Chaotic motion of comets in near-parabolic orbit: Mapping approaches     

Jie Liu  Yi-Sui Sun 《Celestial Mechanics and Dynamical Astronomy》1994,60(1):3-28

There exist many comets with near-parabolic orbits in the Solar System. Among various theories proposed to explain their origin, the Oort cloud hypothesis seems to be the most reasonable (Oort, 1950). The theory assumes that there is a cometary cloud at a distance 10³ – 10⁵ AU from the Sun and that perturbing forces from planets or stars make orbits of some of these comets become of near-parabolic type. Concerning the evolution of these orbits under planetary perturbations, we can raise the question: Will they stay in the Solar System forever or will they escape from it? This is an attractive dynamical problem. If we go ahead by directly solving the dynamical differential equations, we may encounter the difficulty of long-time computation. For the orbits of these comets are near-parabolic and their periods are too long to study on their long-term evolution. With mapping approaches the difficulty will be overcome. In another aspect, the study of this model has special meaning for chaotic dynamics. We know that in the neighbourhood of any separatrix i.e. the trajectory with zero frequency of the unperturbed motion of an Hamiltonian system, some chaotic motions have to be expected. Actually, the simplest example of separatrix is the parabolic trajectory of the two body problem which separates the bounded and unbounded motion. From this point of view, the dynamical study on near-parabolic motion is very important. Petrosky's elegant but more abstract deduction gives a Kepler mapping which describes the dynamics of the cometary motion (Petrosky, 1988). In this paper we derive a similar mapping directly and discuss its dynamical characters.  相似文献   

Improvement of S/N ratio of seismic data by hyperbolic filter algorithm     

Xue Hao  Yue Li  Baojun Yang 《世界地质(英文版)》2006,9(1)

This paper deals with the implementation of the hyperbolic filter algorithm for noise suppression of seismic data. Known the velocity of reflection event, utilizes the resemblance of reflection signal in each seismic trace, the hyperbolic filter algorithm is effective in enhance reflection event and suppress the random noise. This algorithm is used to CDP gathers also is compared with the algorithm of τ-p transform. Simulation shows the hyperbolic filter is effective and better than τ-p transform.  相似文献   

Conservative identification of nodal transmissivities: theory,computational experiments and application to the Rharb coastal aquifer (Morocco)     

B. EL MANSOURI  Y. LOUKILI  D. ESSELAOUI 《水文科学杂志》2013,58(3):377-389

Abstract

In order to calculate the transmissivity from the inverse problem corresponding to the groundwater flow in an isotropic horizontal aquifer, a numerical conservative approach is tested. The method deals with triangulation of the domain and applies the conservation of mass to elements of the mesh using the harmonic mean for internodal transmissivities. An optimal sweeping algorithm is used to evaluate nodal transmissivities from one element to another with a minimal relative error accumulation. The practical importance of the method is demonstrated through two synthetic examples representing those experienced in the field, then through application to a Moroccan aquifer. The computed hydraulic head is well fitted to the reference one, which confirms the validity of the identified transmissivity model.  相似文献   

A CPSO-SVM Model for Ultimate Bearing Capacity Determination     

Hong-bo Zhao  Shunde Yin 《Marine Georesources & Geotechnology》2013,31(1):64-75

In this study, the CPSO-SVM models, which combine chaotic system, particle swarm optimization (PSO) and support vector machine (SVM), are presented and applied to predict the ultimate bearing capacity of shallow foundations. Chaotic mapping enjoys certainty, ergodicity and the stochastic property. Chaotic PSO (CPSO) increases the convergence rate of PSO and precision of the results through introducing chaos mapping into the particle swarm optimization algorithm. Since the selection of parameters for SVM is crucial to its performance of prediction, the CPSO is adopted to search for the optimal parameters. The proposed methods are used to predict the ultimate bearing capacity of shallow foundations based on data of load tests. Results indicate that the proposed methods can appropriately describe the relationship between ultimate bearing capacity and its affective factors, and make good predictions.  相似文献   

基于改进的自适应反馈混沌系统同步     

李青芮  陶文华  孙娜 《华东地质学院学报》2009,32(3):293-297

基于LaSalle不变定理和Lyapunov方法,针对混沌系统同步问题提出了一种改进的自适应反馈方法。与一般线性反馈系统不同,这种方法能自动调整更新规则的可变反馈变量。在该自适应更新规则的控制下,反馈强度可自动调整到新的自适应规则,从而使响应系统的状态全局同步于驱动系统的状态。Chen氏混沌系统和Lu氏混沌系统说明了所设计的自适应反馈方法的有效性。  相似文献   

