One-Dimensional Transport Theory

1995 ◽  
pp. 47-72
Author(s):  
Martin J. C. van Gemert ◽  
A. J. Welch ◽  
Willem M. Star
Keyword(s):  
Transport Theory ◽  
One Dimensional

The Rayleigh model: singular transport theory in one dimension

1982 ◽  
Vol 305 (1490) ◽  
pp. 383-440 ◽  
Keyword(s):  
Time Reversal ◽  
Transport Theory ◽  
Singular System ◽  
Heat Bath ◽  
One Dimension ◽  
Scattering Operator ◽  
One Dimensional ◽  
Test Particles ◽  
Mathematical Problems ◽  
Rayleigh Piston

We present a comprehensive account of the special ‘Rayleigh piston’ model for the spatial and velocity relaxation of an ensemble of labelled test-particles in a one-dimensional heat-bath of particles with identical mass. This model, originally formulated by Rayleigh in 1891 but since largely neglected, is in effect a prototype for all later models in singular particle transport theory and serves to illustrate the mathematical problems associated with the occurrence of singular eigenfunctions and continuous spectra of a scattering operator. Although other idealized scattering models are known, the Rayleigh model remains a unique example of an exactly soluble singular system which, in including conservation laws and time-reversal symmetry in scattering, retains a degree of mechanical realism.

scholarly journals SNARG-1D: A ONE-DIMENSIONAL, DISCRETE-ORDINATE, TRANSPORT-THEORY PROGRAM FOR THE CDC-3600.

1966 ◽  
Author(s):  
G.J. Duffy ◽  
H. Greenspan ◽  
S.D. Sparck ◽  
J.V. Zapatka ◽  
M.K. Butler
Keyword(s):  
Transport Theory ◽  
Discrete Ordinate ◽  
One Dimensional

On eigendistributions in linear transport theory

1979 ◽  
Vol 83 (3-4) ◽  
pp. 303-326 ◽  
Author(s):  
C. G. Lekkerkerker
Keyword(s):  
Transport Theory ◽  
Neutron Transport ◽  
Full Range ◽  
Scattering Function ◽  
Neutron Transport Equation ◽  
One Dimensional ◽  
Factorization Problem ◽  
Linear Transport ◽  
The One ◽  
Linear Transport Theory

SynopsisAn attempt is made to provide a sound basis for the method of singular eigenfunction expansions which has been in vogue in linear transport theory for some decades. The procedure is exemplified by a treatment of the one-dimensional neutron transport equation with a degenerate scattering function. Full-range as well as half-range results are derived. At the end of the paper the implications for a certain matrix factorization problem are given.

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