The stability parameters of three-dimensional periodic three-body orbits

Formulae containing the elements of the variational matrix are obtained which determine the linear isoenergetic stability parameters of three-dimensional periodic orbits of the general three-boy problem. This requires the numerical integration of the variational equations but produces the stability parameters with the effective accuracy of the numerical integration. The conditions for stability, criticality, and bifurcations are briefly examined and the stability determination procedure is tested in the determination of some three-dimensional periodic orbits of low inclination bifurcating from vertical-critical coplanar orbits.     

The skin friction in the unsteady free-convection flow past an accelerated plate

In this paper the unsteady laminar free-convection flow of a viscous incompressible fluid, past an accelerated infinite vertical porous plate subjected to a constant suction (or injection) in considered. Numerical results for the skin-friction on the plate are obtained for the class of accelerated motions whose velocity is of the formU ₀ t ⁿ wheret is time,U ₀ a constant, andn is a positive integer. The skin friction tends to zero with increasingt when the Grashof number Gr=², the Prandtl number =1,n=0, and >0 which corresponds to suction.On leave of absence from the Department of Mathematics, University of Dhaka, Bangladesh.On leave from absence from the Department of Mathematics, University of Dar-es-Salaam, Tanzania.     

Nuclear reactions on accreting neutron star surface

The production of X-rays and gamma-rays in bursts is believed to be due to the rapid burning of matter accreted onto a neutron star surface from its companion, most probably a giant star. The accreted matter consists mainly of hydrogen and helium and a very small amount of heavy elements. Due to the infall of matter, the temperature at the bottom layers is raised to a value of the order of 10⁸ K. The neutron star surface density is>10⁷ g cm^–3. As hydrogen burning is a slow process under any temperature and density conditions, we consider the helium-burning reactions as the source of gamma-rays in the neutron star surface. Under high-density conditions the ordinary laboratory reaction rates should become modified. At high-density conditions, the strong screening effect due to the polarising cloud of electrons around the ions become important and enhances the reaction rates considerably. The helium-burning reactions are calculated under such conditions. The abundances of helium-burning products such as¹²C, 1¹⁶O, and²⁰Ne, etc., are computed. Under high-density and temperature conditions carbon is found to be more abundant than oxygen. Neon is completely absent in almost all the relevant physical conditions in which a strong screening effect is operative. It is suggested that explosive burning of accreted helium of 10^–13 M will account for the observed energy of gamm-ray burst.     

Hydrodynamical models of type II supernovae

A series of hydrodynamical models of type-II supernova outbursts (SNII) has been calculated. Approximate relations connecting the total outburst energy ε, the mass of envelope ejectedM, the presupernova radiusR, and the amount of ionizing quanta radiated by the supernovaeN _H with such values as the duration of the light curve plateau Δt, and absolute magnitude in the wavelength bandV and photospheric velocityU _PH observed near the middle of the plateau have been established. Advantage has been taken of the relations to obtain a preliminary evaluation for the characteristics of the average SN II: ε=7×10⁵⁰ erg,M=6M _⊙,R=500R _⊙,N _H=2×10⁵⁸. The SNIIs with plateau-like light curves seem to be accounted for by thermonuclear explosions of degenerate cores of red giant stars and result in a total disruption of the star without any stellar remnant. To the contrary, SNIIs with linear light curves have substantially different properties (in particular, they throw considerably less massive envelopes off). These SNII must signify the birth of collapsed objects—neutron stars (pulsars) or black holes.     

Preliminary observations of solar radio sources with the Culgoora radioheliograph operating at four frequencies

The Culgoora radioheliograph has been modified for observing at 327.4 MHz, which is in addition to the three frequencies (43.25, 80, and 160 MHz) previously available. At the new frequency the array beamwidth is 56, which represents the highest resolution yet available for metre-wavelength solar mapping.At 327.4 MHz the sources of radio emission are mainly in the lowest layers of the corona. Some preliminary four-frequency observations have been made of type I storms. It is found that the source size generally decreases with increasing observing frequency. This result confirms earlier suggestions that the sources of both type I and type III emission are contained in structures whose boundaries diverge outwards in the corona.     

Silica phase transformations in the petroliferous sequences

The joint evolution of organic matter and silica in petroliferous sequences is considered in the terms of the laws of transformation of dispersion systems. The dispersion systems are transformed under conditions of low-temperature solid-phase processes accompanied by the silica phase transition and dehydration that favors the evolution of organic matter.     

