We study the non-linear stability of the equilibria corresponding to the motion of a particle orbiting around a finite straight segment. The potential is a logarithmic function and may be considered as an approximation to the one generated by elongated celestial bodies. By means of the Arnold's theorem for non-definite quadratic forms we determine the orbital stability of the equilibria, for all values of the parameter k of the problem, resonant cases included. 相似文献
Observational evidence shows that gravitational lensing induces an angular correlation between the distribution of galaxies and much more distant QSOs. We use weak gravitational lensing theory to calculate this angular correlation, updating previous calculations and presenting new results exploring the dependence of the correlation on the large-scale structure. We study the dependence of the predictions on a variety of cosmological models, such as cold dark matter models, mixed dark matter models and models based on quintessence. We also study the dependence on the assumptions made about the nature of the primordial fluctuation spectrum: adiabatic, isocurvature and power spectra motivated by the cosmic string scenario are investigated. Special attention is paid to the issue of galaxy biasing, which is fully incorporated. We show that different mass power spectra imply distinct predictions for the angular correlation, and therefore the angular correlation provides an extra source of information about cosmological parameters and mechanisms of structure formation. We compare our results with observational data and discuss their potential uses. In particular, it is suggested that the observational determination of the galaxy–QSO correlation may be used to give an independent measurement of the mass power spectrum. 相似文献
Apatite fission track (AFT) and (U–Th)/He data from the High Atlas have been obtained for the first time to constrain the tectono‐thermal evolution of the central part of the chain. Results from Palaeozoic basement massifs indicate long residence at low temperatures, consistently with their original location out of the deepest Mesozoic rift troughs and indicating minor exhumation. The best rocks for extracting the Alpine history of the Atlas Mountains are Jurassic intrusives, which yield AFT ages centred on c. 80 Ma; thermal models based on AFT data and constrained by (U–Th)/He suggest that these ages are included in a slow cooling trend from intrusion age to c. 50 Ma ago that we attribute to post‐rift thermal relaxation. This is followed by a stability period of c. 30 Ma and then by a final exhumational cooling until present exposure. Eocene intrusives yield AFT ages similar to those of Rb–Sr and K–Ar suggesting rapid emplacement in the uppermost crust. 相似文献
We revisit some results of perturbation theories by a method of successive elimination of harmonics inspired by some ideas of Delaunay. On the one hand, we give a connection between the KAM theorem and the Nekhoroshev theorem. On the other hand, we support in a quantitative fashion a semi-numerical method of analysis of a perturbed system recently introduced by one of the authors. 相似文献
Low-salinity waters, within the upper layers of the water column, have been observed in the oceanic region of the southeastern limit of the Bay of Biscay (in March, 2007). This contribution assesses the potential role of large surface freshwater discharges from the Adour (France), Nervión, Oria, Deba, Urola, Urumea and Bidasoa (Basque Country) rivers, to explain the presence of these low-salinity waters. Such discharges, within the offshore waters, reached to at least 50 m in depth; likewise, extending over 15–20 km, in the horizontal. This pattern is confirmed by field data collected by offshore buoys, model results, and the analysis of satellite images. The presence of the low-salinity waters is corroborated by numerical simulations, performed by the ROMS (Regional Ocean Modeling System) hydrodynamic model, with the incorporation of river discharges. In order to simulate the freshwater movements and to identify their origin, particles were released at the river mouths and dispersed (by a Lagrangian particle-tracking model, LPTM), supplied by 3-hourly current fields derived from the ROMS model. The plumes of the Nervión, Oria, Urola and Urumea rivers appear to be the main factors contributing to the low-salinity field, at the offshore locations of the buoys. This pattern is related mainly to the prevailing oceano-meteorological conditions, over the period of analysis. 相似文献
In this paper, a novelty-free software to assess an efficient CIPW Norm (± 0.006 wt.% in differences between input and output data) is presented. The package is available in the official repository for user-contributed R packages (CRAN: Comprehensive R Archive Network). The software is able to handle big data sets and considers minor and trace element compositions. The algorithm can calculate odd minerals in igneous rocks, such as cancrinite and calcite, adjust the Fe+3/Fe+2 ratio in different standard approaches, and recalculate the compositions of the rocks in an anhydrous basis (100 ± 0.003 wt.% volatile-free adjusted). Furthermore, the package calculates several petrological parameters, and the graphical outputs are displayed following IUGS scheme standards. The prime aspect of shinyNORRRM is the symbiosis of native R functions with the R package’s shiny (Web Application Framework for R) to run the norm in a user-friendly interface. shinyNORRRM can be executed in any operating system and requires no previous programming knowledge, thus promising to be the universal computational program in this matter. The output data are printed in the standard comma-separated values (*.csv) format, which is highly compatible with general spreadsheet editors. In this work, the algorithm of our program is validated using already compiled whole-rock geochemical databases.