二维Fredholm积分方程Nystrom方法的渐近展开及其外推

本文讨论了求解二维第二类Ｆｒｅｄｈｏｌｍ积分方程的Ｎｙｓｔｒｏｍ方法，得到了数值解的逐项渐近展开，从而可进行Ｒｉｃｈａｒｄｓｏｎ外推，提高数值解的精度。     

圆柱面绕任意轴回转形成的包络面分析

在分析及计算椭圆上距离任意已知点最远或最近的点基础上,分析了最远点及最近点在圆柱面绕任意轴回转形成包络面过程中的作用,从而由最远点及最近点的计算公式导出了多种形式的包络面方程,并由此找出了包络面受各种因素影响的规律.     

轮廓仪检测的系统误差分析

从轮廓仪的工作原理出发，分析了影响轮廓仪检测精度的主要系统误差，并以二次旋转非球面为例计算了系统误差对面形检测精度的影响，得出Talysurf轮廓仪在测量时，系统误差对面形误差的影响随顶点曲率的绝对值、口径以及偏心率函数的增大而增大，随定位误差和不重合误差的增大而增大的结论。最后的实验结果证明了该结论的正确性。     

The suppression of structural phase transformation in LaVO3 and La1−xSrxVO3 thin films fabricated by pulsed laser deposition

Highly oriented (100) thin films of LaVO₃ and La_1−xSr_xVO₃ have been fabricated by pulsed laser deposition in a reducing atmosphere. The films show a transition from insulating to metallic behaviour in the composition region of x, 0.175<x<0.200. In the single crystals of the antiferromagnetic insulating phase, a first-order structural phase transition is observed few degrees below the magnetic transition, which manifests itself as a kink in the temperature dependence of resistivity. In the highly oriented thin films of LaVO₃ and La_1−xSr_xVO₃ fabricated on lattice matched substrates in this study, the structural phase transformation in the insulating phase has been suppressed. The electrical conduction is found to take place via hopping through localized states at low temperatures. The metallic compositions show a non-linear (T^1.5) behaviour in the temperature dependence of resistivity. V (2p) core level spectra of these films show a gradual change in the relative intensities of V³⁺ and V⁴⁺ ions as the value of x increases.     

二极管激光阵列在Talbot外腔中同相模的选择

 从理论和实验上对二极管激光阵列在Talbot外腔中的锁相进行了研究。在同相模和异相模近场分布的基础上，利用1维情况下的菲涅耳衍射公式计算了其远场分布。根据同相模和异相模在Talbot腔中的分布特性，采用1/2 Talbot腔并将外腔镜倾斜一个角度a的方法既能选择同相模，又能使模式的功率损耗最小。二极管激光阵列芯片采用CD金刚石材料,“三明治”结构对其进行封装，明显地减小了阵列的“smile”效应。在实验中实现了二极管激光阵列同相模的锁相输出，远场单瓣模的半高全宽为0.11 mm。     

DSC study of annealing and phase transformations of C60 and C70 polymerized under pressures in the range 9.5-13 GPa

C₆₀ and C₇₀ fullerenes polymerized under pressures between 9.5 and 13 GPa and temperatures between 670 and 1850 K were investigated by differential scanning calorimetry (DSC) in the range 240-640 K. Endothermal heat effects were observed with a peak maximum just below 540 K, a temperature characteristic for breakdown of (2+2) intermolecular links in dimers, 1D and 2D polymers. Exothermal effects, starting from 380 K, were observed for the first time in polymeric fullerenes. These effects are attributed to relaxation processes and to breakdown of other types of intermolecular bonds such as common four-sided rings and (3+3) interlinks.     

A new operational vector approach for time-fractional subdiffusion equations of distributed order based on hybrid functions

This research study deals with the numerical solutions of linear and nonlinear time-fractional subdiffusion equations of distributed order. The main aim of our approach is based on the hybrid of block-pulse functions and shifted Legendre polynomials. We produce a novel and exact operational vector for the fractional Riemann–Liouville integral and use it via the Gauss–Legendre quadrature formula and collocation method. Consequently, we reduce the proposed equations to systems of equations. The convergence and error bounds for the new method are investigated. Six problems are tested to confirm the accuracy of the proposed approach. Comparisons between the obtained numerical results and other existing methods are provided. Numerical experiments illustrate the reliability, applicability, and efficiency of the proposed method.     

A Low Order Nonconforming Mixed Finite Element Method for Non-Stationary Incompressible Magnetohydrodynamics System

A low order nonconforming mixed finite element method (FEM) is established for the fully coupled non-stationary incompressible magnetohydrodynamics (MHD) problem in a bounded domain in 3D. The lowest order finite elements on tetrahedra or hexahedra are chosen to approximate the pressure, the velocity field and the magnetic field, in which the hydrodynamic unknowns are approximated by inf-sup stable finite element pairs and the magnetic field by $H^1(\Omega)$-conforming finite elements, respectively. The existence and uniqueness of the approximate solutions are shown. Optimal order error estimates of $L^2(H^1)$-norm for the velocity field, $L^2(L^2)$-norm for the pressure and the broken $L^2(H^1)$-norm for the magnetic field are derived.     

On mixed finite element approximations of shape gradients in shape optimization with the Navier–Stokes equation

For shape optimization of fluid flows governed by the Navier–Stokes equation, we investigate effectiveness of shape gradient algorithms by analyzing convergence and accuracy of mixed finite element approximations to both the distributed and boundary types of shape gradients. We present convergence analysis with a priori error estimates for the two approximate shape gradients. The theoretical analysis shows that the distributed formulation has superconvergence property. Numerical results with comparisons are presented to verify theory and show that the shape gradient algorithm based on the distributed formulation is highly effective and robust for shape optimization.