Guido Cavallaro

On a magnetically confined plasma with infinite charge

We consider a one-species plasma moving in an infinite cylinder, in which it is confined by means of a magnetic field diverging on the walls of the cylinder. It is assumed that initially the particles have bounded velocities and are distributed according to a density which is bounded, without any decreasing at infinity. The mutual interaction is of Yukawa type, i.e., Coulomb at short distance and exponentially decreasing at infinity. We prove the global in time existence and uniqueness of the time evolution of the plasma and its confinement.

Time Evolution of a Vlasov-Poisson Plasma with Infinite Charge in ℝ3

We study existence and uniqueness of the solution to the Vlasov-Poisson system describing a one-species plasma evolving in ℝ3, 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.

On the Motion of an Elastic Body in a Free Gas

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 − | α 1 | 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 APPROACH TO EQUILIBRIUM FOR A PENDULUM IMMERSED IN A STOKES FLUID

We study the unsteady motion of a sphere immersed in a Stokes fluid and subject to an elastic force. The equations of motion for the sphere lead to an integro-differential equation, whose solution we study asymptotically. We prove that the position of the sphere reaches its equilibrium point with a power-law, t-γ, with γ = 1/2, 3/2, depending on the initial conditions. This behavior is due to the memory effect of the surrounding fluid.

Mathematical models of viscous friction

1. Introduction.- 2. Gas of point particles.- 3. Vlasov approximation.- 4. Motion of a body immersed in a Vlasov system.- 5. Motion of a body immersed in a Stokes fluid.- A Infinite Dynamics.

Dynamics of infinitely extended hard core systems

In 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 ℝ3.

Gas of Point Particles

In this chapter we study the problem of viscous friction in the framework of microscopic models of classical point particles. The system body/medium is modeled by the dynamics of a heavy particle (the body), subjected to a constant force and interacting with infinitely many identical particles (the medium). We discuss conditions on the body/medium interaction that are necessary for the body to reach a finite limiting velocity. Rigorous results are given in the case of quasi-one-dimensional and one-dimensional systems.

Motion of a Body Immersed in a Vlasov System

In this chapter we study the motion of a body immersed in a Vlasov system. Such a choice for the medium allows to overcome problems connected to the irregular motion of the body occurring when it interacts with a gas of point particles. On the contrary, in case of a Vlasov system, the motion is expected to be regular. The interaction body/medium is assumed to be hard core, which implies the existence of a stationary motion for any initial data and any intensity of external constant force acting on the body. Moreover, we investigate the asymptotic approach of the body velocity to the limiting one, showing that in case of not self-interacting medium the approach is proportional to an inverse power of time. Such a behavior, surprising for not being exponential as in many viscous friction problems, is due to the recollisions that a single particle of the medium can deliver with the body.

On the Magnetic Shield for a Vlasov–Poisson Plasma

We study the screening of a bounded body