Emergent topological ordered phase for the Ising-XY model revealed by cluster-updating Monte Carlo method

The two-component cold atom systems with anisotropic hopping amplitudes can be phenomenologically described by a two-dimensional Ising-XY coupled model with spatial anisotropy.At low temperatures,theoretical predictions[Phys.Rev.A 72053604(2005)]and[arXiv:0706.1609]indicate the existence of a topological ordered phase characterized by Ising and XY disorder but with 2XY ordering.However,due to ergodic difficulties faced by Monte Carlo methods at low temperatures,this topological phase has not been numerically explored.We propose a linear cluster updating Monte Carlo method,which flips spins without rejection in the anisotropy limit but does not change the energy.Using this scheme and conventional Monte Carlo methods,we succeed in revealing the nature of topological phases with half-vortices and domain walls.In the constructed global phase diagram,Ising and XY-type transitions are very close to each other and differ significantly from the schematic phase diagram reported earlier.We also propose and explore a wide range of quantities,including magnetism,superfluidity,specific heat,susceptibility,and even percolation susceptibility,and obtain consistent and reliable results.Furthermore,we observed first-order transitions characterized by common intersection points in magnetizations for different system sizes,as opposed to the conventional phase transition where Binder cumulants of various sizes share common intersections.The critical exponents of different types of phase transitions are reasonably fitted.The results are useful to help cold atom experiments explore the half-vortex topological phase.

Volume Dispersion of Point Sets and Quasi-Monte Carlo Methods

Measures of irregularity of a point set or sequence, such as discrepancy and dispersion, play a central role in quasi Monte Carlo methods. In this paper, we introduce and study a new measure of irregularity, called volume dispersion. It is a measure of deviation of point sets from the uniform distribution. We then generalize the concept of volume dispersion to more general cases as measures of representation of point sets for general probability distributions. Various relations among these measures and the traditional discrepancy and dispersion are investigated.

Variance reduction for generalized likelihood ratio method by conditional Monte Carlo and randomized Quasi-Monte Carlo methods

The generalized likelihood ratio(GLR)method is a recently introduced gradient estimation method for handling discontinuities in a wide range of sample performances.We put the GLR methods from previous work into a single framework,simplify regularity conditions to justify the unbiasedness of GLR,and relax some of those conditions that are difficult to verify in practice.Moreover,we combine GLR with conditional Monte Carlo methods and randomized quasi-Monte Carlo methods to reduce the variance.Numerical experiments show that variance reduction could be significant in various applications.

Quasi-Monte Carlo方法及其在金融风险管理中的应用

近年来,Quasi-Monte Carlo(QMC)方法成为国外金融风险管理研究的重要方向。选取代表性文献,综述国外QMC方法及其在金融资产定价、敏感性分析、风险价值估算等方面的主要研究成果及新进展,以推动QMC方法在我国微观金融理论与实务研究中的应用。

Monte Carlo方法在移动通信可靠性分析中的应用

文章主要探讨Monte Carlo方法在移动通信可靠性分析中的应用,并引入重要抽样技术对Monte Carlo方法进行优化。首先,文章介绍Monte Carlo方法的基本原理及其在移动通信可靠性分析中的应用。其次,引入重要抽样技术对该方法进行优化。最后,利用优化网络工程工具(Optimized Network Engineering Tools,OPNET)模拟平台构建相应的移动通信网络模型,并对比Monte Carlo方法和本文研究的优化方法在不同样本数量下的性能差异。结果表明,重要抽样技术的引入显著提高了Monte Carlo方法在移动通信可靠性分析中的准确性和效率,减少了方差,验证了该方法在移动通信可靠性分析中的有效性和实用性。

Uncertainty and energy-sector equity returns in Iran:a Bayesian and quasi-Monte Carlo time-varying analysis

This study investigates whether the implied crude oil volatility and the historical OPEC price volatility can impact the return to and volatility of the energy-sector equity indices in Iran.The analysis specifically considers the refining,drilling,and petrochemical equity sectors of the Tehran Stock Exchange.The parameter estimation uses the quasi-Monte Carlo and Bayesian optimization methods in the framework of a generalized autoregressive conditional heteroskedasticity model,and a complementary Bayesian network analysis is also conducted.The analysis takes into account geopolitical risk and economic policy uncertainty data as other proxies for uncertainty.This study also aims to detect different price regimes for each equity index in a novel way using homogeneous/non-homogeneous Markov switching autoregressive models.Although these methods provide improvements by restricting the analysis to a specific price-regime period,they produce conflicting results,rendering it impossible to draw general conclusions regarding the contagion effect on returns or the volatility transmission between markets.Nevertheless,the results indicate that the OPEC(historical)price volatility has a stronger effect on the energy sectors than the implied volatility has.These types of oil price shocks are found to have no effect on the drilling sector price pattern,whereas the refining and petrochemical equity sectors do seem to undergo changes in their price patterns nearly concurrently with future demand shocks and oil supply shocks,respectively,gaining dominance in the oil market.

