Skip to main content

Chemical Structures and Convection

  • Conference paper
From Chemical to Biological Organization

Part of the book series: Springer Series in Synergetics ((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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. H.L. Swinney and J.P. Gollub (Eds.), Hydrodynamlc Instabilities and the Transition to Turbulence (Springer, Berlin 1985)

    Google Scholar 

  2. P. Glansdorff and I. Prigogine, Thermodynamic Theory of Structures, Stability and Fluctuations (Wiley, NY 1971)

    Google Scholar 

  3. R.J. Field and M. Burger, Eds. Oscillations and Traveling Waves in Chemical Systems (Wiley, NY 1984)

    Google Scholar 

  4. P. Wood and J. Ross, J. Chem. Phys. 82 1924 (1985)

    Article  ADS  Google Scholar 

  5. J.M. Bodet, J. Ross and C. Vidal, J. Chem. Phys. 86 4418 (1987)

    Article  ADS  Google Scholar 

  6. C. Vidal, J. Stat. Phys. 48 1017 (1987)

    Article  ADS  Google Scholar 

  7. K.I. Agladze and V.I. Krinsky, Nature 296 424 (1982)

    Article  ADS  Google Scholar 

  8. S.C. Müller, T. Plesser, B. Hess, Physica 24D 71, 87 (1987)

    ADS  Google Scholar 

  9. A.M. Turing, Philos. Trans. Roy. Soc. London B237 37 (1952)

    ADS  Google Scholar 

  10. G. Nicolis and I. Prigogine, Self Organization in Nonequilibrium Systems (Wiley, NY 1977)

    MATH  Google Scholar 

  11. D. Walgraef, G. Dewel, P. Borckmans, Adv. Chem. Phys. 49 311 (1982)

    Article  Google Scholar 

  12. P.K. Becker and R. Field, J. Phys. Chem. 89 118 (1985)

    Article  Google Scholar 

  13. A. Boiteux and B. Hess, Ber. Bunsenges. Phys. Chem. 84 392 (1980)

    Google Scholar 

  14. A.M. Zhabothinsky and A.N. Zaikin, J. Theor. Biol. 40 45 (1973)

    Article  Google Scholar 

  15. K. Showalter, J. Chem. Phys. 73 3735 (1980)

    Article  ADS  Google Scholar 

  16. M. Orban, J. Am. Chem. Soc. 102 4311 (1980)

    Article  Google Scholar 

  17. 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)

    Article  Google Scholar 

  18. D. Bedeaux, P. Mazur, R.A. Pasmanter, Physica 86A 355 (1977)

    ADS  Google Scholar 

  19. D. Hefer and M. Sheintuch, Chem. Eng. Sci. 41 2285 (1986)

    Article  Google Scholar 

  20. J.A. Vastano, J.E. Pearson, W. Horsthemke, H.L. Swinney, Phys. Lett. A124 320 (1987)

    ADS  Google Scholar 

  21. P. Möckel, Naturwissenschaften 64 224 (1977)

    Article  ADS  Google Scholar 

  22. M. Kagan, A. Levi, D. Avnir, ibid. 69 548 (1982), 70 144 (1983)

    Article  ADS  Google Scholar 

  23. M. Gimenez and J.-C. Micheau, ibid. 70 90 (1983)

    Article  ADS  Google Scholar 

  24. D. Avnir and M. Kagan, Nature 307 717 (1984)

    Article  ADS  Google Scholar 

  25. J.-C Micheau, M. Gimenez, P. Borckmans, G. Dewel, Nature 305 43 (1983)

    Article  ADS  Google Scholar 

  26. S.C. Müller and Th. Plesser, in ref.15 page 246

    Google Scholar 

  27. 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. J. Bdzil and H. Frisch, Phys. Fluids 14 476, 1077 (1971)

    Article  ADS  Google Scholar 

  29. J. Platten and J.-C. Legros, Convection in Liquids (Springer, Berlin 1984) Part D.

    MATH  Google Scholar 

  30. G. Dewel, D. Walgraef, P. Borckmans, Proc. Natl. Acad. Sci. U.S.A. 80 6429 (1983)

    Article  ADS  Google Scholar 

  31. T.J. McDougall, J. Fluid Mech. 126 379 (1983)

    Article  ADS  MATH  Google Scholar 

  32. 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. 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. E. Moses, J. Fineberg, V. Steinberg, Phys. Rev. A35 2757 (1987) R. Heinrichs, G. Ahlers, D.S. Cannell, Ibid. 2761 (1987)

    ADS  Google Scholar 

  35. 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. G.I. Taylor, Proc. Roy. Soc. London A219 186 (1953)

    ADS  Google Scholar 

  37. G.I. Taylor, Proc. Roy. Soc. London A225 473 (1954)

    ADS  Google Scholar 

  38. J.P. Gollub and T.H. Solomon in Chaos Related Nonlinear Phenomena I. Procaccia Ed. (Plenum Press, New York 1987)

    Google Scholar 

  39. B.I. Shraiman, Phys. Rev. A36 261 (1987)

    ADS  Google Scholar 

  40. P. Borckmans, G. Dewel, D. Walgraef, Y. Katayama, J. Stat. Phys. 48 1031 (1987)

    Article  ADS  Google Scholar 

  41. M. Marek and E. Svobodova, Biophys. Chem. 3 263 (1975)

    Article  Google Scholar 

  42. E.A. Spiegel and S. Zalesky, Phys. Lett. 106A 335 (1984)

    ADS  Google Scholar 

  43. Z. Noszticzius, W. Horsthemke, W.D. McCormick, H.L. Swinney, W.Y. Tarn, Nature 329 619 (1987)

    Article  ADS  Google Scholar 

  44. M. Herschkowitz-Kaufman and G. Nicolis, J. Chem. Phys. 56 1890 (1972)

    Article  ADS  Google Scholar 

  45. J.F.G. Auchmuty and G. Nicolis, Bull. Math. Biol. 35 323 (1975)

    MathSciNet  Google Scholar 

  46. J. Boa and D.S. Cohen, SIAM J. Appl. Math. 30 123 (1976)

    Article  MATH  Google Scholar 

  47. I.C. Walton, J. Fluid Mech. 131 455 (1983)

    Article  ADS  MATH  Google Scholar 

  48. G. Dewel, D. Walgraef, P. Borckmans, J. Chim. Phys. 84 1335 (1987)

    Google Scholar 

  49. J. Boissonade, J. Physique (France) 49 541 (1988)

    Article  Google Scholar 

  50. A. Newell and J.A. Whitehead, J. Fluid Mech. 38 279 (1969)

    Article  ADS  MATH  Google Scholar 

  51. S.C. Müller, Th. Plesser, B. Hess, Biophys. Chem. 26 357 (1987) and in ref.29

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1988 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Borckmans, P., Dewel, G. (1988). Chemical Structures and Convection. In: Markus, M., Müller, S.C., Nicolis, G. (eds) From Chemical to Biological Organization. Springer Series in Synergetics, vol 39. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-73688-9_13

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-73688-9_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-73690-2

  • Online ISBN: 978-3-642-73688-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics