1,721,017 research outputs found
Cucker–Smale Type Dynamics of Infinitely Many Individuals with Repulsive Forces
Full text linkWe study the existence and uniqueness of the time evolution of a system of infinitely many individuals, moving in a tunnel and subjected to a Cucker–Smale type alignment dynamics with compactly supported communication kernels and to short-range repulsive interactions to avoid collisions
A comment on the paper "Lower bounds on the energy eigenvalues of systems containing identical particles"
No full textTime Evolution of Concentrated Vortex Rings
Full text linkWe study the time evolution of an incompressible fluid with axisymmetry without swirl when the vorticity is sharply concentrated. In particular, we consider N disjoint vortex rings of size ε and intensity of the order of | log ε| - 1. We show that in the limit ε→ 0 , when the density of vorticity becomes very large, the movement of each vortex ring converges to a simple translation, at least for a small but positive time
Time evolution of a Vlasov–Poisson plasma with different species and infinite mass in R3
Full text linkWe 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
Full text linkWe 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 the Euler equation in an unbounded domain of the plane
No full textWe discuss existence and uniqueness of solutions to the Euler Equation in an unbounded domain of the plane. We only assume the vorticity to be bounded, whereas in this kind of problems assumptions on its decreasing at infinity are usually made. The solution is obtained as limit of solutions to problems with compactly supported data. The existence of such limit physically means that the effects of far away fluid particles on the local evolution is negligible
On the propagation of a perturbation in an anharmonic system
No full textWe give a not trivial upper bound on the velocity of disturbances in an infinitely extended anharmonic system at thermal equilibrium. The proof is achieved by combining a control on the non equilibrium dynamics with an explicit use of the state invariance with respect to the time evolution
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 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
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