Recent progress in the theory of Trojan asteroids     

Boris Garfinkel 《Celestial Mechanics and Dynamical Astronomy》1982,28(1-2):153-154

In previous publications the author has constructed a long-periodic solution of the problem of the motion of the Trojan asteroids, treated as the case of 1:1 resonance in the restricted problem of three bodies. The recent progress reported here is summarized under three headings:

1. The nature on the long-periodic family of orbits is re-examined in the light of the results of the numerical integrations carried out by Deprit and Henrard (1970). In the vicinity of the critical divisor $$D_k \equiv \omega _1 - k\omega _2 ,$$ not accessible to our solution, the family is interrupted by bifurcations and shortperiodic bridges. Parametrized by the normalized Jacobi constant α², our family may, accordingly, be defined as the intersection of admissible intervals, in the form $$L = \mathop \cap \limits_j \left\{ {\left| {\alpha - \alpha _j } \right| > \varepsilon _j } \right\};j = k,k + 1, \ldots \infty .$$ Here, {α_j(m)} is the sequence of the critical α_j corresponding to the exactj: 1 commensurability between the characteristic frequencies ω₁ and ω₂ for a given value of the mass parameterm. Inasmuch as the ‘critical’ intervals |α?α_j|<ε_j can be shown to be disjoint, it follows that, despite the clustering of the sequence {α_j} at α=1, asj→∞, the family extends into the vicinity of the separatrix α=1, which terminates the ‘tadpole’ branch of the family.
2. Our analysis of the epicyclic terms of the solution, carrying the critical divisorD _k , supports the Deprit and Henrard refutation of the E. W. Brown conjecture (1911) regarding the termination of the tadpole branch at the Lagrangian pointL ₃. However, the conjecture may be revived in a refined form. “The separatrix α=1 of the tadpole branch spirals asymptotically toward a limit cycle centered onL ₃.”
3. The periodT(α,m) of the libration in the mean synodic longitude λ in the range $$\lambda _1 \leqslant \lambda \leqslant \lambda _2$$ is given by a hyperelliptic integral. This integral is formally expanded in a power series inm and α² or \(\beta \equiv \sqrt {1 - \alpha ^2 }\) .

The large amplitude of the libration, peculiar to our solution, is made possible by the mode of the expansion of the disturbing functionR. Rather than expanding about Lagrangian pointL ₄, with the coordinatesr=1, θ=π/3, we have expandedR about the circler=1. This procedure is equivalent to analytic continuation, for it replaces the circle of convergence centered atL ₄ by an annulus |r?1|<ε with 0≤θ<2π.  相似文献   

On resonance in celestial mechanics     

Boris Garfinkel 《Celestial Mechanics and Dynamical Astronomy》1982,28(3):275-290

This brief survey of the author's contribution to the theory of resonance in celestial mechanics begins with the genesis of the Small Divisor. The fundamental distinction between theshallow anddeep resonance is illustrated by the 52 Jupiter-Saturn and the 3-2 Neptune-Pluto resonances in the planetary system.The search for aglobal solution through a removal of the small divisor is put into a historical perspective through the work of Laplace, Bohlin, and Poincaré. The author's own contribution to the methodology is the formulation and the solution of the Ideal Resonance Problem. If the resonance issimple, all the singularities in the solution are removed by means of aregularizing function. On the other hand, if the resonance isdouble, the second critical divisor seems irremovable, and a global solution may be precluded.Invited paper, IAU 1979, Commission 7, Montreal, Canada.  相似文献   

Prevention of well clogging during aquifer storage of turbid tile drainage water rich in dissolved organic carbon and nutrients     

Kruisdijk  Emiel  Ros  Julian F.  Ghosh  Devanita  Brehme  Maren  Stuyfzand  Pieter J.  van Breukelen  Boris M. 《Hydrogeology Journal》2023,31(3):827-842

