Two-Group Neutron Transport Theory for Plane and Spherical Geometry

1970 ◽  
Vol 25 (10) ◽  
pp. 1370-1374 ◽  
Author(s):  
K. O. Thielheim ◽  
W. Blöcker
Keyword(s):  
Integral Equation ◽  
Singular Integral ◽  
Fredholm Integral Equation ◽  
Transport Theory ◽  
Neutron Transport ◽  
Spherical Geometry ◽  
Singular Integral Equations ◽  
Neutron Transport Theory ◽  
Critical Problems ◽  
Expansion Coefficients

Abstract Two-Group neutron transport theory is applied to critical problems in plane and spherical geometry. The neutron flux and the density transform for plane and spherical geometry respectively are expanded into singular eigenfunctions of the transport equation. With aid of the theory of singular integral equations the problem is reduced to one Fredholm integral equation for the expansion coefficients. The critical equations are presented as additional conditions.

Two-Group Neutron Transport Theory with Anisotropic Scattering

1970 ◽  
Vol 25 (5) ◽  
pp. 587-594
Author(s):  
K. O. Thielheim ◽  
K. Claussen
Keyword(s):  
Integral Equation ◽  
Transport Theory ◽  
Neutron Transport ◽  
Full Range ◽  
Completeness Theorem ◽  
Anisotropic Scattering ◽  
Neutron Transport Theory ◽  
Coeffi Cients ◽  
Group Transport ◽  
Homogeneous Media

Abstract Two-group transport theory with anisotropic scattering in infinite homogeneous media is pre-sented in this paper. The kernel of the integral equation is expanded into a finite series of Legendre polynomials. Eigenfunctions and eigenvalues of the transformed integral equation are found and the number of discrete eigenvalues is calculated. The full-range completeness theorem as well as the orthogonality and normalization relations are presented. As an example the expansion coeffi-cients of the infinite-medium Green's function are explicitly calculated.

W1,p REGULARITY IN TRANSPORT THEORY

1991 ◽  
Vol 01 (04) ◽  
pp. 477-499 ◽  
Author(s):  
MUSTAPHA MOKHTAR-KHARROUBI
Keyword(s):  
Fourier Analysis ◽  
Singular Integral ◽  
General Class ◽  
Transport Theory ◽  
Neutron Transport ◽  
Convex Domains ◽  
Integral Analysis ◽  
Neutron Transport Theory ◽  
Type C ◽  
Regularity Results

Let T be the streaming operator arising in neutron transport theory, T=−ν(∂/∂x)−σ(ν), with non-incoming boundary conditions in convex domains. The purpose of this paper is to give a general class [Formula: see text] of pair (C1, C2) of collision operators such that C1(λ−T)−1C2 maps continuously Lp into W1,p(1<p<+∞). The result is based on a singular integral analysis of Calderon-Zygmund type. In the case p=2 we obtain, by Fourier analysis, the same result under weaker assumptions. We also derive W1,p regularity results for operators of type C1(λ−T)−1.

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