The solubility of CO2 in triethylene glycol monomethyl ether

The solubility of CO₂ in triethylene glycol monomethyl ether (TEGMME) has been measured at 40, 70 and 100°C at pressures up to 8.8 MPa. The results were correlated with the Peng-Robinson (1976) equation of state. The interaction parameters and Henry's constants were derived.     

PHASE-SPACE DIFFUSION EQUATIONS FOR SINGLE BROWNIAN PARTICLE MOTION NEAR SURFACES

In numerous physical processes involving the motion of micron and submicron sized particles near surfaces, such as the filtration of hydrosols and aerosols, the particle motion is the net result of the combined effects of fluid convection, external forces, particle inertia, Brownian particle motion, and particle-surface fluid dynamic interactions. The most general method of describing particle motion under the combined action of these effects is through the so-called Fokker-Planck equation. In the absence of particle-surface fluid dynamic interactions, the Fokker-Planck equation is well-known, and it has been applied in a general way to problems involving the adsorption or deposition of Brownian particles onto surfaces through a solution technique known as the Brownian dynamics simulation method.

In this study, the Fokker-Planck equation for Brownian particle motion near surfaces is generalized to include particle-surface fluid dynamic interactions. The Fokker-Planck equation is shown to follow from the Liouville equation for the Brownian particle and n-fluid molecules present in the system, thus, establishing a firm theoretical foundation for the Fokker-Planck equation and the various other phase-space diffusion equations that follow from it.

Based on diagonalization of the Fokker-Planck equation, its short-time behavior is also derived here which enables a generalization of the Brownian dynamics method for the study of particle motion near surfaces including fluid dynamic interactions. Additionally, a perturbation solution of the Fokker-Planck equation under the conditions of small, but finite particle Stokes number is also derived. These solutions are shown to agree with previously given representations of the Smoluchowski or convective-diffusion equation for Brownian particle motion near surfaces, as well as with inertial corrections to the Smoluchowski equation available in the literature. This latter equation is also generalized here to include particle-surface fluid dynamic interactions.     

One-shot methods in function space for PDE-constrained optimal control problems

We state and analyse one-shot methods in function space for the optimal control of nonlinear partial differential equations (PDEs) that can be formulated in terms of a fixed-point operator. A general convergence theorem is proved by generalizing the previously obtained results in finite dimensions. As application examples we consider two nonlinear elliptic model problems: the stationary solid fuel ignition model and the stationary viscous Burgers equation. For these problems we present a more detailed convergence analysis of the method. The resulting algorithms are computationally implemented in combination with an adaptive mesh refinement strategy, which leads to an improvement in the performance of the one-shot approach.     

室温离子液体1-烷基-3-甲基咪唑硫酸甲酯的合成及电导率研究

利用硫酸二甲酯分别与N-甲基及N-丁基咪唑在室温下反应,一步合成了离子液体1-甲基-3-甲基咪唑硫酸甲酯和1-丁基-3-甲基咪唑硫酸甲酯,测定了在不同温度下离子液体的电导率.结果表明:随着温度的升高,离子液体的电导率迅速增加;同时电导率与温度的变化关系符合多项式方程和Vogel-Tammann-Fulcher(VTF)方程.     

一类非线性组合系统新的稳定性条件

研究组合大系统存在非线性扰动和不确定性时的稳定性问题。通过对微分方程解的结构研究,应用矩阵相似变换和矩阵指数的特性,将原非线性组合系统的稳定性问题转化为线性系统的稳定性问题。根据线性系统渐近稳定的充分条件,导出了原系统渐近稳定新的判定准则。最后运用数值实例说明了该方法的有效性和可行性。     

Dirichlet边界条件的声波散射问题的两种数值方法

利用单层位势理论将声波散射的外边值问题转化为第一类边界积分方程,采用迭代的Tikhonov正则化和改进的Tikhonov正则化方法求解,给出了二维空间的数值实例。与Nystrom方法相比,计算简单得到的精度却一样。     

关于不定方程x^2＋y^2＋z^2=1＋dxyz的解

通过基本初等变换以及同余定理等有关理论讨论了方程x^2＋y^2＋z^2=1＋dxyz的解,并给出了全部解。     

求解缓变波导中反问题的一种步进方法

对于声学和电磁学中的大尺度反问题,基于直接方法(例如有限元或者无网格方法)的数值计算往往会导致一个巨大的线性系统,因而在计算速度和存储上并不现实.基于求解Helmholtz方程正问题的Dirichlet-to-Neuman(DtN)算子步进方法,提出了一种用于求解波在大尺度缓变波导中传播的反问题的反向基本解算子步进方法(IFOMM).     

基于四次矩阵样条函数的二阶矩阵微分方程近似解

使用四次矩阵样条函数方法来解二阶矩阵微分方程．首先对矩阵微分方程的初始问题进行介绍;然后构造四次矩阵样条函数;并对矩阵样条函数方法进行算法描述;最后通过实例和误差分析来说明四次矩阵样条函数方法的有效性．