Radiation pressure effects in the oscillations of compressible rotating homogeneous spheroids

Earlier models of compressible, rotating, and homogeneous ellipsoids with gas pressure are generalized to include the presence of radiation pressure. Under the assumptions of a linear velocity field of the fluid and a bounded ellipsoidal surface, the dynamical behaviour of these models can be described by ordinary differential equations. These equations are used to study the finite oscillations of massive radiative models with masses 10M and 30M in which the effects of radiation pressure are expected to be important.Models with two different degrees of equilibrium are chosen: an equilibrium (i.e., dynamically stable) model with an initial asymmetric inward velocity, and a nonequilibrium model with a nonequilibrium central temperature and which falls inwards from rest. For each of these two degrees of equilibrium, two initial configurations are considered: rotating spheroidal and nonrotating spherical models.From the numerical integration of the differential equations for these models, we obtain the time evolution of their principal semi-diametersa ₁ anda ₃, and of their central temperatures, which are graphically displayed by making plots of the trajectories in the (a ₁,a ₃) phase space, and of botha ₁ and the total central pressureP _c against time.It is found that in all the equilibrium radiative models (in which radiation pressure is taken into account), the periods of the oscillations of botha ₁ andP _c are longer than those of the corresponding nonradiative models, while the reverse is true for the nonequilibrium radiative models. The envelopes of thea ₁ oscillations of the equilibrium radiative models also have much longer periods; this result also holds for the nonequilibrium models whenever the envelope is well defined. Further, as compared to the nonradiative models, almost all the radiative models collapse to smaller volumes before rebouncing, with the more massive model undergoing a larger collapse and attaining a correspondingly larger peakP _c.When the mass is increased, the dynamical behavior of the radiative model generally becomes more nonperiodic. The ratio of the central radiation pressure to the central gas pressure, which is small for low mass models, increases with mass, and at the center of the more massive model, the radiation pressure can be comparable in magnitude to the gas pressure. In all the radiative models, the average periods as well as the average amplitudes of both thea ₁ andP _c oscillations also increase with mass.When either rotation or radiation pressure effects or both are included in the equilibrium nonradiative model, the period of the envelope of thea ₁ oscillations is increased. The presence of rotation in the equilibrium radiative model, however, decreases this period.Some astrophysical implications of this work are briefly discussed.     

Spectrophotometric studies of two Be stars,α Leo and 17 Tau

The present work deals with spectrophotometric studies of two Be stars ( Leo and 17 Tau) using 74 telescope at Kottamia observatory.The results obtained revealed the presence of variations in the general shape and the equivalent width of the profiles of hydrogen lines in the spectrum of both stars within short period interval.     

The effect of Antarctic O3 decline on night airglow intensity of Na5893Å, O5577Å, OH emissions and its correlation with total solar flare numbers

The paper presents the effect of O₃ depletion on different night airglow emission lines. Calculations based on chemical kinetics show that the airglow intensity of Na5893Å, O5577Å and OH band emissions will also be affected due to the depletion of O₃ concentration. Intensity of Na5893Å is calculated theoretically for Halley Bay (76° S,27° W), British Antarctic Survey Station, during the period 1973 to 1984. It is concluded from the covariation of different emission lines that O5577Å and OH emissions also follow the same trend of variation. A study has been made to find the correlation between the depletion of O₃ concentration and total solar flare numbers. Important results are as follows:

Solution of a transfer equation by a Modified Spherical Harmonic Method in a thin anisotropically scattering atmosphere

Wan, Wilson and Sen (1986) have examined the scope of Modified Spherical Harmonic Method in a plane medium scattering anisotropically. They have used the phase functionp(µ, µ) = 1 +aµµ. In this paper, the Transfer Equation has been solved by the Modified Spherical Harmonic Method using the phase functionp(µ, µ) = 1 + ₁ P ₁(µ)P ₁(µ) + ₂)P ₂(µ)P ₂(µ) and a few sets of numerical solution have been predicted for three different cases.     

