三维位势问题的梯度边界积分方程的新解法

三维位势问题的边界元分析中,关于坐标变量的边界位势梯度的计算是一个困难的问题. 已有一些方法着手解决这个问题,然而,这些方法需要复杂的理论推导和大量的数值计算. 本文提出求解一般边界位势梯度边界积分方程的辅助边值问题法. 该方法构造了与原边界值问题具有相同解域的辅助边值问题,该辅助边值问题具有已知解,因此通过求解此辅助边值问题,可获得梯度边界积分方程对应的系统矩阵,然后将此系统矩阵应用于求解原边值问题,求解过程非常简单,只需求解一个线性系统即可获得原边值问题的解. 值得注意的是,在求解原边值问题时,不再需要重新计算系统矩阵,因此辅助边值问题法的效率并不很差. 辅助边值问题法避免了强奇异积分的计算,具有数学理论简单、程序设计容易、计算精度高等优点,为坐标变量梯度边界积分方程的求解提供了一个新的途径. 3个标准的数值算例验证了方法的有效性.      

Reduced dimensionality (3,2)D NMR experiments and their automated analysis: implications to high‐throughput structural studies on proteins

Protein NMR spectroscopy has expanded dramatically over the last decade into a powerful tool for the study of their structure, dynamics, and interactions. The primary requirement for all such investigations is sequence‐specific resonance assignment. The demand now is to obtain this information as rapidly as possible and in all types of protein systems, stable/unstable, soluble/insoluble, small/big, structured/unstructured, and so on. In this context, we introduce here two reduced dimensionality experiments – (3,2)D‐hNCO canH and (3,2)D‐hN coCA nH – which enhance the previously described 2D NMR‐based assignment methods quite significantly. Both the experiments can be recorded in just about 2–3 h each and hence would be of immense value for high‐throughput structural proteomics and drug discovery research. The applicability of the method has been demonstrated using alpha‐helical bovine apo calbindin‐D9k P43M mutant (75 aa) protein. Automated assignment of this data using AUTOBA has been presented, which enhances the utility of these experiments. The backbone resonance assignments so derived are utilized to estimate secondary structures and the backbone fold using Web‐based algorithms. Taken together, we believe that the method and the protocol proposed here can be used for routine high‐throughput structural studies of proteins. Copyright © 2014 John Wiley & Sons, Ltd.     

Geometrical methods for analyzing the optimal management of tipping point dynamics

Natural resources are not infinitely resilient and should not be modeled as being such. Finitely resilient resources feature tipping points and history dependence. This paper provides a didactical discussion of mathematical methods that are needed to understand the optimal management of such resources: viscosity solutions of Hamilton–Jacobi–Bellman equations, the costate equation and the associated canonical equations, exact root counting, and geometrical methods to analyze the geometry of the invariant manifolds of the canonical equations. Recommendations for Resource Managers

• Management of natural resources has to take into account the possible breakdown of resilience and induced regime shifts.
• Depending on the characteristics of the resource and on its present and future economic importance, either for all initial states the same kind of management policy is optimal, or the type of the optimal management policy depends on the initial state.
• Modeling should reflect the finiteness of the data.

     

Screening gas-phase chemical kinetic models: Collision limit compliance and ultrafast timescales

Detailed gas-phase chemical kinetic models are widely used in combustion research, and many new mechanisms for different fuels and reacting conditions are developed each year. Recent works have highlighted the need for error checking when preparing such models, but a useful community tool to perform such analysis is missing. In this work, we present a simple online tool to screen chemical kinetic mechanisms for bimolecular reactions exceeding collision limits. The tool is implemented on a user-friendly website, cloudflame.kaust.edu.sa, and checks three different classes of bimolecular reactions; (ie, pressure independent, pressure-dependent falloff, and pressure-dependent PLOG). In addition, two other online modules are provided to check thermodynamic properties and transport parameters to help kinetic model developers determine the sources of errors for reactions that are not collision limit compliant. Furthermore, issues related to unphysically fast timescales can remain an issue even if all bimolecular reactions are within collision limits. Therefore, we also present a procedure to screen ultrafast reaction timescales using computational singular perturbation. For demonstration purposes only, three versions of the rigorously developed AramcoMech are screened for collision limit compliance and ultrafast timescales, and recommendations are made for improving the models. Larger models for biodiesel surrogates, tetrahydropyran, and gasoline surrogates are also analyzed for exemplary purposes. Numerical simulations with updated kinetic parameters are presented to show improvements in wall-clock time when resolving ultrafast timescales.     

