Chaotic ray behaviour in regional seismology

Rays propagating through strongly laterally varying media exhibit chaotic behaviour. This means that initially close rays diverge exponentially, rather than according to a power law. This chaotic behaviour is especially pronounced if the medium contains laterally varying interfaces. By studying simple 2-D and 3-D versions of models with laterally varying interfaces, the importance of chaotic ray behaviour is determined. A model of the Moho below Germany produces sharp variations with epicentral distance of the number of arrivals. In addition, the number of caustics grows dramatically: up to 1200 caustics are present between a distance of 0 and 800 km. Using the theory of Hamiltonian systems, a more in-depth study of the chaotic character of the ray equations is obtained. It is found that for realistic heterogeneous models most of the relevant rays will exhibit chaotic behaviour. The degree of chaos is quantified in terms of predictability horizons. Beyond the predictability horizons ray tracing cannot be carried out accurately. For the models under consideration, the length from the source to the predictability horizon has an order of magnitude of 1000 km. The chaotic behaviour of the rays makes it necessary to use extensions of asymptotic ray theory, such as Maslov theory, to compute seismic waveforms. It is shown that pseudo-caustics, an important obstacle in computing Maslov synthetics, are a generic feature of the 2-D laterally varying models that are studied. Eventually, the use of asymptotic methods is restricted because of the inaccuracy in the computation of the ray paths.     

Lyapunov exponent and dimension of the strange attractor of elastic frictional system

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Chaos in the solar system

We have accumulated thousands of orbits of test particles in the Solar System from the asteroid belt to beyond the orbit of Neptune. We find that the time for an orbit to make a close encounter with a perturbing planet, T _c ,is a function of the Lyapunov time, T _ty .The relation is log (T _c /T _o )= a + b log (T _ly T _o )where T _o is a fiducial period which we have taken as the period of the principal perturber or the period of the asteroid. There are exceptions to this rule interior to the 2/3 resonance with Jupiter. There, at least in the restricted problem, for sufficiently small Jupiter mass, orbits may have a positive Lyapunov exponent and still be blocked from having a close approach to Jupiter by a zero velocity curve. Of more serious concern is whether the relation holds for purely secular resonances, and if it does, how to choose T _o .This is the case of interest for the planets in the solar system.     

On the relationship between Lyapunov times and macroscopic instability times

On the basis of the general theory of Hamiltonian systems, we consider the relationship between Lyapunov times and macroscopic diffusion times. We find out that there are two regimes: the Nekhoroshev regime and the resonant overlapping regime. In the first case the diffusion time is exponentially long with respect to Lyapunov times. In the second case, the relationship is polynomial although we do not find any theoretical reason for the existence of a universal power law. We show numerical evidences which confirm our theoretical considerations.     

海温扰动发展的一种热力学判据

本文将非线性热力学理论应用到大尺度海洋系统,找到了一个适合于描述海温扰动发展的热力学判据。计算表明:这种热力学判据能够较好地报出海温异常事件,估计海温异常的强弱。本文还利用这种热力学判据分析了海洋与大气之间的热交换和平流效应对海温扰动演化的影响。     

健康人与心脏病人心电信号混沌特性比较研究

Lyapunov指数是混沌理论的重要参数之一,对分析心电信号特性有重要意义。分别计算健康人和3种心脏病人心电信号的Lyapunov指数,并首次采用室上病变病人作为样本进行研究。对比发现健康人与各类心脏病人的Lyapunov指数之间存在显著差别。同时在重构相空间过程中采用1种同时估计延迟时间τ和嵌入维数m的新方法,并与自相关函数法的计算结果进行对比,在二维相空间重构图上进行验证。结果表明这种方法优于自相关函数法。     

时滞广义时变系统的渐近稳定与镇定

研究了时滞广义时变系统的渐近稳定和镇定问题。首先利用相关不等式,通过建立Lyapunov方程,给出了1个时滞广义时变系统无脉冲、渐近稳定性的充分条件。然后,基于这一工作,利用Riccati方程,进一步研究了时滞广义时变系统的镇定问题。最后,举例说明该结论的可行性。     

基于事件的非周期间歇牵制控制线性复杂网络的同步分析

本文将事件激发和非周期间歇牵制控制进行有机结合,分析了一般线性复杂网络的全局同步问题.通过设计事件激发条件和受控节点选择规则,使受牵制控制节点集在满足一定条件下实现更新,从而不仅极大提高网络实现同步的效率,而且避免现有研究中受控节点集随机选取导致保守性.构造简单的Lyapunov函数,应用稳定性理论和微分不等式,经过严格的数学理论分析得到了使该网络达到渐近指数同步的充分条件,同时也证明了受牵制节点集不可能在有限时间内进行无限次快速切换.     

基于粗糙度的月表虹湾地区地形地貌解译

行星表面粗糙度是表面侵蚀、沉降和隆升等作用在行星表面留下的记录,对其进行的定量分析可以精确地反映其表面地质构造过程.对月球的虹湾地区选取水平方向的12条剖面进行了粗糙度各参数(均方根高程、均方根偏差、均方根坡度、Hurst指数)的计算,结果表明:①在1 km的剖面长度上,虹湾地区均方根高程的平均值在3 m左右;在0.2...     

基于李雅普诺夫指数的矿产资源评价模型的建立

李雅普诺夫指数(Lyapunov exponent)反映了相邻轨迹的分离速率,其重要作用之一就是判断系统的混沌行为。这里建立了以李雅普诺夫指数为基础的资源评价方法的数学模型,并与其它评价方法进行了简单比较,探讨了一种反映混沌成矿的资源预测方法。