Speaker : Kazuo Aoki (Department of Mechanical Engineering and Science, Kyoto University, Japan)
Title : Decay of a linear pendulum in a collisional gas: Spatially one-dimensional case
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 in our paper [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 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. This work is a collaboration with Tetsuro Tsuji (Osaka University, Japan).