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51.
In this article we present a theoretical method for the study of the general three-body problem by computer simulation developed in the Leningrad State University Astronomical Observatory (LSU AO). This method permits statistical methods to be used for studying the behaviour of triple systems. This is achieved by selecting a representative sample of initial conditions which then reveal general features of the evolution.The main results of numerical experiments on the three-body problem carried out at the LSU AO during the past 25 years have been summarized in the reviews by Anosova (1985), Anosova and Orlov (1985), and Anosova (1986).Systematic studies of about 3 × 104 triple systems with negative total energy (E < 0) have yielded the following main results. Most (93.4%) of the systems decay; the decay always occurs after a close triple approach of the components. In a system with unequal masses, the escaping body usually has the smallest mass. A small fraction (4.3%) of stable systems is formed if the angular momentum is non-zero. The qualitative evolution in three-dimensional cases is the same as for planar systems. Small changes in initial conditions sometimes lead to substantial differences in the final outcome. The decay of triple systems is a stochastic process similar to radioactive decay. The estimated mean lifetime is equal to % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% Waa0aaaeaacaWGubaaaaaa!3C56!\[\overline T \] = (107.1 ± 1.8) crossing times for equal-mass components. Thus, for solar mass components and a typical dimension d = 0.01 pc, % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% Waa0aaaeaacaWGubaaaaaa!3C56!\[\overline T \] = (1.6 ± 1.5) × 106 y, and for triple galaxies with M = 101° M 0 and d = 50 kpc, % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% Waa0aaaeaacaWGubaaaaaa!3C56!\[\overline T \] = (1.8 ± 1.7) × 1011 y. The value % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% Waa0aaaeaacaWGubaaaaaa!3C56!\[\overline T \] decreases with increasing mass dispersion.In this article we also carry out a theoretical analysis of the changes of the integrals of motion in the general three-body problem used as the controls on the calculations. The following basic results have been found: (1) analytical functions of the changes of the integrals of motion during the integration time have been obtained; (2) changes in the integrals of the mass-centre of a triple system do not correlate with the cumulative integration errors; (3) the cumulative changes of the integral of energy are proportional to the sum of squares of the cumulative errors in the coordinates and the velocities of the bodies; (4) the cumulative changes of the square of the total angular momentum are proportional to the product of the square of these cumulative errors.The analysis of the accuracy of computer simulations conducted in LSU AO for the 3 × 104 triple systems with E < 0 is summarized by the following basic qualitative results: (1) the unstable triple systems decay after a mean lifetime % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% Waa0aaaeaacaWGubaaaaaa!3C56!\[\overline T \] 100 or % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% Waa0aaaeaacaWGubaaaaaa!3C56!\[\overline T \] 104 % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% Waa0aaaeaacaWGObaaaaaa!3C6A!\[\overline h \]t where is a crossing time, and % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% Waa0aaaeaacaWGObaaaaaa!3C6A!\[\overline h \], is a mean integration step After this integration time % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% Waa0aaaeaacaWGubaaaaaa!3C56!\[\overline T \] the mean cumulative relative changes % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% Waa0aaaeaacaWGebGaamyraaaaaaa!3D10!\[\overline {DE} \] of the integrals of the energy of the triple systems are equal to % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% Waa0aaaeaacaWGebGaamyraaaaaaa!3D10!\[\overline {DE} \] = (0.9±0.1) × 10–4, and the mean cumulative relative changes % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% Waa0aaaeaacaWGebGaamitaaaaaaa!3D17!\[\overline {DL} \] of the area integrals are equal to % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% Waa0aaaeaacaWGebGaamitaaaaaaa!3D17!\[\overline {DL} \] = (1.0±0.1) × 10–6; the mean values of the cumulative errors % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% Gaamiraiaadkhaaaa!3D2C!\[{Dr}\], % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% Waa0aaaeaacaWGebGaamOvaaaaaaa!3D21!\[\overline {Dv} \] in defining the coordinates (r) and velocities (v) of the bodies (during the total integration time % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% Waa0aaaeaacaWGubaaaaaa!3C56!\[\overline T \]) are equal to % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% Waa0aaaeaacaWGebGaamOCaaaaaaa!3D3D!\[\overline {Dr} \] = 0.5 × 10–3 d, % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% Waa0aaaeaacaWGebGaamODaaaaaaa!3D41!