# On the motion of a body in thermal equilibrium immersed in a perfect gas

• Volume: 42, Issue: 2, page 263-275
• ISSN: 0764-583X

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## Abstract

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We consider a body immersed in a perfect gas and moving under the action of a constant force. Body and gas are in thermal equilibrium. We assume a stochastic interaction body/medium: when a particle of the medium hits the body, it is absorbed and immediately re-emitted with a Maxwellian distribution. This system gives rise to a microscopic model of friction. We study the approach of the body velocity V(t) to the limiting velocity ${V}_{\infty }$ and prove that, under suitable smallness assumptions, the approach to equilibrium is $|V\left(t\right)-{V}_{\infty }|\approx \frac{C}{{t}^{d+1}},$ where d is the dimension of the space, and C is a positive constant. This approach is not exponential, as typical in friction problems, and even slower than for the same problem with elastic collisions.

## How to cite

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Aoki, Kazuo, et al. "On the motion of a body in thermal equilibrium immersed in a perfect gas." ESAIM: Mathematical Modelling and Numerical Analysis 42.2 (2008): 263-275. <http://eudml.org/doc/250378>.

@article{Aoki2008,
abstract = { We consider a body immersed in a perfect gas and moving under the action of a constant force. Body and gas are in thermal equilibrium. We assume a stochastic interaction body/medium: when a particle of the medium hits the body, it is absorbed and immediately re-emitted with a Maxwellian distribution. This system gives rise to a microscopic model of friction. We study the approach of the body velocity V(t) to the limiting velocity $V_\infty$ and prove that, under suitable smallness assumptions, the approach to equilibrium is $$|V(t)-V\_\infty|\approx \frac\{C\}\{t^\{d+1\}\},$$ where d is the dimension of the space, and C is a positive constant. This approach is not exponential, as typical in friction problems, and even slower than for the same problem with elastic collisions. },
author = {Aoki, Kazuo, Cavallaro, Guido, Marchioro, Carlo, Pulvirenti, Mario},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Kinetic theory of gases; Boltzmann equation; free molecular gas; friction problem; approach to equilibrium.; approach to equilibrium},
language = {eng},
month = {3},
number = {2},
pages = {263-275},
publisher = {EDP Sciences},
title = {On the motion of a body in thermal equilibrium immersed in a perfect gas},
url = {http://eudml.org/doc/250378},
volume = {42},
year = {2008},
}

TY - JOUR
AU - Aoki, Kazuo
AU - Cavallaro, Guido
AU - Marchioro, Carlo
AU - Pulvirenti, Mario
TI - On the motion of a body in thermal equilibrium immersed in a perfect gas
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2008/3//
PB - EDP Sciences
VL - 42
IS - 2
SP - 263
EP - 275
AB - We consider a body immersed in a perfect gas and moving under the action of a constant force. Body and gas are in thermal equilibrium. We assume a stochastic interaction body/medium: when a particle of the medium hits the body, it is absorbed and immediately re-emitted with a Maxwellian distribution. This system gives rise to a microscopic model of friction. We study the approach of the body velocity V(t) to the limiting velocity $V_\infty$ and prove that, under suitable smallness assumptions, the approach to equilibrium is $$|V(t)-V_\infty|\approx \frac{C}{t^{d+1}},$$ where d is the dimension of the space, and C is a positive constant. This approach is not exponential, as typical in friction problems, and even slower than for the same problem with elastic collisions.
LA - eng
KW - Kinetic theory of gases; Boltzmann equation; free molecular gas; friction problem; approach to equilibrium.; approach to equilibrium
UR - http://eudml.org/doc/250378
ER -

## References

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7. C. Gruber and J. Piasecki, Stationary motion of the adiabatic piston. Physica A268 (1999) 412–423.
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