Effect of temperature gradient on the wave propagation in a self-gravitating medium and its role in the central region of our Galaxy

The wave propagation in a finitely conducting, self-gravitating, non-relativistic hydromagnetic medium with temperature gradient and a heat-energy transport into it has been considered. Firstly, a General Dispersion Relation (G.D.R.) has been derived. The interest has been kept limited for the study of one dimensional wave propagation in a typical medium where magnetic field and it's gradient, density gradient, temperature gradient are all along the direction of wave propagation. The D.R. of such a medium follows from G.D.R. In particular, the effect of temperature gradient on the wave propagation has been studied. Analytical expressions for the wave parameters have been derived under different conditions. It has been found that the longitudinal waves could be sufficiently energetic for being unstable by the temperature gradient. Further, the modified Jeans' criterion (depending on temperature gradient), a criterion important for stability, has also been obtained.On assuming the gas medium in the central region ( 10 pc) of our Galaxy to behave like hydromagnetic fluid, and the direction of wave propagation (z-direction) as the direction perpendicular to the Galactic plane, few numerical estimations for the wave parameters (like wave lengths, phase velocity, etc.) have been made (as application of the above theoretical discussions). It has been found that the phase velocity of longitudinal waves at 1 pc level is at least 170 kms^–1 while at the 10 pc level the longitudinal waves of length less than a parsec may propagate smoothly through the medium. It has been suggested that (i) in the central region ( 10 pc) of our Galaxy the temperature gradient could be one of the major causes of the mass-outflow along the direction perpendicular to the Galactic plane (ii) outside the central region ( 10 pc) of our Galaxy, there may be long term consequences of such mass-outflow like Halo formation.     

Adsorption of fluoride on goethite surfaces-implications on dental epidemiology

Fluoride ion interaction with synthetically prepared goethite has been investigated over a range of pH values (4–9) and F^– concentrations (10^–3–10^–5 M). The amount of F^– retained by goethite suspensions was found to be a function of pH, media ionic strength, F^– concentration, and goethite concentration. The lowest ionic strength (0.001 M KNO₃) gave the highest adsorption medium. Uptake was minimal at pH >7 and increased with decreasing pH. Thermodynamic properties for fluoride adsorption at 298 K and 323 K were investigated. The isosteric heat of adsorption (H _r) was calculated and the heterogeneity and homogeneity of the surface examined for goethite. In view of the importance of fluoride in dental health, the interaction of fluoride on goethite in the physical environment has important implications on dental epidemiology.     

Carbonatites from Eastern Paraguay and genetic relationships with potassic magmatism: C, O, Sr and Nd Isotopes

Summary Geochemical characteristics were systematically determined for Early Cretaceous samples of carbonatitic rocks from Eastern Paraguay (Rio Apa, Amambay and Central Provinces). The data show that all the occurrences have an enriched isotopic signature and that the carbonatites have negligible or absent crustal signature. A petrogenetic model (parent liquids, fractional crystallization, hydrothermal interactions and weathering) is proposed as a function of incompatible trace element, stable (O-C) and radiogenic (Sr-Nd) isotope variations with the aim to test the significance of carbonatitic complexes as a marker of the metasomatized subcontinental lithospheric mantle. The results indicate that the carbonatites and primary carbonates from eastern Paraguay, and those from the north eastern Paraná Basin (SE Brazil), were affected by metasomatic events distinct in time and composition.

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Karbonatite aus Ost-Paraguay und ihre genetische Beziehung zu Kalium-Magmatismus: C O, Sr und Nd isotope

Zusammenfassung Die geochemischen Charakteristika von frühkretazischen Karbonatitproben aus Ostparaguay (Rio Alpa, Amambay und Zentrale Provinzen) wurden untersucht. Die Daten belegen, daß alle Vorkommen eine isotopische Anreicherungssignatur zeigen und daß ihnen eine entsprechende Krustensignatur fehlt. Ein Petrologisches Modell (Ausgangsschmelze, fraktionierte Kristallisation, hydrothermale Interaktion und Verwitterung) wird auf Grund der Verteilung der inkompatiblen Spurenelemente, der stabilen (C-O) und radiogenen (Sr-Nd) Isotope vorgeschlagen. Es versucht die Bedeutung der Karbonatitkomplexe als Markerhorizonte des metasomatischen subkontinentalen Mantels zu überprüfen. Die Ergebnisse zeigen, daß die Karbonatite und die primären Karbonate in Ostparaguay, und jene aus dem Paraná Becken SüdostBrasiliens durch zeitlich und zusammensetzungsmäßig unterschiedliche metasomatische Prozesse erfaßt wurden.

