Global solution of the ideal resonance problem     

Boris Garfinkel 《Celestial Mechanics and Dynamical Astronomy》1973,8(2):207-212

If a dynamical problem ofN degress of freedom is reduced to the Ideal Resonance Problem, the Hamiltonian takes the form 1 $$\begin{array}{*{20}c} {F = B(y) + 2\mu ^2 A(y)\sin ^2 x_1 ,} & {\mu \ll 1.} \\ \end{array} $$ Herey is the momentum-vectory _k withk=1,2?N, x ₁ is thecritical argument, andx _k fork>1 are theignorable co-ordinates, which have been eliminated from the Hamiltonian. The purpose of this Note is to summarize the first-order solution of the problem defined by (1) as described in a sequence of five recent papers by the author. A basic is the resonance parameter α, defined by 1 $$\alpha \equiv - B'/\left| {4AB''} \right|^{1/2} \mu .$$ The solution isglobal in the sense that it is valid for all values of α² in the range 1 $$0 \leqslant \alpha ^2 \leqslant \infty ,$$ which embrances thelibration and thecirculation regimes of the co-ordinatex ₁, associated with α² < 1 and α² > 1, respectively. The solution includes asymptotically the limit α² → ∞, which corresponds to theclassical solution of the problem, expanded in powers of ε ≡ μ², and carrying α as a divisor. The classical singularity at α=0, corresponding to an exact commensurability of two frequencies of the motion, has been removed from the global solution by means of the Bohlin expansion in powers of μ = ε^1/2. The singularities that commonly arise within the libration region α² < 1 and on the separatrix α² = 1 of the phase-plane have been suppressed by means of aregularizing function 1 $$\begin{array}{*{20}c} {\phi \equiv \tfrac{1}{2}(1 + \operatorname{sgn} z)\exp ( - z^{ - 3} ),} & {z \equiv \alpha ^2 } \\ \end{array} - 1,$$ introduced into the new Hamiltonian. The global solution is subject to thenormality condition, which boundsAB″ away from zero indeep resonance, α² < 1/μ, where the classical solution fails, and which boundsB′ away from zero inshallow resonance, α² > 1/μ, where the classical solution is valid. Thedemarcation point 1 $$\alpha _ * ^2 \equiv {1 \mathord{\left/ {\vphantom {1 \mu }} \right. \kern-\nulldelimiterspace} \mu }$$ conventionally separates the deep and the shallow resonance regions. The solution appears in parametric form 1 $$\begin{array}{*{20}c} {x_\kappa = x_\kappa (u)} \\ {y_1 = y_1 (u)} \\ {\begin{array}{*{20}c} {y_\kappa = conts,} & {k > 1,} \\ \end{array} } \\ {u = u(t).} \\ \end{array} $$ It involves the standard elliptic integralsu andE((u) of the first and the second kinds, respectively, the Jacobian elliptic functionssn, cn, dn, am, and the Zeta functionZ (u).  相似文献   

Neotectonics and recent uplift at Kamchatka and Aleutian arc junction, Kamchatka Cape area, NE Russia     

Dorthe Pflanz  Christoph Gaedicke  Ralf Freitag  Matthias Krbetschek  Nikolay Tsukanov  Boris Baranov 《International Journal of Earth Sciences》2013,102(3):903-916

The tectonic position of the Kamchatka Cape Peninsula at the junction of the active Kuril–Kamchatka and Aleutian arcs exposes the coastline of the peninsula to strong neotectonic activities. Fracture zones have variable influence on uplift of the Kamchatka Cape Peninsula. Relevant morphologic indicators of neotectonic activity are multilevel, highly uplifted marine terraces and terraces displaced along active faults. Recent uplift rates of coastal sediments are determined by remote sensing via ASTER and SRTM DEM combined with optically stimulated luminescence dating (OSL). On the Kamchatka Cape Peninsula, terraces from the same generation are mapped at different elevations by remote sensing methods. After defining different areas of uplifted terraces, four neotectonic blocks are identified. According to apatite fission track data, the mean differential exhumation rates range from 0.2 to 1.2 mm year^?1 across the blocks since Late Miocene. The OSL data presented point to significant higher uplift rates of up to 3 ± 0.5 and 4.3 ± 1 mm year^?1, which indicates an acceleration of the vertical movement along the coast of Kamchatka Cape Peninsula in Upper Pleistocene and Holocene times.  相似文献   

