Formal integrals for an autonomous Hamiltonian system near an equilibrium point

In this paper we give a new method to construct formal integrals for an autonomous Hamiltonian system near an equilibrium point. Our construction is reminiscent of the algorithms introduced by Hori and Deprit; we show however how it presents itself quite naturally if one follows the line of attack of Whittaker, Cherry, and Contopoulos.     

On the application of optimization methods to the determination of members of families of periodic solutions

The techniques used for the numerical computation of families of periodic orbits of dynamical systems rely on predictor-corrector algorithms. These algorithms usually depend on the solution of systems of approximate equations constructed from the periodicity conditions of these orbits. In this contribution we transform the root finding procedure to an optimization one which is applied on an objective function based on the exact periodicity conditions. Thus, the determination of periodic solutions and families of such orbits can be accomplished through unconstrained optimization. In this paper we apply and compare some well-known minimization methods for the solution of this problem. The obtained results are promising. This revised version was published online in July 2006 with corrections to the Cover Date.     

GPS接收机的中频信号处理算法研究

该文对GPS接收机的中频信号处理算法进行了研究,内容主要涉及信号捕获、载波恢复和伪码跟踪3部分,详细分析了信号捕获过程中所采用的匹配滤波器法、快速傅里叶算法(FFT)、锁频环(FLL)、锁相环(PLL)以及延迟锁定环(DLL)的算法原理,并对环路滤波器作了相应的阐述,给出环路对应的递推公式．     

Rhessi Images and Spectra of Two Small Flares

We studied the evolution of two small flares (GOES class C2 and C1) that developed in the same active region with different morphological characteristics: one is extended and the other is compact. We analyzed the accuracy and the consistency of different algorithms implemented in Reuven Ramaty High-Energy Spectroscopic Imager (RHESSI) software to reconstruct the image of the emitting sources, for energies between 3 and 12 keV. We found that all tested algorithms give consistent results for the peak position, while the other parameters can differ at most by a factor 2. Pixon and Forward-fit generally converge to similar results but Pixon is more reliable for reconstructing a complex source. We investigated the spectral characteristics of the two flares during their evolution in the 3–25 keV energy band. We found that a single thermal model of the photon spectrum is inadequate to fit the observations and we needed to add either a non-thermal model or a hot thermal one. The non-thermal and the double thermal fits are comparable. If we assume a non-thermal model, the non-thermal energy is always higher than the thermal one. Only during the very final decay phase a single thermal model fits the observed spectrum fairly well.     

The SumThreshold Method for Radio Frequency Interference Detection

Radio frequency interference (RFI) is one of the main challenges in the search of radio targets and their accurate analysis. The efficient RFI detection and mitigation techniques are required in the radio data processing. Existing RFI mitigation algorithms typically fall into three categories: component decomposition methods, threshold-based methods, and machine learning methods. The threshold-based algorithms are widely used in real applications because of its clear principle, simple structure, and easily implementation. Especially, the SumThreshold method is becoming more concerned for its good performance in RFI detection. Therefore, this work investigates the principles and algorithm of SumThreshold, and discusses its characteristics and applicability.     

射频干扰检测的SumThreshold算法

射频干扰(Radio Frequency Interference, RFI)是射电目标搜寻和精确分析研究的关键影响因素,因此RFI检测是相关数据处理中的一个重要环节.已有RFI检测方法可分为成分分解法、阈值分析法、机器学习类方法.从应用广泛性和可解释性方面考虑,阈值分析法最具代表性,特别是SumThreshold是近年备受关注的一个RFI检测方法.从SumThreshold方法的原理、算法设计、优化要点、适用性等方面进行介绍和探讨,以供同行参考.     

