Henyey-Greenstein and Mie phase functions in Monte Carlo radiative transfer computations

Monte Carlo radiative transfer simulation of light scattering in planetary atmospheres is not a simple problem, especially the study of angular distribution of light intensity. Approximate phase functions such as Henyey-Greenstein, modified Henyey-Greenstein, or Legendre polynomial decomposition are often used to simulate the Mie phase function. An alternative solution using an exact calculation alleviates these approximations.     

Homogenization and scattering from heterogeneous media based on finite-difference-time-domain Monte Carlo computations

We present a method to study the scattering by heterogeneous media based on the two-dimensional (2D), finite-difference-time-domain method and a Monte Carlo algorithm. The inhomogeneities may reach wave-length size and their optical constants are in the visible and infrared domain. The algorithm is used to determine an effective propagation constant in a monodisperse medium from the observation of the energy decay in the medium. The result is compared over a large domain of volume fraction with the Keller and the Foldy-Twersky 2D models to determine the domain of their validity. Then the same approach is applied to homogenize the smallest particles in a bidisperse case and determine when such process is adequate.     

Optimization of kinoform lenses with the Monte Carlo method

For the optimization of non-Fourier-type computer-generated phase holograms (kinoform lenses), a method based on the Monte Carlo procedure is suggested. This method can be regarded as analogous to the iterative Fourier transform algorithm method that is widely used for the optimization of Fourier-type computer-generated phase holograms (kinoforms).     

Monte Carlo Optimization,Simulation and Sensitivity of Queueing Networks

The degradation of a drug product over time must be studied carefully to determine the appropriate shelf-life of the product. It is desirable to use data from all batches of the drug product to estimate a common shelf-life. The current Food and Drug Administration Guideline for analyzing data from multiple batches in stability studies emphasizes hypothesis testing for assessing the equality of degradation rates among batches. We propose a definition for a meaningful difference in batch degradation rates. Furthermore, we use simultaneous confidence intervals for estimating differences in batch slopes and for making decisions about pooling data from separate batches. We believe that an estimation procedure based on simultaneous confidence intervals is philosophically and practically a better approach to this problem.     

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.     

基于蒙特卡罗法的平行流冷凝器的翅片参数优化

运用蒙特卡洛法,在家用空调运行工况下,对平行流冷凝器空气侧的传热和流动性能进行了优化计算,分析了翅片的各种几何参数组合对换热系数和压力损失的影响.得出了影响换热系数的主要因素是翅片高度和百叶窗长度,同时增大两者既可以快速增大换热系数又可以降低压力损失;影响压力损失的主要因素是翅片宽度,因为翅片宽度的微减能带来压力损失的大大将低,但换热系数不受翅片宽度的影响;并同时得出影响换热系数和压力损失的次要影响因素是翅片间距和百叶窗角度.翅片间距减少、百叶窗角度增大均会引起换热系数与压力损失的增大.用这种优化方法得出的结论进行翅片参数组合的平行流冷凝器,可以在满足压力损失需要的情况下大大提高其换热性能.     

Dynamic bounds coupled with Monte Carlo simulations

For the reliability analysis of engineering structures a variety of methods is known, of which Monte Carlo (MC) simulation is widely considered to be among the most robust and most generally applicable. To reduce simulation cost of the MC method, variance reduction methods are applied. This paper describes a method to reduce the simulation cost even further, while retaining the accuracy of Monte Carlo, by taking into account widely present monotonicity. For models exhibiting monotonic (decreasing or increasing) behavior, dynamic bounds (DB) are defined, which in a coupled Monte Carlo simulation are updated dynamically, resulting in a failure probability estimate, as well as a strict (non-probabilistic) upper and lower bounds. Accurate results are obtained at a much lower cost than an equivalent ordinary Monte Carlo simulation. In a two-dimensional and a four-dimensional numerical example, the cost reduction factors are 130 and 9, respectively, where the relative error is smaller than 5%. At higher accuracy levels, this factor increases, though this effect is expected to be smaller with increasing dimension. To show the application of DB method to real world problems, it is applied to a complex finite element model of a flood wall in New Orleans.     

Statistical inference and Monte Carlo algorithms

Summary This review article looks at a small part of the picture of the interrelationship between statistical theory and computational algorithms, especially the Gibbs sampler and the Accept-Reject algorithm. We pay particular attention to how the methodologies affect and complement each other. Read before the Spanish Statistical Society at a meeting organized by the University of Granada on Friday, September 27, 1996     

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.     

