两位中国女物理学家对非平衡统计物理学的重要贡献

介绍了两位中国女物理学家王明贞和王承书在20世纪中叶对统计物理发展所作出的重要贡献，王明贞与乌伦贝克(Uhlenbeck)1945年在Review of Modem Physics上发表的有关布朗运动的综述文章。不仅详尽地分析了耦合谐振子的布朗运动特性，而且对随机过程做了完整的科学分类，至今仍被科学界采用，王承书对气体分子动理论所作的大量研究结果，特别是她与乌伦贝克提出的处理多原子分子气体输运系数的王承书-乌伦贝克方程，以及她对麦克斯韦气体的线性化玻尔兹曼方程碰撞算子本征值与本征函数的结果，已经成为现代动理学理论的经典内容，两位中国女物理学家通过她们在物理学史上留下的科学工作，为当代中国妇女攀登科学研究高峰树立了榜样。     

The relativistic Burnett equations and sound propagation

A relaxation-time model for the relativistic Boltzmann equation of a single-component gas is solved to second, or “Burnett”, order using the relativistic version of the Chapman-Enskog method developed by Marle. Expressions are obtained from this second order solution for the “Burnett” contributions to the heat flux and pressure tensor of the gas. Using the “Burnett” equations, which incorporate these contributions, expressions are then derived for the dispersion and absorption of sound in the gas which agree, in the classical limit, with the results of Wang Chang and Uhlenbeck.     

Transport properties of a binary mixture of CO₂-N₂ from the pair potential energy functions based on a semi-empirical inversion method

The potential energy surface of a CO 2 –N 2 mixture is determined by using an inversion method, together with a new collision integral correlation [J. Phys. Chem. Ref. Data 19 1179 (1990)]. With the new invert potential, the transport properties of CO2–N2 mixture are presented in a temperature range from 273.15 K to 3273.15 K at low density by employing the Chapman–Enskog scheme and the Wang Chang–Uhlenbeck–de Boer theory, consisting of a viscosity coefficient, a thermal conductivity coefficient, a binary diffusion coefficient, and a thermal diffusion factor. The accuracy of the predicted results is estimated to be 2% for viscosity, 5% for thermal conductivity, and 10% for binary diffusion coefficient.     

Boltzmann方程的理论和应用

本文对Boltzmann方程的基础、性质和解法作了比较全面的论述,评介了、Hilbert、Enskog、王承书、Grad和在Boltzmann方程领域所做的工作,对新近的成果如BKW模、尾巴温度等作了较详细的阐述,还概括地介绍了Boltzmann方程的应用。     

On the initial layer solution of the Boltzmann equation with small Knudsen number

We extend our method of systematic removal of secular terms in a singular perturbation treatment of the Boltzmann equation with small Knudsen numbers to the initial layer. The requirement that the solution through the initial layer should connect smoothly to the normal solution removes an ambiguity noted in our previous paper. We show that removal of secular terms improves Grad's solution for the initial layer and reintroduces soundlike modes associated with higher moments, first found by Wang Chang and Uhlenbeck.     

Trend to Equilibrium of a Degenerate Relativistic Gas

We examine the problem of the trend to equilibrium for a relativistic gas which may follow Fermi–Dirac, Bose–Einsten, classical Boltzmann statistics. We use the relativistic version of the quasiclassical Boltzmann equation for fermions and bosons, the Uehling–Uhlenbeck equation.     

Towards adaptive kinetic-fluid simulations of weakly ionized plasmas

This paper describes an Adaptive Mesh and Algorithm Refinement (AMAR) methodology for multi-scale simulations of gas flows and the challenges associated with extending this methodology for simulations of weakly ionized plasmas. The AMAR method combines Adaptive Mesh Refinement (AMR) with automatic selection of kinetic or continuum solvers in different parts of computational domains. We first review the discrete velocity method for solving Boltzmann and Wang Chang–Uhlenbeck kinetic equations for rarefied gases. Then, peculiarities of AMR implementation with octree Cartesian mesh are discussed. A Unified Flow Solver (UFS) uses AMAR method with adaptive Cartesian mesh to dynamically introduce kinetic patches for multi-scale simulations of gas flows. We describe fluid plasma models with AMR capabilities and illustrate how physical models affect simulation results for gas discharges, especially in the areas where electron kinetics plays an important role. We introduce Eulerian solvers for plasma kinetic equations and illustrate the concept of adaptive mesh in velocity space. Specifics of electron kinetics in collisional plasmas are described focusing on deterministic methods of solving kinetic equations for electrons under different conditions. We illustrate the appearance of distinct groups of electrons in the cathode region of DC discharges and discuss the physical models appropriate for each group. These kinetic models are currently being incorporated into AMAR methodology for multi-scale plasma simulations.     

The stochastic Boltzmann equation and hydrodynamic fluctuations

Based on the assumption of a kinetic equation in space, a stochastic differential equation of the one-particle distribution is derived without the use of the linear approximation. It is just the Boltzmann equation with a Langevin-fluctuating force term. The result is the general form of the linearized Boltzmann equation with fluctuations found by Bixon and Zwanzig and by Fox and Uhlenbeck. It reduces to the general Landau-Lifshitz equations of fluid dynamics in the presence of fluctuations in a similar hydrodynamic approximation to that used by Chapman and Enskog with respect to the Boltzmann equation.This work received financial support from the Alexander von Humboldt Foundation.     

