The general solution of the HENON–HEILES problem

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.     

Multifractal and Chaotic Analysis of Vrancea (Romania) Intermediate-depth Earthquakes: Investigation of the Temporal Distribution of Events

The Vrancea seismic region contains an isolated cluster of events beneath the Carpathian Arc Bend in Romania, dipping to about 200 km depth. Seismic activity mainly occurs at intermediate depths (h > 60 km). The main goal of the paper is to perform an in-depth, complex analysis of the occurrence times of these intermediate-depth events. We also try to show the versatility of the methods used to characterize different aspects of the seismicity evolution and to offer a user-friendly software toolbox to do most of the related computations. The earthquake catalog used in this study spans from 1974 to 2002 and includes only the intermediate-depth events. In the first part of the paper, we analyze the multifractal characteristics of the temporal distribution of earthquakes. The study reveals two distinct scaling regimes. At small scales we found a clear nonhomogeneous, multifractal pattern, while at large scales the temporal distribution of events shows a monofractal, and close to Poissonian (random), behavior. The multifractal behavior at small scales (minutes-hours) is shown to be clearly an effect of the short aftershock sequences that occurred after some major Vrancea earthquakes. In the second part of the paper we analyze whether our temporal series shows a persistent (or anti-persistent) long-term behavior, by using the Detrended Fluctuation Analysis (DFA) method. The results suggest that the analyzed temporal series of Vrancea earthquakes is a non-correlated process. In part three of the paper we seek to determine whether the dynamics of our earthquake system (described by the occurrence time of Vrancea earthquakes) is deterministically chaotic, deriving from a rather simple evolution law, or whether it is stochastic and is generated by a system that possesses many degrees of freedom. The results suggest that our signal is stochastic (probably does not possess an attractor). The limited time-span of the catalog and the analysis performed in this paper cannot rule out the emergence of an interesting, quasi-deterministic and low-dimensional structure in the case of major Vrancea earthquakes.Acknowledgement One of the authors (BE) is grateful to the Japanese Ministry of Education for providing him a Monbusho scholarship for studying in DPRI, Kyoto University. We thank Z.R. Struzik, M Holschneider, J. Mori and D. Kaplan for their useful comments, and acknowledge the support of the staff of DPRI, Kyoto University and the National Inst. for Earth Physics, Bucharest. We thank the two reviewers, M.B. Geilikman and M. Anghel, for their useful suggestions which improved the quality of this work.     

Collective resonant phenomena on small bodies in the solar system

For both asteroids and meteor streams, and also for comets, resonances play a major role for their orbital evolutions but on different time scales. For asteroids both mean motion resonances and secular resonances not only structure the phase space of regular orbits but are mainly at the origin for the inherent chaos of planet crosser objects.For comets and their chaotic routes temporary trapping into orbital resonances is a well known phenomenon. In addition for slow diffusion through the Kuiper belt resonances are the only candidates for originating a slow chaos.Like for asteroids, resonances with Jupiter play a major role for the orbital evolution of meteor streams. Crossing of separatrix like zones appears to be crucial for the formation of arcs and for the dissolution of streams. In particular the orbital inclination of a meteor stream appears to be a critical parameter for arc formation. Numerical results obtained in an other context show that the competition between the Poynting-Robertson drag and the gravitational interaction of grains near the 2/1 resonance might be very important in the long run for the structure of meteor streams.     

黄土高原东缘晚全新世高精度高分辨率石笋古环境记录

基于山西武乡太行龙洞一支石笋5个230Th年龄和190个氧同位素数据重建4 400~150 a B.P.高分辨率δ18O序列。石笋δ18O值逐渐增加,除最近约600 a外,在千年尺度长期趋势变化上与中国南部其它洞穴记录相一致,表明晚全新世亚洲夏季风强度持续减弱响应于同一驱动机制。一次显著的气候突变事件发生在2 550~2 000 aB.P.,与史料记载的干旱期大致相对应。功率谱分析揭示出106 a周期,与树轮Δ14C太阳活动周期大体一致,说明百年尺度上太阳活动与东亚季风变化有一定关联性。     

豫北一次局地雹暴天气的预警特征和触发机制

利用常规气象观测、多普勒雷达、卫星资料和区域自动站观测资料及NCEP再分析资料,对2011年6月11日豫北局地强对流天气的预报预警特征和触发机制进行分析。结果表明：局地强对流天气是在东北冷涡背景下产生的,高低层中尺度影响系统(槽、切变线、大风速轴)交汇处右侧是强对流发生潜势区。局地强对流天气发生前,CAPE较大,0-6 km垂直风切变达到中等偏强,有利于超级单体的形成和发展。高空冷平流南侵、低层暖平流北上,有利于大气对流不稳定度进一步加大。中-β尺度强对流云团在东北冷涡槽底后部形成,其发展演变对局地强对流天气预报预警有参考意义。强对流回波经历了细胞状、带状发展期和块状减弱期。回波带南侧形成的超级单体造成了局地强风雹天气,冰雹发生时伴有“三体散射”现象。冷空气和地面辐合线是强对流天气的主要触发机制;地面辐合线对强对流天气还有提示作用。     

混沌系统单变量可预报性研究

对于n维的混沌系统, 不同变量的可预报性是不同的。为了研究混沌系统中单个变量的可预报性, 本文在以前提出的混沌系统整体的非线性局部Lyapunov指数基础上(李建平等, 2006), 引入了单变量的非线性局部Lyapunov指数及其相关统计量, 进一步完善了非线性误差增长理论。通过应用到几个混沌个例, 结果表明单变量的非线性局部Lyapunov指数及其相关统计量可以用来定量地研究多维混沌系统中不同变量的可预报性, 系统不同变量的可预报性之间不是相互独立的, 而是单个变量的可预报期限与系统整体的可预报期限之比都近似保持一个常数, 但各个变量的常数值有所不同。     

Influence of filling velocity on stability of subgrade with marine soft soil

Filling velocity and thickness of soft layer are major factors affecting subgrade stability according to an example study by means of finite element stress method (FESM). A case is studied and shows that the subgrade was slided because of excessive filling velocity. To determine a reasonable filling velocity is a key problem to a subgrade with marine soft soil.     

二叠系炭质页岩软弱夹层剪切蠕变特性研究

以西南灰岩山区二叠系炭质页岩软弱夹层为研究对象,开展了原生软岩、层间剪切带和滑带3个演化阶段的矿物组成成分、微结构和不同正应力水平的剪切蠕变力学特性分析。结果表明：软弱夹层在演化过程中,矿物组分发生改变,黏土矿物含量在原生软岩中小于5%,层间剪切带中在5%～10%之间,滑带中大于10%。微结构由致密变得疏松,颗粒间连接力减弱;软弱夹层的蠕变位移和蠕变速率随着剪应力增加而增大,呈非线性关系。在相同剪应力条件下,蠕变位移和蠕变速率的关系为：滑带>层间剪切带>原岩。长期剪切强度逐渐降低,黏聚力的降幅大于内摩擦角,对时间的敏感程度较高。为受软弱夹层控制的层状基岩滑坡的发育发展过程、失稳机制研究提供了重要借鉴意义。     

山东半岛石笋记录的倒数第二次冰消期δ18O变化特征及其气候环境意义

文章基于山东半岛岩溶洞穴(上小峰洞)一根长约41 cm的石笋SD1的铀系测年和稳定同位素组成分析,获得138. 0~125. 8 ka B. P.平均分辨率为30年的石笋δ18O 和δ13C时间序列,并据此讨论了倒数第二次冰消期区域气候和环境变化的特征及与全球变化的联系.在倒数第二次冰消期,上小峰洞石笋( SD1)δ18O的变化与中国南方石笋δ18O的变化具有类似的阶段变化特征,进一步确认了冰消期北大西洋气候对亚洲季风的重要影响.通过对山东石笋高分辨δ18O记录进行时间序列分析,发现该记录存在显著的约60年、 75年和1620年周期,表明太阳活动和北大西洋涛动与该地区气候变化有紧密的联系.同时,通过对比东亚季风区高分辨率石笋记录,认为在倒数第二次冰消期为"两步冰消"的变化特征.除此之外,上小峰洞石笋碳酸盐δ18O冰期和间冰期平均值的差异仅为0. 7‰,远小于内陆洞穴石笋碳酸盐δ18O冰期和间冰期平均值的差异(羊口洞约为1. 4‰,董哥洞约为2. 2‰,三宝洞约为2. 4‰).这一显著差异可能主要源于海岸线迁移造成的海陆格局的变化对区域季风降水及降水氧同位素组成的重要影响;并且冰期-间冰期海平面变化对近海环境记录、大陆架下垫面、海洋沉积物气候指标等都可能产生影响.     

勘查地球化学数据挖掘与弱异常识别

我国积累的大量高质量、多元素、多尺度的地球化学数据,为矿产勘查与环境评价提供了有效的数据支撑。如何对这些数据进行二次开发和再利用,提取有价值的地球化学异常信息并带动找矿突破,是缓解当前矿产资源短缺的重要途径之一。在覆盖区和深部的找矿实践中,由于矿体埋深和覆盖层的影响,往往在表生介质中形成弱小的地球化学异常,识别和评价弱小地球化学异常是当前勘查地球化学数据处理的重要方向之一。本文围绕地球化学异常信息的提取和评价,主要从以下几个方面讨论了相关的国内外研究进展和发展趋势:勘查地球化学数据处理与异常识别方法和模型,勘查地球化学数据闭合效应的影响及其解决方案,基于大数据和机器学习的勘查地球化学数据处理以及弱小地球化学异常的识别和评价。研究发现,在地质环境的约束下,基于大数据思维和机器学习相结合的方法,注重地球化学空间分布模式与已发现矿床的相关关系,同时使用所有地球化学变量能有效刻画具有非线性特征的地球化学空间分布模式,可识别出传统方法无法识别的异常,为开展地球化学空间模式识别与异常提取提供了新的途径。