Computer simulation of two continuous spin models using Wang-Landau-Transition-Matrix Monte Carlo algorithm

Monte Carlo simulation using a combination of Wang-Landau (WL) and Transition Matrix (TM) Monte Carlo algorithms to simulate two lattice spin models with continuous energy is described. One of the models, the one-dimensional Lebwohl-Lasher model has an exact solution and we have used this to test the performance of the mixed algorithm (WLTM). The other system we have worked on is the two-dimensional XY-model. The purpose of the present work is to test the performance of the WLTM algorithm in continuous models and to suggest methods for obtaining best results in such systems using this algorithm.     

Parallel Monte Carlo Driver (PMCD)—a software package for Monte Carlo simulations in parallel

Thanks to the dramatic decrease of computer costs and the no less dramatic increase in those same computer's capabilities and also thanks to the availability of specific free software and libraries that allow the set up of small parallel computation installations the scientific community is now in a position where parallel computation is within easy reach even to moderately budgeted research groups. The software package PMCD (Parallel Monte Carlo Driver) was developed to drive the Monte Carlo simulation of a wide range of user supplied models in parallel computation environments. The typical Monte Carlo simulation involves using a software implementation of a function to repeatedly generate function values. Typically these software implementations were developed for sequential runs. Our driver was developed to enable the run in parallel of the Monte Carlo simulation, with minimum changes to the original code that implements the function of interest to the researcher. In this communication we present the main goals and characteristics of our software, together with a simple study its expected performance. Monte Carlo simulations are informally classified as “embarrassingly parallel”, meaning that the gains in parallelizing a Monte Carlo run should be close to ideal, i.e. with speed ups close to linear. In this paper our simple study shows that without compromising the easiness of use and implementation, one can get performances very close to the ideal.     

Grand canonical auxiliary field Monte Carlo: a new technique for simulating open systems at high density

The computation of open many-particle systems at high densities is a major challenge since many decades due to the inherent limitations of grand canonical simulation methods based on particle exchange algorithms. In this paper we report on the statistical convergence behavior in the high density regime of a recently developed alternative called the grand canonical auxiliary field Monte Carlo method. We show on a common soft matter model widely used in polymer simulation that it possesses a more appropriate statistical behavior in the dense regime than the currently employed grand canonical Monte Carlo methods relying on particle exchange algorithms.     

The importance of introducing a waiting time for Lattice Monte Carlo simulations of a polymer translocation process

For a standard Lattice Monte Carlo (LMC) simulation of a random walker subject to a bias, it is impossible to obtain both a correct mean velocity and diffusion coefficient. To correct this, a modified LMC algorithm has been developed where the introduction of a probability of remaining in the current state allows for a distribution of intervals between jumps. In this paper, we demonstrate the impact of this modification for a first-passage problem: the translocation of a polymer through a nanopore. We find that while either approach yields the correct mean first-passage time, the incorporation of a waiting time is necessary to obtain the correct spread of times.     

马尔可夫系统瞬态不可用度计算的高效率蒙特卡罗方法

当马尔可夫系统规模较大时,需要采用蒙特卡罗方法计算其瞬态不可用度,如果系统的不可用度很小,则需要采用高效率的蒙特卡罗方法.本文在马尔可夫系统寿命过程的积分方程的基础上,给出了系统瞬态不可用度计算的蒙特卡罗方法的统一描述,由此设计了马尔可夫系统瞬态不可用度计算的直接统计估计方法和加权统计估计方法.用直接仿真方法、拟仿真方法、基于直接仿真的统计估计方法、基于拟方仿真的统计估计方法和加权统计估计方法计算了-可修Con/3/30:F系统的瞬态不可用度.结果表明,由于同时采用了偏倚的抽样空间和逐次事件估计量,加权统计估计方法的方差最小,当系统不可用度很小时,该方法效率最高.     

磨矿破碎过程粒度分布的分布式参数蒙特卡洛动力学模拟及加速方法

本文针对磨矿破碎过程,提出一种分布式参数蒙特卡洛动力学方法的粒度分布预测模型和模拟算法.该算法采用了分段思想,将磨机沿着轴向分为若干个虚拟的子磨机;根据破裂、前向和后向移动三类微观事件定义了倾向函数和系统状态矩阵,并设计了分布式算法的调度策略.此外,针对蒙特卡洛动力学算法效率低的问题,提出了基于τ-leap的磨矿过程分布式参数蒙特卡洛模拟加速算法.为了解决分布式参数更新过程中状态不一致的问题,创新性地提出了一种基于缓冲区的同步方法.通过对仿真案例的分析表明,本文提出的分布式参数蒙特卡洛动力学算法具有较高的精度,提出的基于τ-leap的加速算法能够显著提高计算效率,同时保持较好的精度.     

