Proposal of a Transmission Line Model Based on Lumped Elements: An Analytic Solution

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Estudo de titanatos nanoestruturados obtidos por tratamento hidrotérmico de óxido de titânio em meio alcalino

TiTanate NanoTubes (TTNT) were synthesized by hydrothermal alkali treatment of TiO2 anatase followed by repeated washings with distinct degrees of proton exchange. TTNT samples with different sodium contents were characterized, as synthesized and after heattreatment (200-800ºC), by X-ray diffraction, scanning and transmission electron microscopy, electron diffraction, thermal analysis, nitrogen adsorption and spectroscopic techniques like FTIR and UV-Vis diffuse reflectance. It was demonstrated that TTNTs consist of trititanate structure with general formula NaxH2−xTi3O7·nH2O, retaining interlayer water in its multiwalled structure. The removal of sodium reduces the amount of water and contracts the interlayer space leading, combined with other factors, to increased specific surface area and mesopore volume. TTNTs are mesoporous materials with two main contributions: pores smaller than 10 nm due to the inner volume of nanotubes and larger pores within 5-60 nm attributed to the interparticles space. Chemical composition and crystal structure of TTNTs do not depend on the average crystal size of the precursor TiO2-anatase, but this parameter affects significantly the morphology and textural properties of the nanostructured product. Such dependence has been rationalized using a dissolution-recrystallization mechanism, which takes into account the dissolution rate of the starting anatase and its influence on the relative rates of growth and curving of intermediate nanosheets. The thermal stability of TTNT is defined by the sodium content and in a lower extent by the crystallinity of the starting anatase. It has been demonstrated that after losing interlayer water within the range 100-200ºC, TTNT transforms, at least partially, into an intermediate hexatitanate NaxH2−xTi6O13 still retaining the nanotubular morphology. Further thermal transformation of the nanostructured tri- and hexatitanates occurs at higher or lower temperature and follows different routes depending on the sodium content in the structure. At high sodium load (water washed samples) they sinter and grow towards bigger crystals of Na2Ti3O7 and Na2Ti6O13 in the form of rods and ribbons. In contrast, protonated TTNTs evolve to nanotubes of TiO2(B), which easily convert to anatase nanorods above 400ºC. Besides hydroxyls and Lewis acidity typical of titanium oxides, TTNTs show a small contribution of protonic acidity capable of coordinating with pyridine at 150ºC, which is lost after calcination and conversion into anatase. The isoeletric point of TTNTs was measured within the range 2.5-4.0, indicating behavior of a weak acid. Despite displaying semiconductor characteristics exhibiting typical absorption in the UV-Vis spectrum with estimated bandgap energy slightly higher than that of its TiO2 precursor, TTNTs showed very low performance in the photocatalytic degradation of cationic and anionic dyes. It was concluded that the basic reason resides in its layered titanate structure, which in comparison with the TiO2 form would be more prone to the so undesired electron-hole pair recombination, thus inhibiting the photooxidation reactions. After calcination of the protonated TTNT into anatase nanorods, the photocatalytic activity improved but not to the same level as that exhibited by its precursor anatase

Degradação eletroquímica de benzeno, tolueno e xileno via oxidação eletroquímica utilizando eletrodo Ti/Pt

This work is directed to the treatment of organic compounds present in produced water from oil using electrochemical technology. The water produced is a residue of the petroleum industry are difficult to treat , since this corresponds to 98 % effluent from the effluent generated in the exploration of oil and contains various compounds such as volatile hydrocarbons (benzene, toluene, ethylbenzene and xylene), polycyclic aromatic hydrocarbons (PAHs), phenols, carboxylic acids and inorganic compounds. There are several types of treatment methodologies that residue being studied, among which are the biological processes, advanced oxidation processes (AOPs), such as electrochemical treatments electrooxidation, electrocoagulation, electrocoagulation and eletroredution. The electrochemical method is a method of little environmental impact because instead of chemical reagents uses electron through reactions of oxide-reducing transforms toxic substances into substances with less environmental impact. Thus, this paper aims to study the electrochemical behavior and elimination of the BTX (benzene, toluene and xylene) using electrode of Ti/Pt. For the experiment an electrochemical batch system consists of a continuous source, anode Ti/Pt was used, applying three densities of current (1 mA/cm2, 2,5 mA/cm2 and 5 mA/cm2). The synthetic wastewater was prepared by a solution of benzene, toluene and xylene with a concentration of 5 ppm, to evaluate the electrochemical behavior by cyclic voltammetry and polarization curves, even before assessing the removal of these compounds in solution by electrochemical oxidation. The behavior of each of the compounds was evaluated by the use of electrochemical techniques indicate that each of the compounds when evaluated by cyclic voltammetry showed partial oxidation behavior via adsorption to the surface of the Ti/Pt electrode. The adsorption of each of the present compounds depends on the solution concentration but there is the strong adsorption of xylene. However, the removal was confirmed by UV-Vis, and analysis of total organic carbon (TOC), which showed a percentage of partial oxidation (19,8 % - 99,1 % TOC removed), confirming the electrochemical behavior already observed in voltammetry and cyclic polarization curves

