata provide a suitable formal model. As an example of their applicability, we exhibit a computation-universal cellular automata architecture in which the cells consist of charge-transfer quantum dot devices.

Self-organized critically in vector-state automata

We propose a class of cellular automata where on each lattice site the state is characterized by a vector. These vector-state models are observed to display self-organized criticality and lie in the same universality class as that of the sandpile height model. It is found that a conservative quantity is necessary for the systems to reach the self-organized criticality

Quantum field theoretic behavior of a deterministic cellular automaton

A certain class of cellular automata in 1 space + 1 time dimension is shown to be closely related to quantum field theories containing Dirac fermions. In the massless case this relation can be studied analytically, while the introduction of Dirac mass requires numerical simulations. We show that in the last case the cellular automaton describes the corresponding field theory only approximately.

Measure theoretic approach to the classification of cellular automata

Each measurable transformation that commutes with a shift on the set of configurations is proved to have an interesting dynamical property, i.e., for almost all initial configurations their orbits have a common structure. We can put those transformation into four classes according to their dynamical properties. The classification of cellular automata is derived from it.

Determinism and thermodynamics: Ising cellular automata.

Determinism with or without reversibility and the part of it plays in thermodynamics is poorly understood and rarely explored. To investigate the effects of determinism we introduce a class of cellular automata whose rules are constructed from the Boltzmann probabilities of the Ising model. This class of Ising cellular automata (ICA) has as its high-temperature limit the well-studied Kauffman model [S. A. Kauffman, J. Theor. Biol. 22, 437 (1969); Physica D 10, 145 (1984)]. The control of determinism allows us to establish a direct connection between the Kauffman model and percolation and between correlated percolation and these ICA's. A comparison of the chaotic properties offers an informative look at the consequences of determinism. A line of critical points exists between the ``frozen'' and ``chaotic'' phases for ICA, and the zero-field critical temperature is approximately twice that of the Ising model.

Topological classification of cellular automata

The author summarizes an extensive numerical study of basin and attractor sizes among the 88 distinct elementary cellular automata (CA) rules. Based on this study and on previous work in discretized dynamical systems, he proposes a new classification of CA, complementary to that of Wolfram, in which attractor globality is important. With the use of fixed boundary conditions he finds global periodic attractors in CA for the first time. Not a single instance of attractor chaos is observed in this class of rules.

Cellular Automaton Simulation of Polymers

AbstractIn order to improve our ability to simulate the complex behavior of polymers, we introduce dynamical models in the class of Cellular Automata (CA). Space partitioning methods enable us to overcome fundamental obstacles to large scale simulation of connected chains with excluded volume by parallel processing computers. A highly efficient, two-space algorithm is devised and tested on both Cellular Automata Machines (CAMs) and serial computers. Preliminary results on the static and dynamic properties of polymers in two dimensions are reported.

Flow through geometrically irregular media with lattice gas automata

The determination of the permeability is an interesting problem of fluid dynamics of wide interdisciplinary concern. Many authors approached this subject by developing numerical models of flows through porous media at either macro-scale and micro-scale. According to the latter point of view, we present in this paper a verification of Darcy's law and a first determination of the permeability starting by the knowledge of the microstructure of a three-dimensional random medium. The flow is here reproduced by using a particular class of cellular automata with the Boltzmann approximation.

Wolfram's class IV automata and a good life

A comprehensive discussion of Wolfram's four classes of cellular automata is given, with the intention of relating them to Conway's criteria for a good game of Life. Although it is known that such classifications cannot be entirely rigorous, much information about the behavior of an automaton can be gleaned from the statistical properties of its transition table. Still more information can be deduced from the mean field approximation to its state densities, in particular, from the distribution of horizontal and diagonal tangents of the latter. In turn these characteristics can be related to the presence or absence of certain loops in the de Bruijn diagram of the automaton.