Geometric integration methods for general nonlinear dynamic equation based on Magnus and Fer expansions

Ithasbeenknownforalongtimethatthesolu tionofthefollowingdifferentialequation :U· =A(t)U ,　U(t0 ) =I ,(1)whereA (t)standsforasufficientlysmoothn×nmatrixorlinearoperator ,canlocallybewrittenintheform[1]U(t ,t0 ) =eΩ(t,t0 ) ,(2 )whereΩisobtainedasaninfiniteseriesΩ(t ,t0 ) =∑∞k =1Ωk(t,t0 ) . (3)Eqs .(2 )and (3)constitutetheso calledMagnusex pansionofthesolutionofthedifferentialequation(1) .EachtermΩkintheseries (3)isamultiplein tegralofcombinationsofnestedcommutators ,anditcanbeobtain…     

投弃式海流剖面仪探头流场TRPIV测量

 投弃式海流剖面仪(eXpendable Current Profiler,XCP)探头是最新型的投弃式海洋环境剖面测量探头,在海洋调查、科学研究以及军事上有着重要应用。XCP探头在海水中的姿态直接影响海流测量精度,因此试验研究探头水下姿态对投弃式海流测量技术发展有重要意义。本文通过搭建试验装置,应用高时间分辨率PIV(Time Resolution Particle Image Velocimetry,TRPIV)技术在室内低速循环水槽测量了XCP探头水平截面的二维瞬时流场和平均流场。分析了不同旋转速度比及雷诺数对流场的影响,进而根据马格努斯效应分析了XCP探头受到的侧向力。试验结果表明,探头受到的侧向力与旋转速度呈正比关系,并且随雷诺数的增加探头受到的侧向力也增加了。据分析结果可知,实际工作中探头穿越不同的海流层下落时受到变化的侧向力作用,并导致其在海水中以倾斜状态下落。试验结果可为XCP探头在下落过程中倾斜情况的估计提供参考和依据。     

基于非局部梁理论的嵌入式弯曲碳纳米管在移动载荷作用下的振动分析

基于非局部连续介质力学理论,针对嵌入式弯曲碳纳米管建立了两端简支的Euler-Bernoulli梁计算模型,研究碳纳米管在移动载荷作用下的非线性振动问题．利用Galerkin方法对运动微分方程进行近似处理,将原方程从非线性动力学系统转化到二阶动力学系统;对于二阶动力学方程采用Magnus级数方法进行求解;通过数值实验,分析了非局部参数因子,纳米管长径比,移动载荷速度,弯曲波纹幅值,弹性介质常数对碳纳米管振动特性的影响,结果表明上述因素对碳纳米管动力特性有很重要影响．     

风沙跃移运动中的Magnus效应

给出了计及Magnus效应的风一沙耦合跃移运动模型,计算了当风沙流达到自平衡状态后Magnus效应对贴地风速廓线、沙粒跃移轨迹的影响,指出在Msagnus效应影响下,沙粒跃移运动对风速廓线的影响类似于粗糙床面对沙粒跃移的影响,其粗糙度约为沙粒跃移高度的0．8倍。     

单手肩上投篮肘的生物力学分析

篮球运动技术规范化、科学化巳被科技兴体的浪潮推进篮球运动的教学与训练中来。用人体解剖学、运动生理学、运动生物力学、流体力学等多学科知识进行分析,并结合篮球训练的科学理论做指导,阐明单手肩上投篮肘正对篮的科学性,并建议全国高师体育系篮球专业教学,中小学及少体校的篮球教学与训练统一教材,且教材中对技术动作都制定出技术规范要求,彻底改变我国篮球运动技术“五花八门”的落后状态。     

风吹雪跃移运动的稳态数值模型

给出了定常充分发展流场中风、雪粒相互耦合的运动方程 ,并用简化的雪粒 床面碰撞过程求解了方程 .计算结果表明 ,跃移雪粒对贴地风速有重要影响 ,Magnus效应对贴地风速、雪粒跃移轨迹也有显著影响     

Geometric integration methods for general nonlinear dynamic equation based on Magnus and Fer expansions

Based on Magnus or Fer expansion for solving linear differential equation and operator semi-group theory, Lie group integration methods for general nonlinear dynamic equation are studied. Approximate schemes of Magnus type of 4th, 6th and 8th order are constructed which involve only 1, 4 and 10 different commutators, and the time-symmetry properties of the schemes are proved. In the meantime, the integration methods based on Fer expansion are presented. Then by connecting the Fer expansion methods with Magnus expansion methods some techniques are given to simplify the construction of Fer expansion methods. Furthermore time-symmetric integrators of Fer type are constructed. These methods belong to the category of geometric integration methods and can preserve many qualitative properties of the original dynamic system.     

旋转鸭式导弹洗流气动力干扰分析与计算

研究了旋转鸭式导弹前翼涡迹的扭曲变化,提出了计算洗流气动力干扰的数值方法。根据实验观测和分析,建立了计算扭曲涡迹的数学模型。由于导弹绕纵轴旋转,涡强和起始位置均随时间变化。计算旋涡洗流对后体和尾翼的气动力干扰效应有两种方法:一种采用细长体理论,适合于小展弦比尾翼;另一种采用反流定理,适合于中等展弦比尾翼。计算表明:前翼旋涡洗流除降低尾翼升力外,在旋转导弹上还要产生侧向力、偏航力矩和滚动力矩。这种现象可归入攻角和旋转的耦合气动力效应成为马格努斯效应的一个组成部分。     

Plotinus’s conception of unity and multiplicity as the root to the medieval distinction between lux and lumen

Plotinus resolved the paradox of the immanent transcendence, characterizing the relation between the One and the universe, through his theory of the two energeiai. According to this doctrine, all existents have an internal activity and an external activity: the internal activity comprises the true essence and substance of each being; the external activity is emitted outwards as its image. The source of the emission is thus present in the lower layer of being by virtue of its manifold images. The prominence given to light in elucidating this solution led to a distinction between two types of lights: an original light, corresponding to the internal energeia of every existent, and a secondary light, which is the outflow and image of the first light, existing outside of the luminous body.This paper demonstrates the striking similarity between these two Plotinian lights and the concepts of lux and lumen developed by two thirteenth-century philosophers: Robert Grosseteste and Albertus Magnus. Moreover, the paper contends that the purpose of these two medieval concepts of light was identical to what Plotinus had in mind when he first made the distinction: to account for the relation between the one and the many.     

旋转弹丸马格努斯效应数值研究

用黎曼分解和Osher近似方法,计算了旋转和非旋转弹丸三维跨音速绕流场.将计算区域按分块网格和六面体的弹体贴体网格单元划分,为了提高相对流动变量离散中的数值精度,运用了改进的MUSCL格式.选取弹丸旋转频率为0和82赫兹,攻角分别为0°和10°,马赫数0.94,雷诺数为4.0×106条件为算例.获得在中等倾角下,旋转诱导边界层畸变产生了马格努斯效应和不对称涡结构,沿弹底周向压强分布变化和攻角的非线性效应,给出并讨论了弹丸马格努斯力和法向力系数数值结果,计算结果与实验数据吻合良好.