55,647 research outputs found
Gravitation and the Local Symmetry Group of Spacetime
According to general relativity, the interaction of a matter field with
gravitation requires the simultaneous introduction of a tetrad field, which is
a field related to translations, and a spin connection, which is a field
assuming values in the Lie algebra of the Lorentz group. These two fields,
however, are not independent. By analyzing the constraint between them, it is
concluded that the relevant local symmetry group behind general relativity is
provided by the Lorentz group. Furthermore, it is shown that the minimal
coupling prescription obtained from the Lorentz covariant derivative coincides
exactly with the usual coupling prescription of general relativity. Instead of
the tetrad, therefore, the spin connection is to be considered as the
fundamental field representing gravitation.Comment: 8 pages, no figures. Some signs and references corrected; version to
appear in Int. J. Theor. Phy
The whole mesh Deformation Model for 2D and 3D image segmentation
In this paper we present a novel approach for image segmentation using Active Nets and Active Volumes. Those solutions are based on the Deformable Models, with slight difference in the method for describing the shapes of interests - instead of using a contour or a surface they represented the segmented objects with a mesh structure, which allows to describe not only the surface of the objects but also to model their interiors. This is obtained by dividing the nodes of the mesh in two categories, namely internal and external ones, which will be responsible for two different tasks. In our new approach we propose to negate this separation and use only one type of nodes. Using that assumption we manage to significantly shorten the time of segmentation while maintaining its quality
Dynamics of molecular nanomagnets in time-dependent external magnetic fields: Beyond the Landau-Zener-St\"{u}ckelberg model
The time evolution of the magnetization of a magnetic molecular crystal is
obtained in an external time-dependent magnetic field, with sweep rates in the
kT/s range. We present the 'exact numerical' solution of the time dependent
Schr\"{o}dinger equation, and show that the steps in the hysteresis curve can
be described as a sequence of two-level transitions between adiabatic states.
The multilevel nature of the problem causes the transition probabilities to
deviate significantly from the predictions of the Landau-Zener-St\"{u}ckelberg
model. These calculations allow the introduction of an efficient approximation
method that accurately reproduces the exact results. When including phase
relaxation by means of an appropriate master equation, we observe an interplay
between coherent dynamics and decoherence. This decreases the size of the
magnetization steps at the transitions, but does not modify qualitatively the
physical picture obtained without relaxation.Comment: 8 pages, 7 figure
Symplectic matrices with predetermined left eigenvalues
We prove that given four arbitrary quaternion numbers of norm 1 there always
exists a symplectic matrix for which those numbers are left
eigenvalues. The proof is constructive. An application to the LS category of
Lie groups is given.Comment: 7 page
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