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1.
An efficient algorithm is presented for the solution of Kepler's equationf(E)=E–M–e sinE=0, wheree is the eccentricity,M the mean anomaly andE the eccentric anomaly. This algorithm is based on simple initial approximations that are cubics inM, and an iterative scheme that is a slight generalization of the Newton-Raphson method. Extensive testing of this algorithm has been performed on the UNIVAC 1108 computer. Solutions for 20 000 pairs of values ofe andM show that for single precision (10–8) 42.0% of the cases require one iteration, 57.8% two and 0.2% three. For double precision (10–18) one additional iteration is required. Single- and double-precision FORTRAN subroutines are available from the author.  相似文献   

2.
《New Astronomy》2007,12(3):169-181
The main performance bottleneck of gravitational N-body codes is the force calculation between two particles. We have succeeded in speeding up this pair-wise force calculation by factors between 2 and 10, depending on the code and the processor on which the code is run. These speed-ups were obtained by writing highly fine-tuned code for x86_64 microprocessors. Any existing N-body code, running on these chips, can easily incorporate our assembly code programs.In the current paper, we present an outline of our overall approach, which we illustrate with one specific example: the use of a Hermite scheme for a direct N2 type integration on a single 2.0 GHz Athlon 64 processor, for which we obtain an effective performance of 4.05 Gflops, for double-precision accuracy. In subsequent papers, we will discuss other variations, including the combinations of N log N codes, single-precision implementations, and performance on other microprocessors.  相似文献   

3.
An algorithm of an automatic search for HI shells is presentedand results of identifications in the Leiden-DwingelooHI survey are shown. An identification algorithm searches forlocal minima in channel maps, then creates 3-dimensional objects,HI holes. There is no a priori constraint on the shape of an HI hole, only the dimension criterion: dimensions of the structuremust lie in a preselected interval.When this algorithm is applied to the Leiden-Dwingeloo HI survey,it finds about 1000 structures, which are seen in 4 or more consecutivevelocity channels (Δ v ≥ 4 kms-1. A total energy contained in all structures in the Milky Way is of theorder of 1055 erg, which is less than the energy correspondingto the observed SNR. 80% of the energy contained in holes resides at low galactic z-coordinates, |z|<2 kpc.  相似文献   

4.
We present a study of the dynamic range limitations in images produced with the proposed Square Kilometre Array (SKA) using the Cotton-Schwab CLEAN algorithm for data processing. The study is limited to the case of a small field of view and a snap-shot observation. A new modification of the Cotton-Schwab algorithm involving optimization of the position of clean components is suggested. This algorithm can reach a dynamic range as high as 106 even if the point source lies between image grid points, in contrast to about 103 for existing CLEAN-based algorithms in the same circumstances. It is shown that the positional accuracy of clean components, floating point precision and the w-term are extremely important at high dynamic range. The influence of these factors can be reduced if the variance of the gradient of the point spread function is minimized during the array design.  相似文献   

5.
We present a high-performance N-body code for self-gravitating collisional systems accelerated with the aid of a new SIMD instruction set extension of the x86 architecture: Advanced Vector eXtensions (AVX), an enhanced version of the Streaming SIMD Extensions (SSE). With one processor core of Intel Core i7-2600 processor (8 MB cache and 3.40 GHz) based on Sandy Bridge micro-architecture, we implemented a fourth-order Hermite scheme with individual timestep scheme (Makino and Aarseth, 1992), and achieved the performance of ∼20 giga floating point number operations per second (GFLOPS) for double-precision accuracy, which is two times and five times higher than that of the previously developed code implemented with the SSE instructions (Nitadori et al., 2006b), and that of a code implemented without any explicit use of SIMD instructions with the same processor core, respectively. We have parallelized the code by using so-called NINJA scheme (Nitadori et al., 2006a), and achieved ∼90 GFLOPS for a system containing more than N = 8192 particles with 8 MPI processes on four cores. We expect to achieve about 10 tera FLOPS (TFLOPS) for a self-gravitating collisional system with N ∼ 105 on massively parallel systems with at most 800 cores with Sandy Bridge micro-architecture. This performance will be comparable to that of Graphic Processing Unit (GPU) cluster systems, such as the one with about 200 Tesla C1070 GPUs (Spurzem et al., 2010). This paper offers an alternative to collisional N-body simulations with GRAPEs and GPUs.  相似文献   

6.
The apparatus of a correlation gamma function is used to analyze a sample of 2dFGRS galaxies. We suggest a modified gamma-function algorithm with nonintersecting working spheres, which ensures that the counts are independent at each step. The method of nonintersecting spheres has revealed a change in the regime of clustering (a break of the gamma function) on a scale of 10–16h?1 Mpc (H0 = 65 km s?1 Mpc?1). The standard method yields a scale of 30h?1 Mpc. An artificial distribution is used as an example to show that, in some cases, the modified algorithm is more responsive to a mixture of distributions with various properties than the standard method.  相似文献   

