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

Chou, Yen-Liang; Ihle, Thomas

doi:10.1103/physreve.91.022103

Cited by 26 publications

(40 citation statements)

References 84 publications

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“…For gliding bacteria, hydrodynamic interactions are less relevant which makes our modelling an even more appropriate one for this realization. Moreover, a microscopic theory for active depletion [80] is highly desirable to make predictions for the carrier motions which could be based on kinetic [81] or dynamical density functional theory [39,82]. …”

Section: Discussionmentioning

confidence: 99%

Motion of two micro-wedges in a turbulent bacterial bath

Kaiser

Sokolov

Aranson

et al. 2015

Eur. Phys. J. Spec. Top.

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Abstract. The motion of a pair of micro-wedges ("carriers") in a turbulent bacterial bath is explored using computer simulations with explicit modeling of the bacteria and experiments. The orientation of the two micro-wedges is fixed by an external magnetic field but the translational coordinates can move freely as induced by the bacterial bath. As a result, two carriers of same orientation move such that their mutual distance decreases, while they drift apart for an anti-parallel orientation. Eventually the two carriers stack on each other with no intervening bacteria exhibiting a stable dynamical mode where the two micro-wedges follow each other with the same velocity. These findings are in qualitative agreement with experiment on two micro-wedges in a bacterial bath. Our results provide insight into understanding selfassembly of many micro-wedges in an active bath.

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Section: Discussionmentioning

confidence: 99%

Motion of two micro-wedges in a turbulent bacterial bath

Kaiser

Sokolov

Aranson

et al. 2015

Eur. Phys. J. Spec. Top.

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“…(5), whose evolution equation is noise-free. However, if going beyond the mean-field approximation [32] , this equation will also depend on two-point, three-point and higher correlation functions. A thorough discussion on when noise terms are required can be found in Ref.…”

Section: Kinetic Theorymentioning

confidence: 99%

“…More discussions on the validity of this Ansatz in active matter can be found in Refs. [32,34,35]. On the technical level, for a time-discrete model such as the VM, the factorization is only used on the r.h.s of Eq.…”

Section: Kinetic Theorymentioning

confidence: 99%

Chapman–Enskog expansion for the Vicsek model of self-propelled particles

Ihle¹

2016

J. Stat. Mech.

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Abstract. Using the standard Vicsek model, I show how the macroscopic transport equations can be systematically derived from microscopic collision rules. The approach starts with the exact evolution equation for the N-particle probability distribution, and after making the mean-field assumption of Molecular Chaos leads to a multi-particle Enskog-type equation. This equation is treated by a non-standard Chapman-Enskog expansion to extract the macroscopic behavior. The expansion includes terms up to third order in a formal expansion parameter ǫ, and involves a fast time scale. A selfconsistent closure of the moment equations is presented that leads to a continuity equation for the particle density and a Navier-Stokes-like equation for the momentum density. Expressions for all transport coefficients in these macroscopic equations are given explicitly in terms of microscopic parameters of the model. The transport coefficients depend on specific angular integrals which are evaluated asymptotically in the limit of infinitely many collision partners, using an analogy to a random walk. The consistency of the Chapman-Enskog approach is checked by an independent calculation of the shear viscosity using a Green-Kubo relation.

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“…) * However, note that more general kinetic theory approaches can capture two-body (or even higher order) correlations, by using higher order truncations of the BBGKY hierarchy (see, e.g., [116]). …”

Section: Fox Approximation For Langevin Equations With Coloured Noisementioning

confidence: 99%

“…However, this approach still neglects correlations between particles prior to collisions, assuming a factorized form for the pre-collisional N-body distribution. Pre-collisional correlations can be taken into account through an involved "ring-kinetic" theory, which is based on a low-density expansion, through diagrammatic techniques, of the collision operator [116].…”

Section: Self-propelled Particles With Aligning Binary Collisionsmentioning

confidence: 99%

Theoretical approaches to the steady-state statistical physics of interacting dissipative units

Bertin¹

2017

J. Phys. A: Math. Theor.

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Abstract. The aim of this review is to provide a concise overview of some of the generic approaches that have been developed to deal with the statistical description of large systems of interacting dissipative 'units'. The latter notion includes, e.g., inelastic grains, active or self-propelled particles, bubbles in a foam, low-dimensional dynamical systems like driven oscillators, or even spatially extended modes like Fourier modes of the velocity field in a fluid for instance. We first review methods based on the statistical properties of a single unit, starting with elementary mean-field approximations, either static or dynamic, that describe a unit embedded in a 'selfconsistent' environment. We then discuss how this basic mean-field approach can be extended to account for spatial dependences, in the form of space-dependent mean-field Fokker-Planck equations for example. We also briefly review the use of kinetic theory in the framework of the Boltzmann equation, which is an appropriate description for dilute systems. We then turn to descriptions in terms of the full N -body distribution, starting from exact solutions of one-dimensional models, using a Matrix Product Ansatz method when correlations are present. Since exactly solvable models are scarce, we also present some approximation methods that can be used to determine the N -body distribution in a large system of dissipative units. These methods include the Edwards approach for dense granular matter and the approximate treatment of multiparticle Langevin equations with coloured noise, which models systems of self-propelled particles. Throughout this review, emphasis is put on methodological aspects of the statistical modeling and on formal similarities between different physical problems, rather than on the specific behaviour of a given system.

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

Cited by 26 publications

References 84 publications

Motion of two micro-wedges in a turbulent bacterial bath

Motion of two micro-wedges in a turbulent bacterial bath

Chapman–Enskog expansion for the Vicsek model of self-propelled particles

Theoretical approaches to the steady-state statistical physics of interacting dissipative units

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