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 predictio...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.展开更多
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...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.展开更多
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 supercondu...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.展开更多
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 Bei...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.展开更多
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 prot...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.展开更多
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 boun...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.展开更多
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 ...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.展开更多
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 c...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.展开更多
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 accelerati...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.展开更多
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 ...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.展开更多
This paper presents a dynamic and static error transfer model and uncertainty evaluation method for a high-speed variable-slit system based on a two- dimensional orthogonal double-layer air-floating guide rail structu...This paper presents a dynamic and static error transfer model and uncertainty evaluation method for a high-speed variable-slit system based on a two- dimensional orthogonal double-layer air-floating guide rail structure. The motion accuracy of the scanning blade is affected by both the moving component it is attached to and the moving component of the following blade during high-speed motion. First, an error transfer model of the high-speed variable-slit system is established, and the influence coefficients are calculated for each source of error associated with the accuracy of the blade motion. Then, the maximum range of each error source is determined by simulation and experiment. Finally, the uncertainty of the blade displacement measurement is evaluated using the Monte Carlo method. The proposed model can evaluate the performance of the complex mechanical system and be used to guide the design.展开更多
For a local area road network,the available traffic data of traveling are the flow volumes in the key intersections,not the complete OD matrix.Considering the circumstance characteristic and the data availability of a...For a local area road network,the available traffic data of traveling are the flow volumes in the key intersections,not the complete OD matrix.Considering the circumstance characteristic and the data availability of a local area road network,a new model for traffic assignment based on Monte Carlo simulation of intersection turning movement is provided in this paper.For good stability in temporal sequence,turning ratio is adopted as the important parameter of this model.The formulation for local area road network assignment problems is proposed on the assumption of random turning behavior.The traffic assignment model based on the Monte Carlo method has been used in traffic analysis for an actual urban road network.The results comparing surveying traffic flow data and determining flow data by the previous model verify the applicability and validity of the proposed methodology.展开更多
InMarkov ChainMonte Carlo(MCMC)simulations,thermal equilibria quantities are estimated by ensemble average over a sample set containing a large number of correlated samples.These samples are selected in accordance wit...InMarkov ChainMonte Carlo(MCMC)simulations,thermal equilibria quantities are estimated by ensemble average over a sample set containing a large number of correlated samples.These samples are selected in accordance with the probability distribution function,known from the partition function of equilibrium state.As the stochastic error of the simulation results is significant,it is desirable to understand the variance of the estimation by ensemble average,which depends on the sample size(i.e.,the total number of samples in the set)and the sampling interval(i.e.,cycle number between two consecutive samples).Although large sample sizes reduce the variance,they increase the computational cost of the simulation.For a given CPU time,the sample size can be reduced greatly by increasing the sampling interval,while having the corresponding increase in variance be negligible if the original sampling interval is very small.In this work,we report a few general rules that relate the variance with the sample size and the sampling interval.These results are observed and confirmed numerically.These variance rules are derived for theMCMCmethod but are also valid for the correlated samples obtained using other Monte Carlo methods.The main contribution of this work includes the theoretical proof of these numerical observations and the set of assumptions that lead to them.展开更多