Quasi-Monte Carlo Simulation-Based SFEM for Slope Reliability Analysis

Considering the stochastic spatial variation of geotechnical parameters over the slope, a Stochastic Finite Element Method (SFEM) is established based on the combination of the Shear Strength Reduction (SSR) concept and quasi-Monte Carlo simulation. The shear strength reduction FEM is superior to the slice method based on the limit equilibrium theory in many ways, so it will be more powerful to assess the reliability of global slope stability when combined with probability theory. To illustrate the performance of the proposed method, it is applied to an example of simple slope. The results of simulation show that the proposed method is effective to perform the reliability analysis of global slope stability without presupposing a potential slip surface.

Quasi-Monte Carlo Approximations for Exponentiated Quadratic Kernel in Latent Force Models

In this project, we consider obtaining Fourier features via more efficient sampling schemes to approximate the kernel in LFMs. A latent force model (LFM) is a Gaussian process whose covariance functions follow an Exponentiated Quadratic (EQ) form, and the solutions for the cross-covariance are expensive due to the computational complexity. To reduce the complexity of mathematical expressions, random Fourier features (RFF) are applied to approximate the EQ kernel. Usually, the random Fourier features are implemented with Monte Carlo sampling, but this project proposes replacing the Monte-Carlo method with the Quasi-Monte Carlo (QMC) method. The first-order and second-order models’ experiment results demonstrate the decrease in NLPD and NMSE, which revealed that the models with QMC approximation have better performance.

Fe-Cr二元合金微观组织演化的质量密度场耦合动力学Monte-Carlo模拟研究

本文建立了一种全新的将动力学Monte-Carlo粒子模拟与基于归一化Gauss函数基组的质量密度场空间粗粒化模型耦合的杂化模拟算法.采用该杂化模拟算法,系统对比研究了4种Cr原子含量分别为12.8%,20.0%,30.0%和40.0%的Fe-Cr合金中Cr相在温度为673 K下的时效析出动力学机制,及其时效不同阶段微观组织形貌的演变规律.研究得出Fe-Cr(12.8%)合金富Cr相时效组织形貌呈现孤立颗粒状空间分布形态,时效机制属于形核-长大(NG)机制;对于Fe-Cr(30.0%)和Fe-Cr(40.0%),富Cr相时效形貌在形核-生长及熟化阶段均呈现为三维蠕虫状空间分布特征,时效机制属于条幅分解(SD)机制;对于Fe-Cr(20.0%)合金,其富Cr相组织演化特征介于NG和SD机制之间.研究进一步发现Cr原子短程序参量可用来分析富Cr相形核-生长阶段Fe-Cr合金原子尺度结构的演变,但对于时效熟化阶段微观结构组织变化不敏感.基于空间粗粒化后Fe-Cr合金微观组织形貌,进一步分析了4种Cr原子含量下Fe-Cr合金相变动力学参数如富Cr相体积分数、平均粒径及相颗粒数密度随时效时间演变.本文建立的质量密度场耦合动力学Monte-Carlo模拟方法,为开发多尺度算法模拟合金时效动力学机制及微观组织形貌演变提供了新的思路和研究基础.

Statistical Modification Analysis of Helical Planetary Gears based on Response Surface Method and Monte Carlo Simulation

Tooth modification technique is widely used in gear industry to improve the meshing performance of gearings. However, few of the present studies on tooth modification considers the influence of inevitable random errors on gear modification effects. In order to investigate the uncertainties of tooth modification amount variations on system＇s dynamic behaviors of a helical planetary gears, an analytical dynamic model including tooth modification parameters is proposed to carry out a deterministic analysis on the dynamics of a helical planetary gear. The dynamic meshing forces as well as the dynamic transmission errors of the sun-planet 1 gear pair with and without tooth modifications are computed and compared to show the effectiveness of tooth modifications on gear dynamics enhancement. By using response surface method, a fitted regression model for the dynamic transmission error（DTE） fluctuations is established to quantify the relationship between modification amounts and DTE fluctuations. By shifting the inevitable random errors arousing from manufacturing and installing process to tooth modification amount variations, a statistical tooth modification model is developed and a methodology combining Monte Carlo simulation and response surface method is presented for uncertainty analysis of tooth modifications. The uncertainly analysis reveals that the system＇s dynamic behaviors do not obey the normal distribution rule even though the design variables are normally distributed. In addition, a deterministic modification amount will not definitely achieve an optimal result for both static and dynamic transmission error fluctuation reduction simultaneously.

