1,720,988 research outputs found
On the motion of a convex body interacting with a perfect gas in the mean-field approximation
No full textWe consider a convex body in the whole space, moving along the x-axis, immersed in an infinitely extended perfect gas in the mean-field approximation. We assume that
the gas particles interact with the body by means of elastic collisions. Giving to the body
an initial velocity V(0), we prove that, for
|V(0)| small enough, |V (t)| behaves like C t^(-5)
for large t, being C a positive constant depending on the medium and on the shape of the obstacle.
The power law approach to the equilibrium V = 0, instead of the exponential one (typical
in viscous friction problems), is due to the long memory effect of the recollisions. This
paper completes the analysis made in previous papers
in which for simplicity the body was assumed to be a disk
The Vlasov Equation with Infinite Mass
No full textWe discuss about the initial value problem for the Vlasov equation in
case of unbounded total mass. The problem strongly depends on the dimension d of
the physical space and on the singularity of the interaction. In particular, for d = 3,
the more singular the interaction, the faster must be the spatial decay at infinity of
the initial distribution. We describe also an application which gives rise to a viscous
friction model
ON THE MOTION OF AN ELASTIC BODY IN A FREE GAS
No full textWe 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
The gravitational Vlasov-Poisson system with infinite mass and velocities in
Full text linkWe study existence and uniqueness of the solution to the gravitational Vlasov–Poisson system evolving in R^3. It is assumed that initially the particles are distributed according to a spatial density with a power-law decay in space, allowing for unbounded mass, and an exponential decay in velocities given by a Maxwell–Boltzmann law. We extend a classical result which holds for systems with finite total mass
Time Evolution of Two Dimensional Systems with Infinitely Many Particles Mutually Interacting via Very Singular Forces
No full textWe study the existence and uniqueness of the time evolution via the Newton law of a two dimensional system of infinitely many particles with very singular mutual interactions. It is an improvement of the result by Fritz and Dobrushin given in (Comm. Math. Phys. 57:67-81, 1977) for inverse power-like singular interactions
On a Vlasov-Poisson plasma confined in a torus by a magnetic mirror
Full text linkWe study the time evolution of a Vlasov-Poisson plasma moving in a torus, in which it is confined by an unbounded external magnetic field. This field depends on the distance from the border
of the torus, is tangent to the border and singular on it.
We prove the existence and uniqueness of the solution, and also its confinement
inside the torus for all times, i.e. the external field behaves like a magnetic mirror
Dynamics of Infinitely Many Particles Mutually Interacting in Three Dimensions via a Bounded Superstable Long-range Potential
No full textWe show existence and uniqueness for the solutions to the Newton equations
relative to a system of infinitely many particles moving in the three-dimensional
space and mutually interacting via a bounded superstable long-range potential.
The present paper completes an analogous result obtained for positive short-range interaction
DYNAMICS OF INFINITELY EXTENDED HARD CORE SYSTEMS
No full textIn this paper we discuss the time evolution of a classical Hamiltonian system composed of infinitely many particles mutually interacting via a pair potential with a hard core and confined in an unbounded domain D of R-3
Time evolution of a Vlasov-Poisson plasma with infinite charge in R^3
No full textWe study existence and uniqueness of the solution to the Vlasov-Poisson system describing a one-species plasma evolving in R^3, whose particles interact via the Coulomb potential. It is assumed that initially the particles have bounded velocities and are distributed according to a non integrable density
Long Time Evolution of Concentrated Vortex Rings with Large Radius
No full textWe study the time evolution of an incompressible fluid with axial symmetry without swirl when the vorticity is sharply concentrated on N annuli of radii of the order of r0 and thickness ε. We prove that when r0 = | log ε|α , α > 1, the vorticity field of the fluid converges for ε → 0 to the point vortex model, in an interval of time which diverges as log | log ε|. This generalizes previous result by Cavallaro and Marchioro in (J Math Phys 62:053102, 2021),
that assumed α > 2 and in which the convergence was proved for short times only
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