Particles dispersed in a dilute gas. II. From the Langevin equation to a more general kinetic approach

Ferrari, L.

doi:10.1016/j.chemphys.2013.10.024

Cited by 18 publications

(27 citation statements)

References 50 publications

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“…For instance, let us think of the next correction in the systematic expansion in powers of the mass ratio m bf /m introduced in Refs. [58,59], which involves a quartic, proportional to v 4 , term. Incorporating it would result in the coupling of the time evolution of the temperature not only with v 4 , which gives rise to the term proportional to θ 2 a 2 , but also with v 6 , which would give rise to a new term proportional to θ 3 a 3dominant for a quench to low temperatures, where θ 1.…”

Section: Discussionmentioning

confidence: 99%

“…From a phenomenological point of view, it can be regarded as the minimal, simplest, model for a fluid with nonlinear drag [55][56][57]. From a more fundamental point of view, it arises when an ensemble of Brownian particles, with mass m and particle density n, is immersed in an isotropic and uniform background fluid at equilibrium with temperature T s , the particles of which have masses m bf [58,59]. In the socalled Rayleigh limit, where m bf /m → 0, the drag force on the Brownian particles is linear in the velocity, F drag = −mζ 0 v, i.e., the drag coefficient ζ 0 is a constant.…”

Section: Introductionmentioning

confidence: 99%

“…sometimes called the quasi-Rayleigh limit. The nonlinear parameter γ is given as a certain integral that includes the Brownian-particle-background-particle differential cross section [58][59][60], and typical values are limited to γ 0.1-0.2 [49].…”

Section: Introductionmentioning

confidence: 99%

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Strong nonexponential relaxation and memory effects in a fluid with nonlinear drag

2021

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We analyze the dynamical evolution of a fluid with nonlinear drag, for which binary collisions are elastic, described at the kinetic level by the Enskog-Fokker-Planck equation. This model system, rooted in the theory of nonlinear Brownian motion, displays a really complex behavior when quenched to low temperatures. Its glassy response is controlled by a long-lived nonequilibrium state, independent of the degree of nonlinearity and also of the Brownian-Brownian collisions rate. The latter property entails that this behavior persists in the collisionless case, where the fluid is described by the nonlinear Fokker-Planck equation. The observed response, which includes nonexponential, algebraic, relaxation, and strong memory effects, presents scaling properties: the time evolution of the temperature-for both relaxation and memory effects-falls onto a master curve, regardless of the details of the experiment. To account for the observed behavior in simulations, it is necessary to develop an extended Sonine approximation for the kinetic equation-which considers not only the fourth cumulant but also the sixth one.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Strong nonexponential relaxation and memory effects in a fluid with nonlinear drag

2021

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“…In this regard, it is worth mentioning that other types of velocity dependence for drag forces also occur in nature. In fact, interesting advances, both at the theoretical and at the experimental levels, have been recently made in the study of the drag forces experienced by test particles when moving in different types of environments [49][50][51]. These developments allowed for the identification of relevant scenarios, characterized by particular types of interactions between the test particle and the environment particles, leading to clear departures from linear drag.…”

Section: From the Power-law Nlfpe To A Vlasov Equationmentioning

confidence: 99%

From the nonlinear Fokker-Planck equation to the Vlasov description and back: Confined interacting particles with drag

et al. 2018

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Nonlinear Fokker-Planck equations endowed with power-law diffusion terms have proven to be valuable tools for the study of diverse complex systems in physics, biology, and other fields. The nonlinearity appearing in these evolution equations can be interpreted as providing an effective description of a system of particles interacting via short-range forces while performing overdamped motion under the effect of an external confining potential. This point of view has been recently applied to the study of thermodynamical features of interacting vortices in type II superconductors. In the present work we explore an embedding of the nonlinear Fokker-Planck equation within a Vlasov equation, thus incorporating inertial effects to the concomitant particle dynamics. Exact time-dependent solutions of the q-Gaussian form (with compact support) are obtained for the Vlasov equation in the case of quadratic confining potentials.

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“…While for large, heavy test particles the friction coefficient γ is velocity independent, it acquires an explicit velocity dependence for small, light particles [13,14]. It was theoretically shown that [13,14] γ(v) = nσ 8 15…”

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confidence: 99%

Individual Tracer Atoms in an Ultracold Dilute Gas

et al. 2017

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Understanding the motion of a tracer particle in a rarefied gas is of fundamental and practical importance. We report the experimental investigation of individual Cs atoms impinging on a dilute cloud of ultracold Rb atoms with variable density. We study the nonequilibrium relaxation of the initial nonthermal state and detect the effect of single collisions which has eluded observation so far. We show that after few collisions, the measured spatial distribution of the light tracer atoms is correctly described by a generalized Langevin equation with a velocity-dependent friction coefficient, over a large range of Knudsen numbers.

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Particles dispersed in a dilute gas. II. From the Langevin equation to a more general kinetic approach

Cited by 18 publications

References 50 publications

Strong nonexponential relaxation and memory effects in a fluid with nonlinear drag

Strong nonexponential relaxation and memory effects in a fluid with nonlinear drag

From the nonlinear Fokker-Planck equation to the Vlasov description and back: Confined interacting particles with drag

Individual Tracer Atoms in an Ultracold Dilute Gas

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