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.     

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.     

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.     

The 2010 European Venus Explorer (EVE) mission proposal

The European Venus Explorer (EVE) mission described in this paper was proposed in December 2010 to ESA as an ‘M-class’ mission under the Cosmic Vision programme. It consists of a single balloon platform floating in the middle of the main convective cloud layer of Venus at an altitude of 55?km, where temperatures and pressures are benign (～25°C and ～0.5 bar). The balloon float lifetime would be at least 10 Earth days, long enough to guarantee at least one full circumnavigation of the planet. This offers an ideal platform for the two main science goals of the mission: study of the current climate through detailed characterization of cloud-level atmosphere, and investigation of the formation and evolution of Venus, through careful measurement of noble gas isotopic abundances. These investigations would provide key data for comparative planetology of terrestrial planets in our solar system and beyond.     

Evaluation of the impact of oceanic heat transport in the North Atlantic and Barents sea on the Northern Hemispheric climate

In this work, we evaluate the impact of terminated oceanic heat flux in the North Atlantic and Barents Sea on the Northern Hemisphere climate in January by numerical experiments with a coupled model of atmospheric general circulation and a thermodynamic model of the upper mixed layer of the ocean. We analyze the variations in the atmospheric circulation and near-surface temperature. We found that the termi-nation of the oceanic heat flux leads to a depression in atmospheric centers of action in the Northern Hemi-sphere (by 3?C5 hPa) and a significant cooling over the continents with the strongest temperature decrease down to ?10°C in northwestern Eurasia.     

Post‐Late Paleozoic Collisional Framework of Southern Great Altai

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.     

Potential geodynamic relationships between the development of peripheral orogens along the northern margin of Gondwana and the amalgamation of West Gondwana

The Neoproterozoic-Early Cambrian evolution of peri-Gondwanan terranes (e.g. Avalonia, Carolinia, Cadomia) along the northern (Amazonia, West Africa) margin of Gondwana provides insights into the amalgamation of West Gondwana. The main phase of tectonothermal activity occurred between ca. 640–540 Ma and produced voluminous arc-related igneous and sedimentary successions related to subduction beneath the northern Gondwana margin. Subduction was not terminated by continental collision so that these terranes continued to face an open ocean into the Cambrian. Prior to the main phase of tectonothermal activity, Sm-Nd isotopic studies suggest that the basement of Avalonia, Carolinia and part of Cadomia was juvenile lithosphere generated between 0.8 and 1.1 Ga within the peri-Rodinian (Mirovoi) ocean. Vestiges of primitive 760–670 Ma arcs developed upon this lithosphere are preserved. Juvenile lithosphere generated between 0.8 and 1.1 Ga also underlies arcs formed in the Brazilide Ocean between the converging Congo/São Francisco and West Africa/Amazonia cratons (e.g. the Tocantins province of Brazil). Together, these juvenile arc assemblages with similar isotopic characteristics may reflect subduction in the Mirovoi and Brazilide oceans as a compensation for the ongoing breakup of Rodinia and the generation of the Paleopacific. Unlike the peri-Gondwanan terranes, however, arc magmatism in the Brazilide Ocean was terminated by continent-continent collisions and the resulting orogens became located within the interior of an amalgamated West Gondwana. Accretion of juvenile peri-Gondwanan terranes to the northern Gondwanan margin occurred in a piecemeal fashion between 650 and 600 Ma, after which subduction stepped outboard to produce the relatively mature and voluminous main arc phase along the periphery of West Gondwana. This accretionary event may be a far-field response to the breakup of Rodinia. The geodynamic relationship between the closure of the Brazilide Ocean, the collision between the Congo/São Francisco and Amazonia/West Africa cratons, and the tectonic evolution of the peri-Gondwanan terranes may be broadly analogous to the Mesozoic-Cenozoic closure of the Tethys Ocean, the collision between India and Asia beginning at ca. 50 Ma, and the tectonic evolution of the western Pacific Ocean.