Advertisement

The European Physical Journal Special Topics

, Volume 225, Issue 11–12, pp 2287–2299 | Cite as

Collective behavior of active Brownian particles: From microscopic clustering to macroscopic phase separation

  • Thomas SpeckEmail author
Regular Article Collective Behaviour
Part of the following topical collections:
  1. Microswimmers – From Single Particle Motion to Collective Behaviour

Abstract

A pedagogical introduction to the analytical treatment of the collective behavior of active (self-propelled) Brownian particles with short-ranged interactions is presented. The treatment is based on established concepts from the theories of simple liquids and pattern formation. It is shown how microscopic clustering due to self-blocking of directed particle motion leads to macroscopic phase separation described by effective equilibrium concepts holding on length scales larger than the persistence length of the direction motion.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    S. Ramaswamy, Annu. Rev. Cond. Mat. Phys. 1, 323 (2010)ADSCrossRefGoogle Scholar
  2. 2.
    T. Vicsek, A. Zafeiris, Phys. Rep. 517, 71 (2012)ADSCrossRefGoogle Scholar
  3. 3.
    P. Romanczuk, M. Bär, W. Ebeling, B. Lindner, L. Schimansky-Geier, Eur. Phys. J. Special Topics 202, 1 (2012)ADSCrossRefGoogle Scholar
  4. 4.
    M.C. Marchetti, J.F. Joanny, S. Ramaswamy, T.B. Liverpool, J. Prost, M. Rao, R.A. Simha, Rev. Mod. Phys. 85, 1143 (2013)ADSCrossRefGoogle Scholar
  5. 5.
    A. Cavagna, A. Cimarelli, I. Giardina, G. Parisi, R. Santagati, F. Stefanini, M. Viale, Proc. Natl. Acad. Sci. U.S.A. 107, 11865 (2010)ADSCrossRefGoogle Scholar
  6. 6.
    H.H. Wensink, J. Dunkel, S. Heidenreich, K. Drescher, R.E. Goldstein, H. Löwen, J.M. Yeomans, Proc. Natl. Acad. Sci. U.S.A. 109, 14308 (2012)ADSCrossRefGoogle Scholar
  7. 7.
    V. Narayan, S. Ramaswamy, N. Menon, Science 317, 105 (2007)ADSCrossRefGoogle Scholar
  8. 8.
    W.F. Paxton, K.C. Kistler, C.C. Olmeda, A. Sen, S.K. St. Angelo, Y. Cao, T.E. Mallouk, P.E. Lammert, V.H. Crespi, J. Am. Chem. Soc. 126, 13424 (2004)CrossRefGoogle Scholar
  9. 9.
    T. Vicsek, A. Czirók, E. Ben-Jacob, I. Cohen, O. Shochet, Phys. Rev. Lett. 75, 1226 (1995)ADSMathSciNetCrossRefGoogle Scholar
  10. 10.
    F. Ginelli, Eur. Phys. J. Special Topics 225, 2099 (2016)ADSCrossRefGoogle Scholar
  11. 11.
    F. Peruani, A. Deutsch, M. Bär, Phys. Rev. E 74, 030904 (2006)ADSCrossRefGoogle Scholar
  12. 12.
    F. Peruani, Eur. Phys. J. Special Topics 225, 3001 (2016)CrossRefGoogle Scholar
  13. 13.
    J.R. Howse, R.A.L. Jones, A.J. Ryan, T. Gough, R. Vafabakhsh, R. Golestanian, Phys. Rev. Lett. 99, 048102 (2007)ADSCrossRefGoogle Scholar
  14. 14.
    J. Palacci, C. Cottin-Bizonne, C. Ybert, L. Bocquet, Phys. Rev. Lett. 105, 088304 (2010)ADSCrossRefGoogle Scholar
  15. 15.
    I. Buttinoni, G. Volpe, F. Kümmel, G. Volpe, C. Bechinger, J. Phys.: Condens. Matter 24, 284129 (2012)Google Scholar
  16. 16.
    I. Theurkauff, C. Cottin-Bizonne, J. Palacci, C. Ybert, L. Bocquet, Phys. Rev. Lett. 108, 268303 (2012)ADSCrossRefGoogle Scholar
  17. 17.
    J. Palacci, S. Sacanna, A.P. Steinberg, D.J. Pine, P.M. Chaikin, Science 339, 936 (2013)ADSCrossRefGoogle Scholar
  18. 18.
    I. Buttinoni, J. Bialké, F. Kümmel, H. Löwen, C. Bechinger, T. Speck, Phys. Rev. Lett. 110, 238301 (2013)ADSCrossRefGoogle Scholar
  19. 19.
    J. Bialké, T. Speck, H. Löwen, J. Non-Cryst. Solids 407, 367 (2015)ADSCrossRefGoogle Scholar
