Inhomogeneous 2D Lennard-Jones Fluid: Theory and Computer Simulation

In this work, thermodynamical properties of a two-dimensional (2D) Lennard-Jones (LJ) fluid are studied. Here, to increase the accuracy of our theoretical calculations, the correlation functions in three-particle level (triplet) are applied. To obtain the triplet correlation functions, the Attard's source particle method is extended to 2D systems. In the Attard's procedure, the inhomogeneous Ornstein-Zernike (OZ) equation is solved using the Treizenberg-Zwanzwig (TZ) expression and a closure relation like the hypernetted-chain (HNC) approximation. In the present work, we also have performed the Monte Carlo (MC) simulation. The theoretical results are in fairly agreement with the MC simulation. Also, our results show that the approach proposed here is suitable to study the 2D LJ fluid.     

Viscosity of Lennard-Jones fluid: Integral equation method

One of the most useful models to study the real systems is the Lennard-Jones (LJ) potential which has an attractive and repulsive part. In this work we use this potential model and examine the viscosity of one-component LJ fluids and LJ binary fluid mixtures. For this purpose, we apply the integral equation method and solve numerically the Ornstein-Zernike (OZ) integral equation by using the mean spherical approximation (MSA). Thus, we obtain the pair correlation functions to calculate the viscosity of these fluids. Finally, we compare our results with computer simulation results and the available experimental data and illustrate the ability of the LJ model to predict the results.     

Chemical potentials and phase equilibria of Lennard-Jones chain fluids

Computer simulations (molecular dynamics) were performed for ensembles of flexible tangent Lennard-Jones chains consisting of n sites (n = 1, 2, 4, 8, and 16). From these simulations, the orthobaric liquid and vapour densities were calculated not only with the traditional method of simulating a liquid film in coexistence with vapour, but also using the rigorous thermodynamic condition of satisfying the chemical potential equality between the phases in equilibrium. The agreement with literature data, as far as such exist, is excellent.     

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.     

超微弱光子图像的相关检测及计算机模拟

在超微弱发光的研究中（例如生物发光）,由于发光强度极弱,由像增强器得到的光子图像由于样本（光子）数量太少和受系统暗噪声的影响使其信噪比极低,提出了一种基于统计学的光子图像相关积分方法和基于相关处理的光子图像处理方法,用累积光子来提高图像信噪比并得到相应灰度图像并对该方法进行了计算机模拟,同时展示了光子图像和传统灰度图像的信噪比关系,是进行微弱生物发光信号检测的有效方法。     

Further property of Lennard-Jones fluid: Thermal conductivity

In this paper, we calculate the thermal conductivity of noble gases, methane, and three noble gas mixtures including He+Kr, He+Xe, and Kr+Xe assuming they obey Lennard-Jones (LJ) (12-6) model potential. One of the required quantities to calculate the thermal conductivity of these systems is the pair correlation function. Therefore, we solve numerically the Ornstein-Zernike (OZ) integral equation using the mean spherical approximation (MSA) to obtain the pair correlation functions. We use these functions to obtain the thermal conductivity, then compare our results with the available data. According to the results obtained from the present work for pure and mixtures of LJ fluids reveals that the integral equations method is suitable for predicting the thermal conductivity of this class of fluid.     

Linear Fluid Theory for Weakly Inhomogeneous Plasmas with Strong Correlations

Linearized fluid equations for the collective modes of weakly inhomogeneous plasmas including strong coupling effects are derived from a recent kinetic theory based on an extended Singwi‐Tosi‐Land‐Sjölander (STLS) ansatz [H. Kählert, G. J. Kalman, and M. Bonitz, Phys. Rev. E 90 , 011101(R) (2014)]. The equations are analogous to the equations of linearized elasticity theory with space dependent elastic moduli that correspond to those of a bulk system with the local fluid density. The identification of the latter as infinite‐frequency elastic moduli shows that the present version of the extended STLS theory accounts for the elastic properties of the fluid but does not capture the viscous behavior. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Influence of dispersive long-range interactions on properties of vapour–liquid equilibria and interfaces of binary Lennard-Jones mixtures

The influence of dispersive long-range interactions on properties of vapour–liquid equilibria and interfaces of six binary Lennard-Jones (LJ) mixtures was studied by molecular dynamics (MD) simulations and density gradient theory (DGT). The mixtures were investigated at a constant temperature T, at which the low-boiling component, which is the same in all mixtures, is subcritical. Two different high-boiling components were considered: one is subcritical, the other is supercritical at T. Furthermore, the unlike dispersive interaction was varied such that mixtures with three different types of phase behaviour were obtained: ideal, low-boiling azeotrope, and high-boiling azeotrope. In a first series of simulations, the full LJ potential was used to describe these mixtures. To assess the influence of the long-range interactions, these results were compared with simulations carried out with the LJ truncated and shifted (LJTS) potential applying the corresponding states principle. The dispersive long-range interactions have a significant influence on the surface tension and the interfacial thickness of the studied mixtures, whereas the relative adsorption and the enrichment are hardly affected. Furthermore, the influence of the long-range interactions on Henry's law constants and the phase envelopes of the vapour–liquid equilibrium was investigated. The long-range interactions have practically no influence on the composition dependency of the investigated mixture properties.     

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.     

