Hydrodynamics of self-propelled hard rods.

Motivated by recent simulations and by experiments on aggregation of gliding bacteria, we study a model of the collective dynamics of self-propelled hard rods on a substrate in two dimensions. The rods have finite size, interact via excluded volume, and their dynamics is overdamped by the interaction with the substrate. Starting from a microscopic model with nonthermal noise sources, a continuum description of the system is derived. The hydrodynamic equations are then used to characterize the possible steady states of the systems and their stability as a function of the particles packing fraction and the speed of self-propulsion.

[1]  J. Toner,et al.  Hydrodynamics and phases of flocks , 2005 .

[2]  Andreas Deutsch,et al.  Nonequilibrium clustering of self-propelled rods. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  Hong Zhang,et al.  Collective Robotics: From Social Insects to Robots , 1993, Adapt. Behav..

[4]  D. Volfson,et al.  Swirling motion in a system of vibrated elongated particles. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[5]  Sriram Ramaswamy,et al.  Hydrodynamic fluctuations and instabilities in ordered suspensions of self-propelled particles. , 2001, Physical review letters.

[6]  Vijay Narayan,et al.  Nonequilibrium steady states in a vibrated-rod monolayer: tetratic, nematic, and smectic correlations , 2005 .

[7]  T. Lubensky,et al.  Principles of condensed matter physics , 1995 .

[8]  J. McLennan.  Introduction to nonequilibrium statistical mechanics , 1989 .

[9]  Andrés Santos,et al.  Hydrodynamics for granular flow at low density , 1998 .

[10]  Hugues Chaté,et al.  Simple model for active nematics: quasi-long-range order and giant fluctuations. , 2006, Physical review letters.

[11]  Active nematics on a substrate: Giant number fluctuations and long-time tails , 2002, cond-mat/0208573.

[12]  H. Chaté,et al.  Onset of collective and cohesive motion. , 2004, Physical review letters.

[13]  S. Ramaswamy,et al.  Linear and nonlinear hydrodynamics of low-friction adsorbed systems , 1982 .

[14]  Dieter Kaufmann,et al.  Elastic properties of nematoid arrangements formed by amoeboid cells , 2000 .

[15]  Ericka Stricklin-Parker,et al.  Ann , 2005 .

[16]  P. Mazur,et al.  Non-equilibrium thermodynamics, , 1963 .

[17]  Roy D. Welch,et al.  Waves and aggregation patterns in myxobacteria , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[18]  M. Cross,et al.  Pattern formation outside of equilibrium , 1993 .

[19]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[20]  S. Edwards,et al.  The Theory of Polymer Dynamics , 1986 .

[21]  Vijay Narayan,et al.  Long-Lived Giant Number Fluctuations in a Swarming Granular Nematic , 2007, Science.

[22]  M. Marchetti,et al.  Hydrodynamics of isotropic and liquid crystalline active polymer solutions. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[24]  N. Mermin,et al.  Absence of Ferromagnetism or Antiferromagnetism in One- or Two-Dimensional Isotropic Heisenberg Models , 1966 .

[25]  Sriram Ramaswamy,et al.  Active nematics are intrinsically phase separated. , 2006, Physical review letters.

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

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