Analysis of the wide area differential correction for BeiDou global satellite navigation system

The regional BeiDou Satellite System, or BDS2, broadcasts a differential correction as Equivalent Satellite Clock Correction to correct both orbit and satellite clock errors. For the global BDS, or BDS3, satellite orbit and clock corrections conforming with RTCA standards will be broadcast to authorized users. The hybrid constellation and regional monitoring network pose challenges for the high precision separation of orbit and satellite clock corrections. Three correction models of kinematic,dynamic and Two-way Satellite Time Frequency Transfer(TWSTFT)-based dynamic were studied to estimate the satellite orbit and clock corrections. The correction accuracy of the three models is compared and analyzed based on the BDS observation data. Results show that the accuracies(root mean square, RMS) of dual-frequency real-time positioning for the three models are about 1.76 m, 1.78 m and 2.08 m respectively, which are comparable with the performance of WAAS and EGNOS. With dynamic corrections, the precision of Precise Point Positioning(PPP) experiments may reach about 23 cm after convergence.     

The Convergence of Newton–Raphson Iteration with Kepler's Equation

Conway (Celest. Mech. 39, 199–211, 1986) drew attention to the circumstance that when the Newton–Raphson algorithm is applied to Kepler's equation for very high eccentricities there are certain apparently capricious and random values of the eccentricity and mean anomaly for which convergence seems not to be easily reached when the starting guess for the eccentric anomaly is taken to be equal to the mean anomaly. We examine this chaotic behavior and show that rapid convergence is always reached if the first guess for the eccentric anomaly is π. We present graphs and an empirical formula for obtaining an even better first guess. We also examine an unstable situation where iterations oscillate between two in correct results until the instability results in sudden convergence to the unique correct solution. This revised version was published online in July 2006 with corrections to the Cover Date.     

The Spectroscopic Idebtification of Interstellar Grains

It is shown that the condition of matching the 3.3–3.9 μm spectrum of the galactic infrared source GC-IRS 7 leads to a remarkably tight convergence on the transmittance curve measured in the laboratory for the dessicated bacterium E. coli.Other materials, including certain biochemicals and postulated prebiologic compounds, are shown to be deficient with regard to meeting this condition. This revised version was published online in July 2006 with corrections to the Cover Date.     

Radiative Transfer Under Inhomogeneous Configurations

We present, for the first time, three dimensional (3D) radiative transfer (RT) results with realistic atomic models (multilevel) and without using the local thermodinamical equilibrium approximation (non-LTE). We have developed a new code based on efficient iterative methods (Trujillo Bueno, and Fabiani Bendicho 1995; Fabiani Bendicho, Trujillo Bueno and Auer 1997) characterized by a very high convergence rate. With this 3D multilevel code and using a schematic atmospheric model we are able to demonstrate that one may need self-consistent multidimensional RT calculations in order to interpret high spatial resolution solar spectroscopic observations. This revised version was published online in July 2006 with corrections to the Cover Date.     

非圆轨道GPS/LEO掩星反演地球大气参数的算法及讨论

在非圆轨道GPS和LEO卫星条件下，给出一种较为直接的GPS／LEO掩星反演地球大气参数技术中弯曲角序列的迭代算法，并在理论上对该迭代法的收敛性进行了严格的数学证明．利用GPS掩星反演模拟程序，定量估算了卫星圆轨道假设对GPS／LEO掩星反演地球大气参数的影响，并验证了在非圆轨道条件下各种迭代法的一致性．指出了文献中给出的级数展开迭代算法的不足之处．     

基于GPS与三轴磁强计的联合导航算法

为了修正近地轨道(小于1000 km)地磁场模型,提高导航的精度,在地磁导航系统中引入GPS作为一个新的测量设备,提出了一种基于三轴磁强计与GPS的联合导航算法．该算法取卫星的位置和速度向量作为状态向量,建立状态方程;取卫星周围的磁场强度和GPS接收的信号作为观测量,建立观测方程;并以GPS确定的轨道状态量为标准量,去估计磁场模型参数的修正量,构成冷备冗余导航算法．仿真结果表明,提出的导航算法对轨道位置的估计误差小于50 m,速度的估计误差小于0．1 m／s,导航算法的精度和收敛性都优于使用单一地磁导航的系统．     

On the construction of model stellar atmospheres

The construction of model atmospheres by means of differential corrections is discussed. Either flux or flux gradients may be minimized, with arbitrary weighting with depth. For the simple atmospheres studied, no convergence problems were encountered even when very poor first approximations were used; and flux constancy in the radiative case was generally attained in three or four iterations.Quantities computed in one iteration may be re-used, not only in subsequent iterations within the model, but also in the construction of other models with differentT _eff org; and so the method is particularly suited for grid computations.     