Well clogging was studied at an aquifer storage transfer and recovery (ASTR) site used to secure freshwater supply for a flower bulb farm. Tile drainage water (TDW) was collected from a 10-ha parcel, stored in a sandy brackish coastal aquifer via well injection in wet periods, and reused during dry periods. This ASTR application has been susceptible to clogging, as the TDW composition largely exceeded most clogging mitigation guidelines. TDW pretreatment by sand filtration did not cause substantial clogging at a smaller ASR site (2 ha) at the same farm. In the current (10 ha) system, sand filtration was substituted by 40-μm disc filters to lower costs (by 10,000–30,000 Euro) and reduce space (by 50–100 m²). This measure treated TDW insufficiently and injection wells rapidly clogged. Chemical, biological, and physical clogging occurred, as observed from elemental, organic carbon, 16S rRNA, and grain-size distribution analyses of the clogging material. Physical clogging by particles was the main cause, based on the strong relation between injected turbidity load and normalized well injectivity. Periodical backflushing of injection wells improved operation, although the disc filters clogged when the turbidity increased (up to 165 NTU) during a severe rainfall event (44 mm in 3 days). Automated periodical backflushing, together with regulating the maximum turbidity (<20 NTU) of the TDW, protected ASTR operation, but reduced the injected TDW volume by ~20–25%. The studied clogging-prevention measures collectively are only viable as an alternative for sand filtration when the injected volume remains sufficient to secure the farmer’s needs for irrigation.

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The impact of the spatial variability in bottom roughness on tidal dynamics and energetics, a case study: the M 2 surface tide in the North European Basin     

Boris A. Kagan  Ekaterina V. Sofina  Ebrahim Rashidi 《Ocean Dynamics》2012,62(10-12):1425-1442

A modified version of the 3D finite-element hydrostatic model QUODDY-4 is used to quantify the changes in the dynamics and energetics of the M ₂ surface tide in the North European Basin, induced by the spatial variability in bottom roughness. This version differs from the original one, as it introduces a module providing evaluation of the drag coefficient in the bottom boundary layer (BBL) and by accounting for the equilibrium tide. The drag coefficient is found from the resistance laws for an oscillatory rotating turbulent BBL over hydrodynamically rough and incompletely rough underlying surfaces, describing how the wave friction factor as well as other resistance characteristics depend on the dimensionless similarity parameters for the BBL. It is shown that the influence of the spatial variability in bottom roughness is responsible for some specific changes in the tidal amplitudes, phases, and the maximum tidal velocities. These changes are within the model noise, while the changes in the averaged (over a tidal cycle) horizontal wave transport and the averaged dissipation of barotropic tidal energy may be of the same orders of magnitude as are the above energetic characteristics as such. Thus, contrary to present views, ignoring the spatial variability in bottom roughness at least in the North European Basin is only partially correct: it is valid for the tidal dynamics, but is liable to break down for the tidal energetics.  相似文献   

Propagation of seismic waves through liquefied soils     

Mahdi Taiebat  Boris Jeremić  Yannis F. Dafalias  Amir M. Kaynia  Zhao Cheng 《Soil Dynamics and Earthquake Engineering》2010

To predict the earthquake response of saturated porous media it is essential to correctly simulate the generation, redistribution, and dissipation of excess pore water pressure during and after earthquake shaking. To this end, a reliable numerical tool requires a dynamic, fully coupled formulation for solid–fluid interaction and a versatile constitutive model. Presented in this paper is a 3D finite element framework that has been developed and utilized for this purpose. The framework employs fully coupled dynamic field equations with a u–p–U formulation for simulation of pore fluid and solid skeleton interaction and a SANISAND constitutive model for response of solid skeleton. After a detailed verification and validation of the formulation and implementation of the developed numerical tool, it is employed in the seismic response of saturated porous media. The study includes examination of the mechanism of propagation of the earthquake-induced shear waves and liquefaction phenomenon in uniform and layered profiles of saturated sand deposits.  相似文献   

The sediment composition and predictive mapping of facies on the Propeller Mound—A cold-water coral mound (Porcupine Seabight,NE Atlantic)     

