On the use of the variational method for interpreting the solubilities of gases in liquids

The Variational theory of mixtures due to Mansoori and Leland is modified to account for translational quantum effects in solution, and this modified form of the theory is applied to the problem of gas solubilities in liquids. The theory is used to derive expressions for the Henry's law constant, the molar heat of solution at infinite dilution, and the partial molar volume at infinite dilution for a solute in a liquid solution. These expressions are applied, over a range of temperatures, to the following systems; H₂ in each of Ar, N₂, and CH₄; He in each of Ar, N₂, and CH₄; and Ne in each of Ar and N₂. Lennard-Jones 6–12 pair potentials are used for these calculations. The Lennard-Jones parameters are taken from gas-phase second virial coefficient data. The results obtained are compared with experimental data and with previous calculations on these systems based on the Leonard-Henderson-Barker theory. The variational results appear to be in better agreement with experiment for the He-containing systems, while the Leonard-Henderson-Barker theory seems better for the other systems. An explanation for this is suggested.     

CH2O＋O[^3P]→CHO＋OH反应途径和变分速率常数

采用QCISD/6-311G犤d,p犦从头算方法,优化了吸氢反应CH2O+O犤3P犦→CHO+OH的反应物、过渡态和产物的几何结构,并用QCISD(t,full)/6-311G//QCISD/6-311G方法对各驻点进行了单点校正,得出正逆反应的活化位垒分别为38.86kJ·mol-1和67.23kJ·mol-1.IRC(内禀反应坐标)分析指出,该反应是一个C-H键断裂和H-O键生成协同进行的反应,而且在反应途径上存在一个引导反应进行的振动模式,其引导反应进行s区间为-0.4～0.75(amu)1/2.在1300～2270K温度范围内运用改进的变分过渡态理论(ICVT),计算了反应速率常数,与实验结果相当一致.     

The practical implementation of Löwdin's method for spin projection

Based on Löwdin's projector for recovering the symmetry of an Unrestricted Hartree-Fock Slater determinant, a robust and efficient method, which simplifies the multi-determinantal character of the original expansion, is deduced. It has a direct application as a Projection after Variation scheme, providing the exact expected values of spin-projected operators in polynomial time. In the presented approach the (exactly) projected Hamiltonian admits a simple explicit expression when it is written in the “Corresponding Orbitals” basis. This simplicity makes possible to optimize the projected determinant, Variation after Projection, by a direct minimization of the projected energy. Recent successful results obtained from the combination of a projected symmetry broken Slater determinant and post Hartree-Fock methods has strengthen the attention on Projective Methods. In order to achieve a simple application of the reported formalism to the Interaction Configuration method (CI), a new rotation of the CI basis has been proposed and justified.     

A characterization of convex calibrable sets in with respect to anisotropic norms

A set is called “calibrable” if its characteristic function is an eigenvector of the subgradient of the total variation. The main purpose of this paper is to characterize the “-calibrability” of bounded convex sets in with respect to a norm (called anisotropy in the sequel) by the anisotropic mean -curvature of its boundary. It extends to the anisotropic and crystalline cases the known analogous results in the Euclidean case. As a by-product of our analysis we prove that any convex body C satisfying a -ball condition contains a convex -calibrable set K such that, for any V[|K|,|C|], the subset of C of volume V which minimizes the -perimeter is unique and convex. We also describe the anisotropic total variation flow with initial data the characteristic function of a bounded convex set.     

