Characterization of collision kernels
In this paper we show how abstract physical requirements are enough to characterize the classical collision kernels appearing in kinetic equations. In particular Boltzmann and Landau kernels are derived.
Characterization of collision kernels
In this paper we show how abstract physical requirements are enough to characterize the classical collision kernels appearing in kinetic equations. In particular Boltzmann and Landau kernels are derived.
Conservative forms of Boltzmann's collision operator : Landau revisited
Conservative forms of Boltzmann's collision operator: Landau revisited
We show that Boltzmann's collision operator can be written explicitly in divergence and double divergence forms. These conservative formulations may be of interest for both theoretical and numerical purposes. We give an application to the asymptotics of grazing collisions.
Convolutive decomposition and fast summation methods for discrete-velocity approximations of the Boltzmann equation
Discrete-velocity approximations represent a popular way for computing the Boltzmann collision operator. The direct numerical evaluation of such methods involve a prohibitive cost, typically O(N2d + 1) where d is the dimension of the velocity space. In this paper, following the ideas introduced in [C. Mouhot and L. Pareschi, C. R. Acad. Sci. Paris Sér. I Math. 339 (2004) 71–76, C. Mouhot and L. Pareschi, Math. Comput. 75 (2006) 1833–1852], we derive fast summation techniques for the evaluation of...
Corrections to the article “The multivelocity Peierls potential in the problem of refining the classical fundamental acoustic potential near the source of sound in a homogeneous Maxwellian gas”.