We study the non-equilibrium steady-states of a one-dimensional ($1D1V$) fluid in a finite space region of length $L$. Particles interact among themselves by multi-particle collisions and are in contact with two thermal-wall heat reservoirs, located at the boundaries of the region. After an initial ballistic regime, we find a crossover from a normal (kinetic) transport regime to an anomalous (hydrodynamic) one, above a characteristic size $L_*$. We argue that $L_*$ is proportional to the cube of the collision time among particles. Motivated by the physics of emissive divertors in fusion plasma, we consider the more general case of thermal walls injecting particles with given average (non-thermal) velocity. For fast and relatively cold particles, short systems fail to establish local equilibrium and display non-Maxwellian distributions of velocities.
An approach to the description of kinetics which taking into account the large-scale hydrodynamic transport processes for quantum Bose system is proposed. The nonequilibrium statistical operator which consistently describes both the kinetic and nonlinear hydrodynamic fluctuations in quantum liquid is calculated. Using this operator the coupled equations for quantum one-particle distribution function and functional of hydrodynamic variables: densities of momentum, energies and number of particles are obtained.
A consistent statistical description of kinetics and hydrodynamics of dusty plasma is proposed based on the Zubarev nonequilibrium statistical operator method. For the case of partial dynamics the nonequilibrium statistical operator and the generalized transport equations for a consistent description of kinetics of dust particles and hydrodynamics of electrons, ions and neutral atoms are obtained. In the approximation of weakly nonequilibrium process a spectrum of collective excitations of dusty plasma is investigated in the hydrodynamic limit.
Chain of kinetic equations for non-equilibrium single, double and s-particle distribution functions of particles is obtained taking into account nonlin- ear hydrodynamic fluctuations. Non-equilibrium distribution function of non-linear hydrodynamic fluctuations satisfies a generalized Fokker-Planck equation. The method of non-equilibrium statistical operator by Zubarev is applied. A way of calculating of the structural distribution function of hydrodynamic collective variables and their hydrodynamic velocities (above Gaussian approximation) contained in the generalized Fokker-Planck equa- tion…
We investigate the non-equilibrium dynamics of a one-dimensional spin-1/2 XXZ model at zero-temperature in the regime $|Δ|< 1$, initially prepared in a product state with two domain walls i.e, $|\downarrow\dots\downarrow\uparrow\dots\uparrow\downarrow\dots\downarrow\rangle$. At early times, the two domain walls evolve independently and only after a calculable time a non-trivial interplay between the two emerges and results in the occurrence of a split Fermi sea. For $Δ=0$, we derive exact asymptotic results for the magnetization and the spin current by using a semi-classical Wigner function ap…
We use the method of the microscopic phase density to get the kinetic equation for the system of self-propelled particles with Vicsek-like alignment rule. The hydrodynamic equations are derived for the ordered phase taking into account the mean-field force only. The equation for the hydrodynamic velocity plays the role of the Euler equation for the self-propelled Vicsek fluid. The hydrodynamics of such ideal self-propelled fluid demonstrates the dynamical transition from disordered initial state to the completely ordered motion. To take the noise into account we consider how the framework of t…
It is known that a full description of Brownian motion in the entire course of time should incorporate both kinetic and hydrodynamic effects, but a formula accounts for both effects has been established only in three dimension and only for the limiting case when Brownian particles are much bigger and heavier than fluid particles. Nevertheless, for applications, it is important to consider small Brownian particles (sometimes even smaller than fluid particles). In these cases, unfortunately, only formulae in the short (long) time limit considering exclusively kinetic (hydrodynamic) effect are av…
The influence of the heating mechanism on the kinetic energy densities of the components of a vibrated granular mixture is investigated. Collisions of the particles with the vibrating wall are inelastic and characterized by two coefficients of normal restitution, one for each of the two species. By means of molecular dynamics simulations, it is shown that the non-equipartition of kinetic energy is not affected by the differential mechanism of energy injection, aside the usual boundary layer around the wall. The macroscopic state of the mixture in the bulk is defined by intensive variables that…
In this work, we introduce an effective model for both ideal and viscous fluid dynamics within the framework of kinetic field theory (KFT). The main application we have in mind is cosmic structure formation where gaseous components need to be gravitationally coupled to dark matter. However, we expect that the fluid model is much more widely applicable. The idea behind the effective model is similar to that of smoothed particle hydrodynamics. By introducing mesoscopic particles equipped with a position, a momentum, and an enthalpy, we construct a free theory for such particles and derive suitab…
Comment on the paper J. Solsvik and E. Manger, "Kinetic theory models for granular mixtures with unequal granular temperature: Hydrodynamic velocity," Phys. Fluids \textbf{33}, 043321 (2021).