Multi-rendezvous low-thrust trajectory optimization using costate transforming and homotopic approach

This paper investigates a method for optimizing multi-rendezvous low-thrust trajectories using indirect methods. An efficient technique, labeled costate transforming, is proposed to optimize multiple trajectory legs simultaneously rather than optimizing each trajectory leg individually. Complex inner-point constraints and a large number of free variables are one main challenge in optimizing multi-leg transfers via shooting algorithms. Such a difficulty is reduced by first optimizing each trajectory leg individually. The results may be, next, utilized as an initial guess in the simultaneous optimization of multiple trajectory legs. In this paper, the limitations of similar techniques in previous research is surpassed and a homotopic approach is employed to improve the convergence efficiency of the shooting process in multi-rendezvous low-thrust trajectory optimization. Numerical examples demonstrate that newly introduced techniques are valid and efficient.     

Assessing the performance of molecular gas clump identification algorithms

The detection of clumps(cores) in molecular clouds is an important issue in sub-millimetre astronomy. However, the completeness of the identification and the accuracy of the returned parameters of the automated clump identification algorithms are still not clear. In this work, we test the performance and bias of the GaussClumps, ClumpFind, FellWalker, Reinhold, and Dendrograms algorithms in identifying simulated clumps. By designing the simulated clumps with various sizes, peak brightness, and crowdedness, we investigate the characteristics of the algorithms and their performance. In the aspect of detection completeness, FellWalker, Dendrograms, and GaussClumps are the first, second, and third best algorithms, respectively. The numbers of correct identifications of the six algorithms gradually increase as the size and signal-to-noise ratio(SNRs) of the simulated clumps increase and they decrease as the crowdedness increases. In the aspect of the accuracy of retrieved parameters, FellWalker and Dendrograms exhibit better performance than the other algorithms. The average deviations in clump parameters for all algorithms gradually increase as the size and SNR of clumps increase. Most of the algorithms except FellWalker exhibit significant deviation in extracting the total flux of clumps. Taken together, FellWalker, GaussClumps,and Dendrograms exhibit the best performance in detection completeness and extracting parameters. The deviation in virial parameter for the six algorithms is relatively low. When applying the six algorithms to the clump identification for the Rosette molecular cloud, ClumpFind1994, ClumpFind2006, GaussClumps,FellWalker, and Reinhold exhibit performance that is consistent with the results from the simulated test.     

基于图像的天体搜索研究与自动化集成软件开发

天体搜索是天文数据处理流程的一个重要环节,也是以平方公里阵列射电望远镜(Square Kilometre Array, SKA)为代表的下一代射电望远镜在面向海量数据处理中的挑战之一.现今天体自动搜索算法、软件已日趋成熟并投入应用,不过在自动化、兼容性等方面仍具有提升空间.以更自动化、更适应海量数据需求的天体搜索算法研究为宗旨,以现有算法为研究基础,天体自动搜索软件系统得到设计和开发.该系统包含友好的交互式用户操作界面,具备可视化输出数据显示、兼容不同数据输入和输出并包含为实际应用服务的文件管理功能.该系统对于大天区图以及图像集,均能够很好地进行自动化处理.测试结果显示,上述方法对于天体搜索的改进有一定成效.后续将在此基础上对该集成系统做进一步的改进开发,以适应更多的需求.     

无线传感器网络中基于时钟漂移补偿的时间同步技术

在分析和总结现有时间同步算法的特点及其存在问题的基础上,提出了一种在无线传感器网络的时间同步协议（TPSN）中同时考虑节点时钟偏移和频率漂移率的改进算法。该算法利用连续两次同步过程中所记录的时间信息来估算节点时钟的偏移和频率漂移率,并进行补偿。同传统算法相比,此算法通讯成本较低、精度较高。最后通过数学分析和仿真的方法对所提出的改进算法进行了验证。     

Perturbations des systèmes différentiels et résultats de géométrie différentielle

We use classical definitions and results of differential geometry in studying properties of transformations depending on a small parameter, acting on differential systems. Hori's and Deprit's algorithms can be defined for these systems. A lemma is given to show these algorithms are equivalent. The so-called property of covariance is merely established. The canonical systems are then considered as associated with Hamiltonian vectorfields on symplectic manifolds. The property that the infinitesimal generator of a canonical transformation is an Hamiltonian vectorfield permits to establish separately the generality of Hori's and Deprit's algorithms. We suggest that the Hamiltonian vectorfield property can be extended to the generators of transformations depending on several parameters.     

