Calculus demonstrations using MATLAB

The note discusses ways in which technology can be used in the calculus learning process. In particular, five MATLAB programs are detailed for use by instructors or students that demonstrate important concepts in introductory calculus: Newton's method, differentiation and integration. Two of the programs are animated. The programs and the graphical user interface have been specifically designed to help the student understand the processes behind these important introductory concepts. Each program has a series of demonstrations that show unusual, difficult or important cases.     

Local Derivative-Free Approximation of Computationally Expensive Posterior Densities

Bayesian inference using Markov chain Monte Carlo (MCMC) is computationally prohibitive when the posterior density of interest, π, is computationally expensive to evaluate. We develop a derivative-free algorithm GRIMA to accurately approximate π by interpolation over its high-probability density (HPD) region, which is initially unknown. Our local approach reduces the waste of computational budget on approximation of π in the low-probability region, which is inherent in global experimental designs. However, estimation of the HPD region is nontrivial when derivatives of π are not available or are not informative about the shape of the HPD region. Without relying on derivatives, GRIMA iterates (a) sequential knot selection over the estimated HPD region of π to refine the surrogate posterior and (b) re-estimation of the HPD region using an MCMC sample from the updated surrogate density, which is inexpensive to obtain. GRIMA is applicable to approximation of general unnormalized posterior densities. To determine the range of tractable problem dimensions, we conduct simulation experiments on test densities with linear and nonlinear component-wise dependence, skewness, kurtosis and multimodality. Subsequently, we use GRIMA in a case study to calibrate a computationally intensive nonlinear regression model to real data from the Town Brook watershed. Supplemental materials for this article are available online.     

Crack growth on the basal plane in single crystal zinc: experiments and computations

Crack propagation on the basal planes in zinc was examined by means of in situ fracture testing of pre-cracked single crystals, with specific attention paid to the fracture mechanism. During quasistatic loading, crack propagation occurred in short bursts of dynamic crack extension followed by periods of arrests, the latter accompanied by plastic deformation and blunting of the crack-tip. In situ observations confirmed nucleation and propagation of microcracks on parallel basal planes and plastic deformation and failure of the linking ligaments. Pre-existing twins in the crack path serve as potent crack arrestors. The crystallographic orientation of the crack growth direction on the basal plane was found to influence both the fracture load as well as the deformation at the crack-tip, producing fracture surfaces of noticeably different appearances. Finite element analysis incorporating crystal plasticity was used to identify dominant slip systems and the stress distribution around the crack-tip in plane stress and plane strain. The computational results are helpful in rationalizing the experimental observations including the mechanism of crack propagation, the orientation dependence of crack-tip plasticity and the fracture surface morphology.     

基于模糊控制的计算机控制实验平台的设计

为加强计算机控制实验和自动控制理论实验的结合,提高教学实验水平,选择工业生产和科学实验中的重要物理量温度作为被控制量,而模糊控制是目前应用较为广泛、设计简单且在温度控制中取得了较好的控制效果的控制方法,为此开发了基于模糊控制的计算机控制实验平台。论文设计了基于PC机一单片机的分布式温度实时控制系统,根据温度控制系统的特点,给出了温度控制系统模糊控制器的实现方法,实验平台具有硬件透明、软件开放等特点,且模糊规则修改灵活方便,适合于学生实验使用。     

Atomic-scale investigation of the interaction between coniferyl alcohol and laccase for lignin degradation using molecular dynamics simulations and spectroscopy

The interaction between coniferyl alcohol (CA) and laccase (LAC) was investigated using molecular dynamics (MD) simulations and spectral experiments. The mode of interaction between CA and LAC was established by MD simulations. The micro-environmental changes, stability and rigidity of the LAC-CA system were assessed by relevant parameters. These parameters include root mean square deviation (RMSD), root mean square fluctuation (RMSF) and radius of gyration (Rg). The calculated binding free energy (ΔG_binding=??19.99?kcal·mol.^?1), the van der waals (VDW) contribution (ΔG_vdw=?23.99?kcal·mol^?1) and the electrostatic energy (ΔG_ele=?23.09?kcal·mol^?1) of LAC-CA system demonstrated that the interaction of LAC-CA was a spontaneous process and the main interaction forces were van der Waal's and electrostatic forces. The values of ΔG_vdw and ΔG_ele were negative, which demonstrated that VDW interactions and electrostatic interactions were favorable for the binding of CA and LAC. The binding constants, thermodynamic parameters, molecular force types and binding distances confirmed the interaction between CA and LAC and further verified the rationality of the theoretical model by spectral experiments. The MD simulations and experimental approaches provide clues for the discovery of new mediators and useful references for the mechanism of microbial degradation of lignin and industrialization of lignocellulose.     

