Abstract:
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 oscillator (or pendulum) considered previously for a collisionless
gas and for 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, as well as
the compressible Navier-Stokes equation (with the temperature-jump
condition), with special interest in the rate of the decay of the
oscillatory motion of the plateate decays in proportion to an inverse
power of time (power -3/2) for large time. This talk contains some
results of the works in collabo. The result provides numerical evidence
that the displacement of the plration with Tetsuro Tsuji (Osaka
University), Shingo Kosuge (Kyoto University, Japan), and Taiga
Fujiwara (Kyoto University). |