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     

Linear response theory in stochastic many-body systems revisited

The Green–Kubo relation, the Einstein relation, and the fluctuation–response relation are representative universal relations among measurable quantities that are valid in the linear response regime. We provide pedagogical proofs of these universal relations for stochastic many-body systems. Through these simple proofs, we characterize the three relations as follows. The Green–Kubo relation is a direct result of the local detailed balance condition, the fluctuation–response relation represents the dynamic extension of both the Green–Kubo relation and the fluctuation relation in equilibrium statistical mechanics, and the Einstein relation can be understood by considering thermodynamics. We also clarify the interrelationships among the universal relations.     

A study of correlation functions for the delta-function Bose gas

The Gel'fand-Levitan equation for the quantum nonlinear Schrödinger field theory is used to investigate the correlation functions of the delta-function Bose gas. Operator expressions are derived for the field and for nonlocal products of fields in terms of the quantized reflection operators which create and annihilate eigenstates of the Hamiltonian. For the two-point function, an explicit series expression is obtained in which the nth term is determined by well-defined n-body combinatorics in an infinite volume. The inductive properties of this series are discussed and used to express the temperature and chemical potential dependence of the correlation functions entirely in terms of previously known thermodynamic functions. The zero separation limit of the series for the two-point function reproduces the thermodynamics derived by Yang and Yang, while the infinite coupling limit gives the Fredholm determinant result of Schultz and Lenard. The latter is related to the Painlevé V equation by the monodromy arguments of Jimbo, Miwa, Mori, and Sato. The (1/c) correction to the large coupling limit is calculated from the Gel'fand-Levitan series and expressed in terms of solutions to Painlevé V. The asymptotic behavior of the relevant Painlevé function is discussed and related to the long range behavior of the correlation function.     

Green function theory of dynamic conductivity

The transport processes can be discussed either by kinetic equation method or by correlation function method. Using the former, linear transport equations are developed for the study of dynamic conductivity of a quantum imperfect gas employing a resolution of BBGKY hierarchy using Green functions. From this transport equation a modified form of Kubo (correlation function) formula is obtained to show the equivalence between the two methods. This equivalence may be used for the justification of the concept of adiabatic switching of the field. The simple formula derived, gives the conductivity in terms of one-particle Green function, unlike the usual discussions which express it in higher order Green functions.     

Investigation of the characteristics of heat current in a nanofluid based on molecular dynamics simulation

Molecular dynamics simulation of nanofluid system composed of argon liquid and copper nanoparticle was carried out in this paper. To ensure the interatomic force gradually decreases to zero at the cut-off distance, Stoddard and Ford potential function was employed. Green–Kubo method was used to obtain the thermal conductivity. The characteristics of the heat current were measured by its mean value, variance, third moment, and the Shannon entropy. It was found that the thermal conductivity increases as the nanoparticle volume fraction increases, and so do the variance and the Shannon entropy of the heat current. The third moment of the heat current was almost zero, indicating that the probability distribution of the heat current is nearly symmetric about its mean value. Autocorrelation and partial autocorrelation functions of the heat current were used to investigate the correlation between the discrete heat current value and different lags.     

Simulation studies of shear viscosity time correlation functions in liquid CS2

The Green—Kubo time correlation function for the shear viscosity in liquid CS₂ has been simulated by molecular dynamics at several thermodynamic state points. The breakdown of this function into its kinetic and potential contributions as well as the cross-term between the two has been performed. Intermolecular interactions were obtained from a three-centre atom—atom (12/6) Lennard-Jones potential model. The time correlation functions for the potential part of the shear viscosity contain component two-, three- and four-body terms that were explicitly evaluated to show that they partially cancel each other at short times but at long times, they exhibit approximately exponential decays with magnitude ratios corresponding to nearly perfect cancellation. In this respect, the correlation functions for CS₂ resemble those of liquid argon. In addition, the microscopic stress tensor was separated into the portions arising from the repulsive and attractive branches of the Lennard-Jones model. This split gives rise to positive autocorrelation functions involving the repulsive and the attractive forces plus a negative cross-correlation function between the two that partially cancels the contributions of the autocorrelation functions. It is argued that the breakdown of the potential part of the shear viscosity into its component parts is helpful in elucidating the role of molecular re-orientation in determining the separate short and long time behaviours of this time correlation function for liquids such as CS₂.     

Relativistic n-body wave equations in scalar quantum field theory

The variational method in a reformulated Hamiltonian formalism of Quantum Field Theory (QFT) is used to derive relativistic n-body wave equations for scalar particles (bosons) interacting via a massive or massless mediating scalar field (the scalar Yukawa model). Simple Fock-space variational trial states are used to derive relativistic n-body wave equations. The equations are shown to have the Schrödinger non-relativistic limits, with Coulombic interparticle potentials in the case of a massless mediating field and Yukawa interparticle potentials in the case of a massive mediating field. Some examples of approximate ground state solutions of the n-body relativistic equations are obtained for various strengths of coupling, for both massive and massless mediating fields.     