Background:This article investigates the Least-Squares Monte Carlo Method by using different polynomial basis in American Asian Options pricing.The standard approach in the option pricing literature is to choose the b...Background:This article investigates the Least-Squares Monte Carlo Method by using different polynomial basis in American Asian Options pricing.The standard approach in the option pricing literature is to choose the basis arbitrarily.By comparing four different polynomial basis we show that the choice of basis interferes in the option's price.Methods:We assess Least-Squares Method performance in pricing four different American Asian Options by using four polynomial basis:Power,Laguerre,Legendre and Hermite A.To every American Asian Option priced,three sets of parameters are used in order to evaluate it properly.Results:We show that the choice of the basis interferes in the option's price by showing that one of them converges to the option's value faster than any other by using fewer simulated paths.In the case of an Amerasian call option,for example,we find that the preferable polynomial basis is Hermite A.For an Amerasian put option,the Power polynomial basis is recommended.Such empirical outcome is theoretically unpredictable,since in principle all basis can be indistinctly used when pricing the derivative.Conclusion:In this article The Least-Squares Monte Carlo Method performance is assessed in pricing four different types of American Asian Options by using four different polynomial basis through three different sets of parameters.Our results suggest that one polynomial basis is best suited to perform the method when pricing an American Asian option.Theoretically all basis can be indistinctly used when pricing the derivative.However,our results does not confirm these.We find that when pricing an American Asian put option,Power A is better than the other basis we have studied here whereas when pricing an American Asian call,Hermite A is better.展开更多
In this paper we propose a general framework for the uncertainty quantification of quantities of interest for high-contrast single-phase flow problems.It is based on the generalized multiscale finite element method(GM...In this paper we propose a general framework for the uncertainty quantification of quantities of interest for high-contrast single-phase flow problems.It is based on the generalized multiscale finite element method(GMsFEM)and multilevel Monte Carlo(MLMC)methods.The former provides a hierarchy of approximations of different resolution,whereas the latter gives an efficient way to estimate quantities of interest using samples on different levels.The number of basis functions in the online GMsFEM stage can be varied to determine the solution resolution and the computational cost,and to efficiently generate samples at different levels.In particular,it is cheap to generate samples on coarse grids but with low resolution,and it is expensive to generate samples on fine grids with high accuracy.By suitably choosing the number of samples at different levels,one can leverage the expensive computation in larger fine-grid spaces toward smaller coarse-grid spaces,while retaining the accuracy of the final Monte Carlo estimate.Further,we describe a multilevel Markov chain Monte Carlo method,which sequentially screens the proposal with different levels of approximations and reduces the number of evaluations required on fine grids,while combining the samples at different levels to arrive at an accurate estimate.The framework seamlessly integrates the multiscale features of the GMsFEM with the multilevel feature of the MLMC methods following the work in[26],and our numerical experiments illustrate its efficiency and accuracy in comparison with standard Monte Carlo estimates.展开更多
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 developi...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.展开更多
The use of carbon-ion radiotherapy(CIRT)is gradually increasing.Owing to the generation of high-energy secondary neutrons during CIRT,its use presents new challenges in radiation protection.Thus,secondary neutron dose...The use of carbon-ion radiotherapy(CIRT)is gradually increasing.Owing to the generation of high-energy secondary neutrons during CIRT,its use presents new challenges in radiation protection.Thus,secondary neutron dose distributions must be explored and evaluated under clinical scenarios based on different treatment configurations.However,neutron dose and energy spectrum measurements are often difficult.This can be primarily attributed to the inherent limitations of most neutron detectors,such as their unsuitability for spectral measurements and inaccurate responses to neutrons with energies above 20 MeV.Numerical calculation methods based on probabilistic statistical theory are fast and convenient for neutron dose evaluation.In this study,external secondary neutron doses at the heavy ion medical machine in Wuwei,which is equipped with a passive beam delivery system,were calculated using the Monte Carlo method.The dependence of neutron doses on