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
This review of the literature from 2004 and 2005 concerning secondary ion mass spectrometry (SIMS) highlights the contribution the technique has made in the fields of petrology, geochronology, cosmochemistry and material sciences. In petrology, much research was devoted to the measurement of stable isotopes and trace elements by developments in multicollection acquisition, with emphasis on low atomic mass number elements. Elements studied in particular were S (in sulfides), O (in garnets), C (in sedimentary organic matter), Cl (in glasses) and Si. Novel applications of SIMS to geochronology have included the measurement of young zircon grains by the U-Pb and U-Th decay methods. An increasing number of studies have combined U-Pb geochronology with the measurement of trace elements or stable isotopes in zircon. 相似文献
A large amount of deep oil has been discovered in the Tazhong Uplift, Tarim Basin whereas the oil source is still controversial. An integrated geochemical approach was utilized to unravel the characteristics, origin and alteration of the deep oils. This study showed that the Lower Cambrian oil from well ZS1C (1x) was featured by small or trace amounts of biomarkers, unusually high concentration of dibenzothiophenes (DBTs), high δ34S of DBTs and high δ13C value of n-alkanes. These suggest a close genetic relationship with the Cambrian source rocks and TSR alteration. On the contrary, the Middle Cambrian oils from well ZS1 (2a) were characterized by low δ13C of n-alkanes and relatively high δ34S of individual sulfur compounds and a general “V” shape of steranes, indicating a good genetic affinity with the Middle–Upper Ordovician source rocks. The middle Cambrian salt rock separating the oils was suggested to be one of the factors responsible for the differentiation. It was suggested that most of the deep oils in the Tazhong Uplift were mixed source based on biomarkers and carbon isotope, which contain TSR altered oil in varied degree. The percentage of the oils contributed by the Cambrian–Lower Ordovician was in the range of 19–100% (average 57%) controlled by several geological and geochemical events. Significant variations in the δ34S values for individual compounds in the oils were observed suggesting a combination of different extent of TSR and thermal maturation alterations. The unusually high DBTs concentrations in the Tazhong-4 oilfield suggested as a result of mixing with the ZS1C oil (1x) and Lower Ordovician oils based on δ34S values of DBT. This study will enhance our understanding of both deep and shallow oil sources in the Tazhong Uplift and clarify the formation mechanisms of the unusually high DBTs oils in the region. 相似文献
Oxygen isotope compositions were measured in quartz grains extracted from a 7.0 Ma red clay-loess sequence at Lingtai and
six late Pleistocene loess sediments (Malan loess). Results show that the changes in oxygen isotope compositions of Malan
loess are basically controlled by the geochemical characteristics of the source materials, while the effect of weathering
process after dust deposition could be minor. The oxygen isotope distribution of quartz grains from red clay at Lingtai is
similar to that of the overlying loess-paleosol sequence, thus indicating that the red clay at Lingtai has the same eolian
origin as the loess-paleosol deposits. Furthermore, the oscillations of the isotope compositions in 4–16 μm-sized quartz grains
may reflect the changes, to some extent, of the climatic systems of the source region. 相似文献
Stable carbon isotopic composition of ethane and propane over the western North Pacific and eastern Indian Ocean between 31°N
and 26°S was investigated from February through March 2004. The isotopic composition of ethane ranged from −28 to −18‰ and
showed a gradual increase from north to south. Conversely, that of propane was between −31 and −24‰; it showed no systematic
latitudinal variation. Investigation of the ethane/propane ratio indicates that ethane and propane that originated from northern
mid-latitude countries in the eastern part of Eurasia were both transported into the western North Pacific region. However,
the results of the isotopic analyses indicate the contribution of oceanic emission to the atmospheric propane during transport,
although that contribution can not be discerned for ethane. A ship based stationary observation conducted in the western equatorial
North Pacific showed that the isotopic composition of ethane varied from −25 to −19‰ and showed clear systematic diurnal variation:
propane ranged between −32 to −26‰ and no such isotopic diurnal signal was observed. The diurnal variation for ethane is explained
by entrainment of free tropospheric air, whereas the variation for propane was influenced by oceanic emissions as well as
the entrainment. The contribution of oceanic emissions to the atmospheric propane inventory was considered from our isotopic
observation. Isotopic composition of dissolved propane is estimated to be less than −38‰, and the contribution up to 79% was
calculated when the isotopic composition of dissolved propane is assumed to be −40‰. Our study demonstrates that isotopic
analysis can be more useful than ratio-based analysis to improve our present understanding of transport processes, especially
for impact of the oceanic emissions on the atmospheric distribution of low level C2–C5 non-methane hydrocarbons such as propane in the remote marine atmosphere. 相似文献
Separated mass extinction occurred at the beginning and the ending of the Late Permian, called end-Guadalupian and end-Permian mass extinctions, respectively. Palaeoenvironmental changes in the middle of the Late Permian could give more insights into the environmental causes for the Permian extinctions. In this contribution, we analysed carbonate carbon isotope and carbonate-associated-sulphate sulphur isotope compositions to constrain the carbon and sulphur cycles across the Wuchiapingian-Changhsingian boundary (WCB) at Yanglinqiao in Zigui in the Middle Yangtze Platform. Pyrite morphology and pyrite framboids size distribution were used to analyse redox conditions variations across the WCB. Our results show that an episodic euxinia event occurred across the WCB. This anoxic/euxinic event across the WCB was a global event, and was mainly caused by the upwelling during the cooling event. Both inorganic- and organic-carbon isotopic compositions show covariance of a negative shift across the WCB at Yanglinqiao and other places in South China. This carbon-isotopic negative excursion across the WCB was a regional carbon cycle perturbation and may be linked to the light-carbon input from the upwelling water mass. Although the seawater δ34S across the WCB recorded a negative excursion in two locations in South China, it reflects the riverine input of 32S-enriched sulphate and represent a regional signal. These environmental anomalies such as oceanic anoxia/euxinia, global carbon cycle perturbation, cooling, end of the Emeishan large igneous province movement across the WCB may have delayed the recovery from the end-Guadalupian mass extinction. 相似文献
High-resolution oxygen-isotope records of benthic ostracods and molluscs from Ammersee, southern Germany, show high-frequency climatic changes during the last deglaciation and parallel in great detail published faunal and floral variations reconstructed from Norwegian Sea sediments and isotope variations in Greenland ice cores. The marine and the terrestrial records give evidence of a synchronous late glacial climatic development in Greenland, NW- and Mid-Europe. However,14C-ages of the supraregional climatic events and of two tephra layers in the marine sediments of the northeastern Atlantic Ocean are significantly older than the14C-ages of the corresponding horizons on land. These differences strongly suggest that major short-term events have affected the exchangeable carbon on earth during the dramatic environmental changes related to the deglaciation and in particular have affected the CO2-distribution within the ocean and between ocean and atmosphere. Dating methods independent of climatic variations and of the global carbon budget should be given priority to refine the timescales of the marine and atmospheric processes during the last deglaciation.This is the fourth paper in a series of papers published in this issue on high-resolution paleolimnology. These papers were presented at the Sixth International Palaeolimnology Symposium held 19–21 April, 1993 at the Australian National University, Canberra, Australia. Dr. A. F. Lotter and Dr. M. Sturm served as guest editors for these papers. 相似文献