This work describes numerical integration and solution for ordinary differential equations by the Taylor series by different types of integrators. The next part is a description of floating point and fixed point arithmetic. Subsequently, we are presenting designs and calculation methods for parallels multiplication and division integrators in floating point and fixed point arithmetic. The designs were realized in VHDL and implemented on FPGA. Finally we summarizes the proposed solution and compare time complexity with another numerical methods.

Tato disertační práce pojednává o návrhu nových funkčních bloků použitelných v oblasti zpracování analogového signálu. Jde o obvody v proudové módu, které mohou ve vhodné konfiguraci pracovat v proudovém i v napěťovém módu. To umožnílo získat velmi nadějné výsledky v soustavách s nízkým napájecím napětím. Mnohostrannost těchto obvodů nalezne uplatnění v mnoha aplikacích. Zesilovač s proudovou zpětnou vazbou byl zavolen jako hlavní stavební blok pro detailní zkoumání funkce obvodů s RC operační sítí. Tato disertační práce pojednává o studiu, syntéze a návrhových aspektech realizace nových imitančních funkcí, jmenovitě induktivních a superkapacitních, proudových a napěťových konvejorech, kmitočtových filtrech s velkou jakostí, integrátorech a diferenciátorech, fázovacích členech s neminimální fází a napětím řízených oscilátorech. Disertační práce se detailně zabývá těmito novými bloky, které jsou popsány teoreticky a vyhodnoceny na základě simulací vlastností.

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In the past decade, characterizing spiking neuron models has been extensively researched as an essential issue in computational neuroscience. In this thesis, we examine the estimation problem of two different neuron models. In Chapter 2, We propose a modified Izhikevich model with an adaptive threshold. In our two-stage estimation approach, a linear least squares method and a linear model of the threshold are derived to predict the location of neuronal spikes. However, desired results are not obtained and the predicted model is unsuccessful in duplicating the spike locations. Chapter 3 is focused on the parameter estimation problem of a multi-timescale adaptive threshold (MAT) neuronal model. Using the dynamics of a non-resetting leaky integrator equipped with an adaptive threshold, a constrained iterative linear least squares method is implemented to fit the model to the reference data. Through manipulation of the system dynamics, the threshold voltage can be obtained as a realizable model that is linear in the unknown parameters. This linearly parametrized realizable model is then utilized inside a prediction error based framework to identify the threshold parameters with the purpose of predicting single neuron precise firing times. This estimation scheme is evaluated using both synthetic data obtained from an exact model as well as the experimental data obtained from in vitro rat somatosensory cortical neurons. Results show the ability of this approach to fit the MAT model to different types of reference data.

Les ponts roulants sont des engins de levage situés en haut des bâtiments qu'ils équipent. Ils servent à manutentionner des charges très lourdes et parfois critiques. Pendant un séisme, un pont roulant est exposé à des chocs multiples. Ces impacts peuvent causer des dommages importants dans la structure pouvant conduire à une chute de la charge manutentionnée ou du pont roulant lui-même. Donc, la vérification de la tenue des ponts roulants au séisme est une question primordiale. Actuellement, cette vérification est basée sur des méthodes de calcul statiques. Ces méthodes font l'hypothèse d'un comportement purement linéaire des ponts roulants ce qui les rend très conservatives. Depuis quelques années les niveaux sismiques imposés par les autorités nationales augmentent chaque année, et les constructeurs de ponts roulants se trouvent dans l'incapacité de construire à partir des efforts sur-estimés fournis par les méthodes statiques. L'objectif de la thèse est l'étude de la réponse dynamique d'un pont roulant pendant un séisme en prenant en compte les non-linéarités géométriques et matériau. Afin de modéliser ces phénomènes, une analyse dynamique temporelle avec une approche multi-échelle en temps est adoptée. Pour prendre en compte l'aspect haute fréquence des chocs, un intégrateur temporel variationnel explicite, basé sur la méthode des multiplicateurs de Lagrange et dédié au contact/impact, est développé. Ensuite, un intégrateur hétérogène (différents schémas d'intégration) asynchrone (différents pas de temps), basé sur la méthode de couplage GC, est