偏振光在非球形气溶胶中传输特性的Monte Carlo仿真

非球形气溶胶是影响辐射传输的重要因素. 系统给出了矢量辐射传输Monte Carlo模型, 并验证了其准确度; 考虑入射光偏振态, 讨论了不同方向漫射光Stokes矢量对气溶胶形状的敏感性; 分析了气溶胶形状、入射光偏振状态对光波退偏振度、透过率及反射率的影响. 模拟仿真结果表明, 对于不同偏振态的入射光, 不同方向的Stokes矢量对气溶胶形状变化的灵敏程度并不一致, 而在天顶角0°方向区域,Q, U及V分量对形状的灵敏程度普遍不高; 气溶胶形状对反射漫射光退偏程度的影响强于透射漫射光, 入射光偏振态不同, 漫射光退偏程度也存在较大差异. 气溶胶形状对光波整体透过率与反射率影响显著, 且该影响随传播距离增大而增大; 入射光偏振态对透过率与反射率影响相对较小, 与自然光相比, 水平偏振光透过率略偏小, 反射率略偏大, 垂直偏振光反之, 圆偏振光与自然光的模拟结果相当.     

Convergence of a Distributional Monte Carlo Method for the Boltzmann Equation

Direct Simulation Monte Carlo (DSMC) methods for the Boltzmann equation employ a point measure approximation to the distribution function, as simulated particles may possess only a single velocity. This representation limits the method to converge only weakly to the solution of the Boltzmann equation. Utilizing kernel density estimation we have developed a stochastic Boltzmann solver which possesses strong convergence for bounded and $L^\infty$ solutions of the Boltzmann equation. This is facilitated by distributing the velocity of each simulated particle instead of using the point measure approximation inherent to DSMC. We propose that the development of a distributional method which incorporates distributed velocities in collision selection and modeling should improve convergence and potentially result in a substantial reduction of the variance in comparison to DSMC methods. Toward this end, we also report initial findings of modeling collisions distributionally using the Bhatnagar-Gross-Krook collision operator.     

混响室的概率统计分析方法及其蒙特卡罗模拟

提出了一种研究混响室问题的理论分析方法,从理想混响室的离散概率模型出发,采用蒙特卡罗模拟来获得室内电磁场量及其相关物理量的概率统计特性。运用该方法获得了混响室内若干场量（均为归一化值）的概率密度函数、室内一段均匀无耗单导体传输线的负载平均耦合截面及负载电流响应模值的概率分布,所得结果与已有文献给出的结果（包括由解析公式计算或测量所得的结果）吻合良好。由于蒙特卡罗方法的普适性,采用该方法可以获得任意待分析参量的全部概率统计特性（只要样本数足够大）。同时该方法无需针对具体混响室进行,只要在其测试区域能较好地与理想混响室的基本概率模型相吻合,就能给出较精确的计算结果,且其计算量远远小于基于全波分析的蒙特卡罗方法。     

Quantum Monte Carlo assessment of density functionals for π-electron molecules: ethylene and bifuran

ABSTRACT

We perform all-electron, pure-sampling quantum Monte Carlo (QMC) calculations on ethylene and bifuran molecules. The orbitals used for importance sampling with a single Slater determinant are generated from Hartree-Fock and density functional theory (DFT). Their fixed-node energy provides an upper bound to the exact energy. The best performing density functionals for ethylene are BP86 and M06, which account for 99% of the electron correlation energy. Sampling from the π-electron distribution with these orbitals yields a quadrupole moment comparable to coupled cluster CCSD(T) calculations. However, these, and all other density functionals, fail to agree with CCSD(T) while sampling from electron density in the plane of the molecule. For bifuran, as well as ethylene, a correlation is seen between the fixed-node energy and deviance of the QMC quadrupole moment estimates from those calculated by DFT. This suggests that proximity of DFT and QMC densities correlates with the quality of the exchange nodes of the DFT wave function for both systems.     

