Abstract
We consider aligning self-propelled particles in two dimensions. Their motion is given by Langevin equations and includes nonadditive -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.
17 More- Received 25 February 2021
- Revised 9 July 2021
- Accepted 13 August 2021
DOI:https://doi.org/10.1103/PhysRevE.104.034604
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