Exploiting Unstable Periodic Orbits of a Chaotic Invariant Set for Spacecraft Control

The purpose of this work is to show that chaos control techniques (OGY, in special) can be used to efficiently keep a spacecraft around another body performing elaborate orbits. We consider a satellite and a spacecraft moving initially in coplanar and circular orbits, with slightly different radii, around a heavy central planet. The spacecraft, which is the inner body, has a slightly larger angular velocity than the satellite so that, after some time, they eventually go to a situation in which the distance between them becomes sufficiently small, so that they start to interact with one another. This situation is called as an encounter. In previous work we have shown that this scenario is a typical situation of a chaotic scattering for some well-defined range of parameters. Considering this scenario, we first show how it is possible to find the unstable periodic orbits that are located in the chaotic invariant set. From the set of unstable periodic orbits, we select the ones that can be combined to provide the desired elaborate orbit. Then, chaos control technique based on the OGY method is used to keep the spacecraft in the desired orbit. Finally, we analyze the results and make considerations regarding a realistic scenario of space exploration.     

Determining the nature of orbits in a three‐dimensional galaxy model hosting a BL Lacertae object

A three‐dimensional dynamical model for a galaxy hosting a BL Lacertae object is constructed. The model consists of a logarithmic potential representing an elliptical host galaxy with a bulge of radius cb and a dense massive nucleus. Using numerical experiments, we try to distinguish between regular and chaotic motion in both 2D and 3D system. In particular, we investigate how the basic parameters of our model, such as the mass of the nucleus, the internal perturbation and the flattening parameters influence the amount and the degree of chaos. Interesting correlations are presented for both 2D and 3D dynamical models. Our numerical results are explained and supported using elementary theoretical arguments and analytical calculations. Of particular interest is the local integral of motion which have been found to exist in the vicinity of stable periodic points. The obtained numerical outcomes of the present research are linked and also compared with several data derived from observations. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Global Dynamics in Self-Consistent Models of Elliptical Galaxies

We compare two different N-body models simulating elliptical galaxies. Namely, the first model is a non-rotating triaxial N-body equilibrium model with smooth center, called SC model. The second model, called CM model, is derived from the SC by inserting a central mass in it, so that all possible differences between the two models are due to the effect of the central mass. The central mass is assumed to be mainly due to a massive central black hole of mass about 1% of the total mass of the galaxy. By using the fundamental frequency analysis, the two systems are thoroughly investigated as regards the types of orbits described either by test particles, or by the real particles of the systems at all the energy levels. A comparison between the orbits of test particles and the orbits of real particles at various energy levels is made on the rotation number plane. We find that extensive stable regions of phase space, detected by test particles remain empty, i.e. these regions are not occupied by real particles, while many real particles move in unstable regions of phase space describing chaotic orbits. We run self-consistently the two models for more than a Hubble time. During this run, in spite of the noise due to small variations of the potential, the SC model maintains (within a small uncertainly) the number of particles moving on orbits of each particular type. In contrast, the CM model is unstable, due to the large amount of mass in chaotic motion caused by the central mass. This system undergoes a secular evolution towards an equilibrium state. During this evolution it is gradually self-organized by converting chaotic orbits to ordered orbits mainly of the short axis tube type approaching an oblate spheroidal equilibrium. This is clearly demonstrated in terms of the fundamental frequencies of the orbits on the rotation number plane and the time evolution of the triaxiality index.     

变形监测数据的混沌现象分析

本文简述了识别变形数据混沌现象的Lyapunov指数方法和关联维数方法;讨论了变形监测数据的Lyapunov指数和关联维数的计算方法;最后结合大坝观测变形观测数据给出了实际算例。     

新安江模型参数多目标优化研究

水文模型的参数优化率定一直以来是水文预报领域的重要研究内容,当水文模型的结构确定后,水文模型参数的选择对水文模型整体性能和水文预报结果的好坏有着至关重要的影响.针对传统水文模型参数优选采用单一目标不能充分全面挖掘水文观测资料中蕴含的水文特征信息的缺陷,本文以新安江三水源模型为例,尝试采用多目标优化算法优化率定水文模型,算例应用分析表明,通过合理的选择目标函数的种类和数目,采用多目标进化算法优化率定模型参数,可以获得相对于单目标率定模型参数更优的结果.进一步,研究工作针对模型参数优化的结果进行分析,可以明显看出模型参数优化中存在“异参同效”现象,为后续模型参数不确定性分析等相关研究工作的开展做好了铺垫.     

地域结构的演变和预测

本文对地域结构进行了动态化研究,从整体上把握了宏观地域结内的演化规律。其中贯穿了各种区位理论、相互作用理论和扩散理论等。作者认为相互作用理论和扩散理论是关于地域结构形成和发展的机制和过程的理论,而区位理论则是关于地域系统中各元素和子系的位置和分布的理论。     

Characterization of ground motions using recurrence plots

The current analysis of earthquakes is typically based on linear mathematical models that may fail to describe and forecast particular behaviors, because in many cases the data complexity may induce a highly non linear behavior. In this paper the implementation of an alternative method for seismic time series analysis is presented. The RPs (Recurrence Plots) enables recognition and treatment of measured accelerations. An RP obtained from seismic data allows a more efficient interpretation of the ground motions and this explanation contributes to characterize materials and responses. The nonlinear attributes from RPs analysis can be used as filters to reveal patterns or be combined to predict a seismic property. Automated seismic data characterization, based on nonlinear seismic attributes, could rewrite the rules of earthquake phenomena interpretation. The objective of this work is to establish a new methodology for practical application of nonlinear dynamics in seismic pattern/attributes recognition, an evolving and challenging engineering field.     

Randomness: a property of the mathematical and physical systems

ABSTRACT

This article is a concept paper, which discusses the definition of randomness, and the sources of randomness in the mathematical system as well as in the physical system (the Universe). We document that randomness is an inherited property of mathematics and of the physical world, shaping all observed forms and structures, and we discuss its role.

Editor D. Koutsoyiannis; Guest editor E. Volpi     

多参数岩体结构面优势分组方法研究

在岩体力学和水力学分析中,搞清岩体结构面的分布规律是一项重要的基础工作。当岩体结构面的产状一致,而其他性质不一致时,岩体结构面的力学和水力学性质是不同的,而传统的方法仅根据岩体结构面的产状进行分组,这势必存在缺陷。提出了一种基于变尺度混沌优化算法的多参数结构面数据的优势组划分方法,通过度量结构面之间的相似性建立目标函数,运用变尺度混沌优化算法搜索目标函数的最优解来确定聚类中心,可同时考虑结构面的多个参数,把具有相似性质的结构面归并成组。通过计算机模拟的结构面数据验证了此算法的正确性,最后将此算法应用于实际工程中测量的多参数结构面数据的优势组划分,得到了清晰可靠的分组结果。     

形变时序数据性态特征确定方法研究

提出变异函数、主分量分析及关联维的方法分析形变时序数据序列的性态特征,特别是针对沉降数据序列进行实例试算.结果表明,这三种方法用于形变数据序列的性态特征分析是可行的,可以用来确定沉降数据序列的变异性、混沌性及分形维特征.