appliqué au problème du pont roulant. Cette stratégie multi-échelle en temps permet d'adapter le schéma d'intégration et le pas de temps au sous domaine considéré. Par conséquent, l'intégrateur explicite est adopté dans les zones de contact et un schéma implicite de type accélération moyenne, est adopté dans le reste de la structure. Finalement, un démonstrateur de co-simulation entre les logiciels Cast3M et Europlexus est mis en place pour montrer le gain très significatif en temps de calcul dans le cas d'un modèle élément finis tridimensionnel d'un pont roulant industriel. / Bridge cranes are hoisting appliances located overhead in buildings. They are used to handle very heavy and sometimes critical loads. During an earthquake, a bridge crane may be subjected to multiple impacts between wheels and rails. These impacts can cause significant damage to the structure leading to a fall of the handled load or the bridge crane itself. Therefore, the qualification of such equipment, subjected to an earthquake, is very important. Currently, this qualification is based on static methods. These methods assume a purely linear behavior of the bridge cranes, which leads to a very conservative forces. Consequently, the bridge cranes manufacturers are sometimes unable to design the equipement from the over-estimated efforts provided by the static methods. The aim of this work is to study the dynamic response of a bridge crane during an earthquake by taking into account the geometric and material non-linearities. In order to model such phenomena, a time-history dynamic analysis with a multi-scale approach is performed. To take into account the high frequency aspect of the impacts between wheels and rails, a Lagrange explicit contact/impact time integrator is proposed. This work has also led to the development of an explicit–implicit HATI (Heterogeneous Asynchronous Time Integrator) for contact/impact dynamics. This method allows us to adopt an explicit contact/impact time integrator in the contact area and an implicit time integrator with a coarse mesh in the rest of the domain. Finally, a co-simulation demonstrator between Cast3M and Europlexus softwares is set up to show the very significant gain in computation time for a three-dimensional finite element model of an industrial bridge crane.

Cette thèse porte sur le comportement en temps long de solutions d’équations de type Vlasov, principalement le modèle Vlasov-HMF. On s’intéresse en particulier au phénomène d’amortissement Landau, prouvé mathématiquement dans divers cadres, pour plusieurs équations de type Vlasov, comme l’équation de Vlasov-Poisson ou le modèle Vlasov-HMF, et présentant certaines analogies avec le phénomène d’amortissement non visqueux pour l’équation d’Euler 2D. Les résultats qui y sont décrits sont les suivants. Le premier est un théorème d’amortissement Landau pour des solutions numériques du modèle Vlasov-HMF, obtenues par discrétisation en temps de ce dernier via des méthodes de splitting. Nous prouvons en outre la convergence des schémas numériques. Le second est un théorème d’amortissment Landau pour des solutions du modéle Vlasov-HMF linéarisé autour d’états stationnaires inhomogènes. Ce théorème est accompagné de nombreuses simulations numériques destinées à étudier numériquement le cas non-linéaire, et semblant mettre en lumière de nouveaux phénomènes. Enfin, le dernier résultat porte sur la discrétisation en temps de l’équation d’Euler 2D par un intégrateur de Crouch-Grossman symplectique. Nous prouvons la convergence du schéma. / This thesis concerns the long time behavior of certain Vlasov equations, mainly the Vlasov- HMF model. We are in particular interested in the celebrated phenomenon of Landau damp- ing, proved mathematically in various frameworks, foar several Vlasov equations, such as the Vlasov-Poisson equation or the Vlasov-HMF model, and exhibiting certain analogies with the inviscid damping phenomenon for the 2D Euler equation. The results described in the document are the following.The first one is a Landau damping theorem for numerical solutions of the Vlasov-HMF model, constructed by means of time-discretizations by splitting methods. We prove more- over the convergence of the schemes. The second result is a Landau damping theorem for solutions of the Vlasov-HMF model linearized around inhomogeneous stationary states. We provide moreover a quite large amount of numerical simulations, which are designed to study numerically the nonlinear case, and which seem to show new phenomenons. The last result is the convergence of a scheme that discretizes in time the 2D Euler equation by means of a symplectic Crouch-Grossmann integrator.

