关于控制迭代过程的结束条件

迭代法属于逐次逼近法,应用很广。它是求解函数方程、方程组和微分方程等的一种基本而重要的数值方法。在具体求解时,需要给出控制迭代过程结束的条件。现有的某些计算方法(或数值分析)的教材和书,在论述求解函数方程的计算方案、流程图(或框图)及算法语言程序时,常常将此条件取为相邻两次迭代值xk、xk-1的差小于给定的准确度本文指出这个条件是不完全的,讨论了该条件的正确表达式,由误差估计式给出了控制迭代过程结束条件的五种形式。     

AIPS对综合孔径展源的图象处理

本文介绍了用美国国立射电天文台图象处理软件系统—AIPS对综合孔径VLA观测数据的处理方法,特别是对展源,要得到高质量的图象,在编辑及成图中要注意的事项。作者根据自己的实际工作,总结了用AIPS进行图象处理的经验。     

A SPATIALLY-VARYING PARAMETER MODEL OF AFDC PARTICIPATION: EMPIRICAL ANALYSIS USING THE EXPANSION METHOD*

Spatial variation in the importance of determinants of participation in the Aid to Families with Dependent Children program (AFDC) is investigated for the U.S. Casetti's Expansion Method is applied to the two-dimensional space domain by making the model's parameters a function of state x–y centroids. The spatially-varying parameter model suggests that the black population's association with participation is lowest in the Southeast and Northwest and greatest in the Southwest and Northeast.     

Annual and monthly rainfall data generation schemes

Synthetic annual and monthly rainfall data series are generated by using autoregressive (AR) processes, Thomas-Fiering (TF) model, method of fragments (F) and its modified version (MF), two-tier (TT) model, and a newly developed wavelet (W) approach. It is seen that the W approach is as well in preserving the statistical behavior of the observed data series as the classical annual and monthly hydrological data generation schemes used in this study. The W approach is found even better in replacing some particular characteristics such as the mean of the sequence and correlation between the successive months in the series. It is, therefore, proposed as a new annual and monthly hydrological data generation scheme.     

曲线顶管技术及顶进力分析计算

曲线顶管施工技术以其特有的优势和应用领域,越来越受到重视。总结了国际上常用的曲线顶管施工技术,分别以SS MOLE和Ultimate Method两种具有代表性的工法为例介绍了曲线顶管技术的地层适应性、适用管道直径、应用领域和所能达到的最小曲率半径。对曲线顶管施工中顶进力计算这一重点和难点,给出了曲线顶管顶推力计算公式,并举例说明了曲线段顶推力计算公式的实际应用。     

蒙特卡罗不确定性分析在O3模拟中的初步应用

利用蒙特卡罗不确定性分析方法,分析了嵌套网格空气质量模式系统(NAQPMS/IAP)中154个模式输入变量不确定性对臭氧模拟的影响,量化了模式在北京奥运会期间臭氧模拟的不确定性,并确定出了主要不确定性因子。结果表明:(1)在奥运会期间(2008年8月8日～2008年8月24日),北京城区臭氧模拟的平均不确定性为19ppb,不确定性存在明显的日变化特征,白天不确定性大,夜间不确定性小。(2)在白天,北京城区近地层臭氧模拟最重要的不确定性来源是局地前体物排放,其次是NO2光解系数、风向、北京周边前体物排放和垂直扩散系数。另外,地面约150m以上,对臭氧模拟影响最大的不确定性因子是风向和北京周边前体物排放;夜间,北京城区近地层臭氧模拟的最大不确定性来源是局地NOx排放和垂直扩散系数。     

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.     

Relationship between pulse width and energy in GRB 060124: from X-ray to γ-ray bands

GRB 060124 is the first event that both prompt and afterglow emission were observed simultaneously by the three Swift instruments. Its main peak also triggered Konus-Wind and HETE-II. Therefore, investigation on both the temporal and spectral properties of the prompt emission can be extended to X-ray bands. We perform a detailed analysis on the two well identified pulses of this burst, and find that the pulses are narrower at higher energies, and both X-rays and γ-rays follow the same w–E relation for an individual pulse. However, there is no a universal power-law index of the w–E relation among pulses. We find also that the rise-to-decay ratio r/d seems not to evolve with E and the r/d values are well consistent with that observed in typical GRBs. The broadband spectral energy distribution also suggests that the X-rays are consistent with the spectral behavior of the γ-rays. These results indicate that the X-ray emission tracks the γ-ray emission and the emissions in the two energy bands are likely to be originated from the same physical mechanism.     

A Simple Monte Carlo Method for Locating the Three-dimensional Critical Slip Surface of a Slope

Based on the assumption of the plain-strain problem, various optimization or random search methods have been developed for locating the critical slip surfaces in slope-stability analysis, but none of such methods is applicable to the 3D case. In this paper, a simple Monte Carlo random simulation method is proposed to identify the 3D critical slip surface. Assuming the initial slip to be the lower part of a slip ellipsoid, the 3D critical slip surface is located by means of a minimized 3D safety factor. A column-based 3D slope stability analysis model is used to calculate this factor. In this study, some practical cases of known minimum safety factors and critical slip surfaces in 2D analysis are extended to 3D slope problems to locate the critical slip surfaces. Compared with the 2D result, the resulting 3D critical slip surface has no apparent difference in terms of only cross section, but the associated 3D safety factor is definitely higher.