\[\overline {Dv} \] = 0.5 × 10–2 v, where d is the unit of distance, and v is the unit of velocity; the mean local integration errors (of one integration step) are equal to r= 5 × 10–8 d, 6v = 5 × 10–7 v; (2) the process of accumulation of integration errors has a complicated character and correlates strongly with the process of dynamical evolution of the triple systems; (a) because of the strong gravitational interplays of the bodies, the process of the accumulation of the integration errors is very intensive; however, the triple systems with these interplays of the bodies have, as a rule, a small escape time % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% Waa0aaaeaacaWGubaaaaaa!3C56!\[\overline T \] t, and the cumulative calculation errors are small too; (b) in the stable triple systems the local integration errors are practically constant during the numerical study of their evolution, and the calculations can be carried out (if it is necessary) during the time % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% Waa0aaaeaacaWGubaaaaaa!3C56!\[\overline T \] = (2–3) × 103 without disturbing the periodical motions of the bodies; (3) thus, in the general three-body problem with different initial conditions, it is not necessary to carry out the computer simulations over long times, as most of the triple systems decay and do not have very long lifetimes; (4) the mean level of the cumulative errors Dr and Dv of the definitions of the coordinates and velocities of bodies in the different triple systems is practically equal.  相似文献   
52.
The interface between environmentalism and neoliberalism in industrialised nations is dynamic and evolving with each of these significant socio-political movements exerting influence on the other. In the context of Australian environmental policy, ideas of heritage, sense of place and belonging are increasingly invoked to support the current policy emphasis on the role of regional communities for realising goals for land and water conservation and environmental restoration. To explore the broader meaning and consequences of these developments, we focus on the manner in which ideas of heritage are employed and evoked within the Murray–Darling Outreach Project, a collaboration between the Murray–Darling Basin Commission, a key natural resource management agency, and the National Museum of Australia. The Murray–Darling Outreach Project has the aim of increasing community involvement in local environmental issues by promoting ideas of vernacular heritage.  相似文献   
53.
We reconstructed 150 years of ecological change in a shallow boreal lake located on the east shore of the Baltic Sea by integrating different types of environmental evidence: paleolimnological records (XRF-measured elements, fossil pigments and Cladocera assemblages), information from historical limnological surveys and archival maps. We assessed the role of biomanipulation by liming and fish-removal in the disappearance of submerged macrophytes, such as Lobelia dortmanna L., and their replacement by persistent cyanobacterial blooms. The combination of different strands of evidence revealed that the shift from macrophyte to cyanobacterial dominance was part of a long-term ecological response to eutrophication and increased sediment load from catchment disturbances. The findings demonstrate that a gradual loss of wetlands and increase of ditches in a catchment had a more significant effect on the lake ecosystem, compared to the direct, but short-term impact of biomanipulation. The study highlights the importance of catchment land-use and disturbance by ditches in changing the ecology of boreal water bodies. Also, it illustrates that a thorough understanding of the long-term ecosystem dynamics and differentiation among responses to multiple anthropogenic impacts are essential preconditions for addressing the deterioration of habitats and change in aquatic environments.  相似文献   
54.
55.
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57.
This article reviews numerical experiments on the three-body problem carried out at the Leningrad University Astronomical Observatory during the past 20 years. Systematic studies of triple systems with negative total energy have yielded the following main results. Most (95%) of the systems decay; the decay always occurs after a close triple approach of the components. In a system with unequal masses, the escaping body usually has the smallest mass. A small fraction (5%) of quasi-stable systems is formed if the angular momentum is non-zero. The qualitative evolution in three-dimensional cases is the same as for planar systems. Small changes in initial conditions sometimes lead to substantial differences in the final outcome. The decay of triple systems is a stochastic process similar to radioactive decay. The estimated mean lifetime is 100 crossing times for equal-mass components and decreases for increasing mass dispersion.A classification of the close triple approaches which lead to immediate escape is given for equal-mass systems as well as for selected sets of unequal components. Detailed studies of close triple approaches by computer simulations reveal that the early evolutions is determined by the initial ratio of the interaction forces. The review concludes by discussing applications of the results to observational problems of stellar and extragalactic systems.  相似文献   
58.
