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On the mathematical transport theory in microporous media: the billiard approach. (English) Zbl 1202.37055
Summary: This paper is an expository of the main dynamical properties of billiards, which depend on the shape of the walls of the container, and recent developments like the introduction of an external field, which mimics the coupling with a thermostat. The class of dynamical systems dealt with in this paper exhibits characteristics of hybrid systems as it links discrete and continuous, deterministic and stochastic dynamics. The contents is focused on applications. Specifically, transport dynamics in highly-confined regions has been of interest in the last few decades because of industrial and medical applications. Aspects of confined transport remain elusive, considering that, in microporous membranes, whose pore size is about that of the molecules, the transport is sometimes ballistic, and sometimes diffusive. The classical kinetic and macroscopic approach can not be directly applied because collisions of the particle fluid with the walls prevail. The microscopic mathematical billiard theory can be applied as a mathematical tool since the interstices between obstacles can be considered as the pores of the membranes.

MSC:
37D50Hyperbolic systems with singularities (billiards, etc.)
37A35Entropy and other invariants, isomorphism, classification (ergodic theory)
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References:
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