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Decay of a linear pendulum in a free-molecular gas and in a special Lorentz gas. (English) Zbl 1245.82066
Authors’ abstract: A circular disk without thickness is placed in a gas, and an external force, obeying Hooke’s law, is acting perpendicularly on that disk. If the disk is displaced perpendicularly from its equilibrium position and released, then it starts an oscillatory or non-oscillatory unsteady motion, which decays as time progresses because of the drag exerted by the gas molecules. This unsteady motion, i.e., the decay of this linear pendulum, is investigated numerically under the diffuse reflection condition on the surface of the disk with special interest in the manner of its decay for two kinds of gases: one is a collisionless gas (or Knudsen gas) and the other is a special Lorentz gas interacting with the background. It is shown that the decay of the displacement of the disk is slow and is in proportion to an inverse power of time for the collisionless gas. The result complements the existing mathematical study of a similar problem [S. Caprino, G. Cavallaro and C. Marchioro, Math. Models Methods Appl. Sci. 17, No. 9, 1369–1403 (2007; Zbl 1216.70008)] in the case of non-oscillatory decay. It is also shown that the manner of the decay changes significantly for the special Lorentz gas.

MSC:
82D05 Statistical mechanical studies of gases
76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
82C40 Kinetic theory of gases in time-dependent statistical mechanics
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