Browsing by Author "Simonella, Sergio"
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- ItemA kinetic equation for the distribution of interaction clusters in rarefied gases(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2017) Patterson, Robert I.A.; Simonella, Sergio; Wagner, WolfgangWe 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.
- ItemOn the evolution of the empirical measure for the hard-sphere dynamics(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2015) Pulvirenti, Mario; Simonella, SergioWe prove that the evolution of marginals associated to the empirical measure of a finite system of hard spheres is driven by the BBGKY hierarchical expansion. The usual hierarchy of equations for L1 measures is obtained as a corollary. We discuss the ambiguities arising in the corresponding notion of microscopic series solution to the Boltzmann-Enskog equation.