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Progress in Kinetic Theory: Generalization of Boltzmann's Equation

Corngold, Noel (1977) Progress in Kinetic Theory: Generalization of Boltzmann's Equation. In: Rarefied gas dynamics; International Symposium, 10th, Aspen, Colo., July 18-23, 1976, Technical Papers. Vol.2. American Institute of Aeronautics and Astronautics , New York, NY, pp. 651-678. ISBN 978-0-915928-15-6. http://resolver.caltech.edu/CaltechAUTHORS:20141017-152754159

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Abstract

We have recently celebrated the hundredth birthday of Boltzmann's kinetic equation, an equation that has been enormously fruitful in physics and engineering. However, Boltzmann's model of transport processes has its limitations. It is based upon a view of Nature that is 'coarse-grained' in time and space, the intervals of coarse-graining being the duration of a collision, and the range of intermolecular force. In the coarse-grained world of rarefied systems, Boltzmann' s Stosszahlansatz works well. As more data on transport processes in liquids and dense gases accumulate, the need for systematic generalization of Boltzmann's equation (and the Chapman-Enskog analysis) grows. Computer experiments, neutron scattering experiments, and the scattering of laser beams have been particularly stimulating here, for they probe extremely short intervals of space and time in the dynamics of the target system. Coarse-graining, and the Stosszahlansatz are no longer acceptable. It is not widely appreciated that for the past decade, scientists have had a compact and elegant formalism at their disposal, for the construction of generalized kinetic equations. The new equations describe the response of the N-body system in the full frequency and wave-number domain. They are characterized by kernels that exhibit both spatial and temporal 'memory' and are, necessarily, very complicated. We shall review recent progress in the analysis, commenting on 1) the generalization of Boltzmann's equation to higher densities . . . the cluster expansion and the Bogoljubov Ansatz, revisited. 2) the generalized kinetic equations of Zwanzig and Mori 3) progress in analysis and solution.


Item Type:Book Section
Related URLs:
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http://arc.aiaa.org/doi/book/10.2514/4.865251PublisherBook
http://dx.doi.org/10.2514/4.865251DOIBook
Additional Information:© 1977 American Institute of Aeronautics and Astronautics. Paper presented at 10th International Symposium on Rarefied Gas Dynamics; Snowmass, Colorado, July 18-23, 1976. This research was sponsored in part by the National Science Foundation.
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Subject Keywords:Boltzmann Transport Equation, Kinetic Theory, Transport Theory, Bibliographies, Chapman-Enskog Theory, Functions (Mathematics), Liouville Equations, Viscosity
Record Number:CaltechAUTHORS:20141017-152754159
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20141017-152754159
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:50511
Collection:CaltechAUTHORS
Deposited By: Kristin Buxton
Deposited On:20 Oct 2014 15:33
Last Modified:20 Oct 2014 15:33

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