Accurate double many‐body expansion potential energy surface by extrapolation to the complete basis set limit and dynamics calculations for ground state of NH2

An accurate single‐sheeted double many‐body expansion potential energy surface is reported for the title system. A switching function formalism has been used to warrant the correct behavior at the and dissociation channels involving nitrogen in the ground and first excited states. The topographical features of the novel global potential energy surface are examined in detail, and found to be in good agreement with those calculated directly from the raw ab initio energies, as well as previous calculations available in the literature. The novel surface can be using to treat well the Renner–Teller degeneracy of the and states of . Such a work can both be recommended for dynamics studies of the reaction and as building blocks for constructing the double many‐body expansion potential energy surface of larger nitrogen/hydrogen‐containing systems. In turn, a test theoretical study of the reaction has been carried out with the method of quantum wave packet on the new potential energy surface. Reaction probabilities, integral cross sections, and differential cross sections have been calculated. Threshold exists because of the energy barrier (68.5 meV) along the minimum energy path. On the curve of reaction probability for total angular momentum J = 0, there are two sharp peaks just above threshold. The value of integral cross section increases quickly from zero to maximum with the increase of collision energy, and then stays stable with small oscillations. The differential cross section result shows that the reaction is a typical forward and backward scatter in agreement with experimental measurement result. © 2013 Wiley Periodicals, Inc.     

Investigation of the solubilization of car-emitted Pt,Pd and Rh in street dust and spiked soil samples

A sequential extraction procedure (three-step), proposed by the Standards, Measurements and Testing Programme (formerly BCR) of the European Union, was applied to street dust and spiked soil samples for the determination of PGEs. Analyses were carried out using inductively coupled plasma-mass spectrometry (ICP-MS). The results indicate that up to 5% from Pt, 70% from Pd and 14% from Rh are in mobile forms in street dust. The results for the soil samples spiked with crushed catalytic converter are significantly lower indicating that PGEs are oxidised more efficiently in natural conditions. Additionally Pt and Pd bound to humic acids were investigated.     

Du Fort-Frankel格式及DFF-I并行格式的稳定性

 本文对抛物型方程的Du Fort-Frankel(DFF)格式以及基于该格式构造的并行差分格式(DFF-I)进行了稳定性分析。采用矩阵分析方法, 证明了其无条件(LR)稳定性, 给出了DFF格式的稳定性系数的最小值的上界估计, 结果表明其与网格比有关, 从而DFF格式并非绝对稳定。本文改进了并行差分格式(DFF-I)的稳定性分析结果, 证明了其增长矩阵的谱半径严格小于1, 从而具有长时间稳定性。数值算例验证了DFF-I格式具有空间二阶精度, 且有很好的稳定性。     

广义sine-Gordon方程高精度隐式紧致差分方法

本文研究一类二维非线性的广义sine-Gordon(简称SG)方程的有限差分格式.首先构造三层时间的紧致交替方向隐式差分格式,并用能量分析法证明格式具有二阶时间精度和四阶空间精度.然后应用改进的Richardson外推算法将时间精度提高到四阶.最后,数值算例证实改进后的算法在空间和时间上均达到四阶精度.     

三维多面体网格上扩散方程的保正格式

 针对三维任意(星形)多面体网格, 本文构造了扩散方程的一种单元中心型非线性有限体积格式, 证明了该格式具有保正性. 在该格式设计中, 除引入网格中心量外, 还引入网格节点量和网格面中心量作为中间未知量, 它们将用网格中心未知量线性组合表示, 使得格式仅有网格中心未知量作为基本未知量. 在节点量计算中, 利用网格面上的调和平均点, 设计了一种适用于三维多面体网格的局部显式加权方法. 该格式适用于求解非平面的网格表面和间断扩散系数的问题. 数值例子验证了它对光滑解具有二阶精度和保正性.     

基于深度学习的“实验方案设计”主题式复习教学——以“阿司匹林的制备和提纯”为例

针对实验方案设计题的得分率分析和教学现状,基于课程标准、教材、真题和文献研究,构建“阿司匹林的制备和提纯”深度学习主题模型。通过设计制备和提纯阿司匹林的实验方案,构建实验方案设计的思维模型,并以制备七水合硫酸锌为例内化思维模型,在解决真实、复杂的问题过程中实现核心知识结构化,生成指向深度学习的主题式复习教学流程。     

基于“模型认知”的定量实验方案设计的教学实践*——摩尔盐纯度的测定

针对高三定量实验的复习特点,以“摩尔盐纯度的测定”为例进行基于“模型认知”核心素养培养的教学实践。对教学背景、设计思路、教学过程等方面进行研究分析,并从精心选素材,引发模型认知;高质量设问,建构模型认知;点、线、面结合,丰富模型认知等3个角度对促进学生“模型认知”素养提升的化学教学进行分析和阐释。     

CBS还原合成手性1-苯乙醇实验设计*

将学科热点之一催化不对称合成策略引入实验教学中,通过CBS还原制备手性醇。实验以苯乙酮为原料,还原得到粗产物手性1-苯乙醇,经制备色谱仪分离提纯,气相色谱和自动旋光仪表征产物的光学性质。实验为综合型有机化学实验,通过此实验,学生在掌握手性醇合成原理与方法的同时,进一步学习手套箱、气相色谱、制备色谱仪、自动旋光仪等新技术,以提升学生综合科研素质。     

Adaptive discretization for signal detection in statistical inverse problems

We discuss statistical tests in inverse problems when the original equation is replaced by a discretized one, i.e. a linear system of equations. Previous studies revealed that using the discretization level as regularizing procedure is possible, but its application is limited unless discretization is restricted to the singular value decomposition, see C. Marteau and P. Mathé, General regularization schemes for signal detection in inverse problems, 2013. General linear regularization may circumvent this, and we propose a regularization of the discretized equations. The discretization level may be chosen adaptively, which may save computational budget. This results in tests which are known to yield the optimal separation rate up to some constant in many cases.     

An efficient meshfree point collocation moving least squares method to solve the interface problems with nonhomogeneous jump conditions

We are going to study a simple and effective method for the numerical solution of the closed interface boundary value problem with both discontinuities in the solution and its derivatives. It uses a strong‐form meshfree method based on the moving least squares (MLS) approximation. In this method, for the solution of elliptic equation, the second‐order derivatives of the shape functions are needed in constructing the global stiffness matrix. It is well‐known that the calculation of full derivatives of the MLS approximation, especially in high dimensions, is quite costly. In the current work, we apply the diffuse derivatives using an efficient technique. In this technique, we calculate the higher‐order derivatives using the approximation of lower‐order derivatives, instead of calculating directly derivatives. This technique can improve the accuracy of meshfree point collocation method for interface problems with nonhomogeneous jump conditions and can efficiently estimate diffuse derivatives of second‐ and higher‐orders using only linear basis functions. To introduce the appropriate discontinuous shape functions in the vicinity of interface, we choose the visibility criterion method that modifies the support of weight function in MLS approximation and leads to an efficient computational procedure for the solution of closed interface problems. The proposed method is applied for elliptic and biharmonic interface problems. For the biharmonic equation, we use a mixed scheme, which replaces this equation by a coupled elliptic system. Also the application of the present method to elasticity equation with discontinuities in the coefficients across a closed interface has been provided. Representative numerical examples demonstrate the accuracy and robustness of the proposed methodology for the closed interface problems. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1031–1053, 2015