辛算法在近地小行星轨道演化数值研究中的应用

采用改进的显算法对近地小行星的轨道演化进行数值研究，在力学模型中除考虑各大行星的引力摄动外，还考虑了后牛顿效应，而在算法上则着重探索辛算法在近地小行星轨道演化研究中的应用前景，特别是当这类小行星与某一大行星靠近时辛算法的有效性。     

小行星的卫星

 公布太阳系第十大行星的发现两星期后,2005年8月11日的《自然》杂志又公布首次发现一颗小行星有两颗卫星或三重小行星的有趣消息。因为有的小行星可能游荡到地球附近,潜在着撞击地球的重大危害,这就引起人们的普遍关注。小行星的发现和命名天文学家早就感到火星和木星的轨道间距太大,开普勒推测此间距内应当有一颗未知的行星。1766年德国中学教师提丢斯得出,行星的轨道半长径形成简单的数列,1781年柏林天文台台长波得(J.E.Bode)加以宣传,总结成经验规律:an=0.3+2n-2×0.4(天文单位),水星n=-∞,金星n=2,地球n=3,火星n=4,木星n=6,土星n=7,因此称为提丢斯-波得定则。     

人造地球卫星运动方程的代数动力学算法数值解

代数动力学算法首次被用于求人造地球卫星运动方程的数值解，在四阶算法下，与Runge-Kutta算法和辛算法的计算结果作了比较.结果表明，代数动力学算法对于人造地球卫星长期轨道的计算有较高的精度.并讨论了地球四极和八极带谐项对卫星轨道的影响. 关键词： 人造地球卫星运动方程 代数动力学算法数值解 地球四极和八极带谐项对卫星轨道的影响     

预防小行星撞击地球

 20世纪50年代以后，科学界出现了一种新的说法，认为6500万年前的白垩纪末期，一颗直径约10公里的小行星撞击了地球，造成了恐龙等生物大灭绝。1980年，美国阿尔瓦雷斯等人根据意大利一古地层中铱含量异常，明确提出小行星撞击地球造成恐龙绝灭假说。从那时以来，小行星（以及彗星）愈来愈引起科学家和公众的强烈关注。1993年4月，在意大利名叫埃里斯的地方召开了一次专门的国际会议，主要探讨近地小天体可能撞击地球的问题，当时有包括中国在内的10多个国家的60来位科学家参加，会议最后通过并发表了著名的《埃里斯宣言》，以唤起世界人民对近地小天体对地球有潜在威胁的关注。     

探索地外智慧生命

 不可忽略的小行星小行星是一些体积较小的围绕太阳运行的不规则小天体,它们大部分在火星和木星轨道之间,称为“小行星带”。已观测到最大的小行星直径为970千米、最小的可能只有几米甚至几厘米。迄今为止,天文学家们在地面上已观测发现了5000多颗小行星,据估计,仪通过天文望远镜能够用照相方法记录下来的小行星约有50万颗之多。     

巨型望远镜发布了它的第一幅图像

正建设之初,小行星带天文望远镜已经拍摄了一幅无比清晰的系外行星图片。位于火星和木星之间的小行星带正热闹非凡。太阳系的内、外边界处如火如荼的活动,是在建设小行星带天文望远镜(ABAT),这是人类史上最具雄心的科学项目。从地球上看去像是烟火的高强度激光脉冲,正将数十亿颗大小为1—10 m级的小行星打造成一个直径为5个天文单位的巨型天文望远镜的子镜(天文单位AU是距离单位,相当于地球绕太阳的轨道半径)。上个月该     

日外星系的小行星带

 Gliese 581(见主图)是一颗距离地球21光年的红矮星,以行星众多而颇受关注。天文学家在2012 年12 月的《天文学与天体物理学》(Astronomy &Astrophysics)杂志上报道, 赫歇尔空间天文台(Herschel Space Observatory)发现了该恒星又一个类似地球的特征:在距离该恒星遥远的地带存在类似太阳系柯伊伯带(位于海王星轨道之外由远远小于地球的天体组成,其中包括冥王星)的小行星带。     

带电粒子在地磁场中的运动及Mathematica数值模拟

基于单粒子轨道模型和地磁场偶极子模型,考虑相对论效应,对近地球区域磁场中运动的带电粒子轨迹使用Mathematica软件中六阶龙格—库塔算法进行数值计算和模拟,并对极光现象的产生进行了解释,同时讨论了带电粒子在地磁场中运动的引导中心近似.结果表明：1)从地球北极方向观察,被地球磁场捕获的质子沿顺时针方向漂移,电子沿逆时针方向漂移;2)粒子各个分运动的运动周期数值模拟结果与文献中理论值非常吻合;3)从(4R_e,0,0)入射的粒子投掷角小于7.38°时,带电粒子将会与地球表面大气层碰撞而沉降,存在产生极光现象的可能.大于7.38°时,粒子将会被束缚在地磁场中,形成辐射带;4)其他条件相同时,带电粒子投掷点距离地球越远,其漂移速度越大;投掷角越大,其漂移速度也越大;5)对于能量较低的粒子,一阶近似下引导中心轨迹能很好地代表粒子实际运动轨迹.     

圆柱装药近地空爆冲击波峰值超压空间转换模型

为研究近地空爆冲击波峰值超压空间数值关系,基于镜像法、角等分和超压归一化思想,确定了冲击波空间传播界线,建立了混合流场中超压的理论计算方法。首先,利用三波点轨迹与爆高水平线交点、虚拟爆源、真实爆心三者连线构成的几何约束以及马赫反射终点条件,确定了冲击波流场分布界限。其次,等分测点角度,并基于超压归一化值分段线性假设构建归一化值方程。然后将归一化值方程扩展为圆柱装药长径比、爆高、当量、测点角度和比例距离的函数。最后,基于控制变量法,利用符合经验公式和实爆结果的圆柱装药近地空爆AUTODYN-2D数值模型的计算结果代入上述函数求解。结果表明:以长径比、比例爆高、比例距离和测点角度为输入参数的峰值超压空间转换模型可描述圆柱装药近地空爆峰值超压的空间数值关系,转换效果良好。     

小行星撞出地球的风险评估

按照地质年代的划分,从生命在地球上诞生到距今2.25亿年是古生代;2.25亿年—0.65亿年前是中生代,中生代又按先后分为三迭纪、侏罗纪和白垩纪;0.65亿年—100万年前是新生代,它包括第三纪和第四纪.关于恐龙的灭绝,科学家们有两种观点,即“灾变论”和“渐变论”.无论持哪种观点,他们都不否认,在距今6500万年前(在白垩纪与第三纪之交),地球上的生命曾因流星撞击而蒙受灾难.慧星或小行星的轨道可因外扰动而改变,以致于最终飞向地球.如果星体的直径大于2km,撞击或许将毁灭地球的文明.在1998年,曾有媒体炒作:一颗小行星正朝地球飞来,它将于2028年撞…     

一种最优控制数值计算方法

本文为解决非线性微分方程自治系统的周期轨道的数值计算,提出了一种最优控制的数值计算方法。其方法的实质是利用连续的打靶法,在非线性最小二乘公式的监护下,附加惩罚函数进行控制来实现的。并利用该法计算了典型的化学反应模型。     

Effect of Earth's Rotation on the Trajectories of Free-Fall Bodies in Equivalence Principle Experiment

Owing to Earth's rotation a free-fall body would move in an elliptical orbit rather than along a straight line forward to the center of the Earth. In this paper on the basis of the theory for spin-spin coupling between macroscopic rotating bodies we study violation of the equivalence principle from long-distance free-fall experiments by means of a rotating ball and a non-rotating shell. For the free-fall time of 40 s, the difference between the orbits of the two free-fall bodies is of the order of 10-9 cm which could be detected by an SQUID magnetometer because such a magnetometer can be used to measure displacements as small as 10-13 cm.     

Stability of minimal periodic orbits

Symplectic twist maps are obtained from a Lagrangian variational principle. It is well known that nondegenerate minima of the action correspond to hyperbolic orbits of the map when the twist is negative definite and the map is two-dimensional. We show that for more than two dimensions, periodic orbits with minimal action in symplectic twist maps with negative definite twist are not necessarily hyperbolic. In the proof we show that in the neighborhood of a minimal periodic orbit of period n, the nth iterate of the map is again a twist map. This is true even though in general the composition of twist maps is not a twist map.     

Algebraic dynamics solutions and algebraic dynamics algorithm for nonlinear ordinary differential equations

The problem of preserving fidelity in numerical computation of nonlinear ordinary differential equations is studied in terms of preserving local differential structure and approximating global integration structure of the dynamical system. The ordinary differential equations are lifted to the corresponding partial differential equations in the framework of algebraic dynamics, and a new algorithm—algebraic dynamics algorithm is proposed based on the exact analytical solutions of the ordinary differential equations by the algebraic dynamics method. In the new algorithm, the time evolution of the ordinary differential system is described locally by the time translation operator and globally by the time evolution operator. The exact analytical piece-like solution of the ordinary differential equations is expressed in terms of Taylor series with a local convergent radius, and its finite order truncation leads to the new numerical algorithm with a controllable precision better than Runge Kutta Algorithm and Symplectic Geometric Algorithm.     

Dust in the planetary system: Dust interactions in space plasmas of the solar system

Cosmic dust particles are small solid objects observed in the solar planetary system and in many astronomical objects like the surrounding of stars, the interstellar and even the intergalactic medium. In the solar system the dust is best observed and most often found within the region of the orbits of terrestrial planets where the dust interactions and dynamics are observed directly from spacecraft. Dust is observed in space near Earth and also enters the atmosphere of the Earth where it takes part in physical and chemical processes. Hence space offers a laboratory to study dust–plasma interactions and dust dynamics. A recent example is the observation of nanodust of sizes smaller than 10 nm. We outline the theoretical considerations on which our knowledge of dust electric charges in space plasmas are founded. We discuss the dynamics of the dust particles and show how the small charged particles are accelerated by the solar wind that carries a magnetic field. Finally, as examples for the space observation of cosmic dust interactions, we describe the first detection of fast nanodust in the solar wind near Earth orbit and the first bi-static observations of PMSE, the radar echoes that are observed in the Earth ionosphere in the presence of charged dust.     

