Long-term evolution of the spin of Venus: II. numerical simulations

We present here the numerical application of the theoretical results derived in Correia et al. (2003, Icarus 163, 1-23) for the spin evolution of Venus since its formation. We explore a large variety of initial conditions to cover the possible formation and evolutionary scenarios. In particular, we pay special attention to the evolutions which cross the chaotic zone resulting from secular planetary perturbations (Laskar and Robutel, 1993, Nature 361, 608-612). We demonstrate that Venus’ axis can be temporarily trapped in a secular resonance with the node of Neptune’s orbit, which can prevent it from being tilted to 180° and will drive it toward 0°. We test several dissipation models and parameters to evaluate their contribution to the planet’s spin history. We confirm that despite the variations in the models, only three of the four final spin states of Venus are possible (Correia and Laskar, 2001, Nature 411, 767-770) and that the present observed retrograde spin state of Venus can be attained by two different processes. In the first scenario (π−), the axis is tilted toward 180° while its rotation rate slows down, while in the second one, the axis is driven toward 0° obliquity and the rotation rate decreases, stops, and increases again in the reverse direction to a final equilibrium value (0−).     

人地非线性相关作用的探讨

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。     

非线性科学在地球科学中的应用

本文介绍了耗散结构理论、分形理论和混沌理论等非线性科学在地球科学中的研究进展,分析了非线性科学在地球科学中的地位和作用,探讨了将非线性科学引入地球科学的途径和方法。     

混沌功率谱熵方法在识别水淹低阻油层中的应用

储集层孔隙度和电阻率曲线间微差形态波形的复杂程度隐含着储集层含油气性的信息,可以用混沌动力学系统加以刻划。油层相空间庞加莱截面明显具有自相似结构,呈现混沌特性;而水淹层和水层的相空间庞加莱截面显示,其混沌性呈显著减弱之势,系统趋于简单有序。其功率谱密度不论水淹程度如何,整体为一随频率增大其能量按指数递减连续频谱;随水淹程度逐渐减弱,递减幅度减小,整体能量逐渐降低,某些频率成分被吸收削弱,由光滑状逐渐演变成锯齿起伏状,其功率谱熵逐渐增大。基于测井信息的混沌特征和功率谱熵特征识别水淹层的方法,对利用传统测井解释理论判别比较困难的低阻油层有较强的识别能力。     

研究地震和岩石破裂现象的非线性科学方法

本文以地震孕育和岩石破裂过程的阶段(包括裂纹系形成、变形局部化和断层形成、断层活动和松弛)为线索,阐述了非线性科学方法(包括分形几何学,自组织临界现象和混沌动力学)的应用,提出了地震孕育过程和岩石破裂各阶段的普适性特征、机理和要着重研究的课题.     

非线性地震道的混沌反演——Ⅱ.关于Lyapunov指数和吸引子

在本文上篇《非线性地震道的混沌反演——1.理论和数值试验》中讨论了非线性反问题逐次线性化方法及迭代过程的系统特性、递推法和广义线性反演法输出波阻抗序列的特征。本篇参照混沌理论中关于Lyapunov指数、相空间和吸引子的概念,深入研究逐次线性化迭代的状态变化的阶段性及其定量描述.当引用相空间描述系统的演化时,对于随迭代变化的阻尼因子可以发现几种吸引子.最后,总结了非线性地震混沌反演的要点,指出非线性反演迭代的复杂阶段性要川混沌理论来描述,而Lyapunov指数等才是控制迭代过程的实质性参数.     

地球变化磁场的分形和混沌特征

将北京地区地球变化磁场的水平分量作为一无规时间序列,利用谱分析方法求出了１９５９,１９６５,１９７０和１９７６年时间段的分数维布朗运动（ＦＢＭ）的维数Ｄｂ。结果表明Ｄｂ值与太阳活动性呈负相关。进而利用时间延迟方法来重建该序列在相空间的吸引子,计算得到吸引子的维数Ｄ＝４．２±０．４,最大Ｌｙａｐｕｎｏｖ指数总是正值。这表明地球变化磁场可能是混沌的。还利用一简单模型说明太阳活动性对地球变化磁场Ｄｂ值的影响。     

细胞自动机的多重分形特征和动力学根源

用大量弹簧滑块组成的模型可以模拟地震的复杂性，本文以细胞自动机（ＣＡ）为数学工具，结合地震学和岩石力学的结果，考虑了能量的输入和损耗，进行了地震事件的数字模拟。对模型中输出的“地震”事件进行了时间和空间的多分形分析，并对自组织临界（ＳＯＣ）状态进行了讨论，进而得到事件至少在时间域里的分布呈现出层次结构，符合自相似特征。本文的ＣＡ模型属于确定性的混沌系统，而对于处在ＳＯＣ状态下的大量事件的频度和大小的统计与Ｇ－Ｒ指数律很好地吻合。结果表明，虽然自组织（ＳＯ）可能是更准确的地震表征，但ＳＯＣ仍然是研究地震现象的很好的模式。     

地震道的非线性混沌反演——Ⅰ.理论和数值试验

全文以地震道反演的数值实验为例,根据混沌理论讨论了非线性地震反演的以下特性:1.对于带误差的地震数据和极其平滑的初始模型,逐次线性化的迭代过程产生的输出序列最终走向无序,这是非线性反演系统本身的特性决定的;2.迭代（非线性反演）系统是由Poin-care映的或系统方程描述的;3.可以根据地震反问题的特点,用多种不同的方法定义相应的Lyapunov指数,它们的数值和组合是非线性反演系统状态的有效指示;4.取决于系统参数的选取,发现在二维相空间有奇异吸引子的对应物.总之,从混沌理论的角度来研究纯数学的非线性地震反问题,可以揭示某些过去鲜为人知的内在规律性.本文为全文的上篇,主要讨论前两个问题,即理论和地震道反演数值试验结果.     

Deterministic uncertainty in landscapes

Deterministic complexity (chaos) may be common in geomorphic systems, but traditional definitions may have limited practical utility for empirical geomorphology. These definitions are based on sensitivity to initial conditions, which in geomorphology are both unknown and unknowable. Further, chaos analysis depends on distinguishing deterministic complexity from stochastic complexity. This is problematic in geomorphology because some stochastic complexity is virtually always present in addition to any chaos that may be present. While it is important to recognize that some complex, apparently random patterns may derive from inherent non-linear system dynamics, this is of limited use in explaining process–response relationships or mechanics of landscape evolution. A more general term, which subsumes chaos, is deterministic uncertainty, i.e. uncertainty associated with an identifiable but unknown or uncertain source. An analysis of landscape entropy shows that such underlying constraints produce spatial patterns which are apparently chaotic. For the case of geologic controls, the apparent contribution of deterministic chaos to the landscape entropy is a direct non-linear function of the extent of geologic constraints. However, the underlying constraints and their contribution to observed spatial patterns can also be interpreted in non-chaotic terms. Examples are given, involving geologic constraints on stream channel networks and parent material control of surface soil textures. Because both randomness and chaos may be more apparent than real, the concept of deterministic uncertainty is more useful in process geomorphology than that of chaos.