The Homoclinic Tangle of A 1:2 Resonance in a 2-D Hamiltonian System

We study in great detail the geometry of the homoclinic tangle, with respect to the energy, corresponding to an unstable periodic orbit of type 1:2, on a surface of section representing a 2-D Hamiltonian system. The tangle consists of two resonance areas, in contrast with the tangles of type-l or -{l, m, k, x = 0} considered in previous studies, that consist of only one resonance area. We study the intersections of the inner and outer lobes of the same resonance area and of the two resonance areas. The intersections of the lobes follow certain rules. The detailed study of these rules allows us to derive quantitative relations about the number of intersections and to understand the complex behavior of the higher order lobes by studying the lower order lobes. We find 1st, 2nd, 3rd, etc. order intersections formed by lobes making 1, 2, 3, etc. turns around an island. After a sufficiently high order of iterations a lobe may intersect its image and thus produce a Poincaré recurrence. Numerical results for a wide interval of energies are presented. The number of intersections changes through tangencies. In any finite interval of the energy between two tangencies of 1st order, an infinite number of higher order tangencies occur and thus, according to the Newhouse theorem, there exist nearby islands of stability.     

Restricted Three-Body Problem: An Approximation of its General Solution – Part One – the Manifold of Symmetric Periodic Solutions

This paper gives the results of a programme attempting to exploit ‘la seule bréche’ (Poincaré, 1892, p. 82) of non-integrable systems, namely to develop an approximate general solution for the three out of its four component-solutions of the planar restricted three-body problem. This is accomplished by computing a large number of families of ‘solutions précieuses’ (periodic solutions) covering densely the space of initial conditions of this problem. More specifically, we calculated numerically and only for μ = 0.4, all families of symmetric periodic solutions (1st component of the general solution) existing in the domain D:(x ₀ ∊ [−2,2],C ∊ [−2,5]) of the (x ₀, C) space and consisting of symmetric solutions re-entering after 1 up to 50 revolutions (see graph in Fig. 4). Then we tested the parts of the domain D that is void of such families and established that they belong to the category of escape motions (2nd component of the general solution). The approximation of the 3rd component (asymmetric solutions) we shall present in a future publication. The 4th component of the general solution of the problem, namely the one consisting of the bounded non-periodic solutions, is considered as approximated by those of the 1st or the 2nd component on account of the `Last Geometric Theorem of Poincaré' (Birkhoff, 1913). The results obtained provoked interest to repeat the same work inside the larger closed domain D:(x ₀ ∊ [−6,2], C ∊ [−5,5]) and the results are presented in Fig. 15. A test run of the programme developed led to reproduction of the results presented by Hénon (1965) with better accuracy and many additional families not included in the sited paper. Pointer directions construed from the main body of results led to the definition of useful concepts of the basic family of order n, n = 1, 2,… and the completeness criterion of the solution inside a compact sub-domain of the (x ₀, C) space. The same results inspired the ‘partition theorem’, which conjectures the possibility of partitioning an initial conditions domain D into a finite set of sub-domains D i that fulfill the completeness criterion and allow complete approximation of the general solution of this problem by computing a relatively small number of family curves. The numerical results of this project include a large number of families that were computed in detail covering their natural termination, the morphology, and stability of their member solutions. Zooming into sub-domains of D permitted clear presentation of the families of symmetric solutions contained in them. Such zooming was made for various values of the parameter N, which defines the re-entrance revolutions number, which was selected to be from 50 to 500. The areas generating escape solutions have being investigated. In Appendix A we present families of symmetric solutions terminating at asymptotic solutions, and in Appendix B the morphology of large period symmetric solutions though examples of orbits that re-enter after from 8 to 500 revolutions. The paper concludes that approximations of the general solution of the planar restricted problem is possible and presents such approximations, only for some sub-domains that fulfill the completeness criterion, on the basis of sufficiently large number of families.     

Short-term Climate Characteristics at Ny-(A)lesund over the Arctic Tundra Area

Based on the Germany Koldwey Station's 1994-2003 conventional observation hourly data, this paper conducts a statistical analysis on the short-term climate characteristics for an arctic tundra region (Ny-(A)lesund island) where our first arctic expedition station (Huanghe Station) was located. Affected by the North Atlantic warming current, this area has a humid temperate climate, and the air temperature at Ny-(A)lesund rose above 0 ℃ even during deep winter season during our research period. The wind speed in this area was low and appeared most at southeast direction. We find that the temperature at Ny-(A)lesund rose in the faster rate (0.68 ℃/10 a) than those at the whole Arctic area. Compared with the floating ices where our expedition conducted in the Arctic, Ny-(A)lesund was warmer and more humid and had lower wind speed. Comparison of the near surface air temperature derived by NCEP/NCAR reanalysis to the conventional measurements conducted at the Koldwey site in Ny-(A)lesund area shows a good agreement for winter season and a significant difference for summer season.     

Isobaric cooling and anti-clockwise P–T paths in the Variscan Odenwald Crystalline Complex, Germany

Mineral assemblages in Al₂O₃‐rich, SiO₂‐ and K₂O‐poor metapelitic rocks from the western Odenwald Crystalline Complex (Variscan Mid‐German Crystalline Rise, southern Germany) include corundum, spinel, cordierite, sillimanite, garnet and staurolite. Quartz is absent from almost all samples. Therefore, the applicability of conventional geothermobarometry is very limited or even impossible. Detailed petrographic investigation on selected samples permits inference of the sequence of appearance and disappearance of several mineral assemblages. The recognition of such partial re‐equilibration stages and their associated mineral assemblages, together with mineral stabilities predicted from KFMASH pseudosections, enables the determination of the pressure‐temperature (P–T) trajectories experienced by these rocks during the Variscan metamorphism. The rocks were metamorphosed under low‐P/high‐T conditions and underwent an anti‐clockwise P–T evolution. A pressure increase from about 2 kbar to 4 ± 0.5 kbar was accompanied by heating. Peak metamorphic conditions were reached at pressures of 4 ± 0.5 kbar and temperatures of at least 640 °C, probably even higher. The retrograde evolution is characterised by near‐isobaric cooling from ≥ 640 °C to approximately 550 °C. The rocks underwent the anti‐clockwise evolution in a subduction‐related magmatic arc setting. The close spatial association of the low‐P/high‐T rocks with recently discovered metabasic eclogites in the eastern part of the Odenwald Crystalline Complex may indicate a fossil paired metamorphic belt in the Central European Variscides.     

Hysteresis‐based analysis of overland metal transport

Introducing a concept of equivalent mass depth of flow, this study describes the phenomenon of non‐point source pollutant (metal) transport for pavement (or overland) flow in analogy with wave propagation in wide open channels. Hysteretic and normal mass rating curves are developed for runoff rate and mass of 12 dissolved and particulate‐bound metal elements (pollutants) using the rainfall‐runoff and water quality data of the 15 × 20 m² instrumented pavement in Cincinnati, USA. Normal mass rating curves developed for easy computation of pollutant load are found to be of a form similar to Manning's, which is valid for open channel flows. Based on the hysteresis analysis, wave types for dissolution and mixing of particulate‐bound metals are identified. The analysis finds that the second‐order partial‐differential equation normally used for metal transport does not have the efficacy to describe fully the strong non‐linear phenomena such as is described for various metal elements by dynamic waves. In addition, the proportionality concept of the popular SCS‐CN concept is extended for determining the potential maximum metal mass M_p of all the 12 elements transported by a rain storm and related to the antecedent dry period (ADP). For the primary metal zinc element, M_p is found to increase with the ADP and vice versa. Copyright © 2003 John Wiley & Sons, Ltd.     

山西地震综合数据处理系统

《山西地震综合数据处理系统》是遵循《国家地震局数据库技术规范》,以PDP-11/23~+小型机与IBM/PC联机为硬件支撑,以网状型数据库为核心,含前期处理、库管理、数据检索、科学计算、分析会商5个子系统的较大型应用软件系统。具有对数据进行收集、录入、预处理、存储、管理、加工及应用等功能。整个系统通过总控菜单程序实现了异种机间上百个模块的调度,使查询-处理一体化。该系统把地震数据库、日常监测数据处理、专家地震预报系统有机地衔接于一体,可直接服务于地震科研和震情会商。该系统的建设是山西省重大科技攻关项目,也是国家地震局的合同制项目。     

南极威尔克斯地SGR钻孔处雪冰转化过程中的密度变化特征

本文着重描述了SGR钻孔处冰盖上的积雪在密实化过程中的特征变化,并对该过程进行了分段的和全面的回归分析.结果表明,冰盖密度随深度增大,但增长幅度随深度减小.作者提出密度变化减小度的概念.计算得出的所研究冰芯钻取点的密度变化减小度为-0.15kg/m~3·m~2,粒雪成冰前的密实速率平均值为4.08kg/m~3·a.本文得到的冰盖密度变化“临界点”与以往报道的有所不同.分析这一现象时,作者强调当积雪还在活动层时冰盖温度的影响,并以此解释密度剖面的异常变化以及离差的回升.特别指出,积雪的密度变化具有气候学意义,它在一定程度上能够反映出积雪形成及变化过程中气候变化的某些信息.本文由密度变化确定的钻孔点雪冰转化深度为50米.     

