Tailoring the interactions between self-propelled bodies

Abstract

We classify the interactions between self-propelled particles moving at a constant speed from symmetry considerations. We establish a systematic expansion for the two-body forces in the spirit of a multipolar expansion. This formulation makes it possible to rationalize most of the models introduced so far within a common framework. We distinguish between three classes of physical interactions: i) potential forces, ii) inelastic collisions and iii) non-reciprocal interactions involving polar or nematic alignment with an induced field. This framework provides simple design rules for the modeling and the fabrication of self-propelled bodies interacting via physical interactions. A class of possible interactions that should yield new phases of active matter is highlighted.

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References

  1. 1.

    T. Vicsek, A. Zafeiris, Phys. Rep. 517, 71 (2012).

    ADS  Article  Google Scholar 

  2. 2.

    M.C. Marchetti, J.F. Joanny, S. Ramaswamy, T.B. Liverpool, J. Prost, M. Rao, R.A. Simha, Rev. Mod. Phys. 85, 1143 (2013).

    ADS  Article  Google Scholar 

  3. 3.

    P. Romanczuk, M. Bär, W. Ebeling, B. Lindner, L. Schimansky-Geier, Eur. Phys. J. ST 202, 1 (2012).

    Article  Google Scholar 

  4. 4.

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

    ADS  Article  Google Scholar 

  5. 5.

    H. Levine, W.-J. Rappel, I. Cohen, Phys. Rev. E 63, 017101 (2000).

    ADS  Article  Google Scholar 

  6. 6.

    I.D. Couzin, J. Krause, R. James, G.D. Ruxton, N.R. Franks, J. Theor. Biol. 218, 1 (2002).

    Article  MathSciNet  Google Scholar 

  7. 7.

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

    Article  Google Scholar 

  8. 8.

    H. Chaté, F. Ginelli, G. Grégoire, F. Peruani, F. Raynaud, Eur. Phys. J. B 64, 451 (2008).

    ADS  Article  Google Scholar 

  9. 9.

    R. Grossmann, L. Schimansky-Geier, P. Romanczuk, New J. Phys. 15, 085014 (2013).

    ADS  Article  Google Scholar 

  10. 10.

    W.F. Paxton, S. Sundararajan, T.E. Mallouk, A. Sen, Angew. Chem., Int. ed. 45, 5420 (2006).

    Article  Google Scholar 

  11. 11.

    I. Theurkauff, C. Cottin-Bizonne, J. Palacci, C. Ybert, L. Bocquet, Phys. Rev. Lett. 108, 268303 (2012).

    ADS  Article  Google Scholar 

  12. 12.

    J. Palacci, S. Sacanna, A.P. Steinberg, D.J. Pine, P.M. Chaikin, Science 339, 936 (2013).

    ADS  Article  Google Scholar 

  13. 13.

    H.-R. Jiang, N. Yoshinaga, M. Sano, Phys. Rev. Lett. 105, 268302 (2010).

    ADS  Article  Google Scholar 

  14. 14.

    A. Bricard, J.-B. Caussin, N. Desreumaux, O. Dauchot, D. Bartolo, Nature 503, 95 (2013).

    ADS  Article  Google Scholar 

  15. 15.

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

    ADS  Article  Google Scholar 

  16. 16.

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

    ADS  Article  Google Scholar 

  17. 17.

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

    ADS  Article  Google Scholar 

  18. 18.

    N. Kumar, H. Soni, S. Ramaswamy, A.K. Sood, arXiv:1402.4262v1 (2014).

  19. 19.

    V. Schaller, C.A. Weber, C. Semmrich, E. Frey, A.R. Bausch, Nature 467, 73 (2010).

    ADS  Article  Google Scholar 

  20. 20.

    Y. Sumino, K.H. Nagai, Y. Shitaka, D. Tanaka, K. Yoshikawa, H. Chaté, K. Oiwa, Nature 483, 448 (2012).

    ADS  Article  Google Scholar 

  21. 21.

    T. Sanchez, D.T.N. Chen, S.J. DeCamp, M. Heymann, Z. Dogic, Nature 491, 431 (2012).

    ADS  Article  Google Scholar 

  22. 22.

