The calculation of the viscosity from the autocorrelation function using molecular and atomic stress tensors

The stress-stress correlation function and the viscosity of a united-atom model of liquid decane are studied by equilibrium molecular dynamics simulation using two different formalisms for the stress tensor: the atomic and the molecular formalisms. The atomic and molecular correlation functions show dramatic difference in short-time behaviour. The integrals of the two correlation functions, however, become identical after a short transient period which is significantly shorter than the rotational relaxation time of the molecule. Both reach the same plateau value in a time period corresponding to this relaxation time. These results provide a convenient guide for the choice of the upper integral time limit in calculating the viscosity by the Green-Kubo formula.     

Stress-stress correlation functions in lattice gases beyond Boltzmann's approximation

The complete time dependence of the stress-stress correlation functions in lattice gas cellular automata is calculated from the ring kinetic theory using numerical and analytical methods. This provides corrections, typically of 10–20%, to the usual molecular chaos calculations, where correlation functions decay exponentially. The resulting correlation function crosses over from an initial exponential decay to the long-time behavior calculated from mode coupling theory. The present theory, applied to the viscosity, accounts for a substantial part of the observed difference between the Boltzmann theory and simulations.     

Structural evolution of the Tropical Pacific climate network

An attempt is made to develop an equilibrium kinetic equation for a weakly non ideal inhomogeneous gravitational system utilizing the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy of equations. It is shown that the pair correlational function explicitly depends upon the nature of binary interaction between particles. The corresponding kinetic equation containing pair correlation corrections is devoid of the degeneracy present in the collisionless Boltzmann equation with respect to the nature of the two particle interactions, unlike the Vlasov equation that cannot recognize the nature of two particle interaction. A net effect of the particle correlations can be realized only if the spatial symmetry of the correlation interaction is broken due to a spatial inhomogeneity. Such an inhomogeneity is inherently present in a bulk gravitational system in view of the unshielded long range nature of the two-particle interactions. In a finite gravitational system, the effects of pair correlations in the first order kinetic equation can be expressed in terms of the macroscopic gravitational potential to obtain a modified Boltzmann distribution that includes the effects of correlations.     

An interacting particle model with compact hierarchical structure

We present a model interacting particle system with a population of fixed size in which particles wander randomly in space, and pairs interact at a rate determined by a reaction kernel with finite range. The pairwise interaction randomly selects one of the particles (the victim) and instantly transfers it to the position of the other (the killer), thus maintaining the total number. The special feature of the model is that it possesses a closed hierarchical structure in which the statistical moments of the governing master equation lead to closed equations for the reduced distribution functions (the concentration, pair correlation function, and so on). In one spatial dimension, we show that persistent spatial correlations (clusters) arise in this model and we characterize the dynamics in terms of analytical properties of the pair correlation function. As the range of the reaction kernel is increased, the dynamics varies from an ensemble of largely independent random walkers at small range to tightly bound clusters with longer-range reaction kernels.     

R134a迁移性质研究

1引言R134a作为一种新工质，有关对其迁移性质的研究目前还进行的不多，已有的迁移性质计算公式适用范围亦不宽。这些都影响了系统的优化设计和动态仿真。针对这一问题，作者在本文对R134a的导热系数、粘度关系式进行了研究。2有关R134a导热系数、粘度系数的实验研究国内外公开发表的有关R134a导热系数、粘度系数实验研究的报告如表1和表2所示。表1近年来对R134a导热系我实验研究表2近年来对R134a粘应的实验研究本文曾于1996年10月在武夷山召开的中国工程热物理学会工程热力学与能源利用学术会议上宣读．表1、表2列出了各研究者对R134a迁…     

Enhancedt −3/2 long-time tail for the stress-stress time correlation function

Nonequilibrium molecular dynamics is used to calculate the spectrum of shear viscosity for a Lennard-Jones fluid. The calculated zero-frequency shear viscosity agrees well with experimental argon results for the two state points considered. The low-frequency behavior of shear viscosity is dominated by an ^1/2 cusp. Analysis of the form of this cusp reveals that the stress-stress time correlation function exhibits at ^–3/2 long-time tail. It is shown that for the state points studied, the amplitude of this long-time tail is between 12 and 150 times larger than what has been predicted theoretically. If the low-frequency results are truly asymptotic, they imply that the cross and potential contributions to the Kubo-Green integrand for shear viscosity exhibit at ^–3/2 long-time tail. This result contradicts the established theory of such processes.     

Modelling of creep hysteresis in ferroelectrics

In the current paper, a macroscopic model is proposed to simulate the hysteretic dynamics of ferroelectric ceramics with creep phenomenon incorporated. The creep phenomenon in the hysteretic dynamics is attributed to the rate-dependent characteristic of the polarisation switching processes induced in the materials. A non-convex Helmholtz free energy based on Landau theory is proposed to model the switching dynamics. The governing equation of single-crystal model is formulated by applying the Euler–Lagrange equation. The polycrystalline model is obtained by combining the single crystal dynamics with a density function which is constructed to model the weighted contributions of different grains with different principle axis orientations. In addition, numerical simulations of hysteretic dynamics with creep phenomenon are presented. Comparison of the numerical results and their experimental counterparts is also presented. It is shown that the creep phenomenon is captured precisely, validating the capability of the proposed model in a range of its potential applications.     