7.
Accuracy measures are derived for the proper relative extrema in the separation distance function for co-periodic Kepler orbits. The conventional approach involves two numerical iterative processes: the method for solving Kepler’s equation for the eccentric anomaly, and the Newton–Raphson method for identifying times of the extrema. The sensitivity of the accuracy of the solution to the conditioning of the case is determined for stress tests including sequences of cases approaching a constant, then vanishing, separation. Invariance under interchanged satellite labels, single- and double-precision codes, and condition number estimates are compared to determine the number of justifiable digits.  相似文献   

8.
毫秒脉冲星的自转频率非常稳定,提供了一种独立的基于遥远自然天体并能持续数百万乃至数十亿年的时间基准,具有稳定性强、运行时间长、服务范围广等特点.为了减弱毫秒脉冲星计时观测中各种高斯噪声对脉冲星时的影响,研究了一种基于双谱滤波的综合脉冲星时构建算法,处理分析了国际脉冲星计时阵(International Pul-sar Timing Array,IPTA)最新发布的4颗毫秒脉冲星(PSR J0437-4715、J0613-0200、J1713+0747和J1909-3744)的观测数据,分析了不同时间尺度综合脉冲星时的稳定性,并与构成国际原子时(International Atomic Time,TAI)的4家授时单位原子钟稳定性进行了比较.结果表明:双谱滤波算法能够较好地抑制观测噪声,提高综合脉冲星时的稳定性.相比于经典加权算法,综合脉冲星时1 yr、10 yr稳定度从7.77×10-14、8.56×10-16分别提高到1.50×10-14、3.50×10-16,单脉冲星时稳定性的提升也类似.同时发现,综合脉冲星时稳定性在5 yr及以上时间尺度上优于原子钟稳定性,可用于改善当前原子时的长期稳定性.  相似文献   

9.
We present and discuss the characteristics and performance, both in term of computational speed and precision, of a numerical code which integrates the equation of motions of N ‘particles’ interacting via Newtonian gravitation and move in an external galactic smooth field. The force evaluation on every particle is done by mean of direct summation of the contribution of all the other system’s particles, avoiding truncation error. The time integration is done with second-order and sixth-order symplectic schemes. The code, NBSymple, has been parallelized twice, by mean of the Compute Unified Device Architecture (CUDA) to make the all-pair force evaluation as fast as possible on high-performance Graphic Processing Units NVIDIA TESLA C1060, while the O(N) computations are distributed on various CPUs by mean of OpenMP Application Program. The code works both in single-precision floating point arithmetics or in double precision. The use of single-precision allows the use of the GPU performance at best but, of course, limits the precision of simulation in some critical situations. We find a good compromise in using a software reconstruction of double-precision for those variables that are most critical for the overall precision of the code. The code is available on the web site astrowww.phys.uniroma1.it/dolcetta/nbsymple.html.  相似文献   

10.
In this paper a slightly different approach is proposed for the process of determining the functions S m and H m * of the algorithm of the canonical version of Hori method. This process will be referred to as integration theory of the mth order equation of the method. It will be shown that the ordinary differential equation with an auxiliary parameter t * as independent variable, introduced through Hori auxiliary system, can be replaced by a partial differential equation in the time t. In this way, the mth order equation of the algorithm assumes a form very similar to the one of other perturbation methods. In virtue of this new approach of the integration theory for Hori method, Lagrange's variational equations introduced by Sessin are revised. As an example, the Duffing equation is solved through this new approach.  相似文献   

11.
Doyle  J. G.  Banerjee  D.  Perez  M. E. 《Solar physics》1998,181(1):91-101
Line-width measurements of the coronal ion Siviii confirm earlier observations which show an increase in the non-thermal velocity above the solar limb. The present data, taken at the equatorial limb, show an increase from 24 km s-1 at the limb to 28 km s-1 some 25000 km above the limb. The electron density as measured from the Siviii line pair shows a decrease from 3.5 × 108 cm-3 to 1.8 × 108 cm-3 over the same distance. These data imply that the non-thermal velocity is inversely proportional to the quadratic root of the electron density, in excellent agreement with that predicted for undamped radially propagating Alfvén waves.  相似文献   

