Thermodynamic properties of a hard-core Lennard-Jones fluid from computer simulation and the coupling parameter series expansion

ABSTRACT

The thermodynamic properties of a fluid with an interaction potential consisting in a hard-sphere core plus a Lennard-Jones tail have been obtained by Monte Carlo (MC) NVT simulation as a function of the density along several isotherms. In addition, the liquid–vapour coexistence has been determined by means of histogram-reweighting MC. These data have been used to analyse the performance of perturbation theory. To this end, the first three perturbation terms of the inverse temperature expansion of the Helmholtz free energy have been obtained by means of MC NVT simulations to test the convergence of the perturbation series and to compare with the predictions of the coupling parameter series expansion. Then, the predictions of the latter theory for the thermodynamic properties have been compared with the simulations, revealing the overall excellent performance of this perturbation theory for this model fluid, except in the vicinity of the critical point.     

Nonlinear Saturation Amplitude in Classical Planar Richtmyer–Meshkov Instability

The classical planar Richtmyer–Meshkov instability(RMI) at a fluid interface supported by a constant pressure is investigated by a formal perturbation expansion up to the third order,and then according to definition of nonlinear saturation amplitude(NSA) in Rayleigh–Taylor instability(RTI),the NSA in planar RMI is obtained explicitly.It is found that the NSA in planar RMI is affected by the initial perturbation wavelength and the initial amplitude of the interface,while the effect of the initial amplitude of the interface on the NSA is less than that of the initial perturbation wavelength.Without marginal influence of the initial amplitude,the NSA increases linearly with wavelength.The NSA normalized by the wavelength in planar RMI is about 0.11,larger than that corresponding to RTI.     

On the pion decay constant

The pion decay constant fπ$f_{\pi }$ plays a crucial role in many areas of low energy particle physics. Its value may e.g. be deduced from experimental data on leptonic pion decays. Here, we provide comments on several aspects of this evaluation. In particular, we point out that at the present level of experimental accuracy, the value of fπ$f_{\pi }$ is sensitive to the value of the pion mass chosen in its chiral expansion.     

Analytical Approach to Fractional Zakharov-Kuznetsov Equations by He＇s Homotopy Perturbation Method

The aim of this paper is to obtain the approximate analytical solution of a fractional Zakharov-Kuznetsov equation by using homotopy perturbation method （HPM）. The fractional derivatives are described in the Caputo sense. Several examples are given and the results are compared to exact solutions. The results reveal that the method is very effective and simple.     

Approximate solution of the magneto-hydrodynamic flow over a nonlinear stretching sheet

The approximate solution of the magneto-hydrodynamic (MHD) boundary layer flow over a nonlinear stretching sheet is obtained by combining the Lie symmetry method with the homotopy perturbation method. The approximate solution is tabulated, plotted for the values of various parameters and compared with the known solutions. It is found that the approximate solution agrees very well with the known numerical solutions, showing the reliability and validity of the present work.     

Hyperbolic–parabolic singular perturbation for quasilinear equations of Kirchhoff type with weak dissipation

We consider a hyperbolic–parabolic singular perturbation problem for a quasilinear hyperbolic equation of Kirchhoff type with dissipation weak in time. The purpose of this paper is to give time‐decay convergence estimates of the difference between the solutions of the hyperbolic equation above and those of the corresponding parabolic equation, together with the unique existence of the global solutions of the hyperbolic equation above. Copyright © 2009 John Wiley & Sons, Ltd.     

用微扰理论推算超临界流体比定容热容

本文利用统计热力学中的BH微扰理论建立数学模型,推算了Ar超临界区域比定容热容,与文献值比较平均偏差为9.54%。引入了修正函数,重新对比热容公式进行推导,再次对Ar超临界区域部分比定容热容进行计算,计算平均偏差0.39%。对CO、CO₂、CH₄等其余11种简单气体的超临界比定容热容进行计算,平均偏差在1%左右。最后给出了计算中各物质势能参数值。     

Size‐guided multi‐seed heuristic method for geometry optimization of clusters: Application to benzene clusters

Since searching for the global minimum on the potential energy surface of a cluster is very difficult, many geometry optimization methods have been proposed, in which initial geometries are randomly generated and subsequently improved with different algorithms. In this study, a size‐guided multi‐seed heuristic method is developed and applied to benzene clusters. It produces initial configurations of the cluster with n molecules from the lowest‐energy configurations of the cluster with n − 1 molecules (seeds). The initial geometries are further optimized with the geometrical perturbations previously used for molecular clusters. These steps are repeated until the size n satisfies a predefined one. The method locates putative global minima of benzene clusters with up to 65 molecules. The performance of the method is discussed using the computational cost, rates to locate the global minima, and energies of initial geometries. © 2018 Wiley Periodicals, Inc.     

Legendre transform of the noninteracting kinetic energy: Especially from March–Murray perturbation theory based on plane waves

The Legendre transform of the noninteracting kinetic energy is derived from the March–Murray perturbation theory based on plane waves. Further useful relations are summarized, and it is shown that insight can be gained from simple model systems where nonperturbative equations can be derived. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 82: 138–142, 2001     

同向电磁场中氢原子低能级简并的解除

利用同向电磁场的作用使氢原子低能级简并完全解除.