@article {2203,
	title = {Sound dispersion in single-component systems},
	journal = {Physica a-Statistical Mechanics and Its Applications},
	volume = {387},
	number = {16-17},
	year = {2008},
	note = {ISI Document Delivery No.: 312TETimes Cited: 0Cited Reference Count: 46Napier, Duncan G. Shizgal, Bernie D.},
	month = {Jul},
	pages = {4099-4118},
	type = {Article},
	abstract = {The present paper considers the theoretical description of the propagation of sound waves in a one component monatomic gas. The interatomic potential is assumed to vary as the inverse fourth power of the interatomic separation, that is for so-called Maxwell molecules. The eigenvalues and eigenfunctions of the linearized Boltzmann collision operator are known for this model. We emphasize the behaviour of this system in the rarefied, large Knudsen number regime for which the convergence of solutions of the Boltzmann equation can be very slow. We carry out a detailed comparison of the previous formalisms by Wang Chang and Uhlenbeck [C.S. Wang Chang, G.E. Uhlenbeck, The kinetic theory of gases, in: G.E. Uhlenbeck, De Boer, (Eds.), Studies in Statistical Mechanics, vol. 5, Elsevier, New York, 1970, pp. 43-75], Alexeev [B.V. Alexeev, Philos. Trans. R. Soc. A 349 (1994) 357] and Sirovich and Thurber [L. Sirovich, J. K. Thurber, J. Math. Phys. 10 (1969) 239]. The latter exploit a general method of solution of the Boltzmann equation developed by Gross and Jackson. We demonstrate that the Generalized Boltzmann Equation proposed by Alexeev is not appropriate and we show the reasoning for the success of the Sirovich Thurber approach over the Wang Chang and Uhlenbeck calculations. Comparisons are made with experimental data. (c) 2008 Elsevier B.V. All rights reserved.},
	keywords = {BINARY GAS-MIXTURES, Boltzmann equation, BOLTZMANN-EQUATION, KINETIC THEORY, LIGHT-SCATTERING, Maxwell molecules, MODEL, MONATOMIC GASES, SLOW SOUND, sound dispersion, WAVE-PROPAGATION},
	isbn = {0378-4371},
	url = {<Go to ISI>://000256692900007},
	author = {Napier, D. G. and Shizgal, B. D.}
}
@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.}
}
@article {4328,
	title = {The Quadrature Discretization Method (QDM) in comparison with other numerical methods of solution of the Fokker-Planck equation for electron thermalization},
	journal = {Journal of Mathematical Chemistry},
	volume = {24},
	number = {4},
	year = {1998},
	note = {ISI Document Delivery No.: 165EGTimes Cited: 7Cited Reference Count: 67},
	pages = {291-319},
	type = {Article},
	abstract = {The determination of the relaxation of electrons in atomic gases continues to be an important physical problem. The main interest is the determination of the time scale for the thermalization of electrons in different moderators and the nature of the time-dependent electron energy distribution. The theoretical basis for the study of electron thermalization is the determination of the electron distribution function from a solution of the Lorentz-Fokker- Planck equation. The present paper considers a detailed comparison of different numerical methods of solution of the Lorentz-Fokker- Planck equation for the electron distribution function. The methods include a pseudospectral method referred to as the Quadrature Discretization Method (QDM) which is based on non-standard polynomial basis sets, a finite-difference method, and a Lagrange interpolation method. The Fokker-Planck equation can be transformed to a Schrodinger equation, and methods developed for the solution of either equation apply to the other.},
	keywords = {ACCELERATION, BOLTZMANN-EQUATION, DISCRETE-ORDINATE, ENERGY-DISTRIBUTION, FIELD DEPENDENCE, method, MULTITERM CALCULATIONS, QUANTUM-MECHANICS, RARE-GAS MODERATORS, STOCHASTIC, TRANSPORT-COEFFICIENTS, VELOCITY DISTRIBUTION FUNCTION},
	isbn = {0259-9791},
	url = {<Go to ISI>://000078506600001},
	author = {Leung, K. and Shizgal, B. D. and Chen, H. L.}
}
@article {4408,
	title = {Relaxation and transport of molecular systems in the gas phase},
	journal = {International Reviews in Physical Chemistry},
	volume = {17},
	number = {2},
	year = {1998},
	note = {ISI Document Delivery No.: ZQ123Times Cited: 10Cited Reference Count: 108},
	month = {Apr-Jun},
	pages = {185-225},
	type = {Review},