Weak lensing predictions at intermediate scales

As pointed out in previous studies, the measurement of the skewness of the convergence field κ will be useful in breaking the degeneracy among the cosmological parameters constrained from weak lensing observations. The combination of shot noise and finite survey volume implies that such a measurement is likely to be performed in a range of intermediate scales (0.5 to 20 arcmin) where neither perturbation theory nor the hierarchical ansatz applies. Here we explore the behaviour of the skewness of κ at these intermediate scales, based on results for the non-linear evolution of the mass bispectrum. We combined different ray-tracing simulations to test our predictions, and we find that our calculations describe accurately the transition from the weakly non-linear to the strongly non-linear regime. We show that the single lens-plane approximation remains accurate even in the non-linear regime, and we explicitly calculate the corrections to this approximation. We also discuss the prospects of measuring the skewness in upcoming weak lensing surveys.     

Laplacian Orbit Determination and Differential Corrections

Laplace’s method is a standard for the calculation of a preliminary orbit. Certain modifications, briefly summarized, enhance its efficacy. At least one differential correction is recommended, and sometimes becomes essential, to increase the accuracy of the computed orbital elements. Difficult problems, lack of convergence of the differential corrections, for example, can be handled by total least squares or ridge regression. The differential corrections represent more than just getting better agreement with the observations, but a means by which a satisfactory orbit can be calculated. The method is applied to three examples of differing difficulty: to calculate a preliminary orbit of Comet 122/P de Vico from 59 observations made during five days in 1995; a more difficult calculation of a possible new object with a poor distribution of observations; Herget’s method fails for this example; and finally a really difficult object, the Amor type minor planet 1982 DV (3288 Seleucus). For this last object use of L₁ regression becomes essential to calculate a preliminary orbit. For this orbit Laplace’s method compares favorably with Gauss’s.     

Numerical simulations of type III planetary migration – I. Disc model and convergence tests

We investigate the fast (type III) migration regime of high-mass protoplanets orbiting in protoplanetary discs. This type of migration is dominated by corotational torques. We study the details of flow structure in the planet's vicinity, the dependence of migration rate on the adopted disc model and the numerical convergence of models (independence of certain numerical parameters such as gravitational softening).
We use two-dimensional hydrodynamical simulations with adaptive mesh refinement, based on the flash code with improved time-stepping scheme. We perform global disc simulations with sufficient resolution close to the planet, which is allowed to freely move throughout the grid. We employ a new type of equation of state in which the gas temperature depends on both the distance to the star and planet, and a simplified correction for self-gravity of the circumplanetary gas.
We find that the migration rate in the type III migration regime depends strongly on the gas dynamics inside the Hill sphere (Roche lobe of the planet) which, in turn, is sensitive to the aspect ratio of the circumplanetary disc. Furthermore, corrections due to the gas self-gravity are necessary to reduce numerical artefacts that act against rapid planet migration. Reliable numerical studies of type III migration thus require consideration of both the thermal and the self-gravity corrections, as well as a sufficient spatial resolution and the calculation of disc–planet attraction both inside and outside the Hill sphere. With this proviso, we find type III migration to be a robust mode of migration, astrophysically promising because of a speed much faster than in the previously studied modes of migration.     

Numerical Fourier Expansions of the Planetary Disturbing Function

Various Fourier expansions of the planetary disturbing function can be computed numerically with the use of numerical Fourier analysis. The task to compute the most general five-dimensional Fourier expansion of disturbing function has become feasible with typical server-class computers quite recently. In such an expansion two anomalies, two arguments of perihelions and two longitudes of the node are independent angular variables, while two semi-major axes, two eccentricities and two inclinations are fixed numerically. The semianalytical expansion of the disturbing function resulting from numerical Fourier analysis theoretically converges for any values of the parameters except for those sets of parameters which allow the bodies to collide. Various aspects of the numerical computation of the Fourier expansion are discussed. Theoretical and practical convergence of the Fourier series is discussed and illustrated. This revised version was published online in July 2006 with corrections to the Cover Date.     

Convergence of Liapunov series for Huygens–Roche Figures

According to the classical theory of equilibrium figures, surfaces of equal density, potential and pressure concur (let us call them isobars). Isobars can be represented by means of Liapunov power series in small parameter q, up to the first approximation coinciding with the centrifugal to gravitational force ratio at the equator. Liapunov has proved the existence of the universal convergence domain: the above mentioned series converge for all bodies (satisfying a natural condition that the density ρ decreases from the center to the surface) if |q| < q*. Using Liapunov’s algorithm and symbolic manipulation tools, we have found q*= 0.000370916. Evidently, the convergence radius q* may be much greater in common situations. To comfirm it it is reasonable to consider two limiting and one or two intermediate cases for the density behaviour: ρ is a constant, the Dirac’s δ-function, linear function of the distance from the center, etc. And indeed, in the previous paper we find a three orders of magnitude greater value for homogeneous figures. In the present paper we find that in the opposite case of Huygens-Roche figures (a point-mass surrounded by a weightless atmosphere) the convergence radius is unexpectedly large and coincides with the well-known biggest possible value q*= 0.541115598 for such a class of figures. To ascertain it we ought to use numerical calculations, so our main result is demonstrated by means of a computer assisted proof. This revised version was published online in July 2006 with corrections to the Cover Date.     