Monte Carlo Method for the Uncertainty Evaluation of Spatial Straightness Error Based on New Generation Geometrical Product Specification

Straightness error is an important parameter in measuring high-precision shafts. New generation geometrical product speeifieation（GPS） requires the measurement uncertainty characterizing the reliability of the results should be given together when the measurement result is given. Nowadays most researches on straightness focus on error calculation and only several research projects evaluate the measurement uncertainty based on ＂The Guide to the Expression of Uncertainty in Measurement（GUM）＂. In order to compute spatial straightness error（SSE） accurately and rapidly and overcome the limitations of GUM, a quasi particle swarm optimization（QPSO） is proposed to solve the minimum zone SSE and Monte Carlo Method（MCM） is developed to estimate the measurement uncertainty. The mathematical model of minimum zone SSE is formulated. In QPSO quasi-random sequences are applied to the generation of the initial position and velocity of particles and their velocities are modified by the constriction factor approach. The flow of measurement uncertainty evaluation based on MCM is proposed, where the heart is repeatedly sampling from the probability density function（PDF） for every input quantity and evaluating the model in each case. The minimum zone SSE of a shaft measured on a Coordinate Measuring Machine（CMM） is calculated by QPSO and the measurement uncertainty is evaluated by MCM on the basis of analyzing the uncertainty contributors. The results show that the uncertainty directly influences the product judgment result. Therefore it is scientific and reasonable to consider the influence of the uncertainty in judging whether the parts are accepted or rejected, especially for those located in the uncertainty zone. The proposed method is especially suitable when the PDF of the measurand cannot adequately be approximated by a Gaussian distribution or a scaled and shifted t-distribution and the measurement model is non-linear.

Quantum Boltzmann equation solved by Monte Carlo method for nano-scale semiconductor devices simulation

A two-dimensional （2D） full band self-consistent ensemble Monte Carlo （MC） method for solving the quantum Boltzmann equation, including collision broadening and quantum potential corrections, is developed to extend the MC method to the study of nano-scale semiconductor devices with obvious quantum mechanical （QM） effects. The quantum effects both in real space and momentum space in nano-scale semiconductor devices can be simulated. The effective mobility in the inversion layer of n and p channel MOSFET is simulated and compared with experimental data to verify this method. With this method 50nm ultra thin body silicon on insulator MOSFET are simulated. Results indicate that this method can be used to simulate the 2D QM effects in semiconductor devices including tunnelling effect.

具有下界约束混料试验的Monte-Carlo渐近最优设计

在具有下界约束的混料试验设计中,由于难以求得含有未知变量的信息矩阵的行列式的显式表达,所以难以得到各类最优准则下的精确最优设计解。文章使用Monte-Carlo方法构造随机试验点的样本,进而可以通过模拟得出D-准则和MV-准则下的渐近最优设计。

Monte Carlo Analytic Hierarchy Process (MAHP) approach to selection of optimum mining method

One of the most critical and complicated steps in mine design is a selection of suitable mining method based upon geological,geotechnical,geographical,safety and economical parameters.The aim of this study is developing a Monte Carlo simulation to selection the optimum mining method by using effective and major criteria and at the same time,taking subjective judgments of decision makers into consideration.Proposed approach is based on the combination of Monte Carlo simulation with conventional Analytic Hierarchy Process(AHP).Monte Carlo simulation is used to determine the confdence level of each alternative’s score,is calculated by AHP,with the respect to the variance of decision makers’opinion.The proposed method is applied for Jajarm Bauxite Mine in Iran and eventually the most appropriate mining methods for this mine are ranked.