The heart is one the most important organs in the human body and many other live creatures. The electrical activity in the heart controls the heart function, and many heart diseases are linked to the abnormalities in the electrical activity in the heart. Mathematical equations and computer simulation can be used to model the electrical activity in the heart. The heart models are challenging to solve because of the complexity of the models and the huge size of the problems. Several cell models have been proposed to model the electrical activity in a single heart cell. These models must be coupled with a heart model to model the electrical activity in the entire heart. The bidomain model is a popular model to simulate the propagation of electricity in myocardial tissue. It is a continuum-based model consisting of non-linear ordinary differential equations (ODEs) describing the electrical activity at the cellular scale and a system of partial differential equations (PDEs) describing propagation of electricity at the tissue scale. Because of this multi-scale, ODE/PDE structure of the model, splitting methods that treat the ODEs and PDEs in separate steps are natural candidates as numerical methods. First, we need to solve the problem at the cellular scale using ODE solvers. One of the most popular methods to solve the ODEs is known as the Rush-Larsen (RL) method. Its popularity stems from its improved stability over integrators such as the forward Euler (FE) method along with its easy implementation. The RL method partitions the ODEs into two sets: one for the gating variables, which are treated by an exponential integrator, and another for the remaining equations, which are treated by the FE method. The success of the RL method can be understood in terms of its relatively good stability when treating the gating variables. However, this feature would not be expected to be of benefit on cell models for which the stiffness is not captured by the gating equations. We demonstrate that this is indeed the case on a number of stiff cell models. We further propose a new partitioned method based on the combination of a first-order generalization of the RL method with the FE method. This new method leads to simulations of stiff cell models that are often one or two orders of magnitude faster than the original RL method. After solving the ODEs, we need to use bidomain solvers to solve the bidomain model. Two well-known, first-order time-integration methods for solving the bidomain model are the semi-implicit method and the Godunov operator-splitting method. Both methods decouple the numerical procedure at the cellular scale from that at the tissue scale but in slightly different ways. The methods are analyzed in terms of their accuracy, and their relative performance is compared on one-, two-, and three-dimensional test cases. As suggested by the analysis, the test cases show that the Godunov method is significantly faster than the semi-implicit method for the same level of accuracy, specifically, between 5 and 15 times in the cases presented. Second-order bidomain solvers can generally be expected to be more effective than first-order bidomain solvers under normal accuracy requirements. However, the simplest and the most commonly applied second-order method for the PDE step, the Crank-Nicolson (CN) method, may generate unphysical oscillations. We investigate the performance of a two-stage, L-stable singly diagonally implicit Runge-Kutta method for solving the PDEs of the bidomain model and present a stability analysis. Numerical experiments show that the enhanced stability property of this method leads to more physically realistic numerical simulations compared to both the CN and Backward Euler (BE) methods.

