Reduced numerical modeling of flows involving liquid-crystalline polymers

Kinetic theory models involving the Fokker–Planck equation can be accurately discretized using a mesh support (Finite Elements, Finite Differences, Finite Volumes, Spectral Techniques, …). However, these techniques involve a high number of approximation functions. In the finite element framework, widely used in complex flow simulations, each approximation function has only local support and is related to a node that defines the associated degree of freedom. In the technique proposed here, a reduced approximation basis is constructed. The new shape functions have extended support and are defined in the whole domain in an appropriate manner (the most characteristic functions related to the model solution). Thus, the number of degrees of freedom involved in the solution of the Fokker–Planck equation is very significantly reduced. The construction of those new approximation functions is done with an ‘a priori’ approach, which combines a basis reduction (using the Karhunen–Loève decomposition) with a basis enrichment based on the use of some Krylov subspaces. This paper analyzes the application of model reduction to the simulation of non-linear kinetic theory models involving complex behaviors, such as those coming from stability analysis, complex geometries and coupled models. We apply our model reduction approach to the Doi's classical constitutive equation for viscoelasticity of liquid-crystalline polymer.     

Experimental and numerical investigation of a viscoplastic Carbopol gel injected into a prototype 3D mold cavity

A numerical model for free-surface flow of a viscoplastic liquid into a cavity is presented. This flow is regarded as a basic model of injection molding, which is a widely used processing technology. Model experiments of the injection process are performed with a water-based gel with shear-thinning behavior. The filling process is visualized by tracing the free surface of the gel within the cavity. Filling times of the cavity are deduced from the experimental observations. The filling process is also analyzed by means of numerical simulation.The flow equations are integrated according to the finite-volume method. The volume-of-fluid method is employed in order to describe the flow of two incompressible, immiscible phases, the phase interface is resolved by the method of geometric reconstruction or alternatively by the method of surface compression. The Herschel–Bulkley model is used in order to describe the shear-thinning behavior of the gel and the effects of a yielding point. The governing equations of the flow are solved by means of the commercial code Fluent as well as the Open Source code OpenFOAM.The results of the numerical simulations are analyzed in detail. They are compared with the experimental findings. Cavity filling times in the experiments and the simulations are in good agreement. Different patterns of the filling flow depending on the injection parameters are evident in the experiments and the simulations. They are characterized and arranged with respect to the similarity parameters of the flow configuration. Again, the results of the simulation are found to agree well with the experimental observations.     

阶跃光纤的模间色散

利用全反射所产生的相移角导出了全反射光在光纤包层中的横向偏移和光在光纤包层中的渡越时间.考虑光在光纤包层中的渡越时间后导出了模间色散时延差的修正公式,通过模拟计算分析了模间色散随入射角的变化规律.     

Influence of the spin-orbit couplingon nuclear superfluidity along the N = Z line

We show that the spin-orbit potential of the nuclear mean field destroys isoscalar superfluid correlations in self-conjugate nuclei. Using group theory and boson mapping techniques on a Hamiltonian including single particle splittings and a SO _ST(8) pairing interaction, we give analytical expressions for the spin-orbit dependence of some N = Z properties such as the relative position of T = 0 and T = 1 states in odd-odd systems or double binding-energy differences of even-even nuclei. Received: 12 April 2000 / Accepted: 25 May 2000     

ON LINEARIZED FINITE DIFFERENCE SIMULATION FOR THE MODEL OF NUCLEAR REACTOR DYNAMICS

1 hoeductIOuThe dynamics models of one--dimensional continuous medium nuclear reactor are the foelowing initial--boundary value problem of the formsubject to the innal conditionsand the boundary conditionsIn (1. 1), x denotes position along the reactor, which is regarded as a rod of length L, t denotes the time, u(t) the logarithm of the loud reactor POwer, v(x,t) the deviation of the temperature from equilibrium, a(x) the ratio of the temperature coefficient of reactivity to theynean life of…     

Fabrication of high-frequency electron beam moiré grating using multi-deposited layer techniques

This paper proposed new ways for producing multi-layer model grids for electron beam moiré method. An electron beam lithography system was set up under scanning electron microscope which was equipped with a beam blanking device and a pattern generator. The two-deposited-metal layers method was used to manufacture electron beam grating for high-temperature use. The results verify that the Zr–Pt-type grating possesses heat resistance up to 1100°C in vacuum. A new type of composite grating with frequencies 100 lines/mm and 1000 lines/mm using three deposited layers was produced. A 10 000 lines/mm two-deposited-metal layers grating was successfully fabricated using electron beam lithography.     

