非线性双曲型守恒律的高精度MmB差分格式

构造了一维非线性双曲型守恒律方程的一个高精度、高分辨率的广义G odunov型差分格式。其构造思想是:首先将计算区间划分为若干个互不相交的小区间,再根据精度要求等分小区间,通过各细小区间上的单元平均状态变量,重构各等分小区间交界面上的状态变量,并加以校正;其次,利用近似R iem ann解算子求解细小区间交界面上的数值通量,并结合高阶R unge-K u tta TVD方法进行时间离散,得到了高精度的全离散方法。证明了该格式的Mm B特性。然后,将格式推广到一、二维双曲型守恒方程组情形。最后给出了一、二维Eu ler方程组的几个典型的数值算例,验证了格式的高效性。     

井下巷道围岩变形的散斑分析法

通过对散斑计量法原理分析、数学描述及观测实例的论述，证明激光散斑法是研究煤矿地下结构物相似模型变形状态的一种新的无损检测技术，若采用白光作为光源，该项技术可用于二维变形场的实地测试。     

A new σ‐transform based Fourier‐Legendre‐Galerkin model for nonlinear water waves

This paper presents a new spectral model for solving the fully nonlinear potential flow problem for water waves in a single horizontal dimension. At the heart of the numerical method is the solution to the Laplace equation which is solved using a variant of the $\sigma$‐transform. The method discretizes the spatial part of the governing equations using the Galerkin method and the temporal part using the classical fourth‐order Runge‐Kutta method. A careful investigation of the numerical method's stability properties is carried out, and it is shown that the method is stable up to a certain threshold steepness when applied to nonlinear monochromatic waves in deep water. Above this threshold artificial damping may be employed to obtain stable solutions. The accuracy of the model is tested for: (i) highly nonlinear progressive wave trains, (ii) solitary wave reflection, and (iii) deep water wave focusing events. In all cases it is demonstrated that the model is capable of obtaining excellent results, essentially up to very near breaking.     

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为了实现 EAST 装置真空室内的内窥多关节机械臂的实时高精度控制,提出了一种逆运动学算法,即建立机械臂多变量的方程组,转化成为矩阵的特征值问题求解。为了验证和满足实际控制的需要,还基于 VC++6.0 开发了 MFC 运动学算法程序。结果表明,该算法能在 ms 级别内得到机械臂的所有运动学逆解。     

一类完全重构滤波器的精度条件

本文研究了如何构造满足精度条件的小波滤波器.利用频域分析方法,给出了关于尺度函数精度条件的新结果以及满足精度条件的几个例子.     

Three-stage Stiffly Accurate Runge-Kutta Methods for Stiff Stochastic Differential Equations

In this paper we discuss diagonally implicit and semi-implicit methods based on the three-stage stiffly accurate Runge-Kutta methods for solving Stratonovich stochastic differential equations（SDEs）.Two methods,a three-stage stiffly accurate semi-implicit（SASI3） method and a three-stage stiffly accurate diagonally implicit （SADI3） method,are constructed in this paper.In particular,the truncated random variable is used in the implicit method.The stability properties and numerical results show the effectiveness of these methods in the pathwise approximation of stiff SDEs.     

Simultaneous determination of triazine herbicides in rice by high-performance liquid chromatography coupled with high resolution and high mass accuracy hybrid linear ion trap-orbitrap mass spectrometry

A method was developed for the simultaneous determination of 10 triazine herbicides (cyanazine, simazine, simetryn, metribuzin, atrazine, ametryn, terbuthylazine, prometryn, terbutryn, and dimethametryn) in rice samples by high resolution and high mass accuracy hybrid linear ion trap-Orbitrap mass spectrometer. After extraction with acetonitrile and evaporation, the herbicides were redissolved in n-hexane and purified on a Florisil solid-phase extraction column. All compounds were separated within 12 min, producing more than 11 data points for each herbicide and high mass accuracy quantified ions which the mass errors of absolute value were less than 1.9 ppm in pure solution and 2.1 ppm in the matrix-matched standards solution. The method was validated in terms of the limits of detection and the limits of quantification. The linearity was satisfactory, with a correlation coefficient of >0.9975. Precision and recovery studies were evaluated at three concentration levels for Japonica, Indica, and Glutinous rice matrix. The mean recoveries obtained for all analytes in spiked Xiushui 03, Liangyoupeijiu, and Taihunuo rice samples were 83.3–99.0%, 82.0–99.7%, and 84.2–99.4%, respectively, with relative standard deviation in range 1.7–10.6%, 1.2–10.7%, and 1.9–11.6% for spiked rice samples, respectively. The intra-day precision (n = 5) for the 10 herbicides in rice samples spiked at an intermediate level was between 2.8% and 7.9%, and the inter-day precision over 10 days (n = 10) was between 5.5% and 15.9%.     

高精度近场动力学方法:一维键型研究

近些年发展起来的近场动力学方法对于模拟复杂的断裂破坏问题具有显著优势.然而,计算精度不高一直是影响该方法进一步发展的瓶颈问题之一.区域积分不精确和键缺失导致的边界效应是降低该方法计算精度的两个主要原因.针对一维键型近场动力学模型,本文通过修正微模量提高区域积分的精度,通过理性构建固定边界和力边界虚拟键改善边界效应,建立了高精度近场动力学方法.数值结果表明,与经典的近场动力学方法相比,本文方法显著提高了计算精度,准静态常应变问题甚至能够达到机器精度.     

Minimizing convex quadratics with variable precision conjugate gradients

We investigate the method of conjugate gradients, exploiting inaccurate matrix‐vector products, for the solution of convex quadratic optimization problems. Theoretical performance bounds are derived, and the necessary quantities occurring in the theoretical bounds estimated, leading to a practical algorithm. Numerical experiments suggest that this approach has significant potential, including in the steadily more important context of multiprecision computations.     

变系数情形下Criss-Cross三角形线性元的渐近展式与超收敛

本文讨论了二阶椭圆方程变系数情形下Criss-Cross三角形线性元的超收敛性质,得到了有限元的渐进展式、外推及高精度组合公式等结果.