Scientific program construction principles and time allocation scheme for the World Space Observatory—Ultraviolet mission     

Oleg Malkov  Mikhail Sachkov  Boris Shustov  Pavel Kaigorodov  Francisco Javier Yáñez  Ana Ines Gómez de Castro 《Astrophysics and Space Science》2011,335(1):323-327

We present scientific program construction principles and a time allocation scheme developed for the World Space Observatory—Ultraviolet (WSO-UV) mission, which is an international space observatory for observation in UV spectral range 100–300 nm. The WSO-UV consists of a 1.7 m aperture telescope with instrumentation designed to carry out high resolution spectroscopy, long-slit low resolution spectroscopy and direct sky imaging. The WSO-UV Ground Segment is under development by Spain and Russia. They will coordinate the Mission and Science Operations and provide the satellite tracking stations for the project.  相似文献   

Dynamics of intrathermocline vortices in a gyre flow over a seamount chain     

Mikhail A. Sokolovskiy  Boris N. Filyushkin  Xavier J. Carton 《Ocean Dynamics》2013,63(7):741-760

The interaction of meddies with a complex distribution of seamounts is studied in a three-layer quasi-geostrophic model on the f-plane. This study aims at understanding if and how this seamount chain can represent a barrier to the propagation of these eddies and how it can be involved in their decay. The eddies are idealized as vortex patches in the middle layer, interacting with a regional cyclonic current and with ten idealized seamounts. The numerical code is based on the contour surgery technique. The initial position, radius, shape, number and polarity of the eddies are varied. The main results are the following: (1) Though they do not describe the unsteady flow, the streamlines of the regional and topographic flow provide a useful estimate of the vortex trajectories, in particular towards the major seamounts, where stronger velocity shears are expected. (2) The tallest and widest seamounts which have the largest vorticity reservoir are able to considerably erode the vortices, but also to draw anticyclones towards the seamount top. The ability of narrower seamounts to erode vortices is related to their multiplicity. (3) Only 1/3 of the anticyclones with about 30-km radius reach the southern boundary of the seamount chain, and their erosion is larger than 50 %. The other anticyclones are either completely eroded or trapped over a wide seamount top. Cyclones are less affected by seamounts because they oppose the topographic draft towards the seamount top and they drift along the side of the seamount. (4) Large vortices resist topographic erosion more efficiently. The rate of erosion grows from a few percent to about 35–50 % as the vortex radius decreases from about 60 to 30 km. Small cyclones are not eroded, contrary to small anticyclones (which completely decay), in relation with the different trajectories of these eddies in the vicinity of the seamounts. (5) The detailed vortex shape does not appear critical for their evolution, if they are close enough to the seamount chain initially. The interaction between a group of vortices initially north of the seamount chain can modify their trajectory to such an extent that they finally avoid collision with seamounts. (6) Finally, meddy trajectories across the Horseshoe Seamounts (data from the AMUSE experiment) show qualitative similarity with the vortex paths in the model. Several events of vortex decay also occur at comparable locations (in particular over the wide and tall seamounts) in the model and observations.  相似文献   

Uptake of Zn,Cu, Pb,and Cd by water hyacinth in the initial stage of water system remediation     

