The general solution of the HENON–HEILES problem

The general solution of the Henon–Heiles system is approximated inside a domain of the (x, C) of initial conditions (C is the energy constant). The method applied is that described by Poincaré as ‘the only “crack” permitting penetration into the non-integrable problems’ and involves calculation of a dense set of families of periodic solutions that covers the solution space of the problem. In the case of the Henon–Heiles potential we calculated the families of periodic solutions that re-enter after 1–108 oscillations. The density of the set of such families is defined by a pre-assigned parameter ε (Poincaré parameter), which ascertains that at least one periodic solution is computed and available within a distance ε from any point of the domain (x, C) for which the approximate general solution computed. The approximate general solution presented here corresponds to ε = 0.07. The same solution is further improved by “zooming” into four square sub-domain of (x, C), i.e. by computing sufficient number of families that reduce the density parameter to ε = 0.003. Further zooming to reduce the density parameter, say to ε = 10⁻⁶, or even smaller, although easily performable in both areas occupied by stable as well as unstable solutions, was found unnecessary. The stability of all members of each and all families computed was calculated and presented in this paper for both the large solution domain and for the sub-domains. The correspondence between areas of the approximate general solution occupied by stable periodic solutions and Poincaré sections with well-aligned section points and also correspondence between areas occupied by unstable solutions and Poincaré sections with randomly scattered section points is shown by calculating such sections. All calculations were performed using the Runge-Kutta (R-K) 8th order direct integration method and the large output received, consisting of many thousands of families is saved as “Atlas of the General Solution of the Henon–Heiles Problem,” including their stability and is available at request. It is concluded that approximation of the general solution of this system is straightforward and that the chaotic character of its Poincaré sections imposes no limitations or difficulties.     

Prediction of permafrost distribution on the Qinghai-Tibet Plateau in the next 50 and 100 years

The Qinghai-Tibet Plateau(QTP)has the highestand largest permafrost coverage in the low-middlelatitudes all over the world.With the progress ofChina’s Western Development,human activities areincreasing significantly on the QTP.For instance,theQinghai-Tibet Railway project started in June2001iscurrently under construction,but permafrost problemwill be one of the critical factors for the engineeringconstruction.Frost heave and permafrost settlementmay destroy engineering construction[1,2]…     

Numeric examination of multivariate soil samples

Numerical methods for the examination of multivariate soil samples are presented in geometric terms. Techniques of coordinate representation by principal components, by nonmetric scaling, and by a new method are discussed, as are techniques for agglomerative hierarchic cluster analysis. These are illustrated by two sets of previously published data.     

月际地震趋势的数值预测法

考虑到目前地震月趋势以模糊用语进行预测的缺陷,本文提出采用数值预测法能更好地适应社会需求. 这种方法是基于地震有自律现象,通过建立非线性的数学模型予以实现的. 模型试验结果表明,我国大陆地震活动存在有7~8个月左右的循环结构,逐月比较预测与实况的震级误差平均低于0.2级,因而该方法比经验性预报更适宜社会的实际利用.      

锦屏电站坝厂区卸荷岩体力学参数研究

选择具有代表性的区块,根据结构面的性状和规模拟定模型层次和尺寸,建立岩体数值仿真模型,通过计算机数值仿真,采用卸荷非线性力学理论对锦屏电站坝厂区岩体进行卸荷岩体宏观力学特性及参数的数值分析;同时,用RMR法和BP神经网络法对岩体宏观力学特性及参数进行分析,综合确定岩体力学参数,为设计部门提供设计参考依据.     

关于"太阳线性无力场评注和快速傅氏分析法的应用"的评论

“太阳线性无力场评注和快速傅氏分析法的应用”一文对太阳线性无力场的工作做了一些评注,在此基础上对快速傅立叶方法的应用提出了改进的计算方法．该文的某些观点值得商榷,有必要对其中存在的问题予以澄清．另外,对该文关于快速傅氏分析法的工作从理论的角度提出看法．     

DInSAR技术对不同方位形变的敏感性研究

以DEM数据为假想的地面目标,只考虑距离对相位的影响,模拟竖直向、距离向和方位向形变的干涉纹图,从而研究DInSAR技术对空间不同方位形变的敏感性。在所有模拟参数和形变位移大小都相同的情况下,三个不同方位形变所产生的相位从0到2π变化的完整干涉环的数目是各不相同的,揭示DInSAR技术对不同方位地表形变的敏感性存在差异,且敏感性由大到小依次为:竖直向、距离向和方位向。     

