Journal Article10.1007/BF01023483
Linear radiation transport in randomly distributed binary mixtures: A one-dimensional and exact treatment for the scattering case
D. Vanderhaegen,Claude Deutsch +1 more
53
TL;DR: In this article, the most general formalism for radiative transfer within randomly distributed and binary mixtures in one dimension is developed within the framework of the invariant imbedding method.
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Abstract: Scattering effects are considered for radiative transfer within randomly distributed and binary mixtures in one dimension. The most general formalism is developed within the framework of the invariant imbedding method. The lengthL of the random sample thus appears as a new variable. One transmission coefficientT(L) suffices to specify locally the intensities. By analogy with the homogeneous situation, one introduces an effective opacity with 〈T〉=(1+σeff
L)−1 fulfilling σeff<〈σ〉=p
0σ0+p
1σ1(0 and 1 refer, respectively, to the components involved in the mixture). Equality is reached whenL→0, ∞. Otherwise, σeff displays a deep transmission window. It is numerically expressed for three combinations of opacities (σ0,σ1) and average grain sizes (λ0, λ1). These results are of crucial concern in optimizing an ICF compression for a pellet nonuniformly illuminated by intense laser or ion beams.
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Citations
Benchmark results for particle transport in a binary Markov statistical medium
TL;DR: In this paper, the authors give numerical benchmark results for particle transport in a randomly mixed binary medium, with the mixing statistics described as a homogeneous Markov process, and a discrete ordinate numerical transport solution is generated for this realization.
Linear kinetic theory in stochastic media
TL;DR: In this paper, the ensemble-averaged angular flux is analyzed in stochastic heterogeneous media and the analysis includes scattering in a three-dimensional setting and deals with arbitrary time-dependent statistics.
44
Renormalized equations for linear transport in stochastic media
Fausto Malvagi,G. C. Pomraning +1 more
TL;DR: In this paper, the master equation is used to obtain a model describing the ensemble-averaged intensity corresponding to linear particle transport in randomly mixed immiscible fluids, and an asymptotic limit corresponding to small amounts of opaque fluids admixed with large amounts of transparent fluids is employed to reduce the complexity of the description.
30
A model for interface intensities in stochastic particle transport
TL;DR: In this paper, the authors consider particle transport and radiative transfer in a Markovian mixture of two immiscible fluids and derive a higher order balance-like equation for interface intensities.
28
Cussic transport problems in binary homogeneous markov statistical mixtures
TL;DR: In this article, exact analytic solutions are given for certain classic linear transport problems describing particle flow in a statistical medium, where the medium is assumed to consist of two randomly mixed immiscible fluids, with the mixing statistics described as a two state homogeneous Markov process.
28
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