Skip to main content
Log in

Critical Slowing Down on the Dynamics of a Bistable Reaction-Diffusion System in the Neighborhood of Its Critical Point

  • Published:
Journal of Statistical Physics Aims and scope Submit manuscript

Abstract

We investigate the nature of some critical decay processes in a bounded bistable reaction-diffusion system, through a perturbative expansion of its nonequilibrium potential. We elucidate the scaling behavior of the damped relaxation time.

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

Access this article

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

Instant access to the full article PDF.

REFERENCES

  1. G. Nicolis and I. Prigogine, Self-Organization in Nonequilibrium Systems (Wiley, New York, 1977).

    Google Scholar 

  2. H. Haken, Synergetics: An Introduction, 2nd. Ed. (Springer-Verlag, Berlin, 1978).

    Google Scholar 

  3. M. Cross and P. Hohenberg, Rev. Mod. Phys. 65:851 (1993).

    Google Scholar 

  4. A. Mikhailov, Foundations of Synergetics I (Springer-Verlag, Berlin, 1990).

    Google Scholar 

  5. P. Fife, Mathematical Aspects of Reacting and Diffusing Systems (Springer-Verlag, Berlin, 1979).

    Google Scholar 

  6. H. Wio, An Introduction to Stochastic Processes and Nonequilibrium Statistical Physics (World Scientific, Singapore, 1994).

    Google Scholar 

  7. G. Izuüs, J. Reyes de Rueda, and C. Borzi, J. Stat. Phys. 90:103 (1998).

    Google Scholar 

  8. D. Bedeaux, P. Mazur, and R. Pasmanter, Physica A 86:355 (1977).

    Google Scholar 

  9. D. Bedeaux and P. Mazur, Physica A 105:1 (1981).

    Google Scholar 

  10. W. Skocpol, M. Beasley, and M. Tinkham, J. Appl. Phys. 45:4054 (1974).

    Google Scholar 

  11. C. Schat and H. Wio, Physica A 180:295 (1992).

    Google Scholar 

  12. H. Frisch, V. Privman, C. Nicolis, and G. Nicolis, J. Phys. A 23:1147 (1990).

    Google Scholar 

  13. V. Privman and H. Frisch, J. Chem. Phys. 94:8216 (1991).

    Google Scholar 

  14. B. von Haeften, G. Izuüs, R. Deza, and C. Borzi, Phys. Lett. A 236:403 (1997).

    Google Scholar 

  15. G. Izuüs, R. Deza, C. Borzi, and H. Wio, Physica A 237:135 (1997).

    Google Scholar 

  16. D. Zanette, H. Wio, and R. Deza, Phys. Rev. E 53:353 (1996).

    Google Scholar 

  17. F. Castelpoggi, H. Wio, and D. Zanette, Int. J. Mod. Phys. B 11:1717 (1997).

    Google Scholar 

  18. R. Montagne, E. Hernandez-Garcia, and M. San Miguel, Phys. D 96:47 (1996).

    Google Scholar 

  19. G. Izuüs, R. Deza, H. Wio, and C. Borzi, Phys. Rev. E 55:4005 (1997).

    Google Scholar 

  20. G. Izuüs, H. Wio, J. Reyes de Rueda, O. Ramírez, and R. Deza, Int. J. Mod. Phys. B 10:1273 (1996).

    Google Scholar 

  21. R. Graham, in Quantum Statistics in Optics and Solid-State Physics (G. Hoólder, ed.), Springer Tracts in Modern Physics, Vol. 66, p. 1 (Springer-Verlag, Springer, 1973).

    Google Scholar 

  22. P. Hanggi, P. Talkner, and M. Borkovec, Rev. Mod. Phys. 62(2): (1990).

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to C. H. Borzi.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Reyes de Rueda, J.M., Izús, G.G. & Borzi, C.H. Critical Slowing Down on the Dynamics of a Bistable Reaction-Diffusion System in the Neighborhood of Its Critical Point. Journal of Statistical Physics 97, 803–809 (1999). https://doi.org/10.1023/A:1004627611784

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1004627611784

Keywords

Navigation