Fresnel coefficients as hyperbolic rotations

We describe the action of a plane interface between two semi-infinite media in terms of a transfer matrix. We find a remarkably simple factorization of this matrix, which enables us to express the Fresnel coefficients as a hyperbolic rotation.Comment: 6 pages, 3 figure

Iwasawa Effects in Multi-layer Optics

There are many two-by-two matrices in layer optics. It is shown that they can be formulated in terms of a three-parameter group whose algebraic property is the same as the group of Lorentz transformations in a space with two space-like and one time-like dimensions, or the $Sp(2)$ group which is a standard theoretical tool in optics. Among the interesting mathematical properties of this group, the Iwasawa decomposition drastically simplifies the matrix algebra under certain conditions, and leads to a concise expression for the S-matrix for transmitted and reflected rays. It is shown that the Iwasawa effect can be observed in multi-layer optics, and a sample calculation of the S-matrix is given.Comment: RevTex 10 pages including 1 psfi

Constructing Fresnel reflection coefficients by ruler and compass

A simple and intuitive geometical method to analyze Fresnel formulas is presented. It applies to transparent media and is valid for perpendicular and parallel polarizations. The approach gives a graphical characterization particularly simple of the critical and Brewster angles. It also provides an interpretation of the relation between the reflection coefficients for both basic polarizations as a symmetry in the plane

Modeling TiO2/UV–vis bacterial inactivation: Useful tools for reactor optimization and design

Heterogeneous photocatalysis applying TiO2 based catalysts has been widely studied for removing inorganic and organic compounds from water and for bacterial inactivation. This available and low-cost catalyst has demonstrated to be effective in the removal of organic pollutants and inactivation of pathogenic bacteria from water. The design of proper types of industrial-scale photoreactors has not been yet successfully implemented, probably due to the conceptual complexity of modeling this process in real wastewater. As a result, TiO2 based photocatalysis is still considered an effective but energetic-inefficient process. In this work, Escherichia coli (gram-positive) and Enterococcus sp (gram-negative) were selected for studying the kinetics of TiO2 photocatalysis. Since several approaches, such as fist-order kinetics, are not truly representative of the bacterial inactivation process, the experimental data were fitted to different mathematical models, such as Gompertz model, which has demonstrated to describe the process properly. Moreover, the effect of the main variables of the process in the inactivation kinetic constant of the Gompertz model has ben studied. More precisely, light intensity, water matrix, catalyst concentration and bacteria have been under study and their effect has been included in the kinetic equation. Finally, operational and construction parameters of a 20 m3/d annular photoreactor for bacterial inactivation has been successfully optimized applying the proposed kinetic model

In-situ preparation of a highly accessible Pt/CNF catalytic layer on metallic microchannel reactors. Application to the SELOX reaction

A general method to prepare a catalytic coating on the surface of stainless steel microreactors has been developed. The catalytic support consists of a layer of randomly oriented, highly accessible carbon nanofibers (CNFs), directly grown on the surface of the channels by chemical vapor deposition (CVD) of ethanol. These CNFs are functionalized to acquire a positive charge before a solution containing metallic nanoparticles (Pt) is flown through the channels. The nanoparticles adhere to the surface of the CNFs thanks to electrostatic interactions. This process is carried out in-situ and the method can be easily adapted to larger scale production. These catalyst-coated microchannel reactors have been tested in the selective oxidation (SELOX) of CO in the presence of H2. The results were compared to those obtained in a conventional fixed bed reactor packed with Pt/CNTs. The microreactor clearly outperformed the fixed bed reactor at the same space velocity (WSHV = 2220 l/h gPt),), achieving total CO conversion at temperatures 50ºC lower

Glial alterations in human prion diseases

Background: Neuroinflammation has recently been proposed to be a major component of neurodegenerative diseases. The aim of this study was to determine how the interaction between microglia and astroglia, which are the primary immune cell populations in the brain, and pathological prion protein (PrPsc) could influence the development and propagation of this neurodegenerative disease. Because a relevant role for glial response in prion disease has been clearly demonstrated in our previous studies using the natural animal model, a similar approach has been taken here using the natural human model. Methods: A morphological approach has been developed to analyze cerebellar samples from patients with Creutzfeldt-Jakob disease (CJD) in comparison with healthy control cases. Histopathological lesions were assessed, and PrPsc, glial fibrillary acidic protein (GFAP) and reactive microglia were immunolabelled by specific antibodies. Furthermore, co-location studies using confocal microscopy were performed to determine the possible relationships between both types of glial cells in all samples. Results: The results presented in this study support the involvement of both types of glial cells in CJD. Evidence of increased astrocyte and microglia reactivity can be observed in all CJD cases, and a close relationship between the types of glia is demonstrated by co-location studies. Conclusion: Proteinopathies such as Alzheimer, Parkinson, and Huntington diseases, where aberrant proteins spread throughout the brain during disease progression, may share a molecular basis and mechanisms of propagation. Therefore, studies elucidating the interaction between gliosis and prion propagation may be relevant to these other neurodegenerative diseases and may provide new targets for therapeutic intervention

Rotations associated with Lorentz boosts

It is possible to associate two angles with two successive non-collinear Lorentz boosts. If one boost is applied after the initial boost, the result is the final boost preceded by a rotation called the Wigner rotation. The other rotation is associated with Wigner's O(3)-like little group. These two angles are shown to be different. However, it is shown that the sum of these two rotation angles is equal to the angle between the initial and final boosts. This relation is studied for both low-speed and high-speed limits. Furthermore, it is noted that the two-by-two matrices which are under the responsibility of other branches of physics can be interpreted in terms of the transformations of the Lorentz group, or vice versa. Classical ray optics is mentioned as a case in point.Comment: LaTeX, 16 Pages, 4 epsfigure