The Boltzmann-Grad limit of the periodic Lorentz gas in two space dimensions

Details The Boltzmann-Grad limit of the periodic Lorentz gas in two space dimensions The Boltzmann-Grad limit of the periodic Lorentz gas in two space dimensions

2007-10-03

arxiv.org/abs/0710.0716v2

Mathematics

Dynamical Systems

Scientific paper

The periodic Lorentz gas is the dynamical system corresponding to the free motion of a point particle in a periodic system of fixed spherical obstacles of radius $r$ centered at the integer points, assuming all collisions of the particle with the obstacles to be elastic. In this Note, we study this motion on time intervals of order $1/r$ and in the limit as $r\to 0^+$, in the case of two space dimensions.

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