Skip to main content
SpringerLink
Log in

Order–Disorder Phase Transition in Heterogeneous Populations of Self-propelled Particles

  • Published:
Journal of Statistical Physics Aims and scope Submit manuscript

Abstract

Biological systems are typically heterogeneous as individuals vary in their characteristics, their response to the external environment and to each other. For example, cell diversity plays a crucial role in the successful survival of many biological systems. Phenotypic heterogeneity is associated with cellular response to intercellular communications, the response to external environmental cues, motility modes, and proliferation rates. Here we study the effect of phenotypic diversity on the properties of collective motion in the context of the scalar noise model of collective migration. For simplicity, we study a population that is composed of two sub-populations, each with different sensitivities to external noise. We find that the two sub-populations interact non-additively: Within a large range of parameters, the dynamics of the system can be described by an equivalent homogeneous system with an effective temperature that depends on the average circular mean of the phenotypes. However, if one of the sub-populations is sufficiently “cold”, it dominates the dynamics of the group as a whole.

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.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

References

  1. Vicsek, T., Zafeiris, A.: Collective motion. Phys. Rep. 517, 71–140 (2012)

    Article  ADS  Google Scholar 

  2. Couzin, I.D., Krause, J., Franks, N.R., Levin, S.A.: Effective leadership and decision-making in animal groups on the move. Nature 433, 513–516 (2005)

    Article  ADS  Google Scholar 

  3. Mishra, S. Tunstrøm, K., Couzin, I.D., Huepe, C.: Collective dynamics of self-propelled particles with variable speed. Phys. Rev. E 86, 011901 (Jul 2012)

  4. Menzel, A.M.: Collective motion of binary self-propelled particle mixtures. Phys. Rev. E 85, 021912 (2012)

    Article  ADS  Google Scholar 

  5. Nagy, M., Daruka, I., Vicsek, T.: New aspects of the continuous phase transition in the scalar noise model (snm) of collective motion. Physica A 373, 445–454 (2007)

    Article  ADS  Google Scholar 

  6. Vicsek, T., Czirók, A., Ben-Jacob, E., Cohen, I., Shochet, O.: Novel type of phase transition in a system of self-driven particles. Phys. Rev. Lett. 75, 1226–1229 (Aug 1995)

  7. Toner, J., Tu, Y., Ramaswamy, S.: Hydrodynamics and phases of flocks. Ann. Phys. 318(1), 170–244 (2005)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  8. Degond, P., Liu, J.-G., Motsch, S., Panferov, V.: Hydrodynamic models of self-organized dynamics: derivation and existence theory. Methods Appl. Anal. 20, 89–114 (2013)

    MATH  MathSciNet  Google Scholar 

  9. Degond, P., Motsch, S.: Continuum limit of self-driven particles with orientation interaction. Math. Models Methods Appl. Sci. 18, 1193–1215 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  10. Fisher, N.I.: Statistical Analysis of Circular Data. Cambridge University Press, New York (1993)

    Book  MATH  Google Scholar 

  11. Grégoire, G., Chaté, H., Tu, Y.: Moving and staying together without a leader. Physica D 181(3), 157–170 (2003)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  12. Grégoire, G., Chaté, H.: Onset of collective and cohesive motion. Phys. Rev. Lett. 92, 025702 (2004)

    Article  ADS  Google Scholar 

  13. Binder, K.: Finite size scaling analysis of ising model block distribution functions. Zeitschrift für Physik B Condensed Matter 43(2), 119–140 (1981)

    Article  ADS  Google Scholar 

  14. Cesa-Bianchi, N., Freund, Y., Haussler, D., Helmbold, D.P., Schapire, R.E., Warmuth, M.K.: How to use expert advice. Journal of the ACM (JACM), 44(3), 427–485 1997.

  15. Baglietto, G., Albano, E.V., Candia, J.: Gregarious vs individualistic behavior in vicsek swarms and the onset of first-order phase transitions. Statist. Mech. Appl. Physica A 392(15), 3240–3247 (2013)

    Article  ADS  MathSciNet  Google Scholar 

Download references

Acknowledgments

We thank two annonymous referees for useful comments and suggestions. GA acknowledges a Marie-Curie integration grant. EBJ was supported by a grant from the Tauber Family Funds and the Maguy-Glass Chair in Physics of Complex Systems and by the NSF Center for Theoretical Biological Physics, Grant No. PHY-1308264.

Author information

Authors and Affiliations

  1. Department of Mathematics, Bar-Ilan University, 5290002, Ramat-Gan, Israel

    Gil Ariel & Oren Rimer

  2. School of Physics and Astronomy, Tel-Aviv University, 69978, Tel-Aviv, Israel

    Eshel Ben-Jacob

  3. Biological Physics, Rice University, Houston, TX, 77005, USA

    Eshel Ben-Jacob

Authors
  1. Gil Ariel
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Oren Rimer
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Eshel Ben-Jacob
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Gil Ariel.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ariel, G., Rimer, O. & Ben-Jacob, E. Order–Disorder Phase Transition in Heterogeneous Populations of Self-propelled Particles. J Stat Phys 158, 579–588 (2015). https://doi.org/10.1007/s10955-014-1095-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10955-014-1095-7

Keywords

Search

Navigation