Description of a radially polarized Laguerre-Gauss beam beyond the paraxial approximation

Fifth-order corrected expressions for the fields of a radially polarized Laguerre-Gauss (R-TEMn1) laser beams are derived based on perturbative Lax series expansion. When the order of Laguerre polynomial is equal to zero, the corresponding beam reduces to the lowest-order radially polarized beam (R-TEM01). Simulation results show that the accuracy of the fifth-order correction for R-TEMn1 depends not only on the diffraction angle of the beam as R-TEM01 does, but also on the order of the beam. (c) 2007 Optical Society of America.

Exact description of a cylindrically symmetrical complex-argument Laguerre-Gauss beam

Based on the perturbative series representation of a complex-source-point spherical wave an expression for cylindrically symmetrical complex-argument Laguerre-Gauss beams of radial order n is derived. This description acquires the accuracy up to any order of diffraction angle, and its first three corrected terms are in accordance with those given by Seshadri [Opt. Lett. 27, 1872 (2002)] based on the virtual source method. Numerical results show that on the beam axis the number of orders of nonvanishing nonparaxial corrections is equal to n. Meanwhile a higher radial mode number n leads to a smaller convergent domain of radius. (C) 2008 Optical Society of America.

Transonic Aeroelastic Numerical Simulation in Aeronautical Engineering

A lower-upper symmetric Gauss-Seidel (LU-SGS) subiteration scheme is constructed for time-marching of the fluid equations. The Harten-Lax-van Leer-Einfeldt-Wada (HLLEW) scheme is used for the spatial discretization. The same subiteration formulation is applied directly to the structural equations of motion in generalized coordinates. Through subiteration between the fluid and structural equations, a fully implicit aeroelastic solver is obtained for the numerical simulation of fluid/structure interaction. To improve the ability for application to complex configurations, a multiblock grid is used for the flow field calculation and transfinite interpolation (TFI) is employed for the adaptive moving grid deformation. The infinite plate spline (IPS) and the principal of virtual work are utilized for the data transformation between the fluid and structure. The developed code was first validated through the comparison of experimental and computational results for the AGARD 445.6 standard aeroelastic wing. Then, the flutter character of a tail wing with control surface was analyzed. Finally, flutter boundaries of a complex aircraft configuration were predicted.

Saltation in wind blown sand

The Boltzmann equation of the sand particle velocity distribution function in wind-blown sand two-phase flow is established based on the motion equation of single particle in air. And then, the generalized balance law of particle property in single phase granular flow is extended to gas-particle two-phase flow. The velocity distribution function of particle phase is expanded into an infinite series by means of Grad's method and the Gauss distribution is used to replace Maxwell distribution. In the case of truncation at the third-order terms, a closed third-order moment dynamical equation system is constructed. The theory is further simplified according to the measurement results obtained by stroboscopic photography in wind tunnel tests.

风沙两相流中的跃移运动

从单个跃移沙粒在气流中的运动方程出发导出了风沙两相流中沙粒相速度分布函数的Ｂoltzmann方程；并以此将单相颗粒流理论中的广义平衡方程推广到气固两相流的情形。提出用Grad方法将粒子相速度分布函数展成无穷级数，并引入Gauss分布取代单相颗粒流中传统的Maxwell分布。在保留到3次项的情况下，建立了气体－颗粒两相湍流边界层三阶矩封闭理论的动力学方程组。并在风洞频闪摄影实验的基础上，对理论进行简化，得到便于工程应用的简化方程。

一个推广Virial定理的数学方法和应用

本文在提出广义Gauss定理的思路下,提出了广义Stokes定理和一个推广Virial定理的新方法,后者应用于天体磁流体力学和引力平衡问题时得到的结果有:(1)气体具有运动时的平衡系统的判据,(2)磁场对气团形态的影响。应用于实验室等离子体平衡问题时,其结果有:(1)包围在气体中孤立磁场的特性,(2)发现内包无力场必须外包一有力场,(3)无力场的形态,应用于Tokmak等离子体环时的结果有:(1)环的胖瘦对环表面磁压的影响,(2)两个外加磁场分量分别和气压、环的胖瘦,截面形态、环电流分布和逆磁或顺磁的平衡关系,搞清楚了外加磁场约束等离子体总体平衡的物理机制。

