Periodic solutions in the commensurable three-body problem     

A. T. Sinclair 《Celestial Mechanics and Dynamical Astronomy》1970,2(3):350-350

Various families of periodic solutions are shown to exist in the three body problem, in which two of the bodies are close to a commensurability in mean motions about the third body, the primary, which is considerably more massive than the other two. The cases considered are

1. The non-planar circular restricted problem (in which one of the secondary bodies has zero mass, and the other moves in a fixed circular orbit about the primary).
2. The planar non-restricted problem (in which the three bodies move in a plane, and both secondaries have finite mass).
3. The planar elliptical restricted problem (in which the three bodies move in a plane, one of the secondary bodies has zero mass, and the other moves in a fixed elliptical orbit about the primary).

The method used is to eliminate all short period terms from the Hamiltonian of the motion by means of a von Zeipel transformation, leaving only the long period terms which are due to the commensurability. Hence only the long period part of the motion is considered, and the variables used differ from the variables describing the full motion by a series of short-period trigonometric terms of the order of the ratio of the mass of the secondaries to that of the primary body. It is shown that solutions of the long-period problem in which the variables remain constant are equivalent to solutions in the full motion in which the bodies periodically return to the same configuration, and these are the types of periodic solution that are shown to exist. The form of the disturbing function, and hence of the equations of motion, is found up to the fourth powers of the eccentricities and inclination by considering the d'Alembert property. The coefficients of the terms appearing in this expansion are functions of the semi-major axes of the orbits of the secondary bodies. Expressions for these coefficients are not worked out as they are not required. Lete, n, m be the orbital eccentricity, mean motion and mass of one of the secondary bodies, and lete′, n′, m′ be the corresponding quantities for the other. (The mass of the primary is taken as unity). In cases (a) and (c) we will havem=0. In case (a)e′ will be zero, and in case (c) it will be a constant. Leti be the mutual inclination of the orbits of the secondary bodies. Suppose the commensurability is of the form(p+q) n =pn′, wherep andq are relatively prime integers, and put γ=(p+q) n/n′?p. The families of periodic solutions shown to exist are as follows. For q=1 No periodic solutions are found withi≠0 in case (a), and none withe′≠0, in case (c). In case (b) periodic solutions are found in whiche=0 (m′/γ),e′=0 (m/γ) for values of γ away from the exact commensurability. As γ approaches zero thene ande′ become 0 (1). For q≠1 Case (a). Families of periodic solutions bifurcating from the family withe=0, i=0 are shown to exist. Families in whichi=0 ande becomes non-zero exist for all values ofq. Families in whiche=0 andi becomes non-zero exist for even values ofq. Families in whiche andi become non-zero simultaneously exist for odd values ofq. Case (b). No families are found other than those withe=e′=0. Case (c). Families are found bifurcating from the familye=e′=0 in whiche ande′ become non-zero simultaneously. For all these solutions existence is only demonstrated close to the point of bifurcation, where all the variables are small, as the method uses series expansions ine, e′ andi. From the form of the solutions it is clear that the non-zero variables will become large for values of γ away from the bifurcation point.  相似文献   

AFRICAN CITIES: Alternative Visions of Urban Theory and Practice. By Garth Myers     

Dean Sinclair 《Geographical review》2012,102(2):264-265

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Fluid source and thermal history of an epithermal vein deposit,Owen Lake,central British Columbia: evidence from bitumen and fluid inclusions     

M. L. Thomson  M. Mastalerz  A. J. Sinclair  R. M. Bustin 《Mineralium Deposita》1992,27(3):219-225

Fluid source and thermal history are determined for the barite and bitumen-bearing, early Eocene (ca. 50 Ma) polymetallic, epithermal veins of the Owen Lake deposit, central British Columbia, Canada. Carbon isotopic values for the bitumen are highly negative (δ ¹³ C ca −29%) indicating a probable terrigenous source, which may be 1 no older than Late Cretaceous or, 2 Eocene plant-fossil-bearing units stratigraphically above the Owen Lake deposit. Heat generated by suspected magmatic activity resulted in downflow of meteoric water and upflow of hydrothermal water, mixing at the site of deposition. Aqueous and hydrocarbon fluid inclusions occur within barite; Th of both types of inclusions indicate a temperature range of approximately 100° to 180 °C. Tm(ice) of aqueous inclusions range from −4.5 to −0.2 °C indicating a range of 7.2 to 0.4 equivalent weight percent NaCl. Parageneticaly younger bitumen has a vitrinite reflectance of 0.6% indicating maturation level in the temperature range of 80° to 120 °C, strongly suggesting a cooling thermal regime during barite and bitumen deposition, consistent with a late stage paragenesis.  相似文献   

