Representation of transmission lines: comparison of models and parameters distributed discrete parameters

A transmission line is characterized by the fact that its parameters are distributed along its length. This fact makes the voltages and currents along the line to behave like waves and these are described by differential equations. In general, the differential equations mentioned are difficult to solve in the time domain, due to the convolution integral, but in the frequency domain these equations become simpler and their solutions are known. The transmission line can be represented by a cascade of π circuits. This model has the advantage of being developed directly in the time domain, but there is a need to apply numerical integration methods. In this work a comparison of the model that considers the fact that the parameters are distributed (Universal Line Model) and the fact that the parameters considered concentrated along the line (π circuit model) using the trapezoidal integration method, and Simpson's rule Runge-Kutta in a single-phase transmission line length of 100 km subjected to an operation power. © 2003-2012 IEEE.

Estabilidade de pontos de equilíbrio e existência de soluções periódicas em alguns modelos bidimensionais

Pós-graduação em Matemática Universitária - IGCE

Métodos numéricos para equações diferencias ordinárias

Pós-graduação em Matemática Universitária - IGCE

Vibração de barras em pequena amplitude com efeito geométrico

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Modelagem Matemática e Análise de Modelos Matemáticos na Educação Matemática

In this paper we present two studies, the first one completed and the second one in development, which are based in teaching approaches that propose the qualitative study of mathematical models as a strategy for the teaching and learning of mathematical concepts. These teaching approaches focus on subjects from Higher Education such as Introduction to Ordinary Differential Equations and Topics of Differential and Integral Calculus. We denominate this common aspect of the teaching approaches as Model Analysis and in a preliminary level we relate it with Mathematical Modeling. Furthermore, we discuss some questions related with the choice of the theme and the role of Digital Technologies when Model Analysis is applied.

On an energy exchange process and appearance of chaos in a non-ideal portal frame dynamical system

In this paper, we consider non-ideal excitation devices such as DC motors with restrictenergy output capacity. When such motors are attached to structures which needexcitation power levels similar to the source power capacity, jump phenomena and theincrease in power required near resonance characterize the Sommerfeld Effect, actingas a sort of an energy sink. One of the problems often faced by designers of suchstructures is how to drive the system through resonance and avoid this energy sink.Our basic structural model is a simple portal frame driven by a num-ideal powersource-(NIPF). We also investigate the absorption of resonant vibrations (nonlinearand chaotic) by means of a nonlinear sub-structure known as a Nonlinear Energy Sink(NES). An energy exchange process between the NIPF and NES in the passagethrough resonance is investigated, as well the suppression of chaos.

Atratores pullback para equações parabólicas semilineares em domínios não cilíndricos

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Equações diferenciais implícitas com descontinuidade

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Sobre a estabilidade estrutural e regularizações de campos de vetores descontínuos

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Soluções quase automórficas para equações diferenciais abstratas de segunda ordem

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Cálculo fracionário aplicado em dinâmica tumoral: método da Transformada Diferencial generalizada

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Equações diferenciais ordinárias não suaves autônomas e não autônomas

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Equações diferenciais ordinárias não suaves autônomas e não autônomas

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

The effect of flex fuel vehicles in the Brazilian light road transportation

The retaking of the ethanol program in the year 2003 as a fuel for light road transportation in Brazil through the introduction of flex fuel vehicles fleet was a good strategy to overcome the difficulties of the ethanol production sector and did work to increase its market share relative to gasoline. This process, however, may cause a future disequilibrium on the food production and on the refining oil derivates structure. In order to analyze the substitution process resultant of the competition between two opponents fighting for the same market, in this case the gasoline/ethanol substitution process, a method derived from the biomathematics based on the non-linear differential equations (NLDE) system is utilized. A brief description of the method is presented. Numerical adherence of the method to explain several substitution phenomena that occurred in the past is presented in the previous author`s paper, in which the urban gas pipeline system substitution of bottled LPG in the dwelling sector and the substitution of the urban diesel transportation fleet by compressed natural gas (CNG) buses is presented. The proposed method is particularly suitable for prospective analysis and scenarios assessment. (c) 2008 Elsevier Ltd. All rights reserved.

On estimating the basic reproduction number in distinct stages of a contagious disease spreading

In epidemiology, the basic reproduction number R-0 is usually defined as the average number of new infections caused by a single infective individual introduced into a completely susceptible population. According to this definition. R-0 is related to the initial stage of the spreading of a contagious disease. However, from epidemiological models based on ordinary differential equations (ODE), R-0 is commonly derived from a linear stability analysis and interpreted as a bifurcation parameter: typically, when R-0 >1, the contagious disease tends to persist in the population because the endemic stationary solution is asymptotically stable: when R-0 <1, the corresponding pathogen tends to naturally disappear because the disease-free stationary solution is asymptotically stable. Here we intend to answer the following question: Do these two different approaches for calculating R-0 give the same numerical values? In other words, is the number of secondary infections caused by a unique sick individual equal to the threshold obtained from stability analysis of steady states of ODE? For finding the answer, we use a susceptibleinfective-recovered (SIR) model described in terms of ODE and also in terms of a probabilistic cellular automaton (PCA), where each individual (corresponding to a cell of the PCA lattice) is connected to others by a random network favoring local contacts. The values of R-0 obtained from both approaches are compared, showing good agreement. (C) 2012 Elsevier B.V. All rights reserved.