Solution of the finite Milne problem in stochastic media with RVT Technique

  • Howida Slama
  • Nabila A. El-Bedwhey
  • Alia El-Depsy
  • Mustafa M. Selim
Regular Article

Abstract.

This paper presents the solution to the Milne problem in the steady state with isotropic scattering phase function. The properties of the medium are considered as stochastic ones with Gaussian or exponential distributions and hence the problem treated as a stochastic integro-differential equation. To get an explicit form for the radiant energy density, the linear extrapolation distance, reflectivity and transmissivity in the deterministic case the problem is solved using the Pomraning-Eddington method. The obtained solution is found to be dependent on the optical space variable and thickness of the medium which are considered as random variables. The random variable transformation (RVT) technique is used to find the first probability density function (1-PDF) of the solution process. Then the stochastic linear extrapolation distance, reflectivity and transmissivity are calculated. For illustration, numerical results with conclusions are provided.

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Copyright information

© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Theoretical Physics Group, Physics Department, Faculty of ScienceDamietta UniversityNew Damietta CityEgypt
  2. 2.Mathematics Department, Faculty of ScienceDamietta UniversityNew Damietta CityEgypt

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