The European Physical Journal Special Topics

, Volume 224, Issue 7, pp 1359–1376 | Cite as

Orientational hysteresis in swarms of active particles in external field

Regular Article
Part of the following topical collections:
  1. Statistical Physics of Self-Propelled Particles

Abstract

Structure and ordering in swarms of active particles have much in common with condensed matter systems like magnets or liquid crystals. A number of important characteristics of such materials can be obtained via dynamic tests such as hysteresis. In this work, we show that dynamic hysteresis can be observed also in swarms of active particles and possesses similar properties to the counterparts in magnetic materials. To study the swarm dynamics, we use computer simulations of the active Brownian particle model with dissipative interactions. The swarm is confined to a narrow linear channel and the one-dimensional polar order parameter is measured. In an oscillating external field, the order parameter demonstrates dynamic hysteresis with the shape of the loop and its area varying with the amplitude and frequency of the applied field, swarm density and the noise intensity. We measure the scaling exponents for the hysteresis loop area, which can be associated with the controllability of the swarm. Although the exponents are non-universal and depend on the system’s parameters, their limiting values can be predicted using a generic model of dynamic hysteresis. We also discuss similarities and differences between the swarm ordering dynamics and two-dimensional magnets.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    M.A. Krasnosel’skii, A.V. Pokrovskii, Systems with hysteresis (Springer, 1989)Google Scholar
  2. 2.
    I.F. Lyuksyutov, T. Nattermann, V. Pokrovsky, Phys. Rev. B 59, 4260 (1999)ADSCrossRefGoogle Scholar
  3. 3.
    H. Chaté, F. Ginelli, G. Grégoire, F. Raynaud, Phys. Rev. E 77, 046113 (2008)ADSCrossRefGoogle Scholar
  4. 4.
    I.D. Couzin, J. Krause, R. James, G.D. Ruxton, N.R. Franks, J. Theor. Biol. 218, 1 (2002)MathSciNetCrossRefGoogle Scholar
  5. 5.
    T. Ihle, Phys. Rev. E 88, 040303 (2013)ADSCrossRefGoogle Scholar
  6. 6.
    B.K. Chakrabarti, M. Acharyya, Rev. Mod. Phys. 71, 847 (1999)ADSCrossRefGoogle Scholar
  7. 7.
    P. Reimann, R. Kawai, C. Van den Broeck, P. Hänggi, Europhys. Lett. 45, 545 (1999)ADSCrossRefGoogle Scholar
  8. 8.
    T. Vicsek, A. Czirók, E. Ben-Jacob, I. Cohen, O. Shochet, Phys. Rev. Lett. 75, 1226 (1995)ADSCrossRefGoogle Scholar
  9. 9.
    T. Vicsek, A. Zafeiris, Phys. Rep. 517, 71 (2012)ADSCrossRefGoogle Scholar
  10. 10.
    A. Czirók, A.L. Barabasi, T. Vicsek, Phys. Rev. Lett. 82, 209 (1999)ADSCrossRefGoogle Scholar
  11. 11.
    J. Toner, Y. Tu, Phys. Rev. Lett. 75, 4326 (1995)ADSCrossRefGoogle Scholar
  12. 12.
    J. Toner, Y. Tu, Phys. Rev. E 58, 4828 (1998)MathSciNetADSCrossRefGoogle Scholar
  13. 13.
    J. Toner, Y. Tu, S. Ramaswami, Ann. Phys. 318, 170 (2005)ADSCrossRefGoogle Scholar
  14. 14.
    S. Ramaswamy, Annu. Rev. Condens. Matter Phys. 1, 323 (2010)ADSCrossRefGoogle Scholar
  15. 15.
    G. Baglietto, E.V. Albano, Phys. Rev. E 78, 21125 (2008)ADSCrossRefGoogle Scholar
  16. 16.
    M. Romenskyy, V. Lobaskin, Eur. Phys. J. B 86, 91 (2013)ADSCrossRefGoogle Scholar
  17. 17.
    A. Cavagna, A. Cimarelli, I. Giardina, G. Parisi, R. Santagati, F. Stefanini, M. Viale, Proc. Natl. Acad. Sci. USA 107(26), 11865 (2010)ADSCrossRefGoogle Scholar
  18. 18.
    A.P. Solon, J. Tailleur, Phys . Rev. Lett. 111, 078101 (2013)ADSCrossRefGoogle Scholar
  19. 19.
    W. Ebeling, F. Schweitzer, B. Tilch, Biosystems 49, 17 (1999)CrossRefGoogle Scholar
  20. 20.
    W. Ebeling, U. Erdmann, J. Dunkel, M. Jenssen, J. Stat. Phys. 101, 443 (2000)ADSCrossRefGoogle Scholar
  21. 21.
    V. Lobaskin, M. Romenskyy, Phys. Rev. E 87, 052135 (2013)ADSCrossRefGoogle Scholar
  22. 22.
    M. Romensky, D. Scholz, V. Lobaskin, J. R. Soc. Interface 12, 20150015 (2015)CrossRefGoogle Scholar
  23. 23.
    P. Romanczuk, M. Bär, W. Ebeling, B. Lindner, L. Schimansky-Geier, Eur. Phys. J. Special Topics 202, 1 (2012)ADSCrossRefGoogle Scholar
  24. 24.
    P. Español, Phys. Rev. E 52, 1734 (1995)MathSciNetADSCrossRefGoogle Scholar
  25. 25.
    K. Binder, Z. Phys. B Condens. Matter 43, 119 (1981)ADSCrossRefGoogle Scholar
  26. 26.
    H. Chaté, F. Ginelli, G. Grégoire, F. Peruani, F. Raynaud, Eur. Phys. J. B 64, 451 (2008)ADSCrossRefGoogle Scholar
  27. 27.
    L. Verlet, Phys. Rev. 159, 98 (1967)ADSCrossRefGoogle Scholar
  28. 28.
    M. Romensky, V. Lobaskin, T. Ihle, Phys. Rev. E 90, 063315 (2014)ADSCrossRefGoogle Scholar
  29. 29.
    I.D. Mayergoyz, Mathematical models of Hysteresis (Spinger Verlag, New York, 1991)Google Scholar
  30. 30.
    Z. Huang, F. Zhang, Z. Chen, Y. Du, Eur. Phys. J. B 44, 423 (2005)ADSCrossRefGoogle Scholar
  31. 31.
    E. Vatansever, U. Akinci, Y. Yüksel, H. Polat, J. Magn. Magn. Mater. 329, 14 (2013)ADSCrossRefGoogle Scholar
  32. 32.
    G.H. Goldsztein, F. Broner, S.H. Strogatz, SIAM J. Appl. Math. 57, 1163 (1997)MathSciNetCrossRefGoogle Scholar

Copyright information

© EDP Sciences and Springer 2015

Authors and Affiliations

  1. 1.Department of MathematicsUppsala UniversityUppsalaSweden
  2. 2.School of Physics, Complex and Adaptive Systems LabUniversity College DublinBelfield, Dublin 4Ireland

Personalised recommendations