On the efficiency of Runge-Kutta-Nystrom methods with interpolants for solving equations of the form Y″ = F(T,Y, Y′) over short timespans

Runge-Kutta-Nystrom (RKN) codes for the solution of the initial value problem for the general second order differential system have been developed recently, although the methodology on which they are based was known many years ago. In this paper we try to examine the efficiency of several known general Runge-Kutta-Nystrom (GRKN) methods by posing some criteria of cost and accuracy. These methods supplied with the corresponding interpolants, have been applied to some problems of Celestial Dynamics. The results obtained show that these codes have a good response in the approximation of the solution of these problems.Department of Mechanics     

'Stokes imaging' of the accretion region in magnetic cataclysmic variables — I. Conception and realization

Modelling the polarized cyclotron emission from magnetic cataclysmic variables has been a pivotal technique for determining the structure of the accretion zones on the white dwarf. To date, model solutions have been obtained from trial fits to the intensity and polarization data, which have been constructed from emission regions (for example arcs and spots) put in by hand. These models were all inferred indirectly from arguments based on the polarization and X-ray light curves.   We present a more analytical and objective technique using optimization by a genetic algorithm, Tikhonov regularization and Powell's method that robustly models the details of polarized emission.   To demonstrate the success of this technique, we show the results of several simulations in which we calculated the intensity and polarization curves from arbitrarily shaped emission regions on the surface of a sphere and then applied our code to these curves to recover the original test data. We also show how adding artificial noise affects the outcome of the optimization technique.     

TAOS – The Taiwanese‐American Occultation Survey

The Taiwanese‐American Occultation Survey (TAOS) seeks to determine the number and size spectrum for small (∼3 km) bodies in the Kuiper Belt. This will be accomplished by searching for the brief occultations of bright stars (R ∼ 14) by these objects. We have designed and built a special purpose photometric monitoring system for this purpose. TAOS comprises four 50 cm telescopes, each equipped with a 2048 × 2048 pixel CCD camera, in a compact array located in the central highlands of Taiwan. TAOS will monitor up to 2 000 stars at 5 Hz. The system went into scientific operation in the autumn of 2005. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

我国西部特殊景观区化探方法研究进展

西部特殊景观区的化探方法研究一直是中国化探界的一个研究热点和难点.在岩石出露、水系发育地区可以沿用传统的水系沉积物化探方法,但在覆盖景观区,常规化探方法效果并不理想.目前,谢学锦和王学求所提出的深穿透地球化学方法,经过一系列的实验研究,证明其能在覆盖区达到快速有效地圈定战略靶区的作用,具有广泛的应用前景.要做好西部特殊景观区的化探工作,化探科研人员必需采取新方法、新思路,继续系统地开展化探方法技术研究,通过不懈的努力最终找到一套适合中国西部特殊景观区特别是覆盖区的行之有效的化探方法.     

Optimizing point-source parameters for scanning satellite surveys

We describe a method for deriving the position and flux of point and compact sources observed by a scanning survey mission. Results from data simulated to test our method are presented, which demonstrate that at least a 10-fold improvement is achievable over that of extracting the image parameters, position and flux, from the equivalent data in the form of pixel maps. Our method achieves this improvement by analysing the original scan data and performing a combined, iterative solution for the image parameters. This approach allows for a full and detailed account of the point-spread function (PSF), or beam profile, of the instrument. Additionally, the positional information from different frequency channels may be combined to provide the flux-detection accuracy at each frequency for the same sky position. Ultimately, a final check and correction of the geometric calibration of the instrument may also be included. The Planck mission was used as the basis for our simulations, but our method will be beneficial for most scanning satellite missions, especially those with non-circularly symmetric PSFs.     

SECOND-ORDER SOLUTION FOR THE ZONAL PROBLEM OF SATELLITE THEORY

The analytical solution for the perturbations of an artificial satellite due to the zonal part of the geopotential is presented. The Hamiltonian is fully normalized up to the second order by a single averaging transformation and the generating function is given explicitly. The formulas allow an arbitrarily high degree of geopotential harmonics to be included. The transformation from mean to osculating variables or vice versa is performed by means of a numerical method proposed by the author in a previous paper (Breiter,1997): periodic perturbations are computed by means of a Runge-Kutta method of order 2 instead of being explicitly derived from a generator. This revised version was published online in July 2006 with corrections to the Cover Date.     

Seismic Inference using Genetic Algorithms

A flood of reliable seismic data will soon arrive. The migration to largertelescopes on the ground may free up 4-m class instruments for multi-sitecampaigns, and several forthcoming satellite missions promise to yieldnearly uninterrupted long-term coverage of many pulsating stars. We willthen face the challenge of determining the fundamental properties of thesestars from the data, by trying to match them with the output of ourcomputer models. The traditional approach to this task is to make informedguesses for each of the model parameters, and then adjust them iterativelyuntil an adequate match is found. The trouble is: how do we know that oursolution is unique, or that some other combination of parameters will notdo even better? Computers are now sufficiently powerful and inexpensivethat we can produce large grids of models and simply compare all ofthem to the observations. The question then becomes: what range ofparameters do we want to consider, and how many models do we want tocalculate? This can minimize the subjective nature of the process, but itmay not be the most efficient approach and it may give us a false sense ofsecurity that the final result is correct, when it is really justoptimal. I discuss these issues in the context of recent advances inthe asteroseismological analysis of white dwarf stars.     

A modified peak‐bagging technique for fitting low‐𝓁 solar p‐modes

We introduce a modified version of a standard power spectrum ‘peak‐bagging’ technique which is designed to gain some of the advantages that fitting the entire low‐degree p‐mode power spectrum simultaneously would bring, but without the problems involved in fitting a model incorporating many hundreds of parameters. Employing Monte‐Carlo simulations we show that by using this modified fitting code it is possible to determine the true background level in the vicinity of the p‐mode peaks. In addition to this we show how small biases in other mode parameters, which are related to inaccurate estimates of the true background, are also consequently removed. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)