Speeding Up Image Reconstruction Methods in Coded Mask γ Cameras Using Neural Networks: Application to the EM Algorithm

When using γ-ray coded-mask cameras, one does not get a direct image as in classical optical cameras but the correlation of the mask response with the source. Therefore the data must be mathematically treated in order to reconstruct the original sky sources. Generally this reconstruction is based on linear methods, such as correlating the detector plane with a reconstruction array, or non-linear ones such as iterative or maximization methods (i.e. the EM algorithm). The latter have a better performance but they increase the computational complexity by taking a lot of time to reconstruct an image. Here we present a method for speeding up such kind of algorithms by making use of a neural network with a back-propagation learning rule.     

Modelling angular-momentum history in dark-matter haloes

We model the acquisition of spin by dark-matter haloes in semi-analytic merger trees. We explore two different algorithms: one in which halo spin is acquired from the orbital angular momentum of merging satellites, and another in which halo spin is gained via tidal torquing on shells of material while still in the linear regime. We find that both scenarios produce the characteristic spin distribution of haloes found in N -body simulations, namely, a log-normal distribution with mean ≈ 0.04 and standard deviation ≈ 0.5 in the log. A perfect match requires fine-tuning of two free parameters. Both algorithms also reproduce the general insensitivity of the spin distribution to halo mass, redshift and cosmology seen in N -body simulations. The spin distribution can be made strictly constant by physically motivated scalings of the free parameters. In addition, both schemes predict that haloes that have had recent major mergers have systematically larger spin values. These algorithms can be implemented within semi-analytic models of galaxy formation based on merger trees. They yield detailed predictions of galaxy properties that strongly depend on angular momentum (such as size and surface brightness) as a function of merger history and environment.     

CCD图像数字定心算法的比较

从CCD采集的数字图像中提取天体的位置和光度信息对于天文研究具有基础意义.其中,恒星星像中心像素位置的精确测量对于天体测量至关重要.针对国际上常用的三种位置测量算法:修正矩方法、Gauss拟合法和中值法,利用实测的CCD图像进行了试验研究.具体地,采用云南天文台1m望远镜观测的CCD图像同时使用这些算法进行了实际测量,根据每幅图像中测得的像素位置,对这三类定心算法进行了比较和精度分析.可视化方法被用于不同阈值的选取和设定比较.实验数据表明,无阈值的二维Gauss拟合方法是一种精度相对较高的定心算法.     

Semi-analytical integration algorithms based on the use of several kinds of anomalies as temporal variable

One of the main problems in celestial mechanics is the management of long developments in Fourier or Poisson series used to describe the perturbed motion in the planetary system.In this work we shall develop a software package that is suitable for managing these objects. This package includes algorithms to obtain the inverse of the distance based on an iterative method, a set of integration algorithms according to several sets of temporal variables.This paper contains a comparative study on the use of the true, eccentric, and elliptic anomalies in semi-analytical methods on celestial mechanics.     

A High Order Perturbation Analysis of the Sitnikov Problem

The Sitnikov problem is one of the most simple cases of the elliptic restricted three body system. A massless body oscillates along a line (z) perpendicular to a plane (x,y) in which two equally massive bodies, called primary masses, perform Keplerian orbits around their common barycentre with a given eccentricity e. The crossing point of the line of motion of the third mass with the plane is equal to the centre of gravity of the entire system. In spite of its simple geometrical structure, the system is nonlinear and explicitly time dependent. It is globally non integrable and therefore represents an interesting application for advanced perturbative methods. In the present work a high order perturbation approach to the problem was performed, by using symbolic algorithms written in Mathematica. Floquet theory was used to derive solutions of the linearized equation up to 17th order in e. In this way precise analytical expressions for the stability of the system were obtained. Then, applying the Courant and Snyder transformation to the nonlinear equation, algebraic solutions of seventh order in z and e were derived using the method of Poincaré–Lindstedt. The enormous amount of necessary computations were performed by extensive use of symbolic programming. We developed automated and highly modularized algorithms in order to master the problem of ordering an increasing number of algebraic terms originating from high order perturbation theory.     

