Skip to main content
SpringerLink
Log in

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

  • Regular article
  • Published:
The European Physical Journal Special Topics Aims and scope Submit manuscript

Abstract.

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.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Three Dimensional Animals Groups, edited by J.K. Parrish W.M. Hamner (Cambridge University Press, Cambridge, UK, 1997)

  2. A. Cavagna, et al., Proc. Natl. Acad. Sci. 107, 11865 (2010)

    Article  ADS  Google Scholar 

  3. K. Bhattacharya, T. Vicsek, New J. Phys. 12, 093019 (2010)

    Article  ADS  Google Scholar 

  4. D. Helbing, I. Farkas, T. Vicsek, Nature (London) 407, 487 (2000)

    Article  ADS  Google Scholar 

  5. J. Buhl, et al., Science 312, 1402 (2006)

    Article  ADS  Google Scholar 

  6. P. Romanczkuk, I.D. Couzin, L. Schimansky-Geier, Phy. Rev. Lett. 102, 010602 (2009)

    Article  ADS  Google Scholar 

  7. H.P. Zhang, et al., Proc. Natl. Acad. Sci. 107, 13626 (2010)

    Article  ADS  Google Scholar 

  8. V. Schaller, et al., Nature 467, 73 (2010)

    Article  ADS  Google Scholar 

  9. V. Narayan, S. Ramaswamy, N. Menon, Science 317, 105 (2007)

    Article  ADS  Google Scholar 

  10. A. Kudrolli, G. Lumay, D. Volfson, L.S. Tsimring, Phys. Rev. Lett. 100, 058001 (2008)

    Article  ADS  Google Scholar 

  11. A. Kudrolli, Phys. Rev. Lett. 104, 088001 (2010)

    Article  ADS  Google Scholar 

  12. J. Deseigne, O. Dauchot, H. Chaté, Phys. Rev. Lett. 105, 098001 (2010)

    Article  ADS  Google Scholar 

  13. F. Peruani, A. Deutsch, M. Bär, Phys. Rev. E 74, 030904 (2006)

    Article  ADS  Google Scholar 

  14. F. Peruani, A. Deutsch, M. Bär, Eur. Phys. J. Special Topics 157, 111 (2008)

    Article  ADS  Google Scholar 

  15. A. Baskaran, M.C. Marchetti, Phys. Rev. E 77, 011920 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  16. A. Baskaran, M.C. Marchetti, Phys. Rev. Lett. 101, 268101 (2008)

    Article  ADS  Google Scholar 

  17. T. Vicsek, A. Czirok, E. Ben-Jacob, I. Cohen, O. Shochet, Phys. Rev. Lett. 75, 1226 (1995)

    Article  ADS  Google Scholar 

  18. H. Chaté, et al., Eur. Phys. J. B 64, 451 (2008)

    Article  ADS  Google Scholar 

  19. H. Chaté, F. Ginelli, G. Grégoire, F. Raynaud, Phys. Rev. E 77, 046113 (2008)

    Article  ADS  Google Scholar 

  20. S. Mishra, A. Baskaran, M.C. Marchetti, Phys. Rev. E 81, 061916 (2010)

    Article  ADS  Google Scholar 

  21. F. Ginelli, F. Peruani, M. Bär, H. Chaté, Phys. Rev. Lett. 104, 184502 (2010)

    Article  ADS  Google Scholar 

  22. M. von Smoluchowski, Z. Phys. Chem. 92, 129 (1917)

    Google Scholar 

  23. C. Huepe, M. Aldana, Phys. Rev. Lett. 92, 168701 (2004)

    Article  ADS  Google Scholar 

  24. Y. Yang, J. Elgeti, G. Gompper, Phys. Rev. E 78, 061903 (2008)

    Article  ADS  Google Scholar 

  25. F. Peruani, et al. (2010) (unpublished)

  26. H.H. Wensink, H. Löwen, Phys. Rev. E 78, 031409 (2008)

    Article  ADS  Google Scholar 

  27. C. Escudero, F. Maciá, J.J.L. Velazquez, Phys. Rev. E 82, 016113 (2010)

    Article  ADS  Google Scholar 

  28. M. Doi, S.F. Edwards, The Theory of Polymer Dynamic (Clarendon Press, Oxford, 1986)

  29. F. Peruani, L.G. Morelli, Phys. Rev. Lett. 99, 010602 (2007)

    Article  ADS  Google Scholar 

  30. R. Reif, Fundamentals of Statistical and Thermal Physics (McGraw-Hill, New York, 1965)

  31. V. Dossetti, F.J. Sevilla, V.M. Kenkre, Phys. Rev. E 79, 051115 (2009)

    Article  ADS  Google Scholar 

  32. J. Quintanilla, S. Torquato, R.M. Ziff, J. Phys. A: Math. Gen. 33, 399 (2000)

    Article  MathSciNet  ADS  Google Scholar 

  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. 67

  34. F. Schweitzer, L. Schimansky-Geier, W. Ebeling, H. Ulbricht, Physica A 150, 261 (1988)

    Article  ADS  Google Scholar 

  35. F. Schweitzer, L. Schimansky-Geier, W. Ebeling, H. Ulbricht, Physica A 153, 573 (1988)

    Article  ADS  Google Scholar 

  36. S. Ramaswamy, R.A. Simha, J. Toner, Europhys. Lett. 62, 196 (2003)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Max-Planck-Institute for Physics of Complex Systems, Nöthnitzer Str. 38, 01187, Dresden, Germany

    F. Peruani

  2. Institute of Physics, Humboldt University Berlin, Newtonstr. 15, 12489, Berlin, Germany

    L. Schimansky-Geier

  3. Physikalisch-Technische Bundesanstalt, Abbestr. 2-12, 10587, Berlin, Germany

    M. Bär

Authors
  1. F. Peruani
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. L. Schimansky-Geier
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. Bär
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Peruani, F., Schimansky-Geier, L. & Bär, M. Cluster dynamics and cluster size distributions in systems of self-propelled particles. Eur. Phys. J. Spec. Top. 191, 173–185 (2010). https://doi.org/10.1140/epjst/e2010-01349-1

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjst/e2010-01349-1

Keywords

Search

Navigation