单点子域积分与差分

通过稳定性分析、显式与隐式积分，表明了单点子域积分相对于差分法的优越性．     

单点子域积分与多点子域积分

基于单点子域精细积分的思想,针对抛物线型热传导方程初边值问题,提出了多点子域积分的概念,推出了一种多点子域积分的FTCS格式。该格式为显格式,并证明其为无条件稳定。数值算例表明,多点子域积分的FTCS格式具有比单点子域积分的FTCS格式收敛速度快的特点。     

EXACT LINEARIZATION BASED MULTIPLE-SUBSPACE ITERATIVE RESOLUTION TO AFFINE NONLINEAR CONTROL SYSTEM

To the optimal control problem of affine nonlinear system, based on differential geometry theory, feedback precise linearization was used. Then starting from the simulative relationship between computational structural mechanics and optimal control, multiple-substructure method was inducted to solve the optimal control problem which was linearized. And finally the solution to the original nonlinear system was found. Compared with the classical linearizational method of Taylor expansion, this one diminishes the abuse of error expansion with the enlargement of used region.     

非齐次动力方程Duhamel项的精细积分

提出了不需要矩阵求逆运算的求解Duhamel积分项的精细积分方法.通过将精细积分法的关键思想--加法定理和增量存储--直接应用于Duhamel积分响应矩阵的求解,可给出当非齐次项分别为多项式、正弦/余弦以及指数函数等基本形式时Duhamel积分在计算机上的精确解.特别的,该算法不依赖于系统矩阵(或相关矩阵)的形态.当系统矩阵奇异或接近奇异时,其优越性更为显著.算例验证了该算法的有效性.     

精细积分法在含各向异性介质波导不连续性问题中的应用

用精细积分法对含各向异性介质的波导不连续性问题进行了数值模拟与分析. 从矢量波动方程相对应的单变量变分形式出发, 推导出了含有各向异性介质波导横截面离散系数矩阵的表达式, 引入对偶变量, 在Hamilton体系下, 利用精细积分法求出出口刚度矩阵, 进行有限元拼装, 求解了含各向异性介质的波导不连续性问题. 算例表明了该方法的准确性和高效性. 利用本文方法还讨论了介电系数和导磁系数张量的各个分量对波导传输特性的影响. 关键词： 波导不连续性 各向异性介质 Hamilton体系 精细积分法     

精细积分方法的发展与扩展应用

钟万勰院士于1991年首先提出计算矩阵指数的精细积分方法,其要点是2^N类算法和增量存储。精细积分方法可给出矩阵指数在计算机意义上的精确解,为常微分方程的数值计算提供了高精度、高稳定性的算法,现已成功应用于结构动力响应、随机振动、热传导以及最优控制等众多领域。本文首先介绍矩阵指数精细积分方法的提出、基本思想和发展;然后依次介绍在时不变/时变线性微分方程、非线性微分方程以及大规模问题求解中发展起来的各种精细积分方法,分析了其优缺点和适用范围;最后介绍了精细积分方法的基本思想在两点边值问题、椭圆函数和病态代数方程等问题的扩展应用,进一步展示了该思想的特色。     

基于静力悬浮原理的单晶硅球间微量密度差异精密测量方法研究

单晶硅球间微量密度差异测量是阿伏伽德罗常数量子基准定义的重要研究内容, 也是半导体产业中高纯度单晶硅制备工艺质量控制的主要方法. 为了改善现有非接触相移干涉法测量装置复杂和静力称重法测量不确定度低的特点, 根据单晶硅密度精密测量需要, 实现了一种基于静力悬浮原理的单晶硅球密度相对参比测量方法. 通过改变静压力和温度进行三溴丙烷和二溴乙烷混合液体密度的微量调节, 分别使两个待测单晶硅球在液体中悬浮, 根据悬浮状态时的液体温度和悬浮高度计算出待测单晶硅球密度差值. 通过双循环水浴和PID温度控制系统实现±100 μK的恒温液体测量环境. 通过图像识别和迭代拟合算法实现单晶硅球悬浮高度的测量. 使用PID静压力控制系统实现单晶硅球的稳定悬浮控制, 同时减少Joule-Thomson效应引起的液体温度改变. 利用静力悬浮模型中的温度变化和静压力变化线性关系准确测量出标准液体的压缩系数. 试验结果表明, 这种测量方法可以避免液体液面张力的影响, 测量相对标准不确定度达到2.1×10^-7, 能够实现单晶硅球密度差值的精密测量.     

Deep insights into the hydrolysis of N,N‐dialkylaminoethyl methacrylates in aqueous solution with 1H NMR spectroscopy

N,N‐dialkylaminoethyl methacrylate (DAEA) monomers are extensively used to prepare multi‐responsive polymers. However, these monomers face high risk of hydrolysis in their ester groups when being polymerized in water‐containing medias. Here, NMR spectroscopy was employed to continuously track the hydrolysis and solubility of four widely used DAEA monomers [CH₂CH₂R₁COO(CH₂)₂N(R₂)₂; R₁ = H or CH₃; R₂ = CH₃, CH₂CH₃ or CH(CH₃)₂] under typical polymerization conditions. With this technique, the hydrolysis reactivity and absolute hydrolysis amount of these monomers are separately examined, and then their kinetic correlations with solubility, molecular structure, pH, and temperature are established, so that the hydrolysis of DAEA monomers and even other esters with similar cyclic structure can be predicted. The present efforts are expected to provide a general understanding for the hydrolysis of all the DAEA monomers, benefitting to the optimization of polymerization toward well‐defined DAEA copolymers, as well as the design of smart soft matter for specific applications. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2018 , 56, 914–923     

Atomically Precise Nanocluster Assemblies Encapsulating Plasmonic Gold Nanorods

The self‐assembled structures of atomically precise, ligand‐protected noble metal nanoclusters leading to encapsulation of plasmonic gold nanorods (GNRs) is presented. Unlike highly sophisticated DNA nanotechnology, this strategically simple hydrogen bonding‐directed self‐assembly of nanoclusters leads to octahedral nanocrystals encapsulating GNRs. Specifically, the p‐mercaptobenzoic acid (pMBA)‐protected atomically precise silver nanocluster, Na₄[Ag₄₄(pMBA)₃₀], and pMBA‐functionalized GNRs were used. High‐resolution transmission and scanning transmission electron tomographic reconstructions suggest that the geometry of the GNR surface is responsible for directing the assembly of silver nanoclusters via H‐bonding, leading to octahedral symmetry. The use of water‐dispersible gold nanoclusters, Au_≈250(pMBA)_n and Au₁₀₂(pMBA)₄₄, also formed layered shells encapsulating GNRs. Such cluster assemblies on colloidal particles are a new category of precision hybrids with diverse possibilities.