Efficient algorithms for general periodic Lorentz gases in two and three dimensions

Autor:	Kraemer, Atahualpa S., Kryukov, Nikolay, Sanders, David P.
Rok vydání:	2015
Předmět:	Nonlinear Sciences - Chaotic Dynamics Condensed Matter - Statistical Mechanics
Druh dokumentu:	Working Paper
DOI:	10.1088/1751-8113/49/2/025001
Popis:	We present efficient algorithms to calculate trajectories for periodic Lorentz gases consisting of square lattices of circular obstacles in two dimensions, and simple cubic lattices of spheres in three dimensions; these become increasingly efficient as the radius of the obstacles tends to 0, the so-called Boltzmann-Grad limit. The 2D algorithm applies continued fractions to obtain the exact disc with which a particle will collide at each step, instead of using periodic boundary conditions as in the classical algorithm. The 3D version incorporates the 2D algorithm by projecting to the three coordinate planes. As an application, we calculate distributions of free path lengths close to the Boltzmann-Grad limit for certain Lorentz gases. We also show how the algorithms may be applied to deal with general crystal lattices. Comment: 14 pages, 10 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1511.00236 Zobrazit plný text záznamu View this record from Arxiv