On the numerical computation of the Mittag-Leffler function

Recently simple limiting functions establishing upper and lower bounds on the Mittag-Leffler function were found. This paper follows those expressions to design an efficient algorithm for the approximate calculation of expressions usual in fractional-order control systems. The numerical experiments demonstrate the superior efficiency of the proposed method.

Delay approximation of fractional integrals

This paper explores the calculation of fractional integrals by means of the time delay operator. The study starts by reviewing the memory properties of fractional operators and their relationship with time delay. Based on the time response of the Mittag-Leffler function an approximation of fractional integrals consisting of time delayed samples is proposed. The tuning of the approximation is optimized by means of a genetic algorithm. The results demonstrate the feasibility of the new perspective and the limits of their application.

Propagação de vírus informáticos baseada em modelos biológicos

A evolução digital proporcionou às sociedades uma facilidade extraordinária de comunicação. Com o número crescente de computadores e o aumento de acessos à internet, surgiu uma nova forma de criminologia, que cresceu em paralelo com o número de utilizadores. Desta forma, tornou-se comum a criação e difusão de vírus informáticos pelos chamados hackers. Neste trabalho estudam-se modelos de transmissão de vírus informáticos, usando modelos epidemiológicos. Começa-se por fazer uma revisão dos modelos existentes na literatura, de seguida sugerem-se alterações a esses modelos de forma a conseguir uma melhor aproximação à dinâmica real de transmissão de vírus informáticos. As simulações numéricas dos modelos permitem-nos inferir de que uma forma de controlar a transmissão de vírus informáticos é a diminuição da taxa de infeção, isto é, da taxa de transmissão do vírus. No último capítulo enumeram-se as conclusões do trabalho efetuado e indicam-se direções de trabalho futuro.

Desenvolvimento de um procedimento de Numerical Site Calibration para um Parque Eólico usando Dinâmica de Fluidos Computacional

Esta dissertação descreve o desenvolvimento e avaliação de um procedimento de \Numerical Site Calibration" (NSC) para um Parque Eólico, situado a sul de Portugal, usando Dinâmica de Fluídos Computacional (CFD). O NSC encontra-se baseado no \Site Calibration" (SC), sendo este um método de medição padronizado pela Comissão Electrónica Internacional através da norma IEC 61400. Este método tem a finalidade de quantificar e reduzir os efeitos provocados pelo terreno e por possíveis obstáculos, na medição do desempenho energético das turbinas eólicas. Assim, no SC são realizadas medições em dois pontos, no mastro referência e no local da turbina (mastro temporário). No entanto, em Parques Eólicos já construídos, este método não é aplicável visto ser necessária a instalação de um mastro de medição no local da turbina e, por conseguinte, o procedimento adequado para estas circunstâncias é o NSC. O desenvolvimento deste método é feito por um código CFD, desenvolvido por uma equipa de investigação do Instituto Superior de Engenharia do Porto, designado de WINDIETM, usado extensivamente pela empresa Megajoule Inovação, Lda em aplicações de energia eólica em todo mundo. Este código é uma ferramenta para simulação de escoamentos tridimensionais em terrenos complexos. As simulações do escoamento são realizadas no regime transiente utilizando as equações de Navier-Stokes médias de Reynolds com aproximação de Bussinesq e o modelo de turbulência TKE 1.5. As condições fronteira são provenientes dos resultados de uma simulação realizada com Weather Research and Forecasting, WRF. Estas simulações dividem-se em dois grupos, um dos conjuntos de simulações utiliza o esquema convectivo Upwind e o outro utiliza o esquema convectivo de 4aordem. A análise deste método é realizada a partir da comparação dos dados obtidos nas simulações realizadas no código WINDIETM e a coleta de dados medidos durante o processo SC. Em suma, conclui-se que o WINDIETM e as suas configurações reproduzem bons resultados de calibração, ja que produzem erros globais na ordem de dois pontos percentuais em relação ao SC realizado para o mesmo local em estudo.

Electrophoretic protein patterns and numerical analysis of Candida albicans from the oral cavities of healthy children

