9 research outputs found
Effects of concavity on the motion of a body immersed in a Vlasov gas
We consider a body immersed in a perfect gas, moving under the action of a
constant force along the axis . We assume the gas to be described by
the mean-field approximation and interacting elastically with the body. Such a
dynamic was studied in previous papers In these studies the asymptotic trend
showed no sensitivity whatsoever to the shape of the object moving through the
gas. In this work we investigate how a simple concavity in the shape of the
body can affect its asymptotic behavior; we thus consider the case of hollow
cylinder in three dimensions or a box-like body in two dimensions. We study the
approach of the body velocity to the limiting velocity
and prove that, under suitable smallness assumptions, the approach to
equilibrium is both in two or three
dimensions, being a positive constant. This approach is not exponential, as
typical in friction problems, and even slower than for the simple disk and the
convex body in or
Wall Effect on the Motion of a Rigid Body Immersed in a Free Molecular Flow
Motion of a rigid body immersed in a semi-infinite expanse of gas in a
-dimensional region bounded by an infinite plane wall is studied for free
molecular flow on the basis of the free Vlasov equation under the specular
boundary condition. We show that the velocity of the body approaches its
terminal velocity according to a power law by carefully analyzing the pre-collisions due to the presence of
the wall. The exponent is smaller than for the case without the
wall found in the classical work by Caprino, Marchioro and Pulvirenti~[Comm.
Math. Phys., \textbf{264} (2006), pp. 167--189] and thus slower convergence
rate results from the presence of the wall.Comment: 21 pages, 3 figures. Revised according to the referees' comments.
Accepted for publication in "Kinetic and Related Models