A Quantitative Kinetic Theory of Flocking with Three-Particle-Closure

We consider aligning self-propelled particles in two dimensions. Their motion is given by generalized Langevin equations and includes non-additive N-particle interactions. The qualitative behavior is as for the famous Vicsek model. We develop a kinetic theory of flocking beyond mean field. In partic...

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Bibliographic Details
Published in:arXiv.org 2021-02
Main Authors: Kürsten, Rüdiger, Ihle, Thomas
Format: Article
Language:English
Subjects:
Closures
Correlation
Kinetic theory
Mean field theory
Particle interactions
Online Access:Get full text
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Summary:We consider aligning self-propelled particles in two dimensions. Their motion is given by generalized Langevin equations and includes non-additive 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 towards lower noise because directional correlations favor disorder. We compare our theory with a recently developed Landau-kinetic theory.
ISSN:2331-8422
DOI:10.48550/arxiv.2102.13231