A Kinetic Equation for the Distribution of Interaction Clusters in Rarefied Gases

We consider a stochastic particle model governed by an arbitrary binary interaction kernel. A kinetic equation for the distribution of interaction clusters is established. Under some additional assumptions a recursive representation of the solution is found. For particular choices of the interaction...

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Bibliographic Details
Published in:Journal of statistical physics 2017-10, Vol.169 (1), p.126-167
Main Authors: Patterson, Robert I. A., Simonella, Sergio, Wagner, Wolfgang
Format: Article
Language:English
Subjects:
Clusters
Mathematical and Computational Physics
Mathematical models
Physical Chemistry
Physics
Physics and Astronomy
Quantum Physics
Rarefied gases
Statistical Physics and Dynamical Systems
Theoretical
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Summary:We consider a stochastic particle model governed by an arbitrary binary interaction kernel. A kinetic equation for the distribution of interaction clusters is established. Under some additional assumptions a recursive representation of the solution is found. For particular choices of the interaction kernel (including the Boltzmann case) several explicit formulas are obtained. These formulas are confirmed by numerical experiments. The experiments are also used to illustrate various conjectures and open problems.
ISSN:0022-4715
1572-9613
DOI:10.1007/s10955-017-1865-0