Numerical analysis of the symmetric methods

Aimed at the initial value problem of the particular second-order ordinary differential equations,y =f(x, y), the symmetric methods (Quinlan and Tremaine, 1990) and our methods (Xu and Zhang, 1994) have been compared in detail by integrating the artificial earth satellite orbits in this paper. In the end, we point out clearly that the integral accuracy of numerical integration of the satellite orbits by applying our methods is obviously higher than that by applying the same order formula of the symmetric methods when the integration time-interval is not greater than 12000 periods.     

EGUP与黑洞熵的修正值

目前,人们对黑洞Bekenstein-Hawking熵的量子修正值产生了极大的兴趣,尤其是黑洞熵对数修正项的系数.在广义不确定关系(GUP)的基础上,通过引入了推广的广义不确定关系(EGUP),运用面积定理计算了3类时空的黑洞熵的修正值,得到的黑洞熵的修正项的系数是正的.这种计算方法不仅对单视界时空适用,而且对有内视界的黑洞时空依然成立,并且在EGUP基础上计算出黑洞熵的修正值.相比GUP基础上得到的黑洞熵,EGUP可以应用于大尺度时空下,所以应用范围更广.此计算方法简洁明了,物理意义明确,可为黑洞熵对数修正值系数的确定提供参考.     

样本输入方式对极端学习机预报日长变化的影响

针对极端学习机(Extreme Learning Machine,ELM)用于日长(Length-Of-Day,LOD)变化预报过程中,样本输入方式对预报结果的影响进行了研究。采用跨度、连续和迭代3种样本输入方式对日长变化进行预报。结果表明,不同的样本输入方式对预报结果有很大影响,样本按跨度输入的预报精度最低;样本采用连续输入方式在短期和中长期预报中预报精度较高,但计算速度较慢,较适合中长期预报;样本按迭代输入方式的短期预报精度稍优于连续输入方式,而中长期预报精度则不如连续输入方式,但具有较高的预报效率。这对于日长变化的实时快速预报有着较高的现实意义。     

双星轨道拟合的研究进展

双星轨道拟合是天文学的一项基础性研究工作。其主要目的是给出双星系统的二体轨道参数,这些参数不仅是高精度、高网格密度星表参考架的必要组成部分,而且也为理解各种有关观测现象提供了必要的动力学基础;更重要的是,双星轨道拟合可以直接估计恒星物理和星系天文学等领域极有应用价值的恒星质量参数。因此,长期以来双星轨道拟合工作一直受到研究者的广泛关注。近年来,随着高精度的恒星运动学观测资料的大量积累,双星轨道拟合更成为天体测量和天体力学的一个共同的热点课题,有关研究也有了长足的进展。综述了双星轨道拟合的历史及现状,其中着重介绍了目前所用的主要观测资料和各种具体的拟合模型、拟合方法;简要描述了几种主要的双星星表;展望了今后双星轨道拟合工作的发展趋势。     

Simulation of the full two rigid body problem using polyhedral mutual potential and potential derivatives approach

Herein we investigate the coupled orbital and rotational dynamics of two rigid bodies modelled as polyhedra, under the influence of their mutual gravitational potential. The bodies may possess any arbitrary shape and mass distribution. A method of calculating the mutual potential’s derivatives with respect to relative position and attitude is derived. Relative equations of motion for the two body system are presented and an implementation of the equations of motion with the potential gradients approach is described. Results obtained with this dynamic simulation software package are presented for multiple cases to validate the approach and illustrate its utility. This simulation capability is useful both for addressing questions in dynamical astronomy and for enabling spacecraft missions to binary asteroid systems.     

3. Solar System Formation and Early Evolution: the First 100 Million Years

The solar system, as we know it today, is about 4.5 billion years old. It is widely believed that it was essentially completed 100 million years after the formation of the Sun, which itself took less than 1 million years, although the exact chronology remains highly uncertain. For instance: which, of the giant planets or the terrestrial planets, formed first, and how? How did they acquire their mass? What was the early evolution of the “primitive solar nebula” (solar nebula for short)? What is its relation with the circumstellar disks that are ubiquitous around young low-mass stars today? Is it possible to define a “time zero” (t ₀), the epoch of the formation of the solar system? Is the solar system exceptional or common? This astronomical chapter focuses on the early stages, which determine in large part the subsequent evolution of the proto-solar system. This evolution is logarithmic, being very fast initially, then gradually slowing down. The chapter is thus divided in three parts: (1) The first million years: the stellar era. The dominant phase is the formation of the Sun in a stellar cluster, via accretion of material from a circumstellar disk, itself fed by a progressively vanishing circumstellar envelope. (2) The first 10 million years: the disk era. The dominant phase is the evolution and progressive disappearance of circumstellar disks around evolved young stars; planets will start to form at this stage. Important constraints on the solar nebula and on planet formation are drawn from the most primitive objects in the solar system, i.e., meteorites. (3) The first 100 million years: the “telluric” era. This phase is dominated by terrestrial (rocky) planet formation and differentiation, and the appearance of oceans and atmospheres.     

