蒙特卡罗碰撞算法在CHIPIC软件中的数值实现

分析离子源中电子所参与的碰撞,利用电子与其它粒子间的空碰撞模型,研究电子之间的库仑碰撞,采用不同的存储和调用机制研制了两种碰撞模型的蒙特卡罗碰撞处理模块,将数值模块添加到粒子模拟软件CHIPIC中,对离子源JAERI 10A进行模拟验证,通过对模拟结果的分析,表明所设计的三维MCC算法正确.     

系综Monte Carlo方法

本文系统地给出了Monte Carlo模拟的一般方法在各种系综条件下的表述以及它们的算法。     

Simulation of Nuclear Reactor Kinetics by the Monte Carlo Method

The KIR computer code intended for calculations of nuclear reactor kinetics using the Monte Carlo method is described. The algorithm implemented in the code is described in detail. Some results of test calculations are given.     

Transition Matrix Monte Carlo Method

We present a formalism of the transition matrix Monte Carlo method. A stochastic matrix in the space of energy can be estimated from Monte Carlo simulation. This matrix is used to compute the density of states, as well as to construct multi-canonical and equal-hit algorithms. We discuss the performance of the methods. The results are compared with single histogram method, multi-canonical method, and other methods. In many aspects, the present method is an improvement over the previous methods.     

Particle-in-Cell/Monte Carlo Collision simulation of planar DC magnetron sputtering

In this paper a numerical simulation of a planar DC magnetron discharge is performed with the Particle-in Cell/Monte Carlo Collision （PIC/MCC） method. The magnetic field used in the simulation is calculated with finite element method according to experimental configuration. The simulation is carried out under the condition of gas pressure of 0.665 Pa and voltage magnitude of 400V. Typical results such as the potential distribution, charged particle densities, the discharge current density and ion flux onto the target are calculated. The erosion profile from the simulation is compared with the experimental data. The maximum erosion position corresponds to the place where the magnetic field lines are parallel to the target surface.     

Calculation of Prompt Fission Neutron Lifetimes by the Monte Carlo Method

An algorithm for calculation of prompt fission neutron lifetimes in a nuclear reactor by the Monte Carlo method is described. Evaluation of the importance function is carried out with solution of the neutron transport equation without solving the adjoint equation. The results of the prompt neutron lifetime calculations performed within some critical experiments are presented and compared with the experimental results.     

蒙特卡洛方法计算材料表面激发参数

电子非弹性散射平均自由程（IMFP）是用表面电子能谱进行表面化学定量分析时极为重要的一个参数,它可以用测量的弹性峰电子能谱分析以及蒙特卡洛模拟来确定.为了更加精确地确定电子非弹性散射平均自由程,必须对弹性峰电子能谱中的表面激发效应进行修正,通常使用介电响应理论方法计算得到的表面激发参数.然而,通过理论计算得到的表面激发参数不能包含电子在材料内部输运过程中弹性散射的影响,进而影响所测的电子非弹性散射平均自由程的准确度.在这个工作中,我们采用蒙特卡洛方法来确定包含弹性散射效应时的表面激发参数.所得到的表面激发参数在不同能量、角度情况下,尤其是在弹性散射效应显著的60°以上的大角度入射、出射情况下,都与实验测量值符合得非常好.基于这些新确定的表面激发参数,可以在弹性峰电子能谱测量中获得更为准确的电子非弹性散射平均自由程数据.     

Error Estimation in the Histogram Monte Carlo Method

We examine the sources of error in the histogram reweighting method for Monte Carlo data analysis. We demonstrate that, in addition to the standard statistical error which has been studied elsewhere, there are two other sources of error, one arising through correlations in the reweighted samples, and one arising from the finite range of energies sampled by a simulation of finite length. We demonstrate that while the former correction is usually negligible by comparison with statistical fluctuations, the latter may not be, and give criteria for judging the range of validity of histogram extrapolations based on the size of this latter correction.     

The Convergence of Markov Chain Monte Carlo Methods: From the Metropolis Method to Hamiltonian Monte Carlo

From its inception in the 1950s to the modern frontiers of applied statistics, Markov chain Monte Carlo has been one of the most ubiquitous and successful methods in statistical computing. The development of the method in that time has been fueled by not only increasingly difficult problems but also novel techniques adopted from physics. Here, the history of Markov chain Monte Carlo is reviewed from its inception with the Metropolis method to the contemporary state‐of‐the‐art in Hamiltonian Monte Carlo, focusing on the evolving interplay between the statistical and physical perspectives of the method.     

采用加权直方图分析和蒙特卡洛重采样法对自由能级的校正研究

本文采用加权直方图分析方法和蒙特卡洛重采样方法进行自由基校正研究. 生成的自由能表面几乎可以收敛到具有足够采样情况的精准表面,并且比常规的加权直方图分析校正方法能更稳定地处理采样不足的情况,为检测能级校正表面的不确定性提供指南,并且定义了明确的标准用以确定能改善其视觉效果的自由能表面平滑程度. 本文通过水中的丙氨酸二肽和KillerRed蛋白质子转移的自由能图证明该方法的优势,说明蒙特卡洛重采样法可以作为在产生自由能表面实际的系统中的实用工具.     

