共查询到20条相似文献,搜索用时 0 毫秒
1.
《Waves in Random and Complex Media》2013,23(3):189-196
Abstract The Pomraning-Eddington approximation is used to solve the radiative transfer problem for anisotropic scattering in a spherical homogeneous turbid medium with diffuse and specular reflecting boundaries. This approximation replaces the radiative transfer integro-differential equation by a second-order differential equation which has an analytical solution in terms of the modified Bessel function. Here, we calculate the partial heat flux at the boundary of anisotropic scattering on a homogeneous solid sphere. The calculations are carried out for spherical media of radii 0.1, 1.0 and 10 mfp and for scattering albedos between 0.1 and 1.0. In addition, the calculations are given for media with transparent, diffuse reflecting and diffuse and specular reflecting boundaries. Two different weight functions are used to verify the boundary conditions. Our results are compared with those given by the Galerkin technique and show greater accuracy for thick and highly scattering media. 相似文献
2.
The Pomraning-Eddington approximation is used to solve the radiative transfer problem for anisotropic scattering in a spherical homogeneous turbid medium with diffuse and specular reflecting boundaries. This approximation replaces the radiative transfer integro-differential equation by a second-order differential equation which has an analytical solution in terms of the modified Bessel function. Here, we calculate the partial heat flux at the boundary of anisotropic scattering on a homogeneous solid sphere. The calculations are carried out for spherical media of radii 0.1, 1.0 and 10 mfp and for scattering albedos between 0.1 and 1.0. In addition, the calculations are given for media with transparent, diffuse reflecting and diffuse and specular reflecting boundaries. Two different weight functions are used to verify the boundary conditions. Our results are compared with those given by the Galerkin technique and show greater accuracy for thick and highly scattering media. 相似文献
3.
Vladimir P. Budak Sergey V. Korkin 《Journal of Quantitative Spectroscopy & Radiative Transfer》2008,109(2):220-234
The authors developed a numerical method of the boundary-value problem solution in the vectorial radiative transfer theory applicable to the turbid media with an arbitrary three-dimensional geometry. The method is based on the solution representation as the sum of an anisotropic part that contains all the singularities of the exact solution and a smooth regular part. The regular part of the solution could be found numerically by the finite element method that enables to extend the approach to the arbitrary medium geometry. The anisotropic part of the solution is determined analytically by the special form of the small-angle approximation. The method development is performed by the examples of the boundary-value problems for the plane unidirectional and point isotropic sources in a turbid medium slab. 相似文献
4.
Awatif A. Hendi 《Journal of Quantitative Spectroscopy & Radiative Transfer》2002,75(5):647-659
The heat transfer through a spherical media with conduction and radiation is considered. The medium is considered to be turbid and anisotropically scattering with diffusely reflecting boundaries of constant temperatures. The radiative transfer problem is solved using the Galerkin method. An iterative method is used to solve the nonlinear relation between the radiative transfer equation and the conductive energy equation. Calculations are carried out and compared for a homogeneous, isotropically scattering medium with isothermal, transparent boundaries. The results show good agreement with previous work. Calculations are carried out for inhomogeneous media with isotropic, and forward and backward anisotropic scattering. The boundaries of the media are considered to be isothermal and may be transparent or diffusely reflecting boundaries. The calculations are used to study the effects of the single scattering albedo, the anisotropic scattering parameter, the conduction-radiation parameter and the heat source. 相似文献
5.
A.L. Crosbie 《Journal of Quantitative Spectroscopy & Radiative Transfer》1975,15(2):197-200
Numerical results are presented for the dimensionless emissive power at the boundary of a nongray semi-infinite medium in radiative equilibrium. The adsorption coefficient of an array of equal intensity, nonoverlapping bands or lines. Specifically, the rectangular, triangular, exponential, Doppler and Lorentz profiles are considered. 相似文献
6.
A.L. Crosbie J.W. Koewing 《Journal of Quantitative Spectroscopy & Radiative Transfer》1979,21(6):573-595
The source function, radiative flux, and intensity at the boundaries are calculated for a two-dimensional, scattering, finite medium subjected to collimated radiation. The scattering phase function is composed of a spike in the forward direction super-imposed on an isotropic background. Exact radiative transfer theory is used to formulate the problem and Ambarzumian's method is used to obtain results. Using the principle of superposition, the results for any step variation in incident radiation are expressed in terms of universal functions for the semi-infinite step case. Two-dimensional effects are most pronounced at large optical thicknesses and albedos. 相似文献
7.
