Finite Larmor radius effects in the magnetosphere

This article reviews theories and observations related to effects produced by finite (and large) Larmor radii of charged particles in the magnetosphere. The FLR effects depend on =r _H /L, wherer _H is the Larmor radius andL is the spatial scale for field/plasma inhomogeneity. The parameter is a basic expansion parameter for most equations describing plasma dynamics in the magnetosphere. The FLR effects enter naturally the drift approximation for particle motion and represent also non-ideal MHD terms in the fluid formalism. The linear and higher order terms in lead to charge separation, energization of particles, and produce viscosity without collisions. The FLR effects introduce also important corrections to the dispersion relations for MHD waves and drift instabilities. Expansion of plasma into magnetic field leads to filamentation of the plasma boundary and to creation of structures with thickness less than an ion gyroradius. Large Larmor radius effects (1) in curved magnetic field geometry lead to stochastic behaviour of particle trajectories and to deterministic chaos. The tiny scale of the electron and ion gyroradii does not necessarily mean that FLR/LLR phenomena have negligible effect on the macroscopic dynamics and energetics of the whole magnetosphere. On the contrary, the small scale gyro-effects may provide the physical mechanism for gyroviscous coupling between the solar wind and the magnetosphere, the mechanism for triggering disruption of the magnetotail current layer, and the mechanism for parallel electric field that accelerate auroral particles.     

非线性动力学理论及其在机械系统中应用的若干进展

非线性动力学的理论及其工程应用是非线性科学研究的前沿和热点，应用非线性动力学的理论揭示事物动态过程现象的本质和机理，进行自主性原始创新，具有十分重大的理论和应用价值，在科学与工程中具有广阔的应用前景。综述非线性动力学基础理论方面的近期研究成果及其在机械系统中应用的研究进展。理论研究方面主要涉及揭示非线性动力系统周期分岔解与系统结构参数之间关系的C—L方法、高余维分岔的普适分类、高余维非对称分岔的普适开折、约束分岔的分类、计算非线性自治系统正规形的直接方法、计算非线性非自治系统正规形的复内积平均法以及高维非线性系统的降维方法等。应用方面主要涉及大型旋转机械非线性转子系统的失稳机理、分岔解与混沌运动、故障诊断及其综合治理技术；冲击振动机械的稳定性、Hopf分岔、亚谐分岔、余维二分岔和混沌运动；大型共振筛的非线性振动及其动力学设计方法等。     

Influence of Earth’s shadowing effects on space debris stability

Solar radiation pressure affects the evolution of high area-to-mass geostationary space debris. In this work, we extend the stability study of Valk et al. (2009) by considering the influence of Earth’s shadows on the short- and long-term time evolutions of space debris. To assess the orbits stability, we use the Mean Exponential Growth factor of Nearby Orbits (MEGNO), which is an efficient numerical tool to distinguish between regular and chaotic behaviors. To reliably compute long-term space debris motion, we resort to the Global Symplectic Integrator (GSI) of Libert et al. (2011) which consists in the symplectic integration of both Hamiltonian equations of motion and variational equations. We show how to efficiently compute the MEGNO indicator in a complete symplectic framework, and we also discuss the choice of a symplectic integrator, since propagators adapted to the structure of the Hamiltonian equations of motion are not necessarily suited for the associated variational equations. The performances of our method are illustrated and validated through the study of the Arnold diffusion problem. We then analyze the effects of Earth’s shadows, using the adapted conical and cylindrical Earth’s shadowing models introduced by Hubaux et al. (2012) as the smooth shadow function deriving from these models can be easily included into the variational equations. Our stability study shows that Earth’s shadows greatly affect the global behaviour of space debris orbits by increasing the size of chaotic regions around the geostationary altitude. We also emphasize the differences in the results given by conical or cylindrical Earth’s shadowing models. Finally, such results are compared with a non-symplectic integration scheme.     

