Skip to main content

Stochastic Aspects of Nonequilibrium Transitions in Chemical Systems

  • Conference paper
Non-Equilibrium Dynamics in Chemical Systems

Part of the book series: Springer Series in Synergetics ((SSSYN,volume 27))

Abstract

One of the principal preoccupations of the present meeting is the study of the transitions occurring in nonlinear chemical systems far from equilibrium. Experimental evidence provides us with an impressive number of examples, and brings out clearly the diversity of these phenomena, from bistability and sustained oscillations to chaotic dynamics and the formation of spatial patterns in an initially uniform system.

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. J.C. Roux, P. De Kepper and J. Boissonnade: Phys. Letters 97A, 168 (1983)

    ADS  Google Scholar 

  2. T.R. Kirpatrick, E.G.D. Cohen and J.R. Dorfman: Phys. Rev. Lett. 42, 862 (1979);

    Article  ADS  Google Scholar 

  3. T.R. Kirpatrick, E.G.D. Cohen and J.R. Dorfman: Phys. Rev. Lett. 44, 472 (1980);

    Article  ADS  Google Scholar 

  4. T.R. Kirpatrick, E.G.D. Cohen and J.R. Dorfman: Phys. Rev. A 26, 972 (1982);

    Article  ADS  Google Scholar 

  5. T.R. Kirpatrick, E.G.D. Cohen and J.R. Dorfman: Phys. Rev. A 26, 995 (1982)

    Article  ADS  Google Scholar 

  6. G. Nicolis and I. Prigogine: Self Organization in Nonequili-brium Systems (Wiley, New York, 1977)

    Google Scholar 

  7. H. Haken: Advanced Synergetics: Instability Hierarchies of Self-Organizing Systems and Devices (Springer-Verlag, Berlin, 1983)

    MATH  Google Scholar 

  8. D. Walgraef, G. Dewel and P. Borckmans: Phys. Rev. A 21, 397 (1980);

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

  10. T. Kurtz: Stoch. Proc. Applic. 6, 223 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  11. P. Kotelenez: Report No. 81 (UnTversität Bremen, December 1982)

    Google Scholar 

  12. C. Van den Broeck, M. Malek Mansour and F. Baras: J. Stat. Phys. 28, 557 (1982)

    Article  ADS  MATH  Google Scholar 

  13. F. Baras, M. Malek Mansour and C. Van den Broeck: J. Stat. Phys. 28, 577 (1982)

    Article  ADS  MATH  Google Scholar 

  14. H. Lemarchand: Bull. Acad. R. Belgique 67, 343 (1981)

    MathSciNet  MATH  Google Scholar 

  15. E. Knobloch and K.A. Wiesenfeld: J. Stat. Phys. 33, 611 (1983)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  16. M. Malek Mansour, C. Van den Broeck, G. Nicolis and J. W. Turner: Ann. Phys. (New York) 131, 283 (1981)

    Article  ADS  MATH  Google Scholar 

  17. W. Feller: An Introduction to Probability Theory and Its Applications (Wiley, New York, 1967)

    Google Scholar 

  18. G. Nicolis and R. Lefever: Phys. Lett. 62A, 469 (1977)

    ADS  Google Scholar 

  19. G. Nicolis and J.W. Turner: Ann. N.Y. Acad. Sci. 316, 251 (1979)

    Article  MathSciNet  ADS  Google Scholar 

  20. H. Lemarchand: Physica 101A, 518 (1980)

    MathSciNet  ADS  Google Scholar 

  21. H. Lemarchand and G. Nicolis: J. Stat. Phys. (in press, 1984)

    Google Scholar 

  22. A. Fraikin and H. Lemarchand: J. Stat. Phys. (submitted, 1984)

    Google Scholar 

  23. D. Walgraef, G. Dewel and P. Borckmans: J. Chem. Phys. 78, 3043 (1983)

    Article  ADS  Google Scholar 

  24. See, for instance, J. Guckenheimer and P. Holmes: Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields (Springer-Verlag, Berlin 1983)