12.
An improved method of image segmentation is introduced. The object-tracking algorithm, originally developed by Sobotka, Brandt, and Simon (Astron. Astrophys. 328, 682, 1997) is modified with special attentions on splitting and merging of umbral dots (UDs), definition of the umbral boundary, and the birth-frames and the death-frames of UDs. By applying the new method of image segmentation and the object-tracking algorithm on a 67-min series of white-light images of a large pore (Sobotka et al., Astrophys. J. 511, 436, 1999), the physical characteristics of 20 “resolved” UDs with umbral origin were recorded. The most probable lifetime of the UDs is between 7 and 10 min. Umbral dots show a typical size of about 230 km. Their mean speeds are smaller than 2 km s−1 with a distribution around a value less than 1 km s−1. However, their average velocities are less than 0.8 km s−1. Brighter (fainter) UDs are formed in the brighter (dimmer) region of the pore. There is no correlation between time-averaged area or time-averaged speeds and lifetimes. Also, the time-averaged peak intensities of UDs do not show any well-defined dependence on the corresponding time-averaged areas. It seems that there is a relation between average velocities of UDs and their time-averaged peak intensities, with brighter UDs moving more slowly.  相似文献   

13.
A general algorithm for the determination ofT j (n) andZ j *(n) is deduced. This algorithm is obtained from the general solution of non-homogeneous linear differential equations with variable coefficients in their matricial form. To do this a new functionX *(n) associated withZ *(n) is introduced. Then it is possible to calculateZ *(n) such that it contains secular or mixed secular terms and soT (n) is free from these terms.  相似文献   

14.
Many problems in galactic dynamics require computer speeds orders of magnitude larger than what can be achieved on current single-processor machines. In the near future such speeds are likely to become available through computer architectures based on large-scale, fine-grained parallelism. An example of a highly parallel computer is the Connection Machine, with up to 65,636 processors. We have benchmarked gravitationalN-body algorithms on the Connection Machine, and compared those with similar benchmarks which we have obtained on more traditional vector supercomputers. Our conclusions are: (1) The direct summation algorithm, with of orderN 2 interactions forN particles, can be made to run with high efficiency on either type of computer. As a result, the Connection Machine clearly wins in speed over all supercomuters tested, with the exception of an 8-processor ETA, which shows a comparable performance. (2) A more efficient tree algorithm reduces the growth of the number of interactions fromN 2 toN logN. However, the greater complexity of this algorithm causes a considerable degradation of efficiency, by a factor which is larger on the Connection Machine than on vector supercomputers. As a result, out tree code runs at comparable speeds on both types of machines, with the notable exception of the 8-processor ETA, which has an extrapolated speed for running our tree code which is higher than any of the other machines we have tested.  相似文献   

15.
Nonlinear dynamical analysis and the control problem for a displaced orbit above a planet are discussed. It is indicated that there are two equilibria for the system, one hyperbolic (saddle) and one elliptic (center), except for the degenerate h z max, a saddle-node bifurcation point. Motions near the equilibria for the nonresonance case are investigated by means of the Birkhoff normal form and dynamical system techniques. The Kolmogorov–Arnold–Moser (KAM) torus filled with quasiperiodic trajectories is measured in the τ 1 and τ 2 directions, and a rough algorithm for calculating τ 1 and τ 2 is proposed. A general iterative algorithm to generate periodic Lyapunov orbits is also presented. Transitions in the neck region are demonstrated, respectively, in the nonresonance, resonance, and degradation cases. One of the important contributions of the paper is to derive necessary and sufficiency conditions for stability of the motion near the equilibria. Another contribution is to demonstrate numerically that the critical KAM torus of nontransition is filled with the (1,1)-homoclinic orbits of the Lyapunov orbit.  相似文献   

16.
The goal of this study is to develop an efficient and accurate model for using visible–near infrared reflectance spectra to estimate the abundance of minerals on the lunar surface. Previous studies using partial least squares (PLS) and genetic algorithm–partial least squares (GA–PLS) models for this purpose revealed several drawbacks. PLS has two limitations: (1) redundant spectral bands cannot be removed effectively and (2) nonlinear spectral mixing (i.e., intimate mixtures) cannot be accommodated. Incorporating GA into the model is an effective way for selecting a set of spectral bands that are the most sensitive to variations in the presence/abundance of lunar minerals and to some extent overcomes the first limitation. Given the fact that GA–PLS is still subject to the effect of nonlinearity, here we develop and test a hybrid partial least squares–back propagation neural network (PLS–BPNN) model to determine the effectiveness of BPNN for overcoming the two limitations simultaneously. BPNN takes nonlinearity into account with sigmoid functions, and the weights of redundant spectral bands are significantly decreased through the back propagation learning process. PLS, GA–PLS and PLS–BPNN are tested with the Lunar Soil Characterization Consortium dataset (LSCC), which includes VIS–NIR reflectance spectra and mineralogy for various soil size fractions and the accuracy of the models are assessed based on R2 and root mean square error values. The PLS–BPNN model is further tested with 12 additional Apollo soil samples. The results indicate that: (1) PLS–BPNN exhibits the best performance compared with PLS and GA–PLS for retrieving abundances of minerals that are dominant on the lunar surface; (2) PLS–BPNN can overcome the two limitations of PLS; (3) PLS–BPNN has the capability to accommodate spectral effects resulting from variations in particle size. By analyzing PLS beta coefficients, spectral bands selected by GA, and the loading curve of the latent variable with the largest weight in PLS–BPNN, we conclude that spectral information incorporated into the three models is directly derived from the diagnostic absorption bands associated with the individual minerals. It is concluded that the PLS–BPNN model should be applicable to both Clementine UV–VIS–NIRs and Moon Mineralogy Mapper (M3) data.  相似文献   

