On the energy conservation electrostatic particle-in-cell/Monte Carlo simulation: Benchmark and application to the radio frequency discharges

We benchmark and analyze the error of energy conservation （EC） scheme in particle-in-cell/Monte Carlo （PIC/MC） algorithms by simulating the radio frequency discharge. The plasma heating behaviors and electron distributing functions obtained by one-dimensional （1D） simulation are analyzed. Both explicit and implicit algorithms are checked. The results showed that the EC scheme can eliminated the self-heating with wide grid spacing in both cases with a small reduction of the accuracies. In typical parameters, the EC implicit scheme has higher precision than EC explicit scheme. Some ＂numerical cooling＂ behaviors are observed and analyzed. Some other errors are also analyzed. The analysis showed that the EC implicit scheme can be used to qualitative estimation of some discharge problems with much less computational resource cost without much loss of accuracies.

Implicit electrostatic particle-in-cell/Monte Carlo simulation for the magnetized plasma:Algorithms and application in gas-inductive breakdown

An implicit electrostatic particle-in-cell/Monte Carlo （PIC/MC） algorithm is developed for the magnetized discharging device simulation. The inductive driving force can be considered. The direct implicit PIC algorithm （DIPIC） and energy conservation scheme are applied together and the grid heating can be eliminated in most cases. A tensor-susceptibility Poisson equation is constructed. Its discrete form is made up by a hybrid scheme in one-dimensional （1D） and two- dimensional （2D） cylindrical systems. A semi-coarsening multigrid method is used to solve the discrete system. The algorithm is applied to simulate the cylindrical magnetized target fusion （MTF） pre-ionization process and get qualitatively correct results. The potential application of the algorithm is discussed briefly.

Particle-in-cell/Monte Carlo simulation of filamentary barrier discharges

The plasma behavior of filamentary barrier discharges in helium is simulated using a twodimensional（2D） particle-in-cell/Monte Carlo model. Four different phases have been suggested in terms of the development of the discharge： the Townsend phase; the space-charge dominated phase; the formation of the cathode layer, and the extinguishing phase. The spatialtemporal evolution of the particle densities, velocities of the charged particles, electric fields, and surface charges has been demonstrated. Our simulation provides insights into the underlying mechanism of the discharge and explains many dynamical behaviors of dielectric barrier discharge（DBD） filaments.

基于Monte-Carlo仿真的恒应力加速试验方案模拟评价

为了保证可靠性加速试验方案的正确性和可行性,提出基于仿真的模拟评价方法。以最具代表性的Weibull寿命分布产品的恒应力加速寿命试验为例,以代表试验结果准确性和稳定性的指标——中位寿命估计值渐进方差的均值和标准差作为评价指标,通过Monte-Carlo仿真模拟生成失效数据,对不同试验方案的统计精度和稳定性进行评价,为加速寿命试验优化设计的工程实现提供了思路和实例验证。

Implementation of a particle-in-cell method for the energy solver in 3D spherical geodynamic modeling

The thermal evolution of the Earth’s interior and its dynamic effects are the focus of Earth sciences.However,the commonly adopted grid-based temperature solver is usually prone to numerical oscillations,especially in the presence of sharp thermal gradients,such as when modeling subducting slabs and rising plumes.This phenomenon prohibits the correct representation of thermal evolution and may cause incorrect implications of geodynamic processes.After examining several approaches for removing these numerical oscillations,we show that the Lagrangian method provides an ideal way to solve this problem.In this study,we propose a particle-in-cell method as a strategy for improving the solution to the energy equation and demonstrate its effectiveness in both one-dimensional and three-dimensional thermal problems,as well as in a global spherical simulation with data assimilation.We have implemented this method in the open-source finite-element code CitcomS,which features a spherical coordinate system,distributed memory parallel computing,and data assimilation algorithms.

Machine learning-enhanced Monte Carlo and subset simulations for advanced risk assessment in transportation infrastructure

The maintenance of safety and dependability in rail and road embankments is of utmost importance in order to facilitate the smooth operation of transportation networks.This study introduces a comprehensive methodology for soil slope stability evaluation,employing Monte Carlo Simulation(MCS)and Subset Simulation(SS)with the"UPSS 3.0 Add-in"in MS-Excel.Focused on an 11.693-meter embankment with a soil slope(inclination ratio of 2H:1V),the investigation considers earthquake coefficients(kh)and pore water pressure ratios(ru)following Indian zoning requirements.The chance of slope failure showed a considerable increase as the Coefficient of Variation(COV),seismic coefficients(kh),and pore water pressure ratios(ru)experienced an escalation.The SS approach showed exceptional efficacy in calculating odds of failure that are notably low.Within computational modeling,the study optimized the worst-case scenario using ANFIS-GA,ANFIS-GWO,ANFIS-PSO,and ANFIS-BBO models.The ANFIS-PSO model exhibits exceptional accuracy(training R2=0.9011,RMSE=0.0549;testing R2=0.8968,RMSE=0.0615),emerging as the most promising.This study highlights the significance of conducting thorough risk assessments and offers practical insights into evaluating and improving the stability of soil slopes in transportation infrastructure.These findings contribute to the enhancement of safety and reliability in real-world situations.