Corrections to the Cardy-Verlinde formula at the Planck scale

The possible corrections to the thermodynamic quantities of higher dimensional Schwa-rzschild black hole have been investigated by considering the generalized uncertainty principle (GUP) and the modified dispersion relation (MDR) separately. The quantum gravitational corrections to the Hawking temperature, energy and entropy of the black hole have been calculated based on both the GUP and the MDR analysis. The explicit form of the corrections are worked out up to the sixth power of the Planck length. The impacts of GUP and MDR have been used separately to obtain the quantum gravitational corrections to the Cardy-Verlinde (C-V) formula. It has been shown that the usual C-V entropy formula receives some new corrections. Also the renormalized form of the C-V formula has been introduced by redefining Virasoro operator and central charge within both the GUP and the MDR. Through comparison of the corrections obtained from GUP and MDR approaches it has been found that the results of these two alternative approaches should be identical if one uses the suitable expansion coefficients.     

Relativist ic Corrections to the Thermal Sunyaev-Zel''''dovich Power Spectrum

We present a quantitative estimate of the relativistic corrections to the thermal SZ power spectrum produced by the energetic electrons in massive clusters. The corrections are well within 10% for current experiments with working frequencies below v < 100 GHz, but become non-negligible at high frequencies v > 350 GHz. Moreover, the corrections appear to be slightly smaller at higher l or smaller angular scales. We conclude that there is no need to include the relativistic corrections in the theoretical study of the SZ power spectrum especially at low frequencies unless the SZ power spectrum is used for precision cosmology.     

视频CCD观测的星径曲率改正

视频ＣＣＤ观测与低纬子午环原来设计的光子计数狭缝测微器观测有不同之处。在观测数据的归算过程中，应加以考虑的星径曲率改正包括三种改正量；卯酉方向记录时刻的星径曲率改正；卯酉方向天顶距的星径曲率改正以及子午方向天顶距的星径曲率改正。     

有关求解星径曲率改正问题的探讨

对于配置光子计数探测器的低纬子午环，在其观测数据的归算过程中应该加以考虑的星径曲率改正包括三种改正量：卯酉方向记录时刻的星径曲率改正；卯酉方向天顶距的星径曲率改正；子午方向天顶距的星径曲率改正。结合测微器的新视栅形式，本文给出了一种旨在解决星径曲率改正问题的新思路。     

'On Solving Kepler's Equation For Nearly Rectilinear Hyperbolic Orbits'

We deal here with efficient starting points for Kepler's equation in a special case of nearly rectilinear hyperbolic orbits, that is these ones with the eccentricities e1. These orbits appear in stellar dynamics when considering encounters of stars. We test efficiency of these starters for the method for successive approximation (MSA) in its two often applied variants, that is the Newton's method with the quadratic convergence (NM) and in the fixed point method (FPM). Moreover, we determine a dynamical domain of Kepler's equation for this motion.This revised version was published online in October 2005 with corrections to the Cover Date.     

射电源结构对VLBI天体测量的影响

目前利用VLBIMK3系统确定的延迟测量的精度约为30ps,在这样的精度下,改善计算延迟的理论模型,考虑各种微扰改正（包含30ps量级）是非常重要的。在VLBI天休测量和测地计算的各种软件中,至今尚未计及射电源结构对延迟的影响。本文利用两子源模型对源结构延迟的大小及随时间的变化进行了计算,讨论了源结构延迟对VLBI天测和测地参数的影响,指出：（1）除对某些VLBI天测的射电源作长期的监测与研究,给出它们的双频综合图外,对大多数源可采用简单的两子源模型;（2）源结构对延迟的影响主要依赖于基线相对于源形态的主要特征的空间投影;（3）源结构延迟对天测和测地参数的影响达厘米和亚毫角秒量级。     

Quantum corrections for ABGB black hole

In this paper, we study quantum corrections to the temperature and entropy of a regular Ayón-Beato-García-Bronnikov black hole solution by using tunneling approach beyond semiclassical approximation. We use the first law of black hole thermodynamics as a differential of entropy with two parameters, mass and charge. It is found that the leading order correction to the entropy is of logarithmic form. In the absence of the charge, i.e., e=0, these corrections approximate the corresponding corrections for the Schwarzschild black hole.     

北斗广域增强系统星钟和星历误差改正算法研究

区域北斗星基增强系统提供等效钟差改正数统一修正星历和钟差误差。随着系统的建设发展,新一代北斗星基增强系统将区分星历和钟差误差改正信息,以提高差分改正精度。由于北斗卫星混合星座设计及区域监测网的局限,星历和钟差误差的高精度分离计算面临着新的挑战。对北斗星基增强系统的星历和钟差改正算法进行了研究,分别采用动力学和运动学模式计算了卫星星历和钟差改正数,并基于北斗实测数据,对两种处理模式的差分改正精度进行了对比研究。试验结果表明,采用动力学和运动学差分方法,得到的双频伪距实时定位精度分别为1.76m和1.78m,定位精度与WAAS及EGNOS相当。利用运动学和动力学差分改正数后均可得到分米级的精密单点定位(precise point position,PPP)结果,其中采用动力学广域差分改正数,收敛后定位精度可达到15cm;采用运动学广域差分改正数,收敛后定位精度可达45cm。