On a Physically Realistic Fast Dynamo     

Kim  Eun-Jin  Hughes  D. W.  Soward  A. M. 《Studia Geophysica et Geodaetica》1998,42(3):335-342

As a step towards a physically realistic model of a fast dynamo, we study numerically a kinematic dynamo driven by convection in a rapidly rotating cylindrical annulus. Convection maintains the quasi-geostrophic balance whilst developing more complicated time-dependence as the Rayleigh number is increased. We incorporate the effects of Ekman suction and investigate dynamo action resulting from a chaotic flow obtained in this manner. We examine the growth rate as a function of magnetic Prandtl number Pm, which is proportional to the magnetic Reynolds number. Even for the largest value of Pm considered, a clearly identifiable asymptotic behaviour is not established. Nevertheless the available evidence strongly suggests a fast dynamo process.  相似文献   

Generalisation of a Nonlinear Dynamo Model     

Tanner  Sarah E. M.  Hughes  D. W. 《Studia Geophysica et Geodaetica》1998,42(3):343-349

In order to gain a better understanding of the physical processes underlying fast dynamo action it is instructive to investigate the structure of both the magnetic field and the velocity field after the dynamo saturates. Previously, computational results have been presented (Cattaneo, Hughes and Kim, 1996) that indicate, in particular, that Lagrangian chaos is suppressed in the dynamical regime of the dynamo. Here we extend their model by removing the assumption of neglecting the inertial term. This allows for an investigation into the effect of this term on the evolution of the dynamo via a comparison of the two models. Our results indicate that this term plays a crucial role in the physics of the dynamo.  相似文献   

A Survey of Newtonian Core-Shell Systems with Pseudo High Order Symplectic Integrator and Fast Lyapunov Indicator     

Jun-Fang Zhu Xin Wu Da-Zhu Ma 《中国天文和天体物理学报》2007,7(4):601-610

Newtonian core-shell systems, as limiting cases of relativistic core-shell models under the two conditions of weak field and slow motion, could account for massive circumstellar dust shells and rings around certain types of star remnants. Because this kind of systems have Hamiltonians that can be split into a main part and a small perturbing part, a good choice of the numerical tool is the pseudo 8th order symplectic integrator of Laskar ＆ Robutel, and, to match the symplectic calculations, a good choice of chaos indicator is the fast Lyapunov indicator （FLI） with two nearby trajectories proposed by Wu, Huang ＆ Zhang. Numerical results show that the FLI is very powerful when describing not only the transition from regular motion to chaos but also the global structure of the phase space of the system.  相似文献   

基于线性反馈控制的一类混沌系统的同步     

徐瑞萍  高存臣 《中国海洋大学学报(自然科学版)》2014,44(5):114-120

研究一类混沌系统的同步问题。基于李雅普诺夫稳定性理论,利用线性反馈法给出了同步混沌系统的3种控制方案,得到了2个混沌系统同步的充分条件。为了更清楚地了解每种方案下系统的同步行为,还给出了以增益为分岔参数时同步误差的变化图。理论分析和数值仿真结果都表明了文中所给方法的有效性和可行性。  相似文献   

A universal algorithm to generate pseudo-random numbers based on uniform mapping as homeomorphism     

王福来 《海洋学报(英文版)》2010,29(9)

A specific uniform map is constructed as a homeomorphism mapping chaotic time series into [0,1] to obtain sequences of standard uniform distribution. With the uniform map, a chaotic orbit and a sequence orbit obtained are topologically equivalent to each other so the map can preserve the most dynamic properties of chaotic systems such as permutation entropy. Based on the uniform map, a universal algorithm to generate pseudo random numbers is proposed and the pseudo random series is tested to follow the standard 0-1 random distribution both theoretically and experimentally. The algorithm is not complex, which does not impose high requirement on computer hard ware and thus computation speed is fast. The method not only extends the parameter spaces but also avoids the drawback of small function space caused by constraints on chaotic maps used to generate pseudo random numbers. The algorithm can be applied to any chaotic system and can produce pseudo random sequence of high quality, thus can be a good universal pseudo random number generator.  相似文献   

双铰四次弹性拱的混沌行为研究     

叶法林  陈秀丽  刘启宽 《成都信息工程学院学报》2008,23(6):682-686

对双铰四次弹性拱的混沌行为在横向周期荷载下的混沌行为进行了研究。首先利用拱的单元平衡方程建立了拱的二阶三次非线性动力学模型;然后通过变换使方程转化为不含常数项的非线性微分动力系统,并由此得到无扰动系统的3个不动点（一个鞍点,两个中心）与同宿轨道;再用Melnikov函数法给出了发生混沌的临界条件;最后给出了该系统出现定常运动和混沌运动的数值结果。研究表明四次弹性拱在横向周期荷载作用下的外激励振幅在一定范围内会出现混沌现象。  相似文献   

Comparison of chaos detection methods in the circular restricted three‐body problem     

O. Racoveanu 《Astronomische Nachrichten》2014,335(8):877-885

In this study, a sample of orbits is considered in the framework of the planar circular restricted three‐body problem. In order to separate ordered from chaotic orbits three numerical methods are compared: the Largest Lyapunov Characteristic Exponent (LLCE) and the Smaller Alignment Index (SALI) provide a fairly good characterization of the chaotic motions, while the computational time required is of the same order; the Correlation Dimension (CD) has the advantage of correctly classifying sticky orbits, but at the expense of a longer computational time. In order to classify a given orbit, any pair of the three methods can be considered, but LLCE and SALI are recommended due to their speed. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

Poincarè Chaos and the Dynamical Evolution of Systems of Gravitating Bodies     

A. D. Chernin  M. Valtonen  L. P. Ossipkov  Q.-J. Zheng  S. Wiren 《Astrophysics》2002,45(2):240-247

Some general laws of evolution of a system of a large number of gravitating bodies are discussed. If in the initial stage the dynamics of the system is determined by large-scale perturbations of the gravitational potential associated with excitations of a few collective degrees of freedom, then one can assume, by analogy with chaos in the several-body problem (Poincarè chaos), that randomization will occur in the system over several average crossing times. In the next stage of evolution, the energy of collective modes should be transferred by the cascade mechanism to ever smaller scales, down to invididual particles. Numerical experiments and gross-dynamical considerations that could verify this picture and bring out details are discussed.  相似文献   

Dynamics of Two Planets in the 2/1 Mean-Motion Resonance   总被引：1，自引：1，他引：0  

N. Callegari Jr.  T. A. Michtchenko  S. Ferraz-Mello 《Celestial Mechanics and Dynamical Astronomy》2004,89(3):201-234

The dynamics of two planets near a first-order mean-motion resonance is modeled in the domain of the general three-body planar problem. The system studied is the pair Uranus-Neptune (2/1 resonance). The phase space of the resonance and near-resonance regions is studied by means of surfaces of section and spectral analysis techniques. After a thorough investigation of the topology of the phase space, we find that several regimes of motion are possible for the Uranus-Neptune system, and the regions of transition between the regimes of motion are the seats of chaotic motion. This revised version was published online in July 2006 with corrections to the Cover Date.  相似文献   

The general solution of the HENON–HEILES problem     

K.?E.?PapadakisEmail author  C.?L.?Goudas  G.?A.?Katsiaris 《Astrophysics and Space Science》2005,295(3):375-396

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.  相似文献