The WRF model performance for the simulation of heavy precipitating events over Ahmedabad during August 2006

The summer monsoon season of the year 2006 was highlighted by an unprecedented number of monsoon lows over the central and the western parts of India, particularly giving widespread rainfall over Gujarat and Rajasthan. Ahmedabad had received 540.2mm of rainfall in the month of August 2006 against the climatological mean of 219.8mm. The two spells of very heavy rainfall of 108.4mm and 97.7mm were recorded on 8 and 12 August 2006 respectively. Due to meteorological complexities involved in replicating the rainfall occurrences over a region, the Weather Research and Forecast (WRF-ARW version) modeling system with two different cumulus schemes in a nested configuration is chosen for simulating these events. The spatial distributions of large-scale circulation and moisture fields have been simulated reasonably well in this model, though there are some spatial biases in the simulated rainfall pattern. The rainfall amount over Ahmedabad has been underestimated by both the cumulus parameterization schemes. The quantitative validation of the simulated rainfall is done by calculating the categorical skill scores like frequency bias, threat scores (TS) and equitable threat scores (ETS). In this case the KF scheme has outperformed the GD scheme for the low precipitation threshold.     

Controls on porphyroblast size along a regional metamorphic field gradient

Garnet-bearing schists from the Waterville Formation of south-central Maine provide an opportunity to examine the factors governing porphyroblast size over a range of metamorphic grade. Three-dimensional sizes and locations for all garnet porphyroblasts were determined for three samples along the metamorphic field gradient spanning lowest garnet through sillimanite grade, using high-resolution X-ray computed tomography. Comparison of crystal size distributions to previous data sets obtained by stereological methods for the same samples reveals significant differences in mode, mean, and shape of the distributions. Quantitative textural analysis shows that the garnets in each rock crystallized in a diffusion-controlled nucleation and growth regime. In contrast to the typical observation of a correlation between porphyroblast size and position along a metamorphic field gradient, porphyroblast size of the lowest-grade specimen is intermediate between the high- and middle-grade specimens’ sizes. Mean porphyroblast size does not correlate with peak temperatures from garnet-biotite Fe-Mg exchange thermometry, nor is post-crystallization annealing (Ostwald Ripening) required to produce the observed textures, as was previously proposed for these rocks. Robust pseudosection calculations fail to reproduce the observed garnet core compositions for two specimens, suggesting that these calc-pelites experienced metasomatism. For each of these two specimens, Monte Carlo calculations suggest potential pre-metasomatism bulk compositions that replicate garnet core compositions. Pseudosection analyses allow the estimation of the critical temperatures for garnet growth: ∼481, ∼477, and ∼485°C for the lowest-garnet-zone, middle-garnet-zone, and sillimanite-zone specimens, respectively. Porphyroblast size appears to be determined in this case by a combination of the heating rate during garnet crystallization, the critical temperature for the garnet-forming reaction and the kinetics of nucleation. Numerical simulations of thermally accelerated, diffusion-controlled nucleation, and growth for the three samples closely match measured crystal size distributions. These observations and simulations suggest that previous hypotheses linking the garnet size primarily to the temperature at the onset of porphyroblast nucleation can only partially explain the observed textures. Also important in determining porphyroblast size are the heating rate and the distribution of favorable nucleation sites.     

Seasonal patterns of carbon chemistry and isotopes in tufa depositing groundwaters of southwestern Japan

Annually laminated carbonates, known as tufas, commonly develop in limestone areas and typically record seasonal patterns of oxygen- and carbon-isotope compositions. δ¹⁸O values are principally controlled by seasonal changes of water temperature, whereas δ¹³C values are the result of complex reactions among the gaseous, liquid, and solid sources of carbon in the system. We examined the processes that cause the seasonal patterns of δ¹³C in groundwater systems at three tufa-depositing sites in southwestern Japan by applying model calculations to geochemical data. Underground inorganic carbon species are exchanged with gaseous CO₂, which is mainly introduced to the underground hydrological system by natural atmospheric ventilation and by diffusion of soil air. These processes control the seasonal pattern of δ¹³C, which is low in summer and high in winter. Among the three sites we investigated, we identified two extreme cases of the degree of carbon exchange between liquid and gaseous phases. For the case with high radiocarbon composition (Δ¹⁴C) and low pCO₂, there was substantial carbon exchange because of a large contribution of atmospheric CO₂ and a small water mass. For the other extreme case, which was characterized by low Δ¹⁴C and high pCO₂, the contribution of atmospheric CO₂ was small and the water mass was relatively large. Our results suggest that at two of the three sites water residence time within the soil profile was longer than 1 year. Our results also suggested a short residence time (less than 1 year) of water in the soil profile at the site with the smallest water mass, which is consistent with large seasonal amplitude of the springwater temperature variations. The Δ¹⁴C value of tufas is closely related to the hydrological conditions in which they are deposited. If the initial Δ¹⁴C value of a tufa-depositing system is stable, ¹⁴C-chronology can be used to date paleo-tufas.