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Chemical Structures and Convection

  • P. Borckmans
  • G. Dewel
Conference paper
Part of the Springer Series in Synergetics book series (SSSYN, volume 39)

Abstract

Whereas cellular patterns in driven hydrodynamic systems have been known for nearly a century /1/, the observation of organized behavior (periodic oscillations, waves,…) in complex chemical systems is much more recent. It goes back to the work of Belousov and Zhabotinsky and came as a surprise to most chemists. They were indeed at first considered as rather exotic phenomena (although they had been shown, by Glansdorff and Prigogine /2/, not to be in contradiction with basic thermodynamic principles), but it is now apparent that an increasing number of complex chemical networks may exhibit this type of behavior when functioning sufficiently far from thermal equilibrium /3/. Much effort has lately gone into the precise determination of the characteristics of the various kind of waves (fronts /4/, target patterns /5/ and spiral waves /6,7/) in order to understand the mechanism of their formation.

Keywords

Mass Transfer Coefficient Bifurcation Parameter Spiral Wave Convective Motion Turing Instability 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 01.
    H.L. Swinney and J.P. Gollub (Eds.), Hydrodynamlc Instabilities and the Transition to Turbulence (Springer, Berlin 1985)Google Scholar
  2. 02.
    P. Glansdorff and I. Prigogine, Thermodynamic Theory of Structures, Stability and Fluctuations (Wiley, NY 1971)Google Scholar
  3. 03.
    R.J. Field and M. Burger, Eds. Oscillations and Traveling Waves in Chemical Systems (Wiley, NY 1984)Google Scholar
  4. 04.
    P. Wood and J. Ross, J. Chem. Phys. 82 1924 (1985)ADSCrossRefGoogle Scholar
  5. 04a.
    J.M. Bodet, J. Ross and C. Vidal, J. Chem. Phys. 86 4418 (1987)ADSCrossRefGoogle Scholar
  6. 05.
    C. Vidal, J. Stat. Phys. 48 1017 (1987)ADSCrossRefGoogle Scholar
  7. 06.
    K.I. Agladze and V.I. Krinsky, Nature 296 424 (1982)ADSCrossRefGoogle Scholar
  8. 07.
    S.C. Müller, T. Plesser, B. Hess, Physica 24D 71, 87 (1987)ADSGoogle Scholar
  9. 08.
    A.M. Turing, Philos. Trans. Roy. Soc. London B237 37 (1952)ADSGoogle Scholar
  10. 09.
    G. Nicolis and I. Prigogine, Self Organization in Nonequilibrium Systems (Wiley, NY 1977)zbMATHGoogle Scholar
  11. 09a.
    D. Walgraef, G. Dewel, P. Borckmans, Adv. Chem. Phys. 49 311 (1982)CrossRefGoogle Scholar
  12. 10.
    P.K. Becker and R. Field, J. Phys. Chem. 89 118 (1985)CrossRefGoogle Scholar
  13. 11.
    A. Boiteux and B. Hess, Ber. Bunsenges. Phys. Chem. 84 392 (1980)Google Scholar
  14. 12.
    A.M. Zhabothinsky and A.N. Zaikin, J. Theor. Biol. 40 45 (1973)CrossRefGoogle Scholar
  15. 13.
    K. Showalter, J. Chem. Phys. 73 3735 (1980)ADSCrossRefGoogle Scholar
  16. 14.
    M. Orban, J. Am. Chem. Soc. 102 4311 (1980)CrossRefGoogle Scholar
  17. 15.
    M. Marek in Modelling of Patterns in Space and Time. Lecture Notes in Biomathematics Vol.55 (Ed. W. Jäger and J.D. Murray) (Springer, Berlin 1984) page 214 K. Bar-Eli and W. Geiseler, J. Phys. Chem. 85 3461 (1981)CrossRefGoogle Scholar
  18. 16.
    D. Bedeaux, P. Mazur, R.A. Pasmanter, Physica 86A 355 (1977)ADSGoogle Scholar
  19. 17.
    D. Hefer and M. Sheintuch, Chem. Eng. Sci. 41 2285 (1986)CrossRefGoogle Scholar
  20. 18.
    J.A. Vastano, J.E. Pearson, W. Horsthemke, H.L. Swinney, Phys. Lett. A124 320 (1987)ADSGoogle Scholar
  21. 19.
    P. Möckel, Naturwissenschaften 64 224 (1977)ADSCrossRefGoogle Scholar
  22. 20.
    M. Kagan, A. Levi, D. Avnir, ibid. 69 548 (1982), 70 144 (1983)ADSCrossRefGoogle Scholar
