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.

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.

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.

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.

Sequential Monte Carlo Method Toward Online RUL Assessment with Applications

Online assessment of remaining useful life(RUL) of a system or device has been widely studied for performance reliability, production safety, system conditional maintenance, and decision in remanufacturing engineering. However,there is no consistency framework to solve the RUL recursive estimation for the complex degenerate systems/device.In this paper, state space model(SSM) with Bayesian online estimation expounded from Markov chain Monte Carlo(MCMC) to Sequential Monte Carlo(SMC) algorithm is presented in order to derive the optimal Bayesian estimation.In the context of nonlinear & non-Gaussian dynamic systems, SMC(also named particle filter, PF) is quite capable of performing filtering and RUL assessment recursively. The underlying deterioration of a system/device is seen as a stochastic process with continuous, nonreversible degrading. The state of the deterioration tendency is filtered and predicted with updating observations through the SMC procedure. The corresponding remaining useful life of the system/device is estimated based on the state degradation and a predefined threshold of the failure with two-sided criterion. The paper presents an application on a milling machine for cutter tool RUL assessment by applying the above proposed methodology. The example shows the promising results and the effectiveness of SSM and SMC online assessment of RUL.

COMPUTERIZED SIMULATION OF THERMODYNAMICS FOR MOLTEN LiF-KF SOLUTION BY MONTE CARLO METHOD

The structure and behaviour of LiF-KF solution,as a typical common-anion system,has been simulated by Monte Carlo method.The calculation of partial radial distribution function of ions,heat of mixing and potential energy distribution shows that the average distance be- tween Li^+ and F^- ions will significantly narrow after mixing of molten LiF and KF.This is very similar to the lean-on-one-side effect in molten LiF-KCl solution.The calculated heat of mixing is in fair agreement with the measured one.The dominant source of the energy of mixing may be that the decrease of the repulsion energy between cations,the decrease of the attraction energy between cations and anions,and the decrease of the repulsion energy be- tween anions.

Speckle intensity images of target based on Monte Carlo method

Speckle intensity in the detector plane is deduced in the free-space optical system and imaging system based on Van Cittert-Zemike theorem. The speckle intensity images of plane target and conical target are obtained by using the Monte Carlo method and measured experimentally. The results show that when the range extent of target is smaller, the speckle size along the same direction become longer, and the speckle size increase with increasing incident light wavelengths. The speckle size increases and the speckle intensity images of target is closer to the actual object when the aperture scale augments. These findings are useful to access the target information by speckle in laser radar systems.

Direct Monte Carlo Method Simulation of the Synthesis of Carbon Particle Through Coagulation in the Detonation of Explosives

A model is constructed and used in computing the coagulation probability of free carbon during the detonation of explosives. A direct simulation Monte Carlo (DSMC) program is constructed to simulate the coagulation of free carbon particles. The evaluation of the distribution spectrum of particles in the system is obtained. The simulation result is consistent with the experimental curve.

Application of local Monte Carlo method in neutronics calculation of EAST radial neutron camera

The Local Monte Carlo(LMC)method is used to solve the problems of deep penetration and long time in the neutronics calculation of the radial neutron camera(RNC)diagnostic system on the experimental advanced superconducting tokamak(EAST),and the radiation distribution of the RNC and the neutron flux at the detector positions of each channel are obtained.Compared with the results calculated by the global variance reduction method,it is shown that the LMC calculation is reliable within the reasonable error range.The calculation process of LMC is analyzed in detail,and the transport process of radiation particles is simulated in two steps.In the first step,an integrated neutronics model considering the complex window environment and a neutron source model based on EAST plasma shape are used to support the calculation.The particle information on the equivalent surface is analyzed to evaluate the rationality of settings of equivalent surface source and boundary.Based on the characteristic that only a local geometric model is needed in the second step,it is shown that the LMC is an advantageous calculation method for the nuclear shielding design of tokamak diagnostic systems.

Calculation of Neutral Particle Energy Spectra in Tokamak by Using the Monte Carlo Method

Neutral particle energy spectra in the HT-7 tokamak are calculated by using the Monte Carlo method. It can reproduce the spectra measured in experiment. Differences of neutral particle energy spectra in higher and lower electron density plasma are discussed. Results show that the ion temperature given by neutral particle energy spectra is lower than the real ion temperature, but the deviation is within 10% if the ion temperature is less than 800 eV and thecentral chord-averaged electron density does not exceed 3 ×1013 cm-3. But for ion temperature higher than 1000 eV at the central chord-averaged density limit up to 5 ×1013 cm-3, the neutral particle energy spectra can still give the ion temperature within 10% deviation.

