Skip to main content
SpringerLink
Log in
Book cover

Chemical Waves and Patterns pp 609–634Cite as

Internal Noise, Oscillations, Chaos and Chemical Waves

  • Chapter

Part of the book series: Understanding Chemical Reactivity ((UCRE,volume 10))

Abstract

In most circumstances the spatiotemporal dynamics of reacting systems constrained to lie far from equilibrium can be described adequately by reaction-diffusion equations. These equations are valid provided the phenomena of interest occur on distance and time scales that are sufficiently long compared to molecular scales. Naturally, the complete microscopic description of the reacting medium, whether near to or far from equilibrium, must be based on the full molecular dynamics of the system, as embodied in Newton’s or Schrödinger’s equations of motion.

“Noise, n. A stench in the ear. Undomesticated music. The chief product and authenticating sign of civilization.”

Ambrose Bierce, The Devil’s Dictionary

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

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   219.99
Price excludes VAT (USA)
  • Durable hardcover 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Van Kampen, N. G., Stochastic Processes in Physics and Chemistry (North-Holland, Amsterdam, 1981)

    Google Scholar 

  2. Gardiner, C. W., Handbook of Stochastic Processes, (Springer-Verlag, New York, 1985).

    Google Scholar 

  3. Dab, D., Lawniczak, A., Boon, J.-P., and Kapral, R., Phys. Rev. Lett. 64, 2462 (1990)

    Article  CAS  Google Scholar 

  4. Lawniczak, A., Dab, D., Kapral, R., and Boon, J. P., Physica D 47, 132 (1991).

    Article  CAS  Google Scholar 

  5. Kapral, R., Lawniczak, A., and Masiar, P., Phys. Rev. Lett. 66, 2539 (1991)

    Article  CAS  Google Scholar 

  6. Kapral, R., Lawniczak, A., and Masiar, P., J. Chem. Phys. 96, 2762 (1992).

    Article  CAS  Google Scholar 

  7. Dab, D., Boon, J. P., and Li, Y.-X., Phys. Rev. Lett. 66, 2535 (1991).

    Article  CAS  Google Scholar 

  8. Frisch, U., Hasslacher, B., and Pomeau, Y., Phys. Rev. Leu. 56, 1505 (1986)

    Article  CAS  Google Scholar 

  9. d’Humiéres, D., Hasslacher, B., Lallemand, P., Pomeau, Y., and Rivet, J. P., Complex Systems 1, 648 (1987)

    Google Scholar 

  10. Doolen, G. (ed.), Lattice Gas Methods for Partial Differential Equations (Addison-Wesley, New York, 1990).

    Google Scholar 

  11. Gruner, D., Kapral, R., and Lawniczak, A., J. Chem. Phys. 99, 3938 (1993).

    Article  CAS  Google Scholar 

  12. Hasslacher, B., Kapral, R., and Lawniczak, A., Chaos 3, 7 (1993).

    Article  CAS  Google Scholar 

  13. Wu, X.-G. and Kapral, R., Physica A 188, 284 (1992).

    Article  CAS  Google Scholar 

  14. Wu, X.-G. and Kapral, R., Phys. Rev. Lett. 70, 1940 (1993)

    Article  CAS  Google Scholar 

  15. Kapral, R. and Wu, X.-G., Annals N. Y. Acad. Sci.,706 186 (1994

    Article  Google Scholar 

  16. Wu, X.-G. and Kapral, R., J. Chem. Phys. 100, 5936 (1994).

    Article  CAS  Google Scholar 

  17. Willamowski, K.-D. and Rössler, O. E., Z. Naturforsch. 35a, 317 (1980).

    Google Scholar 

  18. Von Neumann, J., in Theory of Self-Reproducing Automata, edited by A. W. Birks (University of Illinois, Urbana, 1966).