计算代数方程组孤立奇异解的符号数值方法

求解代数方程组是计算代数几何的最基本问题之一,孤立奇异解的计算则是其中最具挑战性的课题之一,在科学与工程计算中有着广泛的应用,如机器人、计算机视觉、机器学习、人工智能、运筹学、密码学和控制论等.本文结合作者的研究成果,综述了符号数值方法在计算代数系统孤立奇异解、特别是近似奇异解精化与验证方面的研究进展,并对未来的研究方向提出了展望.     

Rotation-Inversion Isomerization of Tertiary Carbamates: Potential Energy Surface Analysis of Multi-Paths Isomerization Using Boltzmann Statistics

Potential energy surface (PES) analyses at the SMD[MP2/6–311++G(d,p)] level and higher-level energies up to MP4(fc,SDTQ) are reported for the fluorinated tertiary carbamate N-ethyl-N-(2,2,2-trifluoroethyl) methyl carbamate ( VII ) and its parent system N,N-dimethyl methyl carbamate ( VI ). Emphasis is placed on the analysis of the rotational barrier about the CN carbamate bond and its interplay with the hybridization of the N-lone pair (NLP). All rotational transition state (TS) structures were found by computation of 1D relaxed rotational profiles but only 2D PES scans revealed the rotation-inversion paths in a compelling fashion. We found four unique chiral minima of VII , one pair each of E- and Z-rotamers, and we determined the eight unique rotational TS structures associated with every possible E/Z-isomerization path. It is a significant finding that all TS structures feature N-pyramidalization whereas the minima essentially contain sp²-hybridized nitrogen. We will show that the TS stabilities are affected by the synergetic interplay between NLP/CO₂ repulsion minimization, NLP→σ^*(CO) negative hyperconjugation, and two modes of intramolecular through-space electrostatic stabilization. We demonstrate how Boltzmann statistics must be applied to determine the predicted experimental rotational barrier based on the energetics of all eight rotamerization pathways. The computed barrier for VII is in complete agreement with the experimentally measured barrier of the very similar fluorinated carbamate N-Boc-N-(2,2,2-trifluoroethyl)-4-aminobutan-1-ol II . NMR properties of VII were calculated with a variety of density functional/basis set combinations and Boltzmann averaging over the E- and Z-rotamers at our best theoretical level results in good agreement with experimental chemical shifts δ(¹³C) and J(¹³C,¹⁹F) coupling constants of II (within 6 %).     

思维导图在物理化学教学中的应用

通过介绍思维导图的特征以及思维导图软件XMind的主要功能特点,阐述了思维导图应用于物理化学的理论基础。以XMind软件作为绘制工具,以"热力学第二定律"为例,探讨了将思维导图运用于单元总结中,在建构知识体系、把握知识脉络以及训练思维能力方面的有效作用。进一步以本章重要知识点"熵增加原理"为例,尝试思维导图在知识点的理解掌握、拓展应用等方面的具体应用。     

一种新的求非线性方程组的数值延拓法

针对迭代过程中的Jacobi奇异问题,本文提出了一种新的数值延拓法.通过构造双参数同伦算子,采用可控条件和适当选取参数的方式克服Jacobi奇异性,并分析了方法的收敛性.最后,通过数值实验对比,验证了方法的可行性和优越性.特别是具有可调控越过Jacobi奇异(点、线、面)的优势,从而也在某种程度上解决了数值延拓法严重依赖于初值的问题.