A kinetic equation for the distribution of interaction clusters in rarefied gases
- Patterson, Robert I. A.
- Simonella, Sergio
- Wagner, Wolfgang
2010 Mathematics Subject Classification
- 60K35 82B40
- stochastic particle system, interaction clusters, rarefied gases, kinetic equation, numerical experiments
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.
- J. Statist. Phys., 169 (2017), pp. 126--167.