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.     

Oil/source rock correlations in the Polish Flysch Carpathians and Mesozoic basement and organic facies of the Oligocene Menilite Shales: insights from hydrous pyrolysis experiments

The Oligocene Menilite Shales in the study area in the Polish Flysch Carpathians are organic-rich and contain varying mixtures of Type-II, Type-IIS and Type-III kerogen. The kerogens are thermally immature to marginally mature based on atomic H/C ratios and Rock-Eval data. This study defined three organic facies, i.e., sedimentary strata with differing hydrocarbon-generation potentials due to varying types and concentrations of organic matter. These facies correspond to the Silesian Unit and the eastern and western portions of the Skole Unit. Analysis of oils generated by hydrous pyrolysis of outcrop samples of Menilite Shales demonstrates that natural crude oils reservoired in the flysch sediments appear to have been generated from the Menilite Shales. Natural oils reservoired in the Mesozoic basement of the Carpathian Foredeep appear to be predominantly derived and migrated from Menilite Shales, with a minor contribution from at least one other source rock most probably within Middle Jurassic strata. Definition of organic facies may have been influenced by the heterogeneous distribution of suitable Menilite Shales outcrops and producing wells, and subsequent sample selection during the analytical phases of the study.     

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.     

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.     

Keplerian expansions in terms of Henrard's practical variables

Formulae for the Keplerian expansions in terms of Henrard's practical variables are given. Two different methods were applied: one using the Bessel functions and one based on the Lie transforms. The former involves less series products, but the latter is more flexible and universal.