天文望远镜子镜超磁致伸缩驱动器驱动模型及参数识别

采用超磁致伸缩驱动器(GMA,Giant Magnetostrictive Actuator)驱动拼接镜面天文望远镜子镜,并建立GMA精密位移驱动准确模型。针对传统遗传算法在辨识GMA位移模型参数时容易过早收敛到次优解的问题,提出了基于分层遗传算法(HGA,HierarchicalGenetic Algorithm)的参数识别方法,其结果在改善驱动位移模拟准确性和提高求解初期种群多样性,相对于其他算法都有较大程度的提高。研究通过与实验结果对比验证了所提出参数辨识方法和建立模型的有效性,位移预测值和实验值的平均偏离值不超过满行程的1.3%。研究还就驱动磁场强度幅值和预应力等因素对滞回、损耗、饱和磁化强度、饱和磁致伸缩量等模型参数的影响进行了分析。     

A new computational fluid dynamics code I: Fyris Alpha

A new hydrodynamics code aimed at astrophysical applications has been developed. The new code and algorithms are presented along with a comprehensive suite of test problems in one, two, and three dimensions. The new code is shown to be robust and accurate, equalling or improving upon a set of comparison codes. Fyris Alpha will be made freely available to the scientific community.     

On the Photometric Accuracy of RHESSI Imaging and Spectrosocopy

We compare the photometric accuracy of spectra and images in flares observed with the Ramaty High-Energy Solar Spectroscopic Imager (RHESSI) spacecraft. We test the accuracy of the photometry by comparing the photon fluxes obtained in different energy ranges from the spectral-fitting software SPEX with those fluxes contained in the images reconstructed with the Clean, MEM, MEM-Vis, Pixon, and Forward-fit algorithms. We quantify also the background fluxes, the fidelity of source geometries, and spatial spectra reconstructed with the five image reconstruction algorithms. We investigate the effects of grid selection, pixel size, field of view, and time intervals on the quality of image reconstruction. The detailed parameters and statistics are provided in an accompanying CD-ROM and web page. We find that Forward-fit, Pixon, and Clean have a robust convergence behavior and a photometric accuracy in the order of a few percent, while MEM does not converge optimally for large degrees of freedom (for large field of view and/or small pixel sizes), and MEM-Vis suffers in the case of time-variable sources. This comparative study documents the current status of the RHESSI spectral and imaging software, one year after launch. Supplementary material to this paper is available in electronic form at http://dx.doi.org/10.1023/B:SOLA.0000021801.83038.aa     

Topocentric orbit determination: Algorithms for the next generation surveys

The process of calculating a good orbit from astrometric observations of the same object involves three main steps: preliminary orbit determination, least squares orbit fitting, and quality control assessing the orbit's uncertainty and reliability. For the next generation sky surveys, with much larger number density of observations, new algorithms, or at least substantial revisions of the classical ones, are needed. The classical theory of preliminary orbit algorithms was incomplete in that the consequences of the topocentric correction had not been fully studied. We show that it is possible to rigorously account for topocentric observations and that this correction may increase the number of alternate preliminary orbits without impairing the overall performance. We have developed modified least squares algorithms including the capability of fitting the orbit to a reduced number of parameters. The restricted fitting techniques can be used to improve the reliability of the orbit computing procedure when the observed arcs have small curvature. False identification (where observations of different objects are incorrectly linked together) can be discarded with a quality control on the residuals and a ‘normalization’ procedure removing duplications and contradictions. We have tested our algorithms on two simulations based on the expected performance of Pan-STARRS—one of the next generation all-sky surveys. The results confirm that large sets of discoveries can be handled very efficiently resulting in good quality orbits. In these tests we lost only 0.6 to 1.3% of the possible objects, with a false identification rate in the range 0.02 to 0.06%.