FTO客体3m闪光照相的Monte Carlo研究

研究了客体模型FTO的闪光照相系统X光输运过程,给出了直穿照射量、散射照射量、直散比、直穿照射量能谱、散射照射量能谱、直穿X光通量能谱和散射X光通量能谱在记录平面的空间分布。结果表明：后锥是照射量散射成分的主要来源,后锥照射量占总散射量97%;后锥也是造成散射的空间分布不均匀的主要器件,这一不均匀性高达58%。照相系统的最小直散比非常小,表明锥造成的散射已经严重地淹没了直穿（轫致辐射）信号。计算中使用高空间分辨率记录法进行分点,合成图像对吸收系数的复原结果与国外报道的结果相符。     

应用Monte Carlo方法模拟爆轰产物状态方程的研究进展

 应用Monte Carlo方法模拟爆轰产物状态方程,区别于建立在球形分布分子势基础上的传统爆轰产物状态方程计算方法,从原子水平上直接模拟实际炸药的爆轰产物状态方程,克服了传统方法中混合产物状态方程不精确的缺点。综述了该方法的历史背景及发展现状。对模拟中宏观量的描述、统计平均的计算、势函数的选取及边界条件进行了详尽描述。     

The quantum equation of state until the fourth virial coefficient for many‐component plasmas

The aim of the present article is to calculate the quantum excess free energy until the fourth virial coefficient in terms of Slater sums for neutral many‐component plasmas. We used the results to calculate the equation of state; we used the thermal equilibrium plasma. Bound states are not taken into account in this work.     

Quasi-2D Monte Carlo simulations of phase transitions and internal aggregate structures in a highly dense suspension composed of magnetic plate-like particles

The phase transitions and the internal aggregate structures of a highly dense suspension composed of magnetic plate-like particles with a magnetic moment normal to the particle axis have been investigated by means of the Monte Carlo method. The present study considered a quasi-2D system in order to clarify the influences of the volumetric fraction of particles and the magnetic field strength on particle aggregations and phase transitions. The internal structures of particle aggregates have been discussed quantitatively in terms of pair correlation functions, orientational pair correlation functions, nematic and polar order parameters. The main results obtained here are summarized as follows. When the influence of the magnetic interaction between particles is of the same order of that of the perpendicular magnetic field strength, the particles form column-like clusters, and the internal structure of the suspension shows solid-like structures. For the case of a strong applied magnetic field, the internal structure is transformed from solid-like structures into isotropic ones. However, as the volumetric fraction increases, the particles form brick wall-like structures under the situation of a strong applied magnetic field, and the internal structure exhibits solid-like ones. The brick wall-like structures also appear for a relatively weak magnetic field applied along the in-plane direction despite a slightly smaller volumetric fraction compared with the case of the perpendicular applied magnetic field.     

Finite Size Effect in Path Integral Monte Carlo Simulations of 4He Systems

Path integral Monte Carlo (PIMC) simulations are a powerful computational method to study interacting quantum systems at finite temperatures. In this work, PIMC has been applied to study the finite size effect of the simulated systems of ⁴He. We determine the energy as a function of temperature at saturated-vapor-pressure (SVP) conditions in the temperature range of T∈[1.0 K, 4.0 K], and the equation of state (EOS) in the ground state for systems consisted of 32, 64 and 128 ⁴He atoms, respectively. We find that the energy at SVP is influenced significantly by the size of the simulated system in the temperature range of T∈[2.1 K, 3.0 K] and the larger the system is, the better results are obtained in comparison with the experimental values; while the EOS appeared to be unrelated to it.     

