Hydrodynamic Limits of the Kinetic Self-Organized Models

Jiang, Ning; Xiong, Liang; Zhang, Teng-Fei

doi:10.1137/15m1035665

Cited by 28 publications

(26 citation statements)

References 21 publications

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“…The coarse-graining for the Vicsek model alone leads to the 'Self-Organised Hydrodynamics' (SOH) equations derived in Refs. [14,27]. The SOH model is a system of continuum equations for the density and mean velocity orientation of the swimmers.…”

Section: Introductionmentioning

confidence: 99%

Coupled Self-Organized Hydrodynamics and Stokes Models for Suspensions of Active Particles

Degond

Merino-Aceituno

Vergnet

et al. 2019

J. Math. Fluid Mech.

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We derive macroscopic dynamics for self-propelled particles in a fluid. The starting point is a coupled Vicsek-Stokes system. The Vicsek model describes selfpropelled agents interacting through alignment. It provides a phenomenological description of hydrodynamic interactions between agents at high density. Stokes equations describe a low Reynolds number fluid. These two dynamics are coupled by the interaction between the agents and the fluid. The fluid contributes to rotating the particles through Jeffery's equation. Particle self-propulsion induces a force dipole on the fluid. After coarse-graining we obtain a coupled Self-Organised Hydrodynamics (SOH)-Stokes system. We perform a linear stability analysis for this system which shows that both pullers and pushers have unstable modes. We conclude by providing extensions of the Vicsek-Stokes model including short-distance repulsion, finite particle inertia and finite Reynolds number fluid regime.

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Section: Introductionmentioning

confidence: 99%

Coupled Self-Organized Hydrodynamics and Stokes Models for Suspensions of Active Particles

Degond

Merino-Aceituno

Vergnet

et al. 2019

J. Math. Fluid Mech.

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“…The rigorous derivation of such macroscopic models is still ahead of us. By contrast, the derivation of the SOH model from the mean-field Vicsek model is now equipped with a fully rigorous mathematical proof [51]. …”

Section: Methodsmentioning

confidence: 99%

Symmetry-breaking phase transitions in highly concentrated semen

Creppy

Plouraboué

Praud

et al. 2016

J. R. Soc. Interface.

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New experimental evidence of self-motion of a confined active suspension is presented. Depositing fresh semen sample in an annular shaped microfluidic chip leads to a spontaneous vortex state of the fluid at sufficiently large sperm concentration. The rotation occurs unpredictably clockwise or counterclockwise and is robust and stable. Furthermore, for highly active and concentrated semen, richer dynamics can occur such as self-sustained or damped rotation oscillations. Experimental results obtained with systematic dilution provide a clear evidence of a phase transition towards collective motion associated with local alignment of spermatozoa akin to the Vicsek model. A macroscopic theory based on previously derived self-organized hydrodynamics models is adapted to this context and provides predictions consistent with the observed stationary motion.

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“…In some simple cases, it has been rigorously justified the mean field limit from the Vicsek model to SOK, see [4]. The first convergence result from the SOK to SOH was provided by the authors of the current paper with Xiong in [24], which provided a first rigorous justification of the formal analysis in [15], based on the well-posedness results of SOH in [13].…”

Section: Introductionmentioning

confidence: 96%

“…The derivations of both SOH and SOH-NS are based on the Generalized Collision Invariant concept introduced in [15]. This technique has already been successfully applied to a wide range of models inspired by the Vicsek model [10,12,24].…”

Section: Introductionmentioning

confidence: 99%

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Coupled Self-organized Hydrodynamics and Navier–Stokes Models: Local Well-posedness and the Limit from the Self-organized Kinetic-Fluid Models

Jiang

Luo

Zhang

2019

Arch Rational Mech Anal

Self Cite

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A coupled system of self-organized hydrodynamics and Navier-Stokes equations (SOH-NS), which models self-propelled particles in a viscous fluid, was recently derived by Degond et al. [14], starting from a micro-macro particle system of Vicsek-Navier-Stokes model, through an intermediate step of a self-organized kinetic-kinetic model by multiple coarse-graining processes. We first transfer SOH-NS into a non-singular system by stereographic projection, then prove the local in time well-posedness of classical solutions by energy method. Furthermore, employing the Hilbert expansion approach, we justify the hydrodynamic limit from the self-organized kinetic-fluid model to macroscopic dynamics. This provides the first analytically rigorous justification of the modeling and asymptotic analysis in [14].

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Hydrodynamic Limits of the Kinetic Self-Organized Models

Abstract: Abstract. The self-organized hydrodynamic models can be derived from the kinetic version of the Vicsek model. The formal derivations and local well-posedness of the macroscopic equations are done by Degond and his collaborators. In this paper, we rigorously justify this hydrodynamic limit.

Cited by 28 publications

References 21 publications

Coupled Self-Organized Hydrodynamics and Stokes Models for Suspensions of Active Particles

Coupled Self-Organized Hydrodynamics and Stokes Models for Suspensions of Active Particles

Symmetry-breaking phase transitions in highly concentrated semen

Coupled Self-organized Hydrodynamics and Navier–Stokes Models: Local Well-posedness and the Limit from the Self-organized Kinetic-Fluid Models

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