Numerical conformal mapping and mesh generation for polygonal and multiply-connected regions

Details are given of a boundary-fitted mesh generation method for use in modelling free surface flow and water quality. A numerical method has been developed for generating conformal meshes for curvilinear polygonal and multiply-connected regions. The method is based on the Cauchy-Riemann conditions for the analytic function and is able to map a curvilinear polygonal region directly onto a regular polygonal region, with horizontal and vertical sides. A set of equations have been derived for determining the lengths of these sides and the least-squares method has been used in solving the equations. Several numerical examples are presented to illustrate the method.

Invariants of binary differential equations

In this paper, we study binary differential equations a(x, y)dy (2) + 2b(x, y) dx dy + c(x, y)dx (2) = 0, where a, b, and c are real analytic functions. Following the geometric approach of Bruce and Tari in their work on multiplicity of implicit differential equations, we introduce a definition of the index for this class of equations that coincides with the classical Hopf`s definition for positive binary differential equations. Our results also apply to implicit differential equations F(x, y, p) = 0, where F is an analytic function, p = dy/dx, F (p) = 0, and F (pp) not equal aEuro parts per thousand 0 at the singular point. For these equations, we relate the index of the equation at the singular point with the index of the gradient of F and index of the 1-form omega = dy -aEuro parts per thousand pdx defined on the singular surface F = 0.

A Time Efficient Optical Model for GATE Simulation of a LYSO Scintillation Matrix Used in PET Applications

A time efficient optical model is proposed for GATE simulation of a LYSO scintillation matrix coupled to a photomultiplier. The purpose is to avoid the excessively long computation time when activating the optical processes in GATE. The usefulness of the model is demonstrated by comparing the simulated and experimental energy spectra obtained with the dual planar head equipment for dosimetry with a positron emission tomograph ( DoPET). The procedure to apply the model is divided in two steps. Firstly, a simplified simulation of a single crystal element of DoPET is used to fit an analytic function that models the optical attenuation inside the crystal. In a second step, the model is employed to calculate the influence of this attenuation in the energy registered by the tomograph. The use of the proposed optical model is around three orders of magnitude faster than a GATE simulation with optical processes enabled. A good agreement was found between the experimental and simulated data using the optical model. The results indicate that optical interactions inside the crystal elements play an important role on the energy resolution and induce a considerable degradation of the spectra information acquired by DoPET. Finally, the same approach employed by the proposed optical model could be useful to simulate a scintillation matrix coupled to a photomultiplier using single or dual readout scheme.

Síntese, estudo cinético e análise microestrutural do sistema cério-níquel obtido pelo método pechini

The cerium oxide has a high potential for use in removing pollutants after combustion, removal of organic matter in waste water and the fuel-cell technology. The nickel oxide is an attractive material due to its excellent chemical stability and their optical properties, electrical and magnetic. In this work, CeO2-NiO- systems on molars reasons 1:1(I), 1:2(II) e 1:3(III) metal-citric acid were synthesized using the Pechini method. We used techniques of TG / DTG and ATD to monitor the degradation process of organic matter to the formation of the oxide. By thermogravimetric analysis and applying the dynamic method proposed by Coats-Redfern, it was possible to study the reactions of thermal decomposition in order to propose the possible mechanism by which the reaction takes place, as well as the determination of kinetic parameters as activation energy, Ea, pre-exponential factor and parameters of activation. It was observed that both variables exert a significant influence on the formation of complex polymeric precursor. The model that best fitted the experimental data in the dynamic mode was R3, which consists of nuclear growth, which formed the nuclei grow to a continuous reaction interface, it proposes a spherical symmetry (order 2 / 3). The values of enthalpy of activation of the system showed that the reaction in the state of transition is exothermic. The variables of composition, together with the variable temperature of calcination were studied by different techniques such as XRD, IV and SEM. Also a study was conducted microstructure by the Rietveld method, the calculation routine was developed to run the package program FullProf Suite, and analyzed by pseudo-Voigt function. It was found that the molar ratio of variable metal-citric acid in the system CeO2-NiO (I), (II), (III) has strong influence on the microstructural properties, size of crystallites and microstrain network, and can be used to control these properties

Caracterização analítica e geométrica da metodologia geral de determinação de distribuições de Weibull para o regime eólico e suas aplicações

