Chandler—Silbey—Ladanyi integral equation theory for semiflexible molecules

Extension of Chandler—Silbey—Ladanyi (CSL) integral equation theory for the fluid of semi-flexible site—site molecules is proposed. The Percus—Yevick type of the closure is used to describe the structural properties of the fluid consisting of semiflexible linear chain triatomic molecules. Results for the site—site intramolecular and intermolecular radial distribution functions (RDFs) are compared with the corresponding computer simulation results and results of self-consistent reference interaction site model (RISM) theory. In general both theories give reasonably good agreement with corresponding Monte Carlo simulation data. The exception is the RDF between the terminal sites, for which none of the theories is satisfactory. The present version of CSL theory appears to be slightly more accurate than the self-consistent RISM approach.     

Analytic solution of the RISM equation for symmetric diatomics with Yukawa closure

We present the site-site direct correlation function c(r) for a fluid of hard diatomic symmetric molecules obtained from Monte Carlo simulation data via the RISM integral equation. This c(r) ensures that the site-site correlation function given by the RISM equation is exact, and thus provides a basis for critically examining the usual closure for the RISM equation. As an example of an improved closure we present the analytic solution of the RISM integral equation with a Yukawa closure for c(r).     

Structure and equilibrium optical properties of liquid CS2

Equilibrium optical properties of liquid carbon disulphide (CS₂), i.e. its refractive index, Kerr constant and depolarized light scattering intensity are calculated using two models of optical response of the fluid. The first one, the point polarizability approximation (PPA) assumes that a point dipole, proportional to the total polarizability, is induced in each molecule. The second one, the point atomic polarizability approximation (PAPA) assumes that point dipoles are induced in individual atomic sites.

The symmetry components of the intermolecular pair distribution function needed to calculate optical properties of the fluid are obtained by Monte Carlo computer simulation on a hard triatomic model of CS₂ as well as by two approximate approaches using this same model. The approximations are both based on the use of the site superposition approximation (SSA) for the intermolecular pair distribution function. In the first approach, the SSA pair distribution is obtained using the Monte Carlo site-site functions and in the second using the site-site functions calculated using the reference interaction site model (RISM) equations.

Extensive comparisons are carried out between the Monte Carlo results and the two approximations in order to examine the influence of the SSA and the RISM equations on optical properties of CS₂. We conclude that, while these approximations, especially the SSA, have a substantial effect on individual symmetry components of the pair distribution, they predict measurable optical properties with satisfactory accuracy.     

Hybrid MC/RISM technique for simulation of polymer solutions: Monte Carlo+ RISM integral equations

A new (hybrid) method is reported for modelling complex macromolecular systems. The approach combines the traditional atomistic Monte Carlo (MC) computer simulation of flexible polymer chains with the numerical solution of the site-site Ornstein-Zernike-like (RISM) integral equations. The method is used for calculating properties of a linear polymer in dilute solution. Since the condensed-phase environment of a flexible macromolecule affects the equilibrium configuration probability distribution of the macromolecule, the site-site intramolecular correlation function and the intramolecular potential field are treated in a self-consistent manner. Briefly, the MC method is applied to generate the configurations of a single chain molecule. Using the coordinates of chain beads, the averaged intrapolymer correlation function is obtained. Then, solving the coupled RISM equations for a given density of solvent particles, we find the polymer-solvent correlation functions. This yields the medium-induced intrapolymer potential and the corresponding effective intramolecular energies, which are used in the standard Metropolis MC procedure. The structural properties of the polymer chain are computed by averaging over the statistically representative set of configurations. As a result of many such iterations, the intramolecular structure is determined self-consistently. Using the hybrid MC/RISM method, extensive studies have been made of static properties of flexible polymer chains surrounded by LJ particles with purely repulsive interactions between the particles and chain beads. Also, direct molecular dynamics simulations have been carried out and have demonstrated that the hybrid MC/RISM approach gives a quite accurate prediction for condensed-phase effects.     

Coherent effects in multiple scattering of linearly polarized light

Comparing the stochastic Monte Carlo technique with the iteration procedure for solving the Bethe-Salpeter equation in the framework of numerical simulation, the time correlation function and the interference component of the coherent backscattering of a linearly polarized light wave in a multiply scattering medium are calculated. The results of the simulation agree well with theoretical results obtained by generalizing the Milne solution, as well as with experimental data.     

Stochastic modeling of coherent phenomena in strongly inhomogeneous media

A procedure of numerical simulation for coherent phenomena in multiply scattering media is developed on the basis of the juxtaposition of a Monte Carlo stochastic method with an iterative approach to the solution of the Bethe-Salpeter equation. The time correlation function and the interference component of coherent backscattering are calculated for scalar and electromagnetic fields. The results of simulation are in good agreement with experimental results, as well as with theoretical results obtained by generalizing the Milne solution.     

