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

Aoki, Kazuo; Cavallaro, Guido; Marchioro, Carlo; Pulvirenti, Mario

doi:10.1051/m2an:2008007

Cited by 25 publications

(50 citation statements)

References 9 publications

(15 reference statements)

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“…This problem has been studied mathematically [1] as well as numerically [2,3] when the surrounding gas is a collisionless gas (a free-molecular gas or the Knudsen gas), i.e., a gas that is so rarefied that collisions between gas molecules can be neglected. These are extensions of the earlier studies of the rate of approach to the final steady motion of the body when it is subject to a constant external force [1,[4][5][6][7].…”

Section: Introductionmentioning

confidence: 77%

Decay of a linear pendulum in a collisional gas: Spatially one-dimensional case

Tsuji

Aoki

2014

Phys. Rev. E

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An infinitely wide plate, subject to an external force in its normal direction obeying Hooke's law, is placed in an infinite expanse of a rarefied gas. When the plate is displaced from its equilibrium position and released, it starts in general an oscillatory motion in its normal direction. This is the one-dimensional setting of a linear pendulum considered previously for a collisionless gas and a special Lorentz gas by the present authors [T. Tsuji and K. Aoki, J. Stat. Phys. 146, 620 (2012)]. The motion decays as time proceeds because of the drag force on the plate exerted by the surrounding gas. The long-time behavior of the unsteady motion of the gas caused by the motion of the plate is investigated numerically on the basis of the Bhatnagar-Gross-Krook (BGK) model of the Boltzmann equation with special interest in the rate of the decay of the oscillatory motion of the plate. The result provides numerical evidence that the displacement of the plate decays in proportion to an inverse power of time for large time.

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Section: Introductionmentioning

confidence: 77%

Decay of a linear pendulum in a collisional gas: Spatially one-dimensional case

Tsuji

Aoki

2014

Phys. Rev. E

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“…There are more variants studied in the free molecular case: with linear restoring force [5], other rigid body shapes [7,16,26], the rigid body replaced by an elastic body [8] and when the gas fills the half-space [20]. These all assume the specular boundary condition; other boundary conditions including the Maxwell boundary condition were studied in [1,10,11]. It is reasonable to expect that Theorem 1 can be extended to these variants.…”

Section: Discussionmentioning

confidence: 99%

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

Koike

2018

J Stat Phys

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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 independent of the spatial dimension. This demonstrates the idea that interaction of the molecules with the background obstacles destroy the memory effect due to recollision.Keywords Lorentz gas · Rigid body motion · Moving boundary problem · Recollision · Memory effect · Long time behavior IntroductionFluid force acting on a moving body in a fluid is not solely determined by the instantaneous velocity of the body; it also depends on the past history of motion. This is because the disturbance made in the fluid is not immediately wiped away and affects the future motion of the body. The important of this

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“…The field of kinetic equations with moving elements -or in moving domains -is indeed still unexplored and, up to our knowledge, the only available results concern the Knudsen gas [2,13,8].…”

Section: Introductionmentioning

confidence: 99%