On Clifford Subalgebras, Spacetime Splittings and Applications

Z2-gradings of Clifford algebras are reviewed and we shall be concerned with an alpha-grading based on the structure of inner automorphisms, which is closely related to the spacetime splitting, if we consider the standard conjugation map automorphism by an arbitrary, but fixed, splitting vector. After briefly sketching the orthogonal and parallel components of products of differential forms, where we introduce the parallel [orthogonal] part as the space [time] component, we provide a detailed exposition of the Dirac operator splitting and we show how the differential operator parallel and orthogonal components are related to the Lie derivative along the splitting vector and the angular momentum splitting bivector. We also introduce multivectorial-induced alpha-gradings and present the Dirac equation in terms of the spacetime splitting, where the Dirac spinor field is shown to be a direct sum of two quaternions. We point out some possible physical applications of the formalism developed.Comment: 22 pages, accepted for publication in International Journal of Geometric Methods in Modern Physics 3 (8) (2006

The Hamilton-Jacobi Approach to Teleparallelism

We intend to analyse the constraint structure of Teleparallelism employing the Hamilton-Jacobi formalism for singular systems. This study is conducted without using an ADM 3+1 decomposition and without fixing time gauge condition. It can be verified that the field equations constitute an integrable system.Comment: 12 pages, no figur

Absolute Calibration of the Radio Astronomy Flux Density Scale at 22 to 43 GHz Using Planck

The Planck mission detected thousands of extragalactic radio sources at frequencies from 28 to 857 GHz. Planck's calibration is absolute (in the sense that it is based on the satellite's annual motion around the Sun and the temperature of the cosmic microwave background), and its beams are well characterized at sub-percent levels. Thus Planck's flux density measurements of compact sources are absolute in the same sense. We have made coordinated VLA and ATCA observations of 65 strong, unresolved Planck sources in order to transfer Planck's calibration to ground-based instruments at 22, 28, and 43 GHz. The results are compared to microwave flux density scales currently based on planetary observations. Despite the scatter introduced by the variability of many of the sources, the flux density scales are determined to 1-2% accuracy. At 28 GHz, the flux density scale used by the VLA runs 3.6% +- 1.0% below Planck values; at 43 GHz, the discrepancy increases to 6.2% +- 1.4% for both ATCA and the VLA.Comment: 16 pages, 4 figures and 4 table

Angular Momentum of the BTZ Black Hole in the Teleparallel Geometry

We carry out the Hamiltonian formulation of the three- dimensional gravitational teleparallelism without imposing the time gauge condition, by rigorously performing the Legendre transform. Definition of the gravitational angular momentum arises by suitably interpreting the integral form of the constraint equation Gama^ik=0 as an angular momentum equation. The gravitational angular momentum is evaluated for the gravitational field of a rotating BTZ black hole.Comment: 17 pages, no figures, v2: some misprints corrected, Ref.s added, Eq.s revised, submitted to General Relativity and Gravitatio

Removing zero Lyapunov exponents in volume-preserving flows

Baraviera and Bonatti proved that it is possible to perturb, in the c^1 topology, a volume-preserving and partial hyperbolic diffeomorphism in order to obtain a non-zero sum of all the Lyapunov exponents in the central direction. In this article we obtain the analogous result for volume-preserving flows.Comment: 10 page

Using zeros of the canonical partition function map to detect signatures of a Berezinskii-Kosterlitz-Thouless transition

Using the two dimensional $XY-(S(O(3))$ model as a test case, we show that analysis of the Fisher zeros of the canonical partition function can provide signatures of a transition in the Berezinskii-Kosterlitz-Thouless ($BKT$) universality class. Studying the internal border of zeros in the complex temperature plane, we found a scenario in complete agreement with theoretical expectations which allow one to uniquely classify a phase transition as in the $BKT$ class of universality. We obtain $T_{BKT}$ in excellent accordance with previous results. A careful analysis of the behavior of the zeros for both regions $\mathfrak{Re}(T) \leq T_{BKT}$ and $\mathfrak{Re}(T) > T_{BKT}$ in the thermodynamic limit show that $\mathfrak{Im}(T)$ goes to zero in the former case and is finite in the last one

Electromagnetic Fields of Slowly Rotating Magnetized Gravastars

We study the dipolar magnetic field configuration and present solutions of Maxwell equations in the internal background spacetime of a a slowly rotating gravastar. The shell of gravastar where magnetic field penetrated is modeled as sphere consisting of perfect highly magnetized fluid with infinite conductivity. Dipolar magnetic field of the gravastar is produced by a circular current loop symmetrically placed at radius $a$ at the equatorial plane.Comment: 5 pages, 2 figures, accepted for publication to Mod. Phys. Lett.

Chemical Evolution of the Galaxy Based on the Oscillatory Star Formation History

We model the star formation history (SFH) and the chemical evolution of the Galactic disk by combining an infall model and a limit-cycle model of the interstellar medium (ISM). Recent observations have shown that the SFH of the Galactic disk violently variates or oscillates. We model the oscillatory SFH based on the limit-cycle behavior of the fractional masses of three components of the ISM. The observed period of the oscillation ($\sim 1$ Gyr) is reproduced within the natural parameter range. This means that we can interpret the oscillatory SFH as the limit-cycle behavior of the ISM. We then test the chemical evolution of stars and gas in the framework of the limit-cycle model, since the oscillatory behavior of the SFH may cause an oscillatory evolution of the metallicity. We find however that the oscillatory behavior of metallicity is not prominent because the metallicity reflects the past integrated SFH. This indicates that the metallicity cannot be used to distinguish an oscillatory SFH from one without oscillations.Comment: 21 pages LaTeX, to appear in Ap

Imaging 3D seismic velocity along the seismogenic zone of Algarve region (southern Portugal)

The present seismic tomographic study is focused around Algarve region, in South of Portugal. To locate the seismic events and find the local velocity structure of epicentral area, the P and S arrival times at 38 stations are used. The data used in this study were obtained during the Algarve campaign which worked from January/2006 to July/2007. The preliminary estimate of origin times and hypocentral coordinates are determined by the Hy- poinverse program. Linearized inversion procedure was applied to comprise the following two steps: 1) finding the minimum 1D velocity model using Velest and 2) simultaneous relocation of hypocenters and determination of local velocity structure. The velocity model we have reached is a 10 layer model which gave the lowest RMS, after several runnings of eight different velocity models that we used “a priori”. The model parameterization assumes a continuous velocity field between 4.5 km/s and 7.0 km/s until 30 km depth. The earth structure is represented in 3D by velocity at discrete points, and velocity at any intervening point is determined by linear interpolation among the surrounding eight grid points. A preliminary analysis of the resolution capabilities of the dataset, based on the Derivative Weight Sum (DWS) distribution, shows that the velocity structure is better resolved in the West part of the region between the surface to15 km. The resulting tomographic image has a prominent low-velocity anomaly that shows a maximum decrease in P-wave velocity in the first 12 kms in the studied region. We also identified the occurrence of local seismic events of reduced magnitude not catalogued, in the neighbourhood of Almodôvar (low Alentejo). The spatial distribution of epicentres defines a NE-SW direction that coincides with the strike of the mapped geological faults of the region and issued from photo-interpretation. Is still expectable to refine the seismicity of the region of Almodôvar and establish more rigorously its role in the seismotectonic picture of the region. This work is expected to produce a more detailed knowledge of the structure of the crust over the region of Algarve, being able to identify seismogenic zones, potentially generators of significant seismic events and also the identification of zones of active faults