Fractional radiative transport in the diffusion approximation View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2018-02

AUTHORS

André Liemert, Alwin Kienle

ABSTRACT

The fractional radiative transport equation describes the propagation of particles, whose path length distribution p(ℓ)=-∂ℓEα(-σtℓα) satisfies the generalized Lambert–Beer law ∂ℓαp(ℓ)=-σtp(ℓ),ℓ>0,for α∈(0,1] with Eα(x) being the Mittag-Leffler function and σt is the total attenuation coefficient. Within the classical radiative transport theory the diffusion equation is known to be as the most often considered approximation. In this paper, we derive a generalized diffusion model on the basis of the fractional radiative transport equation using the Fourier transform in combination with the Padé approximation method. Moreover, the associated diffusive flux vector is given in form of a generalized Fick’s law containing the fractional gradient operator. It is shown via comparisons to the Monte Carlo method and an exact analytical solution that the derived diffusion approximations agree quite well with the exact solution of the fractional radiative transport equation even for highly absorbing media. More... »

PAGES

317-335

Journal

TITLE

Journal of Mathematical Chemistry

ISSUE

2

VOLUME

56

Author Affiliations

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s10910-017-0792-2

DOI

http://dx.doi.org/10.1007/s10910-017-0792-2

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1091376147


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