界面不稳定性数值模拟中的虚拟流动方法

研究了流体界面不稳定性的一类数值模拟方法——虚拟流动方法(Ghost Fluid Method).在算法中直接针对多维问题设定虚拟区域的流动参数,在流体力学方程的计算中采用了非分裂型的高分辨SCB格式,最后利用该方法完成了R-M和R-T不稳定性问题的数值计算,得到了满意的计算结果.     

半导体温度计的计算机仿真

根据半导体热敏电阻与温度的关系,利用计算机进行仿真半导体温度计的实验,得到了半导体温度计温度—电流曲线。     

Statistical Mechanics Approach for Uniform and Non-uniform Fluid with Hard Core and Interaction Tail

One recently proposed self-consistent hard sphere bridge functional was combined with an exponential function exp(-cr) and a re-normalized indirect correlation function to construct the bridge function for fluid with hard core and interaction tail. In the present approach, the adjustable parameter α was determined by the thermodynamic consistency realized on the compressibility modulus, the re-normalization of the indirect correlation function was realized by a modified Mayer function with the interaction potential replaced by the perturbative part of the interaction potential. As an example, the present bridge function was combined with the Ornstein-Zernike (OZ) equation to predict structure and thermodynamics properties in very good agreement with the simulation data available for Lennard-Jones (L J). Based on the universality principle of the free energy density functional and the test particle trick, the numerical solution of the OZ equation was employed to construct the first order direct correlation function of the non-uniform fluid as a functional of the density distribution by means of the indirect correlation function. In the framework of the density functional theory, the numerically obtained functional predicted the density distribution of LJ fluid confined in two planar hard walls that is in good agreement with the simulation data.     

全息图的计算机模拟及重现

根据光学全息原理,分析了在计算机模拟中把物光、参考光和再现光离散化的方法,并对基元全息和无透镜傅里叶全息进行模拟,实验结果逼真,这有助于学生更好地理解全息摄影的相关理论,为光学全息的理论和实验教学提供了可视化的验证。     

Perturbation and variational approach for the equation of state for hard-sphere and Lennard-Jones fluids

The present work uses the concept of a scaled particle along with the perturbation and variation approach, to develop an equation of state (EOS) for a mixture of hard sphere (HS), Lennard–Jones (LJ) fluids. A suitable flexible functional form for the radial distribution function G(R) is assumed for the mixture, with R as a variable. The function G(R) has an arbitrary parameter m and a different equation of state can be obtained with a suitable choice of m. For m = 0.75 and m = 0.83 results are close to molecular dynamics (MD) result for pure HS and LJ fluid respectively.     

On Average Properties of Inhomogeneous Fluids in General Relativity: Perfect Fluid Cosmologies

For general relativistic spacetimes filled with an irrotational perfect fluid a generalized form of Friedmann's equations governing the expansion factor of spatially averaged portions of inhomogeneous cosmologies is derived. The averaging problem for scalar quantities is condensed into the problem of finding an "effective equation of state" including kinematical as well as dynamical "backreaction" terms that measure the departure from a standard FLRW cosmology. Applications of the averaged models are outlined including radiation-dominated and scalar field cosmologies (inflationary and dilaton/string cosmologies). In particular, the averaged equations show that the averaged scalar curvature must generically change in the course of structure formation, that an averaged inhomogeneous radiation cosmos does not follow the evolution of the standard homogeneous-isotropic model, and that an averaged inhomogeneous perfect fluid features kinematical "backreaction" terms that, in some cases, act like a free scalar field source. The free scalar field (dilaton) itself, modelled by a "stiff" fluid, is singled out as a special inhomogeneous case where the averaged equations assume a simple form.     

Test of the Duh-Haymet-Henderson theory for mixtures: cavity correlation functions and excess volumes

The accuracy of the Duh-Haymet-Henderson (DHH) integral equation theory for predicting the cavity correlation functions of mixtures has been tested by comparison with molecular simulations. We have compared the cavity correlation functions, internal energies, and pressures computed for Lennard-Jones model mixtures of Ar/Kr, Ar/Ne, and Ar/Xe with these same quantities computed from the DHH theory and also, for reference, the Percus-Yevick (PY) integral equation theory. We found that DHH gave much better accuracy than PY at high densities. At low densities DHH and PY give essentially identical predictions. We have computed excess volumes for Ar/Kr mixtures at two pressures (10 and 20?MPa) at 132.32?K, for which experimentally derived data are available. The DHH theory predicts the correct trends and is quantitatively more accurate than the PY theory for predicting the excess volumes. We have tested the local optimality of the DHH theory for pure fluids by adding two adjustable parameters to the DHH bridge function expression to see if it is possible to improve the DHH predictions of the cavity correlation function empirically, holding the form of the bridge function constant. We found that no single set of adjustable parameter values could improve the accuracy of DHH over multiple different isotherms. Furthermore, perturbing DHH leads to a decrease in accuracy of the predictions of both the pressure and energy, although small improvements in the cavity correlation functions were achieved. Thus, the DHH theory is locally optimal, given the form of the bridge function.     

激光直接写入过程的计算机仿真研究

基于光刻胶正胶曝光显影过程的理论模型,用梯度折射率介质光线追迹的方法进行了由于局部溶解 同而造成的显影过程 胶面面形随时间变化过程的计算。对任意给定的曝光量分布及显影时间,可以精确地确定显影后的面形,为激光直写研究提供了一种有效的工具。同时,通过对显影速率作阈值近似后,导出了光刻胶曝光显影后面形与表面所需曝光量分布之间的关系,为激光直接写入提供了理论指导。