On the Structure of Symplectic Mappings. The Fast Lyapunov Indicator: a Very Sensitive Tool     

Claude Froeschlé  Elena Lega 《Celestial Mechanics and Dynamical Astronomy》2000,78(1-4):167-195

It is already known (Froeschlé, Lega and Gonczi, 1997) that the Fast Lyapunov Indicator (FLI), that is the computation on a relatively short time of the largest Lyapunov indicator, allows to discriminate between ordered and weak chaotic motion. We have found that, under certain conditions, the FLI also discriminates between resonant and non-resonant orbits, not only for two-dimensional symplectic mappings but also for higher dimensional ones. Using this indicator, we present an example of the Arnold web detection for four and six-dimensional symplectic maps. We show that this method allows to detect the global transition of the system from an exponentially stable Nekhoroshevs like regime to the diffusive Chirikovs one.  相似文献   

曙光4000A上三维叠前深度偏移并行计算的应用设计     

孔祥宁  方伍宝  赵改善  袁联生 《物探化探计算技术》2006,28(3):205-210

波动方程叠前深度偏移在地震勘探成像处理方面起着不可替代的作用。随着高性能大规模并行计算机技术的发展,波动方程叠前深度偏移计算在地震勘探中的应用有了很大进步。在波动方程叠前深度偏移处理中,庞大的数据规模与海量计算对计算性能提出了很高的要求。曙光4000A超级计算机系统是我国目前峰值速度最快的商用超级计算机系统,无论是硬件平台建设还是应用软件的配置方面,都具有良好的应用性能。基于该系统设计的三维波动方程叠前深度偏移(炮域)PSDM软件,采用动态负载平衡并行计算模式,具有较高的计算效率,高度的可扩展性和可靠性。  相似文献   

基于分布式计算模式的GIS的设计与实现     

刘达  谭继强  窦春和 《测绘与空间地理信息》2007,30(3):150-153

介绍了分布式GIS和分布式计算模式的概念,探讨了基于分布式计算模式的地理信息系统的体系结构、运作机制、关键技术和实现方法,最后对未来的分布式地理信息系统发展进行了展望。  相似文献   

基于混沌时间序列的地下水位多步预测模型     

陈南祥  ;张海丰  ;李松海 《西安地质学院学报》2007,(1):66-69

利用相空间重构技术，并借助G—P算法、C-C方法和Wolf方法从宁陵地区地下水位一维时间序列中提取Lyapunov指数，结果表明此时间序列具有混沌特征。计算了宁陵地区地下水位时间序列的关联维数、时间延迟和最大Lyapunov指数，将局域加权一阶多步预测模型应用于地下水位预测。预测表明，此模型可有效应用于地下水位时间序列的多步预测。  相似文献   

北京市泥石流灾害临界雨量研究   总被引：3，自引：2，他引：3  

白利平  南赟  孙佳丽 《中国地质灾害与防治学报》2007,18(2):34-36,41

降雨是泥石流灾害的主要诱发因素。文章根据北京市历史上泥石流灾害发生时的前期雨量与当日激发雨量,建立了临界雨量判别模型。通过对北京地区泥石流灾害与降雨频率的分析,计算了不同时段的临界雨量;经验证明,计算结果是可信的。基于灾害与降雨频率分析来确定北京地区泥石流发生的临界雨量是一种新的尝试。该方法可用于计算不同泥石流沟道发生泥石流的临界雨量。  相似文献   

Chaotic dynamics of planet‐encountering bodies     

G. Tancredi 《Celestial Mechanics and Dynamical Astronomy》1998,70(3):181-200

The dynamics of two families of minor inner solar system bodies that suffer frequent close encounters with the planets is analyzed. These families are: Jupiter family comets (JF comets) and Near Earth Asteroids (NEAs). The motion of these objects has been considered to be chaotic in a short time scale,and the close encounters are supposed to be the cause of the fast chaos. For a better understanding of the chaotic behavior we have computed Lyapunov Characteristic Exponents (LCEs) for all the observed members of both populations. LCEs are a quantitative measure of the exponential divergence of initially close orbits. We have observed that most members of the two families show a concentration of Lyapunov times (inverse of LCE) around 50–100yr. The concentration is more pronounced for JF comets than for NEAs, among which a lesser spread is observed for those that actually cross the Earth's orbit (mean perihelion distance q < 1.05 AU). It is also observed that a general correspondence exists between Lyapunov times and the time between consecutive encounters. A simple model is introduced to describe the basic characteristics of the dynamical evolution. This model considers an impulsive approach, where the particles evolve unperturbedly between encounters and suffer ‘kicks’ in semimajor axis at the encounters. It also reproduces successfully the short Lyapunov times observed in the numerical integrations and is able to estimate the dynamical lifetimes of comets during a stay in the Jupiter family in correspondence with previous estimates. It has been demonstrated with the model that the encounters with the largest effect on the exponential growth of the distance between initially nearby orbits are neither the infrequent deep encounters, nor the frequent and far ones; instead, the intermediate approaches have the most relevant contribution to the error growth. Such encounters are at a distance a few times the radius of the Hill's sphere of the planet (e.g. 3). An even simpler model allows us to get analytical estimates of the Lyapunov times in good agreement with the values coming from the model above and the numerical integrations. The predictability of the medium‐term evolution and the hazard posed to the Earth by those objects are analysed in the Discussion section. This revised version was published online in July 2006 with corrections to the Cover Date.  相似文献   