Electron moiré method and its application to micro-deformation measurement

In this paper, the single and two deposited metal layers method were proposed to produce the model grating for electron moiré method. The measurement principle of electron moiré method and the techniques for manufacturing model grid are expounded in detail. The accuracy of measuring strain using this method is discussed. The gratings with single deposited layer and two deposited layers with high frequency up to 5000 lines/mm were produced on different substrates. From the experimental results, both single deposited metal layer and two deposited metal layers gratings showed their heat resistance ability. Using the gratings produced and a replicated model grid, the electron moiré method was applied to measure the deformation of the strain around holes in a polyimide resin substrate, thermal strain of electronic packaging component and tensile creep around grain boundary in a pure copper specimen.     

钙矾石吸附水的模型及等温式

钙矾石３ＣａＯ·Ａｌ２Ｏ３·３ＣａＳＯ４·３２Ｈ２Ｏ是水泥熟料水化的重要产物．它易被空气中的ＣＯ２ 分解,常温下的分解反应为３ＣａＯ·Ａｌ２Ｏ３·３ＣａＳＯ４·３２Ｈ２Ｏ ３ＣＯ２ →３ＣａＣＯ３ Ａｌ２Ｏ３·ｘＨ２Ｏ ３（ＣａＳＯ４·２Ｈ２Ｏ） （２６ -ｘ）Ｈ２Ｏ分解机理［１ ,２］是：Ｈ２Ｏ先吸附在钙矾石表面的活性中心上,吸附态水再吸收ＣＯ２ 成为Ｈ２ＣＯ３ ,然后碳酸与钙矾石反应,实现碳化（即分解）．其分解速率［３］为ｖ＝ｋｐｃｏ２ ｐＨ２ｏ（１）可见水的吸附是钙矾石碳化分解的关键步骤,因此探讨…     

人体血糖浓度近红外光谱无创检测过程中温度对结果的影响

利用近红外光谱进行人体血糖浓度无创检测过程中,检测结果会受到很多的因素影响,如测量温度,压力等,另外还有人体的状态。在这诸多的影响因素中,温度是一个不可忽视的因素。为了研究温度对测量结果的定量影响,文章采用葡萄糖水溶液,在15,20,25,30,35,40 ℃等六个温度点处做了研究,样品浓度范围为10～200 mg·dL-1,浓度间隔为10 mg·dL-1,波长范围为1 100～1 700 nm。在各温度点处建立模型,并利用不同的模型进行相互预测。建模结果为RMSEP值最大为11.227 9 mg·dL-1,最小为3.298 8 mg·dL-1,相关系数在0.98左右。当温度改变1 ℃时,预测结果会有平均Δc＝2.662(mg·dL-1·℃-1)的预测误差,这结果表明当建立模型温度与测试时的温度一致时误差最小。另外,文章提出了可以采用两种方法来减小或者补偿由温度给测量结果来的影响。     

光栅光谱仪的整体建模与分析

理论模型是研究光谱技术,开发光谱仪器的重要工具。文章提出了一种对现代光栅光谱仪进行整体建模与分析的方法。与现有方法仅局限于光学成像等局部环节不同,该方法从光谱信息传递和变换的角度将光栅光谱仪分割为光学成像、探测、重建和显示4个功能模块,分析各个模块对光谱信息的影响,建立光栅光谱仪的整体模型并导出它的传递函数。进一步,又利用它们分析了各模块对仪器整体性能的影响规律,并揭示出要获得高质量的光谱图必须增加基带响应,抑制假响应,而重建模块将是重要途径。