On the accuracy of a nonlinear finite volume method for the solution of diffusion problems using different interpolations strategies

In this paper, we consider a nonlinear finite volume method to solve the steady‐state diffusion equation in nonhomogeneous and non‐isotropic media. The method is nonlinear even if the original problem is linear. In its original form, the scheme is monotone, because the coefficient matrix is monotone under certain assumptions and, as a consequence, whenever the analytic operator demands, it preserves the positivity of numerical solutions. On the other hand, the scheme is unable to reproduce piecewise linear solutions exactly. In order to recover this interesting feature, we use two different interpolation strategies. In this case, even though we are unable to prove monotonicity, we show some numerical evidences that the combined method has an improved behavior, producing second order accurate solutions, even for nonhomogeneous and strongly anisotropic media. Copyright © 2013 John Wiley & Sons, Ltd.     

Chebyshev spectral variational integrator and applications

The Chebyshev spectral variational integrator(CSVI) is presented in this paper. Spectral methods have aroused great interest in approximating numerically a smooth problem for their attractive geometric convergence rates. The geometric numerical methods are praised for their excellent long-time geometric structure-preserving properties.According to the generalized Galerkin framework, we combine two methods together to construct a variational integrator, which captures the merits of both methods. Since the interpolating points of the variational integrator are chosen as the Chebyshev points,the integration of Lagrangian can be approximated by the Clenshaw-Curtis quadrature rule, and the barycentric Lagrange interpolation is presented to substitute for the classic Lagrange interpolation in the approximation of configuration variables and the corresponding derivatives. The numerical float errors of the first-order spectral differentiation matrix can be alleviated by using a trigonometric identity especially when the number of Chebyshev points is large. Furthermore, the spectral variational integrator(SVI) constructed by the Gauss-Legendre quadrature rule and the multi-interval spectral method are carried out to compare with the CSVI, and the interesting kink phenomena for the Clenshaw-Curtis quadrature rule are discovered. The numerical results reveal that the CSVI has an advantage on the computing time over the whole progress and a higher accuracy than the SVI before the kink position. The effectiveness of the proposed method is demonstrated and verified perfectly through the numerical simulations for several classical mechanics examples and the orbital propagation for the planet systems and the Solar system.     

DIOPTAS: a program for reduction of two-dimensional X-ray diffraction data and data exploration

The amount of data collected during synchrotron X-ray diffraction (XRD) experiments is constantly increasing. Most of the time, the data are collected with image detectors, which necessitates the use of image reduction/integration routines to extract structural information from measured XRD patterns. This step turns out to be a bottleneck in the data processing procedure due to a lack of suitable software packages. In particular, fast-running synchrotron experiments require online data reduction and analysis in real time so that experimental parameters can be adjusted interactively. Dioptas is a Python-based program for on-the-fly data processing and exploration of two-dimensional X-ray diffraction area detector data, specifically designed for the large amount of data collected at XRD beamlines at synchrotrons. Its fast data reduction algorithm and graphical data exploration capabilities make it ideal for online data processing during XRD experiments and batch post-processing of large numbers of images.     

High-resolution semi-discrete Hermite central-upwind scheme for multidimensional Hamilton–Jacobi equations

We introduce a high resolution fifth-order semi-discrete Hermite central-upwind scheme for multidimensional Hamilton–Jacobi equations. The numerical fluxes of the scheme are constructed by Hermite polynomials which can be obtained by using the short-time assignment of the first derivatives. The extensions of the proposed semi-discrete Hermite central-upwind scheme to multidimensional cases are straightforward. The accuracy, efficiency and stability properties of our schemes are finally demonstrated via a variety of numerical examples.     

第二类端点奇异Fredholm积分方程的分数阶退化核方法

本文针对第二类端点奇异Fredholm积分方程构造基于分数阶Taylor展开的退化核方法，设计了两种计算格式，一是在全区间上使用分数阶Taylor展开式近似核函数，二是在包含奇点的小区间上采用分数阶插值，在剩余区间上采用分段二次多项式插值逼近核函数.讨论了两种退化核方法收敛的条件，并给出了混合插值法的收敛阶估计.数值算例表明对于非光滑核函数分数阶退化核方法有着良好的计算效果，且混合二次插值法比全区间上的分数阶退化核方法有着更广泛的适用范围.     

A new idea to construct the fractal interpolation function

The aim of this paper is to present a new idea to construct the nonlinear fractal interpolation function, in which we exploit the Matkowski and the Rakotch fixed point theorems. Our technique is different from the methods presented in the previous literatures.     

不同于教科书中的标准加入法——开放环境下授课的实例

为了加深学生对标准加入法（standard addition methods,SAM）的理解,将其列为“分析化学英文文献选读”选修课的一个专题,在学习资源开放、学习方式开放和学习结果开放的环境下,经过学习阶段、展示阶段和拓展阶段等密不可分的3阶段式问题导引下的主动学习和讨论,获得了有别于目前教科书内容的、鲜活的SAM内容：（1）由目前的2种类型拓展为9种类型的SAM;（2）由目前的外推法SAM拓展为内插法SAM;（3）由目前的容量法SAM拓展为重量法SAM;（4）新近出现的“稀释标准加入校准法”与这里讨论的SAM存在本质差别。在开放的环境下将传统的教学问题与新思路和新应用结合起来是一种行之有效的教学方法。它至少有以下3个优点：（1）以学生已有的知识为切入点,易于学生接受;（2）所选择的材料紧密跟踪分析化学的新进展,可以激发学生的兴趣;（3）课程以专题的形式展开,逻辑线索清晰。     

防爆型双监探测器的窗口设计

被动红外与主动微波组合的探测器是一种双监探测器,从双监探测器工作机理出发,得出了防爆箱探测窗口基本技术要求,并在此基础上对各类窗口材料进行了计算分析及细节设计,实现了双监探测器的主动微波及被动远红外信号低损耗通过。所设计的防爆箱,解决了双监探测器在具有防爆性要求的\环境中的应用难题,对提升易燃易爆等危险环境下的防入侵监测技术水平有着重要的意义。     

星载多路短波红外探测器温控系统设计

主要针对星载多路短波红外探测器的温度要求设计了高精度在轨温度控制系统。首先,在对工作温度控制需求进行分析的基础上,提出了该系统短波红外探测器的温度高稳定性要求;其次设计了高稳定性温度采集电路、低噪声热控驱动电路,并且在FPGA芯片上基于开关控制算法,产生了脉宽调制信号;然后利用该脉宽调制信号控制热电制冷器的驱动电流,实现了在资源有限的条件下,温度控制高稳定度的要求。最终性能测试的结果表明,温控的精度可以达到±0.1°的高稳定度要求,满足该多路短波红外探测系统星载工作温度要求。     

Integrated Time-to-Digital Converters Based on Interpolation

The main features of two time-to-digital convertersbased on interpolation are presented, together with some measurementresults. The first converter is based on digital delay line interpolatorsand has been implemented in a 1.2 µm CMOS process.It has a single-shot resolution of 1 ns (-value)and a nonlinearity less than ±50 ps in the measurementrange 5 to 500 ns. The power consumption of the circuit is 15mW. The second time digitizer has analog interpolators basedon time-to-voltage conversion and has been implemented in a 1.2 µm BiCMOS process. It has a single-shot resolutionof 50 ps and a nonlinearity less than 150 ps in the measurementrange 1 to 300 ns. The power consumption of this circuit is 200mW.