  23. 21.
    M. Gimenez and J.-C. Micheau, ibid. 70 90 (1983)ADSCrossRefGoogle Scholar
  24. 22.
    D. Avnir and M. Kagan, Nature 307 717 (1984)ADSCrossRefGoogle Scholar
  25. 23.
    J.-C Micheau, M. Gimenez, P. Borckmans, G. Dewel, Nature 305 43 (1983)ADSCrossRefGoogle Scholar
  26. 24.
    S.C. Müller and Th. Plesser, in ref.15 page 246Google Scholar
  27. 24a.
    S.C. Müller, Th. Plesser, B. Hess in Temporal Order, Synergetics N°29. L. Rensing and N. Jaeger Eds. (Springer, Berlin 1985)Google Scholar
  28. 25.
    J. Bdzil and H. Frisch, Phys. Fluids 14 476, 1077 (1971)ADSCrossRefGoogle Scholar
  29. 26.
    J. Platten and J.-C. Legros, Convection in Liquids (Springer, Berlin 1984) Part D.zbMATHGoogle Scholar
  30. 27.
    G. Dewel, D. Walgraef, P. Borckmans, Proc. Natl. Acad. Sci. U.S.A. 80 6429 (1983)ADSCrossRefGoogle Scholar
  31. 28.
    T.J. McDougall, J. Fluid Mech. 126 379 (1983)ADSzbMATHCrossRefGoogle Scholar
  32. 29.
    M. Kagan and D. Avnir in Interfacial Phenomena: Proc. NATO ASI and EPS Summerschool and Conference on Physicochemical Hydrodynamics.Spain 1986. M.G. Velarde and B. Nichols Eds. (Plenum Press, NY to be published)Google Scholar
  33. 30.
    V. Steinberg and E. Moses in Patterns, Defects and Microstructures in Nonequili-brium Systems: NATO ASI (Series E: Applied Sciences N° 121) D. Walgraef Ed. (Martinus Nijhoff, Dordrecht 1987) C.M. Surko, P. Kolodner, A. Passner, R.W. Waiden, Physica D23 220 (1986)Google Scholar
  34. 31.
    E. Moses, J. Fineberg, V. Steinberg, Phys. Rev. A35 2757 (1987) R. Heinrichs, G. Ahlers, D.S. Cannell, Ibid. 2761 (1987)ADSGoogle Scholar
  35. 32.
    G. Dewel, P. Borckmans, D. Walgraef in Chemical Instabilities: NATO ASI (Series C: Mathematical and Physical Sciences N° 120).G. Nicolis and F. Baras Eds. (Reidel, Dordrecht 1984)Google Scholar
  36. 33.
    G.I. Taylor, Proc. Roy. Soc. London A219 186 (1953)ADSGoogle Scholar
  37. 33a.
    G.I. Taylor, Proc. Roy. Soc. London A225 473 (1954)ADSGoogle Scholar
  38. 34.
    J.P. Gollub and T.H. Solomon in Chaos Related Nonlinear Phenomena I. Procaccia Ed. (Plenum Press, New York 1987)Google Scholar
  39. 35.
    B.I. Shraiman, Phys. Rev. A36 261 (1987)ADSGoogle Scholar
  40. 36.
    P. Borckmans, G. Dewel, D. Walgraef, Y. Katayama, J. Stat. Phys. 48 1031 (1987)ADSCrossRefGoogle Scholar
  41. 37.
    M. Marek and E. Svobodova, Biophys. Chem. 3 263 (1975)CrossRefGoogle Scholar
  42. 38.
    E.A. Spiegel and S. Zalesky, Phys. Lett. 106A 335 (1984)ADSGoogle Scholar
  43. 39.
    Z. Noszticzius, W. Horsthemke, W.D. McCormick, H.L. Swinney, W.Y. Tarn, Nature 329 619 (1987)ADSCrossRefGoogle Scholar
  44. 40.
    M. Herschkowitz-Kaufman and G. Nicolis, J. Chem. Phys. 56 1890 (1972)ADSCrossRefGoogle Scholar
  45. 41.
    J.F.G. Auchmuty and G. Nicolis, Bull. Math. Biol. 35 323 (1975)MathSciNetGoogle Scholar
  46. 42.
    J. Boa and D.S. Cohen, SIAM J. Appl. Math. 30 123 (1976)zbMATHCrossRefGoogle Scholar
  47. 43.
    I.C. Walton, J. Fluid Mech. 131 455 (1983)ADSzbMATHCrossRefGoogle Scholar
  48. 44.
    G. Dewel, D. Walgraef, P. Borckmans, J. Chim. Phys. 84 1335 (1987)Google Scholar
  49. 45.
    J. Boissonade, J. Physique (France) 49 541 (1988)CrossRefGoogle Scholar
  50. 46.
    A. Newell and J.A. Whitehead, J. Fluid Mech. 38 279 (1969)ADSzbMATHCrossRefGoogle Scholar
  51. 47.
    S.C. Müller, Th. Plesser, B. Hess, Biophys. Chem. 26 357 (1987) and in ref.29CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • P. Borckmans
    • 1
  • G. Dewel
    • 1
  1. 1.Faculté des SciencesUniversité Libre de BruxellesBrusselsBelgium

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