FAST单元面板面型检测算法研究

500 m口径球面射电望远镜(Five-hundred-meter Aperture Spherical Radio Telescope,FAST)是一个超大口径的可动望远镜,有三项技术创新,一是选址,二是轻型馈源索支撑,三是主动反射面。在主动反射面上,单元面板的面型和面板的出厂加工精度对电磁波在反射面的汇聚有很大影响。FAST主反射面由4 600块三角形反射面板拼接而成,每块面板为边长11 m三角形,这对FAST反射面面板的测量技术提出了更高的要求。摄影测量直接在影像上进行量测,无需接触物体本身;所摄影像信息丰富,可以从中获得所研究物体的大量几何信息和物理信息;适用于大范围、多目标测量,效率高。目前世界上最大的射电望远镜,如GBT和ARECIBO都是采用摄影测量技术进行反射面面形检测。在对现有的面型检测技术调研并试验后,提出基于数字近景摄影测量的方法,对FAST反射面11 m单元面板的面型进行检测,数分钟完成反射面板面型的一次检测,测量精度达到2.5 mm,经过调整后的单元面板的面型精度达到了3.0 mm,结果表明摄影测量应用于FAST反射面单元面板面型检测是可行的。     

The Skewness of a Solar Cycle as a Precursor of the Amplitude of the Next

As a precursor for predicting the maximum amplitude of the coming solar cycle, the skewness of the previous cycle proposed by Ramaswamy (1977) is revisited. The reliability of the prediction method is improved by separating odd and even cycles. A first method is proposed on the basis of calculated skewness. In that case, the prediction is available at the end of the previous cycle. A possibility to anticipate the availability of the skewness by about one year is pointed out. A second method, adding prediction of the skewness itself is studied. The statistical reliability is lower than in the first case, but the prediction of a cycle maximum is available at the maximum of the previous cycle.     

Motion of a satellite in the equatorial plane of a spheroid

An exact, closed-form solution of the problem of the motion of a satellite in the equatorial plane of an oblate body is obtained. It is shown that the classic formula for the motion of the perihelion is a first order approximation to the exact formula.     

Effects of a deformation of a star on the gravitational lensing

We study analytically a gravitational lens due to a deformed star, which is modelled by using a monopole and a quadrupole moment. Positions of the images are discussed for a source on the principal axis. We present explicit expressions for the lens equation for this gravitational lens as a single real 10th-order algebraic equation. Furthermore, we compute an expression for the caustics as a discriminant for the polynomial. Another simple parametric representation of the caustics is also presented in a more tractable form. A simple expression for the critical curves is obtained to clarify a topological feature of the critical curves; the curves are simply connected if and only if the distortion is sufficiently large.     

On the stability of a slow deflagration front at the surface of a degenerate star

On the surface of a degerate star, a slow nuclear combustion process with a wake of escaping matter can exist. The evolution of this process has been studied by solving the nonadiabatic, time-dependent hydrodynamic equations. It has been found that this flow is almost stationary and is stable against small spherical symmetric perturbations.     

About the Influence of a Magnetic Field on the Model Atmosphere of a Magnetic Star

A quasi-static magnetic field similar to that of a large single sunspot is assumed to be embedded in a photospheric model of an Ao star. The differences of the model atmosphere within the magnetic spot relative to the photosphere are calculated by means of the equations of hydromagnetics. The differences are small for τ ≧ I but increase towards smaller τ. The spot model is more transparent in its high layers. In equal geometrical depth the thermodynamic parameters are reduced by the magnetic field. While a small spot is darker than its photospheric surroundings, a large spot appears brighter; the wavelength dependence of its excess in brightness coincides with observations. Compared with the photosphere, the Balmer lines show narrower and deeper cores in the large spot, these differences increase towards larger quantum numbers. Also these features are qualitatively confirmed by observations. An outline is given how to extend and generalize the present model calculations.     