A robust optimisation framework in composite generation and transmission expansion planning considering inherent uncertainties

Abstract

This paper presents a robust optimisation framework for long-term composite generation and transmission expansion planning problem which considers inherent uncertainties such as load growth, fuel cost and renewable energy output uncertainties. In this paper, a bi-level robust optimisation framework is proposed to accommodate wind output uncertainty in line with the uncertain demanded loads and uncertain fuel cost. The addressed optimisation problem is modelled as a mixed-integer optimisation framework with the objective of providing a robust expansion plan while maintaining the minimum cost expansion. In order to evaluate the robustness of each plan, an off-line Lattice Monte Carlo simulation technique is adopted in this study. The validity of the proposed method is examined on a simple six-bus and modified IEEE 118-bus test system as a large-scale case study. The simulation results show that the presented method is both satisfactory and consistent with expectation.     

Vectorizing the Monte Carlo algorithm for lattice gauge theory calculations on the CDC cyber 205

Lattice gauge theory is a technique for studying quantum field theory free of divergences. All the Monte Carlo computer calculations up to now have been performed on scalar machines. A technique has been developed for effectively vectorizing this class of Monte Carlo problems. The key for vectorizing is in finding groups in finding groups of points on the space-time lattice which are independent of each other. This requires a particular ordering of points along diagonals. A technique for matrix multiply is used which enables one to get the whole of the result matrix in one pass. The CDC CYBER 205 is most suitable for this class of problems using random “index-lists” (arising from the ordering algorithm and the use of random numbers) due to the hardware implementation of “GATHER” and “SCATTER” operations performing at a streaming-rate. A preliminary implementation of this method has executed 5 times faster than on the CDC 7600 system.     

基于AMD PC的机群计算系统的设计与实现

文章介绍了一个基于AMDPC的机群计算系统,它由30个计算节点、1个数据服务器及1个登录服务器组成,总共64个CPU,数据服务器使用千兆网络的连接。这个计算系统是用于LHC(LargeHadronCollider)的MonteCarlo模拟以及羊八井中日合作项目的数据分析、MonteCarlo模拟等。由于MonteCarlo模拟部分对计算能力的要求很高,而数据分析部分则对I/O能力的要求很高,因此系统必须兼顾这两个方面的要求。由于物理数据的产生和物理数据的分析是事例间无关的,所以系统使用批作业处理方式。该文选择NASA开发的自由软件PBS作为批作业管理系统。测试结果表明,系统SPEC2000的SPECint和SPECfp值分别为38976和35008,I/O的读写能力分别为62.34MB/s和56.50MB/s,具有很好的性能价格比。     

The estimation of probability distribution of SDE by only one sample trajectory

This paper focuses on the method of the simulation of a stochastic system and the main method of our paper is the Monte Carlo computation simulation method. Taking the stochastic Logistic equation as an example, we present the simulation of the sample trajectory by Euler scheme and the invariant probability distribution of stochastic differential equations with the Monte Carlo method. We also compare the simulation result with the analytical result for the autonomous stochastic Logistic model. Moreover, the stochastic Logistic equation with Markovian switching which is described by a Markov chain taking values in a finite state space is considered.     

Sewing algorithm

We present a procedure that in many cases enables the Monte Carlo sampling of states of a large system from the sampling of states of a smaller system. We illustrate this procedure, which we call the sewing algorithm, for sampling states from the transfer matrix of the two-dimensional Ising model.     

基于蒙特卡罗的星-地单光子通信仿真方法

针对星-地单光子通信研究现状和复杂系统特性,提出一种运用蒙特卡罗方法研究星-地单光子通信全链路仿真过程的方法。基于离散事件仿真器构建星-地单光子通信的全链路仿真系统,采用蒙特卡罗方法对单光子通信过程进行大量模拟计算,得到准确的统计分析结果。仿真考虑了多种影响因素,对系统的关键性能参数做出综合、准确的评价,为系统的设计和优化提供依据,验证蒙特卡罗仿真在单光子通信系统中的可用性。     

Fault detection and isolation in non-linear stochastic systems—A combined adaptive Monte Carlo filtering and likelihood ratio approach

This paper presents the development of a new method for solving fault detection and isolation (FDI) problem in general non-linear stochastic systems. In this paper, the faults are modelled as unknown changes in system parameters and adaptive Monte Carlo filtering approach is used in deriving an FDI scheme. Essentially, a set of adaptive Monte Carlo filters are designed based on the augmented system models along with a nominal Monte Carlo filter designed based on the nominal system model. The likelihood functions of the observations are then evaluated using the particles from these (adaptive) Monte Carlo filters and FDI is eventually achieved via the likelihood ratio test. The simulation results on a highly non-linear system are provided which demonstrates the effectiveness of the proposed method.     

