The unsteady Boltzmann kinetic equation and non-equilibrium thermodynamics of an electron gas for the Rayleigh flow problem

2010 ◽  
Vol 88 (7) ◽  
pp. 501-511 ◽  
Author(s):  
A. M. Abourabia ◽  
T. Z. Abdel Wahid
Keyword(s):  
Distribution Function ◽  
Kinetic Equation ◽  
Velocity Distribution ◽  
Flow Problem ◽  
Electron Gas ◽  
Irreversible Thermodynamics ◽  
Distribution Functions ◽  
Thermodynamic Force ◽  
Model Kinetic Equation ◽  
Non Equilibrium

In the framework of irreversible thermodynamics, the characteristics of the Rayleigh flow problem of a rarified electron gas extracted from neutral atoms is examined and proved to obey the entropic behavior for gas systems. A model kinetic equation of the BGK (Bhatnager–Gross–Krook) type is solved, using the method of moments with a two-sided distribution function. Various macroscopic properties of the electron gas, such as the mean velocity, the shear stress, and the viscosity coefficient, together with the induced electric and magnetic fields, are investigated with respect to both distance and time. The distinction between the perturbed velocity distribution functions and the equilibrium velocity distribution function at different time values is illustrated. We restrict our study to the domain of irreversible thermodynamics processes with small deviation from the equilibrium state to estimate the entropy, entropy production, entropy flux, thermodynamic force, and kinetic coefficient and verify the celebrated Boltzmann H-theorem for non-equilibrium thermodynamic properties of the system. The ratios between the different contributions of the internal energy changes, based upon the total derivatives of the extensive parameters, are predicted via Gibbs’ equation for both diamagnetic and paramagnetic plasmas. The results are applied to a typical model of laboratory argon plasma.

scholarly journals Transport Coefficients and Velocity Distribution Function of an Ion Swarm in an AC Electric Field Obtained from the BGK Kinetic Equation

1994 ◽  
Vol 47 (3) ◽  
pp. 305 ◽  
Author(s):  
RE Robson ◽  
T Makabe
Keyword(s):  
Distribution Function ◽  
Steady State ◽  
Kinetic Equation ◽  
Velocity Distribution ◽  
Transport Coefficients ◽  
Velocity Distribution Function ◽  
Model Kinetic Equation ◽  
Bgk Model ◽  
Ac Electric Field ◽  
Periodic Steady State

The transition to a periodic steady state for an ion swarm in a gas is investigated using the BGK model kinetic equation. Exact expressions for transport coefficients and the velocity distribution function are obtained and the latter is compared with experimental observations of ions in their parerit gases undergoing predominantly charge-transfer collisions.

scholarly journals On the Determination of Kappa Distribution Functions from Space Plasma Observations

Entropy ◽  
2020 ◽  
Vol 22 (2) ◽  
pp. 212 ◽  
Author(s):  
Georgios Nicolaou ◽  
George Livadiotis ◽  
Robert T. Wicks
Keyword(s):  
Distribution Function ◽  
Velocity Distribution ◽  
Space Plasma ◽  
Distribution Functions ◽  
Specific Method ◽  
Kappa Distribution ◽  
Kappa Index ◽  
Velocity Distribution Functions ◽  
Bulk Parameters ◽  
Plasma Bulk

The velocities of space plasma particles, often follow kappa distribution functions. The kappa index, which labels and governs these distributions, is an important parameter in understanding the plasma dynamics. Space science missions often carry plasma instruments on board which observe the plasma particles and construct their velocity distribution functions. A proper analysis of the velocity distribution functions derives the plasma bulk parameters, such as the plasma density, speed, temperature, and kappa index. Commonly, the plasma bulk density, velocity, and temperature are determined from the velocity moments of the observed distribution function. Interestingly, recent studies demonstrated the calculation of the kappa index from the speed (kinetic energy) moments of the distribution function. Such a novel calculation could be very useful in future analyses and applications. This study examines the accuracy of the specific method using synthetic plasma proton observations by a typical electrostatic analyzer. We analyze the modeled observations in order to derive the plasma bulk parameters, which we compare with the parameters we used to model the observations in the first place. Through this comparison, we quantify the systematic and statistical errors in the derived moments, and we discuss their possible sources.