Estimating the significance of a signal in a multi-dimensional search

In experiments that are aimed at detecting astrophysical sources such as neutrino telescopes, one usually performs a search over a continuous parameter space (e.g. the angular coordinates of the sky, and possibly time), looking for the most significant deviation from the background hypothesis. Such a procedure inherently involves a “look elsewhere effect”, namely, the possibility for a signal-like fluctuation to appear anywhere within the search range. Correctly estimating the p-value of a given observation thus requires repeated simulations of the entire search, a procedure that may be prohibitively expansive in terms of CPU resources. Recent results from the theory of random fields provide powerful tools which may be used to alleviate this difficulty, in a wide range of applications. We review those results and discuss their implementation, with a detailed example applied for neutrino point source analysis in the IceCube experiment.     

Structure of the clusters of galaxies a 999, a 1016, and a 1142

The hierarchical structure of the clusters of galaxies A 999, A 1016, and A 1142, which are part of one supercluster, is investigated. The HTree method is used to determine that A 999 and A 1016 are a single, dynamically bound system consisting of two “cores” and a common field of galaxies. The composition of the “cores” includes almost all the E and S0 galaxies, the luminosity function of which is very nearly Gaussian. It is also established that the cluster A 1142 has a nonuniform structure, both in density distribution and in radial velocity distribution. The location of the maxima in density and in the radial velocity distribution correlates with the galaxies that are sources of radio and x-ray emission. Translated from Astrofizika, Vol. 43, No. 1, pp. 45-54, January–March, 2000.     

On the possibility of a secondary explosion in the antipode of a large meteorite impact point

At large distances, due to atmospheric absorption and the dispersion of high-frequency components, the airwaves from the fall of large meteorites or heavy-yield explosions are transformed into an infrasonic wave train propagating over large distances via atmospheric sound channels. In approaching the antipode, the amplitude of infrasonic oscillations increases significantly and the nonlinear effects may trigger the formation of a blast wave, that is, another explosion. The condition which allows such a phenomenon to happen was obtained in this study. Infrasonic waves from the Tunguska fall event and waves generated by the largest nuclear explosions were considered in this study.     

About the stability of the libration points of a rotating triaxial ellipsoid in a degenerate case

The problem of stability of the equilibrium points in the problem of motion of a mass point in the neighbourhood of a rotating triaxial ellipsoid in a degenerate case (the Gaussian of the Hamiltonian is equal to zero) is investigated.It is proved that the equilibrium points in the degenerate case are stable in the strict sence.

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Résumé On étudie le problème de la stabilité des positions d'équilibre relatif dans le problème du mouvement du point matériel au voisinage de l'ellipsoid à trois axes tournant dans un cas dégénéré (le gaussian du Hamiltonian égal zéro).On a démontré que des positions d'équilibre relatif dans le dégénéré sont stables dans le sens rigoureux.

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On the Dynamics of a Deformable Satellite in the Gravitational Field of a Spherical Rigid Body

In this paper, a model is developed for the dynamics of a system of two bodies whose material points are under the influence of a central gravitational force. One of the bodies is assumed to be rigid and spherically symmetric, while the other is assumed to be deformable. To develop a tractable model for the system, the deformable body is modeled using Cohen and Muncaster's theory of a pseudo-rigid body. The resulting model of the system has several of the features, such as angular momentum conservation, exhibited by more restrictive models. We also show how the self-gravitation of the deformable body can be accommodated using appropriate constitutive equations for a force tensor. This enables our model to subsume many existing models of ellipsoidal figures of equilibrium. After the model and its conservations have been discussed, attention is restricted to steady motions of the system. Several results, which generalize recent works on rigid satellites, are established for these motions. For a specific choice of constitutive equations for the pseudo-rigid body, we determine the steady motions with the aid of a numerical continuation method. These results can also be considered as generalizations of earlier works on Roche's ellipsoids of equilibrium.     

Refinement of the phase of a spherical planet located at a small distance from the Sun

Formulas for refining the phase of a spherical planet located a small distance from the Sun are derived. Finite heliocentric distance of the planet results in the formation on its visible disk of the geometric terminator, which is not coincident with the orthographic terminator. The visible disk is assumed to be observed from Earth in orthographic projection. We suggest introducing linear and surface phases for the geometric terminator in accordance with two existing definitions of the phase of a planet. Linear and surface phases of a planet are shown to be given by different sets of formulas. An example of the computation of the phase of Mercury is given.     