Note on Boltzmann Langevin equation and hydrodynamic fluctuations

A microscopic derivation presented of the generalization of the linearized Boltzmann equation with the Langevin fluctuation force, which has earlier been postulated by Bixon and Zwanzig and by Fox and Uhlenbeck in their kinematical discussions on the hydrodynamic fluctuations.     

Transport properties of diatomic gases

The coefficients of shear viscosity and self-diffusion for nitrogen in the dilute gas limit have been calculated within the Mason-Monchick approximation using the intermolecular potential surfaces of Berns and van der Avoird and van Hemert and Berns. The same potentials had previously been used in transport property calculations using the classical limit of the Wang Chang, Uhlenbeck and de Boer theory. Comparisons between the results for each potential surface using the different transport theories reveal surprising discrepancies which increase with increasing temperature. Possible causes of this behaviour are considered.     

The Limiting Kinetic Equation of the Consistent Boltzmann Algorithm for Dense Gases

This paper establishes a theoretical foundation for the Consistent Boltzmann Algorithm (CBA) by deriving the limiting kinetic equation. The formulation is similar to the proof by one of the authors that the Boltzmann equation is the limiting kinetic equation for Direct Simulation Monte Carlo [W. Wagner, J. Statist. Phys. 66:1011 (1992)]. For a simplified model distilled from CBA, the limiting equation is solved numerically, and very good agreement with the predictions of the theory is found.     

Boltzmann equation with fluctuations

From the Liouville equation, by the method of multiple-time-scales, a generalized Boltzmann-equation with fluctuations is obtained on the statistical considerations of the randomness of the many-particle correlations in the macroscopic picture. These fluctuations lead to anH theorem in which theH function decreases, with fluctuations with time toward equilibrium. These fluctuations furnish a source for a random force term introduced by Fox and Uhlenbeck in the Boltzmann equation.     

Asymptotic solution of the Wang-Uhlenbeck recurrence time problem

A Langevin particle is initiated at the origin with positive velocity. Its trajectory is terminated when it returns to the origin. In 1945, Wang and Uhlenbeck posed the problem of finding the joint probability density function (PDF) of the recurrence time and velocity, naming it "the recurrence time problem". We show that the short-time asymptotics of the recurrence PDF is similar to that of the integrated Brownian motion, solved in 1963 by McKean. We recover the long-time t(-3/2) decay of the first arrival PDF of diffusion by solving asymptotically an appropriate variant of McKean's integral equation.     

INVARIANCE OF THE KAUP–KUPERSHMIDT EQUATION AND TRIANGULAR AUTO-BÄCKLUND TRANSFORMATIONS

We report triangular auto-Bäcklund transformations for the solutions of a fifth-order evolution equation, which is a constraint for an invariance condition of the Kaup–Kupershmidt equation derived by E. G. Reyes in his paper titled "Nonlocal symmetries and the Kaup–Kupershmidt equation" [J. Math. Phys. 46 (2005) 073507, 19 pp.]. These auto-Bäcklund transformations can then be applied to generate solutions of the Kaup–Kupershmidt equation. We show that triangular auto-Bäcklund transformations result from a systematic multipotentialization of the Kupershmidt equation.     

On the use temperature parameterized rate coefficients in the estimation of non-equilibrium reaction rates

The present paper considers a detailed analysis of the nonequilibrium effects for a model reactive system with the Chapman–Eskog (CE) solution of the Boltzmann equation as well as an explicit time dependent solution. The elastic cross sections employed are a hard sphere cross section and the Maxwell molecule cross section. Reactive cross sections which model reactions with and without activation energy are used. A detailed comparison is carried out with these solutions of the Boltzmann equation and the approximation introduced by Cukrowski and coworkers [J. Chem. Phys. 97 (1992) 9086; Chem. Phys. 89 (1992) 159; Physica A 188 (1992) 344; Chem. Phys. Lett. A 297 (1998) 402; Physica A 275 (2000) 134; Chem. Phys. Lett. 341 (2001) 585; Acta Phys. Polonica B 334 (2003) 3607.] based on the temperature of the reactive particles. We show that the Cukrowski approximation has limited applicability for the large class of reactive systems studied in this paper. The explicit time dependent solutions of the Boltzmann equation demonstrate that the CE approach is valid only for very slow reactions for which the corrections to the equilibrium rate coefficient are very small.     

A convergent nonequilibrium statistical mechanical theory for dense gases. II. Transport coefficients to first order in the density

Using the two-body distribution function found earlier by the authors with the aid of new boundary conditions, the kinetic equation and the transport coefficients are obtained to zeroth and first order in the density. To zeroth order we recover the Boltzmann kinetic equation. To first order the resulting expressions differ from the ones obtained by Choh and Uhlenbeck, due to effects of the medium.3 Reference 2 will be referred to as I. Here we use the same notation as in I.     

Maximum Path Information and Fokker--Planck Equation

We present a rigorous method to derive the nonlinear Fokker-Planck （FP） equation of anomalous diffusion directly from a generalization of the principle of least action of Maupertuis proposed by Wang [Chaos, Solitons ＆ Fractals 23 （2005） 1253] for smooth or quasi-smooth irregular dynamics evolving in Markovian process. The FP equation obtained may take two different but equivalent forms. It was also found that the diffusion constant may depend on both q （the index of Tsallis entropy [J. Stat. Phys. 52 （1988） 479] and the time t.     

Top Quark Flavor Changing Decay t

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