Spiral Structures and Chaotic Scattering of Coorbital Satellites     

Jacques Henrard  Juan F. Navarro 《Celestial Mechanics and Dynamical Astronomy》2001,79(4):297-314

The fractal nature of the transitions between two sets of orbits separated by heteroclinic or homoclinic orbits is well known. We analyze in detail this phenomenon in Hill's problem where one set of orbits corresponds to coorbital satellites exchanging semi-major axis after close encounter (horse-shoe orbits) and the other corresponds to orbits which do not exchange semi-major axis (passing-by orbits). With the help of a normalized approximation of the vicinity of unstable periodic orbits, we show that the fractal structure is intimately tied to a special spiral structure of the Poincaré maps. We show that each basin is composed of a few well behaved areas and of an infinity of intertwined tongues and subtongues winding around them. This behaviour is generic and is likely to be present in large classes of chaotic scattering problems.This revised version was published online in October 2005 with corrections to the Cover Date.  相似文献   

大气近地层湍流能谱特征的再分析   总被引：5，自引：1，他引：4  

卞建春  乔劲松  吕达仁 《大气科学》2002,26(4):474-480

根据Kolmogorov局地均匀性湍流假设,大气近地层湍流能谱在惯性副区符合"-5/3律".但是作者通过翻阅大量文献以及实测资料分析发现,大气近地层湍流能谱符合"-5/3律"的频率范围比较狭窄,而用幂函数+指数函数形式"fS(f)∝F-ae-bf"拟合更恰当一些,这种能谱函数形式是连续时间混沌系统所特有的.利用HEIHE实验湍流观测资料分析结果表明,对于径向风分量,a＝0.447,b＝0.228;切向风分量:a＝0.489,b＝0.190;垂直风分量:a＝0.551,b＝0.124;温度:a＝0.588,b＝0.123.  相似文献   

The chaotic attractor of the precursory field of the seimogenic system and its fractal dimension     

Zi-Ling Chen  Shuo-Yu Zhou 《地震学报(英文版)》1993,6(4):913-921

In this paper we outlined the chaotic attractor of the precursory field evolution of the seismogenic system and its fractal dimension of the precursory time and space distribution. We developed the calculative method of reconstruction complex system dynamics from single time series and analysed the descent dimension phenomena of the precursory distribution before large earthquakes. We also showed the time-space synthesis method constructed complex system dynamics by many stations or many methodes in the seismogenic system consists of large area tectonic network. This method can describe the self-organization behavior of the system more accurately and get rid of the uncertainty and randomness caused by single station or single method. As an example, we calculated the chaotic attractor of the precursory field evolution and the fractal dimension of the precursory time and space distribution and its change tendencies before large earthquakes in Beijing-Tianjing area. The Chinese version of this paper appeared in the Chinese edition ofActa Seismologica Sinica,15, 463–469, 1993.  相似文献   

晨昏起伏电场对中性片离子的随机加热     

沐建林  濮祖荫 《地球物理学报》1990,33(2):135-143

本文从哈密顿原理出发,讨论磁尾中性片中粒子受晨昏起伏电场的影响问题,并把它归结于讨论标准映射的性质.中性片本身是非线性系统,外加起伏场会导致其进入混沌状态.本文计算了进入该状态的临界电场E_c以及不同E下的粒子轨迹.计算表明,观测到的晨昏电场可以使离子进入混沌状态,但远小于电子的临界场值.这样离子运动是随机的,电子运动是规则的.仅对离子的随机加热可能是导致中性片中离子温度高于电子温度的原因.  相似文献   

最大Lyapunov指数计算的几种方法   总被引：10，自引：0，他引：10  

张军  汪秉宏 《地震》1994,(4):86-92

地震预报以各种时间序列数据为依据，因此如何从大量的时间序列中提取描述地震蕴孕过程的复杂性特征，成为从非线性科学角度探索地震预报的一个重要研究方向。本文讨论了混沌吸子的Ｌｙａｐｕｎｏｖ指数计算问题，并以一个模拟时间序列为例，讨论了如何从实验数据时间序列计算Ｌｙａｐｕｎｏｖ指数的问题，给出了两种实用的计算方法，对数值计算结果作了比较。此方法可用于地震及前兆时间序列复杂性刻划。  相似文献