The general solution of the HENON–HEILES problem     

K.?E.?PapadakisEmail author  C.?L.?Goudas  G.?A.?Katsiaris 《Astrophysics and Space Science》2005,295(3):375-396

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.  相似文献   

    

I. C. Lemmer 《Mathematical Geology》1986,18(7):589-604

For any distribution of grades, a particular cutoff grade is shown here to exist at which the indicator covariance is proportional to the grade covariance to a very high degree of accuracy. The name mononodal cutoff is chosen to denote this grade. Its importance for robust grade variography in the presence of a large coefficient of variation—typical of precious metals—derives from the fact that the mononodal indicator variogram is then linearly related to the grade variogram yet is immune to outlier data and is found to be particularly robust under data information reduction. Thus, it is an excellent substitute to model in lieu of a difficult grade variogram. A theoretical expression for the indicator covariance is given as a double series of orthogonal polynomials that have the grade density function as weight function. Leading terms of this series suggest that indicator and grade covariances are first-order proportional, with cutoff grade dependence being carried by the proportionality factor. Kriging equations associated with this indicator covariance lead to cutoff-free kriging weights that are identical to grade kriging weights. This circumstance simplifies indicator kriging used to estimate local point-grade histograms, while at the same time obviating order relations problems.This paper is based in part on a PhD thesis submitted to the Department of Applied Earth Sciences, Stanford University, Stanford, California 94305, in 1984 (unpublished).  相似文献   

Synthesis, crystal structure and crystal chemistry of ferri-clinoholmquistite, ?Li ₂Mg ₃Fe ³⁺ ₂Si ₈O ₂₂(OH) ₂     

G. Iezzi  F. Cámara  R. Oberti  G. Della Ventura  G. Pedrazzi  J-L Robert 《Physics and Chemistry of Minerals》2004,31(6):375-385

This work reports the synthesis of ferri-clinoholmquistite, nominally _Li2(Mg₃Fe³⁺₂)Si₈O₂₂(OH)₂, at varying f_O2 conditions. Amphibole compositions were characterized by X-ray (powder and single-crystal) diffraction, microchemical (EMPA) and spectroscopic (FTIR, Mössbauer and Raman) techniques. Under reducing conditions ( NNO+1, where NNO = Nickel–Nickel oxide buffer), the amphibole yield is very high (>90%), but its composition, and in particular the FeO/Fe₂O₃ ratio, departs significantly from the nominal one. Under oxidizing conditions ( NNO+1.5), the amphibole yield is much lower (<60%, with Li-pyroxene abundant), but its composition is close to the ideal stoichiometry. The exchange vector of relevance for the studied system is ^M2(Mg,Fe²⁺) ^M4(Mg,Fe²⁺) ^M2Fe³⁺_–1 ^M4Li_–1, which is still rather unexplored in natural systems. Amphibole crystals of suitable size for structure refinement were obtained only at 800 °C, 0.4 GPa and NNO conditions (sample 152), and have C2/m symmetry. The X-ray powder patterns for all other samples were indexed in the same symmetry; the amphibole closest to ideal composition has a = 9.428(1) Å, b = 17.878(3) Å, c = 5.282(1) Å, = 102.06(2)°, V = 870.8(3) ų. Mössbauer spectra show that Fe³⁺ is strongly ordered at M2 in all samples, whereas Fe²⁺ is disordered over the B and C sites. FTIR analysis shows that the amount of ^CFe²⁺ increases for increasingly reducing conditions. FTIR data also provide strong evidence for slight but significant amounts of Li at the A sites.  相似文献   

浅谈高等级三角高程测量在水电工程高程测量中的应用     

贲素香  李青山 《东北测绘》2012,(5):190-193

水电工程一般建在深山峡谷中,陡坎多、高差大,不利于几何水准测量。三角高程测量不受地形起伏限制,外业测量工作量小、速度快,作业人员少,在水电工程低精度高程测量中应用广泛。怎样提高三角高程测量精度,一直是大家关注的问题。本文介绍了溪洛渡水电站三角高程测量的实践经验供大家借鉴。  相似文献   

旋转扰动流体中壁面湍流不稳定及其拟序结构研究Ⅱ：数值模式   总被引：1，自引：1，他引：0  

Enrico Ferrero  张瑛  全利红  Luca Mortarini  Renato Forza 《气象与减灾研究》2009,32(4):14-17

对第一部分的实验结果进行了讨论,指出局地最大、最小涡度的存在与所谓的正压不稳定和大气中经常观测到的滚动涡有关。速度廓线中的拐点和涡度极大值点对应不稳定发展的位置。另外,为了改进湍流的模拟,根据“准正则”近似,发展了一个三阶闭合模式。这个模型已被证明可以描述与湍流过程有关的流体动力学变量的趋势。  相似文献   