various treatment parameters(incident carbon-ion beam energy,spatial location,field size,and spread-out Bragg peak(SOBP)width)was investigated.Furthermore,the feasibility of applying an analytical model to predict the ambient dose equivalent was verified.For the combination involving an energy of 400 MeV=u and SOBP width of 6 cm,the ambient dose equivalent per therapeutic dose(H=D)at the isocenter was 79.87 mSv=Gy:The H=D value decreased rapidly with increasing spatial distance and slightly with increasing aperture size and SOBP width.The H=D values derived from the Monte Carlo simulations were in good agreement with the results reported in the literature.The analytical model could be used to quickly predict the H=D value along the incidence direction of the beam with an error of less than 20%.Thus,our study contributes to the understanding of the relationship between neutron radiation and treatment configuration parameters,which establishes a basis for predicting non-therapeutic radiation doses in CIRT.展开更多
The neutron spectrum unfolding by Bonner sphere spectrometer(BSS) is considered a complex multidimensional model,which requires complex mathematical methods to solve the first kind of Fredholm integral equation. In or...The neutron spectrum unfolding by Bonner sphere spectrometer(BSS) is considered a complex multidimensional model,which requires complex mathematical methods to solve the first kind of Fredholm integral equation. In order to solve the problem of the maximum likelihood expectation maximization(MLEM) algorithm which is easy to suffer the pitfalls of local optima and the particle swarm optimization(PSO) algorithm which is easy to get unreasonable flight direction and step length of particles, which leads to the invalid iteration and affect efficiency and accuracy, an improved PSO-MLEM algorithm, combined of PSO and MLEM algorithm, is proposed for neutron spectrum unfolding. The dynamic acceleration factor is used to balance the ability of global and local search, and improves the convergence speed and accuracy of the algorithm. Firstly, the Monte Carlo method was used to simulated the BSS to obtain the response function and count rates of BSS. In the simulation of count rate, four reference spectra from the IAEA Technical Report Series No. 403 were used as input parameters of the Monte Carlo method. The PSO-MLEM algorithm was used to unfold the neutron spectrum of the simulated data and was verified by the difference of the unfolded spectrum to the reference spectrum. Finally, the 252Cf neutron source was measured by BSS, and the PSO-MLEM algorithm was used to unfold the experimental neutron spectrum.Compared with maximum entropy deconvolution(MAXED), PSO and MLEM algorithm, the PSO-MLEM algorithm has fewer parameters and automatically adjusts the dynamic acceleration factor to solve the problem of local optima. The convergence speed of the PSO-MLEM algorithm is 1.4 times and 3.1 times that of the MLEM and PSO algorithms. Compared with PSO, MLEM and MAXED, the correlation coefficients of PSO-MLEM algorithm are increased by 33.1%, 33.5% and 1.9%, and the relative mean errors are decreased by 98.2%, 97.8% and 67.4%.展开更多
Recently,the family of rare-earth chalcohalides were proposed as candidate compounds to realize the Kitaev spin liquid(KSL)[Chin.Phys.Lett.38047502(2021)].In the present work,we firstly propose an effective spin Hamil...Recently,the family of rare-earth chalcohalides were proposed as candidate compounds to realize the Kitaev spin liquid(KSL)[Chin.Phys.Lett.38047502(2021)].In the present work,we firstly propose an effective spin Hamiltonian consistent with the symmetry group of the crystal structure.Then we apply classical Monte Carlo simulations to preliminarily study the model and establish a phase diagram.When approaching to the low temperature limit,several magnetic long range orders are observed,including the stripe,the zigzag,the antiferromagnetic(AFM),the ferromagnetic(FM),the incommensurate spiral(IS),the multi-Q,and the 120°ones.We further calculate the thermodynamic properties of the system,such as the temperature dependence of the magnetic susceptibility and the heat capacity.The ordering transition temperatures reflected in the two quantities agree with each other.For most interaction regions,the system is magnetically more susceptible in the ab-plane than in the c-direction.The stripe phase is special,where the susceptibility is fairly isotropic in the whole temperature region.These features provide useful information to understand the magnetic properties of related materials.展开更多
During heat treatment or mechanical processing,most polycrystalline materials experience grain growth,which significantly affects their mechanical properties.Microstructure simulation on a mesoscopic scale is an impor...During heat treatment or mechanical processing,most polycrystalline materials experience grain growth,which significantly affects their mechanical properties.Microstructure simulation on a mesoscopic scale is an important way of studying grain growth.A key research focus of this type of method has long been how to efficiently and accurately simulate the grain growth caused by a non-uniform temperature field with temperature gradients.In this work,we propose an improved 3D Monte Carlo Potts(MCP)method to quantitatively study the relationship between non-uniform temperature fields and final grain morphologies.Properties of the aluminum alloy AA6061-T6 are used to establish a trial calculation model and to verify the algorithms with existing experimental results in literature.The detailed grain growth process of the 6061-T6 aluminum alloy under different temperature fields is then obtained,and grain morphologies at various positions are analyzed.Results indicate that while absolute temperature and duration time are the primary factors determining the final grain size,the temperature gradient also has strong influence on the grain morphologies.The relationships between temperatures,temperature gradients and grain growth process have been established.The proposed MCP algorithm can be applied to different types of materials when the proper parameters are used.展开更多
基金Project supported by the Hefei National Research Center for Physical Sciences at the Microscale (Grant No.KF2021002)the Natural Science Foundation of Shanxi Province,China (Grant Nos.202303021221029 and 202103021224051)+2 种基金the National Natural Science Foundation of China (Grant Nos.11975024,12047503,and 12275263)the Anhui Provincial Supporting Program for Excellent Young Talents in Colleges and Universities (Grant No.gxyq ZD2019023)the National Key Research and Development Program of China (Grant No.2018YFA0306501)。
文摘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.
基金Supported by Basic Research and Development Plan of China (973 Program,Grant Nos.2011CB013401,2011CB013402)Special Fundamental Research Funds for Central Universities of China(Grant No.DUT14QY21)
文摘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.
基金support and help in this research.This work was supported by Users with Excellence Program of Hefei Science Center CAS(No.2020HSC-UE012)Comprehensive Research Facility for Fusion Technology Program of China(No.2018-000052-73-01-001228)National Natural Science Foundation of China(No.11605241)。
文摘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.
文摘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.
文摘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.
文摘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.
文摘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.
基金The project has been funded by FORMAS,the Swedish Research Council for Environment,Agricultural Sciences and Spatial Planning and supported by Gothenburg Premises Administration.
文摘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.
基金supported by the National Natural Science Foundation of China(Nos.11775126,11545013,11605101)the Young Elite Scientists Sponsorship Program by CAST(No.2016QNRC001)+1 种基金Science Challenge Project by MIIT of China(No.TZ2018001)Tsinghua University,Initiative Scientific Research Program。
文摘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.
基金the Special Research Fund for the Research on Armored Vehicle Supportability Requirement Analysis(No.51319050302)
文摘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.
基金This work was funded by the National Natural Science Foundation of China(Grant No.51675136)the National Science and Technology Major Project(Grant No.2017ZX02101006-005)+1 种基金the China Postdoctoral Science Foundation(Grant No.2018T110291)the Heilongjiang Natural Science Foundation(Grant No.E2017032).
文摘This paper presents a dynamic and static error transfer model and uncertainty evaluation method for a high-speed variable-slit system based on a two- dimensional orthogonal double-layer air-floating guide rail structure. The motion accuracy of the scanning blade is affected by both the moving component it is attached to and the moving component of the following blade during high-speed motion. First, an error transfer model of the high-speed variable-slit system is established, and the influence coefficients are calculated for each source of error associated with the accuracy of the blade motion. Then, the maximum range of each error source is determined by simulation and experiment. Finally, the uncertainty of the blade displacement measurement is evaluated using the Monte Carlo method. The proposed model can evaluate the performance of the complex mechanical system and be used to guide the design.
基金This paper was based on the result of the research project“Exploring the Characteristics of Travel Behavior under Influence of Public Traffic Guidance Means and Modeling in the Actual Urban Traffic Network,”which was supported by a research grant(Grant No.60804048)from the National Natural Science Foundation of China“Study on Integrated Intelligent Transportation Systemthe Piloting Projects for 2010 EXPO in Shanghai”which was supported by a research grant(No.2006BAG01A02)from the Ministry of Science and Technology of the People’s Republic of China.
文摘For a local area road network,the available traffic data of traveling are the flow volumes in the key intersections,not the complete OD matrix.Considering the circumstance characteristic and the data availability of a local area road network,a new model for traffic assignment based on Monte Carlo simulation of intersection turning movement is provided in this paper.For good stability in temporal sequence,turning ratio is adopted as the important parameter of this model.The formulation for local area road network assignment problems is proposed on the assumption of random turning behavior.The traffic assignment model based on the Monte Carlo method has been used in traffic analysis for an actual urban road network.The results comparing surveying traffic flow data and determining flow data by the previous model verify the applicability and validity of the proposed methodology.
基金supported in part by the King Abdullah University of Science and Technology(KAUST)Center for Numerical Porous Media.In addition,S.Sun would also like to acknowledge the support of this study by a research award from King Abdulaziz City for Science and Technology(KACST)through a project entitled”Study of Sulfur Solubility using Thermodynamics Model and Quantum Chemistry”.
文摘InMarkov ChainMonte Carlo(MCMC)simulations,thermal equilibria quantities are estimated by ensemble average over a sample set containing a large number of correlated samples.These samples are selected in accordance with the probability distribution function,known from the partition function of equilibrium state.As the stochastic error of the simulation results is significant,it is desirable to understand the variance of the estimation by ensemble average,which depends on the sample size(i.e.,the total number of samples in the set)and the sampling interval(i.e.,cycle number between two consecutive samples).Although large sample sizes reduce the variance,they increase the computational cost of the simulation.For a given CPU time,the sample size can be reduced greatly by increasing the sampling interval,while having the corresponding increase in variance be negligible if the original sampling interval is very small.In this work,we report a few general rules that relate the variance with the sample size and the sampling interval.These results are observed and confirmed numerically.These variance rules are derived for theMCMCmethod but are also valid for the correlated samples obtained using other Monte Carlo methods.The main contribution of this work includes the theoretical proof of these numerical observations and the set of assumptions that lead to them.
文摘Background:This article investigates the Least-Squares Monte Carlo Method by using different polynomial basis in American Asian Options pricing.The standard approach in the option pricing literature is to choose the basis arbitrarily.By comparing four different polynomial basis we show that the choice of basis interferes in the option's price.Methods:We assess Least-Squares Method performance in pricing four different American Asian Options by using four polynomial basis:Power,Laguerre,Legendre and Hermite A.To every American Asian Option priced,three sets of parameters are used in order to evaluate it properly.Results:We show that the choice of the basis interferes in the option's price by showing that one of them converges to the option's value faster than any other by using fewer simulated paths.In the case of an Amerasian call option,for example,we find that the preferable polynomial basis is Hermite A.For an Amerasian put option,the Power polynomial basis is recommended.Such empirical outcome is theoretically unpredictable,since in principle all basis can be indistinctly used when pricing the derivative.Conclusion:In this article The Least-Squares Monte Carlo Method performance is assessed in pricing four different types of American Asian Options by using four different polynomial basis through three different sets of parameters.Our results suggest that one polynomial basis is best suited to perform the method when pricing an American Asian option.Theoretically all basis can be indistinctly used when pricing the derivative.However,our results does not confirm these.We find that when pricing an American Asian put option,Power A is better than the other basis we have studied here whereas when pricing an American Asian call,Hermite A is better.
基金Y.Efendiev’s work is partially supported by the U.S.Department of Energy Office of Science,Office of Advanced Scientific Computing Research,Applied Mathematics program under Award Number DE-FG02-13ER26165 and the DoD Army ARO ProjectThe research of B.Jin is partly supported by NSF Grant DMS-1319052.
文摘In this paper we propose a general framework for the uncertainty quantification of quantities of interest for high-contrast single-phase flow problems.It is based on the generalized multiscale finite element method(GMsFEM)and multilevel Monte Carlo(MLMC)methods.The former provides a hierarchy of approximations of different resolution,whereas the latter gives an efficient way to estimate quantities of interest using samples on different levels.The number of basis functions in the online GMsFEM stage can be varied to determine the solution resolution and the computational cost,and to efficiently generate samples at different levels.In particular,it is cheap to generate samples on coarse grids but with low resolution,and it is expensive to generate samples on fine grids with high accuracy.By suitably choosing the number of samples at different levels,one can leverage the expensive computation in larger fine-grid spaces toward smaller coarse-grid spaces,while retaining the accuracy of the final Monte Carlo estimate.Further,we describe a multilevel Markov chain Monte Carlo method,which sequentially screens the proposal with different levels of approximations and reduces the number of evaluations required on fine grids,while combining the samples at different levels to arrive at an accurate estimate.The framework seamlessly integrates the multiscale features of the GMsFEM with the multilevel feature of the MLMC methods following the work in[26],and our numerical experiments illustrate its efficiency and accuracy in comparison with standard Monte Carlo estimates.
文摘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.
基金the National Natural Science Foundation of China(Nos.12005271 and 12005273)the National Key Research and Development Program of China(No.E022223Y)+1 种基金the Western Talent Program of Chinese Academy of Sciences(No.29Y86205)the Key Deployment Project of Chinese Academy of Sciences(No.KFZD-SW-222).
文摘The use of carbon-ion radiotherapy(CIRT)is gradually increasing.Owing to the generation of high-energy secondary neutrons during CIRT,its use presents new challenges in radiation protection.Thus,secondary neutron dose distributions must be explored and evaluated under clinical scenarios based on different treatment configurations.However,neutron dose and energy spectrum measurements are often difficult.This can be primarily attributed to the inherent limitations of most neutron detectors,such as their unsuitability for spectral measurements and inaccurate responses to neutrons with energies above 20 MeV.Numerical calculation methods based on probabilistic statistical theory are fast and convenient for neutron dose evaluation.In this study,external secondary neutron doses at the heavy ion medical machine in Wuwei,which is equipped with a passive beam delivery system,were calculated using the Monte Carlo method.The dependence of neutron doses on various treatment parameters(incident carbon-ion beam energy,spatial location,field size,and spread-out Bragg peak(SOBP)width)was investigated.Furthermore,the feasibility of applying an analytical model to predict the ambient dose equivalent was verified.For the combination involving an energy of 400 MeV=u and SOBP width of 6 cm,the ambient dose equivalent per therapeutic dose(H=D)at the isocenter was 79.87 mSv=Gy:The H=D value decreased rapidly with increasing spatial distance and slightly with increasing aperture size and SOBP width.The H=D values derived from the Monte Carlo simulations were in good agreement with the results reported in the literature.The analytical model could be used to quickly predict the H=D value along the incidence direction of the beam with an error of less than 20%.Thus,our study contributes to the understanding of the relationship between neutron radiation and treatment configuration parameters,which establishes a basis for predicting non-therapeutic radiation doses in CIRT.