Au cours du siècle dernier, la communauté scientifique a traité le contrôle des véhicules aériens principalement par l'élaboration de stratégies ad hoc, mais aucune approche unifiée n'a été développé jusqu'à présent. Cette thèse participe à l'élaboration d'une approche unifiée pour le contrôle des véhicules aériens en prenant en compte les forces aérodynamiques dans la conception de la commande. Nous supposons les effets aérodynamiques de rotation et les effets non stationnaires négligeables. Les actionneurs du véhicule sont supposés être composés d'une force de poussé fixée au corps pour le mouvement en translation, et d'un couple de contrôle pour la régulation d'attitude. Cette thèse se concentre ensuite sur la boucle de guidage, traitant du contrôle de la vitesse linéaire. L'un des principaux objectifs a été de déterminer la façon de réguler la force de poussée et l'orientation du véhicule pour compenser les forces extérieures. Tout d'abord nous abordons la modélisation, l'analyse et le contrôle de la dynamique longitudinale de l'avion. Ensuite nous étendons certaines de ces études aux mouvements tridimensionnels d'avions au corps symétrique, tels que les missiles. Un résultat original de cette thèse est de préciser les conditions sur la force aérodynamique permettant de reformuler le problème du contrôle dans celui de la commande d'un corps sphérique, pour lequel des résultats de stabilité peuvent être démontrés. Les lois de commande proposées intègrent des termes intégraux et anti-wind up sans reposer sur une politique de commutation entre plusieurs lois de commande. / Over the last century, the scientific community has dealt with the control of flying machines by mainly developing different strategies in relation to different classes of aircraft, and no unified control approach has been developed so far. The present thesis contributes towards the development of a unified control approach for aerial vehicles by maintaining aerodynamic forces in the control design. It is assumed, however, that the aerodynamic effects of rotational and unsteady motions are negligible, and that the means of actuation for an aerial vehicle consist of a body-fixed thrust force for translational motion and a control torque for attitude monitoring. This thesis then focuses on the guidance loop of the control problem. One of the main objectives has been to determine how to regulate the thrust intensity and the vehicle orientation to compensate for the orientation-dependent external forces. In particular, the modeling, analysis, and control of the longitudinal aircraft dynamics is first addressed. Then, some of these studies are extended to three-dimensional motions of symmetric aircraft, such as missile-like bodies. An original outcome of this thesis is to state conditions on the aerodynamic force that allow the control problem to be recasted into that of controlling a spherical body. In this case, strong stability results can be shown. The proposed control laws incorporate integral and anti-wind up terms and do not rely on a switching policy between several control laws.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / This work shows and compares three different flux estimator algorithms developed for use in high-performance sensorless ac motor drives. The first algorithm uses a low pass filter with a very low cut off frequency to integrate the back electromotive force (emf). The second one uses a high pass filter to remove the offset present in the signal before it s integration. The third algorithm uses current and voltage model to estimate the flux of induction motor. These algorithms can be used to accurately measure the motor flux including magnitude and phase angle over a wide speed range. The performance of the algorithms is investigated, compared, and verified using simulation and experimental tests. / Este trabalho tem como objetivo apresentar uma comparação entre três algoritmos estimadores de fluxo estatórico diferentes. Estes algoritmos foram desenvolvidos para serem usados no projeto de acionamentos de alto desempenho, sem sensor de velocidade, para motores de indução. O primeiro algoritmo adotado utiliza um filtro passa baixa com uma freqüência de corte baixa para resolver a integração. O segundo algoritmo usa um filtro passa alta para retirar o offset do sinal de entrada do integrador puro. O terceiro algoritmo é um algoritmo híbrido que utiliza os modelos de tensão e corrente em paralelo para estimar o fluxo. Os algoritmos estimam fluxo estatórico em uma ampla faixa de freqüência de funcionamento do motor de indução e foram implementados na forma de simulação e experimentalmente para comparar o funcionamento dos mesmos em diferentes velocidades de operação do motor. / Mestre em Ciências

