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

Abstract

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.

References in corpus (1)

• On the distribution of free-path lengths for the periodic Lorentz gas III

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• On the distribution of the free path length of the linear flow in a honeycomb
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• Efficient algorithms for general periodic Lorentz gases in two and three dimensions
• Kinetic Theory for the Low-Density Lorentz Gas
• Convergence to the equilibrium for the kinetic transport equation in the two-dimensional periodic Lorentz Gas
• The periodic Lorentz gas in the Boltzmann-Grad limit: asymptotic estimates