A new approach to the librational solution in the Ideal Resonance Problem

The librational motion of the Ideal Resonance Problem (Garfinkel, 1966, Jupp, 1969) is treated through an initialnon-canonical transformation which, however, leaves the equations of motion in a quasi-canonical form, with Hamiltonian expressed in standard trigonometric functions amenable to traditional averaging techniques. The perturbed solutions, similarly expressed intrigonometric near-identity transformations, and their frequencies can be found to arbitrary order, with the elliptic integrals expected of the system introduced only in a final explicit quadrature for a Kepler-type equation in the angular variable. The specific transformations and resulting equations of motion are introduced, and explicit solutions for the original variables are found to second order, with mean motion accurate to fifth. Limitation of the present solution to the librational region, the extension of that solution to higher order, and observations on the form of the associated Hamiltonian are also discussed.     

Union republic migration trends in the USSR during the 1980s

"This article examines union republic migration trends in the USSR between 1979 and 1987 and prospects for indigenous out-migration from rural areas in Central Asia. The study is based on migration data derived by the residual technique and migration data from the 1985 microcensus. Results indicate that a south-to-north and probably Russian-dominated migration trend emerged in the 1980s, one which marks an almost complete reversal from earlier periods, especially 1959-70. Although Central Asia continues to have low levels of indigenous out-migration, labor surpluses and relatively waning capital investment in Central Asia may change this situation."     

Combustion as the cause of comet P/Halley's activity

The totality of the results obtained in the VEGA, GIOTTO and SUISEI projects does not lend itself to interpretation within the old sublimation models of comet activity considering solar radiation as the sole source of energy. Among them are the systematic excess of the velocity and temperature of the gas escaping from the nucleus over the theoretical values, the outflow being concentrated in several ( ~ 12–15) narrow ( ~ 300 m in size at the nucleus) hypersonic jets carrying very large amounts of remarkably fine CHON dust and located along continuous lines on the nuclear surface, intense release from the nucleus or very close to it (2 × 10³km) of CO (Q _Co/Q _{H2 O} = 0.05–0.2) with a smaller amount of CO₂ (Q _{CO 2}/ Q _{H2 O} 0.015), large near-nucleus abundances of C, C⁺ (Q _C/Q _CO 0.29), etc.The new observations, together with some earlier data still poorly understood (e.g. the appearance in the coma of large amounts of C₃) can be accounted for by assuming the cometary ices to contain, apart from hydrocarbons, nitrogen-containing compounds, etc. also of free oxygen ( ~ 15 wt.%). Under these conditions, burning should occur in the products of sublimation under deficiency of oxidizer accompanied by the production of soot, smoke, etc. The burning should propagate under the surface crust and localize primarily at a few sites.The presence of oxygen in cometary ices follows from a new eruption theory assuming the minor bodies of the Solar System to have formed in explosions of the massive ice envelopes saturated by electrolysis products on distant moonlike bodies of the type of Ganymede and Callisto.     

A new approach to the possibilities of Σ(D)-dependence and distances of the supernova remnants

A new way of choosing of the calibrators for constructing (D)-dependence of supernova remnants (SNR) is suggested. A knowledge of the distance of an SNR is not sufficient to consider it as a calibrator. It is shown that neither more accurate determination of distance to calibrators, nor an increase in their number, nor an increase in the precision of the remnant angular size and radio flux determination can lead to a considerable improvement of simple (D)-dependence which is suggested in the given work.For remnants with small surface brightnesses there is no (D)-dependence at all. The most accurate remnant distances currently known, are given: these are liable to change only after a large amount of additional observational data accurately compiled.     

Dynamical effects of dark matter in systems of galaxies

SeveralN-body experiments were performed in order to simulate the dynamical behaviour of systems of galaxies gravitationally dominated by a massive dark background.We discuss mass estimates from the dynamics of the luminous component (M _VT) under the influence of such a background, assuming a constant dark/luminous mass ratio (M _D/M _L) and plausible physical conditions. We extend in this way previous studies (Smith, 1980, 1984) about the dependence ofM _VT on the relative distributions of dark and luminous matter (Limber, 1959). We found that the observed ratio of the virial theorem mass to luminosity (M _VT/L) in systems of galaxies of different sizes could be the result of different stages of their post-virialisation evolution as was previously suggested by White and Rees (1978) and Barnes (1983). This evolution is mainly the result of the dynamical friction that dark matter exerts on the luminous component. Thus our results give support to the idea that compact groups of galaxies are dynamically more evolved than large clusters, which is expected from the hierarchical clustering picture for the formation of such structures.     

