Efficient stationary multivariate non-Gaussian simulation based on a Hermite PDF model

An efficient stationary multivariate non-Gaussian simulation method is developed using spectral representation and third order Hermite polynomial translation. An approximate closed form relationship is employed to identify the Hermite translation parameters based on target skewness and kurtosis. This preserves a high degree of accuracy over the entire admissible range of the Hermite translation, and eliminates the need for iterative solution of the translation parameters. The Hermite PDF model is suitable for a wide range of strongly non-Gaussian stochastic process. In addition, an explicit bidirectional relationship between the target non-Gaussian and Gaussian correlation is developed to eliminate the need for iteration or numerical integration to identify the underlying Gaussian correlation. Examples apply the simulation method to both theoretical targets and experimental wind pressure data.     

Existence and construction of translation models for stationary non-Gaussian processes

Translation models are memoryless transformations of Gaussian processes specified by their marginal distribution F and covariance function ξ. Iteration schemes are commonly used to find probability laws of Gaussian images of translation models, although these schemes may not converge since translation models do not exist for arbitrary functions F and ξ. Pairs (F,ξ) for which translation models exist are said to be consistent. Optimization algorithms are developed for constructing translation models that, for consistent pairs (F,ξ), match F and ξ, and, for inconsistent pairs (F,ξ), match F or ξ and approximate ξ or F. The resulting translation models can be used in Monte Carlo simulation studies.     

Response of linear systems to stationary bandlimited non-Gaussian processes

A method is developed for calculating statistics of the state of a linear system subjected to an arbitrary stationary bandlimited non-Gaussian process. The method is based on the representations of the input process obtained from a Shanon’s sampling theorem and Monte Carlo simulation. It is shown that the system output at a time t can be approximated by a finite sum of deterministic functions of t with random coefficients given by equally spaced values of the input process over a window of finite width centered on t. The number of terms in the sum depends on both input and system memory. Numerical examples show that the proposed method is simple to implement, efficient, accurate, and can also be applied to input process that are not bandlimited.     

A translation model for non-stationary, non-Gaussian random processes

A model for simulation of non-stationary, non-Gaussian processes based on non-linear translation of Gaussian random vectors is presented. This method is a generalization of traditional translation processes that includes the capability of simulating samples with spatially or temporally varying marginal probability density functions. A formal development of the properties of the resulting process includes joint probability density function, correlation distortion and lower and upper bounds that depend on the target marginal distributions. Examples indicate the possibility of exactly matching a wide range of marginal pdfs and second order moments through a simple interpolating algorithm. Furthermore, the application of the method in simulating statistically inhomogeneous random media is investigated, using the specific case of binary translation with stationary and non-stationary target correlations.     

An efficient simulation algorithm for non-Gaussian nonstationary processes

A novel algorithm is proposed for simulating univariate non-Gaussian nonstationary processes (NNP) with the specified evolutionary power spectral density (EPSD)/nonstationary auto-correlation function (NACF) and first four-order time-varying marginal moments (TVMMs). The sample realizations of the target NNP are generated as the outputs from a specific time-varying auto-regressive (TVAR) model via filtering the non-Gaussian and nonstationary white noise inputs. These white noise inputs are also non-Gaussian and nonstationary, and their first four-order TVMMs are predetermined using an approach developed herein according to the specified EPSD/NACF and first four-order TVMMs of the outputs. The conventional Johnson transformation is updated to accommodate the nonstationary cases for producing desired white noise inputs. This algorithm is developed from the linear filtering method (LFM), and inherits the simplicity and high efficiency from LFM. It fills the gaps in LFM-based algorithms for simulating NNP. Two numerical examples, i.e., a ground motion acceleration and a downburst velocity, are presented to fully demonstrate the capabilities of the proposed algorithm by comparing the simulation statistics with the targets.     

A spectral representation based model for Monte Carlo simulation

A new model is proposed for generating samples of real-valued stationary Gaussian processes. The model is based on the spectral representation theorem stating that a weakly stationary process can be viewed as a superposition of harmonics with random properties. The classical use of this theorem for Monte Carlo simulation is based on models consisting of a superposition of harmonics with fixed frequencies but random amplitude and phase. The resulting samples have the same period depending on the discretization of the frequency band. In contrast, the proposed model consists of a superposition of harmonics with random amplitude, phase, and frequency so that different samples have different periods depending on the particular sample values of the harmonic frequencies.

A band limited Gaussian white noise process is used to illustrate the proposed Monte Carlo simulation algorithm and demonstrate that the estimates of the covariance function based on the samples of the proposed model are not periodic.     

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.     

