103 research outputs found
Long time evolution of concentrated Euler flows with planar symmetry
We study the time evolution of an incompressible Euler fluid with planar symmetry when the vorticity is initially concentrated in small disks. We discuss how long this concentration persists, showing that in some cases this happens for quite long times. Moreover, we analyze a toy model that shows a similar behavior and gives some hints on the original proble
Time evolution of concentrated vortex rings
We study the time evolution of an incompressible fluid with axisymmetry
without swirl when the vorticity is sharply concentrated. In particular, we
consider disjoint vortex rings of size and intensity of the
order of . We show that in the limit , 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.Comment: 24 pages. This updated version provides a new Appendix B, containing
the corrected proof of Lemma 3.1. For the sake of clarity, this proof has
already been included in arXiv:2102.07807 (where the results of this article
have been extended
The Vlasov-Poisson equation in with infinite charge and velocities
We consider the Vlasov-Poisson equation in with initial data
which are not in space and have unbounded support in the velocities.
Assuming for the density a slight decay in space and a strong decay in
velocities, we prove existence and uniqueness of the solution, thus
generalizing the analogous result given in [5] for data compactly supported in
the velocities
On the magnetic shield for a Vlasov-Poisson plasma
We 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
Efficacy of a magnetic shield against a Vlasov-Poisson plasma
The aim of the paper is to test on a simple model how impenetrable may be a
magnetic shield. We study the time evolution of a single species positive
plasma, confined in the half-space . The confinement is the result of a
balance between a magnetic field and an external field, both singular at
; the magnetic field forbids the entrance of plasma particles in the
region , whereas the external field attracts the plasma particles
towards . The plasma has finite total charge and velocities distributed
with a Maxwell-Boltzmann law.Comment: arXiv admin note: text overlap with arXiv:1602.04164,
arXiv:1706.0873
Dynamics of Infinite Classical Anharmonic Crystals
We consider an unbounded lattice and at each point of this lattice an anharmonic oscillator, that interacts with its first neighborhoods via a pair potential V and is subjected to a restoring force of potential U . We assume that U and V are even nonnegative polynomials of degree 2σ1 and 2σ2. We study the time evolution of this system, with a control of the growth in time of the local energy, and we give a nontrivial bound on the velocity of propagation of a perturbation. This is an extension to the case σ1 < 2σ2 − 1 of some already known results obtained for σ1 ≥ 2σ2 − 1
Long time localization of modified surface quasi-geostrophic equations
We discuss the time evolution of a two-dimensional active scalar flow, which
extends some properties valid for a two-dimensional incompressible nonviscous
fluid. In particular we study some characteristics of the dynamics when the
field is initially concentrated in small disjoint regions, and we discuss
the conservation in time of this localization property. We discuss also how
long this localization persists, showing that in some cases this happens for
quite long times
The social boders of the ethical theme
Тема этического получает новый поворот в свете вопросов статуса социальной структуры. Методологические основания открытого общества не выдерживают критики с позиций морального консерватизма.The ethical theme acquires a new turn in the light of questioning social structure status. Open society has no reliable methodological grounds to counterfeit moral conservative critique
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