Kershaw-type transport equations for fermionic radiation

Kershaw-type transport equations for fermionic radiation Besides the maximum entropy closure procedure, other procedures can be used to close the systems of spectral moment equations. In the case of classical and bosonic radiation, the closed-form analytic Kershaw-type and B-distribution closure procedures have been used. It is shown that the Kershaw-type closure procedure can also be applied to the spectral moment equations of fermionic radiation. First, a description of the Kershaw-type closure for the system consisting of an arbitrary number of one-dimensional moment equations is presented. Next, the Kershaw-type two-field and three-field transport equations for fermionic radiation are analyzed. In the first case, the independent variables are the energy density and the heat flux. The second case includes additionally the flux of the heat flux as an independent variable. The generalization of the former two-field case to three space dimensions is also presented. The fermionic Kershaw-type closures differ from those previously derived for classical and bosonic radiation. It is proved that the obtained one-dimensional systems of transport equations are strictly hyperbolic and causal. The fermionic Kershaw-type closure functions behave qualitatively in the same way as the fermionic maximum entropy closure functions, but attain different numerical values. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Zeitschrift für angewandte Mathematik und Physik Springer Journals

Kershaw-type transport equations for fermionic radiation

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Publisher
Springer International Publishing
Copyright
Copyright © 2017 by Springer International Publishing AG
Subject
Engineering; Theoretical and Applied Mechanics; Mathematical Methods in Physics
ISSN
0044-2275
eISSN
1420-9039
D.O.I.
10.1007/s00033-017-0847-z
Publisher site
See Article on Publisher Site

Abstract

Besides the maximum entropy closure procedure, other procedures can be used to close the systems of spectral moment equations. In the case of classical and bosonic radiation, the closed-form analytic Kershaw-type and B-distribution closure procedures have been used. It is shown that the Kershaw-type closure procedure can also be applied to the spectral moment equations of fermionic radiation. First, a description of the Kershaw-type closure for the system consisting of an arbitrary number of one-dimensional moment equations is presented. Next, the Kershaw-type two-field and three-field transport equations for fermionic radiation are analyzed. In the first case, the independent variables are the energy density and the heat flux. The second case includes additionally the flux of the heat flux as an independent variable. The generalization of the former two-field case to three space dimensions is also presented. The fermionic Kershaw-type closures differ from those previously derived for classical and bosonic radiation. It is proved that the obtained one-dimensional systems of transport equations are strictly hyperbolic and causal. The fermionic Kershaw-type closure functions behave qualitatively in the same way as the fermionic maximum entropy closure functions, but attain different numerical values.

Journal

Zeitschrift für angewandte Mathematik und PhysikSpringer Journals

Published: Aug 10, 2017

References

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