毁伤概率评估的加权蒙特卡洛方法

由于经典蒙特卡洛方法的仿真效率不高,文中利用概率论和数理统计的基本原理,可以推导得到加权蒙特卡洛方法.加权蒙特卡罗方法不但能有效的缩小了样本方差,还能提高目标事件出现概率,相当于提高了样本的抽样效率,从而提高了仿真效率.与此同时,文中分别利用经典蒙特卡洛和加权蒙特卡洛这两种方法对典型目标进行了仿真计算,仿真计算最终证明了加权蒙特卡洛方法的仿真效率明显优于经典蒙特卡洛方法,能使仿真工作量成数量级的衰减.     

Effect of band structure discretization on the performance of full-band Monte Carlo simulation

Full-band Monte Carlo simulation offers a very accurate simulation technique, but is often limited by its high demand on computation time. The advantage of a numerical representation of the band structure over an analytical approximation is the accurate representation of the energy bands in the high energy regime. This allows accurate treatment of hot carrier effects in semiconductors. In this work we outline an efficient full-band Monte Carlo (FBMC) simulator and investigate the accuracy of simulation results for different meshing approaches for the Brillouin zone.     

蒙特卡罗仿真机及其应用

蒙特卡罗仿真机是通过对随机性问题采用Monte Carlo方法进行计算机仿真，从而得出待解问题的解。为了研究复杂的随机问题，文中提出了基于蒙特卡罗的随机模拟法的蒙特卡罗仿真机，并说明了它的基本原理。通过圆周率的计算，实践了蒙特卡罗仿真机的应用过程，从而显示出蒙特卡罗仿真法处理随机性问题的优越性和仿真普遍的适用性。     

基于备件方案的多态PMS可靠性仿真模型

针对多阶段任务系统(PMS)的备件问题,构建基于Monte Carlo方法的仿真模型,给出具体的算法流程。该模型以多态结构函数为基本输入,产生等价于基本设备寿命实现值的随机数,代入仿真模型,经过逻辑运算和统计分析得到系统的可靠度,为多态PMS的备件决策提供依据。应用Matlab软件进行仿真实验分析,结果表明该方法具有较高的仿真精度。     

基于拟蒙特卡罗方法的进化算法搜索鲁棒最优解的性能提高研究

鲁棒最优解在工程应用中具有十分重要的意义,它是进化计算的重要研究内容,也是研究难点．进化算法搜索鲁棒最优解时,通常使用蒙特卡罗积分(MCI)近似估计有效目标函数(EOF),但由于现有的原始蒙特卡罗方法(C-MC)近似精度不高,导致进化算法搜索鲁棒最优解的性能较差．文中提出用拟蒙特卡罗方法(Q-MC)估计有效目标函数,通过大量的数值实验,结果表明,与C-MC相比,文中所引入的Q-MC 方法、SQRT序列、SOBOL序列和Korobov点阵能更精确估计EOF,进而较大提高进化算法搜索鲁棒最优解的性能．     

Fast recall of state-history in kinetic Monte Carlo simulations utilizing the Zobrist key

We present a novel application of the Zobrist hashing method, known in the computer chess literature, to simulation of diffusional phase transformations in metal alloys. A history of previously visited states can be easily maintained, allowing very fast lookup of energies and transition rates calculated earlier in the simulation. The method has been applied to the simulation of a Fe-1at.%Cu system, with simple potentials and a transition rate for diffusional events approximated from the difference in internal energy between trial states. In this simple model at temperatures of 1073 K we find that 61.2% of the states considered during the simulation have been seen previously, and that this proportion rises to 85.1% at 773 K and even to 99.9% at 373 K. Rapid recall of these states reduces the computational time taken for the same sequence of atom-vacancy exchange moves by a factor of 6.3 at 773 K rising to over 100 at 373 K. We suggest that a similar speedup factor will be found using more sophisticated models of diffusion and that the method can, with small modifications, be applied to a wide range of kinetic Monte Carlo simulations of atomistic diffusion processes.     

A parallel implementation of the Wang-Landau algorithm

The Wang-Landau algorithm is a flat-histogram Monte Carlo method that performs random walks in the configuration space of a system to obtain a close estimation of the density of states iteratively. It has been applied successfully to many research fields. In this paper, we propose a parallel implementation of the Wang-Landau algorithm on computers of shared memory architectures by utilizing the OpenMP API for distributed computing. This implementation is applied to Ising model systems with promising speedups. We also examine the effects on the running speed when using different strategies in accessing the shared memory space during the updating procedure. The allowance of data race is recommended in consideration of the simulation efficiency. Such treatment does not affect the accuracy of the final density of states obtained.