60,800 research outputs found
How to excite the internal modes of sine-Gordon solitons
We investigate the dynamics of the sine-Gordon solitons perturbed by
spatiotemporal external forces. We prove the existence of internal (shape)
modes of sine-Gordon solitons when they are in the presence of inhomogeneous
space-dependent external forces, provided some conditions (for these forces)
hold. Additional periodic time-dependent forces can sustain oscillations of the
soliton width. We show that, in some cases, the internal mode even can become
unstable, causing the soliton to decay in an antisoliton and two solitons. In
general, in the presence of spatiotemporal forces the soliton behaves as a
deformable (non-rigid) object. A soliton moving in an array of inhomogeneities
can also present sustained oscillations of its width. There are very important
phenomena (like the soliton-antisoliton collisions) where the existence of
internal modes plays a crucial role. We show that, under some conditions, the
dynamics of the soliton shape modes can be chaotic. A short report of some of
our results has been published in [J. A. Gonzalez et al., Phys. Rev. E, 65
(2002) 065601(R)].Comment: 14 .eps figures.To appear in Chaos, Solitons and Fractal
Ariane 5 verification and associated test facilities
The philosophy of verification tests of the Ariane 5 launcher program is already established. It corresponds to the development and the ground and flight qualification phases for both unmanned and manned launches. The different types of test are outlined for the system, booster, main core and upper structures, allowing the identification of the associated test facilities which are described
Two and three electrons in a quantum dot: 1/|J| - expansion
We consider systems of two and three electrons in a two-dimensional parabolic
quantum dot. A magnetic field is applied perpendicularly to the electron plane
of motion. We show that the energy levels corresponding to states with high
angular momentum, J, and a low number of vibrational quanta may be
systematically computed as power series in 1/|J|. These states are relevant in
the high-B limit.Comment: LaTeX, 15 pages,6 postscript figure
On the Jacobi-Metric Stability Criterion
We investigate the exact relation existing between the stability equation for
the solutions of a mechanical system and the geodesic deviation equation of the
associated geodesic problem in the Jacobi metric constructed via the
Maupertuis-Jacobi Principle. We conclude that the dynamical and geometrical
approaches to the stability/instability problem are not equivalent.Comment: 14 pages, no figure
Few-anyon systems in a parabolic dot
The energy levels of two and three anyons in a two-dimensional parabolic
quantum dot and a perpendicular magnetic field are computed as power series in
1/|J|, where J is the angular momentum. The particles interact repulsively
through a coulombic (1/r) potential. In the two-anyon problem, the reached
accuracy is better than one part in 10^5. For three anyons, we study the
combined effects of anyon statistics and coulomb repulsion in the ``linear''
anyonic states.Comment: LaTeX, 6 pages, 4 postscript figure
Weighted random--geometric and random--rectangular graphs: Spectral and eigenfunction properties of the adjacency matrix
Within a random-matrix-theory approach, we use the nearest-neighbor energy
level spacing distribution and the entropic eigenfunction localization
length to study spectral and eigenfunction properties (of adjacency
matrices) of weighted random--geometric and random--rectangular graphs. A
random--geometric graph (RGG) considers a set of vertices uniformly and
independently distributed on the unit square, while for a random--rectangular
graph (RRG) the embedding geometry is a rectangle. The RRG model depends on
three parameters: The rectangle side lengths and , the connection
radius , and the number of vertices . We then study in detail the case
which corresponds to weighted RGGs and explore weighted RRGs
characterized by , i.e.~two-dimensional geometries, but also approach
the limit of quasi-one-dimensional wires when . In general we look for
the scaling properties of and as a function of , and .
We find that the ratio , with , fixes the
properties of both RGGs and RRGs. Moreover, when we show that
spectral and eigenfunction properties of weighted RRGs are universal for the
fixed ratio , with .Comment: 8 pages, 6 figure
- …