On the perturbations of a sphere

Perturbations in a spherical island Universe are investigated. An illustrative model is presented; the spher is inhomogeneous but static. The stratification in matter distribution may occur in this model.     

Libration points and the general case in the problem of the motion of a star inside a layered inhomogeneous elliptical galaxy with a variable mass

We have found libration points and investigated their Lyapunov stability in the problem of the motion of a star inside a layered inhomogeneous rotating elliptical galaxy with a variable mass. We have constructed the surfaces of zero velocity and obtained stability conditions for unsteady motion in the first approximation. We analyze general case where the densities of the galactic nucleus and layers vary with time according to different laws.     

Stability of a finite disc under the influence of a spherical halo

We have studied the stability of finite gaseous discs, against large-scale perturbations, under the influence of spherical, massive haloes. A surface-density distribution consistent with the observed spiral-tracer profiles in disc galaxies is considered for the disc. We find that growing eigenmodes with both ‘trailing’ and ‘leading’ spirals exist in ‘cold’ discs for a wide range of values of the halo mass and its radius. The amplification rates of the unstable modes reduce as the ratio of the mass of the halo to the mass of the disc is increased. A uniform halo is not very effective towards stabilizing the disc against these modes. The results from the present study are consideredvis-a-vis previous studies on the global modes of self-gravitating discs.     

Influence of a hyperbolic flyby of a small mass on the orbital evolution of a massive binary

Method of variation of arbitrary constants is applied to determining the first order perturbations of the orbital elements of a massive close binary caused by the hyperbolic distant flyby of a small mass. The perturbations are expressed by a sequence of analytical formulas involving definite integrals of the simple type and admitting the straightforward evaluation by computer.     

摆镜平台寿命的Bootstrap估计

摆镜平台是大口径空间天文望远镜图像稳定控制系统中的一个活动部件,为评估其寿命,进行了摆镜平台寿命试验。摆镜平台寿命试验为单子样寿命试验,先验概率信息很少,采用Bayes方法进行寿命估计有一定的困难。Bootstrap方法是一种非参数统计方法,它对未知分布不做任何假设,仅利用计算机对原始样本数据进行再抽样模拟未知分布,通过再生抽样将小样本问题转化成大样本问题。Bootstrap方法要求子样数要大于等于5。采用半经验虚拟增广子样和Bootstrap相结合的方法进行摆镜平台寿命的区间估计。在摆镜平台寿命服从威布尔(Weibull)分布的假定下,通过以往类似产品寿命试验数据推断出威布尔分布形状参数,然后用寿命试验值和威布尔分布形状参数推导出摆镜平台寿命的方差,在此基础上进行子样虚拟增广。虚拟增广子样需要满足两个条件:(1)增广子样的均值等于寿命试验值;(2)虚拟增广子样的方差等于类似产品寿命的经验方差。根据这两个条件建立一个方程组,用数值计算法求解方程组得到增广子样。这些作为Bootstrap区间估计原始样本的增广子样用于计算样本的经验分布和样本重抽样。通过重抽样得到10 000个样本,计算每个样本的均值,然后对10 000个均值进行排序,得到均值μ1≤μ2≤…≤μ10 000,采用分位数法计算置信水平为1-α的Bootstrap置信区间,得到置信区间(μk1,μk2),其中k1=[10 000×α/2],k2=[10 000×(1-α/2)]。寿命试验的加速因子为5.5,目前摆镜平台已正常工作1.25年,按上述方法计算0.95置信水平的Bootstrap置信下限为3.59年,如果正常工作两年,0.95置信水平的Bootstrap置信区间为(5.93年,16.81年)。     

Restriction on the motion of a solid in a gravitational field

As is well known, the orbital and rotational motions of a solid are coupled, and the integrals of energy and angular momentum (in a gravitational field with spherical symmetry) impose restrictions on them. We study the regions allowed to the motion in configurational space. It turns out that even in the crudest model (planar motion of a triple rod) the restrictions on the libration angle and the orbital radius of the center of mass are coupled, so that excessive ellipticity of the orbit excludes stabilization in the neighbourhood of the spoke equilibrium position by gravitational forces only.Chargé de Cours.