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With 10 Figures     

Crystal chemistry of a highly disordered Mg-Al natural spinel

Summary A Mg-Al spinel from a xenolith found in the Sacrofano volcanic area (Latium, Italy) was investigated by X-ray single crystal diffraction and electron microprobe. Its main structural parameters were: a₀ = 8.0922(3) Å and the oxygen coordinate u = 0.26213(4), which gave to tetrahedral and octahedral bond distances of 1.9220(6) Å and 1.9299(3) Å respectively. Cation distribution, obtained from structural and chemical data, showed a very high Mg-Al disorder, with an Al(T) content of 0.205 and an inversion parameter, i, of about 0.23. Comparison with the cation distribution of a spinel with similar chemical composition but occurring in chlorite schists (Shishimsk Mountains, Urals, Russia) with a₀ = 8.1003(3) Å and u=0.26330(3), and with data from the literature concerning spinels from metamorphosed limestones (Kalkbro, Sweden) and websteritic dikes (Balmuccia, Italy), all characterized by much lower Mg-Al disorder (i about 0.13–0.12), suggests a completely different thermal history, with rapid cooling rates and consequent high closure temperature of intracrystalline exchange, consistent with the Sacrofano geological environment.

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Kristallchemie eines stark ungeordneten, natürlichen Mg-Al-Spinells

Zusammenfassung Ein Mg-Al-Spinell aus einem Xenolith des Vulkangebiets von Sacrifano (Latium, Italien) wurde mit Röngten-Einkristallmethoden und der Elektronenmikrosonde untersucht. Die wichtigsten Strukturparameter sind a_o = 8,0922(3) Å und die Sauerstoffkoordinate u = 0,26213(4), was zu den tetraedrischen und oktaedrischen Bindungsabständen von 1,9220(6) Å bzw. 1,9299(3) Å führt. Die aus den strukturellen und chemischen Daten erhaltene Kationenverteilung zeigt eine sehr starke Unordnung Mg-Al mit einem Al (T)-Gehalt von 0,205 und einem Inversionsparameteri von ca. 0,23. Der Vergleich mit der Kationenverteilung eines Spinells ähnlicher chemischer Zusammensetzung, aber aus Chloritschiefern (Schischimsk-Berge, Ural, Rußland) mit a₀ = 8,1003(3) Å und u=0,26330(3), sowie mit Literaturdaten über Spinelle aus metamorphen Kalken (Kalkbro, Schweden) und websteritischen Gängen (Balmuccia, Italien), die alle durch eine viel geringere Mg-Al-Unordnung charakterisiert sind (i etwa 0,13–0,12), weist auf eine völlig andere thermische Geschichte hin, und zwar mit rascher Abkühlungsgeschwindigkeit und hoher Schließungstemperatur des intrakristallinen Austausches, was mit den geologischen Verhältnissen von Sacrofino in Übereinstimmung steht.

     

A Step Towards Evaluation of the Seismic Response Reduction Factor in Multistorey Reinforced Concrete Frames

A seismic nonlinear time-history analysis was made for four-, six-, and eight-storey reinforced concrete buildings. These buildings were made as three-dimensional space frame structures with shear walls in both orthogonal directions. They have five bays with 4.8 m spacing each in the horizontal direction, and three bays with 4.2 m spacing each in the transversal direction. The frames were designed according to the Jordanian Seismic Code of practice for Seismic Zones 4, 3, 2, and 1 as proposed for Jordan by several authors. Time-history analysis was made using the El Centro (N-S) earthquake record of May 1940 as an actual earthquake excitation. The response reduction factor (R) that primarily consists of two factors that are the ductility reduction (Rµ) and the overstrength (), is obtained. It has been seen that the seismic zoning has a slight effect on the ductility reduction factor for different buildings, since it ranges from Zone 4 to Zone 1 as 2.37 to 2.52, 1.72 to 1.78, and 1.14 to 1.18 for four-, six-, and eight-storey buildings, respectively. Moreover, it is observed that, for different buildings and different seismic zones, the ductility reduction factor (Rµ) is slightly different from the system ductility factor (µ) especially for higher values of µ (i.e., Rµ µ). The response reduction factor, called overstrength (), was evaluated. The overstrength factor was found to vary with seismic zones (Z) , number of stories, and design gravity loads. However, the dependency on seismic zones was the strongest. The average overstrength of these buildings in Zones 4 and 1 was 2.61 and 6.94, respectively. The overstrength increased as the number of storeys decreased: overstrength of a four-storey building was higher than an eight-storey building by 36% in Zone 4, and 39% in Zone 1. Furthermore, buildings of the three heights had an average overstrength 165.9% higher in Zone 1 than in Zone 4. These observations have a significant implications for the seismic design codes which currently do not take into account the variation of the response reduction factor, R (i.e., ductility reduction factor times overstrength).