@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 = {<Go to ISI>://000265564800068},
	author = {Chang, Y. B. and Shizgal, B. D.},
	editor = {Abe, T.}
}
@article {1559,
	title = {On the use temperature parameterized rate coefficients in the estimation of non-equilibrium reaction rates},
	journal = {Physica a-Statistical Mechanics and Its Applications},
	volume = {365},
	number = {2},
	year = {2006},
	note = {ISI Document Delivery No.: 044QSTimes Cited: 11Cited Reference Count: 58},
	month = {Jun},
	pages = {317-332},
	type = {Article},
	abstract = {The present paper considers a detailed analysis of the nonequilibrium effects for a model reactive system with the Chapman-Eskog (CE) solution of the Boltzmann equation as well as an explicit time dependent solution. The elastic cross sections employed are a hard sphere cross section and the Maxwell molecule cross section. Reactive cross sections which model reactions with and without activation energy are used. A detailed comparison is carried out with these solutions of the Boltzmann equation and the approximation introduced by Cukrowski and coworkers [J. Chem. Phys. 97 (1992) 9086; Chem. Phys. 89 (1992) 159; Physica A 188 (1992) 344; Chem. Phys. Lett. A 297 (1998) 402; Physica A 275 (2000) 134; Chem. Phys. Lett. 341 (2001) 585; Acta Phys. Polonica B 334 (2003) 3607.] based on the temperature of the reactive particles. We show that the Cukrowski approximation has limited applicability for the large class of reactive systems studied in this paper. The explicit time dependent solutions of the Boltzmann equation demonstrate that the CE approach is valid only for very slow reactions for which the corrections to the equilibrium rate coefficient are very small. (c) 2005 Elsevier B.V. All rights reserved.},
	keywords = {BIMOLECULAR CHEMICAL-REACTION, Boltzmann equation, BOLTZMANN-EQUATION, Chapman-Enskog, CHAPMAN-ENSKOG METHOD, CHEMISTRY, DILUTE GAS, LORENTZ GAS, MULTICOMPONENT SYSTEMS, NITROGEN-ATOMS, nonequilibrium, PERTURBATION, REACTIONS, VELOCITY DISTRIBUTION},
	isbn = {0378-4371},
	url = {<Go to ISI>://000237687900006},
	author = {Shizgal, B. D. and Chikhaoui, A.}
}
