16,590 research outputs found
Steady water waves with multiple critical layers: interior dynamics
We study small-amplitude steady water waves with multiple critical layers.
Those are rotational two-dimensional gravity-waves propagating over a perfect
fluid of finite depth. It is found that arbitrarily many critical layers with
cat's-eye vortices are possible, with different structure at different levels
within the fluid. The corresponding vorticity depends linearly on the stream
function.Comment: 14 pages, 3 figures. As accepted for publication in J. Math. Fluid
Mec
The effects of spin-down on the structure and evolution of pulsar wind nebulae
We present high resolution spherically symmetric relativistic
magnetohydrodynamical simulations of the evolution of a pulsar wind nebula
inside the free expanding ejecta of the supernova progenitor. The evolution is
followed starting from a few years after the supernova explosion and up to an
age of the remnant of 1500 years. We consider different values of the pulsar
wind magnetization parameter and also different braking indices for the
spin-down process. We compare the numerical results with those derived through
an approximate semi-analytical approach that allows us to trace the time
evolution of the positions of both the pulsar wind termination shock and the
contact discontinuity between the nebula and the supernova ejecta. We also
discuss, whenever a comparison is possible, to what extent our numerical
results agree with former self-similar models, and how these models could be
adapted to take into account the temporal evolution of the system. The inferred
magnetization of the pulsar wind could be an order of magnitude lower than that
derived from time independent analytic models.Comment: 11 pages, 7 figures, Accepted for publication on A&
Signal-noise interaction in nonlinear optical fibers: a hydrodynamic approach
We present a new perturbative approach to the study of signal-noise
interactions in nonlinear optical fibers. The approach is based on the
hydrodynamic formulation of the nonlinear Schr\"odinger equation that governs
the propagation of light in the fiber. Our method is discussed in general and
is developed in more details for some special cases, namely the
small-dispersion regime, the continuous-wave (CW) signal and the solitonic
pulse. The accuracy of the approach is numerically tested in the CW case.Comment: Revised version, submitted to Optics express, 15 pages, 6 figure
Completeness on the worm domain and the M\"untz-Sz\'asz problem for the Bergman space
In this paper we are concerned with the problem of completeness in the
Bergman space of the worm domain and its truncated version
. We determine some orthogonal systems and show that they are
not complete, while showing that the union of two particular of such systems is
complete.
In order to prove our completeness result we introduce the Muentz-Szasz
problem for the 1-dimensional Bergman space of the disk and find a sufficient condition for its solution.Comment: 14 pages, Author Accepted Manuscrip
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