Boris S. Smolyakov 《Applied Geochemistry》2012

The removal efficiency of water hyacinth for Zn, Cu, Pb and Cd after their entry into an undisturbed fresh water body was studied using minicosms placed within a reservoir. Variable parameters were water pH (6 or 8), single or multi-metal additions, and the plant biomass. The initial concentrations of Zn, Cu, Pb and Cd in water (500, 250, 250 and 50 μg/L, respectively) quickly decreased in the order Pb ≈ Cu ? Cd ≈ Zn in the first days. Metal removal was more efficient at pH 8 than at pH 6, and it was only slightly higher for single metals compared to multi-metal additions. After 8 days the remaining amounts of metals relative to their initial concentrations for multi-metal pollution treatments were 8% and 24% (Cu), 11% and 26% (Pb), 24% and 50% (Cd), and 18% and 57% (Zn) at pH 8 and pH 6, respectively. Increasing plant biomass promoted faster metal removal. The bioconcentration factor (the ratio of the metal concentration in whole plants to the initial metal concentration in water) exceeds 2000 for all metals (with the exception of Zn and Cd at pH 6). It was concluded that the water hyacinth can be successfully used for fast removal of metals in the initial stage of water body remediation.  相似文献   

Post‐Late Paleozoic Collisional Framework of Southern Great Altai   总被引：1，自引：0，他引：1  

Boris M. CHIKOV  Sergei V. ZINOVIEV  Еugene V. DEYEV 《《地质学报》英文版》2012,86(5):1093-1104

We outline the post-Late Paleozoic (latest Permian to Cenozoic) collisional framework of the southern Great Altai (Central Asia) produced by the convergence between the Tuva-Mongolia and Junggar continental terranes (microplates). The collisional structures in the region classified on the basis of their geometry and deformation style, dynamic metamorphism, and compositions of tectonites are of three main types: (1) mosaic terranes made up of large weakly deformed Paleozoic blocks separated by younger shear zones; (2) contractional deformation systems involving structures formed in post-Late Paleozoic time, parallel faults oriented along collisional deformation systems, and relict lenses of Paleozoic orogenic complexes; and (3) isolated zones of dynamic metamorphism composed mostly of collisional tectonites different in composition and alteration grade.  相似文献   

Properties of low‐frequency trapped mode in viscous‐fluid waveguides          下载免费PDF全文

Anatoly A. Nikitin  Boris D. Plyushchenkov  Arkady Yu. Segal 《Geophysical Prospecting》2016,64(5):1335-1349

We derived the velocity and attenuation of a generalized Stoneley wave being a symmetric trapped mode of a layer filled with a Newtonian fluid and embedded into either a poroelastic or a purely elastic rock. The dispersion relation corresponding to a linearized Navier–Stokes equation in a fracture coupling to either Biot or elasticity equations in the rock via proper boundary conditions was rigorously derived. A cubic equation for wavenumber was found that provides a rather precise analytical approximation of the full dispersion relation, in the frequency range of 10^?3 Hz to 10³ Hz and for layer width of less than 10 cm and fluid viscosity below 0.1 Pa· s [100 cP]. We compared our results to earlier results addressing viscous fluid in either porous rocks with a rigid matrix or in a purely elastic rock, and our formulae are found to better match the numerical solution, especially regarding attenuation. The computed attenuation was used to demonstrate detectability of fracture tip reflections at wellbore, for a range of fracture lengths and apertures, pulse frequencies, and fluid viscosity.  相似文献   

Modeling of wind gap formation and development of sedimentary basins during fold growth: application to the Zagros Fold Belt,Iran          下载免费PDF全文

Marine Collignon  Philippe Yamato  Sébastien Castelltort  Boris J. P. Kaus 《地球表面变化过程与地形》2016,41(11):1521-1535

Mountain building and landscape evolution are controlled by interactions between river dynamics and tectonic forces. Such interactions have been extensively studied, however a quantitative evaluation of tectonic/geomorphic feedbacks, which is imperative for understanding sediments routing within orogens and fold‐and‐thrust belts, remains to be undertaken. Here, we employ numerical simulations to assess the conditions of uplift and river incision necessary to deflect an antecedent drainage network during the growth of one, or several, folds. We propose that a partitioning of the river network into internal (endorheic) and longitudinal drainage arises as a result of lithological differences within the deforming crustal sedimentary cover. Using examples from the Zagros Fold Belt (ZFB), we show that drainage patterns can be linked to the non‐dimensional incision ratio R between successive lithological layers, corresponding to the ratio between their relative erodibilities or incision coefficients. Transverse drainage networks develop for uplift rates smaller than 0.8 mm yr^?1 and low incision ratios (?10 < R < 10). Intermediate drainage networks are obtained for uplift rates up to 2 mm yr^?1 and large incision ratios (R > 20). Parallel drainage networks and the formation of sedimentary basins occur for large values of incision ratio (R > 20) and uplift rates between 1 and 2 mm yr^?1. These results have implications for predicting the distribution of sediment depocenters in fold‐and‐thrust belts, which can be of direct economic interest for hydrocarbon exploration. They also put better constraints on the fluvial and geomorphic responses to fold growth induced by crustal‐scale tectonics. Copyright © 2016 John Wiley & Sons, Ltd.  相似文献   