Katrin Heindel  Jürgen Titschack  Boris Dorschel  Veerle A.I. Huvenne  André Freiwald 《Continental Shelf Research》2010

Here we provide a detailed qualitative and quantitative insight on recent sediment composition and facies distribution of a cold-water coral (CWC) mound using the example of the Propeller Mound on the Irish continental margin (Hovland Mound Province, Porcupine Seabight). Five facies types on Propeller Mound are defined: (1) living coral framework, (2) coral rubble, (3) dropstone, (4) hardground, representing the on-mound facies, and (5) hemipelagic sediment facies, which describes the off-mound area. This facies definition is based on already published video-data recorded by Remotely Operated Vehicle (ROV), photo-data of gravity cores, box cores, and dredges from sediment surfaces as well as on the composition of the sediment fraction coarser than 125 μm, which has been analyzed on five selected box cores. Sediment compositions of the living coral framework and coral rubble facies are rather similar. Both sediment types are mainly produced by corals (34 and 35 wt%, respectively), planktonic foraminifers (22 and 29 wt%, respectively), benthic foraminifers (both 7 wt%), and molluscs (21 and 10 wt%, respectively), whereas the living coral framework characteristically features additional brachiopods (6 wt%). Hardgrounds are well-lithified coral rudstones rich in coral fragments (>30 surf%), foraminifers, echinoderms, and bivalves. The dropstone facies and the hemipelagic sediment typically carry high amounts of lithoclasts (36 and 53 wt%, respectively) and planktonic foraminifers (35 and 32 wt%, respectively); however, their faunal diversity is low compared with the coral-dominated facies (12 and <2 wt% coral fragments, 7 and 6 wt% benthic foraminifers, and 4 and 0 wt% balanids). Using the maximum likelihood algorithm within ArcGIS 9.2, spatial prediction maps of the previously described mound facies are calculated over Propeller Mound and are based on mound morphology parameters, ground-truthed with the sedimentary and faunal information from box cores, photographs, and video-data. This method is tested for the first time for CWC ecosystems and provides areal estimates of the predicted facies, as well as suggests further occurrences of living coral frameworks, coral rubble, and dropstones, which are not discovered in the area yet. Thus, sediment composition analysis combined with facies prediction mapping might provide a potential new tool to estimate living CWC occurrences and sediment/facies distributions on CWC mounds, which is an important prerequisite for budget calculations and definition of marine protected areas, and which will improve our understanding of CWC mound formation.  相似文献   

Forced imbibition into a limestone: measuring P‐wave velocity and water saturation dependence on injection rate     

Sofia Lopes  Maxim Lebedev  Tobias M. Müller  Michael B. Clennell  Boris Gurevich 《Geophysical Prospecting》2014,62(5):1126-1142

Quantitative interpretation of time‐lapse seismic data requires knowledge of the relationship between elastic wave velocities and fluid saturation. This relationship is not unique but depends on the spatial distribution of the fluid in the pore‐space of the rock. In turn, the fluid distribution depends on the injection rate. To study this dependency, forced imbibition experiments with variable injection rates have been performed on an air‐dry limestone sample. Water was injected into a cylindrical sample and was monitored by X‐Ray Computed Tomography and ultrasonic time‐of‐flight measurements across the sample. The measurements show that the P‐wave velocity decreases well before the saturation front approaches the ultrasonic raypath. This decrease is followed by an increase as the saturation front crosses the raypath. The observed patterns of the acoustic response and water saturation as functions of the injection rate are consistent with previous observations on sandstone. The results confirm that the injection rate has significant influence on fluid distribution and the corresponding acoustic response. The complexity of the acoustic response —‐ that is not monotonic with changes in saturation, and which at the same saturation varies between hydrostatic conditions and states of dynamic fluid flow – may have implications for the interpretation of time‐lapse seismic responses.  相似文献   

