Proceedings of the Royal Society of London A Mathematical and Physical Sciences · 1969 · 124 citations · 3 references
Natural SciencesMathematicsPhysicsOpticsRadiation TransportTransport PhenomenaRadiative Heat TransferRadiative ProcessesRadiative TransferScattering ProblemsScattering TheoryTransport In Heterogeneous MediaDiscrete Space RepresentationGeneratorsInfinitesimal GeneratorsMedia Physical PropertiesOperatorsPhysical PropertiesRadiative Transfer EquationsRadiative Transfer Theory
The theory extends Redheffer’s treatment of layer response, describing how a layer of arbitrary thickness reacts to incident fluxes through a linear operator. The paper develops a formal theory of radiative transfer for one‑dimensional scattering media of arbitrary physical constitution. It models each layer by a linear operator and shows that concatenating layers corresponds to a star product, forming a semigroup of operators. The authors prove that the operator semigroup’s infinitesimal generators can be derived from local physical properties, allowing discrete and differential equations to compute transmission, reflection, internal emission, and fluxes.
This paper sets out a formal theory of radiative transfer in one-dimensional scattering media of arbitrary physical constitution. The theory is based on an extension of the treatment of Redheffer, in which the response of a layer of arbitrary thickness to fluxes incident on its boundaries is described by a certain linear operator. Juxtaposition of two such layers gives a third layer, whose operator can be related to those of its constituents by an operation designated as the star product. It is shown that this set of operators constitutes a semigroup under the star product, and that the infinitesimal generators of the semigroup can be computed in term s of the physical properties of the medium , point by point. This makes it possible to write equivalent discrete and differential equations from both of which transmission and reflexion operators, the emission due to internal sources, and the internal fluxes at prescribed levels in the medium can be obtained.
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<i>Difference Methods for Initial-Value Problems</i>
Robert D. Richtmyer, E. H. Dill · Physics Today · 1959 · 3.2K citations · Full text
Solution of radiative transfer problems in planetary atmospheres
I. P. Grant, G. E. Hunt · Icarus · 1968 · 18 citations