    P. Romanczuk, L. Schimansky-Geier, Phys. Rev. Lett. 106, 230601 (2011).

    ADS  Article  Google Scholar 

  23. 23.

    C.A. Weber, T. Hanke, J. Deseigne, S. Léonard, O. Dauchot, E. Frey, H. Chaté, Phys. Rev. Lett. 110, 208001 (2013).

    ADS  Article  Google Scholar 

  24. 24.

    S. Henkes, Y. Fily, M.C. Marchetti, Phys. Rev. E 84, 040301 (2011).

    ADS  Article  Google Scholar 

  25. 25.

    M.R. D'Orsogna, Y.-L. Chuang, A.L. Bertozzi, L.S. Chayes, Phys. Rev. Lett. 96, 104302 (2006).

    ADS  Article  Google Scholar 

  26. 26.

    Y.-L. Chuang, M.R. D'Orsogna, D. Marthaler, A.L. Bertozzi, L.S. Chayes, Physica D 232, 33 (2007).

    ADS  Article  MATH  MathSciNet  Google Scholar 

  27. 27.

    T. Hanke, C. Weber, E. Frey, Phys. Rev. E 88, 052309 (2013).

    ADS  Article  Google Scholar 

  28. 28.

    E. Ferrante, A. Turgut, M. Dorigo, C. Huepe, Phys. Rev. Lett. 268302, 1 (2013).

    Google Scholar 

  29. 29.

    D. Grossman, I.S. Aranson, E. Ben Jacob, New J. Phys. 10, 023036 (2008).

    ADS  Article  Google Scholar 

  30. 30.

    D. Saintillan, M.J. Shelley, C.R. Phys. 14, 497 (2013).

    ADS  Article  Google Scholar 

  31. 31.

    T. Brotto, J.-B. Caussin, E. Lauga, D. Bartolo, Phys. Rev. Lett. 110, 038101 (2013).

    ADS  Article  Google Scholar 

  32. 32.

    I.S. Aranson, C.R. Phys. 14, 518 (2013).

    ADS  Article  Google Scholar 

  33. 33.

    T. Bickel, G. Zecua, A. Würger, Phys. Rev. E 89, 050303 (2014).

    Article  Google Scholar 

  34. 34.

    S. Saha, R. Golestanian, S. Ramaswamy, arXiv:1309.4947 (2013).

  35. 35.

    M.N. Popescu, M. Tasinkevych, S. Dietrich, EPL 95, 28004 (2011).

    ADS  Article  Google Scholar 

  36. 36.

    A. Lefauve, D. Saintillan, Phys. Rev. E 89, 021002 (2014).

    ADS  Article  Google Scholar 

  37. 37.

    F.G. Woodhouse, R.E. Goldstein, Proc. Natl. Acad. Sci. U.S.A. 35, 14132 (2013).

    ADS  Article  Google Scholar 

  38. 38.

    F. Farrell, M.C. Marchetti, D. Marenduzzo, J. Tailleur, Phys. Rev. Lett. 108, 1 (2012).

    Article  Google Scholar 

  39. 39.

    E. Bertin, M. Droz, G. Grégoire, J. Phys. A 42, 445001 (2009).

    ADS  Article  Google Scholar 

  40. 40.

    G. Grégoire, H. Chaté, Phys. Rev. Lett. 92, 025702 (2004).

    ADS  Article  Google Scholar 

  41. 41.

    G.B. Jeffery, P. Roy. Soc. A-Math. Phys. 102, 161 (1922).

    Article  Google Scholar 

  42. 42.

    D. Saintillan, M. J. Shelley, Phys. Rev. Lett. 100, 178103 (2008).

    ADS  Article  Google Scholar 

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Correspondence to Jean-Baptiste Caussin.

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Caussin, J., Bartolo, D. Tailoring the interactions between self-propelled bodies. Eur. Phys. J. E 37, 55 (2014). https://doi.org/10.1140/epje/i2014-14055-8

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Keywords

  • Flowing Matter: Liquids and Complex Fluids