Active matter beyond mean-field: ring-kinetic theory for self-propelled particles

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Yen-Liang Chou, T Ihle

Abstract

Recently, Hanke et al. [Phys. Rev. E 88, 052309 (2013)] showed that mean-field kinetic theory fails to describe collective motion in soft active colloids and that correlations must not be neglected. Correlation effects are also expected to be essential in systems of biofilaments driven by molecular motors and in swarms of midges. To obtain correlations in an active matter system from first principles, we derive a ring-kinetic theory for Vicsek-style models of self-propelled agents from the exact N-particle evolution equation in phase space. The theory goes beyond mean-field and does not rely on Boltzmann's approximation of molecular chaos. It can handle precollisional correlations and cluster formation, which are both important to understand the phase transition to collective motion. We propose a diagrammatic technique to perform a small-density expansion of the collision operator and derive the first two equations of the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy. An algorithm is presented that numerically solves the evolution equation for the two-particle correlations on a lattice. Agent-based simulations are performed and informative quantities such as orientational and density correlation functions are compared w...Continue Reading

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Citations

May 2, 2016·Chaos·Maurizio Porfiri, Gil Ariel
Jan 15, 2016·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Shengtao LuEdwin K L Yeow
Feb 20, 2019·Physical Review. E·L L Bonilla, C Trenado
Jan 17, 2016·The Journal of Chemical Physics·Andreas M MenzelHartmut Löwen
Feb 17, 2018·Physical Review. E·Andreas HärtelThomas Speck

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