Critical phenomenon,crisis and transition to spatiotemporal chaos in plasmas

In a driven/damped drift-wave system a steady wave induces nonlinear variation of the dispersion of a perturbation wave (PW). Competition between the nonlinear dispersion with self-nonlinearity of the PW results in rich wave dynamic behaviors. In particular, a steady wave at the negative tangency slope of a hysteresis becomes unstable due to a saddle instability. It is found that such saddle steady wave (SSW) plays an important role in the discontinuous transition from a spatially coherent state to spatiotemporal chaos (STC). The transition is caused by a crisis due to a collision of the PW attactor to an unstable orbit of the SSW. In the time evolution, it is a ‘pattern resonance’ of the realized wave with the virtual SSW that triggers the crisis. The transition also displays as a critical phenomenon in parameter space, which is related to the change in the symmetry property of the motion of master mode (k = 1) of the PW with respect to that of SSW. In the spatially coherent state the former is trapped by the SSW partial wave, while in the STC it can become free from the latter, its trajectory crosses two unstable orbits of the SSW frequently, causing very turbulent behavior. This revised version was published online in August 2006 with corrections to the Cover Date.     

转子动静碰摩故障试验研究

为了研究转子碰摩时非线性动力学行为,设计了一种可以模拟单点、多点、局部、整周碰摩的转子碰摩实验装置,并且在ZT-3型多功能转子试验器上进行了碰摩故障试验研究,通过改变转子转速和转静件间隙来观察碰摩转子在不同条件下的振动情况,同时运用波形图、频谱图、轴心轨迹分析了转子系统碰摩时的非线性响应。试验结果表明,本文设计的碰摩装...     

分数阶混沌系统同步控制研究进展

分数阶混沌系统由于其复杂的混沌吸引子和独有的记忆特性,非常适合保密通信领域的应用。在介绍分数阶混沌系统混沌特性的基础上,重点综述了近年来分数阶混沌系统同步的研究进展,包括分数阶混沌系统模型、分数阶系统算法、分数阶混沌同步控制方法等;总结了分数阶混沌系统同步在理论和应用方面的研究现状;提出了分数阶混沌系统同步还有待进一步研究的若干方向和内容。     

PCE方法在空间实验室轨道预报误差分析中的应用

应用多项式混沌展开法(PCE)进行空间实验室轨道预报误差分析。通过构建PCE模型对轨道预报的不确定性传播过程进行近似，进而对轨道预报后航天器位置和速度的误差进行分析。分析了不同PCE模型阶数、预报时长以及样本点的数目对构建PCE模型的影响。综合考虑精度和计算效率，给出了适用于空间实验室轨道预报误差分析的PCE模型。将PCE方法与传统方法进行对比，结果表明PCE方法有较好的非线性近似能力，且计算效率高，验证了PCE方法应用于空间实验室轨道预报误差分析的有效性。     

纳卫星隔热层厚度与散热面面积优化设计

在纳卫星热系统动态特性分析与热分析的基础上,根据纳卫星隔热层厚度与散热面面积对纳卫星温度调节的重要作用,提出了运用混沌遗传算法（CGA）对二者进行优化设计的模型与算法。算法以使纳卫星舱内发热元件、散热面及壳体温度尽可能接近设定的安全工作温度为优化目标,以隔热层厚度与散热面面积为优化变量。并以在不同热负荷下工作的太阳同步球形纳卫星为例进行一系列优化计算及分析。结果表明：利用混沌遗传算法进行的优化设计,可以使在不同工况下的纳卫星温度很好地维持在设定的安全工作温度附近。     

基于统计分析的有限元模型修正

响应面模型代替有限元模型进行修正便于与粒子群算法等优化算法结合,有利于提高修正效率和精度。文章用某雷达卫星的简化有限元模型计算基于正交设计的各水平参数下模态频率,用方差分析确定待修正参数并构造二次响应面模型,用最小二乘法确定多项式系数,以响应面计算结果与实测结果的差值构造适应度函数并用之引导含混沌搜索机制的改进粒子群算法对待修正参数的偏移量进行寻优,修正后参数代入原有限元模型得到修正模型。修正后模型不仅能以高精度复现测试频段内的模态频率,而且能以一定精度预测测试频段外频率,证实了修正方法的有效性。     

金属橡胶隔振器产生混沌的解析预测

在考虑金属橡胶隔振系统的非线性刚度和非线性迟滞恢复力的基础上,建立了金属橡胶隔振器的非线性动力学方程.根据非线性振动理论,得出了系统在弱非线性情况下的一次谐波慢变参数的平均化方程;推出了谐波慢变参数状态方程的离散化映射,获得了金属橡胶隔振器出现混沌的解析条件.