优化端点条件的平面二次均匀B样条插值曲线

在利用反求法构造B样条插值曲线时，往往需要选取端点条件。 因此，可对端点条件进行优化选取，使得构造的B样条插值曲线满足特定要求。提出了一种利用曲线内能极小选取平面二次均匀B样条插值曲线端点条件的算法。首先给出了二次均匀B样条插值曲线分控制顶点与首个控制顶点（即端点条件）的递推关系式；然后给出了利用曲线内能极小优化选取首个控制顶点的算法，证明了利用该算法构造的C¹连续二次均匀B样条插值曲线为保形插值，并通过数值算例证明了算法的有效性；最后，为便于实际应用，基于MATLAB平台设计了算法所对应的图形用户界面，用户通过简单的操作即可获得光顺的C¹连续二次均匀B样条保形插值曲线。     

An improved depth-averaged nonhydrostatic shallow water model with quadratic pressure approximation

Phase-resolved information is necessary for many coastal wave problems, for example, for the wave conditions in the vicinity of harbor structures. Two-dimensional (2D) depth-averaging shallow water models are commonly used to obtain a phase-resolved solution near the coast. These models are in general more computationally effective compared with computational fluid dynamics software and will be even more capable if equipped with a parallelized code. In the current article, a 2D wave model solving the depth-averaged continuity equation and the Euler equations is implemented in the open-source hydrodynamic code REEF3D. The model is based on a nonhydrostatic extension and a quadratic vertical pressure profile assumption, which provides a better approximation of the frequency dispersion. It is the first model of its kind to employ high-order discretization schemes and to be fully parallelized following the domain decomposition strategy. Wave generation and absorption are achieved with a relaxation method. The simulations of nonlinear long wave propagations and transformations over nonconstant bathymetries are presented. The results are compared with benchmark wave propagation cases. A large-scale wave propagation simulation over realistic irregular topography is shown to demonstrate the model's capability of solving operational large-scale problems.     

高雷诺数下非混相Rayleigh-Taylor不稳定性的格子Boltzmann方法模拟

本文采用相场格子Boltzmann方法研究了竖直微通道内中等Atwoods数流体的单模Rayleigh-Taylor不稳定性问题,系统分析了雷诺数对相界面动力学行为以及扰动在各发展阶段演化规律的影响.数值结果表明高雷诺数条件下,不稳定性界面扰动的增长经历了四个不同的发展阶段,包括线性增长阶段、饱和速度阶段、重加速阶段及混沌混合阶段.在线性增长阶段,我们计算获得的气泡与尖钉振幅符合线性稳定性理论,并且线性增长率随着雷诺数的增加而增大.在第二个阶段,我们观察到气泡与尖钉将以恒定的速度增长,获得的尖钉饱和速度略高于Goncharov经典势能模型的解析解[Phys.Rev.Lett.200288134502],这归因于系统中产生了多个尺度的旋涡,而涡之间的相互作用促进了尖钉的增长.随着横向速度和纵向速度的差异扩大,气泡和尖钉界面演化诱导产生的Kelvin–Helmholtz不稳定性逐渐增强,从而流体混合区域出现许多不同层次的涡结构,加速了气泡与尖钉振幅的演化速度,并在演化后期阶段,导致界面发生多层次卷起、剧烈变形、混沌破裂等行为,最终形成了非常复杂的拓扑结构.此外,我们还统计了演化后期气泡与尖钉的无量纲加速度,发现气泡和尖钉的振幅在后期呈现二次增长规律,其增长率系数分别为0.045与0.233.而在低雷诺条件下,重流体在不稳定性后期以尖钉的形式向下运动而轻流体以气泡的形式向上升起.在整个演化过程中,界面变得足够光滑,气泡与尖钉在后期的演化速度接近于常数,未观察到后期的重加速与混沌混合阶段.     

A Facile Method for the Separation of Methionine Sulfoxide Diastereomers,Structural Assignment,and DFT Analysis

Methionine (Met) oxidation is an important biological redox node, with hundreds if not thousands of protein targets. The process yields methionine oxide (MetO). It renders the sulfur chiral, producing two distinct, diastereomerically related products. Despite the biological significance of Met oxidation, a reliable protocol to separate the resultant MetO diastereomers is currently lacking. This hampers our ability to make peptides and proteins that contain stereochemically defined MetO to then study their structural and functional properties. We have developed a facile method that uses supercritical CO₂ chromatography and allows obtaining both diastereomers in purities exceeding 99 %. ¹H NMR spectra were correlated with X-ray structural information. The stereochemical interconversion barrier at sulfur was calculated as 45.2 kcal mol⁻¹, highlighting the remarkable stereochemical stability of MetO sulfur chirality. Our protocol should open the road to synthesis and study of a wide variety of stereochemically defined MetO-containing proteins and peptides.     

关于不定方程x3-1=749y2

利用同余式、平方剩余、Pell方程的解的性质、递归序列证明了:不定方程x³-1=749y²仅有整数解(x,y)=(1,0).     

A study of properties of adaptive quadratic grids for three-dimensional near-surface field computations

Curved geometries and the corresponding near-surface fields typically require a large number of linear computational elements. High-order numerical solvers have been primarily used with low-order meshes. There is a need for curved, high-order computational elements. Typical near-surface meshes consist of hexahedral and/or prismatic elements. The present work studies the employment of quadratic meshes that are relatively coarse for field simulations. Directionally quadratic high-order elements are proposed for the near-surface field regions. The quadratic meshes are compared with the conventional low-order ones in terms of accuracy and efficiency. The cases considered include closed surface volume calculations, as well as computation of gradients of several analytic fields. A special method of adaptive local quadratic meshes is proposed and evaluated. Truncation error analysis for quadratic grids yields comparison with the conventional linear hexahedral/prismatic meshes, which are subject to typical distortions such as stretching, skewness, and torsion.     

Identification of metabolites in coriander seeds (Coriandrum Sativum L.) aided by ultrahigh resolution total correlation NMR spectroscopy

NMR is a fast method for obtaining a holistic snapshot of the metabolome and also offers quantitative information without separating the compounds present in a complex mixture. Identification of the metabolites present in a plant extract sample is a crucial step for all plant metabolomics studies. In the present work, we used various two dimensional (2D) NMR methods such as J-resolved NMR, total correlation spectroscopy (TOCSY), and heteronuclear single quantum coherence sensitivity enhanced NMR spectroscopy for the identification of 36 common metabolites present in Coriandrum sativum L. seed extract. The identified metabolites belong to the following classes: organic acids, amino acids, and carbohydrates. ¹H NMR spectra of such complex mixtures in general display tremendous signal overlap due to the presence of a large number of metabolites with closely resonating multiplet signals. This signal overlapping leads to ambiguity in an assignment, and hence, identification of metabolites becomes tedious or impossible in many cases. Therefore, the utility of pure-shift proton spectrum along the indirect (F₁) dimension of the F₁-PSYCHE-TOCSY spectrum is demonstrated for overcoming ambiguity in assignment of metabolites in crowded spectral regions from Coriandrum sativum L. seed extract sample. Because pure-shift NMR methods yield ultrahigh resolution spectrum (i.e., a singlet peak per chemical site) along one or more dimensions, such spectra provide better identification of metabolites compared with regular 2D TOCSY where signal overlap and peak distortions lead to ambiguity in the assignment. Nine metabolites were unambiguously assigned by pure-shift F₁-PSYCHE-TOCSY spectrum, which was unresolved in regular TOCSY spectrum.