Hydrodynamic equations for self-propelled particles: microscopic derivation and stability analysis

@article{Bertin2009HydrodynamicEF,
  title={Hydrodynamic equations for self-propelled particles: microscopic derivation and stability analysis},
  author={Eric Bertin and Michel Droz and Guillaume Gr'egoire},
  journal={Journal of Physics A: Mathematical and Theoretical},
  year={2009},
  volume={42},
  pages={445001}
}
Considering a gas of self-propelled particles with binary interactions, we derive the hydrodynamic equations governing the density and velocity fields from the microscopic dynamics, in the framework of the associated Boltzmann equation. Explicit expressions for the transport coefficients are given, as a function of the microscopic parameters of the model. We show that the homogeneous state with zero hydrodynamic velocity is unstable above a critical density (which depends on the microscopic… 

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