Quantitative kinetic theory of flocking with three-particle closure

Rüdiger Kürsten and Thomas Ihle
Phys. Rev. E 104, 034604 – Published 3 September 2021

Abstract

We consider aligning self-propelled particles in two dimensions. Their motion is given by Langevin equations and includes nonadditive N-particle interactions. The qualitative behavior is as for the famous Vicsek model. We develop a kinetic theory of flocking beyond mean field. In particular, we self-consistently take into account the full pair correlation function. We find excellent quantitative agreement of the pair correlations with direct agent-based simulations within the disordered regime. Furthermore we use a closure relation to incorporate spatial correlations of three particles. In that way we achieve good quantitative agreement of the onset of flocking with direct simulations. Compared to mean-field theory, the flocking transition is shifted significantly toward lower noise because directional correlations favor disorder. We compare our theory with a recently developed Landau-kinetic theory.

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  • Received 25 February 2021
  • Revised 9 July 2021
  • Accepted 13 August 2021

DOI:https://doi.org/10.1103/PhysRevE.104.034604

©2021 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & ThermodynamicsPolymers & Soft Matter

Authors & Affiliations

Rüdiger Kürsten and Thomas Ihle

  • Institut für Physik, Universität Greifswald, Felix-Hausdorff-Strasse 6, 17489 Greifswald, Germany

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Issue

Vol. 104, Iss. 3 — September 2021

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