敦煌莫高窟北区岩体变异变形及修复对策

敦煌莫高窟北区岩体长期以来在特殊的地形地貌、气象水文、岩土性质、地质构造条件下,受人工开挖、重力、风蚀、雨蚀和洪水冲刷等共同作用,岩体发生风化、卸荷等变异以及崩塌、坍塌和危岩、开裂与裂隙(构造裂隙、卸荷裂隙)等多种变形,严重影响岩体的稳定和洞窟的安全。针对上述变异、变形破坏情况,采用PS材料加粉煤灰浆液灌浆封闭裂隙和岩面喷浆加固相结合的修复方法,有效地防止了岩体变异的进一步扩展和表面风化的加剧,减少了岩体变形和表面风化程度,使石窟得以保护和修复。该方法对黄土及干旱地区石窟保护具有良好的借鉴作用。     

不同粒径ZSM-5分子筛在苯与甲醇烷基化反应中催化性能及反应条件优化

采用水热合成法合成了不同粒径的ZSM-5分子筛催化剂,系统考察了分子筛粒径变化对苯与甲醇烷基化反应的影响。研究结果表明,随着ZSM-5分子筛粒径增大,不但苯的转化率和二甲苯选择性降低,而且催化剂稳定性明显下降。其中,粒径为0.25 μm的ZSM-5分子筛在苯烷基化反应中的催化性能最佳,且催化剂稳定性最好。另外,采用拉曼光谱和热重等方法对催化剂积碳物种和失活机理进行了深入研究,发现催化剂失活主要是由于反应过程中生成的大分子稠环芳烃堵塞了分子筛孔道并覆盖活性位点造成的。最后,考察了反应温度、原料组成及空速对苯烷基化反应的影响并优化出最佳的苯烷基化反应条件。     

时变退化时滞微分系统的变易公式

本文将研究时变退化时滞微分系统.给出了该类系统的变易公式.这将在进一步研究退化时滞微分系统时十分有用.     

Variation of Parameters Method for Solving System of Nonlinear Volterra Integro-Differential Equation

It is well known that nonlinear integro-differential equations play vital role in modeling of many physical processes, such as nano-hydrodynamics, drop wise condensation, oceanography, earthquake and wind ripple in desert. Inspired and motivated by these facts, we use the variation of parameters method for solving system of nonlinear Volterra integro-differential equations. The proposed technique is applied without any discretization, perturbation, transformation, restrictive assumptions and is free from Adomian's polynomials. Several examples are given to verify the reliability and efficiency of the proposed technique.     

基于双指标分析法和聚类分析法的鸡骨草红外指纹图谱比较研究

利用双指标分析法和系统聚类分析法,鉴别了不同年限不同产地鸡骨草的红外指纹图谱。结果显示,(1)应用双指标分析法时,只做13点平滑就可以将6种鸡骨草样品完全分开,可以在六维空间中考察不同中药样品之间的相互关系,并可用数量将这些关系精确地表示出来;应用系统聚类分析时只做13点平滑的初始数据聚类效果较差,但13点平滑后再做一阶导数处理,聚类效果很明显,6类鸡骨草样品可以完全分开。(2)应用双指标分析法,在样本量大时,共有峰率变异峰率统计较麻烦,但精确度较高;聚类分析法,精确度相对较低,但是运作比较方便。(3)运用以上两种方法均表明,同一产地栽培鸡骨草化学成分较相似,同一产地不同年限栽培鸡骨草化学成分差异较大。     

A Volterra integral formulation for determining the periodic solutions of some autonomous, nonlinear, third-order ordinary differential equations

A Volterra integral formulation based on the introduction of a term proportional to the velocity times the square of the (unknown) frequency of oscillation, a new independent variable equal to the original one times the (unknown) frequency of oscillation, the method of variation of parameters and series expansions of both the solution and the frequency of oscillation, is used to determine the periodic solutions to three nonlinear, autonomous, third-order, ordinary differential equations. It is shown that the first term of the series expansion of the frequency of oscillation coincides with that determined from a first-order harmonic balance procedure, whereas the two-term approximation to the frequency of oscillation is shown to be more accurate than that of a parameter perturbation procedure for the second equation considered in this paper. For the third equation, it is shown that the two-term approximation presented in this paper is more accurate than the corresponding one for one of the parameter perturbation methods, and for initial velocities less than one, for the other parameter perturbation approach.