Vertical versus horizontal motions in the Alpine orogenic wedge: stratigraphic response in the foreland basin   总被引：3，自引：0，他引：3  

H. D. Sinclair  P. A. Allen 《Basin Research》1992,4(3-4):215-232

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An analysis of errors in the calculation of energy flux densities above vegetation by a Bowen-ratio profile method     

T. R. Sinclair  L. H. Allen Jr.  E. R. Lemon 《Boundary-Layer Meteorology》1975,8(2):129-139

The Bowen-ratio profile method for calculating total carbon dioxide, latent heat, and sensible heat flux density above a corn crop was used by measuring temperature, water vapor, and CO₂ concentrations at several heights in the aerodynamic boundary layer of the crop. The ratio (α) of sensible heat flux density to carbon dioxide flux density as well as the Bowen ratio (β) were used in the computations. The two ratios, α and β were determined graphically from the slopes of linear plots of temperature vs CO₂ concentration and vs water vapor. Each of the energy flux densities was computed from the two ratios and net radiation minus soil heat flux density. An analysis of probable error was performed on the Bowen-ratio profile method to evaluate the accuracy of the flux density estimates. Less than 10% error was found for latent heat flux density and less than 15% for carbon dioxide flux density under normal midday conditions for the instrumentation used. However, the carbon dioxide flux density error increased to over 40% when the sensible heat flux was small.  相似文献   

Isolation, Identification, and Growth of Well-Water Bacteria     

Linda D. Stetzenbach  Lee M. Kelley  Norval A. Sinclair 《Ground water》1986,24(1):6-10

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Assessing the Efficacy of Transition Theory to Identify Industry Transformation: a case study examining the deregulation of Australia's dairy industry     

Katrina Sinclair  Allan Curtis  Emily Mendham  Michael Mitchell 《The Australian geographer》2015,46(1):113-129

Transformation is a key concept in social-ecological systems research, and transition theory in particular; however, the essential elements of a transformation are yet to be clearly articulated. This article explores the changes that took place when Australian governments deliberately set out to restructure the Australian dairy industry. Using the subtropical dairy industry as a case study, we conducted semi-structured interviews with industry stakeholders. Our analysis was structured around transition concepts thus testing the framework's efficacy. We found that deregulation substantially altered the culture of the industry and the structure and working practices of the production system, supply chain, industry organisations and government agencies. Transition theory and its concepts provided a useful framework to explain how systemic change transformed the industry. Transition theory identified the multi-scalar nature of the interactions between structure and practice and the social and power relationships that reinforced change.  相似文献   

Dynamic flood topographies in the Terai region of Nepal     

E.H. Dingle  M.J. Creed  H.D. Sinclair  D. Gautam  N. Gourmelen  A.G.L. Borthwick  M. Attal 《地球表面变化过程与地形》2020,45(13):3092-3102

Flood hazard maps used to inform and build resilience in remote communities in the Terai region of southern Nepal are based on outdated and static digital elevation models (DEMs), which do not reflect dynamic river configuration or hydrology. Episodic changes in river course, sediment dynamics, and the distribution of flow down large bifurcation nodes can modify the extent of flooding in this region, but these processes are rarely considered in flood hazard assessment. Here, we develop a 2D hydrodynamic flood model of the Karnali River in the Terai region of west Nepal. A number of scenarios are tested examining different DEMs, variable bed elevations to simulate bed aggradation and incision, and updating bed elevations at a large bifurcation node to reflect field observations. By changing the age of the DEM used in the model, a 9.5% increase in inundation extent was observed for a 20-year flood discharge. Reducing horizontal DEM resolution alone resulted in a <1% change. Uniformly varying the bed elevation led to a 36% change in inundation extent. Finally, changes in bed elevation at the main bifurcation to reflect observed conditions resulted in the diversion of the majority of flow into the west branch, consistent with measured discharge ratios between the two branches, and a 32% change in inundation extent. Although the total flood inundation area was reduced (−4%), there was increased inundation along the west bank. Our results suggest that regular field measurements of bed elevation and updated DEMs following large sediment-generating events, and at topographically sensitive areas such as large river bifurcations, could help improve model inputs in future flood prediction models. This is particularly important following flood events carrying large sediment loads out of mountainous regions that could promote bed aggradation and channel switching across densely populated alluvial river systems and floodplains further downstream. © 2020 The Authors. Earth Surface Processes and Landforms published by John Wiley & Sons Ltd  相似文献   