A simple and efficient methodology to approximate a general non-Gaussian stationary stochastic process by a translation process

Some widely used methodologies for simulation of non-Gaussian processes rely on translation process theory which imposes certain compatibility conditions between the non-Gaussian power spectral density function (PSDF) and the non-Gaussian probability density function (PDF) of the process. In many practical applications, the non-Gaussian PSDF and PDF are assigned arbitrarily; therefore, in general they can be incompatible. Several techniques to approximate such incompatible non-Gaussian PSDF/PDF pairs with a compatible pair have been proposed that involve either some iterative scheme on simulated sample functions or some general optimization approach. Although some of these techniques produce satisfactory results, they can be time consuming because of their nature. In this paper, a new iterative methodology is developed that estimates a non-Gaussian PSDF that: (a) is compatible with the prescribed non-Gaussian PDF, and (b) closely approximates the prescribed incompatible non-Gaussian PSDF. The corresponding underlying Gaussian PSDF is also determined. The basic idea is to iteratively upgrade the underlying Gaussian PSDF using the directly computed (through translation process theory) non-Gaussian PSDF at each iteration, rather than through expensive ensemble averaging of PSDFs computed from generated non-Gaussian sample functions. The proposed iterative scheme possesses two major advantages: it is conceptually very simple and it converges extremely fast with minimal computational effort. Once the underlying Gaussian PSDF is determined, generation of non-Gaussian sample functions is straightforward without any need for iterations. Numerical examples are provided demonstrating the capabilities of the methodology.     

光子在闪烁晶体中传输的蒙特卡罗模拟

为了找到构筑闪烁晶体探测器的优化方法，使用蒙特卡罗方法对闪烁晶体BGO（Bi4Ge3O12，锗酸铋）的光收集效率进行了模拟研究。模拟结果表明：入射面为粗糙面，其余为抛光面，同时外层包装上高反射率的材料，可得到最大的光输出（约59．1％的光子被收集）；耦合剂的折射率的得到高的光输出也起着非常重要的作用。     

Monte Carlo reliability model for microwave monolithic integrated circuits

A Monte Carlo simulation is reported for analog integrated circuits and is based on the modification of the failure rate of each component due to interaction effects of the failed components. The Monte Carlo technique is the methodology used to treat such circuits, since they are independent of the number of components and the degree of system complexity. The reliability model is applicable over a wide temperature and bias range and may be used to predict reliability of microwave systems. The model is compared with accelerated test results of two analog microwave circuits. Excellent agreement has been obtained for a low noise amplifier as well as for a transimpedence amplifier. Copyright © 2007 John Wiley & Sons, Ltd.     

磁性多层膜系统自旋重取向行为的Monte Carlo模拟

依据Heisenberg模型,利用Monte　Carlo方法模拟了磁性多层膜系统的自旋重取向行为,研究了各向异性、偶极相互作用以及外磁场对系统自旋取向的影响。通过模拟计算,获得了系统组态、磁分量等随偶极相互作用、外加磁场和温度的变化规律,重点研究了磁性多层膜系统在外磁场作用下的磁滞现象。     

Monte Carlo simulation of low density flows

The necessity for adopting a kinetic-theoretical approach to obtain aerodynamic characteristics in low density flow past space vehicles is highlighted in this paper; it is shown how long-standing difficulties in theoretically handling such flows can be circumvented by adopting a Monte Carlo technique. The principles underlying the technique are briefly described, and are first illustrated by applying the technique to the evaluation of the drag of cylinders and cones in collisionless flow. The Markoff process underlying the Monte Carlo simulation of the full Boltzmann equation with collisions is then described in detail. Instead of the time-counter strategy of Bird, a theoretically sounder ‘Random Collision Number’ (RCN) strategy has been adopted in the present simulation. In this strategy the number of collisions in each time-step in the computation is a random number drawn from an appropriate distribution. Computer programs using this strategy have been developed for calculating aerodynamic characteristics like drag and heat transfer for a cone in the transition regime between free molecule and continuum flow. The results obtained from these programs show that both time-counter and RCN strategies require almost the same computer time.     

Genetic algorithms and Monte Carlo simulation for optimal plant design

We present an approach to the optimal plant design (choice of system layout and components) under conflicting safety and economic constraints, based upon the coupling of a Monte Carlo evaluation of plant operation with a Genetic Algorithms-maximization procedure. The Monte Carlo simulation model provides a flexible tool, which enables one to describe relevant aspects of plant design and operation, such as standby modes and deteriorating repairs, not easily captured by analytical models. The effects of deteriorating repairs are described by means of a modified Brown–Proschan model of imperfect repair which accounts for the possibility of an increased proneness to failure of a component after a repair. The transitions of a component from standby to active, and vice versa, are simulated using a multiplicative correlation model. The genetic algorithms procedure is demanded to optimize a profit function which accounts for the plant safety and economic performance and which is evaluated, for each possible design, by the above Monte Carlo simulation.In order to avoid an overwhelming use of computer time, for each potential solution proposed by the genetic algorithm, we perform only few hundreds Monte Carlo histories and, then, exploit the fact that during the genetic algorithm population evolution, the fit chromosomes appear repeatedly many times, so that the results for the solutions of interest (i.e. the best ones) attain statistical significance.     

