Origin of chaos in the Prometheus-Pandora system     

Peter Goldreich  Nicole Rappaport 《Icarus》2003,166(2):320-327

We demonstrate that the chaotic orbits of Prometheus and Pandora are due to interactions associated with the 121:118 mean motion resonance. Differential precession splits this resonance into a quartet of components equally spaced in frequency. Libration widths of the individual components exceed the splitting, resulting in resonance overlap which causes the chaos. Mean motions of Prometheus and Pandora wander chaotically in zones of width 1.8 and 3.1 deg yr⁻¹, respectively. A model with 1.5 degrees of freedom captures the essential features of the chaotic dynamics. We use it to show that the Lyapunov exponent of 0.3 yr⁻¹ arises because the critical argument of the dominant member of the resonant quartet makes approximately two separatrix crossings every 6.2 year precessional cycle.  相似文献   

Dynamics of Two Planets in the 3/2 Mean-motion Resonance: Application to the Planetary System of the Pulsar PSR B1257+12     

N. Callegari Jr  S. Ferraz-Mello  T. A. Michtchenko 《Celestial Mechanics and Dynamical Astronomy》2006,94(4):381-397

This paper considers the dynamics of two planets, as the planets B and C of the pulsar PSR B1257+12, near a 3/2 mean-motion resonance. A two-degrees-of-freedom model, in the framework of the general three-body planar problem, is used and the solutions are analyzed through surfaces of section and Fourier techniques in the full phase space of the system.On the possibility of existence of a fourth planet in distant orbit, see Wolszczan et al., 2000  相似文献   

Frequency modified fourier transform and its application to asteroids     

Miloš Šidlichovský  David Nesvorný 《Celestial Mechanics and Dynamical Astronomy》1996,65(1-2):137-148

Recently a method has been suggested to analyze the chaotic behaviour of a conservative dynamical system by numerical analysis of the fundamental frequencies. Frequencies and amplitudes are determined step by step. As the frequencies are not generally orthogonal, a Gramm-Schmidt orthogonalization is made and for each new frequency the old amplitudes of previously determined frequencies are corrected. For a chaotic trajectory variations of the frequencies and amplitudes determined over different time periods are expected. The change of frequencies in such a calculation is a measure of the chaoticity of the trajectory. While amplitudes are corrected, the frequencies (once determined) are constant. We suggest here simple linear corrections of frequencies for the effect of other close frequencies. The improvement of frequency determination is demonstrated on a model case. This method is applied to the first fifty numbered asteroids.  相似文献   

Analysis and simulation of magma mixing processes in 3D   总被引：2，自引：0，他引：2  

D. Perugini  G. Poli  G. D. Gatta 《Lithos》2002,65(3-4):313-330

Magma mixing structures from the lava flow of Lesbos (Greece) are analyzed in three dimensions using a technique that, starting from the serial sections of rock cubes, allows the reconstruction of the spatial distribution of magmas inside rocks. Two main kinds of coexisting structures are observed: (i) “active regions” (AR) in which magmas mix intimately generating wide contact surfaces and (ii) “coherent regions” (CR) of more mafic magma that have a globular shape and do not show large deformations. The intensity of mingling is quantified by calculating both the interfacial area (IA) between interacting magmas and the fractal dimension of the reconstructed structures. Results show that the fractal dimension is linearly correlated with the logarithm of interfacial area allowing discrimination among different intensities of mingling.

The process of mingling of magmas is simulated using a three-dimensional chaotic dynamical system consisting of stretching and folding processes. The intensity of mingling is measured by calculating the interfacial area between interacting magmas and the fractal dimension, as for natural magma mixing structures. Results suggest that, as in the natural case, the fractal dimension is linearly correlated with the logarithm of the interfacial area allowing to conclude that magma mixing can be regarded as a chaotic process.

