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

Kostantinos Papadakis  Constantine Goudas 《Astrophysics and Space Science》2006,305(2):99-124

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.  相似文献   

The hydrological influence of black locust plantations in the loess area of northwest China     

Wang Yanhui 《水文研究》1992,6(2):241-251

Black locust (Robina pseudoacacia) has become one of the most important shelter species in the loess area of northwest China. This paper summarizes recent research concerning its hydrological influence, including canopy interception, litter absorption capacity, its effect on rainfall kinetic energy, infiltration rates, surface runoff, soil moisture, and evapotranspiration, and its role in soil conservation. Several predictive models are listed. on the basis of existing results, optimum characteristics for an effective plantation are defined, and problems requiring further research are identified.  相似文献   

发挥行业和地域优势开辟经济发展新领域——矿业网站的建设设想     

息飏  张明平 《南方国土资源》2001,14(2):47-51

网络经济已成为新的社会生产力的代表。广西地质矿产勘查开发局应该利用其行业和地域方面的固有优势，积极参与网络经济，以期打开矿业市场。文章提出了建立矿业网站的设想和框架。  相似文献   

多接收器电感耦合等离子体质谱法测定镉标准溶液中镉的同位素组成   总被引：1，自引：1，他引：0  

高博  梁细荣  刘颖  胡光黔  曾文  涂湘林 《岩矿测试》2008,27(5):321-324

建立了多接收器电感耦合等离子体质谱仪对Cd标准溶液同位素组成进行分析的实验方法。仪器的质量分馏校正采用Standard-Sample Bracketing法。实验结果用δ114/110Cd来表达。在此研究基础上,以SPEX Cd标准溶液为参考标准,对国外4种Cd标准溶液进行了测定。结果表明,实验测定的精度在0.07‰~0.13‰(δ114/110Cd),与目前文献报道的结果具有相似的精度。以最新SPEX Cd标准样品(δ114/110Cd=0)为基准,计算的δ114/110CdJMC、δ114/110CdSPEX-1、δ114/110CdBAM1012和δ114/110CdM櫣nster的值分别为0.55‰、0.56‰、-0.65‰和5.14‰,说明不同批次SPEX标准溶液的Cd同位素组成是明显不同的,最新的SPEX Cd标准溶液与SPEX-1 Cd的δ114/110Cd值存在着0.56‰的差别。将以SPEX Cd为参考标准的δ114/110CdBAM1012和δ114/110CdM櫣nster转化为以SPEX-1或JMC为参考标准后,得到的结果与文献报道的结果在误差范围内一致。  相似文献   

Application of MODFLOW and geographic information system to groundwater flow simulation in North China Plain, China   总被引：2，自引：0，他引：2  

Shiqin Wang  Jingli Shao  Xianfang Song  Yongbo Zhang  Zhibin Huo  Xiaoyuan Zhou 《Environmental Geology》2008,55(7):1449-1462

MODFLOW is a groundwater modeling program. It can be compiled and remedied according to the practical applications. Because of its structure and fixed data format, MODFLOW can be integrated with Geographic Information Systems (GIS) technology for water resource management. The North China Plain (NCP), which is the politic, economic and cultural center of China, is facing with water resources shortage and water pollution. Groundwater is the main water resource for industrial, agricultural and domestic usage. It is necessary to evaluate the groundwater resources of the NCP as an entire aquifer system. With the development of computer and internet information technology it is also necessary to integrate the groundwater model with the GIS technology. Because the geological and hydrogeological data in the NCP was mainly in MAPGIS format, the powerful function of GIS of disposing of and analyzing spatial data and computer languages such as Visual C and Visual Basic were used to define the relationship between the original data and model data. After analyzing the geological and hydrogeological conditions of the NCP, the groundwater flow numerical simulation modeling was constructed with MODFLOW. On the basis of GIS, a dynamic evaluation system for groundwater resources under the internet circumstance was completed. During the process of constructing the groundwater model, a water budget was analyzed, which showed a negative budget in the NCP. The simulation period was from 1 January 2002 to 31 December 2003. During this period, the total recharge of the groundwater system was 49,374 × 10⁶ m³ and the total discharge was 56,530 × 10⁶ m³ the budget deficit was −7,156 × 10⁶ m³. In this integrated system, the original data including graphs and attribution data could be stored in the database. When the process of evaluating and predicting groundwater flow was started, these data were transformed into files that the core program of MODFLOW could read. The calculated water level and drawdown could be displayed and reviewed online.  相似文献   

