PARAMETRIC STUDY OF TISSUE OPTICAL CLEARING BY LOCALIZED MECHANICAL COMPRESSION USING COMBINED FINITE ELEMENT AND MONTE CARLO SIMULATION

Tissue Optical Clearing Devices(TOCDs)have been shown to increase light transmission through mechanically compressed regions of naturally turbid biological tissues.We hypothesize that zones of high compressive strain induced by TOCD pins produce localized water displacement and reversible changes in tissue optical properties.In this paper,we demonstrate a novel combined mechanical finite element model and optical Monte Carlo model which simulates TOCD pin compression of an ex vivo porcine skin sample and modified spatial photon fluence distributions within the tissue.Results of this simulation qualitatively suggest that light transmission through the skin can be significantly affected by changes in compressed tissue geometry as well as concurrent changes in tissue optical properties.The development of a comprehensive multi-domain model of TOCD application to tissues such as skin could ultimately be used as a framework for optimizing future design of TOCDs.

Probabilistic stability analyses of undrained slopes by 3D random fields and finite element methods

A long slope consisting of spatially random soils is a common geographical feature. This paper examined the necessity of three-dimensional(3 D) analysis when dealing with slope with full randomness in soil properties. Although 3 D random finite element analysis can well reflect the spatial variability of soil properties, it is often time-consuming for probabilistic stability analysis. For this reason, we also examined the least advantageous(or most pessimistic) cross-section of the studied slope. The concept of"most pessimistic" refers to the minimal cross-sectional average of undrained shear strength. The selection of the most pessimistic section is achievable by simulating the undrained shear strength as a 3 D random field. Random finite element analysis results suggest that two-dimensional(2 D) plane strain analysis based the most pessimistic cross-section generally provides a more conservative result than the corresponding full 3 D analysis. The level of conservativeness is around 15% on average. This result may have engineering implications for slope design where computationally tractable 2 D analyses based on the procedure proposed in this study could ensure conservative results.

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

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

Approach of technical decision-making by element flow analysis and Monte-Carlo simulation of municipal solid waste stream

This paper deals with the procedure and methodology which can be used to select the optimal treatment and disposal technology of municipal solid waste （MSW）, and to provide practical and effective technical support to policy-making, on the basis of study on solid waste management status and development trend in China and abroad. Focusing on various treatment and disposal technologies and processes of MSW, this study established a Monte-Carlo mathematical model of cost minimization for MSW handling subjected to environmental constraints. A new method of element stream （such as C, H, O, N, S） analysis in combination with economic stream analysis of MSW was developed. By following the streams of different treatment processes consisting of various techniques from generation, separation, transfer, transport, treatment, recycling and disposal of the wastes, the element constitution as well as its economic distribution in terms of possibility functions was identified. Every technique step was evaluated economically. The Mont-Carlo method was then conducted for model calibration. Sensitivity analysis was also carried out to identify the most sensitive factors. Model calibration indicated that landfill with power generation of landfill gas was economically the optimal technology at the present stage under the condition of more than 58% of C, H, O, N, S going to landfill. Whether or not to generate electricity was the most sensitive factor. If landfilling cost increases, MSW separation treatment was recommended by screening first followed with incinerating partially and composting partially with residue landfilling. The possibility of incineration model selection as the optimal technology was affected by the city scale. For big cities and metropolitans with large MSW generation, possibility for constructing large-scale incineration facilities increases, whereas, for middle and small cities, the effectiveness of incinerating waste decreases.

Rock-soil slope stability analysis by two-phase random media and finite elements

To investigate the strong random nature of the geometric interfaces between soil and rock, a rock-soil slope is considered as a two-phase random medium. A nonlinear translation of a Gaussian field is utilized to simulate the two-phase random media, such that the soil(or rock) volume fraction and the inclination of the soil layer can be examined. The finite element method with random media incorporated as the material properties is used to determine the factor of safety of the rock-soil slope. Monte-Carlo simulations are used to estimate the statistical characteristics of the factor of safety. The failure mode of the rock-soil slope is examined by observing the maximum principal plastic strain at incipient slope failure. It is found that the critical surface of a rock-soil slope is fairly irregular, and it significantly differs from that of a pure soil slope. The factor of safety is sensitive to the soil volume faction, but it is predictable. The average factor of safety could be well predicted by the weighted harmonic average between the strength of soil and rock; the prediction model is practical and simple. Parametric studies on the inclination of the soil layer demonstrate that the most instable scenario occurs when the slope angle is consistent with the inclination of the soil layer.

