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Motion of a Rigid Body in a Special Lorentz Gas: Loss of Memory Effect

Motion of a Rigid Body in a Special Lorentz Gas: Loss of Memory Effect Linear motion of a rigid body in a special kind of Lorentz gas is mathematically analyzed. The rigid body moves against gas drag according to Newton’s equation. The gas model is a special Lorentz gas consisting of gas molecules and background obstacles, which was introduced in Tsuji and Aoki (J Stat Phys 146:620–645, 2012). The specular boundary condition is imposed on the resulting kinetic equation. This study complements the numerical study by Tsuji and Aoki cited above—although the setting in this paper is slightly different from theirs, qualitatively the same asymptotic behavior is proved: The velocity V(t) of the rigid body decays exponentially if the obstacles undergo thermal motion; if the obstacles are motionless, then the velocity V(t) decays algebraically with a rate $$t^{-\,5}$$ t - 5 independent of the spatial dimension. This demonstrates the idea that interaction of the molecules with the background obstacles destroys the memory effect due to recollision. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Statistical Physics Springer Journals

Motion of a Rigid Body in a Special Lorentz Gas: Loss of Memory Effect

Koike, Kai
Journal of Statistical Physics , Volume 172 (3) – Jun 1, 2018
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29 pages

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Publisher
Springer Journals
Copyright
Copyright © 2018 by Springer Science+Business Media, LLC, part of Springer Nature
Subject
Physics; Statistical Physics and Dynamical Systems; Theoretical, Mathematical and Computational Physics; Physical Chemistry; Quantum Physics
ISSN
0022-4715
eISSN
1572-9613
DOI
10.1007/s10955-018-2072-3
Publisher site
See Article on Publisher Site

Abstract

Linear motion of a rigid body in a special kind of Lorentz gas is mathematically analyzed. The rigid body moves against gas drag according to Newton’s equation. The gas model is a special Lorentz gas consisting of gas molecules and background obstacles, which was introduced in Tsuji and Aoki (J Stat Phys 146:620–645, 2012). The specular boundary condition is imposed on the resulting kinetic equation. This study complements the numerical study by Tsuji and Aoki cited above—although the setting in this paper is slightly different from theirs, qualitatively the same asymptotic behavior is proved: The velocity V(t) of the rigid body decays exponentially if the obstacles undergo thermal motion; if the obstacles are motionless, then the velocity V(t) decays algebraically with a rate $$t^{-\,5}$$ t - 5 independent of the spatial dimension. This demonstrates the idea that interaction of the molecules with the background obstacles destroys the memory effect due to recollision.

Journal

Journal of Statistical Physics – Springer Journals

Published: Jun 1, 2018

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