Impacts of land use on the hydrological response of tropical Andean catchments          下载免费PDF全文

Boris F. Ochoa‐Tocachi  Wouter Buytaert  Bert De Bièvre  Rolando Célleri  Patricio Crespo  Marcos Villacís  Carlos A. Llerena  Luis Acosta  Mauricio Villazón  Mario Guallpa  Junior Gil‐Ríos  Paola Fuentes  Dimas Olaya  Paúl Viñas  Gerver Rojas  Sandro Arias 《水文研究》2016,30(22):4074-4089

Changes in land use and land cover are major drivers of hydrological alteration in the tropical Andes. However, quantifying their impacts is fraught with difficulties because of the extreme diversity in meteorological boundary conditions, which contrasts strongly with the lack of knowledge about local hydrological processes. Although local studies have reduced data scarcity in certain regions, the complexity of the tropical Andes poses a big challenge to regional hydrological prediction. This study analyses data generated from a participatory monitoring network of 25 headwater catchments covering three of the major Andean biomes (páramo, jalca and puna) and links their hydrological responses to main types of human interventions (cultivation, afforestation and grazing). A paired catchment setup was implemented to evaluate the impacts of change using a ‘trading space‐for‐time’ approach. Catchments were selected based on regional representativeness and contrasting land use types. Precipitation and discharge have been monitored and analysed at high temporal resolution for a time period between 1 and 5 years. The observed catchment responses clearly reflect the extraordinarily wide spectrum of hydrological processes of the tropical Andes. They range from perennially humid páramos in Ecuador and northern Peru with extremely large specific discharge and baseflows, to highly seasonal, flashy catchments in the drier punas of southern Peru and Bolivia. The impacts of land use are similarly diverse and their magnitudes are a function of catchment properties, original and replacement vegetation and management type. Cultivation and afforestation consistently affect the entire range of discharges, particularly low flows. The impacts of grazing are more variable but have the largest effect on the catchment hydrological regulation. Overall, anthropogenic interventions result in increased streamflow variability and significant reductions in catchment regulation capacity and water yield, irrespective of the hydrological properties of the original biome. Copyright © 2016 The Authors. Hydrological Processes. Published by John Wiley & Sons Ltd.  相似文献   

Measurements of the elastic and anelastic properties of sandstone flooded with supercritical CO2     

Maxim Lebedev  Boris Gurevich 《Geophysical Prospecting》2014,62(6):1266-1277

The aim of this study was to investigate the effects of supercritical CO₂ (scCO₂) injection on the elastic and anelastic properties of sandstone at seismic and ultrasonic frequencies. We present the results of the low‐frequency and ultrasonic experiments conducted on water‐saturated sandstone (Donnybrook, Western Australia) flooded with scCO₂. The sandstone was cut in the direction perpendicular to a formation bedding plane and tested in a Hoek triaxial pressure cell. During the experiments with scCO_2, the low‐frequency and ultrasonic systems and the pump dispensing scCO₂ were held at a temperature of 42°C. The elastic parameters obtained for the sandstone with scCO₂ at seismic (0.1 Hz–100 Hz) and ultrasonic (～0.5 MHz) frequencies are very close to those for the dry rock. The extensional attenuation was also measured at seismic frequencies for the dry, water‐saturated, and scCO₂‐injected sandstones. The applicability of Gassmann's fluid substitution theory to obtained results was also tested during the experiments.  相似文献