Peaked phase function approximation in the solution of radiative transfer equation

2005 ◽  
Author(s):  
Viatcheslav Kisselev
Keyword(s):  
Radiative Transfer ◽  
Phase Function ◽  
Transfer Equation ◽  
Function Approximation ◽  
Radiative Transfer Equation

scholarly journals Critical point behaviour of the diffusion length for radiative transfer

1985 ◽  
Vol 27 (2) ◽  
pp. 245-257
Author(s):  
I. F. Grant ◽  
B. H. J. McKellar
Keyword(s):  
Radiative Transfer ◽  
Critical Point ◽  
Infinite Series ◽  
Phase Function ◽  
Transfer Equation ◽  
Continued Fraction ◽  
Diffusion Length ◽  
Radiative Transfer Equation ◽  
Homogenous Medium ◽  
Legendre Expansion

AbstractCritical point behaviour of the diffusion length γ for the solutions of the radiative transfer equation deep in a homogenous medium is studied. The Legendre expansion of the medium's phase function P(cos ψ) is taken to be an infinite series and is characterized by the parameters h0, h1h2,…. A characteristic equation for γ is given in terms of an infinite continued fraction. From this equation it is shown that as any one of the hn, say hp, approaches zero, the others being held constant, γ behaves as , where the critical exponent is found to be vp = ½ for all p = 0, 1, 2,….

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