Forced propagation method for Monte Carlo fission source convergence acceleration in the RMC

In loosely coupled or large-scale problems with high dominance ratios,slow fission source convergence can take extremely long time,reducing Monte Carlo(MC)criticality calculation efficiency.Although various acceleration methods have been developed,some methods cannot reduce convergence times,whereas others have been limited to specific problem geometries.In this study,a new fission source convergence acceleration(FSCA)method,the forced propagation(FP)method,has been proposed,which forces the fission source to propagate and accelerate fission source convergence.Additionally,some stabilization techniques have been designed to render the method more practical.The resulting stabilized method was then successfully implemented in the MC transport code,and its feasibility and effectiveness were tested using the modified OECD/NEA,one-dimensional slab benchmark,and the Hoogenboom full-core problem.The comparison results showed that the FP method was able to achieve efficient FSCA.

IMPROVED STRATIFIED SAMPLING MONTE CARLO METHOD TO ANALYZE RELIABILITY OF STRUCTURAL SYSTEMS

A stratified sampling Monte Carlo method to analyze the reliability of structural systems is presented. Introducing a small exploratory simulation, this method overcomes the difficulties for getting the systematic sampling probability of all the strata. Several useful and efficient stratification methods are given and the strategies of stratification and simulation are studied. A general conclusion has been presented corresponding to actual engineering structures. The strict theoretical proof has been given,and it is especially effective to solve probabilistic integration. Statistic error of evaluating failure probability is reduced obviously. Especially in highly non-linear and nonreonvex problems, it is more accurate than other methods. Compared with other variance reduction techniques, this method can obtain a more obvious variance reduction and an increased sampling efficiency. Moreover, without strict limiting condition, it is convenient to use. This method is especially suitable to solve the reliability problem of structural systems with multiple failure modes and highly non-linear safety margin equations.

Monte Carlo Simulation of Fractures Using Isogeometric Boundary Element Methods Based on POD-RBF

This paper presents a novel framework for stochastic analysis of linear elastic fracture problems.Monte Carlo simulation(MCs)is adopted to address the multi-dimensional uncertainties,whose computation cost is reduced by combination of Proper Orthogonal Decomposition(POD)and the Radial Basis Function(RBF).In order to avoid re-meshing and retain the geometric exactness,isogeometric boundary element method(IGABEM)is employed for simulation,in which the Non-Uniform Rational B-splines(NURBS)are employed for representing the crack surfaces and discretizing dual boundary integral equations.The stress intensity factors(SIFs)are extracted by M integral method.The numerical examples simulate several cracked structures with various uncertain parameters such as load effects,materials,geometric dimensions,and the results are verified by comparison with the analytical solutions.

Verification of modified sum-peak method in Monte Carlo simulation of full energy peak and sum-peak efficiencies of a HPGe detector

The modified sum-peak method estimates radioactivity by using only the peak and the sum-peak count rates.To verify the modified sum-peak method,the dependence of the full energy peak efficiency on the source-to-detector distance in a high-purity germanium detector system was studied using a Geant4 Monte Carlo simulation.The effect of the deadlayer in the germanium crystal was estimated by reference to experiments on 241 Am and the relative efficiency of the detector.The peak efficiency dependence on the source-to-detector distance was compared between the simulation and measurements.The modified sum-peak method is discussed with respect to these peak efficiencies.

Seismic fluid identification using a nonlinear elastic impedance inversion method based on a fast Markov chain Monte Carlo method

Elastic impedance inversion with high efficiency and high stability has become one of the main directions of seismic pre-stack inversion. The nonlinear elastic impedance inversion method based on a fast Markov chain Monte Carlo （MCMC） method is proposed in this paper, combining conventional MCMC method based on global optimization with a preconditioned conjugate gradient （PCG） algorithm based on local optimization, so this method does not depend strongly on the initial model. It converges to the global optimum quickly and efficiently on the condition that effi- ciency and stability of inversion are both taken into consid- eration at the same time. The test data verify the feasibility and robustness of the method, and based on this method, we extract the effective pore-fluid bulk modulus, which is applied to reservoir fluid identification and detection, and consequently, a better result has been achieved.

Security Simulation of Continuous-Variable Quantum Key Distribution over Air-to-Water Channel Using Monte Carlo Method

Considering the ocean water＇s optical attenuation and the roughness of the sea surface, we analyze the security of continuous-variable （CV） quantum key distribution （QKD） based Mr-to-water channel. The effects of the absorp- tion and scattering on the transmittance of underwater quantum channel and the maximum secure transmission distance are studied. Considering the roughness of the sea surface, we simulate the performance bounds of CV QKD with different wind speeds using the Monte Carlo method. The results show that even if the secret key rate gradually reduces as the wind speed increases, the maximum transmission distance will not be affected obviously. Compared to the works regarding short-distance underwater optical communication, our research represents a significant step towards establishing secure communication between air platform and submarine vehicle.