Submitted by Edileide Reis (leyde-landy@hotmail.com) on 2013-04-23T12:23:58Z No. of bitstreams: 2 Josue Santos Parte 2.pdf: 931346 bytes, checksum: b1e5922db0717587a7942e5c09cc5b01 (MD5) Josue Santos Parte 1.pdf: 1888156 bytes, checksum: 5a369c2be9a8867bc37dbf7937760f92 (MD5) / Made available in DSpace on 2013-04-23T12:23:58Z (GMT). No. of bitstreams: 2 Josue Santos Parte 2.pdf: 931346 bytes, checksum: b1e5922db0717587a7942e5c09cc5b01 (MD5) Josue Santos Parte 1.pdf: 1888156 bytes, checksum: 5a369c2be9a8867bc37dbf7937760f92 (MD5) Previous issue date: 2004 / Neste trabalho foram avaliadas sete aminas aromáticas O e N-substituídas em condições reacionais otimizadas para a síntese de corantes fenotiazínicos (CFs) simétricos. Entre estas, o N,N-dimetil -p- fenilenodiamino (DMPD), N,N- dietil -p- fenilenodiamino (DEPD), p-fenilenodiamino (PPD), p-aminofenol (PAP) e o p-aminoanisol (PAA) , levando a rendimentos entre 10 e 43%, para diferentes oxidantes (Fe3+ ou ClO-), ácidos (H2SO4 ou HBF4) e contra-íons (ClO4 - ou BF4 -). O DMPD apresentou as menores variaçõesnos rendimentos calculados para as diferentes condições reacionais investigadas. A partir dos resultados obtidos com a síntese dos CFs foi avaliada de forma comparativa a potencialidade do DMPD, DEPD, PPD, PAP e do PAA para determinação espectrofotométrica de sulfeto em sistema de análise em fluxo. Preliminarmente, foram comparados os sinais analíticos gerados pelo espectrofotômetro, em sistema em fluxo, para os corantes fenotiazínicos produzidos a partir das cinco aminas, avaliadas nas mesmas condições. Por apresentarem uma melhor cinética de formação dos respectivos CFs, as aminas DMPD, DEPD e PPD foram selecionadas para investigações mais detalhadas. Os estudos foram realizados empregando planejamento fatorial composto central, visando à otimização das condições em sistema de análise em fluxo. Os parâmetros avaliados foram as concentrações da amina aromática, do oxidante (Fe3+) e do H2SO4 na solução da amina. Nas faixas de concentração avaliadas para as 3 variáveis, somente o DMPD pôde ser otimizado, apresentando, também, robustez para pequenas variações nas concentrações dos parâmetros investigados. Mesmo em condições não otimizadas, o DEPD (LD, 18,34 mg L-1) produziu o corante fenotiazínico com maior absortividade molar. Nas melhores condições para a determinação de sulfeto o PPD e o DMPD apresentaram limite de detecção de 60,1 mg L-1 e 71,46 mg L-1, respectivamente. Adicionalmente, foi investigado um procedimento de análise em fluxo para determinação indireta de sulfito. Este era levado a SO2 e reduzido em linha a H2S na presença de ácido e Znº com uma taxa de conversão estimada em 10,31%. Desta forma, foi desenvolvida uma unidade integradora de operações (UIO), na qual a amostra era preparada (HSO3 - Æ SO2), convertida a H2S, o qual permeava através de membrana de PTFE e reagia com a mistura DMPD e Fe3+ para formar azul de metileno. A membrana de PTFE foi seletiva a H2S frente ao SO2, em diferentes condições. Visando pré-concentrar o H2S produzido na conversão de sulfito, foi desenvolvido um circuito eletrônico para controlar as válvulas solenóides, visando a interrupção do fluxo da solução receptora. As variáveis do sistema foram otimizadas e a recepção em solução de NaOH mostrou-se mais sensível que em DMPD e Fe3+. A utilização de solução transportadora com álcool etílico 15% (v/v) nivelou o efeito do álcool presente nas soluções da amostras de vinho. Para o procedimento em fluxo proposto, o H2S foi interferente para concentrações > 0,5 mg L-1 em condições normais e > 10 mg L-1 se a amostra for tratada previamente com solução de acetato de zinco. O procedimento analítico em fluxo apresentou faixas de trabalho distintas para sulfito livre e total, apresentando limites de detecção (3s) inferiores a 0,35 e 1,2 mg L-1, respectivamente.A potencialidade do processo foi avaliada para a determinação dos teores de sulfito em amostras de sucos e vinhos. Os resultados obtidos foram comparados com aqueles obtidos empregando procedimento de referência e apresentaram boa concordância com 95% de confiança. / Salvador