A posteriori error analysis of a quadratic finite volume method for nonlinear elliptic problems

In this article, we construct and analyze a residual-based a posteriori error estimator for a quadratic finite volume method (FVM) for solving nonlinear elliptic partial differential equations with homogeneous Dirichlet boundary conditions. We shall prove that the a posteriori error estimator yields the global upper and local lower bounds for the norm error of the FVM. So that the a posteriori error estimator is equivalent to the true error in a certain sense. Numerical experiments are performed to illustrate the theoretical results.     

Second moment of error term of mean value for binary Egyptian fractions

We study the mean square of the error term of the mean value for binary Egyptian fractions.We get an asymptotic formula under the Riemann Hypothesis.     

More efficient time integration for Fourier pseudospectral DNS of incompressible turbulence

Time integration of Fourier pseudospectral DNS is usually performed using the classical fourth-order accurate Runge-Kutta method or other second- or third-order methods, with a fixed step size. We investigate the use of higher-order Runge-Kutta pairs and automatic step size control based on local error estimation. We find that the fifth-order accurate Runge-Kutta pair of Bogacki and Shampine gives much greater accuracy at a significantly reduced computational cost. Specifically, we demonstrate speedups of 2× to 10× for the same accuracy. Numerical tests (including the Taylor-Green vortex, Rayleigh-Taylor instability, and homogeneous isotropic turbulence) confirm the reliability and efficiency of the method. We also show that adaptive time stepping provides a significant computational advantage for some problems (like the development of a Rayleigh-Taylor instability) without compromising accuracy.     

一种非正交对称条带束流位置监测器设计

介绍了一种条带束流位置监测器(BPM)的设计与仿真方法。在国家同步辐射实验室"太赫兹近场高通量材料物性测试系统"工程项目中,针对波荡器出口处真空室非正交对称性的问题,设计了矩形真空室和跑道形真空室下的两种非正交对称性条带BPM,并与传统的圆形真空室下条带BPM进行对比。基于边界元法,利用MATLAB软件分别对三种真空室下的条带BPM进行建模和仿真。仿真结果表明:相对于传统的圆形真空室下条带BPM,矩形和跑道形真空室下条带BPM灵敏度提高了30%,阻抗匹配误差相对降低了20%,束流位置拟合误差降低了80%。考虑加工精度,矩形真空室下的条带BPM更适用于该工程。     

不同结构绝对光栅尺的误码机制研究

针对光栅尺具有断电位置复位、无累计误差、高精度优点, 在光学隔振平台上分别建立开放式和封闭式绝对光栅尺实验系统, 绝对光栅尺采用图像识别原理, 以气浮直线电机ArotechABL1500为参考对象, 使用激光干涉仪RENISHAW XL-80校核精度, 研究不同结构绝对光栅尺的误码特点及原因。通过对比实验及研究分析, 表明封闭式绝对尺相对于开放式绝对尺的误码率要高, 开放式绝对式光栅尺的误码率为3%, 封闭式绝对式光栅尺的误码率为8%。     

Multiple Scattering Between Adjacent Sound Sources in Head-Related Transfer Function Measurement System

To accelerate head-related transfer functions (HRTFs) measurement, two or more independent sound sources are usually employed in the measurement system. However, the multiple scattering between adjacent sound sources may influence the accuracy of measurement. On the other hand, the directivity of sound source could induce measurement error. Therefore, a model consisting of two spherical sound sources with approximate omni-directivity and a rigid-spherical head is proposed to evaluate the errors in HRTF measurement caused by multiple scattering between sources. An example of analysis using multipole re-expansion indicates that the error of ipsilateral HRTFs are within the bound of ± 1.0 dB below a frequency of 20 kHz, provided that the sound source radius does not exceed 0.025 m, the source distance relative to head center is not less than 0.5 m, and the angular interval between two adjacent sources is not less than 20 degrees. Similar conclusions under different conditions can also be analyzed and discussed by using this calculation method. Furthermore, the results are verified by measurements of HRTFs for a rigid sphere and a KEMAR artificial head.     

面向内容的立体视频帧重要性区分模型研究

异构网络引起的视频传输失真是影响视频终端感知质量的重要因素，通常只能在解码端进行评估和补偿。因此在编码端建立一个面向内容的立体视频传输失真模型，考虑错误隐藏和错误扩散两种失真，通过近似估计视频中各帧对终端质量的贡献度，从而实现每帧重要性的区分。新模型综合考虑了视频帧编码位置以及表征内容的编码模式、运动矢量、视差矢量等关键信息，可以作为视频在异构网络中传输策略的重要依据。     

基于RFID和指静脉识别的化学药品智能管理柜设计

为保障实验室中存放的药品安全, 提出一种基于射频识别(RFID)和指静脉识别的化学药品智能管理柜. 智能柜采用RFID、指静脉识别等物联网技术, 通过用户身份认证, 化学药品的自动识别、记录以及存储空间的智能控制, 实现实验室化学药品的高效安全管理. 样机实际测试结果表明, 系统可以较好地通过指静脉识别对使用者的身份进行认证, 也能够通过RFID快速识别化学药品; 系统智能化程度高, 各项功能完备, 可显著提高实验室化学药品管理能力.     

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.