Based on the generalized non-Markovian equations obtained earlier for a nonequilibrium one-particle distribution function and potential part of the averaged enthalpy density [Markiv B.B., Omelyan I.P, Tokarchuk M.V., Condens. Matter Phys., 2010, 13, 23005] a spectrum of collective excitations is investigated, where the potential of interaction between particles is presented as a sum of the potential of hard spheres and a certain long-range potential.
Using the method of nonequilibrium statistical operator by Zubarev, an approach is proposed for the description of kinetics which takes into account the nonlinear hydrodynamic fluctuations for a quantum Bose system. Non-equilibrium statistical operator is presented which consistently describes both the kinetic and nonlinear hydrodynamic processes. Both a kinetic equation for the nonequilibrium one-particle distribution function and a generalized Fokker-Planck equation for nonequilibrium distribution function of hydrodynamic variables (densities of momentum, energy and particle number) are obta…
The generalized transport equations for a consistent description of kinetic and hydrodynamic processes in dense gases and liquids are considered. The inner structure of the generalized transport kernels for these equations is established. It is shown how in this approach to obtain the transport equation of molecular hydrodynamics. For the model potential of interaction presented as a sum of the hard spheres potential and certain long-range potential a spectrum of collective modes in the system is investigated.
A consistent description of kinetics and hydrodynamics of systems of interacting particles by means of the nonequilibrium statistical operator method
本文在D. N. Zubarev提出的非平衡统计算符方法的基础上，给出了一种描述相互作用粒子系统动力学和流体力学过程的自洽统计方法。给出了如何得到硬球模型的修正Enskog理论的动力学方程、多步相互作用势的动力学方程和带电硬球系统的Enskog-Landau动力学方程。BBGKY层次结构分析的基础上修改的组扩展。广义输运方程的动力学和流体力学的自洽描述。研究了弱非平衡相互作用粒子系统的时间关联函数、集体激发谱和广义输运系数。
It is shown how to explicitly coarse-grain the microscopic dynamics of the Vicsek model for self-propelled agents. The macroscopic transport equations are derived by means of an Enskog-type kinetic theory. Expressions for all transport coefficients at large particle speed are given. The phase transition from a disordered to a flocking state is studied numerically and analytically.