O regime eólico de uma região pode ser descrito por distribuição de frequências que fornecem informações e características extremamente necessárias para uma possível implantação de sistemas eólicos de captação de energia na região e consequentes aplicações no meio rural em regiões afastadas. Estas características, tais como a velocidade média anual, a variância das velocidades registradas e a densidade da potência eólica média horária, podem ser obtidas pela frequência de ocorrências de determinada velocidade, que por sua vez deve ser estudada através de expressões analíticas. A função analítica mais adequada para distribuições eólicas é a função de densidade de Weibull, que pode ser determinada por métodos numéricos e regressões lineares. O objetivo deste trabalho é caracterizar analítica e geometricamente todos os procedimentos metodológicos necessários para a realização de uma caracterização completa do regime eólico de uma região e suas aplicações na região de Botucatu - SP, visando a determinar o potencial energético para implementação de turbinas eólicas. Assim, foi possível estabelecer teoremas relacionados com a forma de caracterização do regime eólico, estabelecendo a metodologia concisa analiticamente para a definição dos parâmetros eólicos de qualquer região a ser estudada. Para o desenvolvimento desta pesquisa, utilizou-se um anemômetro da CAMPBELL.

Homoclinic bifurcations in reversible Hamiltonian systems

We study the existence of homoclic solutions for reversible Hamiltonian systems taking the family of differential equations u(iv) + au - u +f(u, b) = 0 as a model, where fis an analytic function and a, b real parameters. These equations are important in several physical situations such as solitons and in the existence of finite energy stationary states of partial differential equations, but no assumptions of any kind of discrete symmetry is made and the analysis here developed can be extended to others Hamiltonian systems and successfully employed in situations where standard methods fail. We reduce the problem of computing these orbits to that of finding the intersection of the unstable manifold with a suitable set and then apply it to concrete situations. We also plot the homoclinic values configuration in parameters space, giving a picture of the structural distribution and a geometrical view of homoclinic bifurcations. (c) 2005 Published by Elsevier B.V.

Modelagem dinâmica de transformadores de corrente para uso em estudos de qualidade da energia e proteção do sistema elétrico

Pós-graduação em Engenharia Elétrica - FEB

Frações contínuas que correspondem a séries de potências em dois pontos

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

On the Luminous and Dark Matter Distribution in Early-Type Galaxies

The way mass is distributed in galaxies plays a major role in shaping their evolution across cosmic time. The galaxy's total mass is usually determined by tracing the motion of stars in its potential, which can be probed observationally by measuring stellar spectra at different distances from the galactic centre, whose kinematics is used to constrain dynamical models. A class of such models, commonly used to accurately determine the distribution of luminous and dark matter in galaxies, is that of equilibrium models. In this Thesis, a novel approach to the design of equilibrium dynamical models, in which the distribution function is an analytic function of the action integrals, is presented. Axisymmetric and rotating models are used to explain observations of a sample of nearby early-type galaxies in the Calar Alto Legacy Integral Field Area survey. Photometric and spectroscopic data for round and flattened galaxies are well fitted by the models, which are then used to get the galaxies' total mass distribution and orbital anisotropy. The time evolution of massive early-type galaxies is also investigated with numerical models. Their structural properties (mass, size, velocity dispersion) are observed to evolve, on average, with redshift. In particular, they appear to be significantly more compact at higher redshift, at fixed stellar mass, so it is interesting to investigate what drives such evolution. This Thesis focuses on the role played by dark-matter haloes: their mass-size and mass-velocity dispersion correlations evolve similarly to the analogous correlations of ellipticals; at fixed halo mass, the haloes are more compact at higher redshift, similarly to massive galaxies; a simple model, in which all the galaxy's size and velocity-dispersion evolution is due to the cosmological evolution of the underlying halo population, reproduces the observed size and velocity-dispersion of massive compact early-type galaxies up to redshift of about 2.

