45 research outputs found
Rotating dust solutions of Einstein's equations with 3-dimensional symmetry groups, Part 3: All Killing fields linearly independent of u^{\alpha} and w^{\alpha}
This is the third and last part of a series of 3 papers. Using the same
method and the same coordinates as in parts 1 and 2, rotating dust solutions of
Einstein's equations are investigated that possess 3-dimensional symmetry
groups, under the assumption that each of the Killing vectors is linearly
independent of velocity and rotation at every point
of the spacetime region under consideration. The Killing fields are found and
the Killing equations are solved for the components of the metric tensor in
every case that arises. No progress was made with the Einstein equations in any
of the cases, and no previously known solutions were identified. A brief
overview of literature on solutions with rotating sources is given.Comment: One missing piece, signaled after eq. (10.7), is added after (10.21).
List of corrections: In (3.7) wrong subscript in vorticity; In (3.10) wrong
subscript in last term of g_{23}; In (4.23) wrong formulae for g_{12} and
g_{22}; In (7.17) missing factor in velocity; In (7.18) one wrong factor in
g_{22}; In (10.9) factor in vorticity; In (10.15) - (10.20) y_0 = 0; In
(10.20) wrong second term in y. The rewriting typos did not influence result
Evolution of polarization orientations in a flat universe with vector perturbations: CMB and quasistellar objects
Various effects produced by vector perturbations (vortical peculiar velocity fields) of a flat Friedmann-Robertson-Walker background are considered. In the presence of this type of perturbations, the polarization vector rotates. A formula giving the rotation angle is obtained and, then, it is used to prove that this angle depends on both the observation direction and the emission redshift. Hence, rotations are different for distinct quasars and also for the cosmic microwave background (CMB) radiation coming along different directions (from distinct points of the last scattering surface). As a result of these rotations, some correlations could appear in an initially random field of quasar polarization orientations. Furthermore, the polarization correlations of the CMB could undergo alterations. Quasars and CMB maps are both considered in this paper. In the case of linear vector modes with very large spatial scales, the maximum rotation angles appear to be of a few degrees for quasars (located at redshifts z<2.6) and a few tenths of degree for the CMB. These last rotations produce contributions to the B mode of the CMB polarization which are too small to be observed with PLANCK (in the near future); however, these contributions are large enough to be observed with the next generation of satellites, which are being designed to detect the small B mode produced by primordial gravitational waves
A Method for Magma Viscosity Assessment by Lava Dome Morphology
Lava domes form when a highly viscous magma erupts on the surface. Several types of lava dome morphology can be distinguished depending on the flow rate and the rheology of magma: obelisks, lava lobes, and endogenic structures. The viscosity of magma nonlinearly depends on the volume fraction of crystals and temperature. Here we present an approach to magma viscosity estimation based on a comparison of observed and simulated morphological forms of lava domes. We consider a two-dimensional axisymmetric model of magma extrusion on the surface and lava dome evolution, and assume that the lava viscosity depends only on the volume fraction of crystals. The crystallization is associated with a growth of the liquidus temperature due to the volatile loss from the magma, and it is determined by the characteristic time of crystal content growth (CCGT) and the discharge rate. Lava domes are modeled using a finite-volume method implemented in Ansys Fluent software for various CCGTs and volcanic vent sizes. For a selected eruption duration a set of morphological shapes of domes (shapes of the interface between lava dome and air) is obtained. Lava dome shapes modeled this way are compared with the observed shape of the lava dome (synthesized in the study by a random modification of one of the calculated shapes). To estimate magma viscosity, the deviation between the observed dome shape and the simulated dome shapes is assessed by three functionals: the symmetric difference, the peak signal-to-noise ratio, and the structural similarity index measure. These functionals are often used in the computer vision and in image processing. Although each functional allows to determine the best fit between the modeled and observed shapes of lava dome, the functional based on the structural similarity index measure performs it better. The viscosity of the observed dome can be then approximated by the viscosity of the modeled dome, which shape fits best the shape of the observed dome. This approach can be extended to three-dimensional case studies to restore the conditions of natural lava dome growth
On the Anisotropy of E0 >= 5.51019 eV Cosmic Rays according to Data of the Pierre Auger Collaboration
The Pierre Auger Collaboration discovered, in a solid angle of radius about
18\degree, a local group of cosmic rays having energies in the region E0 \geq
5.5\times1019 eV and coming from the region of the Gen A radio galaxy, whose
galactic coordinates are lG = 309.5\degree and bG = 19.4\degree. Near it, there
is the Centaur supercluster of galaxies, its galactic coordinates being lG =
302.4\degree and bG = 21.6\degree. It is noteworthy that the Great Attractor,
which may have a direct bearing on the observed picture, is also there
A Method for Magma Viscosity Assessment by Lava Dome Morphology
Abstract: Lava domes form when a highly viscous magma erupts on the surface. Several types of lava dome morphology can be distinguished depending on the flow rate and the rheology of magma: obelisks, lava lobes, and endogenic structures. The viscosity of magma nonlinearly depends on the volume fraction of crystals and temperature. Here we present an approach to magma viscosity estimation based on a comparison of observed and simulated morphological forms of lava domes. We consider a two-dimensional axisymmetric model of magma extrusion on the surface and lava dome evolution, and assume that the lava viscosity depends only on the volume fraction of crystals. The crystallization is associated with a growth of the liquidus temperature due to the volatile loss from the magma, and it is determined by the characteristic time of crystal content growth (CCGT) and the discharge rate. Lava domes are modeled using a finite-volume method implemented in Ansys Fluent software for various CCGTs and volcanic vent sizes. For a selected eruption duration a set of morphological shapes of domes (shapes of the interface between lava dome and air) is obtained. Lava dome shapes modeled this way are compared with the observed shape of the lava dome (synthesized in the study by a random modification of one of the calculated shapes). To estimate magma viscosity, the deviation between the observed dome shape and the simulated dome shapes is assessed by three functionals: the symmetric difference, the peak signal-to-noise ratio, and the structural similarity index measure. These functionals are often used in the computer vision and in image processing. Although each functional allows to determine the best fit between the modeled and observed shapes of lava dome, the functional based on the structural similarity index measure performs it better. The viscosity of the observed dome can be then approximated by the viscosity of the modeled dome, which shape fits best the shape of the observed dome. This approach can be extended to three-dimensional case studies to restore the conditions of natural lava dome growth. © 2021, The Author(s).We are grateful to two anonymous reviewers for their constructive comments. Numerical experiments were carried out on the Uran computing cluster (Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Yekaterinburg). The work was supported by the Russian Science Foundation (project no. 19-17-00027)
Energy and Angular Momentum Densities in a Godel-Type Universe in the Teleparallel Geometry
The main scope of this research consists in evaluating the energy-momentum
(gravitational field plus matter) and gravitational angular momentum densities
in the universe with global rotation, considering the Godel-Obukhov metric. For
this, we use the Hamiltonian formalism of the Teleparallel Equivalent of
General Relativity (TEGR), which is justified for presenting covariant
expressions for the considered quantities. We found that the total energy
density calculated by the TEGR method is in agreement with the results reported
by other authors in the literature using pseudotensors. The result found for
the angular momentum density depends on the rotational parameter as expected.
We also show explicitly the equivalence among the field equations of the TEGR
and Einstein equations (RG), considering a perfect fluid and Godel-Obukhov
metric.Comment: 20 pages, no figures. Revised in view of Referee's comments. Version
to appear in the Gravitation and Cosmolog