	abstract = {Some of the properties of gas phase relaxation and transport are reviewed with an emphasis on those properties that are due entirely to the presence of internal states in real molecular systems. The theoretical formulations of such non-equilibrium effects is based on the quantum Boltzmann equation. The conditions for the validity and the properties of this equation are reviewed. This includes a general discussion of how the combination of free molecule motion and collisions is required for the approach to global equilibrium. It is shown how the free motion is equivalent to a phase randomization of the elements of the density operator that are off-diagonal in energy. Spin relaxation and the magnetic field dependence (Senftleben-Beenakker effects) of the viscosity for a gas of diatomics are used to illustrate these aspects of the approach to equilibrium.},
	keywords = {BINARY COLLISION APPROXIMATION, BOLTZMANN-EQUATION, CARTESIAN TENSORS, COEFFICIENTS, CROSS-SECTIONS, ENERGY, IRREDUCIBLE, MODERATELY DENSE GAS, MUON SPIN RELAXATION, QUANTUM KINETIC-THEORY},
	isbn = {0144-235X},
	url = {<Go to ISI>://000073824600003},
	author = {Snider, R. F.}
}
@article {3820,
	title = {Moderately dense gas quantum kinetic theory: Aspects of pair correlations},
	journal = {Journal of Chemical Physics},
	volume = {105},
	number = {8},
	year = {1996},
	note = {ISI Document Delivery No.: VC506Times Cited: 7Cited Reference Count: 22},
	month = {Aug},
	pages = {3057-3065},
	type = {Article},
	abstract = {A recently formulated density corrected quantum Boltzmann equation emphasizes the need to explicitly include pair correlations and the conversion of kinetic energy to potential energy as important effects in the kinetic theory of moderately dense gases. This paper first considers an appropriate evolution equation for the pair correlations which includes their decay via interactions with other particles in the gas. The molecular description is given of such a gas close to local thermal equilibrium, together with expressions for the associated hydrodynamic variables. Wigner functions are used to uniquely separate macroscopic and microscopic properties. An accompanying paper solves the combination of linearized Boltzmann and correlated pair equations to obtain expressions for the transport coefficients. (C) 1996 American Institute of Physics.},
	keywords = {BOLTZMANN-EQUATION},
	isbn = {0021-9606},
	url = {<Go to ISI>://A1996VC50600011},
	author = {Snider, R. F. and Wei, G. W. and Muga, J. G.}
}
@article {3120,
	title = {DISCRETE VELOCITY MODEL FOR AN ESCAPING SINGLE-COMPONENT ATMOSPHERE},
	journal = {Planetary and Space Science},
	volume = {42},
	number = {5},
	year = {1994},
	note = {ISI Document Delivery No.: PF109Times Cited: 3Cited Reference Count: 42},
	month = {May},
	pages = {409-419},
	type = {Article},
	abstract = {The structure of an escaping single-component planetary atmosphere is computed by direct numerical integration the nonlinear Boltzmann equation. The transition from collision-dominated behavior deep in the atmosphere to nearly collisionless behavior at great altitudes is therefore treated self-consistently for the first time. We consider a hypothetical planet having the same mass and radius as the Earth, surrounded by an atmosphere of atoms having the same mass and total hard-sphere collision cross-section as atomic hydrogen. The atmosphere is initially hydrostatic and isothermal, at a temperature of 1000 K. As the computation progresses, the atmosphere gradually escapes. Eventually, a quasi-steady state is reached in which the density decreases significantly more rapidly than the initial barometric distribution, and the temperature decreases nearly 200 K between the planetary surface and an altitude of 10,000 km. The bulk upward flow speed increases with altitude above the exobase. However, because the most energetic particles escape and are not replenished, the atmosphere gradually cools, and the deep, collision-dominated portion of the atmosphere settles towards the planet{\textquoteright}s surface. The high-velocity tail of the velocity distribution function is quite anisotropic over a large range of altitudes, and remains largely depleted of incoming unbound particles even well below the exobase. At the highest altitudes in our simulation, the population of escaping unbound particles is considerably enhanced by the streaming of such particles from the warmer and denser regions below. The computed escape flux is at least 30\% greater than the Jeans flux as a result of this effect. It is suggested that computations similar to this one may prove useful for studying atmospheric escape from the primeval terrestrial planets, comets and Pluto.},
	keywords = {BOLTZMANN-EQUATION, ESCAPE, GASES, HYDRODYNAMIC ESCAPE, PLANETARY ATMOSPHERE, thermal},
	isbn = {0032-0633},
	url = {<Go to ISI>://A1994PF10900006},
	author = {Merryfield, W. J. and Shizgal, B. D.}
}
