Journal of Statistical Physics

, Volume 98, Issue 5–6, pp 1149–1168 | Cite as

Flowing Sand—A Possible Physical Realization of Directed Percolation

  • Haye Hinrichsen
  • Andrea Jiménez-Dalmaroni
  • Yadin Rozov
  • Eytan Domany

Abstract

A simple model for flowing sand on an inclined plane is introduced. The model is related to recent experiments by Douady and Daerr and reproduces some of the experimentally observed features. Avalanches of intermediate size appear to be compact, placing the critical behavior of the model into the universality class of compact directed percolation. On very large scales, however, the avalanches break up into several branches, leading to a crossover from compact to ordinary directed percolation. Thus, systems of flowing granular matter on an inclined plane could serve as a first physical realization of directed percolation.

directed percolation nonequilibrium phase transitions sandpiles 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

REFERENCES

  1. 1.
    W. Kinzel, in Percolation Structures and Processes, G. Deutscher, R. Zallen, and J. Adler, eds., Ann. Isr. Phys. Soc., Vol. 5 (Adam Hilger, Bristol, 1983), p. 425.Google Scholar
  2. 2.
    Currently the most precise estimates for the DP exponents in 1+1 dimensions are given in: I. Jensen, J. Phys. A 32:5233.Google Scholar
  3. 3.
    P. Grassberger, Directed percolation: Results and open problems, in Nonlinearities in Complex Systems(1996), Proceedings of the 1995 Shimla Conference on Complex Systems.Google Scholar
  4. 4.
    S. Douady and A. Daerr, Physics of Dry Granular Media, H. J. Herrmann et al., eds. (Kluwer Academic Publishers, NY, 1998), p. 339.Google Scholar
  5. 5.
    A. Daerr and S. Douady, Nature 399:241 (1999).Google Scholar
  6. 6.
    H. Hinrichsen, A. Jiménez-Dalmaroni, Y. Rozov, and E. Domany, preprint cond-mat/ 9908103; Phys. Rev. Lett. 83:4999 (1999).Google Scholar
  7. 7.
    E. Domany and W. Kinzel, Phys. Rev. Lett. 53:311 (1984).Google Scholar
  8. 8.
    B. Tadic and D. Dhar, Phys. Rev. Lett. 79:1519 (1997).Google Scholar
  9. 9.
    P. Bak, C. Tang, and K. Wiesenfeld, Phys. Rev. Lett. 59:381 (1987).Google Scholar
  10. 10.
    R. Dickman and A. Yu. Tretyakov, Phys. Rev. E 52:3218 (1995).Google Scholar
  11. 11.
    H. K. Janssen, Z. Phys. B 42:151 (1981); P. Grassberger, Z. Phys. B 47:365 (1982).Google Scholar
  12. 12.
    P. Grassberger and A. de la Torre, Ann. Phys. (N.Y.) 122:373 (1979).Google Scholar
  13. 13.
    J. F. F. Mendes, R. Dickman, and H. Herrmann, Phys. Rev. E 54:R3071 (1996).Google Scholar
  14. 14.
    A. G. Moreira and R. Dickman, Phys. Rev. E 54:1 (1996); R. Dickman and A. G. Moreira, Phys. Rev. Lett. 57:1263 (1998).Google Scholar
  15. 15.
    H. K. Janssen, Phys. Rev. E 55:6253 (1997).Google Scholar
  16. 16.
    R. Cafiero, A. Gabrielli, and M. A. Muñoz, Phys. Rev. E 57:5060 (1998).Google Scholar
  17. 17.
    I. Webman, D. ben-Avraham, A. Cohen, and S. Havlin, Phil. Mag. B 77, 1401 (1998).Google Scholar
  18. 18.
    I. Jensen, Phys. Rev. Lett. 77:4988 (1996).Google Scholar
  19. 19.
    H. K. Janssen, Z. Phys. B 42:151 (1981).Google Scholar
  20. 20.
    S. Dippel, G. G. Batrouni, and D. E. Wolf, Phys. Rev. E 54:6845 (1996).Google Scholar
  21. 21.
    J. P. Bouchaud and M. E. Cates, Granular Matter 1:101 (1998).Google Scholar

Copyright information

© Plenum Publishing Corporation 2000

Authors and Affiliations

  • Haye Hinrichsen
    • 1
  • Andrea Jiménez-Dalmaroni
    • 2
    • 3
  • Yadin Rozov
    • 2
  • Eytan Domany
    • 2
  1. 1.Max-Planck-Institut für Physik komplexer SystemeDresdenGermany
  2. 2.Department of Physics of Complex SystemsWeizmann Institute of ScienceRehovotIsrael
  3. 3.Department of Physics-Theoretical PhysicsUniversity of OxfordOxfordUnited Kingdom

Personalised recommendations