D. V. Kuznetsov Vl. K. Roerich M. G. Gladush 《Journal of Experimental and Theoretical Physics》2011,113(4):647-658
The effect of macroscopic parameters of a substance on the optical characteristics of impurity particles is investigated. A generalized control equation is derived for two-level emitters forming an ensemble of optical centers in a transparent dielectric medium. In this equation, the effective values of the acting pump field and the radiative relaxation rate of an optical center are taken into account. The formalism developed here is a completely microscopic approach based on the chain of the Bogoliubov-Born-Green-Kirkwood-Yvon equations for reduced density matrices and correlation operators for material particles and modes of a quantized radiation field. The method used here makes it possible to take into account the effects of individual and collective behavior of emitters, which are associated with the presence of an intermediate medium, consistently without using phenomenological procedures. It is shown that the resultant analytic expression for the effective lifetime of the excited state of an optical center conforms with experimental data. 相似文献
8.
The current state of the theory of massive neutrino radiative decay is reviewed. By extending our previous studies, we thoroughly analyze the process of radiative decay of a massive Dirac neutrino in the strong external magnetic field H ? H 0 = m e 2 c 3 / e? = 4.41 × 1013 G in the presence of medium (degenerate electron gas), and calculate its probability. It is shown that, in the presence of dense medium, the latter quantity becomes much larger than that in the magnetic field in the case of both relativistic and nonrelativistic neutrinos. Possible astrophysical applications of the obtained results are considered. 相似文献
9.
In this paper we apply a numerical method on the equation of radiative transfer in a turbid atmosphere. The solution is obtained by means of direct integration of the equation of radiative transfer without any circuitous series development. 相似文献
10.
Mohsen Razzaghi Seth OppenheimerFalih Ahmad 《Journal of Quantitative Spectroscopy & Radiative Transfer》2002,72(4):439-447
An approximate method for solving the radiative transfer equation in a slab medium with an isotropic scattering is proposed. The method is based upon constructing the double Legendre series to approximate the required solution using Legendre tau method. The differential and integral expressions which arise in the radiative transfer equation are converted into a system of linear algebraic equations which can be solved for the unknown coefficients. Numerical examples are included to demonstrate the validity and applicability of the method and a comparison is made with existing results. 相似文献
11.
N. Ananda Krishna 《Journal of Quantitative Spectroscopy & Radiative Transfer》2006,102(3):432-440
Application of the discrete transfer method (DTM) has been extended to the analysis of radiative heat transfer in a variable refractive index participating medium. To validate the DTM formulation, radiative heat transfer in an absorbing, emitting and isotropically scattering planar medium was considered. The participating medium was assumed to be in radiative equilibrium. For both constant and variable refractive indices of the medium, the DTM results were compared with those available in the literature. The DTM was found to provide accurate results. 相似文献
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13.
M.P. Mengüç R. Viskanta 《Journal of Quantitative Spectroscopy & Radiative Transfer》1983,29(5):381-394
We examine critically the accuracy of the two-flux, spherical harmonics and discrete ordinates methods for predicting radiative transfer in a planar, highly-forward scattering and absorbing medium. Numerical results for the radiative fluxes show that the two-flux and P3-approximations yield accurate results compared to solutions based on the FN-method. Indeed, these approximate methods are relatively simple and have potential for generalization to predict radiative transfer in multidimensional systems, as long as an appropriate simplification of the phase function is utilized. 相似文献
14.
R.D.M. Garcia 《Journal of Quantitative Spectroscopy & Radiative Transfer》2012,113(4):306-317
In many applications of the theory of radiative transfer, it is important to consider the changes in the index of refraction that occur when the physical domain being studied consists of material regions with distinct optical properties. When polarization effects are taken into account, the radiation field is described by a vector of four components known as the Stokes vector. At an interface between two different material regions, the reflected and transmitted Stokes vectors are related to the incident Stokes vector by means of reflection and transmission matrices, which are derived from the Fresnel formulas for the amplitude coefficients of reflection and transmission. Having seen that many works on polarized radiative transfer that allow for changes in the index of refraction exhibit discrepancies in their expressions for the transmission matrix, we present in this work a careful derivation of the relations between the reflected and transmitted Stokes vectors and the Stokes vector incident on an interface. We obtain a general form of a transmission factor that is required to ensure conservation of energy and we show that most of the discrepancies encountered in existing works are associated with the use of improper forms of this factor. In addition, we derive explicit and compact expressions for the Fresnel boundary and interface conditions appropriate to the study of polarized radiative transfer in a multilayer medium. 相似文献
15.
