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An Efficient Solution Technique for the Radiative Transfer Equation
IMPACT of Computing in Science and Engineering, 1993The discretization of the multidimensional radiative transfer equation results in a very large linear system of equations. The standard solution method used by astrophysicists is a simplified fixed point iteration (called approximate \(\Lambda\)-iteration) which becomes slow for the problems most interesting in astrophysics.
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The equation of radiative transfer with scattering
Journal of Quantitative Spectroscopy and Radiative Transfer, 1968Abstract The photon equation of transfer for an arbitrary scattering process and including the effects of induced scattering is examined in full geometric generality in the polarization-independent approximation. Several approximations are introduced which retain the essential physics of the situation but considerably simplify the mathematics.
G.C. Pomraning, B.E. Freeman
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Half-Moment Closure for Radiative Transfer Equations
Journal of Computational Physics, 2002zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Dubroca, B., Klar, A.
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Coupled radiative transfer equation and diffusion approximation
SPIE Proceedings, 2005A coupled radiative transfer equation and diffusion approximation model for photon migration in tissues is proposed. The light propagation is modeled with the radiative transfer equation in sub-domains in which the assumptions of the diffusion approximation are not valid and the diffusion approximation is used elsewhere in the domain.
Tanja Tarvainen +3 more
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The tensor radiative transfer equation
Journal of Physics A: Mathematical and General, 2000Summary: The vector radiative transfer equation is used for the solution of numerous problems in the field of random media optics. It describes the transformation of the Stokes vector of a light beam due to its propagation and scattering in a medium. However, the Stokes vector depends on the choice of a coordinate system. Thus, one needs to account for
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Approximate Scalar Equations for Polarized Radiative Transfer
Advances in Optical Imaging and Photon Migration, 1998An asymptotic analysis of the radiative transfer equation with polarization is developed that leads to a renormalized scalar equation for the total specific intensity of radiation I, the first Stokes parameter, in three-dimensional geometries. The resulting scalar equation can be used without the complexity of performing vector radiative computations ...
G. C. Pomraning, N. J. McCormick
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Derivation of the Radiative Transfer Equation
AIP Conference Proceedings, 2007The radiative transfer equation can be regarded as the potential equation of a classical Markov process. The transition probability of this Markov process can be understood by considering the scattering of a photon by an atom and then taking the limits of geometrical optics and of singular coupling.
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Radiative energy transfer equation
1974The equation of radiative energy transfer can be obtained emphasizing the particle aspect of radiation and considering therefore the radiation field composed by n(r) photons per unit volume.
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The Transport Equation of Radiative Transfer with Axial Symmetry
SIAM Journal on Applied Mathematics, 1968The transport equation of radiative transfer for the isotropic scattering of radiation in a homogeneous axially symmetric medium is discussed. The integral equation for the source function, which replaces the Milne equation in a one-dimensional medium, is derived from the governing integro-partial differential equation for the intensity of radiation ...
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