    Google Scholar 

  19. Wolfram, S. (ed.), Theory and Applications of Cellular Automata (World Scientific, Singapore, 1986).

    Google Scholar 

  20. Greenberg, J. M. and Hastings, S. P., SIAM J. Appl. Math. 34, 515 (1978).

    Article  Google Scholar 

  21. Kapral, R., J. Math. Chem. 6, 113 (1991).

    Article  CAS  Google Scholar 

  22. Fisch, R., Gravner, J., and Griffeath, D., Statistics and Computing 1, 23 (1991)

    Article  Google Scholar 

  23. Fisch, R., Gravner, J., and Griffeath, D., Ann. Applied Probability 3, 935 (1993)

    Article  Google Scholar 

  24. Gravner, J. and Griffeath, D., Trans. Amer. Math. Soc. 340, 837 (1993)

    Article  Google Scholar 

  25. Durrett, R. and Griffeath, D., J. Experimental Math. 2, 183 (1993)

    Article  Google Scholar 

  26. Durrett, R. and Steif, J., J. Theor. Prob. (1991)

    Google Scholar 

  27. Durrett, R., Nonlinear Science Today 1, 1 (1991).

    Article  Google Scholar 

  28. Markus, M. and Hess, B., Nature 347, 56 (1990)

    Article  CAS  Google Scholar 

  29. Schepers, H. E. and Marcus, M., PhysicaA 188, 337 (1992).

    Article  CAS  Google Scholar 

  30. Gerhardt, M., Schuster, H., and Tyson, J. J., Science 247, 1563 (1990)

    Article  CAS  Google Scholar 

  31. Gerhardt, M., Schuster, H., and Tyson, J. J., Physica D 46, 392 (1990).

    Article  Google Scholar 

  32. Multi-speed models have been constructed for hydrodynamics flows. See, for instance, [5].

    Google Scholar 

  33. Zanette, D. H., Phys. Rev. A 46, 7573 (1992)

    Article  CAS  Google Scholar 

  34. Chopard, B., Droz, M., Cornell, S., and Frachebourg, L., Proceedings of the Workshop on Cellular Automata for Astrophysics, Ardennes (1992).

    Google Scholar 

  35. Scott, S. K., Chemical Chaos (Oxford University Press, Oxford, 1991)

    Google Scholar 

  36. Berge, P., Pomeau, Y., and Vidal, C., Order within Chaos (Wiley, New York, 1986).

    Google Scholar 

  37. Aguda, B. D. and Clarke, B. L., J. Chem. Phys. 89, 7428 (1988).

    Article  CAS  Google Scholar 

  38. Nicolis, G. and Prigogine, I., Self-Organization in Non-Equilibrium Systems (Wiley, New York, 1977).

    Google Scholar 

  39. See, for example, Crutchfield, J. P., Farmer, J. D., and Huberman, B. A., Phys. Rep. 92, 45 (1982).

    Article  Google Scholar 

  40. Kapral, R., Schell, M., and Fraser, S., J. Phys. Chem. 86, 2205 (1982):

    Article  CAS  Google Scholar 

  41. Keizer, J. E. and Tilden, J.J. Phys. Chem. 93, 2811 (1989).

    Article  CAS  Google Scholar 

  42. Fox, R. F. and Keizer, J. E.Phys. Rev. Lett. 64, 249 (1990)

    Article  Google Scholar 

  43. Fox, R. F. and Keizer, J. E.Phys. Rev. A 43, 1709 (1991)

    Article  CAS  Google Scholar 

  44. Fox, R. F.Phys. Rev. A 41, 2969 (1990)

    Article  CAS  Google Scholar 

  45. Keizer, J. E. and Fox, R. F.Phys. Rev. A 46, 3572 (1992).

    Article  Google Scholar 

  46. Nicolis, G. and Balakrishnan, V., Phys. Rev. A 46, 3569 (1992)

    Article  Google Scholar 

  47. Peters, P. and Nicolis, G., Physica A 188, 426 (1992)

    Article  Google Scholar 

  48. Geysermans, P. and Nicolis, G., J. Chem. Phys. 99, 8964 (1993).

    Article  CAS  Google Scholar 

  49. Kuramoto, Y., Chemical Oscillations,Waves and Turbulence (Springer-Verlag, Berlin, 1980).

    Google Scholar 

  50. Lemarchand, A., Lesne, A., Perera, A., Moreau, M., and Mareschal, M., Phys. Rev. E 48, 1568 (1993).

    Article  CAS  Google Scholar 

  51. Chee, M.-N., Kapral, R., and Whittington, S. G., J. Chem. Phys. 92, 7302 (1990).

    Article  CAS  Google Scholar 

  52. Guemez, J. and Matias, M., Phys. Rev. E 48, R2351 (1993).

    Article  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, ON, M5S 1A1, Canada

    Raymond Kapral & Xiao-Guang Wu

Authors
  1. Raymond Kapral
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xiao-Guang Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Chemistry, University of Toronto, Toronto, Ontario, Canada

    Raymond Kapral

  2. Department of Chemistry, West Virginia University, Morgantown, WV, USA

    Kenneth Showalter

Rights and permissions

Reprints and permissions

Copyright information

© 1995 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Kapral, R., Wu, XG. (1995). Internal Noise, Oscillations, Chaos and Chemical Waves. In: Kapral, R., Showalter, K. (eds) Chemical Waves and Patterns. Understanding Chemical Reactivity, vol 10. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-1156-0_18

Download citation

  • DOI: https://doi.org/10.1007/978-94-011-1156-0_18

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-4504-9

  • Online ISBN: 978-94-011-1156-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation