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.     

Climatological distribution of lightning density observed by satellites in China and its circumjacent regions

The 0.5°×0.5°grid resolution distribution of lightning density in China and its circumjacent regions have been analyzed by using the satellite-borne OTD (Apr 1995-Mar 2000) and LIS (Dec 1997-Mar 2003) databases. It is shown that: (i) Firstly, the variability of the lightning density (LD) is particularly pronounced over the different subareas, 9 times greater over the south than the north side of Himalayas Mountains, 2.5 times greater over the eastern than the western area of China. While the maximum and minimum LD are respectively 31.4fl/km2/a (in Guangzhou region) and less than 0.2fl/km2/a (in the desert of western China). Secondly, the LD of China's continent regularly varies with latitude and distance off coast, which is consistent with annual mean precipitation in varying trend. In conclusion, the Qinghai-Tibet Plateau, the China's three-step staircase topography and the latitude are three important factors affecting macro-scale characteristics of the LD distribution, (ii) The regional differences     

Dehydration melting of solid amphibolite at 2.0 GPa: Effects of time and temperature

The dehydration melting of the natural rock at high pressure is important to investigating the magma formation in the earth’s interior. Since the 1970s, a lot of geological scientists have paid more atten- tion to the dehydration melting of the natural rock[1―5]. Previous experiments of dehydration melting and observations of fieldwork argued that the dehy- dration melting of the rock was probably the most important fashion for the melting of the lower crust rock[6―12]. The genesis of most …     

<Superscript>40</Superscript>Ar/<Superscript>39</Superscript>Ar chronology and geochemistry of high-K volcanic rocks in the Mangkang basin,Tibet

Our two newly obtained high-quality ⁴⁰Ar/³⁹Ar ages suggest that the high-K volcanic rocks of the Lawuxiang Formation in the Mangkang basin, Tibet were formed at 33.5 ± 0.2 Ma. The tracing of elemental and Pb-Sr-Nd isotopic geochemistry indicates that they were derived from an EM2 enriched mantle in continental subduction caused by transpression. Their evidently negative anomalies in HFSEs such as Nb and Ta make clear that there is an input of continental material into the mantle source. The high-K rocks at 33.5 ± 0.2 Ma in the Mangkang basin may temporally, spatially and compositionally compare with the early one of two-pulse high-K rocks in eastern Tibet distinguished by Wang J. H. et al., implying that they were formed in the same tectonic setting.     

Second Tesseral Harmonic Torque Due to the DynamicS of the Oceanic Surface Layer as Detected by TOPEX/POSEIDON Altimetry 1993-2000

Estimates of the second tesseral torque due to the variations in the radial space position of the mean ocean surface as monitored by TOPEX/POSEIDON altimeter system are derived. The magnitude of the studied torque may be compared to the tidal torque and to the tesseral torque caused by deformations due to the Earths rotation. However, such torque estimates strongly depend on the thickness of the ocean surface layer adopted in the spherical model of which the dynamics is believed to be responsible for the derived torque. The dependence on the thickness is discussed.     

The eruptive history of the Tequila volcanic field, western Mexico: ages, volumes, and relative proportions of lava types

The eruptive history of the Tequila volcanic field (1600 km²) in the western Trans-Mexican Volcanic Belt is based on ⁴⁰Ar/³⁹Ar chronology and volume estimates for eruptive units younger than 1 Ma. Ages are reported for 49 volcanic units, including Volcán Tequila (an andesitic stratovolcano) and peripheral domes, flows, and scoria cones. Volumes of volcanic units 1 Ma were obtained with the aid of field mapping, ortho aerial photographs, digital elevation models (DEMs), and ArcGIS software. Between 1120 and 200 kyrs ago, a bimodal distribution of rhyolite (~35 km³) and high-Ti basalt (~39 km³) dominated the volcanic field. Between 685 and 225 kyrs ago, less than 3 km³ of andesite and dacite erupted from more than 15 isolated vents; these lavas are crystal-poor and show little evidence of storage in an upper crustal chamber. Approximately 200 kyr ago, ~31 km³ of andesite erupted to form the stratocone of Volcán Tequila. The phenocryst assemblage of these lavas suggests storage within a chamber at ~2–3 km depth. After a hiatus of ~110 kyrs, ~15 km³ of andesite erupted along the W and SE flanks of Volcán Tequila at ~90 ka, most likely from a second, discrete magma chamber located at ~5–6 km depth. The youngest volcanic feature (~60 ka) is the small andesitic volcano Cerro Tomasillo (~2 km³). Over the last 1 Myr, a total of 128±22 km³ of lava erupted in the Tequila volcanic field, leading to an average eruption rate of ~0.13 km³/kyr. This volume erupted over ~1600 km², leading to an average lava accumulation rate of ~8 cm/kyr. The relative proportions of lava types are ~22–43% basalt, ~0.4–1% basaltic andesite, ~29–54% andesite, ~2–3% dacite, and ~18–40% rhyolite. On the basis of eruptive sequence, proportions of lava types, phenocryst assemblages, textures, and chemical composition, the lavas do not reflect the differentiation of a single (or only a few) parental liquids in a long-lived magma chamber. The rhyolites are geochemically diverse and were likely formed by episodic partial melting of upper crustal rocks in response to emplacement of basalts. There are no examples of mingled rhyolitic and basaltic magmas. Whatever mechanism is invoked to explain the generation of andesite at the Tequila volcanic field, it must be consistent with a dominantly bimodal distribution of high-Ti basalt and rhyolite for an 800 kyr interval beginning ~1 Ma, which abruptly switched to punctuated bursts of predominantly andesitic volcanism over the last 200 kyrs.Electronic Supplementary Material Supplementary material is available in the online version of this article at Editorial responsility: J. Donnelly-NolanThis revised version was published online in January 2005 with corrections to Tables 1 and 3.An erratum to this article can be found at     

Outgassing-induced effects in the rotational state of comet 67P/Churyumov—Gerasimenko during the Rosetta mission

The new target of the Rosetta mission is comet 67P/Churyumov-Gerasimenko (hereafter 67P/C-G). In order to support the planning of the mission, in particular the strategy during the mapping and landing phases, we have performed numerical simulations of the rotational evolution of a comet in the orbit of 67P/C-G. In these simulations, the currently known observational constraints have been taken into account and a large set of initial conditions were considered. For most of the simulations, we observe that the sublimation-induced torques produce significant changes in the rotational parameters of a 67P/C-G-like comet. Typical rates of change for the spin period from the rendezvous up to the end of the nominal mission range from 0.001 to depending on different circumstances as described in the text. At perihelion, rates of change of the orientation of the angular momentum vector amount to about 0.01-. These simulations suggest that a specific strategy should be defined in order to monitor likely variations of the rotational parameters. As an example we show a possible optimized schedule for observations with the OSIRIS instrument to determine the rotational parameters of comet 67P/C-G and their possible evolution.     

多层界面快速反演在高精度石油重力勘探中的应用

重力勘探作为一种快速普查方法，在深部地质构造研究、区域地质构造划分及找矿勘探中均已取得显著的地质效果。自８０年代后期，由于在重力测地工作中使用红外测距仪及高精度ＧＰＳ定位技术，确保了重力测点位置及高程有较高的精度；在重力观测中普遍采用目前世界上精度最高的Ｌａｃｏｓｔｅ型重力仪进行基点联测，采用对恒温系统改进后的Ｗｏｒｄｅｎ重力仪进行重力测点观测，使得重力测量的质量及精度都有了很大提高，为扩大重力法的应用提供了条件。本文给出的一例是；在我国某含油沉积盆地上，根据对实测１：２５０００高精度重力资料（布格重力异常总观测均方误差：６０×１０￣－８ｍ／ｓ￣２）的处理及约束信息下多层界面反演结果，确定有利油气聚集的圈闭范围，推断含油层的大致规模。     

XPer的新发射相：光谱与红外观测

ＸＰｅｒ的新发射相：光谱与红外观测杭恒荣，夏剑萍中国科学院紫金山天文台，南京２１０００８中国科学院光学天文联合实验室关键词Ｂｅ星／Ｘ射线双星，发射线，ＪＨＫ测光１引言ＸＰｅｒ是一颗Ｂｅ／Ｘ射线双星（４Ｕ０３５２＋３０）的光学对应体［１－３］，中子星的...     

Pliocene—pleistocene boundary in the Kleszczów Graben at Belchatów,central Poland

The Pliocene-Pleistocene boundary, defined using pollen analysis, has been recorded in sections at the Belchatów outcrop, Kleszczów Graben, central Poland. The boundary is located at the top of the green clay subunit of the Tertiary Clayey-sandy unit. A pollen flora of Reuverian C type, dominated by pine, 10–20% of ‘Reuverian elements’ and scarce thermophilous Tertiary trees, was found directly below this subunit. Cold stage floras of Praetiglian type were, in turn, recorded in the ?ekińsko Formation, lying directly on the green clays. The Pliocene—Pleistocene transition at Belchatów demonstrates the characteristic features of this boundary in western Europe, that is, the disappearance of Tertiary thermophilous tree pollen taxa, followed by a cooling to open-forest or forest-steppe conditions. Both pollen analysis and geological data suggest continuous sedimentation at least from the Upper Pliocene to the Prae-Tiglian, with no change of sediment sources and no marked hiatuses. The fluvial deposits of the Praetiglian ?ekińsko Formation, although Pleistocene in age, mark a final period in the Tertiary evolution of the Kleszczów Graben. Later, there is a hiatus to the deposition of the first glacigenic sediments in the region possibly of Elsterian age.