Zeitschrift für Physik

, Volume 270, Issue 1, pp 67–73 | Cite as

Stochastisches Reaktionsmodell für einen Nichtgleichgewichts-Phasenübergang

  • H. K. Janssen
Article
Received:

Stochastic reaction model for a non-equilibrium phase transition

Abstract

The stochastic version of a chemical autocatalytic reaction scheme is discussed. Dependent on the concentrations of reacting substances prescribed from the exterior of the reaction volume, the concentration of an internal substance exhibits a first order transition from a lower to a higher value. The two different phases appear as different quasi-stationary solutions of a master equation. The time constant of the transition is also calculated and indicates, that such systems generally possess metastable states.

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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literatur

  1. 1.
    Glansdorff, P., Prigogine, I.: Thermodynamic Theory of Struc-ture, Stability and Fluctuations. London-New York-Sydney-Toronto: Wiley-Interscience 1971Google Scholar
  2. 2.
    Nicolis, G.: Stability and Dissipative Structures in Open Systems far from Equilibrium, Advances in Chemical Physics, Vol. XIXGoogle Scholar
  3. 3.
    Prigogine, I., Nicolis, G., Babloyantz, A.: Phys. Today25, Nr. 11, 23 (1972)Google Scholar
  4. 4.
    Schlögl, F.: Z. Physik243, 303 (1971)Google Scholar
  5. 5.
    Schlögl, F.: Z. Physik244, 199 (1971)Google Scholar
  6. 6.
    Schlögl, F.: Z. Physik248, 446 (1971)Google Scholar
  7. 7.
    Schlögl, F.: Z. Physik253, 147 (1972)Google Scholar
  8. 8.
    Janssen, H.K.: Z. Physik253, 176 (1972)Google Scholar
  9. 9.
    Nicolis, G., Babloyantz, A.: J. Chem. Phys.51, 2632 (1969)Google Scholar
  10. 10.
    Nicolis, G., Prigogine, I.: Proc. Nat. Acad. Sci. USA68, 2102 (1971)Google Scholar
  11. 11.
    Nicolis, G.: Journ. Statist. Phys.6, 95 (1972)Google Scholar
  12. 12.
    Graham, R., Haken, H.: Z. Physik243, 289 (1971)Google Scholar
  13. 13.
    Graham, R., Haken, H.: Z. Physik245, 141 (1971)Google Scholar
  14. 14.
    Graham, R., Haken, H.: Z. Physik237, 31 (1970)Google Scholar
  15. 15.
    Landauer, R.: Plenarvortrag auf der 36. Physikertagung 1971 Essen, Teubner 1971Google Scholar
  16. 16.
    Dohm, V.: Solid State Communic.11, 1273 (1972)Google Scholar
  17. 17.
    McQuarrie, D.A.: Stochastic Approach to Chemical Kinetics, Suppl. Rev. Series in Appl. Prob. Vol.8. London: Methuen Co Ltd. 1967Google Scholar
  18. 18.
    Abramowitz, M., Stegun, J.A.: Handbook of Mathematical Functions. New York: Dover Publ. Inc. 1964Google Scholar
  19. 19.
    Schlögl, F.: Z. Physik191, 81 (1966)Google Scholar
  20. 20.
    Feder, I., Russel, K.C., Lothe, J., Pound, G.M.: Adv. Phys.15, 111 (1969)Google Scholar
  21. 21.
    Kampen, N.v.: Fluctuation Phenomena in Solids, Ed. Burgess. New York, London: Academic Press 1965Google Scholar
  22. 22.
    Wa\muth, G.: Zur Kinetik auslösbarer Reaktionen. Dissertation Aachen 1970Google Scholar
  23. 23.
    Janssen, H.K.: in VorbereitungGoogle Scholar
  24. 24.
    Kubo, R., Matsuo, K., Kitahara, K.: J. Stat. Phys.9, 51 (1973)Google Scholar

Copyright information

© Springer-Verlag 1974

Authors and Affiliations

  • H. K. Janssen
    • 1
  1. 1.Institut für Festkörperforschung der Kernforschungsanlage JülichBundesrepublik Deutschland

Personalised recommendations