GPS卫星轨道数值积分与广播星历及IGS精密星历的比较

本文采用作者自编的SPPORB IT程序,对GPS卫星轨道的运动方程进行Adam s数值积分求解,同时利用广播星历计算卫星轨道坐标,然后将两者结果同IGS精密星历提供的卫星坐标进行比较,并探讨其轨道误差,计算结果显示广播星历与精密星历差值在2m左右,而数值积分与精密星历的差值在2 cm左右,进一步的分析表明前者误差较大是没有考虑卫星所受的太阳光压、日月引力等影响,而后者考虑了这些影响。鉴于IGS提供的是地固系坐标,而本文数值积分是在惯性系坐标系下进行的,因此本文还举例对惯性坐标系和地固系之间的坐标转换进行了描述。最后,通过实例说明SPPORB IT程序的稳定性以及Adam s数值积分方法的有效性。     

Observations and modelling of the travel time delay and leading negative phase of the 16 September 2015 Illapel,Chile tsunami

The systematic discrepancies in both tsunami arrival time and leading negative phase (LNP) were identified for the recent transoceanic tsunami on 16 September 2015 in Illapel, Chile by examining the wave characteristics from the tsunami records at 21 Deep-ocean Assessment and Reporting of Tsunami (DART) sites and 29 coastal tide gauge stations. The results revealed systematic travel time delay of as much as 22 min (approximately 1.7％ of the total travel time) relative to the simulated long waves from the 2015 Chilean tsunami. The delay discrepancy was found to increase with travel time. It was difficult to identify the LNP from the near-shore observation system due to the strong background noise, but the initial negative phase feature became more obvious as the tsunami propagated away from the source area in the deep ocean. We determined that the LNP for the Chilean tsunami had an average duration of 33 min, which was close to the dominant period of the tsunami source. Most of the amplitude ratios to the first elevation phase were approximately 40％, with the largest equivalent to the first positive phase amplitude. We performed numerical analyses by applying the corrected long wave model, which accounted for the effects of seawater density stratification due to compressibility, self-attraction and loading (SAL) of the earth, and wave dispersion compared with observed tsunami waveforms. We attempted to accurately calculate the arrival time and LNP, and to understand how much of a role the physical mechanism played in the discrepancies for the moderate transoceanic tsunami event. The mainly focus of the study is to quantitatively evaluate the contribution of each secondary physical effect to the systematic discrepancies using the corrected shallow water model. Taking all of these effects into consideration, our results demonstrated good agreement between the observed and simulated waveforms. We can conclude that the corrected shallow water model can reduce the tsunami propagation speed and reproduce the LNP, which is observed for tsunamis that have propagated over long distances frequently. The travel time delay between the observed and corrected simulated waveforms is reduced to <8 min and the amplitude discrepancy between them was also markedly diminished. The incorporated effects amounted to approximately 78％ of the travel time delay correction, with seawater density stratification, SAL, and Boussinesq dispersion contributing approximately 39％, 21％, and 18％, respectively. The simulated results showed that the elastic loading and Boussinesq dispersion not only affected travel time but also changed the simulated waveforms for this event. In contrast, the seawater stratification only reduced the tsunami speed, whereas the earth's elasticity loading was responsible for LNP due to the depression of the seafloor surrounding additional tsunami loading at far-field stations. This study revealed that the traditional shallow water model has inherent defects in estimating tsunami arrival, and the leading negative phase of a tsunami is a typical recognizable feature of a moderately strong transoceanic tsunami. These results also support previous theory and can help to explain the observed discrepancies.     

实时修复双频原始载波相位观测值周跳的虚拟值探测法

利用各频率观测值间物理上的相关性,采用数学变换得到一个含有双频原始载波观测信息的虚拟观测值,与双频数据按长波长特性进行多频组合来放大周跳。对探测出的周跳候选值利用Melbourne-Wubbena组合及多项式拟合作为两个判别条件来进行甄选,达到了实时修复双频原始载波相位观测值周跳的目的。