The Boltzmann Equation.pdf

The Boltzmann Equation

In,1872, Boltzmann published a paper which for the first time provided a precise mathematical basis for a discussion of the approach to equilibrium. The paper dealt with the approach to equilibrium of a dilute gas and was based on an equation - the Boltzmann equation, as we call it now - for the velocity distribution function of such ~ gas. The Boltzmann equation still forms the basis of the kinetic theory of gases and has proved fruitful not only for the classical gases Boltzmann had in mind, but als- if properly generalized - for the electron gas in a solid and the excitation gas in a superfluid. Therefore it was felt by many of us that the Boltzmann equation was of sufficient interest, even today, to warrant a meeting, in which a review of its present status would be undertaken. Since Boltzmann had spent a good part of his life in Vienna, this city seemed to be a natural setting for such a meeting. The first day was devoted to historical lectures, since it was generally felt that apart from their general interest, they would furnish a good introduction to the subsequent scientific sessions. We are very much indebted to Dr. D.

BOLTZMANN Equation Liouville Equation Mass Velocity Collision Operator Rigid Sphere. These keywords were added by machine and not by the authors.

5.12 MB DATEIGRÖSSE
3709183383 ISBN
Englisch SPRACHE
The Boltzmann Equation.pdf

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Sofia Voigt

May 14, 2010 ... Solutions of this equation, beyond current computational capabilities, describe the location of gas molecules probabilistically and predict the ... The Boltzmann equation is an approximation. It is obtained by closing the so- called BBGKY hierarchy that links N-particle distribution functions to N+1 particle  ...

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Hydrodynamic Limits of the Boltzmann Equation The Boltzmann equation models so-called rarefied gases of identical particles, for which all but binary collisions between particles can be neglected. When the mean free path of gas particles is small comparing to the macroscopic length scale, one can derive fluid equations from the Boltzmann equations. The first problem is to establish the acoustic limit for a family of appropriately scaled

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Solving the Boltzmann Equation in N log 2 N | … In [C. Mouhot and L. Pareschi, "Fast algorithms for computing the Boltzmann collision operator," Math. Comp., to appear; C. Mouhot and L. Pareschi, C. R. Math. Acad. Sci. Paris, 339 (2004), pp. 71-76], fast deterministic algorithms based on spectral methods were derived for the Boltzmann collision operator for a class of interactions including the hard spheres model in three dimensions.