A.R. DegheidyM.T. Attia M. Sallah 《Journal of Quantitative Spectroscopy & Radiative Transfer》2002,74(3):285-297
The time-independent radiative transfer problem in a scattering and absorbing planar random medium with general boundary conditions and internal energy source is considered. The medium is assumed to consist of two randomly mixed immiscible fluids, with the mixing statistics described as a two-state homogeneous Markov process. The problem is solved in terms of the solution of the corresponding free-source problem with simple boundary conditions which is solved using Pomraning-Eddington approximation in the deterministic case. A formalism, developed to treat radiative transfer in statistical mixtures, is used to obtain the ensemble-averaged solution. The average partial heat fluxes are calculated in terms of the albedoes of the source-free problem. Results are obtained for isotropic and anisotropic scattering for specular and diffused reflecting boundaries. 相似文献
16.
Robert Spurr Johan de Haan Alexander Vasilkov 《Journal of Quantitative Spectroscopy & Radiative Transfer》2008,109(3):404-425
Rotational Raman scattering (RRS) by air molecules in the Earth's atmosphere is predominantly responsible for the Ring effect: Fraunhofer and absorption-feature filling-in observed in UV/visible backscatter spectra. Accurate determination of RRS effects requires detailed radiative transfer (RT) treatment. In this paper, we demonstrate that the discrete-ordinate RT equations may be solved analytically in a multi-layer multiple scattering atmosphere in the presence of RRS treated as a first-order perturbation. Based on this solution, we develop a generic pseudo-spherical RT model LIDORT-RRS for the determination of backscatter radiances with RRS included; the model will generate output at arbitrary viewing geometry and optical thickness. Model comparisons with measured RRS filling-in effects from OMI observations show very good agreement. We examine telluric RRS filling-in effects for satellite-view backscatter radiances in a spectral range covering the ozone Huggins absorption bands. The model is also used to investigate calcium H and K Fraunhofer filling-in through cloud layers in the atmosphere. 相似文献
17.
Sebastian Otto Thomas Trautmann 《Journal of Quantitative Spectroscopy & Radiative Transfer》2008,109(17-18):2813-2819
This work reports on the use of leaf normal distribution functions (LNDFs) in the radiative transfer theory of turbid vegetation media to calculate the so-called G-function (GF). We revisit the normalisation condition of the LNDFs and present an extended set of fully explicit analytical expressions for GF considering commonly used standard LNDFs from purely vertical to purely horizontal model leaves. Applying them we derive GF for a generalised LNDF, which is written as a series of cosine functions with a number of free parameters. This generalisation opens up the possibility to fit leaf orientation measurements to our generalised LNDF and to determine the respective analytical GF. Thus, an extended range of leaf architectures, beyond the usual and less realistic standard LNDFs, can be considered with respect to applications of the radiative transfer theory in turbid vegetation media. 相似文献
18.
《Waves in Random and Complex Media》2013,23(3):371-385
The formulation and solution of the vector radiative transfer equation in a finite slab of a stochastic precipitation medium of binary rain rates are considered. The electromagnetic wave is supposed to encounter alternating layered segments of the two precipitation media, each with a deterministic rain rate. Both the backscattering coefficient and the bistatic coefficient are derived by taking an ensemble average of the iterative solution for the deterministic vector radiative transfer equation. Computer simulations are given to verify the solutions via the Monte Carlo method, to feature the distinctiveness of stochastic precipitation systems, and to illustrate the relationship between the stochastic parameters and the final results. It is also concluded from the computer simulations that a finite slab of a stochastic precipitation medium could be treated as an average rain-rate precipitation layer with an acceptable approximation. 相似文献
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20.
A.L. Crosbie R.L. Dougherty H.V. Kothari 《Journal of Quantitative Spectroscopy & Radiative Transfer》1977,18(1):69-91
An exact formulation is presented for a nongray two-dimensional, finite, planar, absorbing-emitting medium in radiative equilibrium. The absorption coefficient consists of an array of equal intensity, nonoverlapping bands or lines. Rectangular, triangular, exponential, Doppler and Lorentz shapes are specifically considered. Exact expressions are obtained for a medium subjected to collimated and diffuse radiation. The integral equations are linearized by the narrow-band approximation. The solution for the cosine-varying, collimated, monochromatic radiation model is used to construct the solutions for other boundary conditions. The two-dimensional equations are reduced to one-dimensional equations by the method of separation of variables. Results for the diffuse case are presented for several spatial variations. 相似文献