Nonlinear Field Equations for Aligning Self-Propelled Rods

Anton Peshkov, Igor S. Aranson, Eric Bertin, Hugues Chaté, and Francesco Ginelli
Phys. Rev. Lett. 109, 268701 – Published 27 December 2012
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Abstract

We derive a set of minimal and well-behaved nonlinear field equations describing the collective properties of self-propelled rods from a simple microscopic starting point, the Vicsek model with nematic alignment. Analysis of their linear and nonlinear dynamics shows good agreement with the original microscopic model. In particular, we derive an explicit expression for density-segregated, banded solutions, allowing us to develop a more complete analytic picture of the problem at the nonlinear level.

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  • Received 24 July 2012

DOI:https://doi.org/10.1103/PhysRevLett.109.268701

© 2012 American Physical Society

Authors & Affiliations

Anton Peshkov1,2,3, Igor S. Aranson4,3, Eric Bertin5,3, Hugues Chaté1,2,3, and Francesco Ginelli6

  • 1Service de Physique de l’Etat Condensé, CEA-Saclay, URA 2464 CNRS, 91191 Gif-sur-Yvette, France
  • 2LPTMC, CNRS-UMR 7600, Université Pierre et Marie Curie, 75252 Paris, France
  • 3Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Strasse 38, 01187 Dresden, Germany
  • 4Materials Science Division, Argonne National Laboratory, 9700 South Cass Avenue, Argonne, Illinois 60439, USA
  • 5Université de Lyon, Laboratoire de Physique, ENS Lyon, CNRS, 46 Allée d’Italie, 69007 Lyon, France
  • 6Institute for Complex Systems and Mathematical Biology, King’s College, University of Aberdeen, Aberdeen AB24 3UE, United Kingdom

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Issue

Vol. 109, Iss. 26 — 28 December 2012

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