The aim of this research was to evaluate the protein polymorphism degree among seventy-five C. albicans strains from healthy children oral cavities of five socioeconomic categories from eight schools (private and public) in Piracicaba city, São Paulo State, in order to identify C. albicans subspecies and their similarities in infantile population groups and to establish their possible dissemination route. Cell cultures were grown in YEPD medium, collected by centrifugation, and washed with cold saline solution. The whole-cell proteins were extracted by cell disruption, using glass beads and submitted to SDS-PAGE technique. After electrophoresis, the protein bands were stained with Coomassie-blue and analyzed by statistics package NTSYS-pc version 1.70 software. Similarity matrix and dendrogram were generated by using the Dice similarity coefficient and UPGMA algorithm, respectively, which made it possible to evaluate the similarity or intra-specific polymorphism degrees, based on whole-cell protein fingerprinting of C. albicans oral isolates. A total of 13 major phenons (clusters) were analyzed, according to their homogeneous (socioeconomic category and/or same school) and heterogeneous (distinct socioeconomic categories and/or schools) characteristics. Regarding to the social epidemiological aspect, the cluster composition showed higher similarities (0.788 < S D < 1.0) among C. albicans strains isolated from healthy children independent of their socioeconomic bases (high, medium, or low). Isolates of high similarity were not found in oral cavities from healthy children of social stratum A and D, B and D, or C and E. This may be explained by an absence of a dissemination route among these children. Geographically, some healthy children among identical and different schools (private and public) also are carriers of similar strains but such similarity was not found among other isolates from children from certain schools. These data may reflect a restricted dissemination route of these microorganisms in some groups of healthy scholars, which may be dependent of either socioeconomic categories or geographic site of each child. In contrast to the higher similarity, the lower similarity or higher polymorphism degree (0.499 < S D < 0.788) of protein profiles was shown in 23 (30.6%) C. albicans oral isolates. Considering the social epidemiological aspect, 42.1%, 41.7%, 26.6%, 23.5%, and 16.7% were isolates from children concerning to socioeconomic categories A, D, C, B, and E, respectively, and geographically, 63.6%, 50%, 33.3%, 33.3%, 30%, 25%, and 14.3% were isolates from children from schools LAE (Liceu Colégio Albert Einstein), MA (E.E.P.S.G. "Prof. Elias de Melo Ayres"), CS (E.E.P.G. "Prof. Carlos Sodero"), AV (Alphaville), HF (E.E.P.S.G. "Honorato Faustino), FMC (E.E.P.G. "Prof. Francisco Mariano da Costa"), and MEP (E.E.P.S.G. "Prof. Manasses Ephraim Pereira), respectively. Such results suggest a higher protein polymorphism degree among some strains isolated from healthy children independent of their socioeconomic strata or geographic sites. Complementary studies, involving healthy students and their families, teachers, servants, hygiene and nutritional habits must be done in order to establish the sources of such colonization patterns in population groups of healthy children. The whole-cell protein profile obtained by SDS-PAGE associated with computer-assisted numerical analysis may provide additional criteria for the taxonomic and epidemiological studies of C. albicans.

Numerical analysis of the initial conditions in fractional systems

Fractional dynamics is a growing topic in theoretical and experimental scientific research. A classical problem is the initialization required by fractional operators. While the problem is clear from the mathematical point of view, it constitutes a challenge in applied sciences. This paper addresses the problem of initialization and its effect upon dynamical system simulation when adopting numerical approximations. The results are compatible with system dynamics and clarify the formulation of adequate values for the initial conditions in numerical simulations.

On the numerical computation of the Mittag-Leffler function

Recently simple limiting functions establishing upper and lower bounds on the Mittag-Leffler function were found. This paper follows those expressions to design an efficient algorithm for the approximate calculation of expressions usual in fractional-order control systems. The numerical experiments demonstrate the superior efficiency of the proposed method.

Numerical calculation of the left and right fractional derivatives

The calculation of fractional derivatives is an important topic in scientific research. While formal definitions are clear from the mathematical point of view, they pose limitations in applied sciences that have not been yet tackled. This paper addresses the problem of obtaining left and right side derivatives when adopting numerical approximations. The results reveal the relationship between the resulting distinct values for different fractional orders and types of signals.

An efficient numerical scheme for solving multi-dimensional fractional optimal control problems with a quadratic performance index

The shifted Legendre orthogonal polynomials are used for the numerical solution of a new formulation for the multi-dimensional fractional optimal control problem (M-DFOCP) with a quadratic performance index. The fractional derivatives are described in the Caputo sense. The Lagrange multiplier method for the constrained extremum and the operational matrix of fractional integrals are used together with the help of the properties of the shifted Legendre orthonormal polynomials. The method reduces the M-DFOCP to a simpler problem that consists of solving a system of algebraic equations. For confirming the efficiency and accuracy of the proposed scheme, some test problems are implemented with their approximate solutions.

