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

By E. Bertin, M. Droz, G. Gr'egoire. 2009

297 citations recorded by the source corpus.

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 parameters), signalling the onset of a collective motion. Comparison with numerical simulations on a standard model of self-propelled particles shows that the phase diagram we obtain is robust, in the sense that it depends only slightly on the precise definition of the model. While the homogeneous flow is found to be stable far from the transition line, it becomes unstable with respect to finite-wavelength perturbations close to the transition, implying a non-trivial spatio-temporal structure for the resulting flow. We find solitary wave solutions of the hydrodynamic equations, quite similar to the stripes reported in direct numerical simulations of self-propelled particles.

Subfields: Condensed Matter Physics, Ocean Engineering

View Paper: https://www.semanticscholar.org/paper/1a666609fe08b4f2974da27fa000545f5f5b9fa5

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Citations in the corpus

Hydrodynamics of soft active matter (2013, methodology): “Notice that all microscopic derivations of the continuous equations for various systems of self-propelled particles (Bertin, Droz, and Grégoire, 2006, 2009; Baskaran and Marchetti, 2008b) yield "'> 0.”
Tuned, driven, and active soft matter (2015, background): “The nature of these traveling density bands was discussed in the framework of solitons [379, 380].”
Physics of microswimmers—single particle motion and collective behavior: a review (2014, background): “…of a non-equilibrium phase transition in a system of self-propelled point particles has led to numerous analytical (Baskaran and Marchetti, 2009; Bertin et al., 2009; Golestanian, 2009; Peruani et al., 2008; Ramaswamy et al., 2003; Simha and Ramaswamy, 2002; Toner and Tu, 1995; Toner et al.,…”
Deciphering Interactions in Moving Animal Groups (2012, background): “With such a viewpoint, different models in this class merely differ in the numerical values of their parameters [21–23], very much like different fluids are commonly described by the Navier-Stokes equations and differ only in their viscosity and other constitutive parameters.”
The statistical physics of active matter: From self-catalytic colloids to living cells (2017, methodology): “Systematic perturbation methods have been employed to obtain some closed hydrodynamic equations [37,38,70].”
Active Particles in Complex and Crowded Environments (2016, background): “It has in fact become a challenge for theoretical physics to find minimal statistical models that capture these features (Bertin et al., 2009; Li et al., 2008; Toner et al., 2005).”