基金supported by the National Natural science Foundation of China (No. 42127807)the Sichuan Science and Technology Program (No. 2020YJ0334)the Sichuan Science and Technology Breeding Program (No. 2022041)。
文摘The neutron spectrum unfolding by Bonner sphere spectrometer(BSS) is considered a complex multidimensional model,which requires complex mathematical methods to solve the first kind of Fredholm integral equation. In order to solve the problem of the maximum likelihood expectation maximization(MLEM) algorithm which is easy to suffer the pitfalls of local optima and the particle swarm optimization(PSO) algorithm which is easy to get unreasonable flight direction and step length of particles, which leads to the invalid iteration and affect efficiency and accuracy, an improved PSO-MLEM algorithm, combined of PSO and MLEM algorithm, is proposed for neutron spectrum unfolding. The dynamic acceleration factor is used to balance the ability of global and local search, and improves the convergence speed and accuracy of the algorithm. Firstly, the Monte Carlo method was used to simulated the BSS to obtain the response function and count rates of BSS. In the simulation of count rate, four reference spectra from the IAEA Technical Report Series No. 403 were used as input parameters of the Monte Carlo method. The PSO-MLEM algorithm was used to unfold the neutron spectrum of the simulated data and was verified by the difference of the unfolded spectrum to the reference spectrum. Finally, the 252Cf neutron source was measured by BSS, and the PSO-MLEM algorithm was used to unfold the experimental neutron spectrum.Compared with maximum entropy deconvolution(MAXED), PSO and MLEM algorithm, the PSO-MLEM algorithm has fewer parameters and automatically adjusts the dynamic acceleration factor to solve the problem of local optima. The convergence speed of the PSO-MLEM algorithm is 1.4 times and 3.1 times that of the MLEM and PSO algorithms. Compared with PSO, MLEM and MAXED, the correlation coefficients of PSO-MLEM algorithm are increased by 33.1%, 33.5% and 1.9%, and the relative mean errors are decreased by 98.2%, 97.8% and 67.4%.
基金Project supported by the National Key Research and Development Program of China (Grant Nos. 2017YFA0302904 and 2016YFA0300504)the National Natural Science Foundation of China (Grant Nos. U1932215, 11774419, 11574392, and 11974421)+4 种基金the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDB33010100)the Fundamental Research Funds for the Central Universities,Chinathe Research Funds of Renmin University of China (Grant No. 19XNLG11)the support from Users with Excellence Program of Hefei Science CenterHigh Magnetic Field Facility,CAS
文摘Recently,the family of rare-earth chalcohalides were proposed as candidate compounds to realize the Kitaev spin liquid(KSL)[Chin.Phys.Lett.38047502(2021)].In the present work,we firstly propose an effective spin Hamiltonian consistent with the symmetry group of the crystal structure.Then we apply classical Monte Carlo simulations to preliminarily study the model and establish a phase diagram.When approaching to the low temperature limit,several magnetic long range orders are observed,including the stripe,the zigzag,the antiferromagnetic(AFM),the ferromagnetic(FM),the incommensurate spiral(IS),the multi-Q,and the 120°ones.We further calculate the thermodynamic properties of the system,such as the temperature dependence of the magnetic susceptibility and the heat capacity.The ordering transition temperatures reflected in the two quantities agree with each other.For most interaction regions,the system is magnetically more susceptible in the ab-plane than in the c-direction.The stripe phase is special,where the susceptibility is fairly isotropic in the whole temperature region.These features provide useful information to understand the magnetic properties of related materials.
基金The authors would like to acknowledge the financial support from China Postdoctoral Science Foundation Project(2018M641128)the National Key Research and Development Program of China(2018YFB0703500).
文摘During heat treatment or mechanical processing,most polycrystalline materials experience grain growth,which significantly affects their mechanical properties.Microstructure simulation on a mesoscopic scale is an important way of studying grain growth.A key research focus of this type of method has long been how to efficiently and accurately simulate the grain growth caused by a non-uniform temperature field with temperature gradients.In this work,we propose an improved 3D Monte Carlo Potts(MCP)method to quantitatively study the relationship between non-uniform temperature fields and final grain morphologies.Properties of the aluminum alloy AA6061-T6 are used to establish a trial calculation model and to verify the algorithms with existing experimental results in literature.The detailed grain growth process of the 6061-T6 aluminum alloy under different temperature fields is then obtained,and grain morphologies at various positions are analyzed.Results indicate that while absolute temperature and duration time are the primary factors determining the final grain size,the temperature gradient also has strong influence on the grain morphologies.The relationships between temperatures,temperature gradients and grain growth process have been established.The proposed MCP algorithm can be applied to different types of materials when the proper parameters are used.