    MATH  Google Scholar 

  25. G. Nicolis and M. Malek Mansour: Phys. Rev. A 29, 2845 (1984)

    Article  ADS  Google Scholar 

  26. C.W. Gardiner, K.J. McNeil, D.F. Walls and I.S. Matheson: J. Stat. Phys. 14, 307 (1976)

    Article  ADS  Google Scholar 

  27. A.M. Tremblay, M. Arai and E.D. Siggia: Phys. Rev. A 23, 1451 (1981)

    Article  ADS  Google Scholar 

  28. M. Mareschal and E. Kestemont: Phys. Rev. A 30, 1158 (1984)

    Article  ADS  Google Scholar 

  29. M. Suzuki: in Proc. XVIIth Solvay Conf. Phys. (Wiley, New York, 1981)

    Google Scholar 

  30. B. Caroli, C. Caroli and B. Roulet: J. Stat. Phys. 21, 415 (1979);

    Article  ADS  Google Scholar 

  31. B. Caroli, C. Caroli and B. Roulet: Physica 101A, 581 (1980)

    MathSciNet  ADS  Google Scholar 

  32. N.G. Van Kampen: J. Stat. Phys. 17, 71 (1977)

    Article  ADS  Google Scholar 

  33. F.T. Arecchi, A. Politi and L. Ulivi: Il Nuovo Cim. 71B, 119 (1982)

    ADS  Google Scholar 

  34. B. Matkowsky, Z. Schuss, C. Knessel, C. Tier and M. Mangel, Techn. Rep. No. 8307, Applied Math. Department (Northwestern University, December 1983)

    Google Scholar 

  35. W. Ebeling and L. Shimansky-Geier: Physica 98A, 587 (1979)

    ADS  Google Scholar 

  36. W. Frankowicz and E. Gudowska-Nowak: Physica 116A, 331 (1982)

    ADS  Google Scholar 

  37. D. Borgis and M. Moreau: J. Stat. Phys. (in press, 1984)

    Google Scholar 

  38. F. Baras, G. Nicolis, M. Malek Mansour and J.W. Turner : J. Stat. Phys. 32, 1 (1983)

    Article  ADS  Google Scholar 

  39. M. Frankowicz and G. Nicolis: J. Stat. Phys. 33, 595 (1983)

    Article  ADS  Google Scholar 

  40. G. Nicolis, F. Baras and M. Malek Mansour: in Chemical Instabilities: Applications in Chemistry, Engineering, Geology and Material Science (G. Nicolis and F. Baras Eds., Reidel, Dordrecht, 1984)

    Google Scholar 

  41. G. Broggi and L.A. Lugiato: preprint (1984)

    Google Scholar 

  42. D.A. Frank-Kamenetskii: Diffusion and heat Transfer in Chemical Kinetics (Plenum, New York 1969)

    Google Scholar 

  43. J.C. Lermant and S. Yip: Combustion and Flame (submitted, 1984)

    Google Scholar 

  44. G. Nicolis and H. Frisch: Phys. Rev. A (in press, 1984)

    Google Scholar 

  45. T. Boddington, P. Gray and S.K. Scott, J. Chem. Soc. Faraday Trans. 2 78, 1721 and 1731 (1982)

    Article  Google Scholar 

  46. F. Baras: (to be published, 1984)

    Google Scholar 

  47. Y. Elskens, H. Frisch and G. Nicolis: J. Stat. Phys. 33, 317 (1983)

    Article  MathSciNet  ADS  Google Scholar 

  48. T. Geisel: Phys. Rev. Lett. 48, 7 (1982)

    Article  MathSciNet  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1984 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Nicolis, G., Baras, F., Mansour, M.M. (1984). Stochastic Aspects of Nonequilibrium Transitions in Chemical Systems. In: Vidal, C., Pacault, A. (eds) Non-Equilibrium Dynamics in Chemical Systems. Springer Series in Synergetics, vol 27. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-70196-2_28

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-70196-2_28

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-70198-6

  • Online ISBN: 978-3-642-70196-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics