Biasing the transition probabilities in direct Monte Carlo

The mathematical scheme of the biased direct Monte Carlo method is presented in detail and compared with the corresponding biased analogues Monte Carlo method. With reference to the inhomogeneous Poisson processes, an example in the reliability and safety engineering field is given. This refers to sampling from a three-mode Weibull distribution by forcing each of the three modes to be exponential with decay constants 10 times larger than the natural ones. Since the natural distribution under analysis shows a rather uniform behaviour over most of the range of interest, biasing to a uniform distribution has also been investigated. Both examples are shown to lead to a simplification in the sampling procedure and an improvement in the computational efficiency.     

Quantum Monte Carlo

Progress has been made in the development and applications of quantum Monte Carlo methods for calculations of many-body systems over the past year. Significant advances in methodology, such as new forms of trial wave functions, improved calculations of periodical systems and algorithm developments, have been commented upon, as have applications which include jellium models, H, He, molecular, cluster and solid systems. These results demonstrate that the influence and usefulness of quantum Monte Carlo methods are increasing rapidly.     

Monte Carlo and Multicomponent Approximation Methods for Vector Radiative Transfer by use of Effective Mueller Matrix Calculations

For single scattering in a turbid medium, the Mueller matrix is the 4 x 4 matrix that multiplies the incident Stokes vector to yield the scattered Stokes vector. This matrix contains all the information that can be obtained from an elastic-scattering system. We have extended this concept to the multiple-scattering domain where we can define an effective Mueller matrix that, when operating on any incident state of light, will yield the output state. We have calculated this matrix using two completely different computational methods and compared the results for several simple two-layer turbid systems separated by a dielectric interface. We have shown that both methods give reliable results and therefore can be used to accurately predict the scattering properties of turbid media.     

Atomistic modeling of materials properties by Monte Carlo Simulation

In order to optimize materials properties, in many cases a deeper understanding of the relationship between the chemical-atomistic structure and the physical properties of the solid and fluid phases of the material is necessary. Monte Carlo simulation is a tool that allows the reliable calculation of thermodynamic properties of strongly interacting many-body condensed matter systems. Given a model of effective interatomic or intermolecular interactions (drawn either from quantum-chemical-type interactions or from analysis of suitable experimental data), macroscopic bulk properties of a material can be simulated, as well as interfacial phenomena and certain kinds of slow dynamic processes (of relaxational or diffusive type). After a brief review of the foundations of this approach in statistical mechanics, the wide potential of this method is illustrated with examples taken from magnetism, metallurgy and amorphous polymeric materials. Strengths and limitations of this atomistic approach towards modeling materials properties are discussed and directions of future research are spelled out.     

Monte Carlo simulations in zeolites

In this short review, the applications of Monte Carlo simulations to the study of the adsorption and diffusion of hydrocarbons in zeolites are discussed. We focus on those systems for which the conventional molecular simulation techniques, molecular dynamics and Monte Carlo, are not sufficiently efficient. In particular, to simulate the adsorption and diffusion of long-chain hydrocarbons, novel Monte Carlo techniques have been developed. Here we discuss configurational-bias Monte Carlo (CBMC) and kinetic Monte Carlo (KMC). CBMC was developed to compute the thermodynamic properties. KMC is applied to compute transport properties. The use of these methods is illustrated with examples of technological importance.     

Magnetron sputter deposition as visualized by Monte Carlo modeling

The Monte Carlo code SIMTRA, simulating the transport of atoms from the source to the substrate during physical vapor deposition (PVD), is used in several case studies to highlight important issues related to thin film sputter deposition. Atom collisions during gas-phase transport affect the energy distribution and the deposition profile of sputtered atoms. The model is compared with published models for the thermalization of sputtered atoms, and some features of this process are discussed. The vacuum chamber design can be easily implemented in the Monte Carlo code, and this possibility is used to discuss the use of shutters and masks, and the influence of the deposition geometry. The code can also be used to predict the composition when combing different sources, segmented targets, and during combinatorial synthesis of thin films. As the details of the transport are described, the velocity and the density of the gas-phase atoms can be calculated which can assist in the interpretation of several spectroscopic techniques such as laser induced fluorescence. Not only the energy loss of the transported atoms, but also their remaining energy upon arrival at the substrate is important as the incident energy strongly influences thin film growth. To illustrate the latter, the model is also used to study the growth of biaxially aligned thin films. The key parameters influencing the level of alignment can easily be retrieved using SIMTRA.     

应用蒙特卡罗方法计算带置信水平的不确定度

本文介绍了一种采用蒙特卡罗统计模拟的方法来求解带置信水平的不确定度评定问题，这种方法求得的结果可使合成不确定度与置信水平精确关联，特别是高置信水平的不确定度。文中通过2个实例阐述了这种方法的运行过程并分析了结果。作者认为．这种方法可以作为有关不确定度评定标准的补充。     

Monte Carlo模拟薄膜生长的研究

阐述了Monte Carlo方法在薄膜生长中的应用和最新进展;简要论述了Monte Carlo算法的类型及各自的特点;结合MonteCarlo方法的特点,提出了模拟薄膜生长的模型以及处理方法.同时,归纳出MonteCarlo模拟薄膜生长需要解决的主要问题.     

