On the limiting Markov process of energy exchanges in a rarely interacting ball-piston gas

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. T...

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Bibliographic Details
Published inarXiv.org
Main Authors Bálint, Péter, Gilbert, Thomas, Nándori, Péter, Szász, Domokos, Imre Péter Tóth
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 15.07.2016
Subjects
Elastic scattering
Heat exchange
Markov processes
Mathematical models
Mathematics - Dynamical Systems
Numerical analysis
Physics - Chaotic Dynamics
Physics - Statistical Mechanics
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.1510.06408