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

Kinematics of a Spacetime with an Infinite Cosmological Constant

A solution of the sourceless Einstein's equation with an infinite value for the cosmological constant \Lambda is discussed by using Inonu-Wigner contractions of the de Sitter groups and spaces. When \Lambda --> infinity, spacetime becomes a four-dimensional cone, dual to Minkowski space by a spacetime inversion. This inversion relates the four-cone vertex to the infinity of Minkowski space, and the four-cone infinity to the Minkowski light-cone. The non-relativistic limit c --> infinity is further considered, the kinematical group in this case being a modified Galilei group in which the space and time translations are replaced by the non-relativistic limits of the corresponding proper conformal transformations. This group presents the same abstract Lie algebra as the Galilei group and can be named the conformal Galilei group. The results may be of interest to the early Universe Cosmology.Comment: RevTex, 7 pages, no figures. Presentation changes, including a new Title. Version to appear in Found. Phys. Let

Wheel–rail contact formulation for analyzing the lateral train–structure dynamic interaction

A wheel-rail contact formulation for analyzing the train-structure nonlinear interaction that takes into account the wheel and rail geometry is proposed. Most of the existing methods treat the contact forces as external forces, whereas the present formulation uses a finite element to model the behavior in the contact interface, based on Hertz's theory and Kalker's laws. The equations of motion are complemented with constraint equations that relate the displacements of the vehicle and structure, being the complete system solved directly using an optimized algorithm. The formulation is validated with experimental data from a test performed on a rolling stock plant

Cytotoxicity of triterpenoids-enriched extracts from bark of Eucalyptus nitens against colorectal HCT116 cancer cells

Eucalyptus nitens crops are used in Portugal mainly by the pulp and paper industries, producing substantial bark residues with no added value use [1]. They can, however, be an interesting source of bioactive triterpenic compounds. Here, a lipophilic crude extract (CE) from bark of E. nitens prepared with dichloromethane [1] with about 70% (w/w) of triterpenoids, and a fraction of this (F2) more enriched in triterpenoids (93% w/w), as well as their main compounds betulinic acid (BiA) and betulonic acid (BoA), were used to determine their potential cytotoxicity against the colorectal HCT116 cancer cells. After 48h of incubation, the extracts/compounds inhibited significantly cell growth in a concentration-dependent manner (assessed by the MTT assay), with a GI50 s of 1.3 µg/mL and 2.2 µg/mL for F2 and CE extracts, respectively, and of 0.8µM and 3.9µM for BoA and BiA, respectively. The inhibition of cell growth was shown to be dependent on both the arrest of cell cycle at the G2/M phase, and the induction of cell death (assessed by PI staining). At the higher concentrations tested (up to 25µM), apoptosis was the major contributor to the observed cell death, and that was associated with JNK activation. Using the JNK inhibitor SP600125 and the pan-caspase inhibitor z-VAD, apoptosis induced by the extracts/compounds was shown to be dependent on JNK and caspases activation. At intermediate concentrations of extracts/compounds, a delayed and non-apoptotic type of cell death was present, which was associated with a significant activation of AMPK and a decrease of p53 levels. Altogether, these results demonstrate that the wasted bark of E. nitens can be used as a potential source of interesting cytotoxic natural triterpenoids against cancer cells

Very special relativity as relativity of dark matter: the Elko connection

In the very special relativity (VSR) proposal by Cohen and Glashow, it was pointed out that invariance under HOM(2) is both necessary and sufficient to explain the null result of the Michelson-Morely experiment. It is the quantum field theoretic demand of locality, or the requirement of P, T, CP, or CT invariance, that makes invariance under the Lorentz group a necessity. Originally it was conjectured that VSR operates at the Planck scale; we propose that the natural arena for VSR is at energies similar to the standard model, but in the dark sector. To this end we provide an ab initio spinor representation invariant under the SIM(2) avatar of VSR and construct a mass dimension one fermionic quantum field of spin one half. This field turns out to be a very close sibling of Elko and it exhibits the same striking property of intrinsic darkness with respect to the standard model fields. In the new construct, the tension between Elko and Lorentz symmetries is fully resolved. We thus entertain the possibility that the symmetries underlying the standard model matter and gauge fields are those of Lorentz, while the event space underlying the dark matter and the dark gauge fields supports the algebraic structure underlying VSR.Comment: 19 pages. Section 5 is new. Published version (modulo a footnote, and a corrected typo

A nonlinear vehicle-structure interaction methodology for the assessment of the train running safety

A nonlinear vehicle-structure interaction methodology for the assessment of the train running safety is proposed in this article. The contact formulation between wheel and rail consists in three main steps: the geometrical problem, where the contact point position is detected; the normal contact problem, in which the forces are determined based on the Hertz theory, and the tangential contact problem, where the creep forces are calculated using the rolling friction laws proposed by Kalker. The behavior in the contact interface is reproduced by a contact element developed for this problem. Constraint equations that relate the displacements of the vehicle and structure are imposed using a direct method. The formulation is validated using results of an experimental test performed in a rolling stock test plant of the Railway Technical Research Institute in Japa

A three dimensional train-structure interaction methodology: Experimental validation

A wheel-rail contact method for analyzing the train-structure nonlinear interaction that takes into account the wheel and rail geometry is proposed in this article. The presented formulation is divided into three main parts: 1) the geometric problem consisting of the detection of the contact point and the calculation of all the geometric variables needed for determining the contact forces; 2) the normal contact problem in which the forces are determined based on the Hertz nonlinear theory; 3) the tangential contact problem in which the forces are calculated using the rolling friction laws proposed by Kalker. Most of the existing methods treat the contact forces in the normal and tangential directions as external forces, whereas the present formulation uses a contact element that takes into account the constitutive behaviour in the contact interface. The constraint equations that relate the displacements of the vehicle and structure are imposed using a direct method. The proposed method is validated using the results obtained in an experimental test consisting of a railroad car running over a rolling stock plant subjected to a lateral deviation