N-body simulation for self-gravitating collisional systems with a new SIMD instruction set extension to the x86 architecture, Advanced Vector eXtensions

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.     

Determination of Meteoroid Orbits and Spatial Fluxes by Using High-Resolution All-Sky CCD Cameras

By using high-resolution, low-scan-rate, all-sky CCD cameras, the SPanish Meteor Network (SPMN) is currently monitoring meteor and fireball activity on a year round basis. Here are presented just a sampling of the accurate trajectory, radiant and orbital data obtained for meteors imaged simultaneously from two SPMN stations during the continuous 2006–2007 coverage of meteor and fireball monitoring. Typical astrometric uncertainty is 1–2 arc min, while velocity determination errors are of the order of 0.1–0.5 km/s, which is dependent on the distance of each event to the station and its particular viewing geometry. The cameras have demonstrated excellent performance for detecting meteor outbursts. The recent development of automatic detection software is also providing real-time information on the global meteor activity. Finally, some examples of the all-sky CCD cameras applications for detecting unexpected meteor activity are given.     

Energy and stability in the Full Two Body Problem

The conditions for relative equilibria and their stability in the Full Two Body Problem are derived for an ellipsoid–sphere system. Under constant angular momentum it is found that at most two solutions exist for the long-axis solutions with the closer solution being unstable while the other one is stable. As the non-equilibrium problem is more common in nature, we look at periodic orbits in the F2BP close to the relative equilibrium conditions. Families of periodic orbits can be computed where the minimum energy state of one family is the relative equilibrium state. We give results on the relative equilibria, periodic orbits and dynamics that may allow transition from the unstable configuration to a stable one via energy dissipation.      

On the Distance Function Between Two Keplerian Elliptic Orbits

The problem of finding critical points of the distance function between two Keplerian elliptic orbits is reduced to the determination of all real roots of a trigonometric polynomial of degree 8. The coefficients of the polynomial are rational functions of orbital parameters. Using computer algebra methods we show that a polynomial of a smaller degree with such properties does not exist. This fact shows that our result cannot be improved and it allows us to construct an optimal algorithm to find the minimal distance between two Keplerian orbits. This revised version was published online in July 2006 with corrections to the Cover Date.     

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稀少控制点异轨立体卫星影像区域网平差应用研究

结合PixelGrid软件应用,分析了异轨立体卫星影像区域网平差原理。在稀少控制点情况下,针对大范围高分辨率立体卫星遥感影像的区域网平差处理,提出了5种解决方案,并进行了实验分析,得出明确的结论。     

联合GRACE卫星轨道及距离变率数据反演地球重力场方法研究

基于动力学法,研究联合GRACE卫星精密轨道及距离变率数据反演地球重力场的方法,该方法可对重力位系数及卫星初始状态误差同时进行有效校正。通过对各观测值模拟不同的随机误差,研究了不同精度观测值联合反演所能达到的精度,以及用相同精度的观测值进行联合反演时不同采样率对反演结果的影响,模拟计算结果表明：联合反演模式下,当距离变率精度为1 μm/s,卫星位置精度为2~3 cm,速度精度为0.1~0.5 mm/s时,加速度计精度为(1.0×10 ^-10~1.0×10^-9 m/s ²比较适合;将距离变率精度由1 um/s提高到0.1 um/s时,反演精度可获得相应提高;在观测值精度一定的情况下,联合反演算法宜采用5 s采样率。     

Distance Between Two Arbitrary Unperturbed Orbits

In the paper by Kholshevnikov and Vassilie, 1999, (see also references therein) the problem of finding critical points of the distance function between two confocal Keplerian elliptic orbits (hence finding the distance between them in the sense of set theory) is reduced to the determination of all real roots of a trigonometric polynomial of degree eight. In non-degenerate cases a polynomial of lower degree with such properties does not exist. Here we extend the results to all possible cases of ordered pairs of orbits in the Two–Body–Problem. There are nine main cases corresponding to three main types of orbits: ellipse, hyperbola, and parabola. Note that the ellipse–hyperbola and hyperbola–ellipse cases are not equivalent as we exclude the variable marking the position on the second curve. For our purposes rectilinear trajectories can be treated as particular (not limiting) cases of elliptic or hyperbolic orbits.     

Extension of the Kepler problem towards minimization of energy and gravity softening

The classical Kepler Problem consists in the determination of the relative orbital motion of a secondary body (planet) with respect to the primary body (Sun), for a given time. However, any natural system tends to have minimum energy and is subjected to differential gravitational or tidal forces (called into play mainly due to the finite size and deformability of the secondary body). We formulate the Kepler Problem taking into account the finite size of the secondary body and consider an approximation which tends towards minimum energy orbits, by increasing the dimensionality of the problem. This formulation leads to a conceivable natural explanation of the fact that the planetary orbits are characterized by small eccentricities.     

Ejection-collision orbits with the more massive primary in the planar elliptic restricted three body problem

The main goal of this paper is to give an approximation to initial conditions for ejection-collision orbits with the more massive primary, in the planar elliptic restricted three body problem when the mass parameter µ and the eccentricity e are small enough. The proof is based on a regularization of variables and a perturbation of the two body problem.This work was partially supported by DGICYT grant number PB90-0695.