Quasi-2D Monte Carlo simulations of a colloidal dispersion composed of magnetic plate-like particles with magnetic moment normal to the particle axis

We have investigated aggregation phenomena of a colloidal dispersion composed of magnetic plate-like particles by means of Monte Carlo simulations. Such plate-like particles have been modelled as disk-like particles with magnetic moment normal to the particle axis at the particle centre, with the section shape of a spherocylinder. The main objective of the present study is to clarify the influences of the magnetic field strength and magnetic interactions between particles on particle aggregation phenomena. We have concentrated our attention on a quasi-2D system from an application point of view such as the development of surface quality changing technology using such magnetic plate-like particles. A magnetic field is applied along the direction perpendicular to the plane of the monolayer. Internal structures of particle aggregates are discussed quantitatively in terms of radial distribution and orientational pair correlation functions. For the case of strong magnetic interactions between particles, particles form long column-like clusters with their magnetic moments alternating in direction between the neighbouring particles. These tendencies appear under circumstances of a weak applied magnetic field. However, as the magnetic field strength increases, particles incline towards the magnetic field direction, so that particles do not form such clusters.     

Finite Size Effect in Path Integral Monte Carlo Simulations of ^4He Systems

Path integral Monte Carlo （PIMC） simulations are a powerful computational method to study interacting quantum systems at finite temperatures. In this work, PIMC has been applied to study the finite size effect of the simulated systems of ^4He. We determine the energy as a function of temperature at saturated-vapor-pressure （SVP） conditions in the temperature range of T ∈ [1.0 K,4.0 K], and the equation of state （EOS） in the grmmd state For systems consisted of 32, 64 and 128 ^4He atoms, respectively, We find that the energy at SVP is influenced significantly by the size of the simulated system in the temperature range of T ∈ [2.1 K, 3.0 K] and the larger the system is, the better results are obtained in comparison with the experimental values; while the EOS appeared to be unrelated to it.     

Three Semi-empirical Analytic Expressions for the Radial Distribution Function of Hard Spheres

Three simple analytic expressions satisfying the limitation condition at low densities for the radial distribution function of hard spheres are developed in terms of a polynomial expansion of nonlinear base functions and the Carnahan--Starling equation of state. The simplicity and precision for these expressions are superior to the well-known Percus--Yevick expression. The coefficients contained in these expressions have been determined by fitting the Monte Carlo data for the first coordination shell, and by fitting both the Monte Carlo data and the numerical results of Percus-Yevick expression for the second coordination shell. One of the expressions has been applied to develop an analytic equation of state for the square-well fluid, and the numerical results are in good agreement with the computer simulation data.     

Thermodynamic properties of the Lennard-Jones FCC solid: perturbation theory parameterisation and Monte Carlo simulation

This work is concerned with a valid representation of the solid-phase equation of state (EOS), the validity of which is evaluated by comparing to Monte Carlo (MC) simulation results. The proposed EOS has been developed by employing an optimal division of the Lannard-Jones (LJ) potential and an effective temperature- and density-dependent diameter into the framework of the simplified perturbation theory. Then, with the aim of extending to the chain systems, the conventional chain contribution (i.e. TPT1) is added to the proposed model (i.e. the atomic LJ system). Finally, the solid-state EOS based on Helmholtz free energy will be introduced for low temperature and high density conditions. To verify the accuracy of the proposed model, its performance is compared with the results of MC simulation. The comparison between the obtained results from the proposed model and the MC simulations shows that the EOS can satisfactorily predict the properties of the solid LJ system, both for the atomic system and for the chains.     

Caged H atom and H2 molecule in relation to Monte Carlo study of molecular dissociation at constant volume

Summary Analytic results for electronic kinetic energy are first presented for a hydrogen atom in a spherical cage for two radii near to the corresponding densities employed in the path-integral Monte Carlo study of isochoric molecular dissociation in dense hydrogen by Magroet al. (Magro W. R., Ceperley D. M., Pierleoni C. andBernu B.,Phys. Rev. Lett.,76 (1996) 1240). The relevance of the ?cage? results to the behaviour of dense atomic hydrogen is pointed out. Attention is then shifted to the molecular regime, and the variation with density of electronic kinetic energy for a H₂ molecule in a rigid spheroidal cage is compared and contrasted with the Monte Carlo findings. The rigid-cage model mimics this, as well as bond length contraction, under compression.     

