Cellular automata modeling of multicomponent impurities diffusion

Authors

  • Rubtsov S.E. Kuban State University, Krasnodar, Российская Федерация
  • Pavlova A.V. Kuban State University, Krasnodar, Российская Федерация
  • Olejnikov A.S. Kuban State University, Krasnodar, Российская Федерация

UDC

510.67:554

Abstract

The work is dedicated to cellular automata (CA) modeling of diffusion-reaction processes of multicomponent impurities. Three-dimensional CA models of the following scenarios relating to the dispersion and impurity transformation were constructed: independent dispersion of constituents of a multicomponent contaminant, the absorption of one substance by another (pollutant neutralization model), the appearance of a new substance as a result of the interaction between the two initial (chemical reaction model). In this paper we implemented the CA-diffusion in a spatial domain with a complicated boundary. The binary type parameter was mapped to each block in the base substitution, as a result of which all the blocks were divided into two types: internal and boundary. This parameter, as a result, determines the necessity of the corresponding block's rotation when performing the base substitution. Thereby the boundary of the modeling domain can be specified arbitrarily. For the computer experiments and analysis of results, we developed an application that implements the above models, reproducing the spatio-temporal concentration distribution of the gas impurities and the formation process of a secondary contaminant from precursor gases. The application allows us to consider the constant and pulse emission sources of the pollutant, and also display the distribution of impurity particles in an arbitrary section of the region at any time iteration and at the required distance from the emission source.

Keywords:

cellular-automata models, impurity diffusion, pollutant interaction, transformation

Acknowledgement

Работа выполнена при поддержке гранта РФФИ и Администрации Краснодарского края 16-41-230175_а.

Author Infos

Sergey E. Rubtsov

канд. физ.-мат. наук, доцент кафедры математического моделирования Кубанского государственного университета

e-mail: rub_serg@mail.ru

Alla V. Pavlova

д-р физ.-мат. наук, доцент профессор кафедры математического моделирования Кубанского государственного университета

e-mail: pavlova@math.kubsu.ru

Aleksandr S. Olejnikov

студент кафедры математического моделирования Кубанского государственного университета

e-mail: kmm@fpm.kubsu.ru

References

  1. Marchuk G.I. Matematicheskoe modelirovanie v probleme okruzhajushhej sredy [Mathematical modeling in environmental problem]. Moscow, Nauka Pub., 1982, 320 p. (In Russian).
  2. Aloyan A.E. Modelirovanie dinamiki i kinetiki gazovyh primesej i aehrozolej v atmosphere [Modeling of dynamics and kinetics of gas impurities and aerosols in the atmosphere]. Moscow, Nauka Pub., 2008. 415 p. (In Russian)
  3. Aloyan A.E., Piskunov V.N. Modelirovanie regional'noj dinamiki gazovyh primesej i aehrozolej [Modeling of regional dynamics of gas impurities and aerosols]. Izvestia RAN. Fizika atmosfery i okeana [Bull. of Russian Academy of Science. Atmospheric and ocean physics], 2005, vol. 41, no. 3, pp. 328-340. (In Russian)
  4. Piskunov V.N. Teoreticheskie modeli kinetiki formirovaniya aehrozolej [Theoretical models of aerosol formation kinetics]. Sarov, RFYAC-VNIIEHF, 2000, 209 p. (In Russian)
  5. Fon Nejman Dzh. Teorija samovosproizvodjashhihsja avtomatov [The theory of self-reproducing automatas]. Moscow, Mir Pub., 1971, 384 p. (In Russian)
  6. Toffoli T. Cellular automata as an alternative to rather than approximation of differential equations in modeling physics. Physica D., 1984, vol. 10, pp. 117-127.
  7. Toffolli T., Margolus N. Cellular automata machines. MIT Press, 1987.
  8. Weimar, J. Cellular automata for reaction-diffusion systems. Parallel computing, 1997, vol. 23, no. 11, pp. 1699-1715.
  9. Vanag V.K. Dissipativnye struktury v reakcionno-diffuzionnyh sistemah. Jeksperiment i teorija [Dissipative structures in reaction-diffusion systems. Experiment and Theory]. Izhevsk, IKI pub., 2008, 300 p. (In Russian)
  10. Boccara N. Reaction-Diffusion complex systems. Berlin, Springer, 2004, 397 p.
  11. Bandman O. Parallel simulation of asynchronous cellular automata evolution. In: Proc. of 7th International Conference on Cellular Automata, for Research and Industry (ACRI 2006). 2016. Vol. 4173 of LNCS. Springer, pp. 41-47.
  12. Bandman O.L. A method for construction of cellular automata simulating pattern formation processes. Theoretical background of applied discrete mathematics, 2010, no. 4, pp. 91-99.
  13. Kalgin K.V. Comparative study of parallel algorithms for asynchronous cellular automata simulation on different computer architectures. In: Proc. of ACRI-2010, LNCS 6350. Springer, 2010, pp. 399-408.
  14. Rubtsov S.E., Pavlova A.V., Savenkov S.I. O kletochno-avtomatnyh modelyah konvekcionno-diffuzionnyh processov primesej [About cellular-automatic models of convection-diffusion processes of substances]. Jekologicheskij vestnik nauchnyh centrov Chernomorskogo jekonomicheskogo sotrudnichestva [Ecological Bulletin of Research Centers of the Black Sea Economic Cooperation], 2016, no. 4, pp. 62-68. (In Russian)
  15. Rubtsov S.E., Pavlova A.V. Kletochno-avtomatnye modeli diffuzionno-reakcionnyh processov mnogokomponentnyh primesej [Cellular-automata models of diffusion-reaction processes of multicomponent impurities]. Zashhita okruzhajushhej sredy v neftegazovom komplekse [Environmental protection in the oil and gas sector], 2017, no. 6, pp. 55-60. (In Russian)
  16. Bandman O.L. Invarianty kletochno-avtomatnyh modelej reakcionno-diffuzionnyh processov [Invariants Cellular Automaton models of reaction-diffusion processes]. Prikladnaja diskretnaja matematika [Applied discrete mathematics], 2012, no. 3(17), pp 108-120. (In Russian)
  17. Babeshko V.A., Zaretskaya M.V., Evdokimova O.V., Pavlova A.V., Babeshko O.M., Kruglyakova O.P., Kurilov P.I., Terenozhkin A.M., Gendina I.V. Ocenka vlijanija vulkanicheskih i prirodno-tehnologicheskih zagrjaznenij na jekosistemu Azovskogo morja [Assessing the impact of volcanic and natural-technological pollution on the ecosystem of the Sea of Azov]. Zashhita okruzhajushhej sredy v neftegazovom komplekse [Environmental protection in the oil and gas sector], 2010, no. 9, pp. 6-12. (In Russian).

Issue

Section

Physics

Pages

86-93

Submitted

2017-12-12

Published

2017-12-25

How to Cite

Rubtsov S.E., Pavlova A.V., Olejnikov A.S. Cellular automata modeling of multicomponent impurities diffusion. Ecological Bulletin of Research Centers of the Black Sea Economic Cooperation, 2017, no. 4, pp. 86-93. (In Russian)