气流与化学激光中的碰撞和非均匀加宽效应——理论分析模型

本文把用于气流与化学激光性能计算的理论模型作了分析比较,包括常用的Lorentz-Gauss谱线形因子近似、本文提出的矩形谱线形因子近似以及文献[5]的理论。对气流化学激光的简化扩散混合模型,文中简要地导出了与上述诸理论相对应的具体结果。分析和计算表明:在碰撞与非均匀加宽同时起作用,特别是非均匀加宽占优势的情况下,两种谱线形因子近似以及文献[5]理论的结果三者之间存在显著的差异;矩形谱线形因子近似要比常用的Lorentz-Gauss谱线形因子近似精确,而矩形谱线形因子近似的计算量要比Lorentz-Gauss谱线形因子近似的计算量少。

Numerical Analyses of Transonic Fluid/Structure interaction in Aircraft Engineering

Through the coupling between aerodynamic and structural governing equations, a fully implicit multiblock aeroelastic solver was developed for transonic fluid/stricture interaction. The Navier-Stokes fluid equations are solved based on LU-SGS (lower-upper symmetric Gauss-Seidel) Time-marching subiteration scheme and HLLEW (Harten-Lax-van Leer-Einfeldt-Wada) spacing discretization scheme and the same subiteration formulation is applied directly to the structural equations of motion in generalized coordinates. Transfinite interpolation (TFI) is used for the grid deformation of blocks neighboring the flexible surfaces. The infinite plate spline (IPS) and the principal of virtual work are utilized for the data transformation between fluid and structure. The developed code was fort validated through the comparison of experimental and computational results for the AGARD 445.6 standard aeroelastic wing. In the subsonic and transonic range, the calculated flutter speeds and frequencies agree well with experimental data, however, in the supersonic range, the present calculation overpredicts the experimental flutter points similar to other computations. Then the flutter character of a complete aircraft configuration is analyzed through the calculation of the change of structural stiffness. Finally, the phenomenon of aileron buzz is simulated for the weakened model of a supersonic transport wing/body model at Mach numbers of 0.98 and l.05. The calculated unsteady flow shows, on the upper surface, the shock wave becomes stronger as the aileron deflects downward, and the flow behaves just contrary on the lower surface of the wing. Corresponding to general theoretical analysis, the flow instability referred to as aileron buzz is induced by a stronger shock alternately moving on the upper and lower surfaces of wing. For the rigid structural model, the flow is stable at all calculated Mach numbers as observed in experiment

Transonic Aeroelastic Numerical Simulation in Aeronautical Engineering

A lower-upper symmetric Gauss-Seidel (LU-SGS) subiteration scheme is constructed for time-marching of the fluid equations. The Harten-Lax-van Leer-Einfeldt-Wada (HLLEW) scheme is used for the spatial discretization. The same subiteration formulation is applied directly to the structural equations of motion in generalized coordinates. Through subiteration between the fluid and structural equations, a fully implicit aeroelastic solver is obtained for the numerical simulation of fluid/structure interaction. To improve the ability for application to complex configurations, a multiblock grid is used for the flow field calculation and transfinite interpolation (TFI) is employed for the adaptive moving grid deformation. The infinite plate spline (IPS) and the principal of virtual work are utilized for the data transformation between the fluid and structure. The developed code was first validated through the comparison of experimental and computational results for the AGARD 445.6 standard aeroelastic wing. Then, the flutter character of a tail wing with control surface was analyzed. Finally, flutter boundaries of a complex aircraft configuration were predicted.