Estimating azimuthal stress‐induced P‐wave anisotropy from S‐wave anisotropy using sonic log or vertical seismic profile data          下载免费PDF全文

Olivia Collet  Boris Gurevich  Guy Duncan 《Geophysical Prospecting》2016,64(5):1305-1317

Most sedimentary rocks are anisotropic, yet it is often difficult to accurately incorporate anisotropy into seismic workflows because analysis of anisotropy requires knowledge of a number of parameters that are difficult to estimate from standard seismic data. In this study, we provide a methodology to infer azimuthal P‐wave anisotropy from S‐wave anisotropy calculated from log or vertical seismic profile data. This methodology involves a number of steps. First, we compute the azimuthal P‐wave anisotropy in the dry medium as a function of the azimuthal S‐wave anisotropy using a rock physics model, which accounts for the stress dependency of seismic wave velocities in dry isotropic elastic media subjected to triaxial compression. Once the P‐wave anisotropy in the dry medium is known, we use the anisotropic Gassmann equations to estimate the anisotropy of the saturated medium. We test this workflow on the log data acquired in the North West Shelf of Australia, where azimuthal anisotropy is likely caused by large differences between minimum and maximum horizontal stresses. The obtained results are compared to azimuthal P‐wave anisotropy obtained via orthorhombic tomography in the same area. In the clean sandstone layers, anisotropy parameters obtained by both methods are fairly consistent. In the shale and shaly sandstone layers, however, there is a significant discrepancy between results since the stress‐induced anisotropy model we use is not applicable to rocks exhibiting intrinsic anisotropy. This methodology could be useful for building the initial anisotropic velocity model for imaging, which is to be refined through migration velocity analysis.  相似文献   

Incorporating Super‐Diffusion due to Sub‐Grid Heterogeneity to Capture Non‐Fickian Transport          下载免费PDF全文

Boris Baeumer  Yong Zhang  Rina Schumer 《Ground water》2015,53(5):699-708

Numerical transport models based on the advection‐dispersion equation (ADE) are built on the assumption that sub‐grid cell transport is Fickian such that dispersive spreading around the average velocity is symmetric and without significant tailing on the front edge of a solute plume. However, anomalous diffusion in the form of super‐diffusion due to preferential pathways in an aquifer has been observed in field data, challenging the assumption of Fickian dispersion at the local scale. This study develops a fully Lagrangian method to simulate sub‐grid super‐diffusion in a multidimensional regional‐scale transport model by using a recent mathematical model allowing super‐diffusion along the flow direction given by the regional model. Here, the time randomizing procedure known as subordination is applied to flow field output from MODFLOW simulations. Numerical tests check the applicability of the novel method in mapping regional‐scale super‐diffusive transport conditioned on local properties of multidimensional heterogeneous media.  相似文献   

斯洛文尼亚和中国贵州喀斯特洞穴动物群的比较研究   总被引：1，自引：1，他引：0  

黎道洪  BorisSket 《中国岩溶》2005,24(1):65-70

2003年7-8月,中方专家野外考察了斯洛文尼亚的8个喀斯特洞穴,采集各类洞穴动物标本500余号,并对主要洞穴环境因子进行了测定,收集相关资料200余篇。2004年2月斯方专家野外考察了中国贵州12个喀斯特洞穴,采集各类动物标本1000余号。本文对两国喀斯特洞穴内的主要动物群进行了比较研究,结果是斯洛文尼亚的物种丰富度比贵州的高: 前者有533种,密度为65. 80种/1000km2; 后者有238种,密度为0. 54种/1000km2。从洞穴蝙蝠看,两国均为24种; 但区系成分不同,斯洛文尼亚全为古北界种, 贵州则主要为东洋界成分( 83% )。此外,文中还对比分析了斯洛文尼亚施科茨杨洞和贵州龙洞内的动物群落组成: 前者以水生种为主体,后者全为陆生种。最后,对斯洛文尼亚无真洞穴鱼的问题及两国的洞穴动物起源进行了探讨。   相似文献