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arXiv · 1510.06408

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

Péter Bálint·Thomas Gilbert·Péter Nándori·Domokos Szász·Imre Péter Tóth
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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.

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Péter Bálint, Thomas Gilbert, Péter Nándori, Domokos Szász, Imre Péter Tóth. 2015-10-21. On the limiting Markov process of energy exchanges in a rarely interacting ball-piston gas. https://doi.org/10.1007/s10955-016-1598-5

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