102,532 research outputs found
On a microscopic model of viscous friction
No full textWe consider a body moving along the x-axis under the action of an external force E and immersed in an infinitely extended perfect gas. We assume the gas to be described by the mean-field approximation and interacting elastically with the body. In this setup, we discuss the following statement: "Let V-0 be the initial velocity of the body and V-infinity its asymptotic velocity, then for vertical bar V-0-V-infinity vertical bar small enough it results vertical bar V(t)-V infinity vertical bar approximate to Ct(-d-2) for t large, where V (t) is the velocity of the body at time t, d the dimension of the space and C is a positive constant depending on the medium and on the shape of the body". The reason for the power law approach to the stationary state instead of the exponential one (usually assumed in viscous friction problems), is due to the long memory of the dynamical system. In a recent paper by Caprino, Marchioro and Pulvirenti,(3) the case of E constant and positive, with 0 < V-0 < V-infinity, for a disk orthogonal to the x-axis has been discussed. Here we complete the analysis in the cases E > 0 with V-0 > V-infinity and E = 0. We also approach the problem of an x-dependent external force, by choosing E of harmonic type. In this case we obtain the power-like asymptotic time behavior for the body position X(t). The investigation is done in detail for a disk orthogonal to the x-axis and then, by a sketched proof, extended to a body with a general convex shape
TIME EVOLUTION OF A VLASOV-POISSON PLASMA WITH MAGNETIC CONFINEMENT
No full textWe study the time evolution of a Vlasov-Poisson plasma moving in an infinite cylinder, in which it is confined by an unbounded external magnetic field. This field depends only on the distance from the border of the cylinder, is tangent to the border and singular on it. We prove the existence and uniqueness of the solution, and also its confinement inside the cylinder for all times, i.e. the external field behaves like a magnetic mirror. Possible generalizations are discussed
On the magnetic shield for a Vlasov-Poisson plasma
No full textWe study the screening of a bounded body against the effect of a wind of charged particles, by means of a shield produced by a magnetic field which becomes infinite on the border of .
The charged wind is modeled by a Vlasov-Poisson plasma, the bounded body by a torus, and the external magnetic field is taken close to the border of .
We study two models: a plasma composed by different species with positive or negative charges, and finite total mass of each species, and another made of many species of the same sign, each having infinite mass. We investigate the time evolution of both systems, showing in particular that the plasma particles cannot reach the body.
Finally we discuss possible extensions to more general initial data. We show also that when the magnetic lines are straight lines, (that imposes an unbounded body), the previous results can be improved
Time evolution of a Vlasov–Poisson plasma with different species and infinite mass in R3
No full textWe study existence and uniqueness of the solution to the Vlasov–Poisson system describing a plasma constituted by different species evolving in R3, whose particles interact via the Coulomb potential. The species can have both positive or negative charge. 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, extending a result contained in Caprino et al. (J Stat Phys 169:1066–1097,2017), which was restricted to finite total mass
Global time evolution of concentrated vortex rings
No full textWe study the time evolution of an incompressible fluid with axial symmetry without swirl, assuming initial data such that the initial vorticity is very concentrated inside N small disjoint rings of thickness ε and vorticity mass of the order of | log ε| - 1. When ε→ 0 , we show that the motion of each vortex ring converges to a simple translation with constant speed (depending on the single ring) along the symmetry axis. We obtain a sharp localization of the vorticity support at time t in the radial direction, whereas we state only a concentration property in the axial direction. This is obtained for arbitrary (but fixed) intervals of time. This study is the completion of a previous paper [5], where a sharp localization of the vorticity support was obtained both along the radial and axial directions, but the convergence for ε→ 0 worked only for short times
On a Magnetically Confined Plasma with Infinite Charge
No full textWe 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
On the dynamics of infinitely many charged particles with magnetic confinement
No full textWe study the time evolution of a system of infinitely many charged particles confined by an external magnetic field in an unbounded cylindrical conductor and mutually interacting via the Coulomb force. We prove the existence, uniqueness and quasi-locality of the motion. Moreover, we give some nontrivial bounds on its long time behavior
Time evolution of an infinitely extended Vlasov system with singular mutual interaction
No full textWe study the time evolution of an infinitely extended system in the mean field approximation, governed by the Vlasov equation. This system is confined in an unbounded cylinder by an external force singular on the border. The mutual interaction is assumed singular at short distance as with alpha< 2/3 (or alpha <1 in case of an external Lorentz force) and with a short range. The initial density is assumed bounded. Differently from studies which assume initial data compact in space and/or in velocities, here we consider a system having infinite mass and an exponential bound on the velocities, according to the Maxwell-Boltzmann law
On the calculation of an integral
No full textCalculaton of the partition function of the Calogero lattice performed using the exact solution of the quantum lattice and taking the classical limit after expressing it by a functional integral via the Feynman-Kac formula
"Per tutto l'arco della vita". Impianto per un modello di sviluppo del sistema regionale di educazinoe degli Adulti (EDA)
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