Extrusion of pastes with a piston extruder for the determination of the local solid and fluid concentration, the local porosity and saturation and displacement profiles by means of NMR imaging

 Nuclear Magnetic Resonance (NMR) was used to investigate the extrusion behaviour of PTFE pastes in a ram extruder. By means of ¹H-NMR imaging (MRI) it is possible to determine the local proton density and therefore, the local fluid concentration. The ¹⁹F-MRI provides the local solid concentration. Thus the local saturation and the local porosity can be calculated with the information of the local fluid and solid concentration. Furthermore displacement profiles can be derived from NMR images by means of correlation techniques without any preparation or marking of the pastes. Received: 8 May 2000   Accepted: 1 May 2001     

Numerical solutions of the shallow water equations with discontinuous bed topography

A simple scheme is developed for treatment of vertical bed topography in shallow water flows. The effect of the vertical step on flows is modelled with the shallow water equations including local energy loss terms. The bed elevation is denoted with z_b^‐ for the left and z_b⁺ for the right values at each grid point, hence exactly representing a discontinuity in the bed topography. The surface gradient method (SGM) is generalized to reconstruct water depths at cell interfaces involving a vertical step so that the fluxes at the cell interfaces can accurately be calculated with a Riemann solver. The scheme is verified by predicting a surge crossing a step, a tidal flow over a step and dam‐break flows on wet/dry beds. The results have shown good agreements compared with analytical solutions and available experimental data. The scheme is efficient, robust, and may be used for practical flow calculations. Copyright © 2002 John Wiley & Sons, Ltd.     

关于图的同构判定方法的探讨

对于两图的同构的判定方法进行较深入的探讨,给出判定两图同构和判定两图不同构的几种方法,并对其判定方法的优劣进行比较.     

相对论性无自旋粒子在Hartmann势场中运动的精确解

在标量势等于矢量势的条件下,本文获得了具有Hartmann型势的Klein-Gordon方程的精确解.给出了束缚态的精确的能谱方程和归一化的径向波函数,对于散射态,获得了按“k/2π标度”归一化的径向波函数和相移的解析计算公式.讨论了散射振幅的解析性质和波函数、能谱方程以及相移的非相对论近似.     

非对称量子阱中非线性光学吸收系数的计算

非对称量子阱中的非线性光学效应因其潜在的实用价值而引起人们的广泛关注,而量子阱内带间的光学吸收问题对研究远红外光学探测器件具有重要的理论指导意义.以Pschl-Teller势阱为例研究了影响非对称量子阱中的非线性光学吸收系数的因素.考虑到带间的电子弛豫,用量子力学中的密度矩阵算符理论导出了Pschl-Teller势阱中的线性与三阶非线性光学吸收系数的表达式.因该势阱中有两个可调参数,通过调节系统的参数,发现该系统的非线性光学吸收系数呈规律性的变化.以典型的GaAs/AlGaAs非对称量子阱为例作了数值计算,通过调节系统的参数,数值计算结果表明,入射光强以及系统的非对称性对量子阱的非线性光学吸收系数有较大的影响,从而为实验上研究非对称量子阱的非线性光学效应提供了必要的理论依据.     

小尺寸铕(Ⅲ)配合物荧光纳米颗粒的制备

利用再沉淀法分别制备出了小尺寸(~10nm)纯相和杂相的Eu³⁺配合物荧光纳米颗粒。所制备的纯相的荧光纳米颗粒在水溶液中容易聚集,并且荧光猝灭严重。相比较而言,掺有适量疏水性硅烷的杂相纳米颗粒则具有较强的荧光、均匀的尺寸和良好的分散性。硅烷在碱性环境下(pH=9)迅速地水解,而后在纳米微粒的表面形成二氧化硅薄层。亲水的二氧化硅薄层消除了Eu³⁺配合物纳米颗粒间的疏水相互作用,进而防止了纳米颗粒的聚集,从而导致了杂相荧光纳米颗粒发光性能的提高。     

Remote stereocontrol by the sulfinyl group: Mukaiyama aldol reactions of (S)-2-[2-(p-tolylsulfinyl)phenyl]acetaldehyde in the asymmetric synthesis of β-hydroxyacids and 1,3-diols

(S)-2-[2-(p-Tolylsulfinyl)phenyl]acetaldehyde reacts with different O-silylated ketenethioacetals in the presence of Yb(OTf)₃ yielding β-hydroxythioesters in high yields and diastereoselectivities. The obtained compounds were readily transformed into β-hydroxyacids and their corresponding diols. These Mukaiyama aldol reactions are a direct evidence of the ability of the sulfinyl group to control 1,5- and 1,6-asymmetric induction processes.     

锥形透镜光纤聚焦特性研究

锥形透镜光纤(TLF)是实现光纤与平面光波光路(PLC)芯片高效耦合的核心元件。了解和掌握其聚焦特性是指导平面光波光路尾纤封装技术的关键。给出了表征锥形透镜光纤聚焦特性的两个参量出射光斑直径和远场发散角的理论分析模型,其误差小于1.14%;采用光束传播法数值模拟了锥形透镜光纤中的光波传输和模斑的演化,确定了锥形透镜光纤端面出射光斑的大小;优化锥形透镜光纤结构参量为:拉锥长度300μm,锥角0.733°,透镜曲率半径13.485μm;建立了基于数字摄像机的锥形透镜光纤出射光场测试系统,提出了物理光学反向推演法,计算出锥形透镜光纤聚焦光斑尺寸和远场发散角。理论与实验结果有着良好的一致:对于相同结构参量的锥形透镜光纤,实验反推法得到的出射光斑尺寸与理论值相比误差为3.15%,远场发散角误差为3.67%。     

Hankel convolution operators on entire functions and distributions

In this paper we study the Hankel convolution operators on the space of even and entire functions and on Schwartz distribution spaces. We characterize the Hankel convolution operators as those ones that commute with Hankel translations and with a Bessel operator. Also we prove that the Hankel convolution operators are hypercyclic and chaotic on the spaces under consideration.     

A solution of the DGLAP equation for gluon at low x

We obtain a solution of the DGLAP equation for the gluon at low x first by expanding the gluon in a Taylor series and then using the method of characteristics. We test its validity by comparing it with that of Glück, Reya and Vogt. The convergence criteria of the approximation used are also discussed. We also calculate εF ₂(x,Q)²/ε In Q ² using its approximate relations with the gluon distribution at low x. The predictions are then compared with the HERA data.