Convergence of Liapunov Series for Maclaurin Ellipsoids

According to the classical theory of equilibrium figures surfaces of equal density, potential and pressure concur (let call them isobars). Isobars may be represented by means of Liapunov power series in small parameter q, up to the first approximation coincident with centrifugal to gravitational force ratio on the equator. A. M. Liapunov has proved the existence of the universal convergence radius q : above mentioned series converge for all bodies if q < q . Using Liapunov's algorithm and symbolic calculus tools we have calculated q = 0.000370916. Evidently, convergence radius q ₀ may be much greater in non-pathological situations. We plan to examine several simplest cases. In the present paper, we find q ₀ for homogeneous liquid. The convergence radius turns out to be unexpectedly large coinciding with the upper boundary value q ₀ = 0.337 for Maclaurin ellipsoids.     

Characterizing the phosphorus forms extracted from soil by the Mehlich III soil test

Phosphorus (P) can limit crop production in many soils, and soil testing is used to guide fertilizer recommendations. The Mehlich III (M3) soil test is widely used in North America, followed by colorimetric analysis for P, or by inductively coupled plasma-based spectrometry (ICP) for P and cations. However, differences have been observed in M3 P concentrations measured by these methods. Using ³¹P nuclear magnetic resonance (P-NMR) and mass spectrometry (MS), we characterized P forms in M3 extracts. In addition to the orthophosphate that would be detected during colorimetric analysis, several organic P forms were present in M3 extracts that would be unreactive colorimetrically but measured by ICP (molybdate unreactive P, MUP). Extraction of these P forms by M3 was confirmed by P-NMR and MS in NaOH-ethylenediaminetetraacetic acid extracts of whole soils and residues after M3 extraction. The most abundant P form in M3 extracts was myo-inositol hexaphosphate (myo-IHP, phytate), a compound that may not contribute to plant-available P if tightly sorbed in soil. Concentrations of myo-IHP and other organic P forms varied among soils, and even among treatment plots on the same soil. Extraction of myo-IHP in M3 appeared to be linked to cations, with substantially more myo-IHP extracted from soils fertilized with alum-treated poultry litter than untreated litter. These results suggest that ICP analysis may substantially over-estimate plant-available P in samples with high MUP concentrations, but there is no way at present to determine MUP concentrations without analysis by both colorimetry and ICP. This study also tested procedures that will improve future soil P-NMR studies, such as treatment of acid extracts, and demonstrated that techniques such as P-NMR and MS are complimentary, each yielding additional information that analysis by a single technique may not provide.

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Laboratory investigation of the mechanism of the periodic eddy formation behind capes in a coastal sea

The observations carried out in the Caucasian sector of the Black Sea have shown that, under certain conditions, the Rim Current detaches from the coast behind Cape Idocopas. In these cases, an anticyclonic eddy is formed between the detached Rim Current and the coast. Sometimes, the eddy grows in size until it is captured by the flow and goes downstream. After that, a next eddy is formed nearly at the same place, etc. The conditions of the periodic eddy formation behind a cape are revealed by means of laboratory modeling. The laboratory results are compared with the data of field observations in the Black Sea.     

Sinking of less dense water in the bottom Ekman layer formed by a coastal downwelling current over a sloping bottom

Laboratory experiments on the dynamics of a downwelling coastal current over a sloping bottom were conducted in a tank on a rotating platform. The current was generated by a source of stable water flow of the same density (barotropic case) or of lesser density (baroclinic case) compared with the surrounding water in the tank. It was found that even in the case of the baroclinic current, a less dense water downflow in the bottom Ekman layer was formed under certain conditions. At some moment, this downflow undergoes convective instability. Taking into account the results of the experiment, the parameters of the bottom Ekman layer on the continental shelf/slope of the Black Sea were preliminarily estimated and the possible sinking depth of less dense water was calculated.     

A concept of a space hazard counteraction system: Astronomical aspects

The basic science of astronomy and, primarily, its branch responsible for studying the Solar System, face the most important practical task posed by nature and the development of human civilization—to study space hazards and to seek methods of counteracting them. In pursuance of the joint Resolution of the Federal Space Agency (Roscosmos) and the RAS (Russian Academy of Sciences) Space Council of June 23, 2010, the RAS Institute of Astronomy in collaboration with other scientific and industrial organizations prepared a draft concept of the federal-level program targeted at creating a system of space hazard detection and counteraction. The main ideas and astronomical content of the concept are considered in this article.     

Physical mechanisms of submesoscale eddies generation: evidences from laboratory modeling and satellite data in the Black Sea

Ocean Dynamics - The observed evidence of the implementation of three different mechanisms of the submesoscale eddies generation in the Black Sea previously studied by the field research and...