Solution of the equation of transfer for coherent scattering in an exponential atmosphere by the method of discrete ordinates

A solution of the transfer equation for coherent scattering in stellar atmosphere with Planck's function as a nonlinear function of optical depth, viz., $$B_v (T) = b_0 + b_1 {\text{ }}e^{ - \beta \tau } $$ is obtained by the method of discrete ordinates originally due to Chandrasekhar.     

Exact Bianchi-type VIII and IX models in the presence of the self-creation theory of cosmology

Exact Bianchi-type VIII and IX models in the presence of Barber's second self-creation theory of cosmology are presented, when the source of the gravitational field is a perfect fluid withP=. Some physical and geometrical properties of the models are discussed.     

Frequency-spectra solutions for multiperiodic variable stars: Analysis and interpretation of artificial data

An accurate and extensive analysis on the present possibility of obtaining definite, unambiguous frequency-spectra solutions for multiperiodic -Scuti stars has been performed using artificial data. Some convenient photometric data sampling techniques have been adopted to produce very realistic light curves, with gaps and noise and subsequently critically analyzed. Useful suggestions about those to adopt in order to detect very low-amplitude components of the signal have been inferred.The results obtained point out the need of extensive devoted series of measurements, spread over a very long time span and also over a wide baseline of observers.     

Dynamical conditions in planets and stars

With the available data in planets, stars and galaxies, it is studied the functions of angular momentaJ(M) and amounts of actionA _c(M) (associated to the non rotational terms in the kinetic energy). The results indicate that independently of how are these functionsJ(M),A _c(M) their ratioA _c/J remains a near invariant. It is independent also from the type of angular momenta: intrinsic spins of the bodies or the total angular (orbital) momenta of the bodies forming a system; for instance, the Solar System and the planets.The relationA _c(M) for the Solar System are analogous to these in the FGK stars of the main sequence, and the relationJ(M) (also for the Solar System) is analogous to the lower possible limit for binary stars.The different types of binary stars from the short period, detached systems to contactary systems, gives a range of functionsJ(M),A _c(M) that are the same that one can expect in stars with planetary systems. According to the detection limits given for planetary companions by Campbell, Walker and Yang (1988) (masses of less than 9 Jupiter masses and orbital periods of less than 50 years) we calculate the limits forJ(M) andA _c(M) This gives a lower limitA _c/J 1 associated to stars with planetary systems as 61 Cygni and to short period detached binaries. The upper limitA _c/J 16 correspond to planetary systems as the ours and probably to cataclysmic binaries. There are reasons to suspect that systems as the ours and in range 4 A _c/J 16 (with a lower limit analogous to contactary binaries as Algols and W Ursa Majoris) must be the most common type of planetary systems. The analogies with the functionsJ(M)A _c(M) for galaxies suggest cosmogonical conditions in the stellar formation.Independently of this, one can have boundary conditions for the Jacobi problem when applied to a collapsing cloud. Namely, from the initial stage (a molecular cloud) to the final stage (a formed stellar system: binary or planetary) the angular momenta and amounts of action decayed to 10^~4 the initial values, but in such a form thatA _c(t)/J(t) remains a near invariant.     

Magnetoacoustic-gravity surface waves

The linearized theory for the parallel propagation of magnetoacoustic-gravity surface waves is developed for an interface of a horizontal magnetic field above a field-free medium. The media either side of the interface are taken to be isothermal. The dispersion relation is obtained for the case of a constant Alfvén speed. In the absence of gravity the interface may support one or two surface modes, determined by the relative temperatures and magnetism of the two media. The effect of gravity on the modes is examined and dispersion diagrams and eigenfunctions are given. In the usual - k _x diagnostic diagram, the domain of evanescence is shown to be divided into two distinct regions determining whether a given mode will have a decaying or growing vertical velocity component. In the absence of a magnetic field the transcendental dispersion relation may be rewritten as a polynomial. This polynomial possesses two acceptable solutions only one of which may exist in any given circumstances (depending on the ratio of the densities). If the gas density within the field exceeds that in the field-free medium, then the f-mode may propagate. The f-mode exists in a restricted band of horizontal wavenumber and only when the field-free medium is warmer than the magnetic atmosphere. An analytical form for the wave speed of the f-mode is obtained for small values of the Alfvén speed. It is shown that the f-mode is related to the fast magnetoacoustic surface wave, merging into that mode at short wavelengths.     

