Simulation cellular automata

Iim89] Lim, H.A., Cellular automaton simulations of simple boundary-layer problems, Phys. Rev. A40 (1989) 968-980. 

Cellular automata, then, are models, in the same sense that the Monte Carlo and molecular dynamics approaches are models, which can be employed for the purpose of simulating real systems. We shall use the term cellular automaton (singular) to refer to a model consisting of the following components ... 

Fig. 30. Computer simulation by the cellular automaton technique of spatial pattern evolution during CO oxidation on Pt(100). (From Ref. 32.)...

Many important natural processes ranging from nuclear decay to uni-molecular chemical reactions are first order, or can be approximated as first order, which means that these processes depend only on the concentration to the first power of the transforming species itself. A cellular automaton model for such a system takes on an especially simple form, since rules for the movements of the ingredients are unnecessary and only transition rules for the interconverting species need to be specified. We have recently described such a general cellular automaton model for first-order kinetics and tested its ability to simulate a number of classic first-order phenomena.70... 

Another powerful tool is the cellular automata method invented by John (or Janos) von Neumann and Stanislaw Marcin Ulam (under the name of cellular spaces ). The cellular automata are mathematical models in which space and time both have a granular structure (similar to Monte Carlo simulations on lattices, in MD only time has such a structure). A cellular automaton consists of a periodic lattice of cells (nodes in space). In order to describe the system locally, we assume that every cell has its state representing a vector of N components. Each component is a Boolean variable i.e., a variable having a logical value (e.g., 0 for false and 1 for true ). 

A classical example of reaction-diffusion processes is the Belousov-Zhabotinsky reaction that forms moving Winfree spirals in a two-dimensional reactor. In this reaction the many sequential reaction steps comprise a very complex system, yet the spirals can be simulated with a very simple three-state cellular automaton. This model accounts for the morphology given certain initial conditions but it does not... 

Partial differential equations represent one approach (a computationally intensive one) to simulating reaction-diffusion phenomena. An alternative, more approximate, but often less expensive and more intuitive technique employs cellular automata. A cellular automaton consists of an array of cells and a set of rules by which the state of a cell changes at each discrete time step. The state of the cell can, for example, represent the numbers of particles or concentrations of species in that cell, and the rules, which depend on the current state of the cell and its neighbors, can be chosen to mimic diffusion and chemical reaction. 

An interesting variant of the cellular automaton approach is the lattice gas automaton. Despite the name, lattice gas automata can be used to simulate reactions in condensed as well as gaseous media. They were introduced initially as an alternative to partial differential equations (PDE) for modeling complex problems in fluid flow (Hardy et al., 1976) and have been adapted to include the effects of chemical reaction as well (Dab et al., 1990). Lattice gas automata are similar to cellular automata in that they employ a lattice, but differ because they focus on the motions of individual particles along the lattice and because they can accoimt... 

Mologin DA, Khalatur PG, KhoMov AR. Structural organization of water-containing Nafion a cellular-automaton-based simulation. Macromol Theory Simul 2002 ll(5) 587-606. 

ITS involves a large number of research areas, one of them is maritime traffic and its safety. Applying intelligent transportation systems technologies Vessel Traffic Services can improve maritime transport efficiency and safety. This paper introduces the model of basic cellular automaton for the description of maritime traffic flow in restricted area and brief view how it can be useful in maritime transport safety analysis. Detailed analysis of the simulation results for different traffic schemes can be effectively used in evaluation of waterways traffic organization and optimization. Thereby,... 

P. Cordoba-Torres, R. P. Nogueira, L. de Miranda, L. Brenig, J. Wallenbom, and V. Fairen, Cellular automaton simulation of a simple corrosion mechanism Mesoscopic heterogeneity versus macroscopic homogeneity, Electrochim. Acta 46 2975-2989 (2001). 

Von Neumann was the first to design a cellular automaton capable of universal computation. Since then many others became interested in the problem and either improved on his original construction or have developed alternative constructions. An early example was Alvy Ray Smith (1971), who constructed a series of progressively simpler cellular automata capable of universal computation. The first in the series was a two-dimensional cellular automaton Mg that simulates a given Turing machine M in real time —that is, there is a one-to-one correspondence between the time steps of Mg and the time steps of M. 

First, one might suspect that a quantum Turing machine is more powerful than a classical Turing machine in the sense of complexity theory. Feynman [1] raised this question. He conjectured that it might be difficult to simulate a finite-size quantum system (for example, a quantum cellular automaton) by classical means without an exponential slowdown. 

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