Late Cretaceous‐Palaeogene stratigraphic and basin evolution in the Zhepure Mountain of southern Tibet: implications for the timing of India‐Asia initial collision     

Xiumian Hu  Hugh D. Sinclair  Jiangang Wang  Hehe Jiang  Fuyuan Wu 《Basin Research》2012,24(5):520-543

This article presents combined stratigraphic, sedimentological, subsidence and provenance data for the Cretaceous–Palaeogene succession from the Zhepure Mountain of southern Tibet. This region records the northernmost sedimentation of the Tethyan passive margin of India, and this time interval represents the transition into continental collision with Asia. The uppermost Cretaceous Zhepure Shanpo and Jidula formations record the transition from pelagic into upper slope to delta‐plain environments. The Palaeocene–lower Eocene Zongpu Formation records a carbonate ramp that is overlain by the deep‐water Enba Formation (lower Eocene). The upper part of the Enba Formation records shallowing into a storm‐influenced, outer shelf environment. Detrital zircon U–Pb and Hf isotopic data indicate that the terrigenous strata of the Enba Formation were sourced from the Lhasa terrane. Unconformably overlying the Enba Formation is the Zhaguo Formation comprising fluvial deposits with evidence of recycling from the underlying successions. Backstripped subsidence analysis indicates shallowing during latest Cretaceous‐earliest Palaeocene time (Zhepure Shanpo and Jidula formations) driven by basement uplift, followed by stability (Zongpu Formation) until early Eocene time (Enba Formation) when accelerated subsidence occurred. The provenance, subsidence and stratigraphy suggest that the Enba and Zhaguo formations record foredeep and wedge‐top sedimentation respectively within the early Himalayan foreland basin. The underlying Zongpu Formation is interpreted to record the accumulation of a carbonate ramp at the margin of a submarine forebulge. The precursor tectonic uplift during latest Cretaceous time could either record surface uplift over a mantle plume related to the Réunion hotspot, or an early signal of lithospheric flexure related to oceanic subduction, continental collision or ophiolite obduction. The results indicate that the collision of India with Asia occurred before late Danian (ca. 62 Ma) time.  相似文献   

Seasonal evolution of penitente glaciochemistry at Tapado Glacier,Northern Chile          下载免费PDF全文

Kate E. Sinclair  Shelley MacDonell 《水文研究》2016,30(2):176-186

This study uses stable isotopes and major ions to examine the seasonal evolution of penitentes on the surface of Tapado Glacier, in the Norte Chico region of the Chilean Andes. A snow pit was sampled in November 2011, and penitentes were sampled during the summer (December 2011 and January 2012). The major ion load of the winter snowpack is dominated by Ca²⁺ (60%), SO₄^2? (16%) and NO₃^? (13%), and there is little influence from marine air masses at the site, with most SO₄^2?, Mg²⁺, Ca²⁺ and Na⁺, derived from non‐sea salt sources. During the early ablation season we observe increases in stable isotope ratios and major ion concentrations (particularly lithic ions Na⁺, Mg²⁺ and Ca²⁺) in the upper reaches of penitentes, which is attributed to sublimation and the aeolian deposition of dust particles. In the late‐summer, melt replaces sublimation as the dominant ablation process and results in smoothing of the stable isotope profile and the elution of major ions within the penitente snow and ice matrix. Copyright © 2015 John Wiley & Sons, Ltd.  相似文献