MC simulation results for a hard core model of carbon tetrachloride

Monte Carlo simulations on a hard tetrahedron fluid (hard core model of CCl₄) have been performed. The average site-site correlation functions, their generalized (1, 0, 0) spherical harmonic expansion coefficients, equation of state, and virial coefficients have been calculated and compared with theoretical methods currently available. The RISM equation is less accurate for the model studied than for simpler models considered so far. For the equation of state the best results are obtained from the Boublik-Nezbeda equation which agrees with the simulation results throughout the density range considered.     

The structure of liquid bromine

The atom-atom correlation function for liquid bromine, derived from the X-ray diffraction studies reported in the preceding paper, is compared with the results of Monte Carlo computer simulations and reference site interaction model (RISM) calculations for various bromine-like model molecules. The models used included the two-centre Lennard-Jones interaction model, both by itself and with idealized point quadrupole and quadrupole-induced dipole interaction terms in the computer simulations, and two and three-centre hard-sphere models in RISM. None of these models lead to atom-atom correlation functions which are in good agreement with that obtained from experiment. This suggests that additional information about the interactions between bromine molecules will be needed before the structure of liquid bromine can be completely understood. Finally, by comparing the results of our computer simulations with RISM results for analogous models, we obtain some insight into the accuracy of the reference site interaction model.     

Percus-Yevick theory and the Chandler-Weeks-Andersen reference fluid

Chandler, Weeks and Andersen have recently developed a successful perturbation theory of liquids. In their theory, the radial distribution function of the reference fluid is calculated from that of the hard-sphere fluid. In their published work, the Percus-Yevick theory is used to calculate the hard-sphere radial distribution function. In this paper, the Percus-Yevick theory is used to calculate directly the thermodynamic properties and radial distribution function of the reference fluid. If the Carnahan and Starling averaging procedure is used, the Percus-Yevick thermodynamic properties are excellent. However, the radial distribution function shows the same discrepancies as that of Chandler, Weeks and Andersen. Finally, recent calculations of Chandler, Weeks and Andersen, using the Monte Carlo estimates of the hardsphere radial distribution function are shown to give good results for the reference fluid distribution function. This indicates that the Percus-Yevick theory, rather than fundamental errors in the Chandler, Weeks and Andersen theory, is responsible for the discrepancies.     

Aerothermodynamics of Satellite During Atmospheric Reentry for the Whole Range of Gas Rarefaction: Influence of Inelastic Intermolecular Collisions

The aerothermodynamic characteristics of the Brazilian satellite Satélite de Reentrada Atmosférica were calculated for orbital-flight and atmospheric-reentry conditions with the direct simulation Monte Carlo method for a diatomic gas. The internal modes of molecule energy in the intermolecular interaction, such as the rotational energy, were taken into account. The numerical calculations cover a range of gas rarefactions wide enough to embrace the free-molecule and hydrodynamic regimes. Two Mach numbers were considered: 10 and 20. Numerical results include the drag force of the satellite, the energy flux, pressure coefficient, and skin friction coefficient over the satellite surface, the density and temperature distributions, and streamlines of the gas flow around the satellite. The influence of the satellite temperature upon these characteristics was evaluated at different satellite temperatures.     

Diffusion in heterogeneous lattices

We present here the results of our investigations of particle diffusion over different heterogeneous lattices with deep and shallow adsorption sites. A general analytical expression for chemical diffusion coefficient has been derived for a number of inhomogeneous lattices of different dimensionality and symmetry. We have calculated coverage dependencies of diffusion coefficients. The analytical data have been compared with the numerical data obtained by the kinetic Monte Carlo simulations. Almost perfect agreement between the respective results has been found.     

Charged hard spheres in a uniform neutralizing background

Monte Carlo computations for the thermodynamic properties and pair distribution function of a one-component system of charged hard spheres in a uniform neutralizing background are compared with perturbation theories. These are the ‘mixed’ integral equation approach proposed by Lado, the exponential approximation of Andersen and Chandler, a higher-order cluster expansion approximation due to Stell and Verlet and Weis and the mean spherical approximation (MSA). It is shown that, while none of these approximations gives satisfactory results for the pair distribution function, both the MSA and the mixed integral equation approach give internal energies in excellent agreement with the Monte Carlo results.     

Andersen–Weeks–Chandler Perturbation Theory and One-Component Sticky-Hard-Spheres

We apply second order Andersen–Weeks–Chandler perturbation theory to the one-component sticky-hard-spheres fluid. We compare the results with the mean spherical approximation, the Percus–Yevick approximation, two generalized Percus–Yevick approximations, and the Monte Carlo simulations.     

Far-infra-red absorption of non-polar liquids

A new conformal solution theory using a single pure fluid as a reference substance for the calculation of thermodynamic properties of fluid mixtures is developed. The perturbation theory developed by Weeks, Chandler and Andersen (WCA) and by Verlet and Weis (VW) is used to calculate the reference properties. The mean density approximation and corresponding state principle are used to eliminate the higher order terms in the mixture system and to derive the pseudo-parameters for the reference system. The mixture properties are obtained from the reference properties and their corresponding hard sphere excess functions defined as the properties of the mixture less the value of the properties for the hard sphere mixture.

