Advertisement

The European Physical Journal B

, Volume 64, Issue 3–4, pp 387–393 | Cite as

Singular scaling functions in clustering phenomena

  • M. BarmaEmail author
Article

Abstract

We study clustering in a stochastic system of particles sliding down a fluctuating surface in one and two dimensions. In steady state, the density-density correlation function is a scaling function of separation and system size. This scaling function is singular for small argument — it exhibits a cusp singularity for particles with mutual exclusion, and a divergence for noninteracting particles. The steady state is characterized by giant fluctuations which do not damp down in the thermodynamic limit. The autocorrelation function is a singular scaling function of time and system size. The scaling properties are surprisingly similar to those for particles moving in a quenched disordered environment that results if the surface is frozen.

PACS

05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion 47.40.-x Compressible flows; shock waves 64.75.+g Solubility, segregation, and mixing; phase separation 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    A.J. Bray, Adv. Phys. 43, 357 (1997)CrossRefADSGoogle Scholar
  2. 2.
    N.V. Brilliantov, T. Pöschel, Kinetic Theory of Granular Gases (New York and Oxford, 2004)Google Scholar
  3. 3.
    A. Puglisi, V. Loreto, U.M.B. Marconi, A. Petri, A. Vulpiani, Phys. Rev. Lett. 81, 3848 (1998)CrossRefADSGoogle Scholar
  4. 4.
    S.K. Das, S. Puri, Phys. Rev. E 68, 011302 (2003)CrossRefADSGoogle Scholar
  5. 5.
    H.E. Stanley, Introduction to Phase Transitions and Critical Phenomena (Oxford, New York and Oxford, 1971)Google Scholar
  6. 6.
    P.H. Coleman, L. Pietronero, Phys. Rep. 213, 311 (1992)CrossRefADSGoogle Scholar
  7. 7.
    M. Maxey, J. Fluid Mech. 174, 441 (1987)zbMATHCrossRefADSGoogle Scholar
  8. 8.
    E. Balkovsky, G. Falkovich, A. Fouxon, Phys. Rev. Lett. 86, 2790 (2001)CrossRefADSGoogle Scholar
  9. 9.
    K. Gawedzki, M. Vergassola, Physica D 138, 63 (2000)zbMATHCrossRefADSMathSciNetGoogle Scholar
  10. 10.
    J.M. Deutsch, J. Phys. A 18, 1449 (1985)CrossRefADSMathSciNetGoogle Scholar
  11. 11.
    B. Mehlig, M. Wilkinson, Phys. Rev. Lett. 92, 250602 (2004)CrossRefADSGoogle Scholar
  12. 12.
    D. Das, M. Barma, Phys. Rev. Lett. 85, 1602 (2000)CrossRefADSGoogle Scholar
  13. 13.
    D. Das, M. Barma, S.N. Majumdar, Phys. Rev. E 64, 046126 (2001)CrossRefADSGoogle Scholar
  14. 14.
    G. Manoj, M. Barma, J. Stat. Phys. 110, 1305 (2003)zbMATHCrossRefGoogle Scholar
  15. 15.
    A. Nagar, M. Barma, S.N. Majumdar, Phys. Rev. Lett. 94, 240601 (2005)CrossRefADSGoogle Scholar
  16. 16.
    A. Nagar, S.N. Majumdar, M. Barma, Phys. Rev. E 74, 021124 (2006)CrossRefADSGoogle Scholar
  17. 17.
    S. Chatterjee, M. Barma, Phys. Rev. E 73, 011107 (2006)CrossRefADSGoogle Scholar
  18. 18.
    S. Mishra, S. Ramaswamy, Phys. Rev. Lett. 97, 090602 (2006)CrossRefADSGoogle Scholar
  19. 19.
    M. Shinde, D. Das, R. Rajesh, Phys. Rev. Lett. 99, 234505 (2001)CrossRefADSGoogle Scholar
  20. 20.
    S. Ramaswamy, R. Aditi Simha, J. Toner, Europhys. Lett. 62, 196 (2003)CrossRefADSGoogle Scholar
  21. 21.
    V. Narayan, S. Ramaswamy, N. Menon, Science 317, 105 (2007)CrossRefADSGoogle Scholar
  22. 22.
    G. Porod, in Small Angle X-ray Scattering, edited by O. Glatter, L. Kratky (Academic Press, New York, 1983)Google Scholar
  23. 23.
    T.M. Liggett, Interacting Particle Systems (Springer, 2000)Google Scholar
  24. 24.
    S.F. Edwards, D.R. Wilkinson, Proc. R. Soc. London, Ser. A 381, 17 (1982)CrossRefADSMathSciNetGoogle Scholar
  25. 25.
    M. Kardar, G. Parisi, Y.C. Zhang, Phys. Rev. Lett. 62, 89 (1986)Google Scholar
  26. 26.
    R. Lahiri, S. Ramaswamy, Phys. Rev. Lett. 79, 1150 (1997)CrossRefADSGoogle Scholar
  27. 27.
    R. Lahiri, M. Barma, S. Ramaswamy, Phys. Rev. E 61, 1648 (2000)CrossRefADSGoogle Scholar
  28. 28.
    D. Das, A. Basu, M. Barma, S. Ramaswamy, Phys. Rev. E 64, 021402 (2001)CrossRefADSGoogle Scholar
  29. 29.
    S. Ramaswamy, M. Barma, D. Das, A. Basu, Phase Transit. 75, 363 (2002)CrossRefGoogle Scholar
  30. 30.
    B. Drossel, M. Kardar, Phys. Rev. Lett. 85, 614 (2000)CrossRefADSGoogle Scholar
  31. 31.
    B. Drossel, M. Kardar, Phys. Rev. B 66, 195414 (2002)CrossRefADSGoogle Scholar
  32. 32.
    T. Bohr, A. Pikovsky, Phys. Rev. Lett. 70, 2892 (1993)CrossRefADSGoogle Scholar
  33. 33.
    C.S. Chin, Phys. Rev. E 66, 021104 (2002)CrossRefADSGoogle Scholar
  34. 34.
    M. Gopalakrishnan, Phys. Rev. E 69, 011105 (2003)CrossRefADSGoogle Scholar
  35. 35.
    S.N. Majumdar, C. Sire, A.J. Bray, S.J. Cornell, Phys. Rev. Lett. 77, 2867 (1996)CrossRefADSGoogle Scholar
  36. 36.
    B. Derrida, S.A. Janowsky, J.L. Lebowitz, E.R. Speer, J. Stat. Phys. 73, 813 (1993)zbMATHCrossRefADSMathSciNetGoogle Scholar
  37. 37.
    A. Comtet, C. Texier, Supersymmetry and Integrable Models Proceedings, Chicago, IL, edited by H. Aratyn, T. Imbo, W.Y. Keung, U. Sukhatme (Springer, Berlin, 1998)Google Scholar
  38. 38.
    H. Chaté, F. Ginelli, R. Montagne, Phys. Rev. Lett. 96, 180602 (2006)CrossRefADSGoogle Scholar

Copyright information

© Springer 2008

Authors and Affiliations

  1. 1.Department of Theoretical PhysicsTata Institute of Fundamental ResearchMumbaiIndia

Personalised recommendations