A generalization of Szebehely's equation for three dimensions

Szebehely's equation for the potential generating a prescribed family of orbits in two dimensions is generalized for three-dimensional orbits. A simultaneous system of first-order linear partial differential equations is derived for the determination of the potential in the three-dimensional case. Solutions of this system are found in several cases including Kepler's problem too.Paper presented at the 1981 Oberwolfach Conference on Mathematical Methods in Celestial Mechanics.This paper is dedicated to Professor Victor Szebehely on the occasion of his 60th birthday.     

A multiproxy evaluation of Holocene environmental change from Lake Igaliku, South Greenland

This is the first integrated multiproxy study to investigate climate, catchment evolution and lake ecology in South Greenland. A 4-m-long sedimentary sequence from Lake Igaliku (61o 00?? N, 45o 26?? W, 15?m asl) documents major environmental and climatic changes in south Greenland during the last 10?ka. The chronology is based on a ²¹⁰Pb and ¹³⁷Cs profile and 28 radiocarbon dates. The paleoenvironmental history is interpreted on the basis of magnetic susceptibility, grain size, total organic carbon, total nitrogen and sulphur, sedimentation rates, pollen, and diatom assemblages. The basal radiocarbon date at ca. 10?cal?ka BP provides a minimum age for the deglaciation of the basin, which is followed by ~500?years of high sedimentation rates in a glacio-marine environment. After the glacio-isostatic emergence of the basin ca. 9.5?cal?ka BP, limnological and terrestrial proxies suggests early warmth, which may have been interrupted by a cold, dry and windy period between 8.6 and 8.1?cal?ka BP. A dry and windy event ~5.3?C4.8?cal?ka BP preceded the Neoglacial transition at Lake Igaliku, which is characterized by a shift toward moister and perhaps cooler conditions ~4.8?cal?ka BP, causing major changes in terrestrial and aquatic ecological conditions. Significant cooling is documented after ~3?cal?ka BP. Since ~1?cal?ka BP the climatic-driven changes were overprinted by the human influence of Norse and recent agriculture.     

Nuclear modification factor for quarkonium production in high energy proton-nucleus collisions within the parton saturation approach

In this work, we analyze nuclear effects in the inclusive production of quarkonium in proton-nucleus collisions at high energy regime. A theoretical framework that includes initial state effects like nuclear shadowing and gluon density saturation is considered. Numerical results for nuclear modification factor, $R_{pA}(y)$, as a function of meson rapidity in proton-nucleus collisions are presented. The parameter-free predictions are compared to the available data from the Large Hadron Collider. Discussion on the main theoretical uncertainties is made, with emphasis on the phenomenological models for the nuclear saturation scale.     

A parametric study of stability and resonances around L 4 in the elliptic restricted three-body problem

The size of the stable region around the Lagrangian point L ₄ in the elliptic restricted three-body problem is determined by numerical integration as a function of the mass parameter and eccentricity of the primaries. The size distribution of the stable regions in the mass parameter-eccentricity plane shows minima at certain places that are identified with resonances between the librational frequencies of motions around L ₄. These are computed from an approximate analytical equation of Rabe relating the frequency, mass parameter and eccentricity. Solutions of this equation are determined numerically and the global behaviour of the frequencies depending on the mass parameter and eccentricity is shown and discussed. The minimum sizes of the stable regions around L ₄ change along the resonances and the relative strength of the resonances is analysed. Applications to possible Trojan exoplanets are indicated. Escape from L ₄ is also investigated.     

Snowpack disrupts relationship between young water fraction and isotope amplitude ratio; approximately one fifth of mountain streamflow less than one year old

Previous “fraction of young water” (F_yw) estimates based on relative annual isotopic amplitudes in precipitation (A_p) and streamflow (A_s) produced low F_yw values in mountain catchments, which is contrary to extensive research that reports rapid water transmission in mountains. This study investigated this discrepancy by testing the effect of snow accumulation on the model that underpins the F_yw method. A Monte-Carlo analysis of simulations for 20,000 randomly-generated catchment model configurations used 10 years of precipitation inputs for the Upper Elbow River catchment in the Rocky Mountains (Alberta, Canada) to model discharge with and without snowpack storage of winter precipitation. Neither direct nor modified precipitation input produced a 1:1 relationship between A_s/A_p and F_yw, undermining the applicability of the original F_yw method in mountain watersheds with large seasonal snow accumulation. With snowpack-modified input a given A_s/A_p ratio corresponds to a range of F_yw values, which can still provide semi-quantitative information. In the small (435 km²) Elbow River catchment a F_yw range of 7–23% supports previous findings of rapid transmission in mountain catchments. Further analysis showed that the improved discharge prediction (Nash–Sutcliffe efficiency > 0.9) correlates with higher F_yw values and demonstrated that the interannual shifts in δ¹⁸O can be used to estimate of new water (<1 year) fraction in winter streamflow, and the estimate of 20% for the Elbow River further supports rapid transmission in mountain catchments.     

SPECTROSCOPOLARIMETRIC SENSING OF ENERGY DEPOSITION INTO THE CHROMOSPHERE DURING SOLAR FLARES – I. Observations

Measurements of linear polarization in hydrogen H and H lines, made with the Large Solar Vacuum Telescope of Baikal Astrophysical Observatory and Automated Solar Telescope of Sayan Solar Observatory, affiliated with the Russian Institute of Solar and Terrestrial Physics, are reported in this paper. Short-term polarization associated with solar flares is found to be present in active regions. There is a significant tendency for the H polarization vector to be radial, i.e., in the flare-to-disk-center direction. This polarization may be due to atmospheric bombardment by hecta keV protons. On the other hand, the polarization vector is found to be perpendicular to the radial direction at some locations where the line profile has a typical mustache shape suggesting a bombardment by energetic electrons. The H line is also linearly polarized. However, no preferential direction of polarization is found in this line, which is formed more deeply in the solar atmosphere.     

Identifying the accidental-natural mortality of leporids in the archaeological record: insights from a taphonomical analysis of a pitfall without evidence of human presence

Leporids (Lagomorpha, Mammalia), especially the mountain hare (Lepus timidus) and the European rabbit (Oryctolagus cuniculus), have been among the most abundant small game in western Europe since the Pleistocene. These animals are preferred prey for more than 40 predators, which increases the chances of finding their skeletal remains at archaeological or natural sites, and in particular karstic formations alternately occupied by Palaeolithic human societies and other predators. Moreover, specific eco-ethological characteristics for both species also offer the possibility to produce a substantial quantity of their bones accumulated by natural mortality without predation, making it more difficult to identify their origin in the fossil record. Despite this fact, the taphonomic signature of accidental-natural accumulations of leporids in karsts, such as pitfalls, has never been properly characterised. In order to address these issues, we carried out a detailed taphonomic study of leporid remains in a pitfall without any evidence of human activity, namely at Coulet des Roches (Monieux, Vaucluse, south-eastern France). At this site, leporids are the most abundant species throughout the Last Glacial Maximum sedimentary sequence. The bone accumulation was analysed in order to determine the most relevant criteria to identify a natural accumulation that results from the accidental fall of individuals in the pitfall. The relative proportions of each species are consistent with their current ethology, and their mortality profiles are compatible with the structure of a living natural population. The completeness rate of the different skeletal portions for both species is relatively high, bones are less fragmented and, unlike what might be expected, very few anatomical connections were preserved. The observed anatomical representation, breakage, and bone surface modification patterns are discussed and compared with available data concerning accumulations with predation. Taken together, the identified criteria contribute valuable help in the recognition of accidental mortality in the fossil record, as well as to evaluate the proportion of leporid bones accumulated naturally and those accumulated by predation, human or not, in a deposit.