二维椭圆量子台球中的谱分析

研究了二维椭圆台球中的量子谱和经典轨道之间的对应关系.为尝试求解没有解析波函数和本征能量又不能分离变量的体系，采用了定态展开方法(expansion method for stationary states，简称EMSS)得到尽可能精确的数值解，这是闭合轨道理论被推广到计算开轨道的情况.比较了傅里叶变换谱和经典轨道，发现量子谱的峰位置与经典轨道的长度在可分辨的范围内符合得很好，这是半经典理论为经典与量子力学的联系提供桥梁作用的又一个例子. 关键词： 椭圆量子台球 定态展开方法 闭合轨道理论 量子谱     

Floating and sinking: the imprint of massive scalars around rotating black holes

We study the coupling of massive scalar fields to matter in orbit around rotating black holes. It is generally expected that orbiting bodies will lose energy in gravitational waves, slowly inspiraling into the black hole. Instead, we show that the coupling of the field to matter leads to a surprising effect: because of superradiance, matter can hover into "floating orbits" for which the net gravitational energy loss at infinity is entirely provided by the black hole's rotational energy. Orbiting bodies remain floating until they extract sufficient angular momentum from the black hole, or until perturbations or nonlinear effects disrupt the orbit. For slowly rotating and nonrotating black holes floating orbits are unlikely to exist, but resonances at orbital frequencies corresponding to quasibound states of the scalar field can speed up the inspiral, so that the orbiting body sinks. These effects could be a smoking gun of deviations from general relativity.     

An energy- and charge-conserving,implicit, electrostatic particle-in-cell algorithm

This paper discusses a novel fully implicit formulation for a one-dimensional electrostatic particle-in-cell (PIC) plasma simulation approach. Unlike earlier implicit electrostatic PIC approaches (which are based on a linearized Vlasov–Poisson formulation), ours is based on a nonlinearly converged Vlasov–Ampére (VA) model. By iterating particles and fields to a tight nonlinear convergence tolerance, the approach features superior stability and accuracy properties, avoiding most of the accuracy pitfalls in earlier implicit PIC implementations. In particular, the formulation is stable against temporal (Courant–Friedrichs–Lewy) and spatial (aliasing) instabilities. It is charge- and energy-conserving to numerical round-off for arbitrary implicit time steps (unlike the earlier “energy-conserving” explicit PIC formulation, which only conserves energy in the limit of arbitrarily small time steps). While momentum is not exactly conserved, errors are kept small by an adaptive particle sub-stepping orbit integrator, which is instrumental to prevent particle tunneling (a deleterious effect for long-term accuracy). The VA model is orbit-averaged along particle orbits to enforce an energy conservation theorem with particle sub-stepping. As a result, very large time steps, constrained only by the dynamical time scale of interest, are possible without accuracy loss. Algorithmically, the approach features a Jacobian-free Newton–Krylov solver. A main development in this study is the nonlinear elimination of the new-time particle variables (positions and velocities). Such nonlinear elimination, which we term particle enslavement, results in a nonlinear formulation with memory requirements comparable to those of a fluid computation, and affords us substantial freedom in regards to the particle orbit integrator. Numerical examples are presented that demonstrate the advertised properties of the scheme. In particular, long-time ion acoustic wave simulations show that numerical accuracy does not degrade even with very large implicit time steps, and that significant CPU gains are possible.     

GLOBAL CHAOS CONTROL OF NON-AUTONOMOUS SYSTEMS

This study describes a global approach of controlling chaos to reduce tedious waiting time caused by using conventional local controllers. With Euler's method, a non-autonomous system is approximated by a non-linear difference system and then an approximate global Poincaré map function is derived from the difference system by iterating one or more periods of a periodic excitation. Based on the map function, unstable periodic orbits embedded in a chaotic motion can be detected and a global controller for a targeted unstable periodic orbit is designed. The global controller makes all the unstable periodic orbits vanish except a targeted periodic orbit. Furthermore, a Lyapunov's direct method is applied to confirm that the global controller can asymptotically stabilize the unique periodic orbit. For practical applications, system models are usually unknown. To obtain a mathematical model, non-linear system identification based on the harmonic balance principle is applied to an unknown chaotic system of a noisy environment. Simulation results demonstrate that the global controller successfully regularizes a chaotic motion even if the chaotic trajectory is far from the targeted periodic orbit.     

旋涡动力学方程非定常动边界条件

详细讨论了旋涡动力学方程非定常动边界条件。给出了任意非定常运动边界上速度旋度的确定方法。并采用了“局部线性化及再校正”技术、时间滞后求解方法，求解每一时间步边界上速度旋度值。这样可以很大程度上节省计算时间。并讨论了数值实验结果，指出动边界问题的非线性特征，对这样复杂的非线性问题不宜作过份简化。