Non-linear normal modes,invariance, and modal dynamics approximations of non-linear systems

Non-linear systems are here tackled in a manner directly inherited from linear ones, that is, by using proper normal modes of motion. These are defined in terms of invariant manifolds in the system's phase space, on which the uncoupled system dynamics can be studied. Two different methodologies which were previously developed to derive the non-linear normal modes of continuous systems — one based on a purely continuous approach, and one based on a discretized approach to which the theory developed for discrete systems can be applied-are simultaneously applied to the same study case-an Euler-Bernoulli beam constrained by a non-linear spring-and compared as regards accuracy and reliability. Numerical simulations of pure non-linear modal motions are performed using these approaches, and compared to simulations of equations obtained by a classical projection onto the linear modes. The invariance properties of the non-linear normal modes are demonstrated, and it is also found that, for a pure non-linear modal motion, the invariant manifold approach achieves the same accuracy as that obtained using several linear normal modes, but with significantly reduced computational cost. This is mainly due to the possibility of obtaining high-order accuracy in the dynamics by solving only one non-linear ordinary differential equation.     

从具体例子看惯性流形概念的推广

惯性流形的概念要求所有轨道指数收敛于唯一吸引子[5],这对于很多物理问题,例如sine-Gordon方程是很难满足的[4],本文中给出的人工例子建议了惯性流形的推广形式,这个推广形式去掉了整体吸引子是唯一的预先要求,该推广概念使用于sine-Gordon方程。     

A sharp condition for existence of an inertial manifold

It is shown that a perturbation argument that guarantees persistence of inertial (invariant and exponentially attracting) manifolds for linear perturbations of linear evolution equations applies also when the perturbation is nonlinear. This gives a simple but sharp condition for existence of inertial manifolds for semi-linear parabolic as well as for some nonlinear hyperbolic equations. Fourier transform of the explicitly given equation for the tracking solution together with the Plancherel's theorem for Banach valued functions are used.     

聚酰亚胺薄膜表面粗糙度的影响因素

 采用热蒸发气相沉积聚合方法（VDP）制备了聚酰亚胺(PI)薄膜,研究了设备、衬底温度、升温过程和单体配比因素对PI薄膜表面形貌的影响。利用干涉显微镜和扫描电镜对薄膜表面形貌进行了分析;利用原子力显微镜测定了薄膜表面粗糙度。结果表明：设定蒸发源-衬底距离为74 cm时可成连续膜;蒸发源采用一段升温和多段升温时,膜表面均方根粗糙度分别为291.23 nm和61.99 nm;采用细筛网可防止原料的喷溅;均苯四甲酸二酐和4,4′-二氨基二苯醚（PMDA和ODA）单体沉积速率比值为0.9∶1时,膜表面均方根粗糙度值可减小至3.30 nm;沉积衬底温度保持30 ℃左右时,膜表面均方根粗糙度为4.01 nm, 随温度的上升,膜表面质量会逐渐变差。     

车辆寻北车长镜的设计与实现

 描述了一种车辆寻北车长镜的设计,采用2个光纤陀螺和2个加速度计,解决了惯性测量组件力学编排结构设计与寻北、瞄准线稳定共享陀螺信息的问题,设计系统控制流程和组合算法,在保障车长镜瞄准线稳定精度的同时,增加了车体方位平台非调平状态下任意位置的寻北功能,寻北方法是：车长镜方位固定四位置转动,每个位置点停止、延迟、数据采样、存储,四位置转动完毕后,对存储数据组合、滤波、解算,输出寻北结果。对方案设计、实现途径和解算推导方法作了详细论述,性能测试验证设计实现达到预期效果。     

基于FPGA和DSP的微型惯导系统

 惯导系统的硬件组成直接影响到系统的体积和解算速度,构建合理的硬件系统直接关系到惯导系统的精度指标。针对某小型惯导系统对体积和解算精度的特殊要求,解决已有微型惯导系统的方案缺陷,提出一种工程实用强的惯导系统。该系统用FPGA作为采集控制惯性传感器的核心芯片,设计了并行采集方案,32位浮点型高速DSP实现惯导解算。经过转台测试与外场试验表明：系统具有抗干扰能力强、实时响应迅速、惯性单元标定简便、易实现等优点,系统指标完全满足原设计要求。     

Spectroscopic investigations on NO+(x1∑+,a3∑+,A1Ⅱ) ion using multi-reference configuration interaction method and correlation-consistent sextuple b

Three low-lying electronic states (x¹∑⁺,a³∑⁺,and A¹Ⅱ) of NO⁺ ion are studied using the complete active space self-consistent-field (CASSCF) method followed by highly accurate valence internally contracted multi-reference configuration interaction (MRCI) approach in combination of the correlation-consistent sextuple basis set augmented with diffuse functions, aug-cc-pV6Z. The potential energy curves (PECs) of the NO⁺(x¹∑⁺,a³∑⁺,A¹Ⅱ) are calculated. Based on the PECs, the spectroscopic parameters R_e, D_e, ω_e, ω_eχ_e, α _e, B_e, and D₀ are reproduced, which are in excellent agreement with the available measurements. By numerically solving the radial Schrödinger equation of nuclear motion using the Numerov method, the first 20 vibrational levels, inertial rotation and centrifugal distortion constants of NO⁺(x¹∑⁺,a³∑⁺,A¹Ⅱ) ion are derived when the rotational quantum number J is equal to zero (J = 0) for the first time, which accord well with the available measurements. Finally, the analytical potential energy functions of these states are fitted, which are used to accurately derive the first 20 classical turning points when J = 0. These results are compared in detail with those of previous investigations reported in the literature.     

菲涅耳波带板应用于聚变靶的高分辨X射线成像分析

在惯性约束核聚变研究中,为了实现1μm高空间分辨keV-X射线成像,文中发展了菲涅耳波带板(FZP)直接成像的分析方法,并通过数值计算研究了FZP的成像特性.针对钛K_α线(光子能量4.51 keV,波长0.275 nm),提出了FZP参数,对制作技术的要求较低.研究了靶尺度的影响.FZP的有效视场使它能够对数毫米大尺度靶实现高分辨成像.还研究了入射光的光谱带宽对成像的影响.FZP的色差有助于单色成像,但是带宽超过限度会导致像的反衬度降低.这些结果表明FZP应用于聚变点火靶的高空间分辨X射线成像的能力,也为应用提出了要求. 关键词： X射线成像 惯性约束核聚变 菲涅耳波带板     

聚变反应历程测量系统研制及应用

为了测量惯性约束聚变实验中的聚变反应时间过程,研制了一套时间分辨优于40 ps的聚变反应历程测量系统.该系统由闪烁体及鼻锥部分、光学系统和条纹相机系统三部分组成.其中闪烁体将中子信号转换为可见光信号,光学系统则将闪烁体的发光信号成像在条纹相机上进行记录.为得到信号与入射激光的时间关系,还将时标引入了条纹相机进行记录.在...     

惯性颗粒所见被动标量统计特性的DNS与模型研究

本文采用DNS方法,对惯性颗粒所见各向同性湍流中具有平均标量梯度的被动标量场统计特性进行了研究。结果表明：惯性对颗粒温度脉动强度,两相温度关联,自相关特性以及颗粒热流与两相交叉热流的统计特性具有明显的影响。在PDF方法的框架下,系统地推导了非等温气固两相流的PDF方程,且基于朗之万随机体系对方程进行了封闭,并利用前面的...