On the numerical evaluation of theH-functions of transfer problems in multiplying media

Extensive tables of the values ofH-functionsH ⁰(z, ) andH ₁ ⁰ (z, ) appropriate for the problems of radiative transfer in multiplying media characterized by >1, have been constructed correctly to the sixth decimal place for values of in the range 1.05–10. This accuracy has been attained with the aid of a 32-point Gaussian quadrature.     

The numerical evaluation of theH-functions of radiative transfer in active amplifying media

The present paper contains extensive tables of the values of theH-functionH(z,<0) and of the moments ofQ(x) (in terms of which the moments ofH(z, ) can be determined) appropriate for transfer of radiation in active amplifying media in which<0. These values have been computed correct to the 7th decimal place for values of in the range (–10^–12)-(–10³⁰) and for values of z[0,1] with the aid of a 48-point gaussian quadrature formula.     

A new representation of theH-functions of radiative transfer

The energetics involved in the formation of neutron stars in close binaries as a result of supernova explosions are considered. The gravitational binding energy of the neutron star must find proper outlets. The mass ejection and cosmic ray particles can carry away only a small fraction (up to a few per cent) of this energy. Most of the binding energy goes into rotational kinetic energy, gravitational radiation and neutrino emissions. A scenario is considered in which most of the gravitational binding energy goes into rotational kinetic energy and is, ultimately, radiated away as gravitational waves.     

Exact solution of transport equation in finite multiplying media

One speed neutron transport equation in a finite multiplying medium is exactly and uniquely solved following the first author's new technique (Das Gupta, 1978b) based on Laplace transformation and Wiener-Hopf technique, to obtain the angular neutron density at any depth. Criticality condition is derived.     

Non-coherent scattering in transfer problems in spherical shell media

The Combined Operations Method is utilised to solve Diffuse Reflection and Transmission Problems in inhomogeneous, isotropically and non-coherently scattering, spherical shell media. The source function is assumed to be frequency independent. TheN-solution of an auxiliary equation is sought, and tractable equations for the scattering and transmission functions are established. The solution of the problem for a scattering and emitting medium have been considered for a perfectly absorbing core.     

A note on modified spherical-harmonic method for radiative transfer problems with reflective boundary conditions

The modified double-interval spherical-harmonic method is used to compute the radiative flux in a linearly anisotropically scattering plane-parallel medium with specularly and diffusely reflecting boundaries.     

Application of the escape-probability method to transfer problems in stochastic media

Byurakan Astrophysical Observatory. Translated from Astrofizika, Vol. 31, No. 1, pp. 162–176, July–August, 1989.     

Generalised eddington approximation for radiative transfer problems in spherically-symmetric moving media

A moment method with three stream division of the radiation field was suggested by Wilson, Wan and Sen (1980) for solving radiative transfer problems in stationary, non-grey extended shells surrounding a central star. Use was made of the generalised Eddington relations as the closure conditions of the moment equations. In the present paper the same method has been utilised to study the radiative transfer problems in a non-grey, expanding gaseous spherical shells surrounding a central star. The transfer equation has been set in comoving frame in spherical geometry. The radiation and material quantities, angles and frequencies have been expressed in comoving frame. The mean intensity, flux and K-integrals have been calculated for extensive atmospheres in the presence of different velocity fields.     

On combined operations method for transfer problems in homogeneous,cylindrical media

The problem of diffuse reflection by a homogeneous, isotropically scattering, infinite cylindrical medium has been considered. The relevant auxiliary equation has been formulated, the scattering function defined and the integro-differential equation for such function deduced. For a medium having cylindrical distribution of source in addition to the incident flux at the outer surface, the integro-differential equation for the emergent intensity has been established.     

A note on independent variables for restricted three-body problems

In studies of the elliptic restricted three-body problem, the true anomaly of the motion of the primaries is often used as the independent variable. The equations of motion then show invariancy in form from the circular case. It is of interest whether other independent variables exist, such that the invariant form of the equations is maintained. It is found that true anomaly is the only such variable.     

On combined operational method for transfer problems in homogeneous,spherical media

In this paper, the Combined Operational Method developed by Busbridge (1961) in connection with the radiative transfer problems in plane-parallel atmospheres has been extended to similar problems in isotropic scattering, homogeneous spherical media. The relevant auxiliary equation has been formulated, the scattering function defined and the integro-differential equation for such function deduced. For a medium having radial distribution of source in addition to the incident flux at the outer surface, the integro-differential equations for source function and emergent intensity have been established.     

Unified structure of analytical solutions for radiative transfer problems in plane-parallel,homogeneous media

The basic concepts for developing a system of analytic solutions for the standard problems of radiative transfer theory are discussed. These solutions, which are found using Ambartsumyan’s layer addition method in Sobolev’s probabilistic interpretation for radiative diffusion problems, are maximally compact and easily used in numerical computations. New expressions are obtained for the resolvents and the resolvent functions, as well as a unified structure for the form of an integral representation for solving different radiative transfer problems in semi-infinite media and in finite layers. Block diagrams of the sequence of stages for solving these problems are provided, where the Ambartsumyan function φ(η) (more precisely, 1/φ(η)) plays a fundamental role in the case of semi-infinite media while the functions a(η, τ₀ ) and b(η, τ₀) play an analogous role for finite layers.     

Probabilistic model for radiative transfer problems in cylindrical shell media with complete redistribution in frequency

A probabilistic model for solving transfer problems in non-homogeneous, isotropic, and non-coherent scattering cylindrical shell media has been proposed. The source function is considered to be frequency independent. The scattering and transmission functions have been defined for the case of complete redistribution in frequency. A tractable integrodifferential equation for the scattering function has been derived.     

Radiation transfer in stochastic media

The present paper deals with certain problems of the radiation transfer in one-dimensional and three-dimensional infinite media with the assumption that the quantum survival probability is a homogeneous isotropic gaussian arbitrary field. The Dyson equation relative to the first moment of the source function is obtained, and the condition of its soluvability is studied. In the known Bourret approximation, the average number of the quantum scatterings and radiation intensities are calculated.     

A note on the energy transfer from the solar wind to the magnetosphere

The dimensional analysis of the energy transfer from the solar wind to the magnetosphere is formulated to include the effect of finite lifetime of the ring current particles. It is found that the solar wind energy input rate should be re-evaluated by considering the lifetime of the ring current particles.     

Anisotropic radiation transfer in dispersive media

Equations for radiation, scattered anisotropically from dispersive media are obtained for general boundary conditions. The Padé approximant technique is used to calculate the reflection coefficients for these media. Numerical results are given for diffuse reflected boundary condition.