Impacts of at-site wastewater disposal systems on the groundwater aquifer in arid regions: case of Sfax City, Southern Tunisia     

Ibticem Chamtouri  Habib Abida  Hafedh Khanfir  Salem Bouri 《Environmental Geology》2008,55(5):1123-1133

Groundwater in Sfax City (Tunisia) has been known since the beginning of the century for its deterioration in quality, as a result of wastewater recharge into the aquifer. An average value of 12 × 10⁶ m³ of untreated wastewater reaches the groundwater aquifer each year. This would result not only in a chemical and biological contamination of the groundwater, but also in an increase of the aquifer piezometric level. Quantitative impacts were evaluated by examining the groundwater piezometric level at 57 surface wells and piezometers. The survey showed that, during the last two decades, the groundwater level was ever increasing in the urban area with values reaching 7 m in part; and decreasing in Sidi Abid (agricultural area) with values exceeding −3 m. Groundwater samples for chemical and microbial analysis were collected from 41 wells spread throughout the study area. Results showed significantly elevated levels of sodium, chlorides, nitrates and coliform bacteria all over the urban area. High levels (NO₃: 56–254 mg/l; Na >1,500 mg/l; Coliforms >30/100 ml) can be related to more densely populated areas with a higher density of pit latrine and recharge wells. Alternatively results showed a very variable chemical composition of groundwater, e.g. electrical conductivity ranges from 4,040 to19,620 μs/cm and the dry residual varies between 1.4 and 14 g/l with concentrations increasing downstream. Furthermore a softening of groundwater in Set Ezzit (highly populated sector) was observed.  相似文献   

Hydrogeochemical investigations and groundwater provinces of the Friuli Venezia Giulia Plain aquifers,northeastern Italy   总被引：2，自引：0，他引：2  

Franco Cucchi  Giuliana Franceschini  Luca Zini 《Environmental Geology》2008,55(5):985-999

Water resources are a key factor, particularly for the planning of the sustainable regional development of agriculture, as well as for socio-economic development in general. A hydrochemical investigation was conducted in the Friuli Venezia Giulia aquifer systems to identify groundwater evolution, recharge and extent of pollution. Temperature, pH, electric conductivity, total dissolved solids, alkalinity, total hardness, SAR, Ca²⁺, Na⁺, K⁺, Mg²⁺, Cl⁻, SO₄ ²⁻, NO₃ ⁻, HCO₃ ⁻ _, water quality and type, saturation indexes and the environmental stable isotope δ¹⁸O were determined in 149 sampling stations. The pattern of geochemical and oxygen stable isotope variations suggests that the sub-surface groundwater (from phreatic and shallow confined aquifers) is being recharged by modern precipitations and local river infiltrations. Four hydrogeological provinces have been recognised and mapped in the Friuli Venezia Giulia Plain having similar geochemical signatures. These provinces have different degrees of vulnerability to contamination. The deep confined groundwater samples are significantly less impacted by surface activities; and it appears that these important water resources have very low recharge rates and would, therefore, be severely impacted by overabstraction.  相似文献   

Glacier change and glacier runoff variation in the Tuotuo River basin,the source region of Yangtze River in western China   总被引：3，自引：0，他引：3  

Yong Zhang  Shiyin Liu  Junli Xu  Donghui Shangguan 《Environmental Geology》2008,56(1):59-68

