We study the motion of an elastic body immersed in a three-dimensional perfect gas (Knudsen gas) in the mean-field approximation. The body is a homogeneous cylinder moving along an x-axis perpendicular to its bases, which as a consequence of collisions with the gas particles, and of its elasticity, modifies its length along the x-axis. The body interacts with the gas particles by means of elastic collisions. We perturb initially the body, and study the approach of the body to equilibrium (rest), proving that, depending on the initial conditions, it can reach equilibrium with an exponential rate e(-vertical bar alpha t vertical bar t) or with a power-law t(-4). The exponential approach is characterized by the absence of recollisions between gas particles and body (for kinematic reasons), while the power-law approach is due to the presence of recollisions, which affect the motion by a long memory term.
ON THE MOTION OF AN ELASTIC BODY IN A FREE GAS / Cavallaro, Guido; Marchioro, Carlo. - In: REPORTS ON MATHEMATICAL PHYSICS. - ISSN 0034-4877. - STAMPA. - 69:2(2012), pp. 251-264. [10.1016/s0034-4877(12)60030-5]
ON THE MOTION OF AN ELASTIC BODY IN A FREE GAS
CAVALLARO, GUIDO;MARCHIORO, Carlo
2012
Abstract
We study the motion of an elastic body immersed in a three-dimensional perfect gas (Knudsen gas) in the mean-field approximation. The body is a homogeneous cylinder moving along an x-axis perpendicular to its bases, which as a consequence of collisions with the gas particles, and of its elasticity, modifies its length along the x-axis. The body interacts with the gas particles by means of elastic collisions. We perturb initially the body, and study the approach of the body to equilibrium (rest), proving that, depending on the initial conditions, it can reach equilibrium with an exponential rate e(-vertical bar alpha t vertical bar t) or with a power-law t(-4). The exponential approach is characterized by the absence of recollisions between gas particles and body (for kinematic reasons), while the power-law approach is due to the presence of recollisions, which affect the motion by a long memory term.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