The velocity distribution function within a shock wave

1967 ◽  
Vol 30 (3) ◽  
pp. 479-487 ◽  
Author(s):  
G. A. Bird
Keyword(s):  
Shock Wave ◽  
Distribution Function ◽  
Velocity Distribution ◽  
Numerical Experiments ◽  
Equilibrium Distribution ◽  
Velocity Distribution Function ◽  
Distribution Functions ◽  
Rigid Sphere ◽  
Lateral Velocity ◽  
Shock Profile

The structure of normal shock waves in a gas composed of rigid sphere molecules is investigated by numerical experiments with a simulated gas on a digital computer. The non-equilibrium between the temperatures based on the longitudinal and lateral velocity components is studied and the results compared with the theory of Yen (1966). Details of the velocity distribution function are presented for a shock of Mach number 10. The distribution functions for both the longitudinal and lateral velocity components are plotted for a number of locations in the shock profile and are compared with the equilibrium distribution.

A study of the mass ratio dependence of the mixed species collision integral for isotropic velocity distribution functions

1982 ◽  
Vol 27 (1) ◽  
pp. 135-148 ◽  
Author(s):  
A. J. M. Garrett
Keyword(s):  
Distribution Function ◽  
Velocity Distribution ◽  
Particle Distribution ◽  
Velocity Distribution Function ◽  
Collision Integral ◽  
Distribution Functions ◽  
Velocity Space ◽  
Particle Distribution Function ◽  
Collision Term ◽  
Test Species

This paper is concerned with the Boltzmann collision integral for the one-particle distribution function of a test species of particle undergoing elastic collisions with particles of a second species which is in thermal equilibrium. This expression is studied as a function of the ratio of the masses of the test and host particles for the case when the test particle distribution function is isotropic in velocity space. The analysis can also be considered as referring to the zeroth-order spherical harmonic in velocity space of a general velocity distribution function. The resulting collision term, due originally to Davydov, is of Fokker–Planck form and effectively describes a diffusion in energy. The method of derivation employed here is more systematic than hitherto, and is used to calculate the first correction to the Davydov term. Differences between classical and quantum cross-sections are considered; the correction to the Davydov term is checked by means of a comparison with the exact solution of the associated eigenvalue problem for the special case of Maxwell interactions treated classically.

Statistical Inferences of Lift-Off Velocity Distribution Function Form for Saltating Particles

2010 ◽  
Vol 108-111 ◽  
pp. 783-788
Author(s):  
Jian Jun Wu ◽  
Li Hong He
Keyword(s):  
Distribution Function ◽  
Weibull Distribution ◽  
Velocity Distribution ◽  
Goodness Of Fit ◽  
Velocity Distribution Function ◽  
Forward Direction ◽  
Distribution Functions ◽  
Velocity Distribution Functions ◽  
Lift Off ◽  
Log Normal

The lift-off velocity distribution of saltating particles, which have been proposed to characterize the dislodgement state of saltating particles, is one of the key issues in the theoretical study of windblown sand transportation. But there were various statistical relations in the early researches. In this paper, the Kolmogorov-Smirnov test for goodness-of-fit is adopted to make an inference of the most probable form of lift-off velocity distribution functions for saltating particles on the basis of the experimental data. The statistical results show that the distribution function of vertical lift-off velocities conforms better to Weibull distribution function than to the normal, log-normal, gamma and exponential ones; while, the distribution function of the absolute values of horizontal lift-off velocities is best described by log-normal distribution in forward direction and Weibull distribution in backward direction, respectively. Finally, two more examples prove to support the above conclusions.

