An Analytic Model of Three-Body Mean Motion Resonances     

D. Nesvorný  A. Morbidelli 《Celestial Mechanics and Dynamical Astronomy》1998,71(4):243-271

It has been recently shown that the resonances among the mean motions of an asteroid, Jupiter and Saturn are very important for the origin of chaos in the asteroid belt. We develop an analytic model for these three-body resonances which allows quantitative predictions on their amplitude and libration timescale. We also discuss why these resonances are chaotic. This revised version was published online in July 2006 with corrections to the Cover Date.  相似文献   

流域降雨径流时间序列的混沌识别及其预测研究进展   总被引：38，自引：2，他引：38       下载免费PDF全文

黄国如  芮孝芳 《水科学进展》2004,15(2):255-260

混沌和随机在本质上是两种不同的特征,对这两种特征的描述方法各不相同,确定流域降雨径流时间序列的混沌性和随机性是对其进行模拟和预测的重要基础。近10多年来,许多学者相继开展了流域降雨径流时间序列的混沌识别及其预测研究。着重回顾其中最为重要的相空间重构、混沌识别和混沌预测方法,对将混沌理论应用于降雨径流时间序列的限制条件(序列的数据量大小和数据噪声)也进行了探讨。  相似文献   

Strange attractors in magmas: evidence from lava flows     

G. Poli  D. Perugini 《Lithos》2002,65(3-4):287-297

Magma mixing structures from three different lava flows (Salina, Vulcano and Lesbos) are studied in order to assess the possible chaotic origin of magma mixing processes. Structures are analysed using a new technique based on image analysis procedures that extract time series that are representative of the relative change in composition through the structures. These time series are then used to reconstruct the attractors underlying the magma mixing process and to calculate the fractal dimension of the attractors. Results show that attractors exist and possess fractional dimensions. This evidence suggests that the mixing of magmas is a chaotic process governed by a low number of degrees of freedom. In addition, fractal dimension analyses allows us to discriminate between different regimes of mixing in the three lava flows. In particular our analyses suggest that the lava flow of Salina underwent more turbulent mixing than the lava flows of Lesbos and Vulcano.  相似文献   

湘西金矿含矿石英脉厚度变化的分形和混沌分析   总被引：3，自引：3，他引：3  

谢焱石  谭凯旋  赵志忠 《大地构造与成矿学》2002,26(1):62-68

本文对湘西金矿主要矿脉的厚度变化进行了分形分析。各矿脉的厚度变化均具有分形结构特征,其中V1脉的分维值最小,V4脉的分维值最大;并且同一条矿脉在不同中段的分维值也有较大变化。通过对矿脉厚度变化的相空间重构,表明各矿脉厚度空间变化序列均为混沌演化序列,在相空间维数达到6～7时出现混沌吸引子,混沌吸引子的分维值为1.2～6.0。矿脉厚度变化的分维值越小,矿脉的平均厚度越大,其构造和流体活动也越强烈。构造变形、流体活动、矿物沉淀与岩石渗透率之间的非线性耦合作用以及矿脉通过连通而生长是导致矿脉厚度分形分布与混沌演化的主要动力学机理。  相似文献   

A new look at the response surface method for reliability analysis using chaos theory     

Youliang Ding  Aiqun Li  Yang Deng 《地震工程与工程振动(英文版)》2008,7(3):329-335

To overcome excessive computation errors and convergence failures encountered in an iterative calculation of the reliability index using the response surface method （RSM） for some nonlinear limit state functions, this study investigates an essential factor based on chaotic dynamics theory. The bifurcation diagrams of the reliability index are presented for some typical nonlinear limit state functions, and the computation results from the mapping functions due to the RSM iterations show the complicated dynamic phenomena such as the periodic oscillation, as well as bifurcation and chaos. From the numerical examples, it is concluded that the parameter of selection range fplays an important role in the convergence of the RSM iteration, and an improved RSM iterative algorithm is proposed with regard to the incorporation of the iterative sequential function of selection rangef The proposed method is shown to be efficient and to yield accurate results.  相似文献   

强震地面运动的混沌特性分析     

杨迪雄  杨丕鑫 《地震学刊》2009,(3):252-260

引入非线性动力学理论和混沌时间序列分析方法考察强震地面运动加速度时程的非线性特征。首先采用功率谱分析法、主成份分析法和Cao方法定性判断地震动加速度时程具有混沌特性,然后应用混沌时间序列分析方法定量计算了30条地震动加速度时程的三个非线性特征参数。计算表明,这些地震动时程的关联维数为2．0～4．0的分数维,Kolmogorov熵K2为大于零的有限正值,最大Lyapunov指数在o～i．0之间。结果说明,强震地面运动具有混沌特性,地震动的高度不规则和复杂性是地震过程强非线性的反映。  相似文献   

