Journal ArticleDOI
Invariant imbedding and radiation dosimetry: VIII. reflection function from a double layer— finite order functions
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In this paper, the Riccati equation is used to calculate the reflection function of a given finite order, for a particle that has suffered a specified number of scatterings in the two portions of the total medium.Abstract:
In computing the total reflection function for two media of given scattering properties adjoined together, the usual techniques require a knowledge of reflection and transmission functions of both the media. An alternate method developed here depends only on solving a Riccati equation with suitable initial conditions. By following this procedure, we are able to calculate the reflection function of a given finite order, for a particle that has suffered a specified number of scatterings in the two portions of the total medium. Such calculations may be useful in radiation dosimetry problems where the body to be irradiated is placed on reflecting materials.read more
Citations
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Journal ArticleDOI
Optical properties of turbid media with specularly reflecting boundaries: applications to biological problems.
TL;DR: A simple multiple scattering model of a leaf is shown to account well for its measured optical properties and a method is proposed for finding accurate absorption spectra of pigment-containing cells.
Journal ArticleDOI
The first three orders of scattering in vertically inhomogeneous scattering-absorbing media.
Kiyoshi Kawabata,S. Ueno +1 more
TL;DR: In this article, the optical thickness integrations of the Cauchy system for reflection and transmission functions originating from the first three orders of scattering were carried out for a plane-parallel, vertically inhomogenous, scattering absorbing media.
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The basic reproduction number and the probability of extinction for a dynamic epidemic model.
TL;DR: It is shown that for n=2, the basic reproduction number, R₀, is maximised by a constant length infectious period and is decreasing in ς, the speed of movement between the two populations.
Journal ArticleDOI
Cauchy system for the scattering function in the searchlight problem
TL;DR: In this paper, an initial value solution of the scattering function in the searchlight problem is presented for finite, vertically inhomogeneous atmospheres with anisotropic scattering in slab geometry.
Journal ArticleDOI
Invariant imbedding and order-of-scattering theory in radiation field☆
S. Ueno,Alan P Wang +1 more
TL;DR: In this paper, the invariant imbedding concept was introduced in the study of radiative transfer in planetary atmospheres and then extensively extended to astrophysics by Ambarzumian and Chandrasekhar.
References
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Journal ArticleDOI
The Probabilistic Method for Problems of Radiative Transfer. X. Diffuse Relfection and Transmission in a Finite Inhomogeneous Atmosphere.
Journal ArticleDOI
Invariant imbedding and radiation dosimetry: Finite order scattering and transmission function
TL;DR: In this article, the authors present a method of computing the scattering and transmission functions of radiation which has undergone a finite number n(n ⩾ 1) of scatterings before emergence from the homogeneous, isotropically scattering slab.
Journal ArticleDOI
Invariant imbedding and radiation dosimetry: II. Integral recurrence relations for the finite order scattering and transmission functions☆
TL;DR: In this article, an easy method of obtaining numerical results is outlined for determining the amount of dosage received by the irradiated parts of the body of material involved in a semi-infinite slab.