低场低能区金刚石内载流子飞行时间的蒙特卡洛模拟

金刚石是一种重要的宽禁带半导体材料,对金刚石内载流子输运过程的研究将有助于了解金刚石用作各种电子器件的潜能。利用Monte Carlo模拟方法,研究了在低场低能区金刚石内载流子的飞行时间。在模拟中考虑了抛物线型能带模型和声学声子散射机制,以及样品对光的吸收和载流子在Brillouin区边界的Bragg反射。通过模拟,得到了低场低能区金刚石材料内载流子的飞行时间分布,并与相关的实验结果进行了比较分析,验证了该模拟模型的正确性。研究结果表明,在低场低能区,金刚石材料内主要的散射机制是声学声子散射。在研究金刚石材料内载流子的迁移输运问题时,可以采用较为简单的抛物线型能带模型,但在研究薄样品中的载流子输运时应当考虑材料的光吸收对初始载流子分布的影响,而且在场强较高以及样品厚度较大时,应当考虑载流子在Brillouin区边界的Bragg反射。     

Pressure-volume relations for Zn,Cd, Ga,In and TI at room temperature to 30 GPa and above

Abstract

The elemental metals Zn, Cd, Ga, In and TI are studied by energy dispersive X-ray diffraction under pressures up to 30 GPa and above. Room temperature equation of state (EOS) data are derived and compared with results of earlier static and dynamic measurements at lower and higher pressures, respectively.     

液相及固/液混合相区金属物态方程Grover模型存在的问题及修正

借助无序熵的概念, 直接推导出了液相金属的物态方程. 再利用固/液混合相区的熔化分数与其中固相、液相比体积之间的一般性关系, 替代了传统Grover模型中采用的熔化分数与温度成正比的近似条件, 得出更准确的固/液混合相区状态方程的表述形式. 修正后的物态方程解决了传统Grover模型中的固线、液线以及熔化线在P-T图上不一致的问题, 得到了更为符合物理事实的结果.     

A unified Monte Carlo treatment of the transport of electromagnetic energy, electrons, and phonons in absorbing and scattering media

The scalar Boltzmann transport equation (BTE) is often applicable to radiative energy transfer, electron-beam propagation, as well as thermal conduction by electrons and phonons provided that the characteristic length of the system is much larger than the wavelength of energy carriers and that certain interference phenomena and the polarization nature of carriers are ignored. It is generally difficult to solve the BTE analytically unless a series of assumptions are introduced for the particle distribution function and scattering terms. Yet, the BTE can be solved using statistical approaches such as Monte Carlo (MC) methods without simplifying the underlying physics significantly. Derivations of the MC methods are relatively straightforward and their implementation can be achieved with little effort; they are also quite powerful in accounting for complicated physical situations and geometries. MC simulations in radiative transfer, electron-beam propagation, and thermal conduction by electrons and phonons have similar simulation procedures; however, there are important differences in implementing the algorithms and scattering properties between these simulations. The objective of this review article is to present these simulation procedures in detail and to show that it is possible to adapt an existing MC computer code, for instance, in radiative transfer, to account for physics in electron-beam transport or phonon (or electronic thermal) conduction by sorting out the differences and implementing the correct corresponding steps. Several simulation results are presented and some of the difficulties associated with different applications are explained.     

Monte Carlo algorithm for drift and diffusion of ions in anisotropic,non-homogeneous media

A new Monte Carlo algorithm for ion transport in two-dimensional anisotropic media is reported. It is based on physical considerations of drift and diffusion in anisotropic media with or without an impermeable boundary. Inhomogeneities in the medium and electric field can be taken into account by averaging along the ion trajectory. The algorithm has been applied to the calculation of ion transport in liquid crystal displays and has been successfully compared with a finite difference program on a one-dimensional liquid crystal structure.