An Analytical Expression for the Hubble diagram of supernovae and gamma-ray bursts

A recent paper by Harmut Traunm\"uller shows that the most adequate equation to interpret the observations on magnitude and redshift from 892 type 1a supernovae would be mu = 5 log[(1+z) ln(1+z)] + const. We discuss this result which is exacly the one we have obtained few years ago when postulating a relation between the speed of light and the expansion of the universe. We also compare our analytical result to the conclusion of Marosi who studied 280 supernovae and gamma-ray bursts in the range 0.1014 < z < 8.1. The difference between his results and ours is at worst of 0.3 %.Comment: 7 pages, 1 figur

Generalized composition law from 2x2 matrices

Many results that are difficult can be found more easily by using a generalization in the complex plane of Einstein's addition law of parallel velocities. Such a generalization is a natural way to add quantities that are limited to bounded values. We show how this generalization directly provides phase factors such as the Wigner angle in special relativity and how this generalization is connected in the simplest case with the composition of 2x2 S matrices.Comment: Accepted for publication in Am. J. Phy

Investigation of Ilmenite from Oxygen Carrier Aided Combustion: Sulfur Interactions and Recovery of Elements

Oxygen- Carrier- Aided Combustion (OCAC) is a promising technology for the combustion of solid heterogeneous fuels such as biomass and waste in fluidized-bed (FB) units. In OCAC the conventional bed material silica sand is replaced by an oxygen carrier (OC). Replacing the bed material with an OC has many advantages. It allows the use of heterogeneous fuels, provides a better oxygen distribution inside the combustion chamber and thereby a more even temperature distribution. In this thesis, ilmenite is used as OC bed material.Even though ilmenite has shown to be a promising OC, the higher price per kg of material compared to the traditionally silica sand is a drawback. In fluidized bed units, the attrition of the bed particles and therewith the loss of bed particles as fines in fly ashes leads to the need of a continuous addition of new bed material. At the same time, because of the ash interactions, parts of the bed material are also removed as a waste stream. Combined these two effects result in a large consumption of bed material. For the case of ilmenite, the loss of bed material by both mechanisms can result in significantly higher cost, if compared with the scenario where sand is used as bed material. Thus, ways to prolong the residence time of the bed material in the boiler and its value should be investigated.Biomass which can be used as a renewable source of energy is a fuel which is hard to handle. Notably, its alkali content can cause corrosion of the equipment and increase of maintenance costs. One way to counteract corrosion is through addition of sulfur. The effect of sulfur on ilmenite performance has not been investigated earlier which is one of the main questions of the present work. Furthermore, to increase the value of the ilmenite after its use in boilers, a modified process for the recovery of elements from the ilmenite waste flows has been examined and adapted to already existing process. The work presented in this thesis is based on a two-week campaign which was carried out in the 12 MWth Circulating Fluidized Bed (CFB) semi-industrial unit. During the campaign, sulfur addition was tested. A range of methods were utilized to study the sulfur effect on the bed particles, including use of SEM-EDX and ICP to characterize the obtained samples. Further use of a laboratory scale quartz reactor to mimic oxidizing and reducing conditions was also performed.For waste ilmenite generated during the campaign, digestion of ilmenite samples with sulfuric acid has been carried with the aim of recovering Ti. This work shows that sulfur is captured by the ilmenite particles and is mainly bind to the ash elements and that sulfur can also be released, depending on the redox conditions. This allows for a better management of the composition of used bed material. Furthermore, it was found that the used ilmenite from OCAC can represent an advantage for Ti extraction and recovery due to development of pore and cracks, and due to the natural separation of the Ti and Fe phase occurring under FB combustion conditions

Role of Wood anomalies in optical properties of thin metallic films with a bidimensional array of subwavelength holes

Recents works deal with the optical transmission on arrays of subwavelength holes in a metallic layer deposited on a dielectric substrate. Making the system as realistic as possible, we perform simulations to enlighten the experimental data. This paper proposes an investigation of the optical properties related to the transmission of such devices. Numerical simulations give theoretical results in good agreement with experiment and we observe that the transmission and reflection behaviour correspond to Fano's profile correlated with resonant response of the eigen modes coupled with nonhomogeneous diffraction orders. We thus conclude that the transmission properties observed could conceivably be explained as resulting from resonant Wood's anomalies.Comment: 7 pages, 10 figures, 2 table

Composition law for polarizers

The polarization process when polarizers act on an optical field is studied. We give examples for two kinds of polarizers. The first kind presents an anisotropic absorption - as in a polaroid film - and the second one is based on total reflection at the interface with a birefringent medium. Using the Stokes vector representation, we determine explicitly the trajectories of the wave light polarization during the polarization process. We find that such trajectories are not always geodesics of the Poincar\'e sphere as it is usually thought. Using the analogy between light polarization and special relativity, we find that the action of successive polarizers on the light wave polarization is equivalent to the action of a single resulting polarizer followed by a rotation achieved for example by a device with optical activity. We find a composition law for polarizers similar to the composition law for noncollinear velocities in special relativity. We define an angle equivalent to the relativistic Wigner angle which can be used to quantify the quality of two composed polarizers.Comment: 23 pages, 9 figures, accepted for publication in Physical Review

Berry Phase and Traversal Time in Asymmetric Graphene Structures

The Berry phase and the group-velocity-based traversal time have been calculated for an asymmetric non-contacted or contacted graphene structure, and significant differences have been observed compared to semiconductor heterostructures. These differences are related to the specific, Dirac-like evolution law of charge carriers in graphene, which introduces a new type of asymmetry. When contacted with electrodes, the symmetry of the Dirac equation is broken by the Schrodinger-type electrons in contacts, so that the Berry phase and traversal time behavior in contacted and non-contacted graphene differ significantly