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.

Enhancing Precision in Radiotherapy Delivery: Validating Monte Carlo Simulation Models for 6 MV Elekta Synergy Agility LINAC Photon Beam Using Two Models of the GAMOS Code

The most crucial requirement in radiation therapy treatment planning is a fast and accurate treatment planning system that minimizes damage to healthy tissues surrounding cancer cells. The use of Monte Carlo toolkits has become indispensable for research aimed at precisely determining the dose in radiotherapy. Among the numerous algorithms developed in recent years, the GAMOS code, which utilizes the Geant4 toolkit for Monte Carlo simula-tions, incorporates various electromagnetic physics models and multiple scattering models for simulating particle interactions with matter. This makes it a valuable tool for dose calculations in medical applications and throughout the patient’s volume. The aim of this present work aims to vali-date the GAMOS code for the simulation of a 6 MV photon-beam output from the Elekta Synergy Agility linear accelerator. The simulation involves mod-eling the major components of the accelerator head and the interactions of the radiation beam with a homogeneous water phantom and particle information was collected following the modeling of the phase space. This space was po-sitioned under the X and Y jaws, utilizing three electromagnetic physics mod-els of the GAMOS code: Standard, Penelope, and Low-Energy, along with three multiple scattering models: Goudsmit-Saunderson, Urban, and Wentzel-VI. The obtained phase space file was used as a particle source to simulate dose distributions (depth-dose and dose profile) for field sizes of 5 × 5 cm2 and 10 × 10 cm2 at depths of 10 cm and 20 cm in a water phantom, with a source-surface distance (SSD) of 90 cm from the target. We compared the three electromagnetic physics models and the three multiple scattering mod-els of the GAMOS code to experimental results. Validation of our results was performed using the gamma index, with an acceptability criterion of 3% for the dose difference (DD) and 3 mm for the distance-to-agreement (DTA). We achieved agreements of 94% and 96%, respectively, between simulation and experimentation for the three electromagnetic physics models and three mul-tiple scattering models, for field sizes of 5 × 5 cm2 and 10 × 10 cm2 for depth-dose curves. For dose profile curves, a good agreement of 100% was found between simulation and experimentation for the three electromagnetic physics models, as well as for the three multiple scattering models for a field size of 5 × 5 cm2 at 10 cm and 20 cm depths. For a field size of 10 × 10 cm2, the Penelope model dominated with 98% for 10 cm, along with the three multiple scattering models. The Penelope model and the Standard model, along with the three multiple scattering models, dominated with 100% for 20 cm. Our study, which compared these different GAMOS code models, can be crucial for enhancing the accuracy and quality of radiotherapy, contributing to more effective patient treatment. Our research compares various electro-magnetic physics models and multiple scattering models with experimental measurements, enabling us to choose the models that produce the most reli-able results, thereby directly impacting the quality of simulations. This en-hances confidence in using these models for treatment planning. Our re-search consistently contributes to the progress of Monte Carlo simulation techniques in radiation therapy, enriching the scientific literature.

Chord length sampling correction analysis for dispersion fuel in Monte Carlo simulation

Dispersion fuels,knowned for their excellent safety performance,are widely used in advanced reactors,such as hightemperature gas-cooled reactors.Compared with deterministic methods,the Monte Carlo method has more advantages in the geometric modeling of stochastic media.The explicit modeling method has high computational accuracy and high computational cost.The chord length sampling(CLS)method can improve computational efficiency by sampling the chord length during neutron transport using the matrix chord length?s probability density function.This study shows that the excluded-volume effect in realistic stochastic media can introduce certain deviations into the CLS.A chord length correction approach is proposed to obtain the chord length correction factor by developing the Particle code based on equivalent transmission probability.Through numerical analysis against reference solutions from explicit modeling in the RMC code,it was demonstrated that CLS with the proposed correction method provides good accuracy for addressing the excludedvolume effect in realistic infinite stochastic media.