Brownian motion has served as a pilot of studies in diffusion and other transport phenomena for over a century. The foundation of Brownian motion, laid by Einstein, has generally been accepted to be far from being complete since the late 1960s, because it fails to take important hydrodynamic effects into account. The hydrodynamic effects yield a time dependence of the diffusion coefficient, and this extends the ordinary hydrodynamics. However, the time profile of the diffusion coefficient across the kinetic and hydrodynamic regions is still absent, which prohibits a complete description of Bro…
Kinetic and hydrodynamic theories are widely employed for describing the collective behaviour of active matter systems. At the fluctuating level, these have been obtained from explicit coarse-graining procedures in the limit where each particle interacts weakly with many others, so that the total forces and torques exerted on each of them is of order unity at all times. Such limit is however not relevant for dilute systems that mostly interact via alignment; there, collisions are rare and make the self-propulsion direction to change abruptly. We derive a fluctuating kinetic theory, and the cor…
In this review, a theoretical description is provided for the solid (granular) phase of the gas-solid flows that are the focus of this book. Emphasis is placed on the fundamental concepts involved in deriving a macroscopic hydrodynamic description for the granular material in terms of the hydrodynamic fields (species densities, flow velocity, and the granular temperature) from a prescribed "microscopic" interaction among the grains. To this end, the role of the interstitial gas phase, body forces such as gravity, and other coupling to the environment are suppressed and retained only via a poss…
The particle diffusion in a fluid is a classical topic that dates back to more than one century ago. However, a full solution to this issue still lacks. In this work the velocity autocorrelation function and the diffusion constant are derived analytically, and the hydrodynamics effect on the particle diffusion is analyzed in detail. Unlike previous studies, the ring-collision effect is exhaustively considered in our treatment, and the hydrodynamics approach is extended to the whole time range. Large scale molecular dynamics simulations for the hard-disk fluid show that our analytical results a…
We introduce non-perturbative analytical techniques for the derivation of the hydrodynamic manifolds from kinetic equations. The new approach is analogous to the Schwinger-Dyson equation of quantum field theories, and its derivation is demonstrated with the construction of the exact diffusion manifold for a model kinetic equation. The novel approach is superior to the classical Chapman-Enskog method.
We study the kinetics of assembly of two plates of varying hydrophobicity, including cases where drying occurs and water strongly solvates the plate surfaces. The potential of mean force and molecular-scale hydrodynamics are computed from molecular dynamics simulations in explicit solvent as a function of particle separation. In agreement with our recent work on nanospheres [J. Phys. Chem. B 116, 378 (2012)] regions of high friction are found to be engendered by large and slow solvent fluctuations. These slow fluctuations can be due to either drying or confinement. The mean first passage times…
We use the Boltzmann equation in the relaxation time approximation to study the expansion of a dilute Fermi gas at unitarity. We focus, in particular, on the approach to the hydrodynamic limit. Our main finding are: i) In the regime that has been studied experimentally hydrodynamic effects beyond the Navier-Stokes approximation are small, ii) mean field corrections to the Boltzmann equation are not important, iii) experimental data imply that freezeout occurs very late, that means that the relaxation time remains smaller than the expansion time during the entire evolution of the system, iv) th…
We use fluctuating hydrodynamics to evaluate the enhancement of thermally excited fluctuations in laminar fluid flow using plane Couette flow as a representative example. In a previous publication [J. Stat. Phys. vol. 144 (2011) p. 774] we derived the energy amplification arising from thermally excited wall-normal fluctuations by solving a fluctuating Orr-Sommerfeld equation. In the present paper we derive the energy amplification arising from wall-normal vorticity fluctuation by solving a fluctuating Squire equation. The thermally excited wall-normal vorticity fluctuations turn out to yield t…
Reductionism is a prevalent viewpoint in science according to which all physical phenomena can be understood from fundamental laws of physics. Anderson [Science, 177, 393 (1972)], Laughlin and Pines [PNAS, 97, 28 (2000)], and others have countered this viewpoint and argued in favour hierarchical structure of the universe and laws. In this paper we advance the latter perspective by showing that some of the complex flow properties derived using hydrodynamic equations (macroscopic laws) are very difficult, if not impossible, to describe in microscopic framework---kinetic theory. These properties …
We present a new way of quantum kinetic equation derivation. This method appears as a natural generalization of the many-particle quantum hydrodynamic method. Kinetic equations are derived for different system of particles. First of all we consider quantum plasma and pay special attention to the spin evolution. We show that we need a set of two kinetic equations for description of spinning particles. One of these equations is the equation for distribution function, however this equation contains new function, even in the self-consistent field approximation. This is a spin-distribution function…