On the effect of the correlation in phonon motion on the viscosity of impure dielectrics

The effect of the correlation in phonon motion on the viscosity of impure dielectrics is studied. It is shown that for perfect dielectrics the relaxation times entering the expressions for the absorption of longitudinal and transverse acoustic waves are different due to phonon correlations. The influence of impurities on the viscosity of dielectrics is discussed. Special emphasis is given to the problem of longitudinal-acoustic-wave absorption in impure dielectrics. It is shown that the effect of impurities on phonon correlations can lead to a substantial change in absorption of longitudinal waves.     

基于分子动力学模拟流体输运性质的稳定性分析

利用线性响应理论对Ar流体输运参数进行了分子动力学模拟,结果发现:导热系数和黏度会随着自相关积分函数积分时间的增加而产生剧烈波动,而扩散系数却相对稳定. 针对积分稳定性这一问题,对导热系数和黏度中的热流密度和应力张量进行了分解分析,发现含分子间作用力项是影响稳定性的最大因素. 从牛顿力学出发对作用力项的影响机理进行了分析,指明减小这种影响的最主要方法是使在体系进行统计输运参数前达到稳定平衡状态,即最小的预平衡步数应该满足使体系达到该状态下熵最大或者能量最低,并尽量减小温度对体系的影响. 同时,还对模拟盒尺寸、统计步长等因素对积分稳定性的影响进行了分析,给出了保持稳定性的建议. 关键词： 分子动力学 输运性质 自相关函数 稳定性     

Wave motion of incompressible turbulent fluid

Evolution of small disturbances in a fully developed incompressible turbulent flow is considered on the base of the transport equation for the single-point probability density function (PDF) of velocity fluctuations. It is shown that at high frequencies this equation is similar to the Vlasov equation for charged plasma in a self-consistent electromagnetic field having longitudinal wave solutions for turbulent stresses similar to Langmuir waves. It is found that the longitudinal waves of turbulent stresses have a constant phase velocity and can be damped, neutral, or growing waves, depending on the type of undisturbed probability density function of velocity fluctuations. The obtained result differs from the previously published solutions to this problem using the statistical moments closures according to which the wave disturbances should be neutral or damped. The possibilities of experimental observation of longitudinal waves of turbulent stresses are analyzed.     

Surface dynamics of polymer films

The dynamics of supported polymer films were studied by probing the surface height fluctuations as a function of lateral length scale using x-ray photon correlation spectroscopy. Measurements were performed on polystyrene (PS) films of thicknesses varying from 84 to 333 nm at temperatures above the PS glass transition temperature. Within a range of wave vectors spanning 10(-3) to 10(-2) nm(-1), good agreement is found between the measured surface dynamics and the theory of overdamped thermal capillary waves on thin films. Quantitatively, the data can be accounted for using the viscosity of bulk PS.     

Particle-particle correlation and fluctuations in non-equilibrium Fermi/Bose gases

A theory of fluctuations and correlations in non-equilibrium Fermi and Bose gases is developed. A specific quantum correlation is predicted in non-equilibrium collisional quasi-classical gases, created by collisions between particles. The expressions for correlation sources entering the equation for an equal-time two-particle correlation function are obtained and analyzed. The expressions are valid for arbitrary particle-particle interaction potentials. The possibility of display of the quantum correlation in the macroscopic characteristics of fluctuation phenomena in non-equilibrium gases (e.g., current fluctuations in semiconductors) is discussed. A comparison with correlations in a Lorentz gas is made.     

Why many theories of shock waves are necessary: Kinetic functions,equivalent equations,and fourth-order models

We consider several systems of nonlinear hyperbolic conservation laws describing the dynamics of nonlinear waves in presence of phase transition phenomena. These models admit under-compressive shock waves which are not uniquely determined by a standard entropy criterion but must be characterized by a kinetic relation. Building on earlier work by LeFloch and collaborators, we investigate the numerical approximation of these models by high-order finite difference schemes, and uncover several new features of the kinetic function associated with physically motivated second and third-order regularization terms, especially viscosity and capillarity terms.On one hand, the role of the equivalent equation associated with a finite difference scheme is discussed. We conjecture here and demonstrate numerically that the (numerical) kinetic function associated with a scheme approaches the (analytic) kinetic function associated with the given model – especially since its equivalent equation approaches the regularized model at a higher order. On the other hand, we demonstrate numerically that a kinetic function can be associated with the thin liquid film model and the generalized Camassa–Holm model. Finally, we investigate to what extent a kinetic function can be associated with the equations of van der Waals fluids, whose flux-function admits two inflection points.     

