Topological Properties from Einstein's Equations?

In this work we propose a new procedure for to extract global information of a space-time. We considered a space-time immersed in a higher dimensional space and we formulate the equations of Einstein through of the Frobenius conditions to immersion. Through of an algorithm and the implementation into algebraic computing system we calculate normal vectors from the immersion to find out the second fundamental form. We make a application for space-time with spherical symmetry and static. We solve the equations of Einstein to the vacuum and we obtain space-times with different topologies.Comment: 7 pages, accepted for publication in Int. J. Mod. Phys.

Embedding Versus Immersion in General Relativity

We briefly discuss the concepts of immersion and embedding of space-times in higher-dimensional spaces. We revisit the classical work by Kasner in which he constructs a model of immersion of the Schwarzschild exterior solution into a six-dimensional pseudo-Euclidean manifold. We show that, from a physical point of view, this model is not entirely satisfactory since the causal structure of the immersed space-time is not preserved by the immersion.Comment: 5 page

Minimal resonances in annular non-Euclidean strips

Differential growth processes play a prominent role in shaping leaves and biological tissues. Using both analytical and numerical calculations, we consider the shapes of closed, elastic strips which have been subjected to an inhomogeneous pattern of swelling. The stretching and bending energies of a closed strip are frustrated by compatibility constraints between the curvatures and metric of the strip. To analyze this frustration, we study the class of "conical" closed strips with a prescribed metric tensor on their center line. The resulting strip shapes can be classified according to their number of wrinkles and the prescribed pattern of swelling. We use this class of strips as a variational ansatz to obtain the minimal energy shapes of closed strips and find excellent agreement with the results of a numerical bead-spring model. Within this class of strips, we derive a condition under which a strip can have vanishing mean curvature along the center line.Comment: 14 pages, 13 figures. Published version. Updated references and added 2 figure

Magnetovac Cylinder to Magnetovac Torus

A method for mapping known cylindrical magnetovac solutions to solutions in torus coordinates is developed. Identification of the cylinder ends changes topology from R1 x S1 to S1 x S1. An analytic Einstein-Maxwell solution for a toroidal magnetic field in tori is presented. The toroidal interior is matched to an asymptotically flat vacuum exterior, connected by an Israel boundary layer.Comment: to appear in Class. Quant. Gra

A note on the computation of geometrically defined relative velocities

We discuss some aspects about the computation of kinematic, spectroscopic, Fermi and astrometric relative velocities that are geometrically defined in general relativity. Mainly, we state that kinematic and spectroscopic relative velocities only depend on the 4-velocities of the observer and the test particle, unlike Fermi and astrometric relative velocities, that also depend on the acceleration of the observer and the corresponding relative position of the test particle, but only at the event of observation and not around it, as it would be deduced, in principle, from the definition of these velocities. Finally, we propose an open problem in general relativity that consists on finding intrinsic expressions for Fermi and astrometric relative velocities avoiding terms that involve the evolution of the relative position of the test particle. For this purpose, the proofs given in this paper can serve as inspiration.Comment: 8 pages, 2 figure

‘Unequal mobilities’ in the Lisbon Metropolitan Area: daily travel choices and private car use

Mobilities have been looked at in increasingly greater depth over the last few decades, posing a growing set of theoretical and methodological problems for urban studies. One of the approaches that are being taken in this field is to consider the relationship between social inequalities and the various different mobility conditions. The present article seeks to show the extent to which mobility behaviours of Lisbon Metropolitan Area residents vary in accordance with a range of inequality variables, such as gender, education, social class, and age, thus generating clearly marked social profiles. Special attention is paid to car use. Statistical analysis of a questionnaire applied to 1,500 residents shows that regular car use is still relatively circumscribed to one social group, to which it offers the advantage of less time spent on daily travel, notwithstanding the increased costs. On the other hand, populations who regularly use public transport are at a disadvantage, spending more of their day travelling from one place to another.info:eu-repo/semantics/publishedVersio

Crystalline Order On Riemannian Manifolds With Variable Gaussian Curvature And Boundary

We investigate the zero temperature structure of a crystalline monolayer constrained to lie on a two-dimensional Riemannian manifold with variable Gaussian curvature and boundary. A full analytical treatment is presented for the case of a paraboloid of revolution. Using the geometrical theory of topological defects in a continuum elastic background we find that the presence of a variable Gaussian curvature, combined with the additional constraint of a boundary, gives rise to a rich variety of phenomena beyond that known for spherical crystals. We also provide a numerical analysis of a system of classical particles interacting via a Coulomb potential on the surface of a paraboloid.Comment: 12 pages, 8 figure

The influence of material density on bipolar charge transport in polymer-based electronic applications

Using a mesoscopic modelling approach, the authors performed computer experiments to study the influence of polymer density on bipolar charge evolution through thin layers of polydiacetylene (PDA) exhibiting specific microstructures. We found that the competition between charge transport, trapping and recombination within the polymer layer leads to several general trends, some of them being non-intuitive, as one varies polymer density. Our results show that polymer density mainly affects current and recombination efficiencies in the absence of defects or impurity states. The overall trends depend both on chain orientation relative to the electrodes and on the strength of the external applied electric field. These results suggest that adequate modelling of charge transport in electronic and optoelectronic devices based on conducting and semiconducting polymers, such as PDA, must include their structure and related key factors at mesoscopic scale. Such models provide the necessary knowledge-base to optimize the polymer film structure for electronic applications.Fundação para a Ciência e a Tecnologia (FCT) – Programa Operacional “Ciência , Tecnologia, Inovação” – POCTI/CTM/41574/2001 e SFRH/BD/11231/2002Comunidade Europeia (CE). Fundo Europeu de Desenvolvimento Regional (FEDER

The Rubiaceae family in the Carrancas Mountain Complex, state of Minas Gerais, southeastern Brazil

Rubiaceae is the fourth largest family of the angiosperms in terms of species diversity worldwide. It is present in all plant physiognomies and occupies various vegetation strata, being one of the most important components of tropical vegetation. It is easily recognized by the opposite leaves, interpetiolar stipules, gamopetalous corolla, and inferior ovary. The main objective of this study was to investigate the diversity of the Rubiaceae in the Carrancas Mountain Complex, Minas Gerais, Brazil. This region encompasses approximately 17,609 km2, extending from the southern border of the state of Minas Gerais, approaching the Itatiaia Plateau, to the Sao Joao del-Rei and Barbacena region, where the Sao Francisco River basin begins. It includes the municipalities of Lavras, Itumirim, Ingaí, Itutinga, Carrancas, and Minduri. Situated in an ecotone between the Atlantic Forest and Cerrado domains, it presents a surface covered by various vegetation types, such as campo rupestre, savannas, open fields, scrublands, seasonal semideciduous forests, riparian or gallery forests, and cloud forests at the higher elevations. A total of 681 herbarium specimens were analysed, most of them deposited at the ESAL herbarium, which holds most of the collections made in the region. In this study, 26 genera and 51 species were recorded. These represent noteworthy 37.7% of the genera and 13.5% of the species of Rubiaceae recorded in Minas Gerais, including 14 endemic species to Brazil. Borreria and Palicourea were the most diverse genera (five species each), followed by Cordiera, Galianthe, and Psychotria (four species each). Therefore, this work enriches the taxonomic knowledge of the Rubiaceae family in the state of Minas Gerais, particularly for the flora of the Carrancas Mountain Complex