Oscillation of Linear Ordinary Differential Equations: On a Theorem of A. Grigoriev

We give a simplified proof and an improvement of a recent theorem of A. Grigoriev, placing an upper bound for the number of roots of linear combinations of solutions of systems of linear equations with polynomial or rational coefficients. To Yulij Sergeevich Ilyashenko on his 60th birthday. 2000 Mathematics Subject Classification. 34C08, 34C10, 34M10. Gershon Kekst professorial chair in Mathematics.     

多点抽运光纤激光器速率方程组的近似解析解

为了方便地对多点抽运光纤激光器的特性进行分析,采用保留上能级粒子再发射项主体部分的方法以提高精确度,解析求解了多点抽运掺镱光纤激光器的稳态二能级速率方程组,得到了光纤激光器的输出功率的近似解析解。并将输出功率的解析解与数值解进行了对比。结果表明,解析解与数值解差别小于5%。讨论了抽运光的利用效率与抽运点位置的关系,得到抽运源应该尽量靠近光纤端面的结论。同时,对比了单点抽运和多点抽运方案中抽运功率在光纤中的分布,可以看到,多点抽运时,抽运功率的分布较为均匀,能够缓解因包层对抽运光吸收引起的光纤局部过高的温升所造成的一系列问题,是实现大功率激光输出的良好选择。     

Dynamic Study on Rigid and Flexible Coupling System for Terminally Sensitive Submunition

A kinetic model of the rigid and flexible coupling system for terminally sensitive submunition is set up with Kane＇s method. The parachute is considered as a flexible body, the flexible displacement is expressed with modal spread method, the position of the parachute is expressed with a hybrid coordinate method, and the kinematics of the terminally sensitive submunition is analyzed. Ten generalized coordinates relative to the attitude of the terminally sensitive submunition are chosen, and the correlative generalized active forces, the generalized inertial forces, the generalized internal forces are calculated in turn. On the base of the Kane＇s method, the ten degrees of freedom dynamic equations for the coupled terminally sensitive submunition are finally set up. This model can be used to expediently simulate and analyze accurately the exterior ballistic trajectory of terminally sensitive submunition, and provide the overall design of the terminally sensitive submunition with some helpful references.     

高速水下航行体超空化通气参数数值研究

超空化技术是水下航行体减阻增速的一种重要方式。通过求解N-S方程,利用两方程湍流模型和全空化模型对通气空化流场进行了数值模拟,研究了通气参数对空化流场结构的影响,揭示了通气超空化减阻机理和场内流动状况,分析了超空化航行体阻力特性,数值结果表明供气量是决定空泡形态和超空化航行体减阻效果的最关键因素,供气位置和方向对空泡形态及水动力特性的影响并不显著。     

某导弹发射箱箱盖开盖角度优化研究

采用求解三维、非定常、雷诺平均的N-S方程的方法,对某车载导弹发射过程中的燃气流场进行了非定常数值模拟。紊流模型采用标准的k-ε二方程模型,计算方法为有限体积法,计算网格为结构化网格。在此基础上研究了箱盖受力与开盖角度之间的关系,给出了最优开盖角度。     

大型稀疏线性方程组新的ICCG方法

有限元线性方程组的系数矩阵一般具有稀疏性和对称性的特点,全稀疏存贮方法就是利用这些特点,只存贮对称部分的非零元素,采用链表式管理,即节省存贮空间,又便于动态更改．在完全Cholesky分解的基础上,构造出了新的预处理方法,应用适当的对角元修正策略,得到了一种新的ICCG方法,能够确保方程组高效准确的分解和求解．数值算例证明该算法在时间和存贮上都较为占优,可靠高效,能够应用于有限元线性方程组的求解．     

广义预测控制中 Diophantine矩阵多项式方程的显式解

直接利用被控对象的离散差分方程推导出多变量广义预测控制中Diophantine矩阵多项式方程的显式解,从而避免了其递推求解或迭代求解,使广义预测控制的应用更加方便．     

导体-介质组合体散射分析两种积分方程法比较

采用耦合积分方程和单积分方程两种方法,分析了三维导体-介质组合体目标的电磁散射问题.与传统的耦合积分方程法相比,单积分方程法使介质体表面的未知量数目减少一半,并且能获得更快的迭代解.讨论了导体-介质交界线上RWG基函数的正确处理问题.对介质锥-导体柱组合体、导体-介质组合球和某导弹模型的雷达截面(RCS)进行了计算和比较,验证了两种积分方程方法的正确性,且数值结果表明单积分方程法更加有效.     

A bridge between projection methods and SIMPLE type methods for incompressible Navier–Stokes equations

A bridge is built between projection methods and SIMPLE type methods (Semi‐Implicit Method for Pressure‐Linked Equation). A general second‐order accurate projection method is developed for the simulation of incompressible unsteady flows by employing a non‐linear update of pressure term as Θⁿ?pⁿ⁺¹+(I?Θⁿ)?pⁿ, where Θⁿ is a coefficient matrix, which may depend on the grid size, time step and even velocity. It includes three‐ and four‐step projection methods. The standard SIMPLE method is written in a concise formula for steady and unsteady flows. It is proven that SIMPLE type methods have second‐order temporal accuracy for unsteady flows. The classical second‐order projection method and SIMPLE type methods are united within the framework of the general second‐order projection formula. Two iteration algorithms of SIMPLE type methods for unsteady flows are described and discussed. In addition, detailed formulae are provided for general projection methods by using the Runge–Kutta technique to update the convective term and Crank–Nicholson scheme for the diffusion term. Copyright © 2007 John Wiley & Sons, Ltd.     

光纤布拉格光栅非线性孤子的特性分析

以非线性耦合模理论为基础，用数值计算的方法分析了光纤光栅非线性孤子的特性。结果表明，在较弱光脉冲输入时，脉冲被展宽幅度降低；在强光脉冲输入时，脉冲的幅度，速度和脉宽保持不变，孤子形成；当更强光脉冲输入时，脉冲被压缩同时产生随距离而变的线性啁啾。当波长位于负色散区的弱脉冲和位于正常色散区的强泵浦脉冲共同传输时，输入弱脉冲被压缩。