Probabilistic analysis of embankment slope stability in frozen ground regions based on random finite element method

Prediction on the coupled thermal-hydraulic fields of embankment and cutting slopes is essential to the assessment on evolution of melting zone and natural permafrost table, which is usually a key factor for permafrost embankment design in frozen ground regions. The prediction may be further complicated due to the inherent uncertainties of material properties. Hence, stochastic analyses should be conducted. Firstly, Karhunen-Loeve expansion is applied to attain the random fields for hydraulic and thermal conductions. Next, the mixed-form modified Richards equation for mass transfer （i.e., mass equation） and the heat transport equation for heat transient flow in a variably saturated frozen soil are combined into one equation with temperature unknown. Furthermore, the finite element formulation for the coupled thermal-hydraulic fields is derived. Based on the random fields, the stochastic finite element analyses on stability of embankment are carried out. Numerical results show that stochastic analyses of embankment stability may provide a more rational picture for the distribution of factors of safety （FOS）, which is definitely useful for embankment design in frozen ground regions.

Solving the Schrodinger Equation on the Basis of Finite-Difference and Monte-Carlo Approaches

The paper presents a method of numerical solution of the Schrodinger equation, which combines the finite-difference and Monte-Carlo approaches. The resulting method was effective and economical and, to a certain extent, not improved, i.e. optimal. The method itself is formalized as an algorithm for the numerical solution of the Schrodinger equation for a molecule with an arbitrary number of quantum particles. The method is presented and simultaneously illustrated by examples of solving the one-dimensional and multidimensional Schrodinger equation in such problems: linear one-dimensional oscillator, hydrogen atom, ion and hydrogen molecule, water, benzene and metallic hydrogen.

Identification of Water Quality Model Parameter Based on Finite Difference and Monte Carlo

Identification results of water quality model parameter directly affect the accuracy of water quality numerical simulation. To overcome the difficulty of parameter identification caused by the measurement’s uncertainty, a new method which is the coupling of Finite Difference Method and Markov Chain Monte Carlo is developed to identify the parameters of water quality model in this paper. Taking a certain long distance open channel as an example, the effects to the results of parameters identification with different noise are discussed under steady and un-steady non-uniform flow scenarios. And also this proposed method is compared with finite difference method and Nelder Mead Simplex. The results show that it can give better results by the new method. It has good noise resistance and provides a new way to identify water quality model parameters.

A Multiscale Multilevel Monte Carlo Method for Multiscale Elliptic PDEs with Random Coefficients

We propose a multiscale multilevel Monte Carlo(MsMLMC)method to solve multiscale elliptic PDEs with random coefficients in the multi-query setting.Our method consists of offline and online stages.In the offline stage,we construct a small number of reduced basis functions within each coarse grid block,which can then be used to approximate the multiscale finite element basis functions.In the online stage,we can obtain the multiscale finite element basis very efficiently on a coarse grid by using the pre-computed multiscale basis.The MsMLMC method can be applied to multiscale RPDE starting with a relatively coarse grid,without requiring the coarsest grid to resolve the smallestscale of the solution.We have performed complexity analysis and shown that the MsMLMC offers considerable savings in solving multiscale elliptic PDEs with random coefficients.Moreover,we provide convergence analysis of the proposed method.Numerical results are presented to demonstrate the accuracy and efficiency of the proposed method for several multiscale stochastic problems without scale separation.

基于Neumann展开Monte-Carlo有限元法的随机温度场分析

利用Neumann展开Monte-Carlo随机有限元法,对导热系数、换热系数、热流密度、环境温度以及内热源等物理参数同时具有随机性的温度场问题进行了分析,给出了节点温度响应的均值、变异系数和节点温度落在某一区间内的概率计算公式.通过算例考察了各随机变量的变异性大小对节点温度响应的影响,并表明随着结构的自由度数目增大,文中方法呈现出计算效率高的优点.

随机温度场Monte-Carlo法的一类近似处理

以非线性热辐射边界条件下多种材料构成的层叠板为研究对象,利用伽辽金法得到了瞬态非线性热传导微分方程组。考虑结构所有物理、几何和环境参数均具有随机性时,通过引入随机因子并提出一类关于热传导矩阵和热容矩阵的近似处理方法,实现了对随机温度场Monte-Carlo数值模拟时间的节省;并通过灵敏度和一阶泰勒展开线性化的方法去近似求解由于前面近似处理所造成的温度场数字特征的误差;算例表明了所给方法能节省大量的Monte-Carlo数值模拟时间,且给出的误差估计具有一定的精度。

Monte-Carlo随机有限元结构可靠度分析新方法

基于条件抽样、对偶抽样及Neumann展开技术,同时,为试图一定程度地解决"计算模型的不确定性"问题,考虑到岩石、混凝土等材料的单轴抗压强度σc和双轴等压强度σcc不同的特性,将3参数统一强度理论引入随机有限元程序,建立了Monte-Carlo三维非线性随机有限元结构可靠性分析模型。模拟成果表明,采用该模型的模拟收敛性良好,模拟效率较高、成本较低,可靠指标β值精度满足实用要求,在大型复杂结构的设计及可靠度分析研究中具有实用价值。

