Ni25+离子1s23s-1s2np跃迁的全能域理论研究

用全实加关联方法计算了Ni25+离子1s23s和1s2np (n  9)态的能量.通过引入价电子的有效核电荷,在类氢近似下,估算了对能量的高阶相对论修正和QED修正.计算了该离子1s23s-1s2np的跃迁能,波长和在三种规范下的振子强度.依据量子亏损理论,确定了Rydberg系列1s2np的量子数亏损,据此可以实现对任意高激发态(n  10)的能量的可靠预言;得到该离子从1s23s态到电离阈附近高激发1s2np态间的跃迁振子强度以及到相应连续态跃迁的振子强度密度.     

类铍离子1s22s2p 3P1, 2 能级之间的磁偶极跃迁

用多组态Dirac-Fock和相对论组态相互作用的扩展优化能级方法,在计算中包含了Breit相互作用,真空极化,自能以及有限核质量修正,计算了核电荷数从Z=6到80的类铍离子等电子序列的1s22s2p 3P1, 2的精细结构能级,磁偶极跃迁几率和振子强度。结果与目前可靠的结果在其不确定度范围内符合得很好,另外也得到一些与其他早期理论计算不同的结果。     

参外联合激励复合非线性振子的分岔分析

讨论了参外联合激励复合非线性振子的动力学行为.对其定常解在一阶近似下的方程进行了局部分岔分析,给出了简单分岔和Hopf分岔发生的条件,并通过对近似方程和原系统的数值模拟加以验证.分析了多种参数对该振子动力学行为演化过程的影响.根据全局分岔理论探讨了该振子在不同条件下发生同宿、异宿分岔的必要条件,其结论与数值计算的结果大致符合. 关键词： 复合非线性振子 局部分岔 全局分岔 混沌     

Improved nonlinear optimization in the storage ring of the modern synchrotron radiation light source

In the storage ring of the third generation light sources, nonlinear optimization is an indispensable course in order to obtain ample dynamic acceptances and to reach high injection efficiency and long beam lifetime, especially in a low emittance lattice. An improved optimization algorithm based on the single resonance approach, which takes relative weight and initial Harmonic Sextupole Integral Strength （HSIS） as search variables, is discussed in this paper. Applications of the improved method in several test lattices are presented. Detailed analysis of the storage ring of the Shanghai Synchrotron Radiation Facility （SSRF） is particularly emphasized. Furthermore, cancellation of the driving terms is investigated to reveal the physical mechanism of the harmonic sextupole compensation. Sensitivity to the weight and the initial HSIS as well as dependence of the optimum solution on the convergent factor is analyzed.     

Coalescence in coupled DulTing oscillators

The forced Duffing oscillator has a pair of symmetrical attractors in a proper parameter regime. When a lot of Duffing oscillators are coupled linearly, the system tends to form dusters in which the neighboring oscillators fall onto the same attractor. When the coupling strength is strong, all of the oscillators fall onto one attractor. In this work, we investigate coalescence in the coupled forced Duffing oscillators. Some phenomena are found and explanations are presented.     

混沌Mathieu-Duffing振子的开闭环控制

基于开闭环控制的思想,设计了一类由外激力与线性误差反馈组成的开闭环控制器,研究了Mathieu-Duffing振子混沌轨道至任意目标周期轨道的控制问题;同时,利用Liapunov稳定性理论与二阶常微分方程初值问题的一个比较定理,证明了上述开闭环控制夹带盆(basin of entrainment)的全局性.最后,利用数值模拟,验证了理论结果的正确性.     

考虑互耦的半波振子线阵辐射和散射方向图综合

对于半波振子阵列天线,可用感应电动势法算得其阻抗矩阵,依据等效电路原理计入单元间的互耦计算辐射场.将其推广至考虑互耦的散射场计算,基于此辐射场和散射场的计算公式,提出一种考虑互耦同时综合半波振子阵列天线辐射和散射方向图的新方法.运用粒子群优化算法,通过优化振子的间距,同时综合指定辐射和散射方向图.运用该方法,通过对中心工作频率处的辐射和散射特性以及在威胁角度给定频带内的散射特性优化,有效降低半波振子阵在中心工作频率处的辐射和散射方向图的副瓣电平,并减小其在威胁角度给定频带内的雷达散射截面.计算结果与FEKO仿真结果吻合良好,验证方法的正确性.     

Flux vector splitting solutions for coupling hydraulic transient of gas-liquid-solid three-phase flow in pipelines

The gas-liquid-solid three-phase mixed flow is the most general in multiphase mixed transportation. It is significant to exactly solve the coupling hydraulic transient problems of this type of multiphase mixed flow in pipelines. Presently, the method of characteristics is widely used to solve classical hydraulic transient problems. However, when it is used to solve coupling hydraulic transient problems, excessive interpolation errors may be introduced into the results due to unavoidable multiwave interpolated calculations. To deal with the problem, a finite difference scheme based on the Steger-Warming flux vector splitting is proposed. A flux vector splitting scheme is established for the coupling hydraulic transient model of gas-liquid-solid three-phase mixed flow in the pipelines. The flux subvectors are then discretized by the Lax-Wendroff central difference scheme and the Warming-Beam upwind difference scheme with second-order precision in both time and space. Under the Rankine-Hugoniot conditions and the corresponding boundary conditions, an effective solution to those points located at the boundaries is developed, which can avoid the problem beyond the calculation region directly induced by the second-order discrete technique. Numerical and experimental verifications indicate that the proposed scheme has several desirable advantages including high calculation precision, excellent shock wave capture capability without false numerical oscillation, low sensitivity to the Courant number, and good stability.     

HE PRELIMINARY INVESTIGATION ON DESIGN AND EXPERIMENTAL RESEARCH OF NONLINEAR CHARACTERISTICS OF SD OSCILLATOR

具有光滑与不连续转迁特征的SD振子发现和提出以来,引起了广泛关注.基于双稳系统大位移特征的测量法困难,SD振子的实验研究还未见报道.该文提出并设计了具有SD振子系统光滑特征的非线性实验装置,用实验的方法揭示由几何关系产生的强非线性系统的非线性动力学行为.设计的非线性实验装置基本振动参数均有良好的可调性和可测量性,对SD振子在不同频率及幅值的简谐激励作用下的非线性动力学响应进行了实验研究.为克服大位移测量难题,研究采用高速摄像机采集振子振动视频信号并进行分析.结果表明,SD振子系统在一定的参数条件下会产生周期振动、周期5振动及混沌运动等复杂非线性动力学现象,在相同实验参数条件下进行了数值仿真,仿真结果与实验结果一致.     

利用T r a c k e r软件验证机械能守恒定律

T r a c k e r软件是一种广泛使用的视频分析软件. 利用T r a c k e r软件分别对单摆、 弹簧振子和自由落体运 动的实验视频进行分析, 通过自动追踪研究对象的运动轨迹, 同步描绘研究对象在运动过程中重力势能、 弹性势能 和动能随时间变化的图像, 验证了机械能守恒定律