Detailed <Superscript>40</Superscript>Ar/<Superscript>39</Superscript>Ar dating of geologic events associated with the Mantos Blancos copper deposit,northern Chile

The ⁴⁰Ar/³⁹Ar geochronological method was applied to date magmatic and hydrothermal alteration events in the Mantos Blancos mining district in the Coastal Cordillera of northern Chile, allowing the distinction of two separate mineralization events. The Late Jurassic Mantos Blancos orebody, hosted in Jurassic volcanic rocks, is a magmatic-hydrothermal breccia-style Cu deposit. Two superimposed mineralization events have been recently proposed. The first event is accompanied by a phyllic hydrothermal alteration affecting a rhyolitic dome. The second mineralization event is related to the intrusion of bimodal stocks and sills inside the deposit. Because of the superposition of several magmatic and hydrothermal events, the obtained ⁴⁰Ar/³⁹Ar age data are complex; however, with a careful interpretation of the age spectra, it is possible to detect complex histories of successive emplacement, alteration, mineralization, and thermal resetting. The extrusion of Jurassic basic to intermediate volcanic rocks of the La Negra Formation is dated at 156.3 ± 1.4 Ma (2σ) using plagioclase from an andesitic lava flow. The first mineralization event and associated phyllic alteration affecting the rhyolitic dome occurred around 155–156 Ma. A younger bimodal intrusive event, supposed to be equivalent to the bimodal stock and sill system inside the deposit, is probably responsible for the second mineralization event dated at ca. 142 Ma. Other low-temperature alteration events have been dated on sericitized plagioclase at ca. 145–146, 125, and 101 Ma. This is the first time that two distinct mineralization events have been documented from radiometric data for a copper deposit in the metallogenic belt of the Coastal Cordillera of northern Chile. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Statistical analysis of sand grain/bed collision process recorded by high-speed digital camera

A high‐speed digital camera was employed to record the sand grain/bed collision process. With image processing and a statistical method, a series of parameters of the collision process were obtained. The results show that the collision process of a grain with rebounding can be represented by two parameters: the kinetic energy restitution coefficient and the collision angle. Both parameters satisfy a normal distribution, and they are dependent on one another. With an increase of the collision angle, the distribution of the kinetic energy restitution gradually reduces from a broad to a narrow range with low values. The percentage of vertical velocity restitution coefficients greater than 1 can reach 70% or more, which ensures that the settling time of the sand grains in the air increases and that they receive more energy from the air to progress the saltation movement.     

Possible chemical structures and biological precursors of different vitrinites in coal measure in Northwest China

Chemical structure of Jurassic vitrinites isolated from the coals in basins in NW China have been checked using solid state ¹³C NMR and flash pyrolysis-GC/MS. Study shows some Jurassic collodetrinites are rich in aliphatic products in pyrolysates, consisting with the high amount of methylene carbon in ¹³C NMR spectra. In contrast, pyrolysates of Jurassic collotelinites are rich in phenols and alkylbenzenes. Also one Pennsylvanian and one Permian vitrinite selected from the Ordos basin, NW China have been checked for comparison. The proportion of aliphatics is low in pyrolysates, and aliphatic carbon peak in ¹³C NMR spectrum of Permian vitrinite is mostly composed of gas-prone carbons compared with collodetrinites in those Jurassic basins. But both pyrolysis and ¹³C NMR data shows the Pennsylvanian vitrinite is not only gas-prone but also oil-prone. Relatively high proportion of long chain aliphatic structure of some Jurassic vitrinite in Junggar, Turpan-Hami basins may be due to the contribution of liptodetrinites, which may be included during the formation of vitrinites. And it seems that suberinite is the most possible precursor of long chain aliphatics in the structure of Jurassic collodetrinite.