Monte Carlo方法在B样条函数分频理论中的应用

针对弹道参数的B样条表示问题,运用Monte Carlo方法对B样条函数分频理论进行仿真论证,得到B样条延拓节点的补充方法,并验证B样条函数逼近空间相容性定理的正确性.比较Monte Carlo方法和B样条分频算法的计算结果,说明分频算法合理.将该算法应用于外弹道跟踪测量数据的处理中,可以确定出表示弹道所需要的样条节点个数及样条节点序列的排布,有效减少待估参数个数.     

蒙特卡罗方法的两个基本问题

随机数的产生和概率分布的随机抽样方法,是蒙特卡罗方法的两个最基本的问题。对这两个问题的处理目前仍然因循60年前蒙特卡罗方法诞生初期的技术途径,因此长期受一些无法彻底解决的问题所困扰,同时也面临一些新问题的挑战。分析了上述问题,分别对随机数的产生和任意分布的抽样方法给出了新的技术解决途径。The producation of random number and the sampling of random distribution are two foundational problems in Monte Carlo Mothed. In this paper, we carry out some new ways to treat the problems.     

非线性中子输运问题的蒙特卡罗模拟

针对考虑中子之间相互碰撞的非线性中子输运方程,提出一种线性化近似处理方法,导出相应的积分输运方程,利用蒙特卡罗方法求解此方程,数值实验表明算法的有效性,为研究超高能中子产生与输运问题提供了必要的模拟工具.     

Monte Carlo Methods for Estimating Interfacial Free Energies and Line Tensions

Excess contributions to the free energy due to interfaces occur for many problems encountered in the statistical physics of condensed matter when coexistence between different phases is possible (e.g. wetting phenomena, nucleation, crystal growth, etc.). This article reviews two methods to estimate both interfacial free energies and line tensions by Monte Carlo simulations of simple models, (e.g. the Ising model, a symmetrical binary Lennard-Jones fluid exhibiting a miscibility gap, and a simple Lennard-Jones fluid). One method is based on thermodynamic integration. This method is useful to study flat and inclined interfaces for Ising lattices, allowing also the estimation of line tensions of three-phase contact lines, when the interfaces meet walls (where “surface fields” may act). A generalization to off-lattice systems is described as well. The second method is based on the sampling of the order parameter distribution of the system throughout the two-phase coexistence region of the model. Both the interface free energies of flat interfaces and of (spherical or cylindrical) droplets (or bubbles) can be estimated, including also systems with walls, where sphere-cap shaped wall-attached droplets occur. The curvature-dependence of the interfacial free energy is discussed, and estimates for the line tensions are compared to results from the thermodynamic integration method. Basic limitations of all these methods are critically discussed, and an outlook on other approaches is given.     

Dimensional reduction by Monte Carlo

A Monte Carlo method for mapping a field theoretical or statistical system to a new theory embedded in a space-time of lesser dimensionality is presented. Typically, the critical properties of the dimensionally reduced system depend upon the details of the mapping. As an example, the two-dimensional Ising model is mapped to a one-dimensional Ising model with long-range forces and a phase transition. Systems with long-range interactions and known exponents can thus be constructed with this procedure.     

用蒙特卡罗方法计算棒状放大器内的泵浦能量分布

建立了用蒙特卡罗和光线跟踪法计算高功率固体激光系统棒状放大器能量沉积分布的模拟程序。在本文的模型中正确考虑了光线在反射器激光棒上的多次反射，氙灯的辐射光谱以及钕玻璃的吸收光谱。计算结果与作者用阈值法测量的增益均匀性以及用哈特曼网格法测量的氙灯泵浦对激光波面畸变的影响是一致的。     

基于蒙特卡罗方法的光固化模拟

采用蒙特卡罗方法分析了光子在树脂中的输运过程,建立了紫外光单点固化模型,并进行了单点固化过程的模拟计算,通过曝光固化实验验证了该算法的可靠性.理论模拟和实验结果表明,当曝光能量达到临界值,固化点的高度和直径随曝光时间、功率的增大呈对数关系增大.利用该算法可以模拟各种不同光强分布的曝光固化过程,为加工分辨率的提高和工艺参量的优化提供理论基础.     

Particle in Cell/Monte Carlo Collision Method for Simulation of RF Glow Discharges: Effect of Super Particle Weighting

A parallel Particle in Cell/Monte Carlo Collision (PIC/MCC) numerical code for glow discharge plasma simulations is developed and verified. This method is based on simultaneous solution of the Lorentz equations of motion of super particles, coupled with the Poisson's equation for electric field. Collisions between the particles are modelled by the Monte Carlo method. Proper choice of particle weighting is critically important in order to perform adequate and efficient PIC simulations of plasma. Herein, effects of particle weighting on the simulations of capacitive radio‐frequency argon plasma discharges are studied in details. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)