The anisotropic approximations of the Henyey-Greenstein phase function for neutron transport equation
The effect of anisotropic scattering on the eigenvalues of a multiplying (c >1) and non-multi-plying (c < 1) slab in one-speed neutron transport equation is studied. We have made some calculations, not only for the cases c<1 and 0 < g < 1, but also the cases of c >1 and -1...
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doaj-ab85b85053024bca9ddb90840f5b24122020-11-24T21:16:49ZengVINCA Institute of Nuclear SciencesNuclear Technology and Radiation Protection1451-39942014-01-0129210210710.2298/NTRP1402102K1451-39941402102KThe anisotropic approximations of the Henyey-Greenstein phase function for neutron transport equationKacira Kadir0Bilgic Huseyin1Yasa Faruk2Kahramanmaras Sutcu Imam University, Faculty of Arts and Science, Department of Physics, K. Maras, TurkeyKahramanmaras Sutcu Imam University, Faculty of Arts and Science, Department of Mathematics, K. Maras, TurkeyKahramanmaras Sutcu Imam University, Faculty of Arts and Science, Department of Physics, K. Maras, TurkeyThe effect of anisotropic scattering on the eigenvalues of a multiplying (c >1) and non-multi-plying (c < 1) slab in one-speed neutron transport equation is studied. We have made some calculations, not only for the cases c<1 and 0 < g < 1, but also the cases of c >1 and -1<g<0 by using the linear and quadratic approximations of the Henyey-Greenstein scattering kernel. The asymmetry parameter g consists of isotropic, backward and forward bias. An extensive numerical survey is carried out for the eigenvalues in order to provide an accurate evaluation. The numerical results indicate that the discrete eigenvalue increases with forward scattering and decreases with backward scattering in expansions of linear and quadratic anisotropic scattering.http://www.doiserbia.nb.rs/img/doi/1451-3994/2014/1451-39941402102K.pdfHenyey-Greenstein scatteringtransport equationeigenvalue problemdiffusion length |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Kacira Kadir Bilgic Huseyin Yasa Faruk |
spellingShingle |
Kacira Kadir Bilgic Huseyin Yasa Faruk The anisotropic approximations of the Henyey-Greenstein phase function for neutron transport equation Nuclear Technology and Radiation Protection Henyey-Greenstein scattering transport equation eigenvalue problem diffusion length |
author_facet |
Kacira Kadir Bilgic Huseyin Yasa Faruk |
author_sort |
Kacira Kadir |
title |
The anisotropic approximations of the Henyey-Greenstein phase function for neutron transport equation |
title_short |
The anisotropic approximations of the Henyey-Greenstein phase function for neutron transport equation |
title_full |
The anisotropic approximations of the Henyey-Greenstein phase function for neutron transport equation |
title_fullStr |
The anisotropic approximations of the Henyey-Greenstein phase function for neutron transport equation |
title_full_unstemmed |
The anisotropic approximations of the Henyey-Greenstein phase function for neutron transport equation |
title_sort |
anisotropic approximations of the henyey-greenstein phase function for neutron transport equation |
publisher |
VINCA Institute of Nuclear Sciences |
series |
Nuclear Technology and Radiation Protection |
issn |
1451-3994 |
publishDate |
2014-01-01 |
description |
The effect of anisotropic scattering on the eigenvalues of a multiplying (c
>1) and non-multi-plying (c < 1) slab in one-speed neutron transport equation
is studied. We have made some calculations, not only for the cases c<1 and
0 < g < 1, but also the cases of c >1 and -1<g<0 by using the linear and
quadratic approximations of the Henyey-Greenstein scattering kernel. The
asymmetry parameter g consists of isotropic, backward and forward bias. An
extensive numerical survey is carried out for the eigenvalues in order to
provide an accurate evaluation. The numerical results indicate that the
discrete eigenvalue increases with forward scattering and decreases with
backward scattering in expansions of linear and quadratic anisotropic
scattering. |
topic |
Henyey-Greenstein scattering transport equation eigenvalue problem diffusion length |
url |
http://www.doiserbia.nb.rs/img/doi/1451-3994/2014/1451-39941402102K.pdf |
work_keys_str_mv |
AT kacirakadir theanisotropicapproximationsofthehenyeygreensteinphasefunctionforneutrontransportequation AT bilgichuseyin theanisotropicapproximationsofthehenyeygreensteinphasefunctionforneutrontransportequation AT yasafaruk theanisotropicapproximationsofthehenyeygreensteinphasefunctionforneutrontransportequation AT kacirakadir anisotropicapproximationsofthehenyeygreensteinphasefunctionforneutrontransportequation AT bilgichuseyin anisotropicapproximationsofthehenyeygreensteinphasefunctionforneutrontransportequation AT yasafaruk anisotropicapproximationsofthehenyeygreensteinphasefunctionforneutrontransportequation |
_version_ |
1726015492858052608 |