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   

Numerical simulation of tides in the World Ocean: 3. A solution to the spectral problem     

Dr. Vadim Yu. Gotlib  Prof. Boris A. Kagan 《Ocean Dynamics》1982,35(2):45-58

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A modified turbulent energy model for diffusion from elevated and ground point sources in neutral boundary layers     

Boris Galperin 《Boundary-Layer Meteorology》1986,37(3):245-262

A simple model for turbulent diffusion is proposed based on a turbulent energy model modified by Galperin and Hassid (1986) wherein local equilibrium in the concentration flux equation is assumed resulting in a turbulent diffusivity tensor. The early stage of plume development is simulated through adjustment of the integral length scale of diffusion. A simple semi-empirical formulation is also proposed for the dissipation length scale of concentration variance. Although it is substantially simpler than that of Sykes et al. (1984), the model is shown to compare well with the measurements of Fackrell and Robins (1982a, b).  相似文献   

Engineering Geology (developments in geotechnical engineering, 10): Q. Zaruba and V. Mencl. Elsevier,Amsterdam, 1976, 504 pp., Dfl. 97.00 or U.S. $ 37.50     

Boris Aisenstein 《Sedimentary Geology》1978,21(1):67-68

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Unusual grain size effect on trace metals and organic matter in contaminated sediments   总被引：1，自引：0，他引：1  

Boris S. Krumgalz 《Marine pollution bulletin》1989,20(12):608-611

Grain size effect on trace metals (cadmium, copper, lead, zinc, and iron) and total organic content distribution in various fractions (<0.063, 0.063–0.105, 0.105–0.250, 0.250–0.500, and 0.500–1.000 mm) of contaminated sediment has been studied. Selective partitioning of the studied contaminants in sediment fractions was observed, with a minimum content in the fine sand fraction of grain size 0.125–0.250 mm. Anomalously high concentrations of trace metals and organic matter content in the medium and coarse sediment fractions (>0.250 mm) was explained by the formation of large agglomerates (clusters) during the generally recommended drying procedures. These large agglomerates, formed from smaller sediment fraction particles enriched by various contaminants kept on their large specific area by adsorption forces, have been observed in photographs of the medium and coarse sediment fractions only. The formed agglomerates consist of small particles cemented either by dissolved organic matter or by sea salts present in the marine sediment. The formation of such agglomerates should be taken into consideration when conducting metal contamination studies on sediments.  相似文献   

A theory of libration     

Boris Garfinkel 《Celestial Mechanics and Dynamical Astronomy》1976,13(2):229-246

It is shown here that many problems of libration in celestial mechanics can be reduced to a perturbation of anintermediary defined by the Hamiltonian $$F = B\left( y \right) + 2\mu ^2 A\left( y \right)f\left( x \right).$$ This generalization of the Ideal Resonance Problem, with a periodic functionf(x) replacing sin² x, is solved here toO(μ ²) by an algorithm that is essentially the same as the one used in the original formulation. The solution is of the formx=x(u), u=u(t), y=y(x), with the functionx(u) commonly involving the inversion of a hyperelliptic integralu(x), evaluated by quadrature. Libration may be simple or multiple, depending on the nature of the functionf(x) and on the initial conditions. Double libration is illustrated here by the horseshoe-shaped orbits enclosing two libration centers.  相似文献   

Shear Fractures of Extreme Dynamics     

Boris Tarasov 《Rock Mechanics and Rock Engineering》2016,49(10):3999-4021

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Closure of Fracture Due to Cover Stress Re-establishment After Coal Mining     

Wenxue Wang  Tong Jiang  Boris Faybishenko  Zhongfu Wang  Wei Hu  Qingjie Zhao 《Geotechnical and Geological Engineering》2016,34(5):1525-1537

In situ measurements of deformations, stresses, and closure of fractures, affecting water inflow following coal mining, are challenging due to the inaccessibility of fractured rock. In this paper, the authors studied the closure process of the fractured rock mass with the cover stress re-establishment based on a theoretical analysis and a scale model testing. A quantitative analysis is used to study the fracture distribution in the fractured zone. A function to describe a fracture aperture distribution in the fractured zone is proposed, which takes into account the curvature and thickness of the fractured rock. The theoretical analysis and a scale model testing both indicate that the cover stress re-establishment with mining distance increasing and the relationship between the fracture closure and cover stress re-establishment both satisfy a logarithmic function. The scale model test also shows the following features: (1) the fracture ratio (which is the fracture area divided by the total area of fracture and intact rock with a unit width in the vertical or horizontal direction) in the lower part of the fractured rock mass is greater than that in the upper part; (2) the initially fast decreased of fracture ratios is then followed by a slower decrease during the cover stress re-establishment process; (3) in the upper part of the rock mass, the vertical directional fractures with small apertures are being closed with cover stress re-establishment, which indicates an increase in the water resistance reducing the seepage from these parts of the fractured zone. This study improves the general understanding of the fracture closure process and cover stress re-establishment in the fractured rock mass after coal mining ceased, and provides a theoretical basis for water resource protection in case of underground coal mining.  相似文献   

Numerical models of a subsidence mechanism in intracratonic basins: application to North American basins     

Boris M. Naimark  Ali T. Ismail-Zadeh 《Geophysical Journal International》1995,123(1):149-160

McKenzie's model of sedimentary basin evolution and its modification, widely used in geophysics, sometimes fails to explain discrepancies between predicted and observed values of extension, thinning and subsidence of the Earth's crust, as for the North Sea. We develop a numerical model of sedimentary basin evolution based on the mechanism suggested by Lobkovsky. In the course of rifting, accompanied by thinning of lower parts of the lithosphere, the roof of the underlying asthenosphere moves upward. the material of the mantle lifts and partially melts owing to the reduction of pressure. the density difference between the melt and the crystalline skeleton results in the filtration of the lighter melt and its accumulation in the form of a magmatic lens. Due to changed P-T conditions, the material of the lens undergoes the gabbro-eclogite phase transformation. the resultant anomalously heavy eclogite lens sinks in the surrounding material. This induces a viscous flow, changing the surface topography and forming a sedimentary basin. We construct a 2-D numerical model describing a viscous flow induced by subsidence of a heavy body and compute changes of surface topography. to compute the flow we employ the Galerkin-spline approach, with modifications allowing for density discontinuities and time dependence of the phase transformation. We apply the model to the cases of the Illinois, Michigan and Williston basins. the computed and tectonic subsidence curves agree well for these cases. the proposed model is compatible with the seismic structure of the crust and upper mantle below these basins. the model is also consistent with gravity data. the approach is applicable to other intracratonic basins.  相似文献