Reynolds stress models applied to canonical shock-turbulence interaction

Shock waves in high-speed flows can drastically alter the nature of Reynolds stresses in a turbulent flow. We study the canonical interaction of homogeneous isotropic turbulence passing through a normal shock, where the shock wave generates significant anisotropy of Reynolds stresses. Existing Reynolds stress models are applied to this canonical problem to predict the amplification of the stream-wise and transverse normal Reynolds stresses across the shock wave. In particular, the efficacy of the different models for the rapid pressure–strain correlation is evaluated by comparing the results with available direct numerical simulation (DNS) data. The model predictions are found to be grossly inaccurate, especially at high-Mach numbers. We propose physics-based improvement to the Reynolds stress-transport equation in the form of shock-unsteadiness effect and enstrophy amplification for turbulent dissipation rate . The resulting model is found to capture the essential physics of Reynolds stress amplification, and match DNS data for a range of Mach numbers. Numerical error encountered at shock waves are also analysed and the model equations are cast in conservative form to obtain physically consistent results with successive grid refinement. Finally, the proposed model for canonical shock-turbulence interaction is generalised to multi-dimensional flows with shock of arbitrary orientation.     

Energy spectrum of the ensemble of weakly nonlinear gravity-capillary waves on a fluid surface

We consider nonlinear gravity-capillary waves with the nonlinearity parameter ? ～ 0.1–0.25. For this nonlinearity, time scale separation does not occur and the kinetic wave equation does not hold. An energy cascade in this case is built at the dynamic time scale (D-cascade) and is computed by the increment chain equation method first introduced in [15]. We for the first time compute an analytic expression for the energy spectrum of nonlinear gravity-capillary waves as an explicit function of the ratio of surface tension to the gravity acceleration. We show that its two limits—pure capillary and pure gravity waves on a fluid surface—coincide with the previously obtained results. We also discuss relations of the D-cascade model with a few known models used in the theory of nonlinear waves such as Zakharov’s equation, resonance of modes with nonlinear Stokes-corrected frequencies, and the Benjamin-Feir index. These connections are crucial in understanding and forecasting specifics of the energy transport in a variety of multicomponent wave dynamics, from oceanography to optics, from plasma physics to acoustics.     

Weak Nonlinear Matter Waves in a Trapped Spin-1 Condensates

The dynamics of the weak nonlinear matter solitary waves in a spin-1condensates with harmonic external potential are investigated analytically by a perturbation method. It is shown that, in the small amplitude limit, the dynamics of the solitary waves are governed by a variable-coefficient Korteweg-de Vries (KdV) equation. The reduction to the (KdV) equation may be useful tounderstand the dynamics of nonlinear matter waves in spinor BECs. The analytical expressions for the evolution of soliton show that the small-amplitude vector solitons of the mixed types perform harmonic oscillations in the presence of the trap. Furthermore, the emitted radiation profiles and the soliton oscillation frequency are also obtained.     

Envelope self-similar solutions for the nonautonomous and inhomogeneous nonlinear Schrödinger equation

By means of the similarity transformation connecting with the solvable stationary equation, the self-similar combined Jacobian elliptic function solutions and fractional form solutions of the generalized nonlinear Schrödinger equation (NLSE) are obtained when the dispersion, nonlinearity, and gain or absorption are varied. The propagation dynamics in a periodic distributed amplification system is investigated. Self-similar cnoidal waves and corresponding localized waves including bright and dark similaritons (or solitons) for NLSE and arch and kink similaritons (or solitons) for cubic-quintic NLSE are analyzed. The results show that the intensity and the width of chirped cnoidal waves (or similaritons) change more distinctly than that of chirp-free counterparts (or solitons).     

Shear viscosity of strongly coupled Yukawa systems on finite length scales

The Yukawa shear viscosity has been calculated using nonequilibrium molecular dynamics. Near the viscosity minimum, we find exponential decay consistent with the Navier-Stokes equation, with significant deviations on finite length scales for larger viscosity values. The viscosity is determined to be nonlocal on a scale length consistent with the correlation length, revealing the length scales necessary for obtaining transport coefficients in the hydrodynamic limit by nonequilibrium molecular dynamics methods. Our results are quasiuniversal with respect to excess entropy for excess entropies well below unity.     

Direct and indirect correlations in low density supercritical Lennard-Jones fluids

We have carried out a detailed comparison of the direct and indirect correlation functions obtained from canonical molecular dynamics (NVT-MD) simulation of supercritical Lennard-Jones fluids to the results obtained by solving the Ornstein-Zernike equation with the approximate Duh-Henderson (DH) closure. The variations of equilibrium correlations are studied as functions of density at two supercritical isotherms near and away from the critical point. The direct and indirect correlations predicted using the DH closure provides a very good agreement with our simulation results at low densities. However, a marked deviation is observed at higher densities. These results are correlated to the discrepancies between the density and temperature dependence of the underlying bridge function. The implication of these results on the calculation of chemical potential and the Krichevskii parameter is also presented.