共查询到20条相似文献，搜索用时 46 毫秒
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Combined-Operations method has been utilised to solve the problem of diffuse reflection by a homogeneous, isotropic, non-coherent scattering spherical medium. The source function is considered to be frequency independent. The auxiliary equation has been formulated, the scattering function defined, and the integro-differential equation for this function deduced. A method for obtaining the emergent intensity and the internal source function for non-zero internal source distribution has been suggested for a given line profile. 相似文献
3.
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. 相似文献
4.
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. 相似文献
5.
A complete set of transfer equations required for the order-of-scattering analysis of partially polarized radiation in inhomogeneous, anisotropically scattering atmospheres is provided. The equations have been derived for both a local study using the radiative transfer equation and its associated auxiliary equation for the source-matrix, and a global study in terms of the scattering and transmission matrices; they account for the polarity of the scattering medium. Their derivations for the finite order scattering and the finitely cumulative scattering, in particular, have yielded important new equations expressing the invariance principles and the integro-differential recurrences for the scattering and transmission matrices. These novel expressions contain as a special case Bellmanet al's (1972) equations for the simpler case of isotropic scattering of unpolarized light in homogeneous atmospheres. 相似文献
6.
To improve the accuracy of calculations for the reflection and transmission functions, doubling techniques are in use. The central theme of this method is to derive the total reflection function when two portions of a medium are adjoined together. The synthesis is done by the use of star product techniques which require a knowledge of theS andT functions of both parts of the medium. Infinite series expansion is necessary to compute the total reflection. The method developed in this article splits the total reflected beam into two parts, one relating to that flux which suffers no scattering at all in the first portion of the medium and the second portion that undergoes at least one scattering in the first portion. The first part can be evaluated simply by knowing the reflection function of the second portion of the medium. The other part of the total reflection for variations of the thickness of the first portion of the medium is found to obey a simple Riccati type integro-differential equation with zero initial conditions. Knowledge of theT functions is not necessary and integration has to be performed over the interval corresponding to thickness of the first portion of the medium. Order-of-scattering analysis is also carried out. 相似文献
7.
Rabindra Nath Das 《Astrophysics and Space Science》1979,62(1):143-147
By performing the one-sided Laplace transform on the matrix integro-differential equation for a semi-infinite plane parallel imperfect Rayleigh scattering atmosphere we derive an integral equation for the emergent intensity matrix. Application of the Wiener-Hopf technique to this integral equation will give the emergent intensity matrix in terms of singularH-matrix and an unknown matrix. The unknown matrix has been determined considering the boundary condition at infinity to be identical with the asymptotic solution for the intensity matrix. 相似文献
8.
Rabindra Nath Das 《Astrophysics and Space Science》1978,57(2):419-427
By performing the one-sided Laplace transform on the scalar integro-differential equation for a semi-infinite plane-parallel isotropic scattering atmosphere with a scattering albedo 0 1, an integral equation for the emergent intensity has been derived. Application of the Wiener-Hopf technique to this integral equation will give the emergent intensity. The intensity at any optical depth for a positive scattering angle is also derived by inversion. The intensity at any optical depth for a negative scattering angle is also derived in terms of Cauchy's principal value using Plemelj's formulae. 相似文献
9.
The exact analytic expression for the density of energetic charged particles, which were injected by an instantaneous point
source at a particular pitch angle into the interplanetary medium, has been derived. We start from the Boltzmann kinetic equation
with the collision integral describing the isotropic particle scattering by "massive" magnetic clouds. The solution has been
obtained without any expansion parameters in the 3-dimensional vector form, then it was projected into the cylindrical coordinate
system. The space-time particle distribution is disscussed.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
10.
Rabindra Nath Das 《Astrophysics and Space Science》1980,71(1):25-35
A finite atmosphere having distribution of intensity at both surfaces with definite form of scattering function and source function is considered here. The basic integro-differential equation for the intensity distribution at any optical depth is subjected to the finite Laplace transform to have linear integral equations for the surface quantities under interest. These linear integral equations are transformed into linear singular integral equations by use of the Plemelj's formulae. The solution of these linear singular integral equations are obtained in terms of theX-Y equations of Chandrasekhar by use of the theory of linear singular operators which is applied in Das (1978a). 相似文献
11.
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. 相似文献
12.
A. Peraiah 《Journal of Astrophysics and Astronomy》1990,11(2):193-208
We have solved the equation of radiative transfer with Compton scattering. The specific intensity has been expanded by Taylor series with respect to wavelength and the first three terms have been retained in solving the transfer equation. It is noted that in a medium stratified in plane parallel layers, the multiple Compton scattering redistributes the initial energy over a range of 3 to 5 Compton wavelengths. A good fraction of the incident radiation is transferred across the layer with redistribution in wavelength, the actual value depending on the optical thickness of the medium 相似文献
13.
We have solved the equation of radiative transfer in spherical symmetry with scattering and absorbing medium. We have set the albedo for single scattering to be equal to 0.5. We have set the Planck function constant throughout the medium in one case and in another case the Planck function has been set to vary asr
–2. The geometrical extension of the spherical shell has been taken as large as one stellar radius. Two kinds of variations of the optical depth are employed (1) that remains constant with radius and (2) that varies asr
–2. In all these cases the internal source vectors and specific intensities change depending upon the type of physics we have employed in each case. 相似文献
14.
