Self-propelled hard disks: implicit alignment and transition to collective motion

We formulate a model of self-propelled hard disks whose dynamics is governed by mutually coupled vectors for velocity and body orientation. Numerical integration at low densities reveals that the expected transition from isotropic to aligned collective motion is present. However, the transition at the Landau mean-field level is strongly first-order, while it is continuous in the Vicsek model. We show that this difference is rooted in the completely opposite effect that individual scattering events have on alignment. We argue that such differences will generically hold for systems of self-propelled particles with repulsive short-ranged interactions. We obtain these results by matching the numerical results to the framework of Boltzmann theory, based on the statistics of binary scattering properties, always assuming that the system is small enough to stay homogeneous. We further show that the presence of noise in the dynamics can change the nature of the transition from discontinuous to continuous.

[1]  M. Grunwald.  Principles Of Condensed Matter Physics , 2016 .

[2]  Khanh-Dang Nguyen Thu Lam,et al.  Polar active liquids: a universal classification rooted in nonconservation of momentum , 2014, 1410.4520.

[3]  Hugues Chaté,et al.  From phase to microphase separation in flocking models: the essential role of nonequilibrium fluctuations. , 2014, Physical review letters.

[4]  Thomas Ihle,et al.  Tricritical points in a Vicsek model of self-propelled particles with bounded confidence. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[5]  E. Bertin,et al.  Boltzmann-Ginzburg-Landau approach for continuous descriptions of generic Vicsek-like models , 2014, 1404.3275.

[6]  H. Chaté,et al.  Emergent spatial structures in flocking models: a dynamical system insight. , 2014, Physical review letters.

[7]  Understanding collective dynamics of soft active colloids by binary scattering. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  H. Chaté,et al.  Long-range ordering of vibrated polar disks. , 2013, Physical review letters.

[9]  G. Baglietto,et al.  Gregarious versus individualistic behavior in Vicsek swarms and the onset of first-order phase transitions , 2013, 1303.6315.

[10]  H. Swinney,et al.  Scale-invariant correlations in dynamic bacterial clusters. , 2012, Physical review letters.

[11]  W. Ebeling,et al.  Active Brownian particles , 2012, The European Physical Journal Special Topics.

[12]  H. Chat'e,et al.  Vibrated polar disks: spontaneous motion, binary collisions, and collective dynamics , 2012, 1201.6021.

[13]  M Cristina Marchetti,et al.  Athermal phase separation of self-propelled particles with no alignment. , 2012, Physical review letters.

[14]  Silke Henkes,et al.  Active jamming: self-propelled soft particles at high density. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  T. Ihle.  Kinetic theory of flocking: derivation of hydrodynamic equations. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[16]  Erwin Frey,et al.  Polar patterns of driven filaments , 2010, Nature.

[17]  Hugues Chaté,et al.  Collective motion of vibrated polar disks. , 2010, Physical review letters.

[18]  H. Swinney,et al.  Collective motion and density fluctuations in bacterial colonies , 2010, Proceedings of the National Academy of Sciences.

[19]  Markus Bär,et al.  Large-scale collective properties of self-propelled rods. , 2009, Physical review letters.

[20]  Harry L. Swinney,et al.  Swarming dynamics in bacterial colonies , 2009 .

[21]  Igor S. Aranson,et al.  Emergence of agent swarm migration and vortex formation through inelastic collisions , 2008 .

[22]  H. Chaté,et al.  Collective motion of self-propelled particles interacting without cohesion. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[23]  M Cristina Marchetti,et al.  Hydrodynamics of self-propelled hard rods. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[24]  T. Vicsek,et al.  Phase transition in the collective migration of tissue cells: experiment and model. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[25]  F. Peruani,et al.  Nonequilibrium clustering of self-propelled rods. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[26]  E. Bertin,et al.  Boltzmann and hydrodynamic description for self-propelled particles. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[27]  L. Tsimring,et al.  Pattern formation of microtubules and motors: inelastic interaction of polar rods. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[28]  H. Chaté,et al.  Large-scale finite-wavelength modulation within turbulent shear flows. , 2002, Physical review letters.

[29]  Faculteit der Wiskunde en Natuurwetenschappen,et al.  Large-Scale Finite-Wavelength Instability within Turbulent Shear Flow , 2002 .

[30]  P. Manneville,et al.  Patterning and Transition to Turbulence in Subcritical Systems: The Case of Plane Couette Flow , 2001 .

[31]  H. Hinrichsen.  Non-equilibrium critical phenomena and phase transitions into absorbing states , 2000, cond-mat/0001070.

[32]  Tu,et al.  Long-Range Order in a Two-Dimensional Dynamical XY Model: How Birds Fly Together. , 1995, Physical review letters.

[33]  Vicsek,et al.  Novel type of phase transition in a system of self-driven particles. , 1995, Physical review letters.