On the periodical structures in populations of galaxies and of clusters of galaxies

Analysing the distribution of the redshift of clusters of galaxies, obtained from the catalogue of SCHMIDT (1986), two already known periodical structures were confirmed and both periods were extended by a number of periods — approximately by two times (We elucidated 5 new periods in the first structure and 4 in the second.). The statistical significance of these structures was estimated to 0.01 in the first case and to 0.02 in the second one. Particularly, the second structure may be the largest known object in the Universe (about 900 Mpc at H = 75 km s^-1 Mpc^-1). These results agree with the predictions of the axion-dominated early Universe. In addition, we discovered periodical structures of an another type — in luminosity functions of galaxies, which are members of rich clusters. Bei der Analyse des Katalogs von SCHMIDT (1986) wurden zwei periodische Strukturen in den Verteilungen der Rotverschiebungen von Galaxienhaufen festgestellt. In den beiden Strukturen wurden 5 bzw. 4 neue Perioden beobachtet, weshalb sich die Periodenzahl in jeder der beiden Strukturen etwa verdoppelt hat. Die statistische Signifikanzen dieser Strukturen wurden zu 0.01 und 0.02 abgeschätzt. Möglicherweise entspricht die zweite Struktur dem größten bekannten Objekt des Weltalls (etwa 900 Mpc bei H = 75 km s^-1 Mpc^-1). Diese Resultate stützen die Theorie eines axiondominierten frühen Universums. Außerdem wurden weitere periodische Strukturen in der Leuchtkraftfunktion von Galaxien aus reichen Galaxien-haufen entdeckt.     

在6厘米波长对类星体3C454.3的九站VLBI观测

3C454.3是近几年引起广泛注意的一个强活动射电类星体,它有毫角秒尺度的核——喷流结构,其核在1981年的一次流量密度大爆发之后,显示出“超光速增亮”现象,在6厘米波长,用包括欧洲、美国及南非的9个射电望远镜,于1983年10月对3C454.3进行了甚长基线干涉网观测。观测结果除了证实其核——喷流结构,显示了从毫角秒到角秒尺度上该类星体结构的系统弯曲外,还清楚地揭示了“超光速增亮”所预期的,在1981年8月到1983年1月期间,核的超光速膨胀现象。     

On the variational approach to the periodic n-body problem

This expository paper gathers some of the results obtained by the author in recent works in collaboration with Davide Ferrario and Vivina Barutello, focusing on the periodic n-body problem from the perspective of the calculus of variations and minimax theory. These researches were aimed at developing a systematic variational approach to the equivariant periodic n-body problem in the two and three-dimensional space. The purpose of this paper is to expose the main problems and achievements of this approach. The material here was exposed in the talk that given at the Meeting CELMEC IV promoted by SIMCA (Società italiana di Meccanica Celeste).     

Magnetic draping of merging cores and radio bubbles in clusters of galaxies

Sharp fronts observed by the Chandra satellite between dense cool cluster cores moving with near-sonic velocity through the hotter intergalactic gas, require strong suppression of thermal conductivity across the boundary. This may be due to magnetic fields tangential to the contact surface separating the two plasma components. We point out that a super-Alfvenic motion of a plasma cloud (a core of a merging galaxy) through a weakly magnetized intercluster medium leads to 'magnetic draping', formation of a thin, strongly magnetized boundary layer with a tangential magnetic field. For supersonic cloud motion,   M _s≥ 1  , magnetic field inside the layer reaches near-equipartition values with thermal pressure. Typical thickness of the layer is  ∼ L / M ²_A≪ L   , where L is the size of the obstacle (plasma cloud) moving with Alfvén Mach number   M _A≫ 1  . To a various degree, magnetic draping occurs for both subsonic and supersonic flows, random and ordered magnetic fields and it does not require plasma compressibility. The strongly magnetized layer will thermally isolate the two media and may contribute to the Kelvin–Helmholtz stability of the interface. Similar effects occur for radio bubbles, quasi-spherical expanding cavities blown up by active galactic nucleus jets; in this case, the thickness of the external magnetized layer is smaller,  ∼ L / M ³_A≪ L   .