The European Physical Journal Special Topics

, Volume 191, Issue 1, pp 173–185 | Cite as

Cluster dynamics and cluster size distributions in systems of self-propelled particles

  • F. Peruani
  • L. Schimansky-Geier
  • M. Bär
Regular article


Systems of self-propelled particles (SPP) interacting by a velocity alignment mechanism in the presence of noise exhibit rich clustering dynamics. Often, clusters are responsible for the distribution of (local) information in these systems. Here, we investigate the properties of individual clusters in SPP systems, in particular the asymmetric spreading behavior of clusters with respect to their direction of motion. In addition, we formulate a Smoluchowski-type kinetic model to describe the evolution of the cluster size distribution (CSD). This model predicts the emergence of steady-state CSDs in SPP systems. We test our theoretical predictions in simulations of SPP with nematic interactions and find that our simple kinetic model reproduces qualitatively the transition to aggregation observed in simulations.


Liquid Crystal European Physical Journal Special Topic Noise Intensity Cluster Dynamic Cluster Size Distribution 
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  1. 1.
    Three Dimensional Animals Groups, edited by J.K. Parrish W.M. Hamner (Cambridge University Press, Cambridge, UK, 1997)Google Scholar
  2. 2.
    A. Cavagna, et al., Proc. Natl. Acad. Sci. 107, 11865 (2010)CrossRefADSGoogle Scholar
  3. 3.
    K. Bhattacharya, T. Vicsek, New J. Phys. 12, 093019 (2010)CrossRefADSGoogle Scholar
  4. 4.
    D. Helbing, I. Farkas, T. Vicsek, Nature (London) 407, 487 (2000)CrossRefADSGoogle Scholar
  5. 5.
    J. Buhl, et al., Science 312, 1402 (2006)CrossRefADSGoogle Scholar
  6. 6.
    P. Romanczkuk, I.D. Couzin, L. Schimansky-Geier, Phy. Rev. Lett. 102, 010602 (2009)CrossRefADSGoogle Scholar
  7. 7.
    H.P. Zhang, et al., Proc. Natl. Acad. Sci. 107, 13626 (2010)CrossRefADSGoogle Scholar
  8. 8.
    V. Schaller, et al., Nature 467, 73 (2010)CrossRefADSGoogle Scholar
  9. 9.
    V. Narayan, S. Ramaswamy, N. Menon, Science 317, 105 (2007)CrossRefADSGoogle Scholar
  10. 10.
    A. Kudrolli, G. Lumay, D. Volfson, L.S. Tsimring, Phys. Rev. Lett. 100, 058001 (2008)CrossRefADSGoogle Scholar
  11. 11.
    A. Kudrolli, Phys. Rev. Lett. 104, 088001 (2010)CrossRefADSGoogle Scholar
  12. 12.
    J. Deseigne, O. Dauchot, H. Chaté, Phys. Rev. Lett. 105, 098001 (2010)CrossRefADSGoogle Scholar
  13. 13.
    F. Peruani, A. Deutsch, M. Bär, Phys. Rev. E 74, 030904 (2006)CrossRefADSGoogle Scholar
  14. 14.
    F. Peruani, A. Deutsch, M. Bär, Eur. Phys. J. Special Topics 157, 111 (2008)CrossRefADSGoogle Scholar
  15. 15.
    A. Baskaran, M.C. Marchetti, Phys. Rev. E 77, 011920 (2008)CrossRefMathSciNetADSGoogle Scholar
  16. 16.
    A. Baskaran, M.C. Marchetti, Phys. Rev. Lett. 101, 268101 (2008)CrossRefADSGoogle Scholar
  17. 17.
    T. Vicsek, A. Czirok, E. Ben-Jacob, I. Cohen, O. Shochet, Phys. Rev. Lett. 75, 1226 (1995)CrossRefADSGoogle Scholar
  18. 18.
    H. Chaté, et al., Eur. Phys. J. B 64, 451 (2008)CrossRefADSGoogle Scholar
  19. 19.
    H. Chaté, F. Ginelli, G. Grégoire, F. Raynaud, Phys. Rev. E 77, 046113 (2008)CrossRefADSGoogle Scholar
  20. 20.
    S. Mishra, A. Baskaran, M.C. Marchetti, Phys. Rev. E 81, 061916 (2010)CrossRefADSGoogle Scholar
  21. 21.
    F. Ginelli, F. Peruani, M. Bär, H. Chaté, Phys. Rev. Lett. 104, 184502 (2010)CrossRefADSGoogle Scholar
  22. 22.
    M. von Smoluchowski, Z. Phys. Chem. 92, 129 (1917)Google Scholar
  23. 23.
    C. Huepe, M. Aldana, Phys. Rev. Lett. 92, 168701 (2004)CrossRefADSGoogle Scholar
  24. 24.
    Y. Yang, J. Elgeti, G. Gompper, Phys. Rev. E 78, 061903 (2008)CrossRefADSGoogle Scholar
  25. 25.
    F. Peruani, et al. (2010) (unpublished)Google Scholar
  26. 26.
    H.H. Wensink, H. Löwen, Phys. Rev. E 78, 031409 (2008)CrossRefADSGoogle Scholar
  27. 27.
    C. Escudero, F. Maciá, J.J.L. Velazquez, Phys. Rev. E 82, 016113 (2010)CrossRefADSGoogle Scholar
  28. 28.
    M. Doi, S.F. Edwards, The Theory of Polymer Dynamic (Clarendon Press, Oxford, 1986)Google Scholar
  29. 29.
    F. Peruani, L.G. Morelli, Phys. Rev. Lett. 99, 010602 (2007)CrossRefADSGoogle Scholar
  30. 30.
    R. Reif, Fundamentals of Statistical and Thermal Physics (McGraw-Hill, New York, 1965)Google Scholar
  31. 31.
    V. Dossetti, F.J. Sevilla, V.M. Kenkre, Phys. Rev. E 79, 051115 (2009)CrossRefADSGoogle Scholar
  32. 32.
    J. Quintanilla, S. Torquato, R.M. Ziff, J. Phys. A: Math. Gen. 33, 399 (2000)CrossRefMathSciNetADSGoogle Scholar
  33. 33.
    L. Schimansky-Geier, F. Schweitzer, W. Ebeling, H. Ulbricht, in Self-organization by Nonlinear Irreversible Processes, edited by W. Ebeling, H. Ulbricht (Springer, Berling, Heidelberg, New York, 1986), p. 67Google Scholar
  34. 34.
    F. Schweitzer, L. Schimansky-Geier, W. Ebeling, H. Ulbricht, Physica A 150, 261 (1988)CrossRefADSGoogle Scholar
  35. 35.
    F. Schweitzer, L. Schimansky-Geier, W. Ebeling, H. Ulbricht, Physica A 153, 573 (1988)CrossRefADSGoogle Scholar
  36. 36.
    S. Ramaswamy, R.A. Simha, J. Toner, Europhys. Lett. 62, 196 (2003)CrossRefADSGoogle Scholar

Copyright information

© EDP Sciences and Springer 2011

Authors and Affiliations

  • F. Peruani
    • 1
  • L. Schimansky-Geier
    • 2
  • M. Bär
    • 3
  1. 1.Max-Planck-Institute for Physics of Complex SystemsDresdenGermany
  2. 2.Institute of Physics, Humboldt University BerlinBerlinGermany
  3. 3.Physikalisch-Technische BundesanstaltBerlinGermany

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