Self-similar cosmologies in 5D: spatially flat anisotropic models

In the context of theories of Kaluza-Klein type, with a large extra dimension, we study self-similar cosmological models in 5D that are homogeneous, anisotropic and spatially flat. The "ladder" to go between the physics in 5D and 4D is provided by Campbell-Maagard's embedding theorems. We show that the 5-dimensional field equations $R_{AB} = 0$ determine the form of the similarity variable. There are three different possibilities: homothetic, conformal and "wave-like" solutions in 5D. We derive the most general homothetic and conformal solutions to the 5D field equations. They require the extra dimension to be spacelike, and are given in terms of one arbitrary function of the similarity variable and three parameters. The Riemann tensor in 5D is not zero, except in the isotropic limit, which corresponds to the case where the parameters are equal to each other. The solutions can be used as 5D embeddings for a great variety of 4D homogeneous cosmological models, with and without matter, including the Kasner universe. Since the extra dimension is spacelike, the 5D solutions are invariant under the exchange of spatial coordinates. Therefore they also embed a family of spatially {\it inhomogeneous} models in 4D. We show that these models can be interpreted as vacuum solutions in braneworld theory. Our work (I) generalizes the 5D embeddings used for the FLRW models; (II) shows that anisotropic cosmologies are, in general, curved in 5D, in contrast with FLRW models which can always be embedded in a 5D Riemann-flat (Minkowski) manifold; (III) reveals that anisotropic cosmologies can be curved and devoid of matter, both in 5D and 4D, even when the metric in 5D explicitly depends on the extra coordinate, which is quite different from the isotropic case.Comment: Typos corrected. Minor editorial changes and additions in the Introduction and Summary section

Performance and emissions of an agricultural diesel engine fuelled with different diesel and methyl ester blends

This paper shows the results of an investigation carried out to assess the application of different fuels produced by blending diesel fuel with methyl ester obtained from mixture of 75% (v/v) sunflower oil and 25% (v/v) used cooking oil on a Kubota agricultural indirect injection diesel engine, natural aspirated, and with a rated horsepower of 19.7 kW. Seven fuels, namely diesel fuel; 90:10, 80:20, 70:30, 50:50, 25:75 and 0:100 (%v/v) blends were prepared and tested for the performance of the diesel engine in accordance with the standardised OECD test code 2. The test results showed that the performance of the engine was satisfactory without a significant reduction in power output and torque with blends smaller than 50%. Fuel consumptions with biodiesel were higher than that when fuelled with diesel but differences were not very marked up to 30% blends. As the reduction of the engine thermal efficiency was less than the corresponding reduction in heating value of the different biodiesel blends, the latter resulted in a more complete combustion in comparison with diesel fuel. The oxides of nitrogen (NOx) emissions were found to be reduced as the biodiesel concentration increase, particularly with 70% and 100% blends. The emissions of carbon monoxide (CO) were lower and increased at a lower rate with the oxygen concentration of the exhaust as the biodiesel blends were equal or higher than 50%

Wave-like Solutions for Bianchi type-I cosmologies in 5D

We derive exact solutions to the vacuum Einstein field equations in 5D, under the assumption that (i) the line element in 5D possesses self-similar symmetry, in the classical understanding of Sedov, Taub and Zeldovich, and that (ii) the metric tensor is diagonal and independent of the coordinates for ordinary 3D space. These assumptions lead to three different types of self-similarity in 5D: homothetic, conformal and "wave-like". In this work we present the most general wave-like solutions to the 5D field equations. Using the standard technique based on Campbell's theorem, they generate a large number of anisotropic cosmological models of Bianchi type-I, which can be applied to our universe after the big-bang, when anisotropies could have played an important role. We present a complete review of all possible cases of self-similar anisotropic cosmologies in 5D. Our analysis extends a number of previous studies on wave-like solutions in 5D with spatial spherical symmetry

Eusebi Molera i Bros. Aproximació a la figura d’un vigatà inquiet

Se m’ha demanat que enguany, en aquesta inauguració del curs 1996-1997, parli de la vida i de l’obra de l’insigne vigatà Eusebi Molera i Bros, paradoxalment tan reconeguda al seu país d’adopció i alhora tan poc coneguda i reconeguda a Catalunya, com massa sovint passa, malauradament, amb altres figures decisives de la història. Nascut a Vic el 13 de novembre de 1847 (1846 segons altres fonts), va estudiar al Seminari per després cursar la carrera d’enginyer militar. Va formar part del grup de l’Esbart de Vic, amb els membres del qual va mantenir una estreta relació d’amistat que es va perllongar durant tota la vida, i fou soci actiu del Círcol Literari. Als 25 anys va abandonar la carrera militar i va marxar a Califòrnia, on es va casar amb la filla d’un gran terratinent de Monterrey. Al llarg de la seva dilatada vida va excel·lir en un extens ventall d’activitats professionals entre les quals destaquen les d’enginyer, urbanista, arquitecte, cartògraf, inventor i empresari. Mecenes de les arts i de la ciència, va formar part de les principals institucions acadèmiques i científiques de Califòrnia. Va morir a San Francisco el 14 de gener de 1932 amb els honors i el reconeixement dels estaments públics i privat

An exact self-similar solution for an expanding ball of radiation

We give an exact solution of the $5D$ Einstein equations which in 4D can be interpreted as a spherically symmetric dissipative distribution of matter, with heat flux, whose effective density and pressure are nonstatic, nonuniform, and satisfy the equation of state of radiation. The matter satisfies the usual energy and thermodynamic conditions. The energy density and temperature are related by the Stefan-Boltzmann law. The solution admits a homothetic Killing vector in $5D$, which induces the existence of self-similar symmetry in 4D, where the line element as well as the dimensionless matter quantities are invariant under a simple "scaling" group.Comment: New version expanded and improved. To appear in Int. J. Mod. Phys.

Density functional theory study of the nematic-isotropic transition in an hybrid cell

We have employed the Density Functional Theory formalism to investigate the nematic-isotropic capillary transitions of a nematogen confined by walls that favor antagonist orientations to the liquid crystal molecules (hybrid cell). We analyse the behavior of the capillary transition as a function of the fluid-substrate interactions and the pore width. In addition to the usual capillary transition between isotropic-like to nematic-like states, we find that this transition can be suppressed when one substrate is wet by the isotropic phase and the other by the nematic phase. Under this condition the system presents interface-like states which allow to continuously transform the nematic-like phase to the isotropic-like phase without undergoing a phase transition. Two different mechanisms for the disappearance of the capillary transition are identified. When the director of the nematic-like state is homogeneously planar-anchored with respect to the substrates, the capillary transition ends up in a critical point. This scenario is analogous to the observed in Ising models when confined in slit pores with opposing surface fields which have critical wetting transitions. When the nematic-like state has a linearly distorted director field, the capillary transition continuously transforms in a transition between two nematic-like states.Comment: 31 pages, 10 figures, submitted to J. Chem. Phy