Molecular dynamics computation of clusters in liquid Fe–Al alloy

By means of constant pressure molecular dynamics (MD) simulation technique, a series of simulations of the Fe₅₀Al₅₀ alloy have been carried out. The atoms interact via semi-empirical n-body noncentral potential. The pair correlation functions and the pair analysis technique is applied to reveal the cluster evolution in the process of quick solidification. By using the bond orientation order parameters, we have measured both local and extended orientation symmetries for computer-generated models of dense liquid and glass. A lot of polyhedra in liquid system, for example, icosahedra, are also obtained. In order to test the reliance of the computation results, corresponding X-ray diffraction experiments have been performed on the material.     

Molecular dynamical calculations on the transport properties of a square-well fluid: IV. The influence of the well-width on the viscosity and the thermal conductivity

The coefficients of the viscosity and thermal conductivity for a system consisting of square-well molecules have been determined at constant temperature as a function of the well-width. The densities considered in these calculations range from rather low values up to a density which is just below the fluid-solid phase transition. The superposition of even a narrow attractive well on hard spheres has a significant influence on the viscosity. An influence is also seen on the kinetic, the potential and the cross terms of the thermal conductivity, but these terms partially cancel each other. Moreover, short time effects in the correlation functions for the potential terms have been found.     

Green–Kubo relations for dynamic interfacial excess properties

In this paper we analyze the fluctuations of the in-plane interfacial excess fluxes in multiphase systems, in the context of the extended irreversible thermodynamics formalism. We derive expressions for the time correlation functions of the surface extra stress tensor, the surface mass flux vector, and the surface energy flux vector, and use these expressions to derive Green–Kubo relations for the surface shear viscosity, the surface dilatational viscosity, the surface diffusion coefficient, and the surface thermal conductivity. These Green-Kubo relations can be used to compute these excess transport coefficients using for example molecular dynamics simulations.     

Anharmonic Excitations,Time Correlations and Electric Conductivity

We study the influence of anharmonic mechanical excitations of a classical ionic lattice on its electric properties. First, to illustrate salient features, we investigate a simple model, an one‐dimensional (1D) system consisting of ten semiclassical electrons embedded in a lattice or a ring with ten ions interacting with exponentially repulsive interactions. The lattice is embedded in a thermal bath. The behavior of the velocity autocorrelation function and the dynamic structure factor of the system are analyzed. We show that in this model the nonlinear excitations lead to long lasting time correlations and, correspondingly, to an increase of the conductivity in a narrow temperature region, where the excitations are supersonic soliton‐like. In the second part we consider the quantum statistics of general ion‐electron systems with arbitrary dimension and express ‐ following linear response transport theory ‐ the quantum‐mechanical conductivity by means of equilibrium time correlation functions. Within the relaxation time approach an expression for the effective collision frequency is derived in Born approximation, which takes into account quantum effects and dynamic effects of the ion motion through the dynamic structure factor of the lattice and the quantum dynamics of the electrons. An evaluation of the influenec of solitons predicts for 1D‐lattices a conductivity increase in the temperature region where most thermal solitons are excited, similar as shown in the classical Drude‐Lorentz‐Kubo framework. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

强磁场下的输运过程与Liouville方程的两种定态解

本文中讨论了在外场中Liouville方程的两种定态解,指出在用Kubo公式计算输运系数时的关键之处是:在完成Kubo公式中的时间积分之前,必须把关联函数的时间行为表示成趋向平衡的形式。注意到这一点就能得到正确的输运系数表示式。用这种办法,我们重新计算了文献[1]中曾讨论过的强磁场下的电导率,得到了正确的非零的结果。 关键词：     

Ion diffusion and momentum correlation functions in dilute electrolytes

The convergent cluster expansion of the ion-ion momentum time correlation functions in a dilute electrolyte, recently derived by Friedman, is applied here for the calculation of the limiting law for ion self-diffusion. Considering only the non-chain cluster terms leads to a result analogous to the Debye-Hückel limiting law for ionic conductivity. Taking into account the additional chain terms leads to exactly the Onsager result. We also use the cluster expansion to determine the long-time behaviour of the ion momentum time auto-correlation function, which we find goes as t ^-3/2, with a coefficient proportional to the square root of the solute concentration. Similar results are given for the associated memory function and the ion-ion momentum time correlation function.     

