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The hydrodynamic description for the system of self-propelled particles: Ideal Viscek fluid

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  • Chepizhko, Oleksandr
  • Kulinskii, Vladimir

Abstract

We use the method of the microscopic phase density to get the kinetic equation for the system of self-propelled particles with Vicsek-like alignment rule. The hydrodynamic equations are derived for the ordered phase taking into account the mean-field force only. The equation for the hydrodynamic velocity plays the role of the Euler equation for the self-propelled Vicsek fluid. The hydrodynamics of such ideal self-propelled fluid demonstrates the dynamical transition from disordered initial state to the completely ordered motion. To take the noise into account we consider how the framework of the local equilibrium approximation affects the hydrodynamic equations and the viscous tensor and show that in such approximation the shear viscosity vanishes.

Suggested Citation

  • Chepizhko, Oleksandr & Kulinskii, Vladimir, 2014. "The hydrodynamic description for the system of self-propelled particles: Ideal Viscek fluid," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 415(C), pages 493-502.
    • Handle: RePEc:eee:phsmap:v:415:y:2014:i:c:p:493-502
    DOI: 10.1016/j.physa.2014.08.027
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    References listed on IDEAS

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    1. Nagy, Máté & Daruka, István & Vicsek, Tamás, 2007. "New aspects of the continuous phase transition in the scalar noise model (SNM) of collective motion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 373(C), pages 445-454.
    2. Antoine Bricard & Jean-Baptiste Caussin & Nicolas Desreumaux & Olivier Dauchot & Denis Bartolo, 2013. "Emergence of macroscopic directed motion in populations of motile colloids," Nature, Nature, vol. 503(7474), pages 95-98, November.
    3. Chepizhko, A.A. & Kulinskii, V.L., 2010. "On the relation between Vicsek and Kuramoto models of spontaneous synchronization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(23), pages 5347-5352.
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