Heaviside generalized functions and shock waves for a Burger kind equation

The purpose of the work is to study the existence and nonexistence of shock wave solutions for the Burger equations. The study is developed in the context of Colombeau's theory of generalized functions (GFs). This study uses the equality in the strict sense and the weak equality of GFs. The shock wave solutions are given in terms of GFs that have the Heaviside function, in x and ( x, t) variables, as macroscopic aspect. This means that solutions are sought in the form of sequences of regularizations to the Heaviside function, in R-n and R-n x R, in the distributional limit sense.

Composition and invertibility for a class of generalized functions in the Colombeau's theory

In this work we define the composite function for a special class of generalized mappings and we study the invertibility for a certain class of generalized functions with real values.

Rotura gástrica por barotrauma

Barogenic rupture of the stomach is a rare complication following cardiopulmonary resuscitation, administration of nasal oxygen by catheter and diving accidents. We report a case of gastric barotrauma following oroesophageal intubation. In most cases, the tears occur along the lesser curvature, what have been already attributed to Laplace's formula and, more recently, to morphological features of the stomach.

Sistema não-Intrusivo para Estimação da Direção do olhar utilizando redes neurais artificiais

The fundamental senses of the human body are: vision, hearing, touch, taste and smell. These senses are the functions that provide our relationship with the environment. The vision serves as a sensory receptor responsible for obtaining information from the outside world that will be sent to the brain. The gaze reflects its attention, intention and interest. Therefore, the estimation of gaze direction, using computer tools, provides a promising alternative to improve the capacity of human-computer interaction, mainly with respect to those people who suffer from motor deficiencies. Thus, the objective of this work is to present a non-intrusive system that basically uses a personal computer and a low cost webcam, combined with the use of digital image processing techniques, Wavelets transforms and pattern recognition, such as artificial neural network models, resulting in a complete system that performs since the image acquisition (including face detection and eye tracking) to the estimation of gaze direction. The obtained results show the feasibility of the proposed system, as well as several feature advantages.

Localização de faltas em linhas de transmissão usando morfologia matemática

This work an algorithm for fault location is proposed. It contains the following functions: fault detection, fault classification and fault location. Mathematical Morphology is used to process currents obtained in the monitored terminals. Unlike Fourier and Wavelet transforms that are usually applied to fault location, the Mathematical Morphology is a non-linear operation that uses only basic operation (sum, subtraction, maximum and minimum). Thus, Mathematical Morphology is computationally very efficient. For detection and classification functions, the Morphological Wavelet was used. On fault location module the Multiresolution Morphological Gradient was used to detect the traveling waves and their polarities. Hence, recorded the arrival in the two first traveling waves incident at the measured terminal and knowing the velocity of propagation, pinpoint the fault location can be estimated. The algorithm was applied in a 440 kV power transmission system, simulated on ATP. Several fault conditions where studied and the following parameters were evaluated: fault location, fault type, fault resistance, fault inception angle, noise level and sampling rate. The results show that the application of Mathematical Morphology in faults location is very promising

Modelo de risco com dependência entre os valores das indenizações e seus intervalos entre ocorrências

We present a dependent risk model to describe the surplus of an insurance portfolio, based on the article "A ruin model with dependence between claim sizes and claim intervals"(Albrecher and Boxma [1]). An exact expression for the Laplace transform of the survival function of the surplus is derived. The results obtained are illustrated by several numerical examples and the case when we ignore the dependence structure present in the model is investigated. For the phase type claim sizes, we study by the survival probability, considering this is a class of distributions computationally tractable and more general

Usando a história da resolução de alguns problemas para introduzir conceitos: sistemas lineares, determinantes e matrizes.

