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

Cosmic microwave background constraints on the epoch of reionization

We use a compilation of cosmic microwave anisotropy data to constrain the epoch of reionization in the Universe, as a function of cosmological parameters. We consider spatially-flat cosmologies, varying the matter density $\Omega_0$ (the flatness being restored by a cosmological constant), the Hubble parameter $h$ and the spectral index $n$ of the primordial power spectrum. Our results are quoted both in terms of the maximum permitted optical depth to the last-scattering surface, and in terms of the highest allowed reionization redshift assuming instantaneous reionization. For critical-density models, significantly-tilted power spectra are excluded as they cannot fit the current data for any amount of reionization, and even scale-invariant models must have an optical depth to last scattering of below 0.3. For the currently-favoured low-density model with $\Omega_0 = 0.3$ and a cosmological constant, the earliest reionization permitted to occur is at around redshift 35, which roughly coincides with the highest estimate in the literature. We provide general fitting functions for the maximum permitted optical depth, as a function of cosmological parameters. We do not consider the inclusion of tensor perturbations, but if present they would strengthen the upper limits we quote.Comment: 9 pages LaTeX file with ten figures incorporated (uses mn.sty and epsf). Corrects some equation typos, superseding published versio

A STEP BY STEP DESIGN GUIDE FOR A SOLAR WATER HEATING SYSTEM CONSIDERING THERMAL LOSSES

A clear and direct guide for the design of a solar heating system is presented herein, focused on industrial applications. This guide focuses on the design of solar water heating systems for nonresidential applications. The importance of considering climatic conditions throughout the year is highlighted herein, along with reliable solar radiation data. Solar heating water systems are essential for the diversification of the Brazilian energy matrix and rationalization of the energy resources available. The system is initially dimensioned without the consideration of losses. Then, the required procedure to calculate thermal losses is described, and it is verified that the main losses occur in solar collectors and storage. After careful consideration of the hot water consumption profile and the results obtained in the calculation of the main thermal losses, the storage volume was doubled to guarantee the satisfaction of energy demands

Vapour reactive distillation process for hydrogen production by hi decomposition from hi-i2-h2o solutions

In this contribution, a sequential and hierarchical approach for the feasibility analysis and the preliminary design of reactive distillation columns is extended to systems involving vapour phase chemical reaction and is successfully applied to the HI vapour phase decomposition to produce H2. The complex phase and physico chemical behaviour of the quaternary HI-H2-I2-H2O system is represented by the Neumann’s thermodynamic model and instantaneous vapour phase chemical equilibrium is assumed. Then, from minimal information concerning the physicochemical properties of the system, three successive steps lead to the design of the unit and the specification of its operating conditions: the feasibility analysis, the synthesis and the design step. First, the analysis of reactive condensation curve map method (rCCM), assuming infinite internal liquid and vapour flow rate and infinite reflux ratio, is used to assess the feasibility of the process. It determines the column structure and estimates the attainable compositions. These results are used as inputs data for the synthesis step. Based on the boundary value design method (BVD), considering finite internal liquid and vapour flow rate and finite reflux ratio while neglecting all thermal effects and assuming a constant heat of vaporisation, the synthesis step provides more precise information about the process configuration (minimum reflux ratio, number of theoretical stages, localisation and number of reactive plates, position of the feed plate). Finally, the BVD method results are used to initialise rigorous simulations, based on an equilibrium stage model with energy balance, to estimate the reflux ratio taking into account thermal effect on the process. The resulting design configuration consists in a single feed and entirely reactive distillation column. The column operates under a pressure of 22 bars. The feed of the reactive distillation column, coming from the Bunsen reaction section [xHI=0.10; xI2=0.39 xH2O=0.51], is at its boiling temperature. The residue consists in pure iodine. Water and produced hydrogen are recovered at the distillate. The column operates at a reflux ratio of 5 and is composed of 11 theoretical plates including the reboiler and the partial condenser with the feed at the stage 10 (counted downwards). The obtained HI dissociation yield is 99.6%