Hermitian curve interpolation for CT-data re-sampling

Purpose: Development of an interpolation algorithm for re‐sampling spatially distributed CT‐data with the following features: global and local integral conservation, avoidance of negative interpolation values for positively defined datasets and the ability to control re‐sampling artifacts. Method and Materials: The interpolation can be separated into two steps: first, the discrete CT‐data has to be continuously distributed by an analytic function considering the boundary conditions. Generally, this function is determined by piecewise interpolation. Instead of using linear or high order polynomialinterpolations, which do not fulfill all the above mentioned features, a special form of Hermitian curve interpolation is used to solve the interpolation problem with respect to the required boundary conditions. A single parameter is determined, by which the behavior of the interpolation function is controlled. Second, the interpolated data have to be re‐distributed with respect to the requested grid. Results: The new algorithm was compared with commonly used interpolation functions based on linear and second order polynomial. It is demonstrated that these interpolation functions may over‐ or underestimate the source data by about 10%–20% while the parameter of the new algorithm can be adjusted in order to significantly reduce these interpolation errors. Finally, the performance and accuracy of the algorithm was tested by re‐gridding a series of X‐ray CT‐images. Conclusion: Inaccurate sampling values may occur due to the lack of integral conservation. Re‐sampling algorithms using high order polynomialinterpolation functions may result in significant artifacts of the re‐sampled data. Such artifacts can be avoided by using the new algorithm based on Hermitian curve interpolation

Steiner’s formula in the Heisenberg group

Steiner’s tube formula states that the volume of an ϵ-neighborhood of a smooth regular domain in Rn is a polynomial of degree n in the variable ϵ whose coefficients are curvature integrals (also called quermassintegrals). We prove a similar result in the sub-Riemannian setting of the first Heisenberg group. In contrast to the Euclidean setting, we find that the volume of an ϵ-neighborhood with respect to the Heisenberg metric is an analytic function of ϵ that is generally not a polynomial. The coefficients of the series expansion can be explicitly written in terms of integrals of iteratively defined canonical polynomials of just five curvature terms.

Meromorphic continuation of functions and arbitrary distribution of interpolation points

We characterize the region of meromorphic continuation of an analytic function ff in terms of the geometric rate of convergence on a compact set of sequences of multi-point rational interpolants of ff. The rational approximants have a bounded number of poles and the distribution of interpolation points is arbitrary.

Use of intrinsic modes in biology: Examples of indicial response of pulmonary blood pressure to ± step hypoxia

Recently, a new method to analyze biological nonstationary stochastic variables has been presented. The method is especially suitable to analyze the variation of one biological variable with respect to changes of another variable. Here, it is illustrated by the change of the pulmonary blood pressure in response to a step change of oxygen concentration in the gas that an animal breathes. The pressure signal is resolved into the sum of a set of oscillatory intrinsic mode functions, which have zero “local mean,” and a final nonoscillatory mode. With this device, we obtain a set of “mean trends,” each of which represents a “mean” in a definitive sense, and together they represent the mean trend systematically with different degrees of oscillatory content. Correspondingly, the oscillatory content of the signal about any mean trend can be represented by a set of partial sums of intrinsic mode functions. When the concept of “indicial response function” is used to describe the change of one variable in response to a step change of another variable, we now have a set of indicial response functions of the mean trends and another set of indicial response functions to describe the energy or intensity of oscillations about each mean trend. Each of these can be represented by an analytic function whose coefficients can be determined by a least-squares curve-fitting procedure. In this way, experimental results are stated sharply by analytic functions.

Chemical analysis of powdered metallurgical slags by X-ray fluorescence spectrometry

Slag composition determines the physical and chemical properties as well as the application performance of molten oxide mixtures. Therefore, it is necessary to establish a routine instrumental technique to produce accurate and precise analytical results for better process and production control. In the present paper, a multi-component analysis technique of powdered metallurgical slag samples by X-ray Fluorescence Spectrometer (XRFS) has been demonstrated. This technique provides rapid and accurate results, with minimum sample preparation. It eliminates the requirement for a fused disc, using briquetted samples protected by a layer of Borax(R). While the use of theoretical alpha coefficients has allowed accurate calibrations to be made using fewer standard samples, the application of pseudo-Voight function to curve fitting makes it possible to resolve overlapped peaks in X-ray spectra that cannot be physically separated. The analytical results of both certified reference materials and industrial slag samples measured using the present technique are comparable to those of the same samples obtained by conventional fused disc measurements.

Application of Subordination Principle to Log-Harmonic alpha-spirallike Mappings

MSC 2010: 30C45, 30C55