A study using Monte Carlo Simulation for failure probability calculation in Reliability-Based Optimization

In this study, a Reliability-Based Optimization (RBO) methodology that uses Monte Carlo Simulation techniques, is presented. Typically, the First Order Reliability Method (FORM) is used in RBO for failure probability calculation and this is accurate enough for most practical cases. However, for highly nonlinear problems it can provide extremely inaccurate results and may lead to unreliable designs. Monte Carlo Simulation (MCS) is usually more accurate than FORM but very computationally intensive. In the RBO methodology presented in this paper, limit state approximations are used in conjunction with MCS techniques in an approximate MCS-based RBO that facilitates the efficient calculation of the probabilities of failure. A FORM-based RBO is first performed to obtain the initial limit state approximations. A Symmetric Rank-1 (SR1) variable metric algorithm is used to construct and update the quadratic limit state approximations. The approximate MCS-based RBO uses a conditional-expectation-based MCS, that was chosen over indicator-based MCS because of the smoothness of the probability of failure estimates and the availability of analytic sensitivities. The RBO methodology was implemented for an analytic test problem and a higher-dimensional, control-augmented-structure test problem. The results indicate that the SR1 algorithm provides accurate limit state approximations (and therefore accurate estimates of the probabilities of failure) for these test problems. It was also observed that the RBO methodology required two orders of magnitude fewer analysis calls than an approach that used exact limit state evaluations for both test problems.     

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。     

用改进的Monte Carlo算法模拟晶粒生长

材料微观组织结构决定材料的宏观力学性能.Potts模型是实现晶粒生长过程仿真的一种重要方法.在Radhakrishnan和Zacharia提出的Monte Carlo算法的基础上提出了一种改进的Monte Carlo算法,利用该算法对晶粒生长过程进行了模拟,模拟的微观组织多为等轴晶,晶粒生长指数为0.512.模拟结果表明,该算法能够准确模拟晶粒生长过程.     

Monte Carlo Simulation of Agglomeration and Grinding

ABSTRACT

We present a new Monte Carlo (MC) method to simulate particles undergoing simultaneous agglomeration and break up. Conventional MC methods applied to agglomeration and fragmentation fail when the number of particles in the simulation becomes too small (agglomeration) or too large (fragmentation). These simulations must be terminated when a predetermined number of particles is reached. We developed an MC method that utilizes a constant number of particles, and will show that it can be successfully used to simulate agglomeration, grinding, and generally any other process that involves generation and depletion of particles. Simulations by this method may proceed essentially indefinitely with minimal effect on the accuracy of the calculation. Among the advantages of this method are the ease of implementation and the ability to perform long simulations even on personal computers. We demonstrate the method by discussing examples of agglomeration and grinding of powders.     

失配误差的蒙特卡洛分析

针对极限相位法评定失配误差引入的测量不确定度普遍偏大的问题,提出了采用蒙特卡洛法对其评定的新方法。以交替比较法校准功率座为实例,研究了蒙特卡洛法评定失配误差引入的测量不确定度的具体实现方法,并将其得到的结果与极限相位法进行比较。结果表明,蒙特卡洛法更适合用于失配误差引入的测量不确定度进行评定。     

Monte Carlo model of nonlinear chromatography

A stochastic approach to the nonlinear chromatography theory, based on the Monte Carlo simulation method, is presented. A computer program, acting as a "virtual chromatograph" and performing a discrete event simulation, is described. Such a program allows one to choose the column type, operating conditions, sample composition, injection method, mobile-phase dispersion model, and stationary-phase sorption-desorption kinetics. Nonlinearity is accounted for by continuously monitoring and updating both the column and the solute status and by moving individual molecules step by step along the column according to specific random modes. The program has been validated through a series of statistical tests and comparing the results with the well-known achievements of the classical stochastic theory. A first application is presented, referred to a real case benzene elution on a gas solid capillary column, where the Langmuir adsorption isotherm is assumed. The effect of both the sorption modes and the site capacity are investigated. Possible applications to investigate open problems in several fields of separation science are emphasized. In addition, several specific points such as the down-scaling of a real case and the correspondence of specific adsorption dynamics with the equilibrium Langmuir isotherm are described.