- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review E

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Renormalization-group analysis of a noisy Kuramoto-Sivashinsky equation

Rodolfo Cuerno and Kent Baekgaard Lauritsen

  • Center for Polymer Studies and Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215

PDF

Phys. Rev. E 52, 4853 – Published 1 November, 1995

DOI: https://doi.org/10.1103/PhysRevE.52.4853

Abstract

We have analyzed the Kuramoto-Sivashinsky equation with a stochastic noise term through a dynamic renormalization-group calculation. For a system in which the lattice spacing is smaller than the typical wavelength of the linear instability occurring in the system, the large distance and long-time behavior of this equation is the same as for the Kardar-Parisi-Zhang equation in one and two spatial dimensions. For the d=2 case the agreement is only qualitative. On the other hand, when coarse graining on larger scales the asymptotic flow depends on the initial values of the parameters.

View figure in article

References (37)

  1. J. Krug and H. Spohn, in Solids far from Equilibrium: Growth, Morphology and Defects, edited by C. Godrèche (Cambridge University Press, Cambridge, England, 1991).
  2. Dynamics of Fractal Surfaces, edited by F. Family and T. Vicsek (World Scientific, Singapore, 1991).
  3. P. Meakin, Phys. Rep. 235, 189 (1993).
  4. A. L. Barabási and H. E. Stanley, Fractal Concepts in Surface Growth (Cambridge University Press, Cambridge, England, 1995).
  5. T. Halpin Healey and Y. C. Zhang, Phys. Rep. 254, 215 (1995).
  6. M. Kardar, G. Parisi and Y. C. Zhang, Phys. Rev. Lett. 56, 889 (1986).
  7. E. Medina, T. Hwa, M. Kardar and Y. C. Zhang, Phys. Rev. A 39, 3053 (1989).
  8. Y. Kuramoto and T. Tsuzuki, Prog. Theor. Phys. 55, 356 (1977).
  9. G. I. Sivashinsky, Acta Astronaut. 6, 569 (1979).
  10. Y. Kuramoto, Chemical Oscillations, Waves and Turbulence (Springer, Berlin, 1984).
  11. M. C. Cross and P. C. Hohenberg, Rev. Mod. Phys. 65, 851 (1993).
  12. S. Zaleski, Physica D 34, 427 (1989).
  13. K. Sneppen, J. Krug, M. H. Jensen, C. Jayaprakash and T. Bohr, Phys. Rev. A 46, R7351 (1992).
  14. F. Hayot, C. Jayaprakash and Ch. Josserand, Phys. Rev. E 47, 911 (1993).
  15. J. Li and L. M. Sander (unpublished).
  16. C. C. Chow and T. Hwa, Physica D 84, 494 (1995).
  17. V. L'vov, V. V. Lebedev, M. Paton and I. Procaccia, Nonlinearity 6, 25 (1993).
  18. V. Yakhot, Phys. Rev. A 24, 642 (1981).
  19. V. S. L'vov and I. Procaccia, Phys. Rev. Lett. 69, 3543 (1992).
  20. I. Procaccia, M. H. Jensen, V. S. L'vov, K. Sneppen and R. Zeitak, Phys. Rev. A 46, 3220 (1992).
  21. C. Jayaprakash, F. Hayot and R. Pandit, Phys. Rev. Lett. 71, 12 (1993); V. L'vov and I. Procaccia, ibid. 72, 307 (1994); C. Jayaprakash, F. Hayot and R. Pandit, ibid. 72, 308 (1994).
  22. E. A. Eklund, R. Bruinsma, J. Rudnick and R. S. Williams, Phys. Rev. Lett. 67, 1759 (1991); E. A. Eklund, E. J. Snyder and R. S. Williams, Surf. Sci. 285, 157 (1993).
  23. E. Chason, T. M. Mayer, B. K. Kellerman, D. T. McIlroy and A. J. Howard, Phys. Rev. Lett. 72, 3040 (1994); T. M. Mayer, E. Chason and A. J. Howard, J. Appl. Phys. 76, 1633 (1994).
  24. J. Krim, I. Heyvaert, C. Van Haesendonck and Y. Bruynseraede, Phys. Rev. Lett. 70, 57 (1993); H. N. Yang, G. C. Wang and T. M. Lu, Phys. Rev. B 50, 7635 (1994).
  25. G. Carter, B. Navinšek, and J. L. Whitton, in Sputtering by Particle Bombardment, edited by R. Behrisch (Springer Verlag, Heidelberg, 1983), Vol. II.
  26. R. Cuerno and A. L. Barabási, Phys. Rev. Lett. 74, 4746 (1995).
  27. C. Herring, J. Appl. Phys. 21, 301 (1950); W. W. Mullins, Phys. Rev. Lett. 28, 333 (1957).
  28. P. Sigmund, Phys. Rev. 184, 383 (1969); J. Mater. Sci. 8, 1545 (1973) R. M. Bradley and J. M. E. Harper, J. Vac. Sci. Technol. A 6, 2390 (1988).
  29. S. K. Ma, Modern Theory of Critical Phenomena, Frontiers in Physics Vol. 46 (Benjamin, Reading, 1976).
  30. D. Forster, D. R. Nelson and M. J. Stephen, Phys. Rev. A 16, 732 (1977).
  31. K. B. Lauritsen, Ph.D. thesis, Aarhus University, 1994.
  32. The RG flow for Eq. ( refeq:ks) in the limit |ν| ll K has previously been studied near d=8 in the context of interfaces relaxing by surface diffusion, see L. Golubović and R. Bruinsma, Phys. Rev. Lett. 66, 321 (1991); ć and ibid. 67, 2747(E) (1991).
  33. S. F. Edwards and D. R. Wilkinson, Proc. R. Soc. London, Ser. A 381, 17 (1982).
  34. D. E. Wolf and J. Villain, Europhys. Lett. 13, 389 (1990).
  35. J. Villain, J. Phys. (France) I 1, 19 (1991).
  36. Z. W. Lai and S. Das Sarma, Phys. Rev. Lett. 66, 2348 (1991).
  37. G. Grinstein (private communication). See also endnote No. 14 in the first reference in [21] above.

Outline

Information

Phys. Rev. E 52, 4853– Published 1 November, 1995
  • Received 5 May 1995

© 1995 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation