ISSDE:基于第一性原理随机微分方程的碰撞等离子体隐式模拟

开发一种适用于求解含库仑碰撞等离子体随机微分方程（SDE）的第一性原理隐式模拟程序——Implicit Stratonovich Stochastic Differential Equations （ISSDE）.该程序基于Fokker-Planck （FP）方程与Stratonovich SDE的等价性理论，通过精确求解Stratonovich SDE达到对FP方程的高效第一性原理计算的目标.ISSDE采用隐式格式保证求解的数值稳定性，同时可以保证粒子碰撞过程的能量守恒.ISSDE基于C++语言开发，具有标准接口和灵活的可扩展模组.通过模拟电子束在非磁化和磁化致密等离子体中的慢化过程验证ISSDE的正确性，并展示该程序在碰撞等离子体模拟中的应用.     

Dynamic properties of the Monte Carlo method in statistical mechanics

By means of the Monte Carlo sampling technique the equilibrium thermodynamics of fluids and magnets can be calculated numerically. We show that the questions of convergence and accuracy of this method can be understood in terms of the dynamics of the appropriate stochastic model. Also, we discuss to what extent various choices of transition probabilities lead to different dynamic properties of the system. As examples of applications, we consider Ising and Heisenberg spin systems. The numerical results about the dynamic correlation functions are compared to simple approximations taken from the theory of the kinetic Ising model.     

Reverse Monte Carlo iterative algorithm for quantification of X-ray fluorescence analysis based on MCNP6 simulation code

Reverse Monte Carlo iterative algorithm has been developed for quantification of energy-dispersive X-ray fluorescence analysis in order to calculate the concentrations of the elementary composition in solid substances. The core of the simulation code was the MCNP6 that is a well-established and widely applied software package in the nuclear research and practice for simulation of nuclear systems or the full process of gamma- or X-ray spectrometry. The reverse Monte Carlo algorithm and the full analytical procedure was tested by quantitative XRF analysis of reference alloy samples. The atomic compositions of the reference samples were determined by reverse Monte Carlo technique and also fundamental parameter method and by spark emission atomic spectroscopy. The agreement between the results of these three analytical methods was found within the standard deviations of the major elements of the samples. The total duration of the reverse Monte Carlo numerical computation was minimized to a few minutes using the variance reduction procedures available in the MCNP6.     

基于VERA基准题的cosRMC程序验证

为了验证反应堆物理软件和方法的计算能力,美国CASL (Consortium for Advanced Simulation of LWRs) 项目提出了VERA (Virtual Environment for Reactor Application) 堆芯物理基准题。该基准题以Watts Bar初始堆芯为模型,涵盖从二维单栅元到三维全堆芯的燃耗及换料的十个基准问题。针对VERA基准题模型,利用COSINE软件包中的反应堆蒙特卡罗分析程序cosRMC进行临界计算,得到了有效增殖因子、组件功率分布、控制棒微积分价值和反应性系数等结果。通过与基准题中提供的KENO结果对比,两种蒙特卡罗程序的计算结果吻合良好。这表明cosRMC程序具有从组件到堆芯的计算能力,其临界计算精度基本与KENO程序相当。     

A comment on the paper “Stochastic feedback, nonlinear families of Markov processes, and nonlinear Fokker-Planck equations” by T.D. Frank

The purpose of this comment is to correct mistaken assumptions and claims made in the paper “Stochastic feedback, nonlinear families of Markov processes, and nonlinear Fokker-Planck equations” by T. D. Frank [T.D. Frank, Stochastic feedback, non-linear families of Markov processes, and nonlinear Fokker-Planck equations, Physica A 331 (2004) 391]. Our comment centers on the claims of a “non-linear Markov process” and a “non-linear Fokker-Planck equation.” First, memory in transition densities is misidentified as a Markov process. Second, the paper assumes that one can derive a Fokker-Planck equation from a Chapman-Kolmogorov equation, but no proof was offered that a Chapman-Kolmogorov equation exists for the memory-dependent processes considered. A “non-linear Markov process” is claimed on the basis of a non-linear diffusion pde for a 1-point probability density. We show that, regardless of which initial value problem one may solve for the 1-point density, the resulting stochastic process, defined necessarily by the conditional probabilities (the transition probabilities), is either an ordinary linearly generated Markovian one, or else is a linearly generated non-Markovian process with memory. We provide explicit examples of diffusion coefficients that reflect both the Markovian and the memory-dependent cases. So there is neither a “non-linear Markov process”, nor a “non-linear Fokker-Planck equation” for a conditional probability density. The confusion rampant in the literature arises in part from labeling a non-linear diffusion equation for a 1-point probability density as “non-linear Fokker-Planck,” whereas neither a 1-point density nor an equation of motion for a 1-point density can define a stochastic process. In a closely related context, we point out that Borland misidentified a translation invariant 1-point probability density derived from a non-linear diffusion equation as a conditional probability density. Finally, in the Appendix A we present the theory of Fokker-Planck pdes and Chapman-Kolmogorov equations for stochastic processes with finite memory.     

Investigating the spatial specificity of S2-SSFP fMRI: A Monte Carlo simulation approach

The desirable spatial specificity of spin echo (SE) fMRI cannot be efficiently utilized in high fields due to specific absorption rate (SAR) and B1 inhomogeneity problems. Consequently, S2-SSFP fMRI has been suggested as an alternative to mitigate these problems. Nevertheless, no accurate analysis has been performed thus far to evaluate spatial specificity of this technique. To study spatial specificity, we performed Monte Carlo simulations for evaluating the micro-vasculature contribution in functional contrast along with vessel size sensitivity estimations for a range of relevant imaging parameters. Results showed a spatial specificity at the level of SE fMRI. Simulations further revealed that similar to SE fMRI, an effective echo time (TE) close to the tissue T₂ maximizes the micro-vasculature contribution in the obtained contrast. The amount of this contribution, however, showed a slight decrease at ultra-high fields compared to SE fMRI. As for vessel size sensitivity, simulations presented a pattern for S2-SSFP similar to SE fMRI but with a minor shift toward larger vessels. These results are in general agreement with reported experimental studies. Our findings also suggest that the effect of older pathways, rather than primary SE pathway, might be responsible for the observed discrepancies between S2 and SE. Based on this study, provided that optimum experimental parameters are used, S2, with its desirable micro-vasculature contribution and high sensitivity to small vessels, is a promising low SAR approach to replace SE fMRI in high field.     

基于负氢离子源的全三维PIC/MCC模拟算法研究

在分析负氢离子源中等离子体物理机理基础下, 研究并优化粒子模拟算法, 设计高效的粒子存储方法. 研究并运用粒子碰撞蒙特卡罗方法, 考虑等离子体势以及带电粒子间库仑碰撞, 研制了全三维粒子模拟/蒙特卡罗算法(PIC/MCC). 采用磁荷模型, 运用时域有限差分方法计算多峰磁场, 并结合国外负氢离子源JT-60U, 考虑负氢离子源中主要反应, 对全三维PIC/MCC模拟算法模拟验证.     

基于蒙特卡罗的小尺度参考辐射装置屏蔽研究

针对移动式小尺度参考辐射（MRR）装置（移动式校准装置）,在进行射线辐射剂量测量的仪器仪表标定或刻度时,应满足其辐射屏蔽安全限值5 Sv/h的屏蔽技术要求,采用蒙特卡罗输运程序MCNP,开展了移动式小尺度参考辐射装置表面剂量场屏蔽的模拟计算和研究分析工作。研究结果表明,通过MCNP模拟的屏蔽设计方法可以详尽反映MRR装置各个表面的剂量分布特征和规律,实现移动式小尺度参考辐射装置屏蔽设计,采用的铅钢材料复合屏蔽方案能够保证装置硬度且显著地减轻屏蔽体的重量,最终获取的优化MRR屏蔽箱体重量约为271.9 kg。     

AO3D: A Monte Carlo code for modeling of environmental light propagation

A Monte Carlo radiative transfer program (Atmosphere-Ocean 3-Dimensional, AO3D) for modeling the coupled atmosphere-ocean environment has been developed. The code allows for the specification of optical properties for the atmosphere, land and ocean. Light rays are tracked as they pass between the atmosphere and the ocean, reflect off the ocean surface, the ocean floor, and off land, or are absorbed. In this version the polarization of light rays is not considered. The optical properties of each horizontally homogeneous layer within the atmosphere and ocean can be set on a layer-by-layer basis with a choice of phase functions, absorption and scattering coefficients, and index of refraction. A wind-dependent Cox and Munk ocean surface realization (with whitecaps) is implemented to model refraction and reflection from surface waves. Either spherical- or flat-Earth models can be used, and all refraction and reflection are accounted for. The AO3D model has been tested by parts, and as a whole by comparison with single- and total-scattering calculations from other radiative transfer codes. Comparisons with Monte Carlo calculations by Adams and Kattawar (agreement in TOA radiance within the published precision ∼2%), MODTRAN4 (agreement in spherical-shell atmosphere (SSA) sky radiance within about 2%) and Coupled DIScrete Ordinate Radiative Transfer (COART) (agreement in plane-parallel (PP) sky radiance within 2%) are shown. Sun photometer measurements (including large air mass values) at the Mauna Loa Observatory are compared to AO3D simulations (for a spherical Earth) and suggest that a thin aerosol layer was present above the observatory at the time of the measurements.     

Solvable models of the Fokker-Planck equation: An approach based on the Gel'fand-Levitan method

From a given solvable Fokker-Planck equation one can construct a number of other solvable models for diffusion in a stable or bistable potential fields using the Gel'fand-Levitan method of the inverse scattering theory. The simplest way of achieving this is to change the lowest eigenvalue and/or the normalization of the lowest eigenfunction of the ordinary differential equation obtained by separating the time-dependent part. For these cases it is shown that the new probability distribution is expressible in terms of integrals involving the original probability distribution and the Gel'fand-Levitan kernel. The possibility of changing the lowest eigenvalue enables one to find bistable potential fields which would correspond to a well-defined long time relaxation rate for the probability current.     

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.     

一种晶体表面水平纳米线生长机理的蒙特卡罗模拟研究

采用动力学蒙特卡罗方法模拟,发现在较低过饱和度流体中对称性破缺的简单立方晶体光滑（001）表面上基于晶核的水平纳米线的生长机理．在此基础上,进一步研究了各向异性的表面上经向和纬向热粗糙度对纳米线形貌的影响,分析了纳米线的生长随时间的变化,并系统讨论了纳米线生长速率与表面经向和纬向热粗糙度、过饱和度、晶面尺寸以及表面扩散作用的依赖关系．     

基于Monte Carlo的热脉冲法数据分析

热脉冲法是测量聚合物介质薄膜空间电荷分布的有效方法之一, 其数据的分析涉及第一类Fredholm积分方程, 只能采用合适的数值计算方法进行求解, 而Monte Carlo法是近年来提出的数值求解该方程的方法之一. 本文尝试使用Monte Carlo法在频域内实现热脉冲数据的分析, 通过一系列模拟计算讨论Monte Carlo法的分析效果. 计算结果表明: Monte Carlo法可实现对热脉冲法实验数据的有效分析, 提取被测薄膜内的电场分布, 而且计算的电场分布在整个样品厚度上都与真实分布较好地符合, 可有效地弥补尺度变换法只在样品表面附近获得较高准确度的缺陷. 该方法的局限性在于计算结果存在一定的振荡, 且在噪声和数据误差的影响下, 其准确性很大程度上依赖于奇异值分解过程中容差的选择, 在应用的方便程度方面还有待进一步提升.     

基于蒙卡和粒子示踪程序的电子成像模拟分析

借助理论分析和数值模拟,设计了基于高能电子束团的辐射成像系统,并通过Geant4和GPT软件对成像系统的相关参数进行了优化。模拟中分析了影响系统空间分辨率及物质厚度分辨率的因素,结果显示,模拟中设计的成像系统空间分辨率达到m量级,并且具有一定的厚度分辨能力。该设计指标满足对一定厚度及结构的样品进行成像的要求。     

闪烁光纤在γ射线辐照下部分特性的蒙特卡罗模拟

 闪烁光纤在射线成像方面的应用越来越广泛。为了进一步了解闪烁光纤在射线辐照下的基本特性，基于蒙特卡罗方法，利用计算机模拟分析了γ射线在闪烁光纤中的好事例率与光纤长度及射线能量的关系，能量沉积效率与光纤长度及射线能量的关系。此项工作对于闪烁光纤阵列在射线成像，剂量场测量等方面的研究很有价值。     

The effect of inactive impurities on a surface in NO-CO reaction: A Monte Carlo simulation

The interaction among the reacting species in the NO-CO reaction on a metal catalytic surface that proceeds according to the Langmuir-Hinshelwood thermal mechanism is studied by means of Monte Carlo simulations. The study of this system is essential for the understanding of the influence of impurities on the catalytic oxidation of NO by CO. It is found that this complex system exhibits irreversible phase transitions between active states with sustained reaction and poisoned states without reaction. The same system has also been investigated by non-thermal (Eley-Rideal) mechanism. Both the phase diagrams of the surface coverage and the steady state production of CO₂ and N₂ are evaluated as a function of the partial pressures of the reactants in the gas phase. From this study, it is observed that with the increase of impurities, the production rate reduces and the reaction stops at a certain point. Moreover, the first order transition in the phase diagram converts into second order phase transition that is in accordance with the experimental findings. Therefore, the first order phase transition, which is a characteristic of such catalytic reactions, is eliminated.     

Sol-gel obtained YSZ nanocrystals on a substrate: A Monte Carlo approach of the crystallographic orientation

Sol-gel obtained yttria stabilized zirconia (YZS) nanocrystals have different morphologies when they grow on an α-alumina substrate after thermal treatment. When the substrate has planar defects, the nanocrystals grow in height and are narrow with a crystallographic orientation in the vertical direction, while when the substrate is a perfect plane at the nanometric scale, the nanocrystals are rather extended over the substrate and do not grow in height, with a crystallographic orientation in the vertical direction. We present here a Monte Carlo approach which computes the actions of the substrate on the nanocrystals during thermal treatment: one action is the change in crystallographic orientation depending on the presence of defects and the other is the action on the morphology of the nanocrystals. The equivalent of thermal treatment is obtained after applying the Metropolis algorithm with adequate expressions of the energy depending on the inter-plane spacings and surface diffusion. Our numerical approach is in good agreement with the experimental results on the orientations and morphologies of the YSZ nanocrystals growing on a α-alumina substrate with planar defects [R. Bachelet, A. Boulle, B. Soulestin, F. Rossignol, A. Dauger, R. Guinebretiere, Thin Solid Films 515 (2007) 7080].     

基于Monte Carlo模拟的三种不同结构单电子动态存储器特性比较

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Mobility of large clusters on a semiconductor surface:Kinetic Monte Carlo simulation results

The mobility of clusters on a semiconductor surface for various values of cluster size is studied as a function of temperature by kinetic Monte Carlo method. The cluster resides on the surface of a square grid. Kinetic processes such as the diffusion of single particles on the surface, their attachment and detachment to/from clusters, diffusion of particles along cluster edges are considered. The clusters considered in this study consist of 150–6000 atoms per cluster on average.A statistical probability of motion to each direction is assigned to each particle where a particle with four nearest neighbors is assumed to be immobile. The mobility of a cluster is found from the root mean square displacement of the center of mass of the cluster as a function of time. It is found that the diffusion coefficient of clusters goes as D = A(T)Nαwhere N is the average number of particles in the cluster, A(T) is a temperature-dependent constant and α is a parameter with a value of about-0.64 α -0.75. The value of α is found to be independent of cluster sizes and temperature values(170–220 K)considered in this study. As the diffusion along the perimeter of the cluster becomes prohibitive, the exponent approaches a value of-0.5. The diffusion coefficient is found to change by one order of magnitude as a function of cluster size.