In this work we studied the method to solving linear equations system, presented in the book titled "The nine chapters on the mathematical art", which was written in the first century of this era. This work has the intent of showing how the mathematics history can be used to motivate the introduction of some topics in high school. Through observations of patterns which repeats itself in the presented method, we were able to introduce, in a very natural way, the concept of linear equations, linear equations system, solution of linear equations, determinants and matrices, besides the Laplacian development for determinants calculations of square matrices of order bigger than 3, then considering some of their general applications

MATHEMATICA notebook for computing tetrahedral finite element shape functions and matrices for the Helmholtz equation

A MATHEMATICA notebook to compute the elements of the matrices which arise in the solution of the Helmholtz equation by the finite element method (nodal approximation) for tetrahedral elements of any approximation order is presented. The results of the notebook enable a fast computational implementation of finite element codes for high order simplex 3D elements reducing the overheads due to implementation and test of the complex mathematical expressions obtained from the analytical integrations. These matrices can be used in a large number of applications related to physical phenomena described by the Poisson, Laplace and Schrodinger equations with anisotropic physical properties.

On asymptotic solutions of integrable wave equations

Asymptotic 'soliton train' solutions of integrable wave equations described by inverse scattering transform method with second-order scalar eigenvalue problem are considered. It is shown that if asymptotic solution can be presented as a modulated one-phase nonlinear periodic wavetrain, then the corresponding Baker-Akhiezer function transforms into quasiclassical eigenfunction of the linear spectral problem in weak dispersion limit for initially smooth pulses. In this quasiclassical limit the corresponding eigenvalues can be calculated with the use of the Bohr Sommerfeld quantization rule. The asymptotic distributions of solitons parameters obtained in this way specify the solution of the Whitham equations. (C) 2001 Elsevier B.V. B.V. All rights reserved.

An exact equation for the free surface of a fluid in a porous medium

We study the problem of the evolution of the free surface of a fluid in a saturated porous medium, bounded from below by a. at impermeable bottom, and described by the Laplace equation with moving-boundary conditions. By making use of a convenient conformal transformation, we show that the solution to this problem is equivalent to the solution of the Laplace equation on a fixed domain, with new variable coefficients, the boundary conditions. We use a kernel of the Laplace equation which allows us to write the Dirichlet-to-Neumann operator, and in this way we are able to find an exact differential-integral equation for the evolution of the free surface in one space dimension. Although not amenable to direct analytical solutions, this equation turns out to allow an easy numerical implementation. We give an explicit illustrative case at the end of the article.

Miscibility in a degenerate fermionic mixture induced by linear coupling

We consider a one-dimensional mean-field-hydrodynamic model of a two-component degenerate Fermi gas in an external trap, each component representing a spin state of the same atom. We demonstrate that the interconversion between them (linear coupling), imposed by a resonant electromagnetic wave, transforms the immiscible binary gas into a miscible state, if the coupling constant, kappa, exceeds a critical value, kappa(cr). The effect is predicted in a variational approximation, and confirmed by numerical solutions. Unlike the recently studied model of a binary Bose-Einsten condensate with the linear coupling, the components in the immiscible phase of the binary fermion mixture never fill two separated domains with a wall between them, but rather form antilocked (pi-phase-shifted) density waves. Another difference from the bosonic mixture is spontaneous breaking of symmetry between the two components in terms of the numbers of atoms in them, N(1) and N(2). The latter effect is characterized by the parameter nu equivalent to(N(1)-N(2))/(N(1)+N(2)) (only N(1)+N(2) is a conserved quantity), the onset of miscibility at kappa >=kappa(cr) meaning a transition to nu equivalent to 0. At kappa

QUASIDISTRIBUTIONS and COHERENT STATES FOR FINITE-DIMENSIONAL QUANTUM SYSTEMS

In recent years, an approach to discrete quantum phase spaces which comprehends all the main quasiprobability distributions known has been developed. It is the research that started with the pioneering work of Galetti and Piza, where the idea of operator bases constructed of discrete Fourier transforms of unitary displacement operators was first introduced. Subsequently, the discrete coherent states were introduced, and finally, the s-parametrized distributions, that include the Wigner, Husimi, and Glauber-Sudarshan distribution functions as particular cases. In the present work, we adapt its formulation to encompass some additional discrete symmetries, achieving an elegant yet physically sound formalism.