Transport of sputtered atoms investigated by Monte Carlo method

Increasing attention has been paid to the sputtering process as a tool to deposit films and to the study of the interaction between the film properties and the deposition parameters. It is obvious that the energy and direction of these particles arriving at the substrate is in close relation with the transport process from the target to the substrate. This work deals with the computer simulation of the sputtered Ag atoms trajectories through the background gas in a diode-sputtering configuration. For that, we have developed a numerical model to simulate the transport process. We followed the three-dimensional trajectory of each sputtered atom separately and calculated the scattering angle and the energy loss if a collision took place. A statistical method, Monte Carlo simulations is used. The model predicts the flux of Ag atoms arriving at the substrate, their energies and angular distribution. The dependence of the deposition rates of Ag atoms on the gas pressure and the distance between target to substrate were investigated.     

Validation by Monte Carlo sampling of experimental observation functionals

We present and analyze a validation procedure for a given state estimate u ^? of the true field u ^true based on Monte Carlo sampling of experimental observation functionals. Our method provides, given a set of N possibly noisy local experimental observation functionals over the spatial domain Ω, confidence intervals for the L ²(Ω) error in state and the error in L ²(Ω) outputs. For L ²(Ω) outputs, our approach also provides a confidence interval for the output itself, which can be used to improve the initial output estimate based on u ^?. Our approach implicitly takes advantage of variance reduction, through the proximity of u ^? to u ^true, to provide tight confidence intervals even for modest values of N . We present results for a synthetic model problem to illustrate the elements of the methodology and confirm the numerical properties suggested by the theory. Finally, we consider an experimental thermal patch configuration to demonstrate the applicability of our approach to real physical systems.     

Analysis of light-emitting diodes by Monte Carlo photon simulation

A Monte Carlo photon simulation method, which is based on statistical tracing of photons inside the chip, has been developed for analysis of LED's in quantitative terms. Also included in the analysis is practical modeling of textured surfaces, which are often employed for enhanced light output. The method with its unique versatility is applicable to virtually any chip geometry and measures various important parameters such as photon-output-coupling efficiency, detailed photon flight statistics, and photon-output distribution patterns. It is speculated that the method can easily be extended to development of LED lamps and packages.     

应用Monte Carlo算法研究大分子蠕动阻力的影响因素

采用一种基于高分子Monte Carlo模拟算法分析分子蠕动阻力的软件,借助于二维空间中的8配位点键长涨落的格子链模型,对不同温度、分子量、共混小分子时的大分子蠕动行为进行了模拟分析,考察了温度、分子长、共混小分子等因素对蠕动阻力的影响,得到了随着温度增加、分子长减小和共混浓度增加,大分子蠕动阻力减小的结果,这与传统经验理论相符合。这些结果为选择大分子量添加剂黄原胶作为抗结块剂,以及选择β-环糊抑制玻璃化转变等提供了理论依据。     

Polarization Properties of Ferroelectric Superlattice Studied by Monte Carlo Simulation

The polarization property of a ferroelectric superlattice formed from two alternating materials was studied using Monte Carlo computer simulation. Our study has been developed in a framework of the transverse king model with nearest-neighbor interactions. Both the effect of the transverse field and interface coupling strength have been taken into consideration. In view of our results which is in good agreement with previous theoretical results, it is concluded that the Curie temperature of the superlattice increases with the increase of the interface coupling strength J(AB) The remanent polarization and saturation coercive force of the superlattice are also presented.     

Monte Carlo calculations of iceberg draft changes caused by roll

Draft changes in iceberg roll have been investigated using a Monte Carlo technique for generating iceberg shapes of constant, polygonal cross section. Stability is assessed from the potential energy curves calculated assuming vertical but not rotational hydrostatic equilibrium. No modelling of the roll dynamics has been included. The draft changes are approximately normally distributed, with increases almost as probable as decreases. Extreme draft changes (defined to be those in excess of 20%) are not uncommon. The mean draft change, standard deviation, skewness and kurtosis depend on the number of sides in the berg model, and on the ratio of berg ice density to seawater density. In particular the fraction of extreme draft changes is a sensitive function of this ratio.     

Node placement for triangular mesh generation by Monte Carlo simulation

A new approach of node placement for unstructured mesh generation is proposed. It is based on the Monte Carlo method to position nodes for triangular or tetrahedral meshes. Surface or volume geometries to be meshed are treated as atomic systems, and mesh nodes are considered as interacting particles. By minimizing system potential energy with Monte Carlo simulation, particles are placed into a near‐optimal configuration. Well‐shaped triangles or tetrahedra can then be created after connecting the nodes by constrained Delaunay triangulation or tetrahedrization. The algorithm is simple, easy to implement, and works in an almost identical way for 2D and 3D meshing. Copyright © 2005 John Wiley & Sons, Ltd.