The thermal continuum in coronal loops: The influence of finite resistivity on the continuous spectrum

The normal mode spectrum for the linearized MHD equations is investigated for a cylindrical equilibrium. This spectrum is examined for zero perpendicular thermal conduction, with both zero and non-zero scalar resistivity. Particular attention is paid to the continuous branches of this spectrum, or continuous spectra. For zero resistivity there are three types of continuous spectra present, namely the Alfvén, slow, and thermal continua. It is shown that when dissipation due to resistivity is included, the slow and Alfvén continua are removed and that the thermal continuum is shifted to a different position (where the shift is independent of the exact value of resistivity). The old location of the thermal continuum is covered by a dense set of nearly singular discrete modes called a quasi-continuum. The quasi-continuum is investigated numerically, and the eigenfunctions are shown to have rapid spatial oscillating behaviour. These oscillations are confined to the most unstable part of the equilibrium based on the Field criterion, and may be the cause of fine structure in prominences.     

Hall effects on heat and mass transfer flow with variable suction and heat generation

A study of the combined buoyancy effects of thermal and mass diffusion on MHD convection flow in the presence of Hall currents with variable suction and heat generation has been carried out. Analytical expressions for the velocity and the temperature of the fluid are given. The effects of Hall currents, parameterm, and heat source parameter on the velocity are discussed.     

Unusually low coronal radio emission at the solar minimum

We present two-dimensional observations of the quiet Sun at 73.8, 50.0, and 38.5 MHz obtained with the Clark Lake Radioheliograph during the sunspot minimum period of September 1986. The observed peak brightness temperatures during the entire period of sunspot minimum are found to be extremely low, lying in the range (0.6 × 10⁵ K – 2.5 × 10⁵ K). It is shown that these low values cannot be explained by the generally adopted models for N _e and T _e in a homogeneous corona. The effect of scattering by random density fluctuations is introduced in order to decrease the values of predicted T _b . The value of peak T _b is computed as a function of relative r.m.s. density fluctuations = <N _e >/N _e ; and it is found that should be in the range from 0.07 to 0.19, 0.1 to 0.25, and 0.15 to 0.35, respectively, at 38.5, 50.0, and 73.8 MHz, respectively, to explain the observed low brightness temperatures.On leave from Indian Institute of Astrophysics, Bangalore, India.     

Urban settlement size trends in the former USSR: 1970-1989

"Based upon recently published data, this paper investigates urban settlement size trends in the former USSR and its republics during the intercensal periods of 1970-1979 and 1979-1989. Results indicate that although a trend toward largeness of the Soviet urban hierarchy continues, a slowing in this direction has occurred. Among republics, all had an increasing trend towards largeness on at least one and usually all three summary measures of urban settlement size structure. The RSFSR [Russia] and Armenia especially consistently evidenced a relatively high degree of largeness, while the former Baltic republics generally revealed a relative smallness."     

Applications of AnnAGNPS model for soil loss estimation and nutrient loading for Malaysian conditions

The study evaluated the performance and suitability of AnnAGNPS model in assessing runoff, sediment loading and nutrient loading under Malaysian conditions. The watershed of River Kuala Tasik in Malaysia, a combination of two sub-watersheds, was selected as the area of study. The data for the year 2004 was used to calibrate the model and the data for the year 2005 was used for validation purposes. Several input parameters were computed using methods suggested by other researchers and studies carried out in Malaysia. The study shows that runoff was predicted well with an overall R² value of 0.90 and E value of 0.70. Sediment loading was able to produce a moderate result of R² = 0.66 and E = 0.49, nitrogen loading predictions were slightly better with R² = 0.68 and E = 0.53, and phosphorus loading performance was slightly poor with an R² = 0.63 and E = 0.33. The erosion map developed was in agreement with the erosion risk map produced by the Department of Agriculture, Malaysia. Rubber estates and urban areas were found to be the main contributors to soil erosion. The simulation results showed that AnnAGNPS has the potential to be used as a valuable tool for planning and management of watersheds under Malaysian conditions.