Since chemical exchange and physical dispersion of one magma inside another by stretching and folding are closely related, we performed coupled numerical simulations of chaotic advection and chemical diffusion in three dimensions. Our analysis reveals the occurrence in the same system of “active mixing regions” and “coherent regions” analogous to those observed in nature. We will show that the dynamic processes are able to generate magmas with wide spatial heterogeneity related to the occurrence of magmatic enclaves inside host rocks in both plutonic and volcanic environments.  相似文献   

Extracting flow structures from tracer data     

Judit Schneider  Tamás Tél 《Ocean Dynamics》2003,53(2):64-72

A method of visualizing structures in closed chaotic flows out of homogenous particle distributions is presented in the example of models of a meandering jet. To this end, the system will be leaked or opened up by defining a region of the flow, so that a particle is considered to be escaped if it leaves this region. By applying this method to an ensemble of nonescaped tracers, we are able to characterize mixing processes by visualizing the converging and stretching filamentations (stable and unstable manifolds) in the flow without using additional mathematical tools. The possibility of applying the algorithm to analyze buoy data, and a comparison with the finite time manifolds are discussed.  相似文献   

Epistemological possibilities and imperatives of complexity research: a reply to Reitsma     

Steven M Manson 《Geoforum》2003,34(1):17-20

Reitsma (A response to ‘simplifying complexity’. Geoforum 34 (1) (2003) 13), in response to the article ‘Simplifying Complexity’ (Manson, S.M., Simplifying complexity: a review of complexity theory. Geoforum 32 (3) (2001) 405), highlights a number of interesting and important aspects of complexity theory that invite further discussion. In particular, there are three areas of complexity research that are open to deeper exploration: (1) the width and breadth of ‘complexity’ defined as a scientific endeavor; (2) the role of theory relative to practice and their relationship with pattern and process in complex systems; and (3) the need for greater discussion and exploration in order to define the conceptual bounds of complexity theory.  相似文献   

一种基于浑沌理论的联想记忆神经网络模型   总被引：3，自引：0，他引：3  

曹杰  谢应齐 《热带气象学报》1997,13(1):82-87

根据联想记忆神经网络的基本原理，提出了一种基于浑沌理论的联想记忆神经网络模型及相应的求解方案，并对该种模型进行了预报试验。结果表明，该种模型的历史预报准确率和实际预报准确率均超过一般随机预报，值得进一步研究和应用。  相似文献   

人地非线性相关作用的探讨   总被引：12，自引：2，他引：12  

刘继生  陈涛 《地理科学》1997,17(3):224-230

从自组织系统思想出发，提出了人地关系的基本特性，通过逻辑斯蒂听数学变换，分析了人地非线性相关作用的混沌特性，进而讨论了人地关系的分形性质。基于混 过程与分形结构的因果关系，指出：地球表层系统中的人文分形景观乃是人地非线性关系的混沌作用所致。  相似文献   

Intermittent chaos in nonlinear wave–wave interactions in space plasmas     

Rodrigo A. Miranda  Erico L. Rempel  Abraham C.-L. Chian  Felix A. Borotto 《Journal of Atmospheric and Solar》2005,67(17-18):1852

There is increasing observational evidence of nonlinear wave–wave interactions in space and astrophysical plasmas. We first review a number of theoretical models of nonlinear wave–wave interactions which our group has developed in the past years. We next describe a nonlinear three-mode truncated model of Alfvén waves, involving resonant interactions of one linearly unstable mode and two linearly damped modes. We construct a bifurcation diagram for this three-wave model and investigate the phenomenon of intermittent chaos. The theoretical results presented in this paper can improve our understanding of intermittent time series frequently observed in space and astrophysical plasmas.  相似文献   

磁层顶等离子体中的混沌现象     

王乃权 《地球物理学报》1991,34(4):523-526

本文研究了磁层顶等离子体的一个基本模型,得到了一新的非线性常微分方程组.数值分析表明,在一定的磁Reynolds数范围内,系统呈现混沌行为,相轨道趋向于奇异吸引子.  相似文献