Superconvergence of discontinuous Galerkin finite element method for the stationary Navier‐Stokes equations

This article focuses on discontinuous Galerkin method for the two‐ or three‐dimensional stationary incompressible Navier‐Stokes equations. The velocity field is approximated by discontinuous locally solenoidal finite element, and the pressure is approximated by the standard conforming finite element. Then, superconvergence of nonconforming finite element approximations is applied by using least‐squares surface fitting for the stationary Navier‐Stokes equations. The method ameliorates the two noticeable disadvantages about the given finite element pair. Finally, the superconvergence result is provided under some regular assumptions. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 23: 421–436, 2007     

用参考圆法演示简谐振动

对受迫振动仪进行了改进，通过参考圆法，演示了作镁速圆周运动的质点在直径方向上的投影所作的运动为简谐振动。     

Improved experimental tracking techniques for validating discrete element method simulations of tumbling mills

We report on further developments in the three-dimensional tracking of a particle deep within the tumbling ball charge of an experimental mill. The experimental X-ray program employing the use of bi-planar X-ray angiography now includes the tracking of a typical 6 mm bulk charge particle in three dimensions with a spatial resolution that is accurate to within 0.15 mm. The improved experimental tracking techniques presented were developed for the purpose of generating accurate three-dimensional particle trajectory data against which to validate a numerical method for the simulation of discrete media, namely the discrete element method (DEM). These improvements are complimented with techniques for comparing charge profiles between numerical DEM simulations and three-dimensional experimental trajectory data.     

Numerical simulation of soft palate movement and airflow in human upper airway by fluid-structure interaction method

In this paper, the authors present airflow field characteristics of human upper airway and soft palate movement attitude during breathing. On the basis of the data taken from the spiral computerized tomography images of a healthy person and a patient with Obstructive Sleep Apnea-Hypopnea Syndrome (OSAHS), three-dimensional models of upper airway cavity and soft palate are reconstructed by the method of surface rendering. Numerical simulation is performed for airflow in the upper airway and displacement of soft palate by fluid-structure interaction analysis. The reconstructed three-dimensional models precisely preserve the original configuration of upper airways and soft palate. The results of the pressure and velocity distributions in the airflow field are quantitatively determined, and the displacement of soft palate is presented. Pressure gradients of airway are lower for the healthy person and the airflow distribution is quite uniform in the case of free breathing. However, the OSAHS patient remarkably escalates both the pressure and velocity in the upper airway, and causes higher displacement of the soft palate. The present study is useful in revealing pathogenesis and quantitative mutual relationship between configuration and function of the upper airway as well as in diagnosing diseases related to anatomical structure and function of the upper airway. The project supported by the National Natural Science Foundation of China (10672036, 10472025 and 10421002), the Natural Science Foundation of Liaoning Province (20032109). English text was polished by Yunming Chen.     

四阶方程两点边值问题Hermite有限元解的渐近展式与外推

1引言有限元解的渐近展式是提高微分方程数值解精度的重要工具,比如亏量校正和外推就是建立在有限元解的渐近展式的基础之上．许多作者对此进行了大量的研究(见[1]-[4]),特别是文[1],提出了在研究有限元解的渐近展式中十分有用的能量嵌入技巧．本文利用能量嵌入定理得到了四阶方程两点边值问题Hermite有限元解及其二阶平均导数的渐近展式,进一步我们还讨论了它们的Richardson外推公式．考虑四阶方程两点边值问题     

表面细分技术在二维声辐射和声散射中的应用

把表面细分技术应用于求解边界积分方程，既能把CAD模型直接用于边界元分析，又能精确描述复杂的边界几何形状，实现网格自动加密和形函数自动升阶，满足误差要求。把它应用于简单的二维声辐射和声散射，结果表明对提高边界元方法的计算精度是有效的。     

用线性插值法求单摆运动周期的近似解

利用线性插值的方法,提出了一个任意摆角条件下的单摆运动周期的近似公式.并利用Mathematica软件将该公式与精确解进行了比较,还与其他近似公式进行了对比.结果表明,该公式的近似程度相当好.     

THE FIRST EXPERIMENT OF A THz GYROTRON WITH A PULSE MAGNET

A THz gyrotron with a pulse magnet has been designed, constructed and operated in FIR FU. It is developed as one of high frequency gyrotrons included in Gyrotron FU Series. The gyrotron has already achieved the first experimental result for high frequency operations whose radiation frequency exceeds 1 THz. In this paper, the design detail and the operation test results for sub-terahertz to terahertz range are described. The second harmonic operation is confirmed experimentally at the expected frequency of 1.005 THz due to TE_6,11 cavity mode at the magnetic field intensity of 19.0 T.     

相干叠加态高次谐波发射的时间行为分析

本文研究了一维模型分子离子(初态为基态和一个激发束缚态叠加的相干态)在超强超短激光脉冲作用下的谐波发射谱.我们发现在高次谐波谱平台区域出现了周期性的结构变化.我们利用小波变换对谐波谱进行了暂态时间频率分析,结果表明该谐波结构产生的原因是由电离电子返回母离子时与不同束缚态复合而产生的谐波光脉冲之间相干叠加.同时采用半经典计算,对所得到的计算结果进行了分析,验证了我们的结论.     

光学相干控制中脉冲光束等相面的实时测控

描述了飞秒脉冲基频光、倍频光光束位相差对相干控制光电流注入的控制作用，提出一种控制基频光、倍频光在全光孔径干涉光场内的等相面保持一致的实验方案，制作了一套相位差稳定自动控制系统，并应用于光学相干控制光电流实验中，获得较好的实时控制结果.