用改进的有限元Monte-Carlo法分析金属矿山点柱的可靠性

以某铜矿为例,简介无间柱连续采矿法。提出了基于MCS-ANN-FEM的改进的有限元Monte-Carlo法。通过无间柱连续采矿凿岩硐室点柱的强度和应力的计算,建立可靠性分析的隐式极限状态方程,然后运用基于MCS-ANN-FEM的改进的有限元Monte-Carlo分析方法,对点柱进行全面的可靠性分析和设计。

基于Monte-Carlo法和有限元的起重机结构可靠性研究

结合板壳元提出将蒙特卡罗法和有限元法相结合计算起重机结构可靠度的方法 ,以天津某港务局 4 0 t门座起重机为例 ,进行了灵敏度分析 ,定量给出了各随机因素对整体结构可靠性的影响 .该方法充分利用了现有软件的二次开发和输出能力 ,自编程序量小 .程序化。

Monte Carlo模拟法与基坑变形的可靠度分析

将ＭｏｎｔｅＣａｒｌｏ模拟法与有限元技术结合，对基坑变形的稳定性进行可靠度分析，并通过重构响应面来提高ＭｏｎｔｅＣａｒｌｏ模拟法的计算效率。研究表明该方法可行，计算结果较符合实际。

基于Monte Carlo方法数值反演区域初始构造应力场——以巴颜喀拉块体为例

构造应力场往往对地震活动性具有控制作用,应力快速集中的地方常常是地震频繁发生的地方.本文以巴颜喀拉块体及其边界断裂带近20年来的7次中强震为例,结合区域历史地震震源信息、地质背景及GPS等观测数据,利用MonteCarlo方法和库仑-摩尔破裂准则为计算依据,反演该块体的震前初始构造应力场.通过将初始应力场反演中不确定部分限定在一个合理的上下限范围内进行独立的重复性随机试验,并运用统计学方法得到了巴颜喀拉块体1997年玛尼MW7.5地震震前区域初始应力场.计算结果显示:(1)巴颜喀拉块体10km深度处最大水平主应力方向自西向东呈顺时针旋转趋势,由NS向转变为近EW向,与浅部实测地应力数据、历史地震类型和板块运动方向吻合较好.(2)最大/最小水平主应力和二者差值自西向东均逐渐增加,最大水平主压应力值~400MPa,最小水平主压应力值~250MPa.差应力在昆仑山断裂带与阿尔金断裂带交汇处及甘孜—玉树断裂带西段较低(~150MPa);在昆仑山断裂带东端和甘孜—玉树断裂带的东南段局部地区较高(~220MPa).

表面单层组装多环芳烃荧光行为的Monte Carlo模拟

用MonteCarlo方法模拟了惰性基片表面单层组装多环芳烃 (传感元素 )的荧光行为 ,考察了基片表面传感元素固定化百分率、传感元素激发百分率 (光吸收效率 )以及传感元素分子在介质中相互缔合形成激基缔合物趋势大小 (用P表示 ,P值介于 0到 1)等因素对传感元素激基缔合物荧光发射强度与单体荧光发射强度之比所产生的影响 .结果表明 ,具有中等光吸收效率的多环芳烃适宜于作为传感元素 。

基于Neumann展开的Monte-Carlo随机扩展有限元法

基于Neumann级数展开的Monte-Carlo随机有限元在涉及几何构形存在随机性的问题时,需要对网格进行重新划分,需要极大的计算量。为解决该问题,提高运算效率,提出一种新的计算裂纹问题的随机方法。该方法结合了扩展有限元法与随机有限元法的优点,通过对扩展有限元控制方程进行Neumann展开,可方便地处理几何构形的随机性,不需重新划分网格。该方法具有计算量小,计算效率高的优点,并能保持较高的计算精度。利用矩阵级数理论讨论了该方法的收敛性。最后通过数值算例验证了该方法的有效性。

不确定性结构区间分析的改进Monte Carlo方法

将结构系统中的不确定性参数用区间数来表示,建立了系统的区间有限元控制方程。利用Monte Carlo数值仿真方法对区间有限元控制方程进行求解,得到了结构的位移和应力响应区间。并针对一般Monte Carlo方法在区间仿真中存在的缺陷,对其进行了改进,使其计算效率大为提高。数值仿真算例表明:经改进的Monte Carlo方法仿真求解计算量大为减少,且能给出较高精度的响应区间,并克服了区间运算中的扩张问题。

Monte-Carlo法的黑体腔高温传感器有效发射率研究

基于Monte-Carlo法建立了圆筒形黑体空腔模型,对黑体空腔模型的有效发射率进行计算,分析了不同腔体几何结构、腔体材料发射率、探测器距腔口距离等因素对黑体腔有效发射率的影响,并与有限元分析法所得结果进行对比。结果表明:由Monte-Carlo法得到的结果与有限元分析法基本符合,即长径比较大、孔径比较小、腔体材料发射率较大时,黑体腔有效发射率较大。