Numerous studies of the brightest Cambridge pulsar, B1133+16, have revealed little order in its individual pulses, apart from a weak 30-odd-rotation-period fluctuation feature and that some 15 per cent of the star's pulsars are 'nulls'. New Arecibo observations confirm this fluctuation feature and that it modulates all the emission, not simply the 'saddle' region. By replacing each pulse with a scaled version of the average profile, we were able to quench all subpulse modulation and thereby demonstrate that the star's 'null' pulses exhibit a similar periodicity. A subbeam carousel model with a sparse and irregular 'beamlet' population appears to be compatible with these characteristics.  相似文献   
59.
Cellular automaton modelling for the simulation of dune field formation and evolution has developed progressively in aeolian geomorphology in the last decade or so. A model that incorporates the effects of vegetation and its interactions with geomorphic landscape development – the Discrete Ecogeomorphic Aeolian Landscapes (DECAL) model – can replicate a number of important visual and qualitative aspects of the complex evolution of aeolian dune landscapes under the influence of vegetation dynamics in coastal environments. A key challenge in this research area is the analysis and comparison of both simulated and real‐world vegetated dune landscapes using objective and quantifiable principles. This study presents a methodological framework or protocol for numerically quantifying various ecogeomorphic attributes, using a suite of mathematically defined landscape metrics, to provide a rigorous and statistical evaluation of vegetated dune field evolution. Within this framework the model parameter space can be systematically explored and simulation outcomes can be methodically compared against real‐world landscapes. Based on a simplified scenario of parabolic dunes developing out of blow‐outs the resulting dune field realizations are investigated as a function of variable growth vigour of two simulated vegetation types (pioneer grass and successional woody shrub) by establishing a typological phase‐diagram of different landscape classes. The set of simulation outcomes furthermore defines a higher‐dimensional phase‐space, whose axes or dimensions can be interpreted by analysing how individual ecogeomorphic landscape metrics, or state variables, contribute to the data distribution. Principal component analysis can reduce this to a visual three‐dimensional (3D) phase‐space where landscape evolution can be plotted as time‐trajectories and where we can investigate the effects of changing environmental conditions partway through a simulation scenario. The use of landscape state variables and the construction of a 3D phase‐space presented here may provide a general template for quantifying many other eco‐geomorphic systems on the Earth's surface. Copyright © 2010 John Wiley & Sons, Ltd.  相似文献   
60.
The lithogenic flux of sediment trap material was analyzed from a three year time series (February 2002–March 2005) at 2000 m depth in the Northeast Atlantic (Kiel 276, 33°N, 22°W) with regards to the seasonal and interannual variability of flux intensity and mineralogy—by applying an automated particle SEM-EDX analysis (scanning electron microscope-energy dispersive X-ray analysis). The lithogenic flux shows strong interannual variations with highest lithogenic flux rates occurring during January–February and April–March coupled to the total particle flux. Mean lithogenic flux rates for the sample years are 7.1 (2002–2003), 5.1 (2003–2004) and 16.1 mg m?2 d?1 (2004–2005). Mineral assemblages from the three sample years reveal distinct major minerals related to specific source regions. Clay minerals dominate the lithogenic fraction within the years 2002 and 2004 with illite (2002–2003) and palygorskite (2003–2004) being the major clay minerals. During the year 2004–2005, quartz is the major lithogenic mineral accompanied by smectite. The mineral assemblages hint to a mixture of North African source areas with dominant sources in Mauritania and north western parts of NW Africa for the years 2002–2004 and central Sahara (Algeria–Mali) within the year 2004–2005.  相似文献   
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