Evaluation of the Reliability of a System: Approach by Monte Carlo Simulation and Application

The objective of this paper is to evaluate the reliability of a system in its different states (absence of failures, partial failure and total failure) and to propose actions to improve this reliability by an approach based on Monte Carlo simulation. It consists of a probabilistic evaluation based on Markov Chains. In order to achieve this goal, the functionalities of Markov Chains and Monte Carlo simulation steps are deployed. The application is made on a production system. .

Health risk assessment of trace metal(loid)s in agricultural soils based on Monte Carlo simulation coupled with positive matrix factorization model in Chongqing, southwest China

This study aimed to investigate the pollution characteristics, source apportionment, and health risks associated with trace metal(loid)s(TMs) in the major agricultural producing areas in Chongqing, China. We analyzed the source apportionment and assessed the health risk of TMs in agricultural soils by using positive matrix factorization(PMF) model and health risk assessment(HRA) model based on Monte Carlo simulation. Meanwhile, we combined PMF and HRA models to explore the health risks of TMs in agricultural soils by different pollution sources to determine the priority control factors. Results showed that the average contents of cadmium(Cd), arsenic (As), lead(Pb), chromium(Cr), copper(Cu), nickel(Ni), and zinc(Zn) in the soil were found to be 0.26, 5.93, 27.14, 61.32, 23.81, 32.45, and 78.65 mg/kg, respectively. Spatial analysis and source apportionment analysis revealed that urban and industrial sources, agricultural sources, and natural sources accounted for 33.0%, 27.7%, and 39.3% of TM accumulation in the soil, respectively. In the HRA model based on Monte Carlo simulation, noncarcinogenic risks were deemed negligible(hazard index <1), the carcinogenic risks were at acceptable level(10^(-6)<total carcinogenic risk ≤ 10^(-4)), with higher risks observed for children compared to adults. The relationship between TMs, their sources, and health risks indicated that urban and industrial sources were primarily associated with As, contributing to 75.1% of carcinogenic risks and 55.7% of non-carcinogenic risks, making them the primary control factors. Meanwhile, agricultural sources were primarily linked to Cd and Pb, contributing to 13.1% of carcinogenic risks and 21.8% of non-carcinogenic risks, designating them as secondary control factors.

Evaluation of Particle Properties of MgO/TiO2 Material by Monte Carlo Simulation Method

The simulation by the Monte Carlo method executed by the software PyPENELOPE proved effective to specify the particle propagation characteristics by calculating the absorption fractions, backscattering and transmission of electrons and secondary photons under the incidence of 0.5 to 20 KeV range of primary electrons. More than 99.9% of the primary electrons were transmitted in the 125 nm thick MgO/TiO2 material at 20 KeV. This occurred because several interactions took place in the transmitted primary irradiation such as characteristic, fluorescence, and bremsstrahlung produced when of the occupation of the KL3, KL2, KM3, and KM2 shell and sub-shell of titanium and magnesium which are the elements with a high atomic number in the material. The transmission particle characteristic of this material is therefore an indicator capable of improving the electrical performance and properties of the sensor.

基于多元最小二乘-Monte Carlo模型在土石方测量中的应用研究

针对目前土方测量效率低,计算土方量精度差的现状,提出利用无人机进行土方测量,利用MATLAB软件进行编程,构建多元最小二乘-Monte Carlo模型对土方量进行计算,与传统的GNSS-RTK数据采集方法以及利用南方CASS软件计算结果对比,结果表明,利用无人机采集数据效率高,多元最小二乘-Monte Carlo模型取得结果精度更高。

基于Monte Carlo随机模拟算法的电动汽车无序充电负荷计算模型

为了有效降低电动汽车无序充电负荷对于电力系统稳定性的影响,研究了基于Monte Carlo随机模拟算法的计算模型。综合考虑用户充电行为各参数的概率密度,使得构建的模型更精确。分析了不同的充电策略对于充电负荷曲线的影响,并利用综合策略模型使得用户的充电成本更低,利用基于Levy飞行策略的改进麻雀算法对综合充电策略的权重系数进行寻优计算,以使得用户的成本和电网稳定均能获得不错的效果。在此基础上,提出利用双层优化模型对模型进一步优化,综合考虑用户满意度和电力波动的情况,结果表明改进后的模型,可以节省充电成本15.9%,降低电力系统负荷峰谷差约10.1%。

N_2-H_2容性耦合等离子体电非对称效应的particle-in-cell/Monte Carlo模拟

H_2-N_2混合气体电容性耦合射频放电在有机低介电系数材料刻蚀中具潜在研究意义.采用paxticle-incell/Monte Carlo模型模拟了双频(13.56 MHz/27.12 MHz)电压源分别接在结构对称的两个电极上的H_2-N_2容性耦合等离子体特征,研究了其电非对称效应.模拟结果表明,通过调节两谐波间的相位角θ,可以改变其电场、等离子体密度、离子流密度的轴向分布及离子轰击电极的能量分布.当相位角θ为0°时,低频电极(晶片)附近主要离子(H_3^+)的密度最小,离子(H_3^+,H_2^+,H^+)轰击低频电极的流密度及平均能量最高;当θ从0°变化90°时,低频电极的自偏压从-103V到106V近似线性增加,轰击电极的离子流密度变化约±18%,H^+离子轰击低频电极的最大能量约减小2.5倍,轰击电极的平均能量约变化2倍,表明氢离子能量和离子流几乎能独立控制.

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

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

基于Monte-Carlo迭代求解策略的局部社区发现算法

针对现有的局部社区发现算法因采用贪心策略进行社区扩张而导致的过早收敛和查全率低的问题,提出一种基于Monte-Carlo迭代求解策略的局部社区发现算法。首先,在每轮迭代的社区扩张阶段,根据节点对社区紧密度增益的贡献比例为所有邻接候选节点赋予选择概率,并结合此概率,再随机选择一个节点加入社区。然后,为避免随机选择导致扩张方向偏离目标社区,根据社区质量变化情况判断本轮迭代中是否触发节点淘汰机制。若触发,计算各个已加入社区节点与社区内其他节点的相似度和,根据相似度和的倒数赋予淘汰概率,并结合此概率,再随机淘汰一个节点。最后,在给定数量的最近迭代轮次中,根据社区规模是否增加判断是否继续迭代。在三个真实的网络数据集上进行实验,相较于局部紧密度扩展(LTE)算法、Clauset算法、加权共同邻居节点(CNWNN)算法和模糊相似关系(FSR)算法,所提算法的局部社区发现结果的F-score值分别提升了32.75、17.31、20.66和25.51个百分点,且能够有效避免查询节点在社区中所处位置对局部社区发现结果的影响。

基于二次电子发射的Monte Carlo仿真模拟

二次电子发射特性在现代先进真空电子器件中有着广泛的应用,准确测量二次电子的产额数据对进一步确定二次电子发射特性至关重要。然而,目前的实验条件无法保证高真空的实验环境和高精准的测量技术,导致得出的实验数据往往存在着不可避免的误差。因此,利用Monte Carlo计算方法模拟电子束与金属固体的相互作用过程已然成为了一种较为实用的解题方法。此方法是一种基于随机模拟的数值计算方法,通过重复随机采样,根据采样结果计算目标量的期望值,进而得到数值解,它在研究电子运输问题上具有极强的解题能量。模型采用经验Mott散射截面公式来快速描述电子的弹性散射过程,利用介电函数模型来描述电子的非弹性散射过程,从而快速计算出二次电子在金属内部的散射运动轨迹,通过定量分析出二次电子发射产额的影响因素。研究发现,二次电子产额随着入射粒子能量的增加而增加,在一定范围内产额随能量增加的趋势比较明显,但达到一定能量后,产额将趋于饱和。此外,入射角度对二次电子的产额分布也有显著影响。

具有下界约束混料试验的Monte-Carlo渐近最优设计

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

基于Monte Carlo方法的磁驱动准等熵压缩实验不确定度量化评估

磁驱动准等熵压缩实验是研究材料偏离Hugoniot状态高压物性和动力学行为的重要实验技术之一,开展不确定量化评估具有重要意义和价值。基于Monte Carlo原理,结合磁驱动准等熵压缩实验过程分析、Lagrange分析和特征线正向数据处理方法建立了适用于此类实验的Monte Carlo不确定度量化评估方法,实现利用磁驱动准等熵压缩实验获取材料声速、应力、应变等物理量以及状态方程和本构关系等物理模型的不确定度量化评估。利用建立的不确定度评估方法,对文献中已开展的钽、铜和NiTi合金的磁驱动准等熵压缩实验结果进行不确定度量化评估与分析。结果表明,基于本文中方法的评估结果与国外文献以相同原理得到的评估结果一致。对基于CQ-4装置开展的NiTi合金磁驱动准等熵压缩实验的评估结果表明,设计的磁驱动准等熵压缩实验是一种可靠的精密物理实验。在此基础上,深入讨论了磁驱动准等熵压缩实验的误差相关性和敏感性。结果表明:台阶样品厚度和粒子速度的测量是影响实验精度的主要因素。