Introducing numerical analysis tools in engineering: a Scilab user case in electronics course

Software tools in education became popular since the widespread of personal computers. Engineering courses lead the way in this development and these tools became almost a standard. Engineering graduates are familiar with numerical analysis tools but also with simulators (e.g. electronic circuits), computer assisted design tools and others, depending on the degree. One of the main problems with these tools is when and how to start use them so that they can be beneficial to students and not mere substitutes for potentially difficult calculations or design. In this paper a software tool to be used by first year students in electronics/electricity courses is presented. The growing acknowledgement and acceptance of open source software lead to the choice of an open source software tool – Scilab, which is a numerical analysis tool – to develop a toolbox. The toolbox was developed to be used as standalone or integrated in an e-learning platform. The e-learning platform used was Moodle. The first approach was to assess the mathematical skills necessary to solve all the problems related to electronics and electricity courses. Analysing the existing circuit simulators software tools, it is clear that even though they are very helpful by showing the end result they are not so effective in the process of the students studying and self learning since they show results but not intermediate steps which are crucial in problems that involve derivatives or integrals. Also, they are not very effective in obtaining graphical results that could be used to elaborate reports and for an overall better comprehension of the results. The developed tool was based on the numerical analysis software Scilab and is a toolbox that gives their users the opportunity to obtain the end results of a circuit analysis but also the expressions obtained when derivative and integrals calculations, plot signals, obtain vector diagrams, etc. The toolbox runs entirely in the Moodle web platform and provides the same results as the standalone application. The students can use the toolbox through the web platform (in computers where they don't have installation privileges) or in their personal computers by installing both the Scilab software and the toolbox. This approach was designed for first year students from all engineering degrees that have electronics/electricity courses in their curricula.

Improved Numerical Simulation for a Novel Adaptive Control Using Fractional Order Derivatives

A novel control technique is investigated in the adaptive control of a typical paradigm, an approximately and partially modeled cart plus double pendulum system. In contrast to the traditional approaches that try to build up ”complete” and ”permanent” system models it develops ”temporal” and ”partial” ones that are valid only in the actual dynamic environment of the system, that is only within some ”spatio-temporal vicinity” of the actual observations. This technique was investigated for various physical systems via ”preliminary” simulations integrating by the simplest 1st order finite element approach for the time domain. In 2004 INRIA issued its SCILAB 3.0 and its improved numerical simulation tool ”Scicos” making it possible to generate ”professional”, ”convenient”, and accurate simulations. The basic principles of the adaptive control, the typical tools available in Scicos, and others developed by the authors, as well as the improved simulation results and conclusions are presented in the contribution.

Heat recovery from wastewater: numerical modelling of sewer systems

Dissertação para obtenção do Grau de Mestre em Engenharia do Ambiente, perfil Engenharia Sanitária

Numerical Evaluation of Ventilation Performance in Children Day Care Centres

Modelling of ventilation is strongly dependent on the physical characteristics of the building of which precise evaluation is a complex and time consuming task. In the frame of a research project, two children day care centres (CDCC) have been selected in order to measure the envelope air permeability, the flow rate of mechanical ventilation systems and indoor and outdoor temperature. The data obtained was used as input to the computer code CONTAM for ventilation simulations. The results obtained were compared with direct measurements of ventilation flow from short term measurements with CO2 tracer gas and medium term measurements with perfluorocarbon tracer (PFT) gas decay method. After validation, in order to analyse the main parameters that affect ventilation, the model was used to predict the ventilation rates for a wide range of conditions. The purpose of this assessment was to find the best practices to improve natural ventilation. A simple analytical method to predict the ventilation flow rate of rooms is also presented. The method is based on the estimation of wind effect on the room through the evaluation of an average factor and on the assessment of relevant cross section of gaps and openings combined in series or in parallel. It is shown that it may be applied with acceptable accuracy for this type of buildings when ventilation is due essentially to wind action.

Numerical methods and tangible interfaces for pollutant dispersion simulation

Dissertação apresentada para obtenção do Grau de Doutor em Engenharia do Ambiente, pela Universidade Nova de Lisboa, Faculdade de Ciências e Tecnologia

Predictive analytical and numerical modeling for orthogonal cutting

In this thesis, a predictive analytical and numerical modeling approach for the orthogonal cutting process is proposed to calculate temperature distributions and subsequently, forces and stress distributions. The models proposed include a constitutive model for the material being cut based on the work of Weber, a model for the shear plane based on Merchants model, a model describing the contribution of friction based on Zorev’s approach, a model for the effect of wear on the tool based on the work of Waldorf, and a thermal model based on the works of Komanduri and Hou, with a fraction heat partition for a non-uniform distribution of the heat in the interfaces, but extended to encompass a set of contributions to the global temperature rise of chip, tool and work piece. The models proposed in this work, try to avoid from experimental based values or expressions, and simplifying assumptions or suppositions, as much as possible. On a thermo-physical point of view, the results were affected not only by the mechanical or cutting parameters chosen, but also by their coupling effects, instead of the simplifying way of modeling which is to contemplate only the direct effect of the variation of a parameter. The implementation of these models was performed using the MATLAB environment. Since it was possible to find in the literature all the parameters for AISI 1045 and AISI O2, these materials were used to run the simulations in order to avoid arbitrary assumption.