Effects of mass transfer on an oscillating free-convection flow in the Stokes's problem past an infinite porous vertical limiting surface with heat sources and variable suction

An analysis of the effects of the mass transfer on the unsteady free-convection flow of a viscous incompressible fluid, past an impulsively started infinite porous vertical limiting surface with heat sources is presented, when the free-stream velocity and the suction velocity, are oscillating in the time about constant mean values. Approximate solutions for the coupled nonlinear equations are derived for the mean velocity, the mean temperature, the mean skin-friction, and the mean rate of heat transfer. All the above quantities are shown graphically followed, by a discussion.     

The role of cavities and mantles in the ultraviolet extinction peak of graphite spheres with particular reference to a possibly discovered C60 structure

A computer routine using rigorous Güttler theory was developed to consider effects of concentric cavities and organic mantles within and around graphite spheres, with a view to assessing the stability of the extinction peak near 4.60 m^–1. The newly discovered stable carbon molecule of 60 atoms gives an absorption band at 4.60 m^–1 which closely agrees with the observed; moreover, it leads to the observed extinction rise in the far UV and can possibly explain the fine structure around the 5.5–7 m^–1 dip, while its own structure deals successfully with the main objections to previous carbon-graphite models. The role of the electric vector component perpendicular to the basal plane of the crystal in achieving the fit is stressed.     

Possible mass limits for quantum double galaxies

When cosmic quantum mechanics is applied to a double galaxy, the result is mass limits in order for the two galaxies to form a quantum binary system. For a non-relativistic theory (based on the Schrödinger wave equation), the mass limits are: (m _g)_max 10¹² M and (m _g)_min 10¹⁰ M . One possible consequence appears to be a Newtonian gravitational constant that varies with cosmic time, with its value larger in the cosmic past.     

Cylindrical oscillations of force-free electromagnetic fields

This paper is devoted to Force-Free Electromagnetic Oscillations in a constant magnetic field. A correction is made in the derivation of the basic equation. The paper confirms the predicted spectrum of frequencies, namely _n = _o (n + 1)^1/2;n = 0, 1, 2, .... In addition it is suggested that hybrid frequency _n = ( _n ² + _H ² )^1/2 should be found in observational data.     

Evolution of galaxies: One-zone model with a birth-rate stellar function depending on gas density and temperature

In this paper closed one-zone models with a birth-rate stellar function depending on gas density and temperature are built up, in order to make a zeroth order approximation of thermo-chemical evolution of galaxies. To get a more realistic picture, the models are allowed first to expand with the universe and then to contract according to three successive time-scales, in order to simulate violent relaxation, rapid contraction, and slow contraction processes.Star formation occurs according to a birth-rate (m, t) _g ⁿ T ^r m ^p ( _g , gas density;T, gas temperature; andm, star mass), which reproduces the usual Schmidt-type law in the limitr0. Further we suppose that synthesized metals and helium are instantaneously mixed when returned to gas component at star death, and that relative metal abundances are time-independent: ( any element heavier than He, ). An energy fraction of each typical supernova event is assumed to heat interstellar medium, which is also though always to maintain a steady state.Under these hypotheses it becomes possible to use the interstellar cooling function of Dalgarno and McCray (1972), which is related to a special cosmic abundance of elements, to express analytically an interstellar cooling function related to any abundance. At this stage, numerical computations are performed up to about 12 Gy and the results analyzed in order to reproduce some morphological features observed in the galaxy, namely: (i) the extreme scarcity of stars with nearly zero metal content; (ii) the metal content and mass fraction of halo stars; (iii) the metal content and mass fraction of disk stars; and (iv) the ratio of the present-day birth-rate to the past birth-rate averaged over the age of the disk. It is found that a whole class of theoretical models exist, with slope of the mass spectrum between –2.5 and –2.6, which range from a Schmidt's law limitn=1.3 andr=0 to the opposite limitn=0 andr=–1.2, and are able to fit more or less at the same extent the observations mentioned above. On the analysis of further computations, it is also shown that an universal birth-rate stellar function is in contradiction with neither a dynamical hystory starting from the initial expansion of proto-galaxies, nor a morphological sequence where the amount of angular momentum is the only free parameter for any given mass, at least for what concerns spiral types. Finally, possible refinements for future work are briefly outlined.