Kubo formula for frequency dispersion of dielectric permittivity and static conductivity of the Coulomb system

It is proved that the Kubo formula for the conductivity σ(ω) is valid at real frequencies ω. On this basis, an exact relation is derived for the static conductivity σst of the Coulomb system. It is shown that the static conductivity is determined by the time correlation function in the limit t→∞. It is proved that the permittivity ε(ω) satisfies the Kramers-Kronig relations which take into account a singularity associated with static conductivity.     

Exact short time dynamics for steeply repulsive potentials

The autocorrelation functions for the force on a particle, the velocity of a particle and the transverse momentum flux are studied for the power law potential v(r)=ε(σr)^ν (soft spheres). The latter two correlation functions characterize the Green–Kubo expressions for the self-diffusion coefficient and shear viscosity. The short-time dynamics is calculated exactly as a function of ν. The dynamics is characterized by a universal scaling function S(τ), where τ=t/τ_ν and τ_ν is the mean time to traverse the core of the potential divided by ν. In the limit of asymptotically large ν this scaling function leads to delta function in time contributions in the correlation functions for the force and momentum flux. It is shown that this singular limit agrees with the special Green–Kubo representation for hard-sphere transport coefficients. The domain of the scaling law is investigated by comparison with recent results from molecular dynamics simulation for this potential.     

Integer quantum Hall effect in Kekulé-patterned graphene

Y-shaped Kekulébond textures in a honeycomb lattice on a graphene-copper superlattice have recently been experimentally revealed.In this paper,the effects of such a bond modulation on the transport coefficients of Kekulé-patterned graphene are investigated in the presence of a perpendicular magnetic field.Analytical expressions are derived for the Hall and longitudinal conductivities using the Kubo formula.It is found that the Y-shaped Kekulébond texture lifts the valley degeneracy of all Landau levels except that of the zero mode,leading to additional plateaus in the Hall conductivity accompanied by a split of the corresponding peaks in the longitudinal conductivity.Consequently,the Hall conductivity is quantized as±ne²/h for n=2,4,6,8,10,...,excluding some plateaus that disappear due to the complete overlap of the Landau levels of different cones.These results also suggest that DC Hall conductivity measurements will allow us to determine the Kekulébond texture amplitude.     

Effect of electrostatics techniques on the estimation of thermal conductivity via equilibrium molecular dynamics simulation: application to methane hydrate

Equilibrium molecular dynamics (MD) simulations for three system sizes of fully occupied methane hydrate have been performed at around 265 K to estimate the thermal conductivity using the Ewald, Lekner, reaction field, shifted-force and undamped Fennell–Gezelter methods. The TIP4P water model was used in conjunction with a fully atomistic methane potential with which it had been parameterized from quantum simulation. The thermal conductivity was evaluated by integration of the heat flux autocorrelation function (ACF) derived from the Green–Kubo formalism; this approach vas validated by estimation of the average phonon mean free path. The thermal conductivities predicted by non-periodic techniques were in reasonable agreement with the experimental results of 0.62 and 0.68 W/m K, although it was found that the estimates by the non-periodic techniques were up to 25% larger than those of Lekner and Ewald estimates, particularly for larger systems. The results for the Lekner method exhibited the least variation with respect to system size. A decomposition of the heat flux vector into its respective contributions revealed the importance of electrostatic interactions, and how different electrostatic treatments affect the contribution to the thermal conductivity.     

Theoretical and experimental investigation on enhanced thermal behaviour in chunk-shaped nano ZnO

Thermal properties of chunk-shaped ZnO nanostructures are studied for diffusivity, conductivity, and effusivity by photoacoustics (PA) and simulation methods. Thermal conductivity of nano ZnO was determined from simulation in the temperature range of 100–1000 K. Thermal conductivity of ZnO nanostructures at room temperature is approximately 52 and 128 times lower than that of bulk ZnO for PA and simulation, respectively. For simulation, Tersoff potential is used for the interatomic interaction. The velocity autocorrelation function and Green–Kubo relation are used to compute the thermal conductivity.     

Sphaleron Transition Rate in Lattice Gluodynamics

The sphaleron transition rate in gluodynamics at the temperature T /T_c = 1.24 has been calculated by lattice simulation. The calculations involve the Kubo formula, which relates the sphaleron transition rate to the correlation function of the topological charge density. The gradient flow method has been used to calculate the correlation function of the topological charge density. The Kubo formula has been inverted by the Backus–Gilbert method. The results have been compared to those obtained by other methods.     

Green–Kubo Expressions for a Granular Gas

The transport coefficients for a gas of smooth, inelastic hard spheres are obtained from the Boltzmann equation in the form of Green–Kubo relations. The associated time correlation functions are not simply those constructed from the fluxes of conserved densities. Instead, fluxes constructed from the reference local homogeneous distribution occur as well. The analysis exposes some complexities to be expected in the application of linear response methods to granular systems.