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Bulletin of the Lebedev Physics Institute

, Volume 45, Issue 6, pp 165–169 | Cite as

Study of the Mechanism of the Autowave Structure Formation at the Reaction Front

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Abstract

A qualitative mechanism of the formation of wave structures at the reaction front is proposed. It is assumed that the structures are formed as a result of the interaction of two subsystems, one of which is responsible for the front formation, and the other is responsible for the formation of structures themselves. Three models are considered; two-dimensional analogues of concentric and spiral waves are numerically demonstrated in each. Fitzhugh–Nagumo, Fisher–Kolmogorov–Petrovskii–Piscounov (Fisher–KPP), and Oregonator models were used as subsystems.

Keywords

autowaves instabilities at the reaction front mathematical modeling 

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References

  1. 1.
    R. E. Liesegang, Naturwiss.Wochenschr. 11, 353 (1896).Google Scholar
  2. 2.
    A. G. Merzhanov, in Physical Chemistry. Current 10 Modern Problems. A Year-Book, Ed. by Akad. I.M. Kolotyrkin (Khimiya, Moscow, 1983), p. 6 [in Russian].Google Scholar
  3. 3.
    G. I. Sivashinsky, Ann. Rev. FluidMech. 15, 179 (1983).ADSCrossRefGoogle Scholar
  4. 4.
    G. Wang, Y. Li, W. Yuan, et al., Combust. Flame 191, 368 (2018).CrossRefGoogle Scholar
  5. 5.
    S. K. Scott, J. Wang, and K. Showalter, J. Chem. Soc., Faraday Trans. 93, 1733 (1997).CrossRefGoogle Scholar
  6. 6.
    G. Jomaas, J. K. Bechtold, and C. K. Law, Proc. Combust. Inst. 31, 1039 (2007).CrossRefGoogle Scholar
  7. 7.
    G. Jomaas and C. K. Law, Phys. Fluids 22, 124102 (2010).ADSCrossRefGoogle Scholar
  8. 8.
    S. Kumar, K. Maruta, S. Minaev, and R. Fursenko, Phys. Fluids, 20, 024101 (2008).ADSCrossRefGoogle Scholar
  9. 9.
    R. FitzHugh, Bull.Math. Biophys. 17, 257 (1955).CrossRefGoogle Scholar
  10. 10.
    R. A. Fisher, Ann. Eugenics 7, 353 (1937).Google Scholar
  11. 11.
    A. N. Kolmogorov, I.G. Petrovskii, and N. S. Piskunov, Bull.MGU.Matematika i Mekhanika 1(6), 1 (1937).Google Scholar
  12. 12.
    R. J. Field and R. M. Noyes, J. Chem. Phys. 60, 1877 (1974).ADSCrossRefGoogle Scholar
  13. 13.
    J. J. Tyson and P. C. Fife, J. Chem. Phys. 73, 2224 (1980).ADSMathSciNetCrossRefGoogle Scholar

Copyright information

© Allerton Press, Inc. 2018

Authors and Affiliations

  1. 1.Lebedev Physical InstituteRussian Academy of SciencesMoscowRussia

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