Geometric Algebras and Extensors

This is the first paper in a series (of four) designed to show how to use geometric algebras of multivectors and extensors to a novel presentation of some topics of differential geometry which are important for a deeper understanding of geometrical theories of the gravitational field. In this first paper we introduce the key algebraic tools for the development of our program, namely the euclidean geometrical algebra of multivectors Cl(V,G_{E}) and the theory of its deformations leading to metric geometric algebras Cl(V,G) and some special types of extensors. Those tools permit obtaining, the remarkable golden formula relating calculations in Cl(V,G) with easier ones in Cl(V,G_{E}) (e.g., a noticeable relation between the Hodge star operators associated to G and G_{E}). Several useful examples are worked in details fo the purpose of transmitting the "tricks of the trade".Comment: This paper (to appear in Int. J. Geom. Meth. Mod. Phys. 4 (6) 2007) is an improved version of material appearing in math.DG/0501556, math.DG/0501557, math.DG/050155

Ediacaran Obduction of a Fore-Arc Ophiolite in SW Iberia: A Turning Point in the Evolving Geodynamic Setting of Peri- Gondwana

The Calzadilla Ophiolite is an ensemble of mafic and ultramafic rocks that represents the transition between lower crust and upper mantle of a Cadomian (peri-Gondwanan) fore arc. Mapping and structural analysis of the ophiolite demonstrates that it was obducted in latest Ediacaran times, because the Ediacaran-Early Cambrian sedimentary series (Malcocinado Formation) discordantly covers it. The ophiolite and emplacement-related structures are affected by Variscan deformation (Devonian-Carboniferous), which includes SW verging overturned folds (D1) and thrusts (D2), upright folds (D3), extensional faults (D4), and later faults (D5). These phases of deformation are explained in the context of Variscan tectonics as the result of the progressive collision between Gondwana and Laurussia. Qualitative unstraining of Variscan deformation reveals the primary geometry of Ediacaran-Cambrian structures and uncovers the generation of east verging thrusts as responsible for the primary obduction of the Calzadilla Ophiolite. Restoration of planar and linear structures associated with this event indicates an Ediacaran, east directed obduction of the ophiolite, that is, emplacement of the Cadomian fore arc onto inner sections of the northern margin of Gondwana. According to regional data, the obduction separates two extension-dominated stages in the tectonic evolution of the African margin of northern Gondwana preserved in southern Europe. Preobduction extension brought about the onset and widening of fore-arc and back-arc basins in the external part of the continent, while postobduction extension facilitated the formation of extensional migmatitic domes, an oceanward migration of back-arc spreading centers across peri-Gondwana, and the eventual opening of a major basin such as the Rheic Ocean

The influence of magnetic field geometry on magnetars X-ray spectra

Nowadays, the analysis of the X-ray spectra of magnetically powered neutron stars or magnetars is one of the most valuable tools to gain insight into the physical processes occurring in their interiors and magnetospheres. In particular, the magnetospheric plasma leaves a strong imprint on the observed X-ray spectrum by means of Compton up-scattering of the thermal radiation coming from the star surface. Motivated by the increased quality of the observational data, much theoretical work has been devoted to develop Monte Carlo (MC) codes that incorporate the effects of resonant Compton scattering in the modeling of radiative transfer of photons through the magnetosphere. The two key ingredients in this simulations are the kinetic plasma properties and the magnetic field (MF) configuration. The MF geometry is expected to be complex, but up to now only mathematically simple solutions (self-similar solutions) have been employed. In this work, we discuss the effects of new, more realistic, MF geometries on synthetic spectra. We use new force-free solutions in a previously developed MC code to assess the influence of MF geometry on the emerging spectra. Our main result is that the shape of the final spectrum is mostly sensitive to uncertain parameters of the magnetospheric plasma, but the MF geometry plays an important role on the angle-dependence of the spectra.Comment: 6 pages, 4 figures To appear in Proceedings of II Iberian Nuclear Astrophysics Meeting held in Salamanca, September 22-23, 201

Quark Cluster Model Study of Isospin-Two Dibaryons

Based on a quark cluster model for the non-strange sector that reproduces reasonably well the nucleon-nucleon system and the excitation of the $\Delta$ isobar, we generate a nucleon-$\Delta$ interaction and present the predictions for the several isospin two channels. The only attractive channels are $0^+$ and $0^-$, but not attractive enough to generate a resonance. If a resonance is artificially generated and is required to have the observed experimental mass, then our model predicts a width that agrees with the experimental result.Comment: 12 pages, 5 poscript figures available under request. To appear in Phys. Rev.

On the void explanation of the Cold Spot

The integrated Sachs-Wolfe (ISW) contribution induced on the cosmic microwave background by the presence of a supervoid as the one detected by Szapudi et al. (2015) is reviewed in this letter in order to check whether it could explain the Cold Spot (CS) anomaly. Two different models, previously used for the same purpose, are considered to describe the matter density profile of the void: a top hat function and a compensated profile produced by a Gaussian potential. The analysis shows that, even enabling ellipticity changes or different values for the dark-energy equation of state parameter $\omega$, the ISW contribution due to the presence of the void does not reproduce the properties of the CS. Finally, the probability of alignment between the void and the CS is also questioned as an argument in favor of a physical connection between these two phenomena

Poisson approximations for the Ising model

A $d$-dimensional Ising model on a lattice torus is considered. As the size $n$ of the lattice tends to infinity, a Poisson approximation is given for the distribution of the number of copies in the lattice of any given local configuration, provided the magnetic field $a=a(n)$ tends to $-\infty$ and the pair potential $b$ remains fixed. Using the Stein-Chen method, a bound is given for the total variation error in the ferromagnetic case.Comment: 25 pages, 1 figur