Convergence of Liapunov series for Huygens–Roche Figures

According to the classical theory of equilibrium figures, surfaces of equal density, potential and pressure concur (let us call them isobars). Isobars can be represented by means of Liapunov power series in small parameter q, up to the first approximation coinciding with the centrifugal to gravitational force ratio at the equator. Liapunov has proved the existence of the universal convergence domain: the above mentioned series converge for all bodies (satisfying a natural condition that the density ρ decreases from the center to the surface) if |q| < q*. Using Liapunov’s algorithm and symbolic manipulation tools, we have found q*= 0.000370916. Evidently, the convergence radius q* may be much greater in common situations. To comfirm it it is reasonable to consider two limiting and one or two intermediate cases for the density behaviour: ρ is a constant, the Dirac’s δ-function, linear function of the distance from the center, etc. And indeed, in the previous paper we find a three orders of magnitude greater value for homogeneous figures. In the present paper we find that in the opposite case of Huygens-Roche figures (a point-mass surrounded by a weightless atmosphere) the convergence radius is unexpectedly large and coincides with the well-known biggest possible value q*= 0.541115598 for such a class of figures. To ascertain it we ought to use numerical calculations, so our main result is demonstrated by means of a computer assisted proof. This revised version was published online in July 2006 with corrections to the Cover Date.     

Annual report of IGCP Project No.440 in 2003 Rodinia assembly and breakup

With the latest information on geology, isotop chronology, geochemistry and aerial geophysics, the structural enviroment, geological event characterists and evolution history of component units of Rodinia Supercontinent on a global scale are discussed. And some neo views and genetic pattern are provided. The East Eurppean Craton had a complex evolution history between 1.7 and 0.9 Ga. The arthors propose a new reconstruction of Laurentia acient land and Siberia at ca. 1 050-1 000 Ma. The largest litho-structural record of the Meso-Neoproterozoic orogenic collage in South America made up the western border of the South American Platform African Cratons are the result of convergence of Paleoproterozoic/Archaem Cratonic blocks. A part of Eastern Antarctica attached to southern Africa in Mesoproterozoic.Neoproterozoic felsic magmatic events in New India made the western border of Rodinia Pre-Grevoillian Laurentia was established as a major continental block by the end of the Paleoproterozoic. South China is geologically plausible to be between southern Laurentia and eastern Australia. Yangzi-Tarim connection or neighborhood is proposed. According to the abovementionded, the assembly and breakup paattem of Rodinia proposed by Pisarevsky is tested. It telles that primary break up is along the western border of Laurentia ancient land, which is similar to northern Atlantic. Another characteristic is that some continents are not considered as component parts of Rodinia, eg. India, Congo and San-Francisco.     

Algorithm grwat for Automated Hydrograph Separation by B.I. Kudelin’s Method: Problems and Perspectives

Water Resources - An algorithm for automated graph-analytical separation of hydrograph, underlying grwat software package is described in detail and analyzed. This system is designed for separation...     

Consistent estimation of geodetic parameters from SLR satellite constellation measurements

In this paper, we consistently estimate geodetic parameters such as weekly 3-D station coordinates, Earth orientation parameters (EOP) including daily x/y-pole coordinates and the excess length of day \(\Delta \hbox {LOD}\), and selected weekly Earth’s gravitational field (Stokes) coefficients up to degree and order 6 from Satellite Laser Ranging measurements to up to 11 geodetic satellites. The SLR constellation consists of LAGEOS-1/2, Etalon-1/2, Stella, Starlette, Ajisai, Larets, LARES, BLITS and WESTPAC, and its observations cover a time span of 38 years ranging from February 16, 1979, to April 30, 2017. If multiple satellites with various altitudes and orbit inclinations are combined, correlations between estimated parameters are significantly reduced. This allows us (i) to investigate the ability of satellite constellations to reduce existing correlations and (ii) to estimate reliable parameters with higher precision compared to the standard 4-satellite constellation (LAGEOS-1/2, Etalon-1/2) which is currently used by the International Laser Ranging Service for the determination of the Terrestrial Reference Frame (TRF) and EOP products. In particular, the Stokes coefficients, EOP and TRF datum parameters (three translations, three rotations, one scale factor), which are highly correlated with satellite-specific orbit parameters, are improved. From our investigations, we found for an 11-satellite solution compared to the above-mentioned 4-satellite solution a decrease in the scatter of the TRF datum parameters of up to 37%, the transformation residuals are decreased by up to 22%, the scatter of the EOP is decreased by up to 22%, and their mean values are decreased by up to 84% w.r.t. the reference solutions. The largest improvement is obtained for the Stokes coefficients which significantly benefit from a combination of multiple satellites (inclinations and orbit altitudes). In total, single coefficients are improved by up to 93% and the overall improvement is up to 74%. Moreover, it could be clearly identified that Ajisai significantly disturbs the TRF solution due to an erroneous center-of-mass correction. We further quantify the impact of specific satellites on the determination of different geodetic parameters and finally evaluate the potential of the existing SLR-tracked spherical satellite constellation to support the goals of GGOS.     

Specifying the atmospheric pollutant distribution forecast using the mathematical modeling and measurement data

Considered is a possibility of specifying the forecast of volcanic aerosol distribution in the atmosphere using the data of ground-based actinometric measurements. To simulate the aerosol distribution, the FlexPart software (Norwegian Institute for Air Research) was used. Using the FlexGraph software (Planeta Research Center for Space Hydrometeorology), the visualization and interactive analysis were carried out of aerosol concentration fields at different time moments. The prognostic concentration of volcanic ash from Grímsvötn volcano (May 2011) is bound to the results of measurements of aerosol optical depth in Hamburg at one of the points of AERONET global network. The comparison of the corrected aerosol concentration with the measurements at other AERONET points demonstrated the competence of the proposed approach. To specify the aerosol cloud distribution forecast on the territory of Russia, the Roshydromet actinometric network data can be used.     

Brane cosmology from observational surveys and its comparison with standard FRW cosmology

Several simple dark energy models on the brane are investigated. They are compared with corresponding models in the frame of 4d Friedmann-Robertson-Walker cosmology. For constraining the parameters of the models considered, recent observational data, including SNIa apparent magnitude measurements, baryon acoustic oscillation results, Hubble parameter evolution data and matter density perturbations are used. Also, explicit formulas of the so-called state-finder parameters in teleparallel theories are found that could be useful to test these models and compare Loop Quantum Cosmology and Brane Cosmology. The conclusion is reached that a joint analysis as the one developed here allows to estimate, in a very clear way, possible deviation of our cosmology from the standard Friedmann-Robertson-Walker one.