Escapes and Recurrence in a Simple Hamiltonian System

Many physical systems can be modeled as scattering problems. For example, the motions of stars escaping from a galaxy can be described using a potential with two or more escape routes. Each escape route is crossed by an unstable Lyapunov orbit. The region between the two Lyapunov orbits is where the particle interacts with the system. We study a simple dynamical system with escapes using a suitably selected surface of section. The surface of section is partitioned in different escape regions which are defined by the intersections of the asymptotic manifolds of the Lyapunov orbits with the surface of section. The asymptotic curves of the other unstable periodic orbits form spirals around various escape regions. These manifolds, together with the manifolds of the Lyapunov orbits, govern the transport between different parts of the phase space. We study in detail the form of the asymptotic manifolds of a central unstable periodic orbit, the form of the escape regions and the infinite spirals of the asymptotic manifolds around the escape regions. We compute the escape rate for different values of the energy. In particular, we give the percentage of orbits that escape after a finite number of iterations. In a system with escapes one cannot define a Poincaré recurrence time, because the available phase space is infinite. However, for certain domains inside the lobes of the asymptotic manifolds there is a finite minimum recurrence time. We find the minimum recurrence time as a function of the energy.This revised version was published online in October 2005 with corrections to the Cover Date.     

Bias and uncertainty in regression-calibrated models of groundwater flow in heterogeneous media

Groundwater models need to account for detailed but generally unknown spatial variability (heterogeneity) of the hydrogeologic model inputs. To address this problem we replace the large, m-dimensional stochastic vector β that reflects both small and large scales of heterogeneity in the inputs by a lumped or smoothed m-dimensional approximation γθ_∗, where γ is an interpolation matrix and θ_∗ is a stochastic vector of parameters. Vector θ_∗ has small enough dimension to allow its estimation with the available data. The consequence of the replacement is that model function f(γθ_∗) written in terms of the approximate inputs is in error with respect to the same model function written in terms of β, f(β), which is assumed to be nearly exact. The difference f(β) − f(γθ_∗), termed model error, is spatially correlated, generates prediction biases, and causes standard confidence and prediction intervals to be too small. Model error is accounted for in the weighted nonlinear regression methodology developed to estimate θ_∗ and assess model uncertainties by incorporating the second-moment matrix of the model errors into the weight matrix. Techniques developed by statisticians to analyze classical nonlinear regression methods are extended to analyze the revised method. The analysis develops analytical expressions for bias terms reflecting the interaction of model nonlinearity and model error, for correction factors needed to adjust the sizes of confidence and prediction intervals for this interaction, and for correction factors needed to adjust the sizes of confidence and prediction intervals for possible use of a diagonal weight matrix in place of the correct one. If terms expressing the degree of intrinsic nonlinearity for f(β) and f(γθ_∗) are small, then most of the biases are small and the correction factors are reduced in magnitude. Biases, correction factors, and confidence and prediction intervals were obtained for a test problem for which model error is large to test robustness of the methodology. Numerical results conform with the theoretical analysis.     

双频相位求差法探测与修复周跳特性分析

周跳的探测与修复是GPS载波相位数据处理中一项重要的任务。首先介绍了双频相位求差法探测与修复周跳的原理;其次,利用Fortran语言编制了相应的程序,并通过实例分析了在不同采样率下探测周跳与修复的效果;最后讨论了该方法探测周跳的不足。     

边界层风廓线雷达在降水时段中的在线分析应用研究

本研究提出了一种在边界层风廓线雷达连续运行的降水探测时段中对降水频谱进行在线分析的新的应用方式。详细介绍了边界层风廓线雷达在线分析原理和方法。同时结合典型降水频谱个例,分析了可获得的多个潜在的气象参数和信息。并指出,该在线分析方式的实施可以使风廓线雷达的应用领域从晴空探测向降水测量拓展;有效缓解当前风廓线雷达应用存在的瓶颈问题;间接证明边界层风廓线雷达组网间距不固定的观点。文章分析说明,随着在线分析方式的推广应用,边界层风廓线雷达将成为单站精细化气象探测和预报/服务的重要工具。     

当代生物多样性剧减与古-中生代之交生物绝灭的对比

18世纪以来人类活动对环境造成了强烈破坏,给生物多样性带来了巨大损失.为了了解生物多样性的变化趋势,利用"绝灭物种统计法"、"种-区曲线法"和化石记录对400年以来的生物多样性和古-中生代之交的生物绝灭进行了分析.当代生物多样性剧减表现为物种的快速绝灭(从8×104种/Ma增大到1.2×106种/Ma),而属的绝灭几乎为0;古-中生代之交生物绝灭的初始阶段也表现为物种的快速绝灭(从40种/Ma增大到150种/Ma),并且这个阶段的属的绝灭速率远低于绝灭高峰阶段的相应值(即66属/Ma远小于465属/Ma),可见当代生物多样性剧减相当于二叠-三叠系之交生物绝灭的初始阶段.     

基于区间非概率可靠性方法的岩溶区桩基下溶洞顶板稳定性评价

岩溶区桩基下溶洞顶板稳定性影响因素取值的不确定性及其样本数量的有限性,给桩基下溶洞顶板稳定性的评价带来了一定困难。根据现有研究成果,建立桩基下溶洞顶板抗冲切、抗剪切和抗弯力学简化模型,并从理论上推导相应的稳定性验算公式。在此基础上,结合区间分析理论和结构非概率可靠性度量方法,提出了基于区间非概率可靠性方法的桩基下溶洞顶板稳定性评价方法。该方法采用MATLAB中的INTLAB工具箱进行区间运算,并运用截断法消除运算过程中的区间扩展现象,最后通过比较溶洞顶板体系的非概率可靠性指标η与1的大小来判断桩基下溶洞顶板稳定性。以丹霞高速互通中D匝道2#桩基下溶洞为例,计算出该桩基下溶洞顶板体系的非概率可靠性指标η=7.95,该值大于1说明该桩基下溶洞顶板处于稳定状态,且评价结果与工程实际相符,表明了该方法的合理性与可行性。分别以3种功能函数为单位,研究当区间变量的变异系数C不同时(C从0.01递增至0.1),对应非概率可靠性指标η的变化规律。研究表明,随各区间变量变异系数C的增大,相应非概率可靠性指标呈不同程度的降低,其中溶洞顶板厚度h的变异性对评价结果影响最大,其次为桩端阻力分担比T,桩顶反力F的影响相对最小。     

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.     

鄂尔多斯盆地渭北地区上三叠统延长组长7油层组碳酸盐结核中自生碳酸盐矿物的特征

早期形成的碳酸盐结核在埋藏期间会经历多种碳酸盐矿物相沉淀的复杂胶结作用,岩石学研究是探究结核成因的关键。通过野外剖面观察、岩石学观察和阴极发光技术,分析了鄂尔多斯盆地渭北地区上三叠统延长组长7油层组泥页岩中各种形状的方解石和白云石结核中自生碳酸盐矿物的特征。这些结核为成岩早期的产物,构成结核的自生碳酸盐矿物特征显著:(1)球粒方解石结核中,方解石呈纤维状或刃片状,球粒间充填晶粒方解石或因压实呈贴面结合,纤维状方解石发桔红色和暗红色2种光,刃片状方解石发暗红色光;(2)粉晶方解石结核中,方解石呈他形粒状,含有机质包裹体或纤维状晶形残余,晶间含沥青和纤维状方解石残余,主要发暗红色光;(3)白云石结核有泥晶和粉晶2种晶体类型,粉晶白云石结核含较多泥质,泥质条带或有机质条带处常见纤柱状白云石;(4)沿裂缝充填的方解石和白云石常呈纤维状或纤柱状结构,发暗红色光或不发光。研究区长7油层组碳酸盐结核中的方解石和白云石具有不同的成因类型和复杂的胶结作用:球粒方解石和泥晶白云石代表了结核开始形成时的胶结作用,可以准确地反映结核的成因;粉晶方解石、粉晶白云石反映了交代成因;裂缝中纤维状、纤柱状方解石和白云石集合体则为结核经历了较强压实作用之后充填裂缝而成。     

SEISMIC GEOLOGY

正20141967An Zhanghui(Lanzhou Base of Institute of Earthquake Prediction,CEA,Lanzhou 730000,China);Du Xuebin Study onthe Geo-Electric Field Variation of Sichuan Lushan MS7.0and Wenchuan MS8.0Earthquake(Chinese Journal of Geophysics,ISSN0001-5733,CN11-2074/P,56(11),