The excess functions of mixing for several liquid mixtures of Lennard-Jones fluids, obeying the Lorentz-Berthelet rule, are calculated by the new method (VW-HSE). Comparison with the results of other theories and Monte Carlo data shows definite improvement. Since only the properties of a pure reference fluid are directly calculated, the method can be applied to more complicated multicomponent systems without additional computational effort as required by other theories.     

Perturbation theory for mixtures of simple liquids

The perturbation approach developed by Weeks, Chandler, and Andersen (WCA) and by Verlet and Weis (VW) for pure systems is here generalized to the case of mixtures. We study binary mixtures of molecules interacting with the 12–6 Lennard-Jones potential, for which Monte Carlo simulations are available for comparison. The work is divided into two parts: The first part presents results of Monte Carlo calculations on mixtures of hard spheres of 864 and 1000 particles. The radial distribution functions generated are used to test the VW representation for the correlation functions of hard-sphere mixtures. This representation is found to work satisfactorily within the expected error limits. The second part deals with the two-step perturbation procedure for calculating the thermodynamic quantities of the Lennard-Jones system. The Lennard-Jones potential is divided into a reference potential, which is strictly repulsive, and an attractive part. The system of the reference potential is represented by a system of hard-sphere mixture with equivalent diameters determined by the WCA rule. Analytical expressions are given for evaluating these equivalent diameters. The Lennard-Jones system is then recovered to the first order by a λ expansion over the reference system. Comparison with Monte Carlo results for a mixture of Lennard-Jones molecules, obeying the Berthelot rule, shows that the total thermodynamic properties are reproduced by the perturbation theory to 1 per cent, while the agreement in excess properties is only moderately successful, similar to some other analytical theories compared here. To reproduce these excess properties, which are extremely small, a precision of 0·1 per cent in the theory is required. The present theory is estimated to be accurate to 1 per cent in view of the successive approximations made.     

A Monte Carlo model for seeded atomic flows in the transition regime

A simple model for the numerical determination of separation effects in seeded atomic gas flows is presented. The model is based on the known possibility to provide a statistically convergent estimate of the exact solution for a linear transport equation using the test particle Monte Carlo method. Accordingly, the flow field of the main gas is preliminary calculated and as a second step the linear transport equations obtained by fixing the target distribution in the collision term of the Boltzmann equation for both main and minority components are solved. Both solutions are based on appropriately devised test particle Monte Carlo methods. The second step, the critical one in evaluating the separation effects, is exact and thereby completely free of numerical diffusion. The model is described in details and illustrated by 2D test cases of atomic separation in shock fronts.     

考虑中子泄漏修正的快堆蒙特卡罗少群截面参数制作与验证方法

一种基于B1均匀化方程的泄漏修正模型在连续能量蒙特卡罗程序TRIPOLI4中得以实现并且用于制作少群截面参数。此蒙卡泄漏修正模型通过在连续能量的蒙卡模拟以及求解B1均匀化方程之间迭代,最终得到蒙卡模拟下的临界状态。通过此方法得到的少群截面参数较其他蒙卡以及确定论方法有两点显著优势：用于求解B1均匀化方程的少群常数是用通过临界状态的通量谱得到的;考虑了泄漏效应的蒙卡模拟可以更真实地反映组件计算时的能谱状态。为验证此泄漏修正模型,一个由连续能量的TRIPOLI4模拟而得到的数值临界实验被用于分析与比较。通过与其他蒙卡程序SERPENT以及确定论程序ECCO进行结果对比,可证明此B1泄漏修正方法能够给出更精确的用于堆芯计算的少群截面参数。     

用全带Monte Carlo方法模拟纤锌矿相GaN和ZnO材料的电子输运特性

报告了用全带MonteCarlo方法模拟纤锌矿相GaN和ZnO材料电子输运特性的结果.模拟所用的能带结构数据是用经验赝势法算得的.通过模拟得到了两种材料的平均漂移速度和平均能量与电场强度关系曲线,求得了电子迁移率.并且将两种材料的结果以及文献报道的GaAs的模拟结果进行了比较 关键词： 蒙特卡罗模拟 GaN ZnO 输运特性 能带结构     

Long-wavelength coherent radio radiation of cascades. I. Calculation within the cascade theory

The long-wavelength limit for radio radiation from high-energy particle cascades was calculated within the cascade theory taking into account the processes resulting in an negative excess. The results obtained were compared to the results of Monte Carlo numerical calculations.     

The scattering spectra and color of disperse systems of weakly absorbing particles

The scattering spectra of weakly absorbing systems of spherical particles are calculated using various approximate and numerical methods. Comparative estimates are made for applicability of the single-scattering and mean-field approximations and the Monte Carlo computer simulation for different scattering multiplicities. The results of the calculations well agree with the experimental scattering spectra of the crystalline lens. Based on the spectral characteristics obtained, the chromaticity coordinates are calculated and regularities in variations of the color characteristics are analyzed as functions of the disperse system parameters.