Skip to main content
SpringerLink
Log in

Kink propagation induced by multiplicative noise

  • Published:
Zeitschrift für Physik B Condensed Matter

Abstract

The influence of spatio-temporal external multiplicative fluctuations on a single kink in a bistable distributed system is studied. For this purpose we derive a stochastic dynamic equation for the position of the shifted kink. An analytical estimate for spatio-temporally uncorrelated fluctuations is represented and discussed. We draw the conclusion that multiplicative noise induces a propagation of the most probable kink into the region of larger noise. This effect is demonstrated in numerical simulations.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Ebeling, W., Feistel, R.: Physik der Selbstorganisation und Evolution. Berlin: Akademie-Verlag 1982, 1986, (in German); Feistel, R., Ebeling, W.: Evolution of complex systems. Dordrecht: Kluwer Acad. Publ. 1989.

    Google Scholar 

  2. Malchow, H., Schimansky-Geier, L.: Noise and diffusion in bistable nonequilibrium systems. Teubner-Texte zur Physik 5. Berlin: Teubner 1985

    Google Scholar 

  3. Landauer, R.: J. Appl. Phys.33 2209 (1962); Landauer, R.: J. Stat. Phys.52, 1/2, 233 (1988); Kampen, N. van: IBM J. Res. Devel.32, 1, 107 (1988)

    Google Scholar 

  4. Horsthemke, W., Lefever, R.: Noise-induced transitions. In: Synergetics. Vol. 15. Berlin, Heidelberg, New York: Springer 1984

    Google Scholar 

  5. Büttiker, M.: Z. Phys. B-Condensed Matter68, 161 (1987)

    Google Scholar 

  6. Petuchov, B.V., Pokrovsky, V.L.: Zh. Eksp. Theor. Fiz.63, 634 (1972); Büttiker, M., Landauer, R.: Phys. Rev. A23, 1397 (1981)

    Google Scholar 

  7. McLaughlin, D.W., Scott, A.C.: Phys. Rev. A18, 1652 (1978); Marchesoni, F., Hänggi, P., Sodano, P.: In: Universalities in condensed matter. In: Springer Proceedings in Physics. Jullien, R., Peliti, L., Rammal, R., Boccara, N. (eds.) Vol. 32, p. 88. Berlin, Heidelberg, New York: Springer 1988 Hänggi, P., Marchesoni, F., Sodano, P.: Phys. Rev. Lett.60, 2563 (1988)

    Google Scholar 

  8. Buckel, W.: Supraleitung. Weinheim: Physik-Verlag 1977

    Google Scholar 

  9. Jackson, K.A., Kurtze, D.A.: J. Cryst. Growth71 385 (1985)

    Google Scholar 

  10. Zeldovich, Ya.B., Barenblatt, G.I., Librovich, V.B., Makhviladze, G.M.: The mathematical theory of combustions and explosions. New York, London: Consultants Bureau 1985

    Google Scholar 

  11. Kabashima, S., Kawakubo, T.: Phys. Lett. A70, 375 (1979); Purwins, H.G., Klempt, G., Berkemeier, J.: Adv. Solid State Phys.27, 27 (1987)

    Google Scholar 

  12. Mikhailov, A.S., Schimansky-Geier, L., Ebeling, W.: Phys. Lett. A96, 453 (1983) Schimansky-Geier, L., Mikhailov, A.S., Ebeling, W.: Ann. Phys. (Leipzig)40, 277 (1983)

    Google Scholar 

  13. Engel, A., Ebeling, W.: Phys. Lett. A122, 20 (1987)

    Google Scholar 

  14. Gurevich, A.Vl., Leikin, S.L., Mints, R.G.: Phys. Lett. A105, 31 (1984)

    Google Scholar 

  15. Landauer, R.: In: The maximum entropy formalism. Levine, R.D., Tribus, M. (eds.) p. 321. Cambridge: MIT Press 1979

    Google Scholar 

  16. Engel, A.: Phys. Lett. A113, 139 (1985)

    Google Scholar 

  17. Schlögl, F.: Z. Phys. B-Condensed Matter253, 147 (1972)

    Google Scholar 

  18. Nitzan, A., Ortoleva, P., Ross, J.: J. Chem. Phys.61, 1056 (1976)

    Google Scholar 

  19. Polak, L.S., Mikhailov, A.S.: Selforganization in nonequilibrium physico-chemical systems. Moskva: Nauka 1983 (in Russian)

    Google Scholar 

  20. Schlögl, F., Escher, C., Berry, R.S.: Phys. Rev. A27, 2698 (1983)

    Google Scholar 

  21. Magyari, E.: J. Phys. A15, L139 (1982)

    Google Scholar 

  22. Kawasaki, K., Ohta, T.: Prog. Theor. Phys.67, 147;68, 120 (1982)

    Google Scholar 

  23. Kuramoto, Y.: Chemical oscillations, waves, and turbulence In: Synergetics. Vol. 19. Berlin, Heidelberg, New York: Springer 1984

    Google Scholar 

  24. Stratonovich, R.L.: Topics in the theory of random noise 1. New York: Gordon and Breach 1967

    Google Scholar 

  25. Gardiner, C.W.: Handbook of stochastic methods. In: Synergetics. Vol. 13. Berlin, Heidelberg, New York: Springer 1983

    Google Scholar 

  26. Sancho, J.M., San Miguel, M.: Z. Phys. B-Condensed Matter and Quanta36, 357 (1980) series. Moskva: Nauka 1981 (in Russian) nbr. 2.4.4.5. at p. 353

    Google Scholar 

  27. Press, W.H., Flannery, B.P., Teukovsky, S.A. Vetterling, W.T.: Numerical recipes. Cambridge: Cambridge University Press 1986

    Google Scholar 

  28. Doering, Ch.R.: Phys. Lett. A122, 133 (1987)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Sektion Physik der Humboldt-Universität zu Berlin, Invalidenstrasse 42, Bereich 04, O-1040, Berlin, Germany

    L. Schimansky-Geier & Ch. Zülicke

Authors
  1. L. Schimansky-Geier
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ch. Zülicke
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Schimansky-Geier, L., Zülicke, C. Kink propagation induced by multiplicative noise. Z. Physik B - Condensed Matter 82, 157–162 (1991). https://doi.org/10.1007/BF01313999

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01313999

Keywords

Search

Navigation