地球物理台网仪器维修信息管理的研究与实现     

刘高川  滕云田  庞晶源  瞿旻  杨正纲 《地震研究》2021,44(1):121-128

针对地球物理台网仪器维修信息化薄弱的现状,提出一个规范的地球物理台网仪器维修流程,并对故障仪器的流通和维修订单的处理动作等信息进行研究,设计了满足地球物理台网仪器维修信息管理的数据库结构,设计和实现了基于B/S架构的仪器维修管理系统,并在全国地球物理台网业务中部署使用。该系统具有可视化流程操作、维修资源弹性可扩展、维修信息共享和维修资源协同化的特点,满足地球物理台网仪器维修信息化管理需要,并为其它地震仪器信息化管理系统的设计提供了借鉴。  相似文献   

基于假三元模型的透辉石-硬玉固溶体热力学性质计算     

刘鑫  陆现彩 《岩石矿物学杂志》2019,38(1):104-112

自然界中矿物多以固溶体形式存在,据其晶体化学特征计算热力学性质是开展矿物成因理论研究的基础。本文引入描述二元矿物固溶体热力学性质的假三元模型,计算得到了透辉石-硬玉固溶体系列的热力学性质。该模型通过构造一种高度有序的中间相,同时考虑长程和短程有序效应,基于热力学平衡态矿物固溶体自由能最低的规律,可以计算特定组分下矿物的平衡自由能、焓和熵等热力学参数。本文针对透辉石-硬玉固溶体体系,取绿辉石为其中间有序态,计算了其活度-成分关系和温度-组分相图等,发现绿辉石随温度升高的有序无序相变为一级相变,相变温度为1 148±25 K,与实验研究结果一致。本文获得的透辉石-绿辉石-硬玉体系的热力学参数可用于视剖面图方法研究MORB成分的岩石的榴辉岩相变质作用过程。  相似文献   

一阶弹性波交错网格时间高阶差分格式及稳定性分析     

田雪丰 《中国煤炭地质》2019,(5):70-78

弹性波模拟或逆时偏移时,对空间偏导数采用高阶差分格式可提高计算精度,但这种算法的稳定性条件过于严格,要求差分离散的时间步长必须足够小以确保算法稳定。在常规空间高阶差分格式的基础上,将速度(应力)对时间的高阶导数转化为不同精度的应力(速度)对空间的差分,得到了一种新的基于交错网格的时间高阶、空间高阶差分格式。通过对交错网格时间高阶差分格式稳定性的分析,认为该算法的稳定性条件较常规算法宽松,在弹性波场的求解过程中可以采用更大的时间步长。  相似文献   

Dynamic,discontinuous stream networks: hydrologically driven variations in active drainage density,flowing channels and stream order          下载免费PDF全文

S. E. Godsey  J. W. Kirchner 《水文研究》2014,28(23):5791-5803

Despite decades of research on the ecological consequences of stream network expansion, contraction and fragmentation, surprisingly little is known about the hydrological mechanisms that shape these processes. Here, we present field surveys of the active drainage networks of four California headwater streams (4–27 km²) spanning diverse topographic, geologic and climatic settings. We show that these stream networks dynamically expand, contract, disconnect and reconnect across all the sites we studied. Stream networks at all four sites contract and disconnect during seasonal flow recessions, with their total active network length, and thus their active drainage densities, decreasing by factors of two to three across the range of flows captured in our field surveys. The total flowing lengths of the active stream networks are approximate power‐law functions of unit discharge, with scaling exponents averaging 0.27 ± 0.04 (range: 0.18–0.40). The number of points where surface flow originates obey similar power‐law relationships, as do the lengths and origination points of flowing networks that are continuously connected to the outlet, with scaling exponents averaging 0.36–0.48. Even stream order shifts seasonally by up to two Strahler orders in our study catchments. Broadly, similar stream length scaling has been observed in catchments spanning widely varying geologic, topographic and climatic settings and spanning more than two orders of magnitude in size, suggesting that network extension/contraction is a general phenomenon that may have a general explanation. Points of emergence or disappearance of surface flow represent the balance between subsurface transmissivity in the hyporheic zone and the delivery of water from upstream. Thus the dynamics of stream network expansion and contraction, and connection and disconnection, may offer important clues to the spatial structure of the hyporheic zone, and to patterns and processes of runoff generation. Copyright © 2014 John Wiley & Sons, Ltd.  相似文献   

Solid–fluid transition modelling in geomaterials and application to a mudflow interacting with an obstacle     

Noémie Prime  Frédéric Dufour  Félix Darve 《国际地质力学数值与分析法杂志》2014,38(13):1341-1361

Given the contrasting behaviour observed for geomaterials, for example, during landslides of the flow type, this contribution proposes an original constitutive model, which associates both an elasto‐plastic relation and a Bingham viscous law linked by a mechanical transition criterion. This last is defined as the second‐order work sign for each material point, which is a general criterion for divergence instabilities. Finite element method with Lagrangian integration points is chosen as a framework for implementing the new model because of its well‐known ability to deal with both solid and fluid behaviours in large deformation processes. A first boundary model considering a sample of initially stable soil, a slope and an obstacle is performed. The results show the power of the constitutive model because the consistent evolution of initiation, propagation and arrest of the mudflow is described. A parametric study is led on various plastic and viscous parameters to determine their influence on the flow development and arrest. Finally, forces against the obstacle are compared with good agreement with those of other authors for the same geometry and a pure viscous behaviour. Copyright © 2014 John Wiley & Sons, Ltd.  相似文献