scholarly journals Non-equilibrium quasiparticles in superconducting circuits: photons vs. phonons

2019 ◽  
Vol 6 (1) ◽  
Author(s):  
Gianluigi Catelani ◽  
Denis Basko
Keyword(s):  
Distribution Function ◽  
Kinetic Equation ◽  
Stationary Solution ◽  
Low Frequency ◽  
Photon Absorption ◽  
Superconducting Circuits ◽  
Superconducting Device ◽  
Phonon Emission ◽  
Device Operation ◽  
Non Equilibrium

We study the effect of non-equilibrium quasiparticles on the operation of a superconducting device (a qubit or a resonator), including heating of the quasiparticles by the device operation. Focusing on the competition between heating via low-frequency photon absorption and cooling via photon and phonon emission, we obtain a remarkably simple non-thermal stationary solution of the kinetic equation for the quasiparticle distribution function. We estimate the influence of quasiparticles on relaxation and excitation rates for transmon qubits, and relate our findings to recent experiments.

THE PAIR DISTRIBUTION FUNCTION OF AN INTERACTING ELECTRON GAS

1967 ◽  
Vol 45 (9) ◽  
pp. 3139-3161 ◽  
Author(s):  
D. J. W. Geldart
Keyword(s):  
Distribution Function ◽  
Pair Distribution Function ◽  
Electron Gas ◽  
Pauli Principle ◽  
Distribution Functions ◽  
Upper And Lower Bounds ◽  
Wave Number ◽  
Many Body ◽  
Many Body Perturbation Theory ◽  
Simple Class

The pair distribution function, in the limit of zero separation, of an interacting electron gas at high and metallic densities is investigated by many-body perturbation theory. It is shown that the usual methods for maintaining self-consistency in approximate calculations violate, in general, the nonnegativity of the pair distribution function. In particular, the Pauli principle yields a rigorous sum rule for the parallel spin density fluctuation propagator which is not satisfied. Upper and lower bounds on one-loop and multiloop contributions to the pair distribution functions are given. These bounds are used to discuss correlation corrections. An improved wave-number dependence is given for Hubbard's (1957) approximation to the screening function and numerical results are given for a simple class of exchange corrections.

scholarly journals About one decision of the quasiclassical kinetic equation

2018 ◽  
Vol 7 (2.23) ◽  
pp. 270
Author(s):  
Gladkov S O ◽  
Bogdanova S B
Keyword(s):  
Distribution Function ◽  
Perturbation Theory ◽  
Relaxation Time ◽  
Kinetic Equation ◽  
General Solution ◽  
Time Approximation ◽  
Relaxation Time Approximation ◽  
Fermi Statistics ◽  
Non Equilibrium

It has been proved that the solution of the quasi-classical kinetic equation for Bose and Fermi statistics can be represented in the general form, using the relaxation time approximation. The general solution found for the distribution function  helps calculate any non – equilibrium characteristics of metals, magnets, and dielectrics in any order of the perturbation theory according to the relaxation time .  

Flowing Granular Materials and the Maxwell-Boltzmann Velocity Distribution

2000 ◽  
Author(s):  
Edward J. Boyle
Keyword(s):  
Distribution Function ◽  
Velocity Distribution ◽  
Hard Sphere ◽  
Body Force ◽  
Canonical Ensemble ◽  
Granular Flows ◽  
Velocity Distribution Function ◽  
Distribution Functions ◽  
Velocity Distribution Functions ◽  
Single Granule

Abstract The single-granule velocity distribution function is shown to be Maxwell-Boltzmann for hard-sphere granular flows at steady-state exhibiting no gradients and absent a body-force. This is accomplished by approximating the two-granule velocity distribution function as the product of two single-granule velocity distribution functions and a correlating function and by applying to a canonical ensemble a function analogous to Boltzmann’s H-function.

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