C语言编程在精馏实验数据处理中的应用

在以水-乙醇溶液为基础进行的精馏塔效率测定实验中,数据处理过程耗时,且通过一般手工作图法所得理论塔板数结果存在较大误差。根据逐板计算法原理,运用C语言编程进行数据处理,将结果输出为dat格式文件,并直接导入Origin 9.0软件中作图。该方法不仅对于有一定编程基础的学生而言通俗易懂、操作简单、结果准确、极为高效,而且有助于进一步改善现有教学方法。     

在线社交网络控制实验的现状与展望

在线社交网络已发展成为一个独特的电子生态系统，其应用深刻影响着人们生活的方方面面。由于在线社交网络特性复杂，分析在线社交网络形成和变化中的规律成为当前计算机科学、社会学和物理学的一项挑战。传统上，在线社交网络实证研究主要采用计算机辅助的被动数据获取和分析方式。近年来，在真实大规模在线社交网络上直接进行控制实验从而主动获取数据并开展分析研究的方式广受关注。评述了这一领域的研究进展，包括：社交网络控制实验的主要研究模式；控制实验方法在社交网络结构、信息传播、行为和心理学等领域取得的主要成果以及主要实验工具的适用条件和局限性。最后，展望了人工智能技术在社交网络控制实验中的应用潜力，分析了智能算法对降低实验成本和提高实验效率的作用。     

Experimental study on age and gender differences in microscopic movement characteristics of students

Campus security has aroused many concerns from the whole society. Stampede is one of the most frequent and influential accidents in campus. Studies on pedestrian dynamics especially focusing on students are essential for campus security, which are helpful to improve facility design and emergency evacuation strategy. In this paper, primary and middle school students were recruited to participate in the single-file experiments. The microscopic movement characteristics,including walking speed, headway, gait characteristics(step length, step frequency and swaying amplitude) and their relations were investigated. Age and gender differences in the headway-speed diagram and space requirements were analyzed by statistical tests. The results indicated that the impacts of age and gender were significant. There were three stages for the influence of gender on the headway-speed diagram for both age groups. The impacts on students' space requirements were consistent for different age and gender groups. But the impacts of age and gender on free-flow speed were affected by each other. Due to the connection of walking speed and gait characteristics, the comparisons of gait characteristics between different ages and genders were performed to understand the corresponding differences in speed more deeply. The results showed that differences in step length and swaying amplitude between males and females were significant for both age groups. The effect of gender on step frequency was significant for primary students. But for middle school students,whether gender had significant impact on step frequency was not clear here because of the large P-value. Besides, the influence of age on gait characteristics changed with gender.     

Electrochemical Iodine-Mediated Oxidation of Enamino-Esters to 2H-Azirine-2-Carboxylates Supported by Design of Experiments

An electrochemical iodine-mediated transformation of enamino-esters for the synthesis of 2H-azirine-2-carboxylates is presented. In addition, a thermic conversion of azirines to 4-carboxy-oxazoles in quantitative yield without purification was described. Both classes 2H-azirines-2-carboxylates and the 4-carboxy-oxazoles are substructures in natural products and therefore are of considerable interest for synthetic and pharmaceutical chemists. The optimization was not performed in a conventional manner with a one-factor-at-a-time process but with a Design of Experiments (DoE) approach. Beside a broad substrate scope the reaction was also employed to a robustness screen, a sensitivity assessment, and complemented with mechanistic considerations from cyclic voltammetry experiments.     

Re-casting traditional organic experiments into green guided-inquiry based experiments: student perceptions

ABSTRACT

Green Chemistry principles can be used to re-cast traditional Organic chemistry experiments into more guided-inquiry based experiments. Inquiry questions related to green chemistry principles and metrics have been incorporated into our laboratory for the development of more guided-inquiry based experiments. Re-casting traditional experiments provides time for guided-inquiry by allowing students to evaluate reaction conditions and wastefulness of reactions. This includes evaluating solvent choices, heating methods, use of renewal materials, and contemplating reactants and products impacts on human health and environment. Students examine the changes as it pertains to green chemistry, the success of the reaction and the potential impacts on the mechanism. Involving students in these discoveries rooted in a guiding question made the Organic experiments guided-inquiry. Students were surveyed about their exposure to green chemistry and guided-inquiry based labs. Examples of some of the re-casted experiments, excerpts from student reports, and student impressions of the theme are presented.