Simultaneous Reconstruction of Two Parameters for Transport Equation in a Stratified Half-Space

1996 ◽  
Vol 125 (2) ◽  
pp. 434-439 ◽  
Author(s):  
Jinpin Ying ◽  
Feng Wu ◽  
Wei Sun
Keyword(s):  
Transport Equation ◽  
Half Space ◽  
Simultaneous Reconstruction ◽  
Two Parameters

Approximate solutions to the half-space integral transport equation near a plane boundary

1980 ◽  
Vol 58 (9) ◽  
pp. 1291-1310 ◽  
Author(s):  
Michael S. Milgram
Keyword(s):  
Transport Equation ◽  
Half Space ◽  
Matrix Multiplication ◽  
Solution Space ◽  
Plane Geometry ◽  
Plane Boundary ◽  
Infinite Plane ◽  
Algebraic Equations ◽  
Linear Algebraic Equations ◽  
Integral Transport

A set of functions spanning the solution space of the integral transport equation near a boundary in semi-infinite plane geometry is obtained and used to reduce the problem to that of a system of linear algebraic equations. Expressions for the boundary angular flux are obtained by matrix multiplication, and the theory is extended to adjacent half-space problems by matching the angular flux at the boundary. Thus a unified theory is obtained for well-behaved arbitrary sources in semi-infinite plane geometry. Numerical results are given for both Milne's problem and the problem of constant production in adjacent half-spaces, and albedo problems in semi-infinite geometry. The solutions for the flux density are best near the boundary, and for the angular flux are best for angles near the plane of the boundary; it is conjectured that the theory will prove most useful when extended to arrays of finite slabs.

Half-space albedo problem for the Anlı-Güngör scattering function

Kerntechnik ◽  
2022 ◽  
Vol 0 (0) ◽  
Author(s):  
Ali Zafer Bozkır ◽  
Recep Gökhan Türeci ◽  
Dinesh Chandra Sahni
Keyword(s):  
Transport Equation ◽  
Half Space ◽  
Legendre Polynomials ◽  
Neutron Transport ◽  
Homogeneous Medium ◽  
Second Order ◽  
Scattering Function ◽  
Neutron Transport Equation ◽  
Albedo Problem ◽  
Svd Method

Abstract One speed, time-independent and homogeneous medium neutron transport equation is solved for second order scattering using the Anlı-Güngör scattering function which is a recently investigated scattering function. The scattering function depends on Legendre polynomials and the t parameter which is defined on the interval [−1,  1]. A half-space albedo problem is examined with the FN method and the recently developed SVD method. Albedo values are calculated with two methods and tabulated. Thus, the albedo values for the Anlı-Güngör scattering are compared with these methods. The behaviour of the scattering function is similar to İnönü’s scattering function according to calculated results.

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