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Motility-Induced Phase Separation of Active Particles in the Presence of Velocity Alignment

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Abstract

Self-propelled particle (SPP) systems are intrinsically out of equilibrium systems, where each individual particle converts energy into work to move in a dissipative medium. When interacting through a velocity alignment mechanism, and with the medium acting as a momentum sink, even momentum is not conserved. In this scenario, a mapping into an equilibrium system seems unlikely. Here, we show that an entropy functional can be derived for SPPs with velocity alignment and density-dependent speed, at least in the (orientationally) disordered phase. This non-trivial result has important physical consequences. The study of the entropy functional reveals that the system can undergo phase separation before the orientational-order phase transition known to occur in SPP systems with velocity alignment. Moreover, we indicate that the spinodal line is a function of the alignment sensitivity and show that density fluctuations as well as the critical spatial diffusion, that leads to phase separation, dramatically increase as the orientational-order transition is approached.

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Acknowledgments

We acknowledge enlightening discussions with O. Dauchot, P. Degond, and J. Tailleur and financial support from the PEPS-PTI “Anomalous fluctuations in the collective motion of self-propelled particles”. The suggestion by J. Tailleur of adding a white noise to Eq. (1) has proved to be very fruitful for the present study. FP thanks the Kavli Institute for Theoretical Physics (University of California, Santa Barbara) and the organizers of the bioacter14 program for hospitality and financial support.

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Authors and Affiliations

  1. Laboratoire J.A. Dieudonné, UMR CNRS 7351, Université Nice Sophia Antipolis, Parc Valrose, 06108,  Nice Cedex 02, France

    Julien Barré, Raphaël Chétrite, Massimiliano Muratori & Fernando Peruani

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  1. Julien Barré
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Correspondence to Fernando Peruani.

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Barré, J., Chétrite, R., Muratori, M. et al. Motility-Induced Phase Separation of Active Particles in the Presence of Velocity Alignment. J Stat Phys 158, 589–600 (2015). https://doi.org/10.1007/s10955-014-1008-9

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