17.
An automated cloud tracking algorithm is applied to Cassini Imaging Science Subsystem high-resolution apoapsis images of Saturn from 2005 and 2007 and moderate resolution images from 2011 and 2012 to define the near-global distribution of zonal winds and eddy momentum fluxes at the middle troposphere cloud level and in the upper troposphere haze. Improvements in the tracking algorithm combined with the greater feature contrast in the northern hemisphere during the approach to spring equinox allow for better rejection of erroneous wind vectors, a more objective assessment at any latitude of the quality of the mean zonal wind, and a population of winds comparable in size to that available for the much higher contrast atmosphere of Jupiter. Zonal winds at cloud level changed little between 2005 and 2007 at all latitudes sampled. Upper troposphere zonal winds derived from methane band images are ～10 m s?1 weaker than cloud level winds in the cores of eastward jets and ～5 m s?1 stronger on either side of the jet core, i.e., eastward jets appear to broaden with increasing altitude. In westward jet regions winds are approximately the same at both altitudes. Lateral eddy momentum fluxes are directed into eastward jet cores, including the strong equatorial jet, and away from westward jet cores and weaken with increasing altitude on the flanks of the eastward jets, consistent with the upward broadening of these jets. The conversion rate of eddy to mean zonal kinetic energy at the visible cloud level is larger in eastward jet regions (5.2 × 10?5 m2 s?3) and smaller in westward jet regions (1.6 × 10?5 m2 s?3) than the global mean value (4.1 × 10?5 m2 s?3). Overall the results are consistent with theories that suggest that the jets and the overturning meridional circulation at cloud level on Saturn are maintained at least in part by eddies due to instabilities of the large-scale flow near and/or below the cloud level.  相似文献   

18.
A numerical algorithm using a two stage, two level difference scheme has been developed to solve the heat transfer equation with nonlinear heat diffusion and bulk energy losses. The algorithm is an extension of the scheme developed by Meek and Norbury (1982). The first stage calculates an intermediate value which is used in a second stage to estimate a new value. The scheme is consistent, second-order convergent in space and almost second order in time. It has been applied to the nonlinear stability and time evolution of thermal structures constituted by optically thin plasmas with solar abundances. The configuration has been assumed to be heated at a rate Tm, cooled at a rate Tn and a thermal conduction coefficient Tk. In particular, the second order analytical approximation considered in previous papers (Ibáñez and Rosenzweig, 1995; Steele and Ibáñez, 1997) has been worked out for arbitrary amplitude of the initial temperature disturbance. Particular cases of interest in Astrophysics are considered.  相似文献   

19.
In the current study, a double-averaged analytical model including the action of the perturbing body’s inclination is developed to study third-body perturbations. The disturbing function is expanded in the form of Legendre polynomials truncated up to the second-order term, and then is averaged over the periods of the spacecraft and the perturbing body. The efficiency of the double-averaged algorithm is verified with the full elliptic restricted three-body model. Comparisons with the previous study for a lunar satellite perturbed by Earth are presented to measure the effect of the perturbing body’s inclination, and illustrate that the lunar obliquity with the value 6.68∘ is important for the mean motion of a lunar satellite. The application to the Mars-Sun system is shown to prove the validity of the double-averaged model. It can be seen that the algorithm is effective to predict the long-term behavior of a high-altitude Martian spacecraft perturbed by Sun. The double-averaged model presented in this paper is also applicable to other celestial systems.  相似文献   

20.
Sunspots are the most conspicuous aspects of the Sun. They have a lower temperature, as compared to the surrounding photosphere; hence, sunspots appear as dark regions on a brighter background. Sunspots cyclically appear and disappear with a 11-year periodicity and are associated with a strong magnetic field ( ～103 G) structure. Sunspots consist of a dark umbra, surrounded by a lighter penumbra. Study of umbra–penumbra area ratio can be used to give a rough idea as to how the convective energy of the Sun is transported from the interior, as the sunspot’s thermal structure is related to this convective medium.An algorithm to extract sunspots from the white-light solar images obtained from the Kodaikanal Observatory is proposed. This algorithm computes the radius and center of the solar disk uniquely and removes the limb darkening from the image. It also separates the umbra and computes the position as well as the area of the sunspots. The estimated results are compared with the Debrecen photoheliographic results. It is shown that both area and position measurements are in quite good agreement.  相似文献   

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