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Chemical Waves in Oscillatory Media

  • Christian Vidal
Part of the NATO ASI Series book series (NSSB, volume 237)

Abstract

Chemical waves are a striking phenomenon that occurs in some reacting systems evolving far from equilibrium. They consist in concentration differences which propagate through the medium at the expense of the chemical free energy content of the reactants. Thus, in contrast to the other kinds of wave (e.g. acoustic or electromagnetic, etc.), they do not carry energy. Owing to this, they exhibit several peculiar properties, such as for instance: conservation of amplitude and waveform while propagating in a dispersive medium, annihilation in head-on collisions, lack of ceflection and interference. These qualitative features make them so much distinguishable that one may wonder whether the word “wave” is still appropriate; another word, like “autowave” used in the russian literature, would emphasize how specific are these chemical propagation phenomena.

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References

  1. 1.
    R. Luther, Z. Elektrochem., 12:596 (1906)Google Scholar
  2. 2.
    R. J. Field and M. Burger, in: “Oscillations and traveling waves in chemical systems”, Wiley, New York (1985)Google Scholar
  3. A. Pacault and C. Vidal, J. Chie. Phys., 79: 691 (1982)CrossRefGoogle Scholar
  4. C. Vidal and P. Hanusse, Int. Rev. Phys. Chem., 5: 1 (1926)CrossRefGoogle Scholar
  5. 3.
    W. Y. Tam, W. Horsthemke, Z. Noszticius and H. L. Swinney, J. Chem. Phys, 88: 3395 (1988)CrossRefGoogle Scholar
  6. 4.
    N. Kopell, and L. N. Howard, Science, 180: 1171 (1973)CrossRefGoogle Scholar
  7. 5.
    A. Winfree, Science, 175: 634 (1972)CrossRefGoogle Scholar
  8. 6.
    P. Ortoleva and J. Ross, J. Chem. Phys., 58: 5673 (1973)CrossRefGoogle Scholar
  9. 7.
    P. S. Hagan, Adv. Appl. Math., 2: 400 (1981)MathSciNetCrossRefGoogle Scholar
  10. 8.
    J. M. Bodet, J. Ross and C. Vidal, J. Chem. Phys., 86: 4418 (1987)CrossRefGoogle Scholar
  11. 9.
    P. C. Fife, in: “Mathematical aspects of reacting and diffusing systems”, Springer-Verlag, Heidelberg (1979)CrossRefGoogle Scholar
  12. 10.
    P. M. Wood and J. Ross, J. Chem. Phys., 82:1924 (1985)CrossRefGoogle Scholar
  13. I. Kuhnert and H. J. Krug, J. Phys. Chem., 91: 730 (1987)CrossRefGoogle Scholar
  14. 11.
    P. Mockel, Naturwiss., 64: 224 (1977)CrossRefGoogle Scholar
  15. 12.
    J. C. Micheau, M. Gimenez, P. Borckmans and G. Dewel, Nature, 305: 43 (1983)CrossRefGoogle Scholar
  16. 13.
    D. Avnir and M. Kagan, Nature, 307: 717 (1984)CrossRefGoogle Scholar
  17. 14.
    A. M. Zhabotinsky and A. N. Zaikin, J. Theor. Biol., 40: 45 (1973)CrossRefGoogle Scholar
  18. 15.
    K. Showalter, J. Chem. Phys., 73: 3735 (1980)CrossRefGoogle Scholar
  19. 16.
    M. Orban, J. Am. Chem. Soc., 102: 4311 (1980)CrossRefGoogle Scholar
  20. 17.
    H. Miike, S. C. Muller and B. Hess, Chem. Phys. Lett., 144: 515 (1988)CrossRefGoogle Scholar
  21. 18.
    J. Rodriguez and C. Vidal, J. Phys. Chem., in pressGoogle Scholar
  22. 19.
    A. Pagola, J. Ross and C. Vidal, J. Phys. Chem, 92: 163 (1988)CrossRefGoogle Scholar
  23. 20.
    P. Keener and J. Tyson, Physica D, 21: 307 (1986)MathSciNetCrossRefGoogle Scholar
  24. 21.
    S. C. Muller, T. Plesser and B. Hess, Physica D, 24:71 and 87 (1987)CrossRefGoogle Scholar
  25. 22.
    P. S. Hagan, SIAM J. Appl. Math., 42: 762 (1982)MathSciNetCrossRefGoogle Scholar
  26. 23.
    P. C. Fife, in: “Non-epuilibrium dynamics in chemical systems”, C. Vidal and A. Pacault eds, Springer-Verlag, Heidelberg, p. 76 (1984)Google Scholar
  27. E. Meron and P. Pelce, Phys. Rev. Lett., 60: 1880 (1988)MathSciNetCrossRefGoogle Scholar
  28. 24.
    C. Vidal, A. Pagola, J. M. Bodet, P. Hanusse and E. Bastardie, J. Phys., 47: 1999 (1986)CrossRefGoogle Scholar
  29. 25.
    D. Walgraef, G. Dewel and P. Borckmans, J. Chem. Phys., 78: 3043 (1983)CrossRefGoogle Scholar
  30. 26.
    A. Pagola and C. Vidal, J. Phys. Chem., in pressGoogle Scholar

Copyright information

© Plenum Press, New York 1990

Authors and Affiliations

  • Christian Vidal
    • 1
  1. 1.Centre de Recherche Paul Pascal (CNRS)Université de Bordeaux ITalence, CédexFrance

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