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.

Effective model for rare-earth Kitaev materials and its classical Monte Carlo simulation

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.

Solving quantum rotor model with different Monte Carlo techniques

We systematically test the performance of several Monte Carlo update schemes for the(2+1)d XY phase transition of quantum rotor model.By comparing the local Metropolis(LM),LM plus over-relaxation(OR),Wolff-cluster(WC),hybrid Monte Carlo(HM),hybrid Monte Carlo with Fourier acceleration(FA)schemes,it is clear that among the five different update schemes,at the quantum critical point,the WC and FA schemes acquire the smallest autocorrelation time and cost the least amount of CPU hours in achieving the same level of relative error,and FA enjoys a further advantage of easily implementable for more complicated interactions such as the long-range ones.These results bestow one with the necessary knowledge of extending the quantum rotor model,which plays the role of ferromagnetic/antiferromagnetic critical bosons or Z_(2)topological order,to more realistic and yet challenging models such as Fermi surface Yukawa-coupled to quantum rotor models.

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.

ON THE MONTE CARLO SIMULATION OF NORMAL GRAIN GROWTH

The microstructures and their kinetics of normal grain growth are simulated using different Monte Carlo （MC） algorithms. Compared with the relative figures and the theoretical normal grain growth exponents of n =0.5, the effects of some factors of MC algorithm, i.e. the lattice types, the methods of selecting lattice sites, and the neighbors selection for energy calculations, on the simulation results of grain growth are studied. Two methods of regression were compared, and the three-parameter nonlinear regression is much more suitable for fitting the grain growth kinetics. A better model with appropriate factors included triangular lattice, the attempted site randomly selected, and the first and second nearest neighbors for energy calculations is obtained.

A MONTE CARLO SIMULATION OF THE CVD DIAMOND FILM

A Monte Carlo algorithm has been developed by the authors to simulate the chemical vapor deposition (CVD) processes of diamond films. The method considers both the diffusion and the incorporation of the growth radicals on the growing surface in simulating the evolution of the morphology and microstructure. The calculation of configuration energy is used to determine the orientation of adsorbed growth radicals. The effect of processing variables such as nucleation density and substrate temperature on the morphology and microstructure is discussed. It is found that competitive characteristic and coarsening effect exist in the simulation results, which agree with the experimental observations.

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.

Sorption and permeation of gaseous molecules in amorphous and crystalline PPX C membranes: molecular dynamics and grand canonical Monte Carlo simulation studies

Amorphous and crystalline poly （chloro-p-xytylene） （PPX C） membranes are constructed by using a novel com- putational technique, that is, a combined method of NVT＋NPT-molecular dynamics （MD） and gradually reducing the size （GRS） methods. The related free volumes are defined as homology clusters. Then the sorption and the permeation of gases in PPX C polymers are studied using grand canonical Monte Carlo （GCMC） and NVT-MD methods. The results show that the crystalline PPX C membranes provide smaller free volumes for absorbing or transferring gases relative to the amorphous PPX C area. The gas sorption in PPX C membranes mainly belongs to the physical one, and H bonds can appear obviously in the amorphous area. By cluster analyzing on the mean square displacement of gases, we find that gases walk along the x axis in the crystalline area and walk randomly in the amorphous area. The calculated permeability coefficients are close to the experimental data.

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.

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.

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 study of the neutron ambient dose equivalent at the heavy ion medical machine in Wuwei

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.

Hydrogen storage in BC_3 composite single-walled nanotube:a combined density functional theory and Monte Carlo investigation

This paper applies a density functional theory （DFT） and grand canonical Monte Carlo simulations （GCMC） to investigate the physisorptions of molecular hydrogen in single-walled BC3 nanotubes and carbon nanotubes. The DFT calculations may provide useful information about the nature of hydrogen adsorption and physisorption energies in selected adsorption sites of these two nanotubes. Furthermore, the GCMC simulations can reproduce their storage capacity by calculating the weight percentage of the adsorbed molecular hydrogen under different conditions. The present results have shown that with both computational methods, the hydrogen storage capacity of BC3 nanotubes is superior to that of carbon nanotubes. The reasons causing different behaviour of hydrogen storage in these two nanotubes are explained by using their contour plots of electron density and charge-density difference.

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.