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Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2015, Volume 25, Issue 4, Pages 492–500 (Mi vuu503)  

MATHEMATICS

The application of theory of probability to the modelling of chemical kinetics systems

M. N. Nazarov

Chair of Higher Math. 1, National Research University of Electronic Technology, pl. Shokina, 1, Zelenograd, Moscow, 124498, Russia

Abstract: The paper considers a model of chemical kinetics for which the derivation of equations does not rely on the law of mass action, but is rather based on such principles as geometric probability and joint probability. For this model a generalization is constructed for the case of reaction-diffusion systems in heterogeneous medium, with respect to the convective and diffusive transfer of heat. The construction of this generalization is carried out by an alternative methodology, which is based fully on systems of ordinary differential equations, without a transition to partial derivatives. The description of this new method is a bit similar to the finite volume method, except that it uses statistical simplifying positions and geometric probability to describe diffusion processes. Such approach allows us to greatly simplify the numerical implementation of the resulting model, as well as to simplify its quantitative analysis by dynamical systems theory methods. Moreover, the efficiency of parallel implementation of the numerical method is increased for the resulting model. In addition, the author considers an application of this model for the description of some example reaction with quasi-periodic regime, as well as an algorithm for the transition from standard models with dimensional kinetic constants to its formalism.

Keywords: chemical kinetics, catalysis, convection, diffusion, dynamical systems.

Full text: PDF file (233 kB)
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UDC: 517.958+544.4
MSC: 92E20, 80A32, 76R99
Received: 05.08.2015

Citation: M. N. Nazarov, “The application of theory of probability to the modelling of chemical kinetics systems”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 25:4 (2015), 492–500

Citation in format AMSBIB
\Bibitem{Naz15}
\by M.~N.~Nazarov
\paper The application of theory of probability to the modelling of chemical kinetics systems
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2015
\vol 25
\issue 4
\pages 492--500
\mathnet{http://mi.mathnet.ru/vuu503}
\elib{http://elibrary.ru/item.asp?id=25109970}


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