Procedures of Monte Carlo transport simulation for applications in system engineering

Monte Carlo (MC) simulation is the most promising tool for performing realistic reliability and availability analysis of complex systems. Yet, the efficient use of MC simulation technique is not trivial in large scale applications.This paper considers the two commonly adopted approaches to MC simulation: the direct, component-based approach and the indirect, system-based approach. The mathematical details of the two approaches are worked out in detail, so as to show their probabilistic equivalence. The proper formulation for biasing the simulation is introduced, thus leading to the correct expressions for the statistical weights.Both approaches are applied, in an analog as well as in a biased scheme, to a simple system of the literature and comparisons are made with respect to the computing time and the goodness of the estimate, as measured by the variance of the results.     

Monte Carlo simulation of nucleation and growth of thin films

We study thin film growth using a lattice-gas, solid-on-solid model employing the Monte Carlo technique. The model is applied to chemical vapour deposition (CVD) by including the rate of arrival of the precursor molecules and their dissociation. We include several types of migration energies including the edge migration energy which allows the diffusive movement of the monomer along the interface of the growing film, as well as a migration energy which allows for motion transverse to the interface. Several well-known features of thin film growth are mimicked by this model, including some features of thin copper films growth by CVD. Other features reproduced are—compact clusters, fractal-like clusters, Frank-van der Merwe layer-by-layer growth and Volmer-Weber island growth. This method is applicable to film growth both by CVD and by physical vapour deposition (PVD).     

Multi-lattice Monte Carlo model of thin films

In previous publications, an atomistic simulator based on a single-lattice or a dual-lattice Monte Carlo method has been proposed and applied to the studies of microstructure evolution in thin films. In this paper, a multi-lattice Monte Carlo model, an extension to our atomistic simulator of deposition in three dimensions (ADEPT), is presented and applied to the studies of texture competition in thin films. Multiple lattices are mapped onto a single reference lattice, with resulting computational demands (memory and speed) being comparable to those in the single-lattice Monte Carlo model. It is therefore possible to simulate growth competition among crystallites of different orientations, and to study texture formation and explore optimal deposition conditions. As an application, the predominant texture is investigated as a function of collimation and deposition rate. Grains with low energy surfaces parallel to the substrate are found to dominate under the condition of low deposition rate and collimated beam. On the other hand, grains with high surface energy are found to dominate for high deposition rate and uncollimated sputtered beam, and their dominance disappears at extremely high deposition rates. This revised version was published online in July 2006 with corrections to the Cover Date.     

A Monte Carlo simulation approach to the availability assessment of multi-state systems with operational dependencies

This paper deals with multi-state systems (MSS), whose performance can settle on different levels, e.g. 100%, 80%, 50% of the nominal capacity, depending on the operative conditions of the constitutive multi-state elements. Examples are manufacturing, production, power generation and gas and oil transportation systems. Often in practice, MSS are such that operational dependencies exist between the system state and the state of its components. For example, in a production line of nodal series structure, with no buffers between the nodes, if one of the nodes throughput changes (e.g. switches from 100% to 50% due to a deterministic or stochastic transition of one of its components), the other nodes must be reconfigured (i.e. their components must deterministically change their states) so as to provide the same throughput.In this paper, we present a Monte Carlo simulation technique which allows modelling the complex dynamics of multi-state components subject to operational dependencies with the system overall state. A correlation method is tailored to model the automatic change of state of the relevant components following a change in one of the system nodes. The proposed technique is verified on a simple case study of literature.     

Monte Carlo simulation of grating-based neutron phase contrast imaging at CPHS

Since the launching of the Compact Pulsed Hadron Source (CPHS) project of Tsinghua University in 2009, works have begun on the design and engineering of an imaging/radiography instrument for the neutron source provided by CPHS. The instrument will perform basic tasks such as transmission imaging and computerized tomography. Additionally, we include in the design the utilization of coded-aperture and grating-based phase contrast methodology, as well as the options of prompt gamma-ray analysis and neutron-energy selective imaging. Previously, we had implemented the hardware and data-analysis software for grating-based X-ray phase contrast imaging. Here, we investigate Geant4-based Monte Carlo simulations of neutron refraction phenomena and then model the grating-based neutron phase contrast imaging system according to the classic-optics-based method. The simulated experimental results of the retrieving phase shift gradient information by five-step phase-stepping approach indicate the feasibility of grating-based neutron phase contrast imaging as an option for the cold neutron imaging instrument at the CPHS.     

Prediction of micro-channel flows using direct simulation Monte Carlo

The direct simulation Monte Carlo (DSMC) method is a particle-based numerical modeling technique. It is recently used for simulating gaseous flow in micro-electro-mechanical-systems (MEMS) where micron-scale features become important. In this paper, numerical simulations of fluid flow in micro-channels are carried out using the DSMC method. The details in determining the parameters critical for DSMC applications in micro-channels are provided. Streamwise velocity distributions in the slip-flow regime are compared with the analytical solution based on the Navier–Stokes equations with slip velocity boundary condition. Satisfactory agreements have been achieved. Effects of the entrance and exit regions on simulation results are discussed. Simulations are then extended to transition flow regime (Kn>0.1) and compared with the analytical solution. It is shown that the results are distinguished with the analytical solutions, which fail to predict the flow due to the break down of continuum assumption. It is indicated that the gradient of the pressure along the channel direction dominates the motion of the fluid flow.