8,104 research outputs found
Angular Pseudomomentum Theory for the Generalized Nonlinear Schr\"{o}dinger Equation in Discrete Rotational Symmetry Media
We develop a complete mathematical theory for the symmetrical solutions of
the generalized nonlinear Schr\"odinger equation based on the new concept of
angular pseudomomentum. We consider the symmetric solitons of a generalized
nonlinear Schr\"odinger equation with a nonlinearity depending on the modulus
of the field. We provide a rigorous proof of a set of mathematical results
justifying that these solitons can be classified according to the irreducible
representations of a discrete group. Then we extend this theory to
non-stationary solutions and study the relationship between angular momentum
and pseudomomentum. We illustrate these theoretical results with numerical
examples. Finally, we explore the possibilities of the generalization of the
previous framework to the quantum limit.Comment: 18 pages; submitted to Physica
A topological charge selection rule for phase singularities
We present an study of the dynamics and decay pattern of phase singularities
due to the action of a system with a discrete rotational symmetry of finite
order. A topological charge conservation rule is identified. The role played by
the underlying symmetry is emphasized. An effective model describing the short
range dynamics of the vortex clusters has been designed. A method to engineer
any desired configuration of clusters of phase singularities is proposed. Its
flexibility to create and control clusters of vortices is discussed.Comment: 4 pages, 3 figure
On the classification of type D spacetimes
We give a classification of the type D spacetimes based on the invariant
differential properties of the Weyl principal structure. Our classification is
established using tensorial invariants of the Weyl tensor and, consequently,
besides its intrinsic nature, it is valid for the whole set of the type D
metrics and it applies on both, vacuum and non-vacuum solutions. We consider
the Cotton-zero type D metrics and we study the classes that are compatible
with this condition. The subfamily of spacetimes with constant argument of the
Weyl eigenvalue is analyzed in more detail by offering a canonical expression
for the metric tensor and by giving a generalization of some results about the
non-existence of purely magnetic solutions. The usefulness of these results is
illustrated in characterizing and classifying a family of Einstein-Maxwell
solutions. Our approach permits us to give intrinsic and explicit conditions
that label every metric, obtaining in this way an operational algorithm to
detect them. In particular a characterization of the Reissner-Nordstr\"{o}m
metric is accomplished.Comment: 29 pages, 0 figure
On the separable quotient problem for Banach spaces
While the classic separable quotient problem remains open, we survey general
results related to this problem and examine the existence of a particular
infinitedimensional separable quotient in some Banach spaces of vector-valued
functions, linear operators and vector measures. Most of the results presented
are consequence of known facts, some of them relative to the presence of
complemented copies of the classic sequence spaces c_0 and l_p, for 1 <= p <=
\infty. Also recent results of Argyros - Dodos - Kanellopoulos, and Sliwa are
provided. This makes our presentation supplementary to a previous survey (1997)
due to Mujica
Black-hole binaries: life begins at 40 keV
In the study of black-hole transients, an important problem that still needs
to be answered is how the high-energy part of the spectrum evolves from the
low-hard to the high-soft state, given that they have very different
properties. Recent results obtained with RXTE and INTEGRAL have given
inconsistent results. With RXTE, we have found that the high-energy cutoff in
GX 339-4 during the transition first decreases (during the low-hard state),
then increases again across the Hard-Intermediate state, to become unmeasurable
in the soft states (possibly because of statistical limitations). We show
Simbol-X will be able to determine the spectral shape with superb accuracy. As
the high-energy part of the spectrum is relatively less known than the one
below 20 keV, Simbol-X will provide important results that will help out
understanding of the extreme physical conditions in the vicinity of a
stellar-mass black hole.Comment: Proc. "Simbol-X: Focusing on the Hard X-Ray Universe", Paris, 2-5
Dec. 2008, ed. J. Rodriguez and P. Ferrando; 4 pages, 3 figure
Automatic classification system of Raman spectra applied to pigments analysis
Raman spectroscopy is one of the few non-destructive techniques capable of identifying pigments in art works. Raman spectra contain powerful information that can be used to identify unknown compounds and their chemical structures. However, the analysis of spectral data comes with some difficulties, and therefore the spectral interpretation is not straightforward. Sometimes, there are very little differences in the spectral data concerning to specific identification objectives, for instance, in polymorphic discrimination or in the discrimination of natural and synthetic forms of certain pigments. Moreover, this discrimination is often performed manually so that the process can be repetitive, subjective and particularly time-consuming. The result is an increasing motivation to automate the identification process involved in the classification of pigments in paint. In this paper, we propose a system to automatically classify the spectral data into specific and well-known classes, i.e. reference classes. The proposal is based on a combination of chemometric techniques, which provides a powerful way to achieve spectral separability so that it is possible to discriminate between very similar spectra in an automatic way. In this regard, a decision-making algorithm was specifically developed to select the corresponding reference class with no user input, which was successfully validated using simulated spectra. The implemented methodology was used to classify Raman spectra of pigments commonly present in artist's paints in experimental cases, providing reliable and consistent results. Therefore, the presented system can play a good auxiliary role in the analysts' endpoint classification.Peer ReviewedPostprint (author's final draft
Vacuum type I spacetimes and aligned Papapetrou fields: symmetries
We analyze type I vacuum solutions admitting an isometry whose Killing
2--form is aligned with a principal bivector of the Weyl tensor, and we show
that these solutions belong to a family of type I metrics which admit a group
of isometries. We give a classification of this family and we study the
Bianchi type for each class. The classes compatible with an aligned Killing
2--form are also determined. The Szekeres-Brans theorem is extended to non
vacuum spacetimes with vanishing Cotton tensor.Comment: 19 pages; a reference adde
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