Variability of polar motion oscillations with periods from 20 to 150 days in 1979–1991

Variability of short period oscillations of polar motion with periods ranging from 20 to 150 days were investigated in the period 1979–1991. The new computation method of time variable band pass filter spectra and the Wavelet Transform method were applied. These oscillations are elliptical with variable amplitudes. Modulation periods of amplitude variations of these oscillations of about two and three years were found. Correlations of short period oscillations of polar motion and of effective atmospheric angular momentum (EAAM) excitation functions show annual variations and connections of their increases with El Niño phenomena.     

Mixing processes in wide open channels

The work contains analyses of two cases of stream diffusion under conditions of turbulent flow in an open channel. The analysed cases were: a source of rectangular cross-section placed in the channel axis and at the wall. To describe the mixing process the known equation of the turbulent diffusion was used. Verification of the solution for the considered cases was made based on research performed on models.     

Thermomagnetic properties of some Late Mesozoic diabase dikes of South Spitsbergen

Summary Laboratory investigations of thermomagnetic properties of specimens from seven diabase dikes of South Spitsbergen have been performed. Studies of temperature variation of isothermal saturation remanence combined with Hopkinson effect measurements and investigations of low temperature remanence give information on the mineral composition of the magnetic phases present in the magnetic fraction of the diabases. The experiments show that the clean natural remanence of these dikes has been acquired at the time of their, consolidation in the Late Mesozoic, though three of them may have been partially remagnetized at the time of Tertiary orogeny. Since the dikes reveal several normal and reversed directions of clean natural remanence, it is concluded that they were formed at different times in the Late Mesozoic, even though some of them may have been subjected to secondary influences at a later date.     

Nonlinearity of Nonradial Modes in Evolved Stars

We show that in evolved stars, even at relatively low surfaceamplitudes, nonradial modes become strongly nonlinear in thehydrogen shell source, where the Brunt-Väisälä frequency hasits absolute maximum. The measure of nonlinearity is the productof horizontal displacement times the radial wavenumber, . It becomes large already in evolved -Scuti stars.This nonlinearity presents a major problem for interpretations ofamplitude modulation in RR Lyrae stars in terms of nonradial modeexcitation.     

Double Material Segment as the Model of Irregular Bodies

We propose a new, simple model to describe the gravity field of irregular, nonspherical celestial bodies, like small moons or minor asteroids. The simple idea of Duboshin to use a material straight segment for such bodies is extended by combining two perpendicular segments of different lengths and masses. In typical situations, when the longest axis of the body coincides with one segment, the remaining segment must have an imaginary length. The potential remains a real function even if one segment is imaginary. The new model is confronted with the exact form of an ellipsoid's potential and with two alternative simple models for a two-axial and a three-axial ellipsoid.     

Ptolemaic Transformation in Keplerian Problem

We propose the Ptolemaic transformation: a canonical change of variables reducing the Keplerian motion to the form of a perturbed Hamiltonian problem. As a solution of the unperturbed case, the Ptolemaic variables define an intermediary orbit, accurate up to the first power of eccentricity, like in the kinematic model of Claudius Ptolemy. In order to normalize the perturbed Hamiltonian we modify the recurrent Lie series algorithm of HoriuuMersman. The modified algorithm accounts for the loss of a term's order during the evaluation of a Poisson bracket, and thus can be also applied in resonance problems. The normalized Hamiltonian consists of a single Keplerian term; the mean Ptolemaic variables occur to be trivial, linear functions of the Delaunay actions and angles. The generator of the transformation may serve to expand various functions in Poisson series of eccentricity and mean anomaly.     

Nonlinear Stability of the Lagrangian Libration Points in the Chermnykh Problem

In this paper we consider the problem of motion of an infinitesimal point mass in the gravity field of an uniformly rotating dumb-bell. The aim of our study is to investigate Liapunov stability of Lagrangian libration points of this problem. We analyze the stability of libration points in the whole range of parameters ω, μ of the problem. In particular, we consider all resonance cases when the order of resonance is not greater than five. This revised version was published online in August 2006 with corrections to the Cover Date.     

Energy gap and density in SiO2 polymorphs

A relationship between the energy gap (E _G) and density (ρ) for pure SiO₂ polymorphs is derived from atomic weights and first ionization potentials of free silicon and oxygen atoms. Theoretical considerations are based on the Lorentz electron theory of solids. The eigenfrequency v₀ of elementary electron oscillators, in energy units h v₀, is identified with the energy gap of a solid. The numerical relation is expressed as \(E_G = \sqrt {139.24 - 13.8327\rho } \) is in eV. For low-quartz with a density of 2.65 g/cm³ and also for stishovite with a density of 4.28 g/cm³, the energy gap E _G=10.1 eV and 8.9 eV, respectively. From laboratory measurements for low-quartz E _G=10.2 eV. The energy gap-density relation suggests a critical density value of ρ_x ≈ 10.1 g/cm³ for an SiO₂ phase when the energy gap vanishes (E _G=0), which is consistent with estimated densities for a high pressure silica polymorph with the fluorite structure.