黄河流域泥沙时序混沌特征——地理学综合研究的一种尝试(英文)     

马建华  孙艳丽  楚纯洁 《地理学报(英文版)》2010,20(2):219-230

The sediment content of the Yellow River is resulted from the interactions of natural, economic,and social factors,so it includes some evolutive information of the Yellow River Basin system.Sediment contents from 1952 to 2007 on Toudaoguai,Tongguan,Huayuankou and Lijin sections along the river are chosen as the study time series,and correlation dimensions(D2),Kolmogorov entropies(K2),and Hurst indexes(H)of the time series were calculated.Correlation dimensions on Toudaoguai,Tongguan,Huayuankou,and Lijin sec...  相似文献   

Chaotic characters of the Yellow River Basin based on the sediment time series: An attempt to integrated research in geography     

MA Jianhua  SUN Yanli  CHU Chunjie 《地理学报》2010,20(2):219-230

The sediment content of the Yellow River is resulted from the interactions of natural, economic, and social factors, so it includes some evolutive information of the Yellow River Basin system. Sediment contents from 1952 to 2007 on Toudaoguai, Tongguan, Huayuankou and Lijin sections along the river are chosen as the study time series, and correlation dimensions (D2), Kolmogorov entropies (K2), and Hurst indexes (H) of the time series were calculated. Correlation dimensions on Toudaoguai, Tongguan, Huayuankou, and Lijin sections are 3.24, 5.69, 6.57 and 7.34 respectively, and the Kolmogorov entropies are 0.13, 0.37, 0.40 and 0.38 respectively, which indicates that the systems controlled by different sections along the Yellow River are chaotic systems and the chaotic degrees increase gradually from the upper to lower section. The average predictable period of the sediment contents is 8 years on Toudaoguai section and 3 years on the other sections with the reciprocals of the Kolmogorov entropies. The more obvious the chaotic degree is, the shorter the average predictable period is. Hurst indexes on the sections are above 0.5, with the maximum of 0.86 on Tongguan section and the minimum of 0.68 on Toudaoguai section, which indicates that the time series have persistent trends in the average predictable period. Eight state variables and two control parameters are necessary to construct the dynamic model of the Yellow River Basin system.  相似文献   

A Symplectic Mapping Model for the Study of 2:3 Resonant Trans-Neptunian Motion     

K. G. Hadjifotinou  John D. Hadjidemetriou 《Celestial Mechanics and Dynamical Astronomy》2002,84(2):135-157

A symplectic mapping is constructed for the study of the dynamical evolution of Edgeworth-Kuiper belt objects near the 2:3 mean motion resonance with Neptune. The mapping is six-dimensional and is a good model for the Poincaré map of the real system, that is, the spatial elliptic restricted three-body problem at the 2:3 resonance, with the Sun and Neptune as primaries. The mapping model is based on the averaged Hamiltonian, corrected by a semianalytic method so that it has the basic topological properties of the phase space of the real system both qualitatively and quantitatively. We start with two dimensional motion and then we extend it to three dimensions. Both chaotic and regular motion is observed, depending on the objects' initial inclination and phase. For zero inclination, objects that are phase-protected from close encounters with Neptune show ordered motion even at eccentricities as large as 0.4 and despite being Neptune-crossers. On the other hand, not-phase-protected objects with eccentricities greater than 0.15 follow chaotic motion that leads to sudden jumps in their eccentricity and are removed from the 2:3 resonance, thus becoming short period comets. As inclination increases, chaotic motion becomes more widespread, but phase-protection still exists and, as a result, stable motion appears for eccentricities up to e = 0.3 and inclinations as high as i = 15°, a region where plutinos exist.  相似文献   

基于地震数据结构梯度张量属性的采空区识别方法     

陈强  许玉莹  曾维望 《中国煤炭地质》2013,(7):42-47

通过介绍结构张量矩阵构建及其特征向量与特征值的算法原理,提出了利用梯度结构张量矩阵特征值计算Chaos及其边缘属性,以提高不同类型采空区三维地震资料解释精度的技术思路,并讨论了在地震数据结构张量chaos、边缘检测属性计算中的关键环节。实例分析表明,chaos和边缘属性可以精细描述不同类型采空区的地震反射结构特征变化规律:工作面采空区可形成明显的杂乱反射结构,平面呈连续密实的团块状或宽条带状异常;巷道采空区则表现为微波状弯曲反射结构,具有串珠状、短而弯曲的线状、窄条状平面特征。基于地震数据梯度结构张量算法的属性分析是精细识别和解释采空区的一个有效工具。  相似文献