  20. 20.
    A.T. Brown, W.C.K. Poon, Soft Matter 10, 4016 (2014)ADSCrossRefGoogle Scholar
  21. 21.
    S. Samin, R. van Roij, Phys. Rev. Lett. 115, 188305 (2015)ADSCrossRefGoogle Scholar
  22. 22.
    A. Würger, Phys. Rev. Lett. 115, 188304 (2015)ADSCrossRefGoogle Scholar
  23. 23.
    M. Popescu, W. Uspal, S. Dietrich, Eur. Phys. J. Special Topics 225, 2189 (2016)ADSCrossRefGoogle Scholar
  24. 24.
    Y. Fily, M.C. Marchetti, Phys. Rev. Lett. 108, 235702 (2012)ADSCrossRefGoogle Scholar
  25. 25.
    G.S. Redner, M.F. Hagan, A. Baskaran, Phys. Rev. Lett. 110, 055701 (2013)ADSCrossRefGoogle Scholar
  26. 26.
    T. Speck, J. Bialké, A. M. Menzel, H. Löwen, Phys. Rev. Lett. 112, 218304 (2014)ADSCrossRefGoogle Scholar
  27. 27.
    Y. Fily, S. Henkes, M.C. Marchetti, Soft Matter 10, 2132 (2014)ADSCrossRefGoogle Scholar
  28. 28.
    J. Bialké, J.T. Siebert, H. Löwen, T. Speck, Phys. Rev. Lett. 115, 098301 (2015)ADSCrossRefGoogle Scholar
  29. 29.
    A.P. Solon, M.E. Cates, J. Tailleur, Eur. Phys. J. Special Topics 224, 1231 (2015)ADSCrossRefGoogle Scholar
  30. 30.
    M.E. Cates, J. Tailleur, EPL 101, 20010 (2013)ADSCrossRefGoogle Scholar
  31. 31.
    M.E. Cates, J. Tailleur, Annu. Rev. Condens. Matter Phys. 6, 219 (2015)ADSCrossRefGoogle Scholar
  32. 32.
    D. Marenduzzo, Eur. Phys. J. Special Topics 225, 2065 (2016)ADSCrossRefGoogle Scholar
  33. 33.
    A. Wysocki, R.G. Winkler, G. Gompper, EPL 105, 48004 (2014)ADSCrossRefGoogle Scholar
  34. 34.
    J. Stenhammar, D. Marenduzzo, R.J. Allen, M.E. Cates, Soft Matter 10, 1489 (2014)ADSCrossRefGoogle Scholar
  35. 35.
    A.P. Solon, Y. Fily, A. Baskaran, M.E. Cates, Y. Kafri, M. Kardar, J. Tailleur, Nature Phys. 11, 673 (2015)ADSCrossRefGoogle Scholar
  36. 36.
    W. Yan, J.F. Brady, Soft Matter 11, 6235 (2015)ADSCrossRefGoogle Scholar
  37. 37.
    E.P. Bernard, W. Krauth, Phys. Rev. Lett. 107, 155704 (2011)ADSCrossRefGoogle Scholar
  38. 38.
    T. Ishikawa, J.T. Locsei, T.J. Pedley, J. Fluid Mech. 615, 401 (2008)ADSCrossRefGoogle Scholar
  39. 39.
    A. Zöttl, H. Stark, Phys. Rev. Lett. 112, 118101 (2014)ADSCrossRefGoogle Scholar
  40. 40.
    R.G. Winkler, Eur. Phys. J. Special Topics 225, 2079 (2016)ADSCrossRefGoogle Scholar
  41. 41.
    J. Bialké, H. Löwen, T. Speck, EPL 103, 30008 (2013)ADSCrossRefGoogle Scholar
  42. 42.
    T. Speck, A.M. Menzel, J. Bialké, H. Löwen, J. Chem. Phys. 142, 224109 (2015)ADSCrossRefGoogle Scholar
  43. 43.
    J. Stenhammar, A. Tiribocchi, R.J. Allen, D. Marenduzzo, M.E. Cates, Phys. Rev. Lett. 111, 145702 (2013)ADSCrossRefGoogle Scholar
  44. 44.
    J. Toner, Y. Tu, Phys. Rev. Lett. 75, 4326 (1995)ADSCrossRefGoogle Scholar
  45. 45.
    M.C. Cross, P.C. Hohenberg, Rev. Mod. Phys. 65, 851 (1993)ADSCrossRefGoogle Scholar
  46. 46.
    J.W. Cahn, J.E. Hilliard, J. Chem. Phys. 28, 258 (1958)ADSCrossRefGoogle Scholar
  47. 47.
    J.D. Weeks, D. Chandler, H.C. Andersen, J. Chem. Phys. 54, 5237 (1971)ADSCrossRefGoogle Scholar
  48. 48.
    A.P. Solon, J. Stenhammar, R. Wittkowski, M. Kardar, Y. Kafri, M.E. Cates, J. Tailleur, Phys. Rev. Lett. 114, 198301 (2015)ADSCrossRefGoogle Scholar
  49. 49.
    T.F.F. Farage, P. Krinninger, J.M. Brader, Phys. Rev. E 91, 042310 (2015)ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences and Springer 2016

Authors and Affiliations

  1. 1.Institut für Physik, Johannes Gutenberg-Universität MainzMainzGermany

Personalised recommendations