@inbook {2381,
title = {Pseudospectral Solution of the Boltzmann Equation: Quantum Cross Sections},
booktitle = {Rarefied Gas Dynamics},
series = {Aip Conference Proceedings},
volume = {1084},
year = {2009},
note = {ISI Document Delivery No.: BJF97Times Cited: 0Cited Reference Count: 18Chang, Yongbin Shizgal, Bernie D.Proceedings Paper26th International Symposium on Rarefied Gas Dynmaics (RGD26)JUN 20-JUL 25, 2008Kyoto, JAPANJapan Soc Promot Sci, Japan Aerpspace Explorat Agcy, Soc Promot Space Sci, Iwantani Naoji Fdn, Inoue Fdn Sci, Casio Sci Promot Fdn, Kaijma Fdn, IHI Corp, IHI Aerospac Engn Co Ltd, Osaka Vaccuun Ltd, Nissin Inc2 HUNTINGTON QUADRANGLE, STE 1NO1, MELVILLE, NY 11747-4501 USA},
pages = {421-426},
publisher = {Amer Inst Physics},
organization = {Amer Inst Physics},
address = {Melville},
abstract = {The relaxation of it nonequilibrium test particle population of mass m(1) in contact with a background gas of particles of mass m(2) at temperature T-b is studied with the spatially homogeneous Boltzmann equation. A pseudospectral method of solution is employed which is based on the discretization of the distribution function at a nonuniform grid that coincides with a quadrature. In order to implement this approach, the integral collision operator of the Boltzmann equation is expressed explicitly in terms of a kernel which is also discretized. This procedure fails if the classical differential collision cross section is used as it diverges for small scattering angles and the kernel is no longer well defined. In the present paper, we choose the interaction potential between the test particles and the background particles to be the Maxwell molecule interaction, that is, V (r) = V-o(d/r)(4) for which the eigenvalues and eigenfunctions are well known. We employ the quantum mechanical differential cross section for this potential, which is finite at zero scattering angle and we apply a pseudospectral approach based on speed polynomials. We compare the well known results for the eigenvalue spectrum of the Boltzmann collision operator for the classical differential cross section with the new results with the quantum differential cross section and the basis set defined by the speed polynomials. The relaxation to equilibrium of initial nonequilibrium distribution functions is studied with both methods.},
keywords = {Boltzmann equation, DISTRIBUTIONS, DYNAMICS, GASES, Maxwell molecules, pseudospectral method, quantum cross section, relaxation, VELOCITY DISTRIBUTION},
isbn = {0094-243X978-0-7354-0615-5},
url = {://000265564800068},
author = {Chang, Y. B. and Shizgal, B. D.},
editor = {Abe, T.}
}