On the limiting Markov process of energy exchanges in a rarely interacting ball-piston gas
Abstract
We analyse the process of energy exchanges generated by the elastic collisions between a point-particle, confined to a two-dimensional cell with convex boundaries, and a `piston', i.e. a line-segment, which moves back and forth along a one-dimensional interval partially intersecting the cell. This model can be considered as the elementary building block of a spatially extended high-dimensional billiard modeling heat transport in a class of hybrid materials exhibiting the kinetics of gases and spatial structure of solids. Using heuristic arguments and numerical analysis, we argue that, in a regime of rare interactions, the billiard process converges to a Markov jump process for the energy exchanges and obtain the expression of its generator.
Keywords
Cite
@article{arxiv.1510.06408,
title = {On the limiting Markov process of energy exchanges in a rarely interacting ball-piston gas},
author = {Péter Bálint and Thomas Gilbert and Péter Nándori and Domokos Szász and Imre Péter Tóth},
journal= {arXiv preprint arXiv:1510.06408},
year = {2016}
}
Comments
23 pages, 6 figures