计算流体力学

基于图像处理的陶瓷基复合材料的微结构表征

本文综述了目前边界元法研究现状和进展，分析了边界元法长期以来存在着超奇异积分和几乎超奇异积分的计算难题，该问题一直困扰着边界元法的应用范围和效率。文中针对二维边界积分方程中几乎奇异积分问题，取用二节点线性单元，剖析了边界积分方程中出现几乎奇异积分的根源。提出了接近度概念，定量地度量了单元上积分发生几乎奇异性的程度。作者寻找到一些积公式，采用分部积分法将几乎奇异积分转化为无奇异积分和解析积分之和，从而获得正则化算法。针对三维边界元法中几乎奇异面积分问题，取用三角形线性单元，在三角形平面内采用极坐标（ρ，θ），建立一种半解析算法，对变量ρ施用分部积分法将几乎强奇异和超奇异面积分转化为沿单元围道的一系列线积分，然后Gauss数值积分能够胜任这些线积的计算。对于高阶单元，提出将高阶单元细分为若干线性单元策略进行处理。对二、三维问题的几乎奇异积分分别给出了数值实验，即使接近度非常小，本文方法计算值与精确值非常一致。本文将正则化算法和半解析算法运用于二、三维弹性力学问题边界元法中，直接地计算出单元上的几乎强奇异和超奇异积分，成功地求解了近边界点的位移和应力。与已有算法比较，本文方法简单，易于施行，精度高。同样，本文方法在边界方法计算位势问题中几乎超奇异积分也获得成功。另则，因为几乎奇异积分的障碍，一种观点认为边界元法无力求解薄壁弱性体问题，本文的正则化算法同样成功地计算了源点在边界时的边界积分方程中几乎奇异积分，显示了边元法能够有效地分析薄壁结构及组合结构。导数场边界积分方程中存在着超奇异主值积分的计算屏障。对于弹性力学平面问题，本文提出以符号算子δ_(ij)和∈_(ij)（排列张量）分别作用于位移导数边界积分方程，运用一系列数学技巧将边界位移、面力和位移导数变换为新的边界变量，从而获得一个新的导数场边界积分方程－自然边界积分方程。自然边界积分方程仅存在Cauchy主值积分，文中导出了相应的主值积分列式和奇性系数。自然边界积分方程与位移边界积分方程联合可直接获取边界应力，并且精度与位移相当。自然边界积分方程的一个优点是可以仅在我们感兴趣的局部边界段建立求解。文中提出联合位移边界积分方程和自然边界积分方程计算二维弹性裂纹体的位移场、应力场和应力强度因子，结合几乎奇异积分的正则化算法，求解了含狭窄孔洞的高度应力集中问题。若干算例显示了本文方法计算结果与分析解吻合的很好。因为位移边界积分方程在裂纹面上是不适定的，本文建议采用位移边界积分方程、自然边界积分方程和差分关系联立求解一般的二维断裂力学问题的位移场和应力场，由此求得应力强的因子。

Numerical simulation of wavefronts diffracted by apertures with circular symmetry

The numerical simulation of the wavefronts diffracted by apertures with circular symmetry is realized by a numerical method. It is based on the angular spectrum of plane waves, which ignored the vector nature of light. The on-axial irradiance distributions of plane wavefront and Gauss wavefront diffracted by the circular aperture have been calculated along the propagation direction. Comparisons of the simulation results with the analytical results and the experimental results tell us that it is a feasible method to calculate the diffraction of apertures. (c) 2006 Published by Elsevier GmbH.

基于频域相位共轭技术的光纤偏振信号的失真抑制

理论分析了信号在频域中的相位共轭变换,分析表明,当输入信号取频域相位共轭后,其输出信号相当于输入信号时域包络的相位共轭和时间反转.在此基础上,分析了在双折射光纤中基于频域相位共轭技术的偏振信号失真的抑制和补偿机理,数值模拟了偏振孤子信号和偏振Gauss信号在中距相位共轭光纤系统中的传输演化过程.结果表明,利用频域相位共轭技术能够准确复原双折射光纤系统中的初始输入偏振信号,同时能够补偿色散和复原非线性效应所导致的信号失真.