Glaciers in the Tuotuo River basin, western China, have been monitored in recent decades by applying topographical maps and high-resolution satellite images. Results indicate that most of glaciers in the Tuotuo River basin have retreated in the period from 1968/1971 to 2001/2002, and their shrinkage area is 3.2% of the total area in the late 1960s. To assess the influence of glacier runoff on river runoff, a modified degree–day model including potential clear-sky direct solar radiation has been applied to the glaciated regions of the river basin over the period 1961–2004. It was found that glacier runoff has increased in the last 44 years, especially in the 1990s when a two-thirds increase in river runoff was derived from the increase in glacier runoff caused by loss of ice mass in the entire Tuotuo River basin.  相似文献   

Mineralogy and geochemistry of the Texeo Cu–Co mine site (NW Spain): screening tools for environmental assessment     

J. Loredo  R. Álvarez  A. Ordóñez  T. Bros 《Environmental Geology》2008,55(6):1299-1310

The Cu–Co–Ni Texeo mine has been the most important source of Cu in NW Spain since Roman times and now, approximately 40,000 m³ of wastes from mine and metallurgical operations, containing average concentrations of 9,263 mg kg⁻¹ Cu, 1,100 mg kg⁻¹ As, 549 mg kg⁻¹ Co, and 840 mg kg⁻¹ Ni, remain on-site. Since the cessation of the activity, the abandoned works, facilities and waste piles have been posing a threat to the environment, derived from the release of toxic elements. In order to assess the potential environmental pollution caused by the mining operations, a sequential sampling strategy was undertaken in wastes, soil, surface and groundwater, and sediments. First, screening field tools were used to identify hotspots, before defining formal sampling strategies; so, in the areas where anomalies were detected in a first sampling stage, a second detailed sampling campaign was undertaken. Metal concentrations in the soils are highly above the local background, reaching up to 9,921 mg kg⁻¹ Cu, 1,373 mg kg⁻¹ As, 685 mg kg⁻¹ Co, and 1,040 mg kg⁻¹ Ni, among others. Copper concentrations downstream of the mine works reach values up to 1,869 μg l⁻¹ and 240 mg kg⁻¹ in surface water and stream sediments, respectively. Computer-based risk assessment for the site gives a carcinogenic risk associated with the presence of As in surface waters and soils, and a health risk for long exposures; so, trigger levels of these elements are high enough to warrant further investigation.  相似文献   

A transdisciplinary analysis of water problems in the mountainous karst areas of Morocco     

C. de Jong  S. Cappy  M. Finckh  D. Funk 《Engineering Geology》2008,99(3-4):228

Water management and engineering in the karstic High Atlas of Morocco are difficult tasks under the prevailing geological, hydrogeological, geomorphological, vegetational and climatic conditions. It is important to be able to understand and predict the characteristics and availability of water for future water planning in the region under changing climatic and agricultural conditions. An interdisciplinary analysis of problems and adequate hydrological modelling tools developed by geologists, hydrologists and biologists are necessary. The karst areas of the High Atlas Mountains are characterised by impermeable triassic basalt underlying substantial subsurface reservoirs with high potential discharge rates. The karst groundwater aquifers are extensive but largely unknown in dimension, probably with a hierarchical network of groundwater flow paths. It is estimated that approximately 70% of the surface water is directly lost to groundwater. Steep landslide- and debris flow prone slopes exist next to coarse-grained, highly porous river beds. Infrequent, high intensity rainfall or snowmelt causes a particularly high flood risk to these karst areas. In addition, agriculture and land use changes have degraded the karst areas. The most important driving forces for degradation include permanent overgrazing even during droughts and the use of firewood by a continually growing population. Large scale degradation of vegetation has occurred in the oro-mediterranean (mountainous Mediterranean) zone, between 2600 and 3400 m which coincides with the most important zone for karstic groundwater creation. The combination of high amounts of groundwater flow and rapid surface flow due to sparse vegetation has increased the problems of flood flow.  相似文献