Propagation of two dimensional cylindrical fast magnetoacoustic solitary waves in a warm dust plasma
A set of multi-fluid equations and Maxwell’s equations are carried out to investigate the properties of nonlinear fast magnetoacoustic solitary waves with the combined effects of dusty plasma pressure and transverse perturbation in the bounded cylindrical geometry. The reductive perturbation method has been applied to the dynamical system causeway and the derived two dimensional cylindrical Kadomtsev–Petviashvili equation (CKP) predicts different natures of solitons in complex plasma. Under a suitable coordinate transformation the CKP equation can be solved analytically. The change in the soliton structure due to mass of dust, ion temperature, ion density, and dust temperature is studied by numerical calculation of the CKP equation. It is noted that the dust cylindrical fast magnetoacoustic solitary waves in warm plasmas may disappear slowly because of an increase in dust mass. The present analysis could be helpful for understanding the nonlinear ion-acoustic solitary waves propagating in interstellar medium and pulsar wind,which contain an excess of superthermal particles. 相似文献
15.
The non-linear heating of electrons in the ionospheric plasma due to high-power radio wave propagation has been investigated through an integro-differential equation derived from Boltzmann velocity-moment equations. Various processes appropriate to the situation under study are taken into account. The numerical solution of the derived equation is presented graphically.Department of Applied Mathematics, University of Calcutta, India. 相似文献
16.
Equations connecting the transmission and reflection functions of a finite medium to the reflection function of a semi-infinite one are used to get the albedos in the slowing-down region. The transport equation is solved by the modified Eddington method using Fermi's backward-forward scattering model, modulated to allow for different orders of backward-forward and isotropic scattering. Numerical results for the energy albedos are obtained and compared.On leave of absence from Atomic Energy Center, Inchass, Egypt. 相似文献
17.
N.A. Tsyganenko 《Planetary and Space Science》1982,30(5):433-437
An investigation of pitch-angle scattering of energetic particles in magnetic field configurations with a current sheet similar to that observed in the geomagnetotail has been performed. The magnetic field model is specified by two parameters which are the current sheet thickness in units of particle gyroradius and the angle between the magnetic field lines and the sheet plane. Computations of a considerable number of trajectories (about 20,000 for each model case) has provided the possibility of obtaining the matrix of pitch-angle scattering and the corresponding kernel function of the integral equation for the stationary particle distribution function. Solution of this equation shows that isotropic distributions are formed only in the case of a sufficiently thick current sheet. Particle scattering in a thin field reversal region leads to the formation of an anisotropic stationary distribution. The results can be used for interpretation of the data on the spatial distribution of energetic particle fluxes in the near part of the magnetospheric tail and in the vicinity of the outer boundary of the radiation belt. 相似文献
18.
In the present paper, with the aid of invariance principles in connection with the scattering matrix, we get the exact solution of diffuse reflection and transmission problems by finite inhomogeneous, anisotropically scattering atmospheres bounded by reflecting sufaces. On making use of the reflection and transmission integral operators, we show how to obtain the non-linear integro-differential equations for these operators, which do not depend on the initial condition. Then, we have a system of the required integro-differential equations for the scattering and transmission functions. The obtained result is new, so far as we know. Finally, using the scattering matrix, we reduce the diffuse reflection and transmission problems for planetary atmospheres with reflecting surfaces to the standard diffuse reflection and transmission problems.Supported by the National Science Foundation under Grant No. GP29049 and the Atomic Energy Comminission, Division of Research under Contract No. AT(40-3)-133, Project 19. 相似文献
19.
The physics of scattering of electromagnetic waves by media in which the particles are in contact, such as planetary regoliths, has been thought to be relatively well understood when the particles are larger than the wavelength. However, this is not true when the particles are comparable with or smaller than the wavelength. We have measured the scattering parameters of planetary regolith analogs consisting of suites of well-sorted abrasives whose particles ranged from larger to smaller than the wavelength. We measured the variation of reflectance as the phase angle varied from 0.05° to 140°. The following parameters of the media were then deduced: the single scattering albedo, single scattering phase function, transport mean free path, and scattering, absorption, and extinction coefficients. A scattering model based on the equation of radiative transfer was empirically able to describe quantitatively the variation of intensity with angle for each sample. Thus, such models can be used to characterize scattering from regoliths even when the particles are smaller than the wavelength. The scattering parameters were remarkably insensitive to particle size. These results are contrary to theoretical predictions, but are consistent with earlier measurements of alumina abrasives that were restricted to small phase angles. They imply that a basic assumption made by virtually all regolith scattering models, that the regolith particles are the fundamental scattering units of the medium, is incorrect. Our understanding of scattering by regoliths appears to be incomplete, even when the particles are larger than the wavelength. 相似文献
20.
M. S. Abdel Krim 《Astrophysics and Space Science》1990,164(1):69-77
Radiative transfer equation in a plane-parallel medium with isotropic boundary conditions for linearly anisotropic scattering phase function is considered. Two coupled integral equations for total density of radiation and total radiation flux are obtained. The Galerkin method is used to solve these equations. Numerical results for the radiative fluxes at the boundaries show that the Galerkin method yields accurate results compared well with other exact methods. 相似文献