Multi-Scale Variation Prediction of PM2.5 Concentration Based on a Monte Carlo Method

Haze concentration prediction,especially PM2.5,has always been a significant focus of air quality research,which is necessary to start a deep study.Aimed at predicting the monthly average concentration of PM2.5 in Beijing,a novel method based on Monte Carlo model is conducted.In order to fully exploit the value of PM2.5 data,we take logarithmic processing of the original PM2.5 data and propose two different scales of the daily concentration and the daily chain development speed of PM2.5 respectively.The results show that these data are both approximately normal distribution.On the basis of the results,a Monte Carlo method can be applied to establish a probability model of normal distribution based on two different variables and random sampling numbers can also be generated by computer.Through a large number of simulation experiments,the average monthly concentration of PM2.5 in Beijing and the general trend of PM2.5 can be obtained.By comparing the errors between the real data and the predicted data,the Monte Carlo method is reliable in predicting the PM2.5 monthly mean concentration in the area.This study also provides a feasible method that may be applied in other studies to predict other pollutants with large scale time series data.

Calculation of Neutron-Proton Mass Difference by the Monte Carlo Method

Calculation results of the Monte Carlo method of the average energy of the electrostatic interaction between the quarks are presented to the neutron and proton. The proposed model of the distribution of quarks in protons and neutrons is possible to assess the area which included a strong (gluon) interaction. Given the fact that the probability of finding a quark in the field with strong interaction is less than one, there is a good agreement between the experimental and calculated values of the mass difference between the neutron and the proton.

Evaluation the Price of Multi-Asset Rainbow Options Using Monte Carlo Method

Solution of the system stochastic differential equations in multi dimensional case using Monte Carlo method had many useful features in compare with the other computational methods. One of them is the solution of boundary value problems to be found at just one point, if required (with associated saving in computation), whereas deterministic methods necessarily find the solution at large number of points simultaneously. This property can be particularly useful in problems such option pricing, where the value of an option is required only at the time of striking, and for the state of the market at that time. In this work we consider a European multi-asset options which mathematically described by the system of stochastic differential equations. We will apply Monte Carlo method for the solution of that system which is the price of Multi-asset rainbow options.

On Solving a System of Volterra Integral Equations with Relaxed Monte Carlo Method

A random simulation method was used for treatment of systems of Volterra integral equations of the second kind. Firstly, a linear algebra system was obtained by discretization using quadrature formula. Secondly, this algebra system was solved by using relaxed Monte Carlo method with importance sampling and numerical approximation solutions of the integral equations system were achieved. It is theoretically proved that the validity of relaxed Monte Carlo method is based on importance sampling to solve the integral equations system. Finally, some numerical examples from literatures are given to show the efficiency of the method.

Impact of weather conditions and building design on contaminant infiltration from crawl spaces in Swedish schools-Numerical modeling using Monte Carlo method

Some Swedish school buildings built in the 1960s and 1970s experience indoor air quality problems,where the contaminants are suspected to come from the crawl space underneath the building.The poor indoor air quality causes discomfort among pupils and teachers.Installing an exhaust fan to maintain a negative pressure difference in the crawl space relative to indoors or increasing the ventilation in the classroom are two examples of common measures taken to improve the indoor air quality.However,these measures are not always effective,and sometimes the school building has to be demolished.The relation between pressure distribution,contaminant concentration in the classroom,outdoor temperature,wind,mechanical ventilation,and air leakage distribution is complex.A better understanding of these relations is crucial for making decisions on the most efficient measure to improve the indoor air quality.In this paper,a model for contaminant infiltration from the crawl space is used together with the Monte Carlo method to study these relations.Simulations are performed for several cases where different building shapes,building orientations,shielding conditions,and geographical locations are simulated.Results show,for example,that for a building with an imbalanced ventilation system,air is leaking from the crawl space to the classroom for the majority of cases and that concentration levels in the classroom are usually the highest during mild and calm days.

Light Propagation along the Pericardium Meridian at Human Wrist as Evidenced by the Optical Experiment and Monte Carlo Method

Objective： To explore the characteristics of light propagation along the Pericardium Meridian and its surrounding areas at human wrist by using optical experiment and Monte Carlo method. Methods： An experiment was carried out to obtain the distribution of diffuse light on Pericardium Meridian line and its surrounding areas at the wrist, and then a simplified model based on the anatomical structure was proposed to simulate the light transportation within the same area by using Monte Carlo method. Results： The experimental results showed strong accordance with the Monte Carlo simulation that the light propagation along the Pericardium Meridian had an advantage over its surrounding areas at the wrist. Conclusion： The advantage of light transport along Pericardium Merdian line was related to components and structure of tissue, also the anatomical structure of the area that the Pericardium Meridian line runs.

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.

Research on Equipment Support Activity Process Simulation Based on Monte Carlo Method

The influencing factors of the equipment support activity process have the characteristics of nonlinearity, high dimension, many constraints, random uncertainty and fuzzy uncertainty. Monte Carlo method can solve the above problems commendably. This paper analyzes the main equipment support activity process and establishes the sampling plan and simulation model of the medium maintenance process based on Monte Carlo method, and the simulation result verifies a fact that the medium maintenance time can be effectively reduced when parallel operation on some procedures is used. It has a practical value and can give good advice to achieve the capability of equipment supportability.

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.