Analysis of seismic dynamical systems     

M. Urquizú  A. M. Correig 《Journal of Seismology》1998,2(2):159-171

A procedure is presented for the analysis of complex stationary time series for which the Fourier power spectra reveals broadband noise or broadened pulses. We first determine the Hurst exponent from which we may know whether the time series under study is mainly random or if the data points present correlations. If the data are correlated, a chaotic analysis will reveal whether they may be interpreted as a low dimensional nonlinear system (defined by a low correlation dimension and a finite and positive Kolmogorov entropy and largest positive Lyapunov exponent) or as a stochastic process. We have studied three kind of temporal series: inter-event time series of infrasonic pulses recorded at Stromboli volcano, and, S-coda waves and microseisms, that have been recorded at the eastern Pyrenees. Results show that microseisms and Coda waves can be modeled as a low dimensional deterministic system, Correlation dimensions 2.3, 3.2, respectively. At the contrary infrasonic has resulted stochastic. This chaotic character can be attributed to the medium properties. Coda waves with scattering through a fractal distribution of scatters or to multiple reflection inside resonators (for example sedimentary basins) and microseisms as a propagation of wave guide of variable cross section which have the same temporal characteristics as a nonlinear forced oscillator.  相似文献   

Lattice dynamical system modelling of molecular clouds     

G. Rousseau  H. Chaté  & J. Le Bourlot 《Monthly notices of the Royal Astronomical Society》1998,294(3):373-390

Because a comprehensive microscopic treatment of interstellar molecular clouds is out of reach, an alternative approach is proposed in which most of the crucial ingredients of the problem are considered, but at some 'minimal' level of modelling. This leads to the elaboration of a lattice dynamical system , i.e. a time-dependent, spatially extended, deterministic system of macroscopic cells coupled through radiative transfer. Each cell is characterized by a small set of variables and supports a caricatural chemistry possessing the essential dynamical features of more realistic reaction schemes.   This approach naturally precludes quantitative results, but allows heretofore unavailable insights into some of the basic mechanisms at play. We focus on the response of the transfer process and the chemistry to a frozen 'turbulent' velocity field. It is shown that the system settles generically into a state where the effective coupling between cells is neither local nor global, and for which no single length-scale exists.   The spectral lines reconstructed from the spatiotemporal evolution of our model may, depending on the velocity field, exhibit profiles ranging from Gaussian to bimodal with strong realization effects. In the bimodal case, the model intrinsically displays an energy cascade transport mechanism to the cells that cool most efficiently: the feedback of chemistry on radiative transfer cannot be neglected.   Finally, extensions of this work are discussed and future developments are outlined.  相似文献   

Modulation and symmetry changes in stellar dynamos     

E. Knobloch  S. M. Tobias  & N. O. Weiss 《Monthly notices of the Royal Astronomical Society》1998,297(4):1123-1138

Stellar dynamos are governed by non-linear partial differential equations (PDEs) which admit solutions with dipole, quadrupole or mixed symmetry (i.e. with different parities). These PDEs possess periodic solutions that describe magnetic cycles, and numerical studies reveal two different types of modulation. For modulations of Type 1 there are parity changes without significant changes of amplitude, while for Type 2 there are amplitude changes without significant changes in parity. In stars like the Sun, cyclic magnetic activity is interrupted by grand minima that correspond to Type 2 modulation. Although the Sun's magnetic field has maintained dipole symmetry for almost 300 yr, there was a significant parity change at the end of the Maunder Minimum. We infer that the solar field may have flipped from dipole to quadrupole polarity (and back) after deep minima in the past and may do so again in the future. Other stars, with different masses or rotation rates, may exhibit cyclic activity with dipole, quadrupole or mixed parity. The origins of such behaviour can be understood by relating the PDE results to solutions of appropriate low-order systems of ordinary differential equations (ODEs). Type 1 modulation is reproduced in a fourth-order system while Type 2 modulation occurs in a third-order system. Here we construct a new sixth-order system that describes both types of modulation and clarifies the interactions between symmetry-breaking and modulation of activity. Solutions of these non-linear ODEs reproduce the qualitative behaviour found for the PDEs, including flipping of polarity after a prolonged grand minimum. Thus we can be confident that these patterns of behaviour are robust, and will apply to stars that are similar to the Sun.  相似文献   

A two-layer αω-dynamo model with dynamic feedback on the ω-effect     

Colin B. Roald 《Monthly notices of the Royal Astronomical Society》1998,300(2):397-410

In an attempt to produce a simple representation of an interface dynamo, I examine a dynamo model composed of two one-dimensional (radially averaged) pseudo-spherical layers, one in the convection zone and possessing an α-effect, and the other in the tachocline and possessing an ω-effect. The two layers communicate by means of an analogue of Newton's law of cooling, and a dynamical back-reaction of the magnetic field on ω is provided. Extensive bifurcation diagrams are calculated for three separate values of η, the ratio of magnetic diffusivities of the two layers. I find recognizable similarities to, but also dramatic differences from, the comparable one-layer model examined by Roald &38; Thomas. In particular, the solar-like dynamo mode found previously is no longer stable in the two-layer version; in its place there is a sequence of periodic, quasi-periodic and chaotic modes probably created in a homoclinic bifurcation. These differences are important enough to provide support for the view that the solar dynamo cannot be meaningfully modelled in one dimension.  相似文献