Geodesic
Parallel implementation of catalytic reaction ($\mathrm{CO+O_2\to CO_2}$) by asynchronous cellular automata
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ Vyčislitelʹnaâ matematika i informatika, no. 2 (2012), pp. 112-126
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Parallel implementation of cellular automata (CA) model of heterogeneous catalysis classical reaction, namely carbon monoxide oxidation ($CO$) reaction over platinum surface is presented. Catalytic reactions when being far from equilibrium may be accompanied by such critical phenomena as oscillations, kinetic phase transitions and chaos. Besides fundamental interest studying of basic kinetic laws of physicochemical processes on metals of platinum group has the important practical application. These reactions are used for environmental cleaning of exhaust from $CO$. The asynchronous cellular automata being sometimes referred to as Monte-Carlo method are the most suitable for describing of complex behavior of nonlinear catalytic systems. CA simulation of heterogeneous catalysis reactions requires to solve problems of very large size, therefore it is necessary to use efficient algorithms of parallelization. For the asynchronous CA of efficient parallel implementation is stiff problem. Therefore to solve this problem the asynchronous CA is transformed in block-synchronous CA. The block-synchronous mode of CA operation decreases the stochasticity of the process. Therefore it is necessary to check, whether block-synchronous CA conserves asynchronous CA evolution. This is done by comparative analysis of simulation characteristics such as probability distribution of reagents concentrations mathematical expectation and dispersion of concentrations and bifurcation diagrams of oxidation reaction obtained by CA simulation with asynchronous and block-synchronous operation modes. Obtained characteristics coincidence of asynchronous and block-synchronous CA evolutions is shown. In addition, comparison asynchronous and block-synchronous CA evolutions for models “ZGB” and “naive diffusion” are performed. Consequently, conclusion about acceptable accuracy of approximation of asynchronous mode to block-synchronous one for the class “reaction – diffusion” models is made. Parallel implementation of block-synchronous CA algorithm results and estimations of its efficiency are presented.
Mots-clés : asynchronous cellular automata, parallel implementation.
Keywords: block-synchronous mode, catalytic oxidation reaction 
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A. E. Sharifulina. Parallel implementation of catalytic reaction ($\mathrm{CO+O_2\to CO_2}$) by asynchronous cellular automata. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ Vyčislitelʹnaâ matematika i informatika, no. 2 (2012), pp. 112-126. http://geodesic.mathdoc.fr/item/VYURV_2012_2_a9/

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