Table of Contents
Journal of Thermodynamics
Volume 2013, Article ID 915297, 13 pages
http://dx.doi.org/10.1155/2013/915297
Research Article

Nonlinear Closure Relations for Electron Transport in Hydrodynamical Models

1Faculté des Sciences Juridiques Economiques et Sociales Ain Sebaa, Université Hassan II-Mohammedia, Beausite, BP 2634, Ain sebaa, Casablanca, Morocco
2Laboratoire de Physique de la Matière Condensée (LPMC), Faculté des Sciences Ben M'sik, Université Hassan II-Mohammedia, BP 7955, Casablanca, Morocco

Received 9 September 2013; Accepted 22 October 2013

Academic Editor: Brian J. Edwards

Copyright © 2013 A. Salhoumi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Closure relations problem of hydrodynamical models in semiconductors is considered by expressing third- and fourth-order closure relations for the moments of the distribution function in terms of second-order Lagrange multipliers using a generalized Maxwell-Boltzmann distribution function within information theory. Calculation results are commented and compared with others to justify the accuracy of the approach developed in this paper. The comparison involves, in the first part with good agreements, the closure relations results obtained within extended thermodynamics which were checked by means of Monte Carlo simulations, in the second part, the results obtained by Grad's method which expands the distribution function up to fourth-order in Hermite polynomials. It is seen that the latter method cannot give any restriction on closure relations for higher-order moments, within the same conditions proposed in our approach. The important role of Lagrange multipliers for the determination of all closure relations is asserted.