title: Decay of a linear pendulum in a collisional gas: spatially one-dimensional case.
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 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.
authors.affiliation: Department of Mechanical Science and Bioengineering, Osaka University, Osaka 560-8531, Japan.
authors.forename: Tetsuro
authors.initials: T
authors.lastname: Tsuji
authors.affiliation: Department of Mechanical Engineering and Science and Advanced Research Institute of Fluid Science and Engineering, Kyoto University, Kyoto 615-8540, Japan.
authors.forename: Kazuo
authors.initials: K
authors.lastname: Aoki
mesh_terms: D003198:Computer Simulation; D017276:Friction; D005740:Gases / Q000737:chemistry*; D016014:Linear Models; D008956:Models, Chemical; D012212:Rheology / Q000379:methods*; D033081:Shear Strength; D013314:Stress, Mechanical
chemical_list: D005740:Gases