Neste trabalho analisamos, de maneira descritiva utilizando simulações, o desempenho um conjunto de estimadores para os parâmetros funcionais f, g, h e k de uma equação diferencial parcial. Para as simulações, selecionamos doze EDPs nas quais aplicaremos os estimadores as soluções dessas EDPs. Iremos medir o desempenho dos estimadores utilizando o erro quadrático entre as estimativas obtidas e os coeficientes conhecidos das EDPs. As estimativas dos coeficientes serão obtidas para soluções com e sem ruídos. Os estimadores propostos serão comparados com um grupo de estimadores diretos. Os programas para as simulações foram desenvolvidos com programas no repositório R, versão 3.2.3. Veremos que os estimadores propostos apresentaram um desempenho superior aos dos estimadores diretos, para soluções com e sem ruídos. Nas soluções com ruídos os estimadores propostos tiveram um desempenho mais significativo que para soluções sem ruídos. / In this paper we shall analyze, on a descriptive way using simulations, the performance of a set of estimators for the coefficients f, g, h and k using the following. For the simulations, we select twelve EDPs in which we will apply the estimators from the solutions from the mentioned EDPs. We will measure the performance using the quadratic error between the estimates obtained and the known coefficients from the EDPs. The estimates will be obtained for solutions with and without noises. The proposed estimators will be compared with a group of direct estimators. The programs used for the simulations were developed with the programs in the repository R, version 3.2.3. We shall see that the proposed estimators present a superior performance compared to the direct estimators, for solutions with or without noises. The proposed estimators have had a better performance in the solutions with noises than in the solutions without a noise.

Neste trabalho analisamos, de maneira descritiva utilizando simulações, o desempenho um conjunto de estimadores para os parâmetros funcionais f, g, h e k de uma equação diferencial parcial. Para as simulações, selecionamos doze EDPs nas quais aplicaremos os estimadores as soluções dessas EDPs. Iremos medir o desempenho dos estimadores utilizando o erro quadrático entre as estimativas obtidas e os coeficientes conhecidos das EDPs. As estimativas dos coeficientes serão obtidas para soluções com e sem ruídos. Os estimadores propostos serão comparados com um grupo de estimadores diretos. Os programas para as simulações foram desenvolvidos com programas no repositório R, versão 3.2.3. Veremos que os estimadores propostos apresentaram um desempenho superior aos dos estimadores diretos, para soluções com e sem ruídos. Nas soluções com ruídos os estimadores propostos tiveram um desempenho mais significativo que para soluções sem ruídos. / In this paper we shall analyze, on a descriptive way using simulations, the performance of a set of estimators for the coefficients f, g, h and k using the following. For the simulations, we select twelve EDPs in which we will apply the estimators from the solutions from the mentioned EDPs. We will measure the performance using the quadratic error between the estimates obtained and the known coefficients from the EDPs. The estimates will be obtained for solutions with and without noises. The proposed estimators will be compared with a group of direct estimators. The programs used for the simulations were developed with the programs in the repository R, version 3.2.3. We shall see that the proposed estimators present a superior performance compared to the direct estimators, for solutions with or without noises. The proposed estimators have had a better performance in the solutions with noises than in the solutions without a noise.

Serial or parallel buses are widely used to communicate information in most electronic devices. The energy consumed by bus interconnects may comprise a significant portion of the overall energy consumption of the device. Hence, techniques to reduce the energy consumption of bus interconnects have become an important area of research. One common method adopted to reduce energy is Bus Encoding, where redundant bits are added to the original data stream either in time or space to reduce the energy consumption. In this thesis, a novel bus encoding technique, called the Multiple Codebook Approach (MCA), is presented to reduce the Energy-Delay-Product (EDP) and Energy for data transmission over serial buses. For any symbol that is to be transmitted on the bus, the best code is selected (from an EDP or energy minimization standpoint) from among a set of codebooks. In particular, the implementation utilizes 3 codebooks. To minimize EDP, the codeword for each symbol is selected based on the product of the number of transitions resulting from its transmission in a serial manner, and the codeword length. To minimize energy, the codeword for each symbol is selected based on the number of transitions alone. The MCA is compared with other reported techniques in the literature, and the results are quite promising. The MCA achieves a 11% improvement in EDP and 3% improvement iv in Energy over the best approach known for serial data transmission, which was reported by Macii and others.

Presenta dos problemas básicos de la teoría de las ecuaciones diferenciadas parciales lineares

Le cadre de cette thèse est la théorie des surfaces minimales. En 2001, C. Cosin et A. Ros démontrent que, si un polygone borde un disque immergé, ce polygone est le polygone de flux d'un r-noide Alexandrov-plongé symétrique de genre 0. Leur démonstration se fonde sur l'étude de l'espace de ces surfaces minimales. Notre travail présente une démonstration plus constructive de leur résultat. Notre méthode repose sur la résolution du problème de Dirichlet pour l'équation des surfaces minimales. A cette fin, nous étudions la convergence de suites de solutions de cette équation. Nous définissons la notion de lignes de divergence de la suite qui sont les points ou la suite des gradients est non-bornées. L'étude de ces lignes permet de conclure sur la convergence d'une suite. Les r-noides sont alors construits comme les surfaces conjuguées aux graphes de solutions du problème de Dirichlet sur des domaines fixés par les polygones. Dans une seconde partie, nous montrons que, sous l'hypothèse de border un disque immergé, un polygone est aussi le polygone de flux d'un r-noide Alexandrov-plongé symétrique de genre $1$. La démonstration repose sur une amélioration des idées de celle du premier résultat, elle nécessite entre autre la résolution d'un problème de période. Cette résolution passe par l'étude du comportement limite de certaines suites de surfaces minimales.

Apuntes  para un curso dictado en Perú, contienen dos partes bien definidas. La Primera: Breve introducción a la teoría general de ecuaciones diferenciales incluyendo los teoremas de existencia y unicidad de soluciones, diferenciabilidad con respecto a condiciones iniciales y algunos otros resultados importantes;  La Segunda: Introducción a la teoría cualitativa de las ecuaciones diferenciales o Sistemas Dinámicos. Se  dan algunos conceptos fundamentales para describir las propiedades dinámicas de un sistema y se exponen algunos resultados fundamentales.

In this work the compression behavior of masonry was investigated. After a detailed review of code approaches and different research works, a new formula was suggested to describe the compression strength of masonry, based on the mechanical and geometrical properties of its components, when deformation properties of units are larger than the ones of mortar. Later on, a new model, Extended Drucker-Prager Cap Yielding Function, is suggested to describe the three axial compression stress state of mortar in masonry in case deformation properties of mortar are larger than the ones of mortar, and to describe the three axial compression stress state of brick in the other case. This includes defining its parameters based on test diagrams of the mortar material, implementing the model in the numerical software ANSYS, and the numerical results are evaluated for simple cube example. The controlling equations of creep based on the visco-elastic creep theory are presented in the general case of three axial creep under three axial loading conditions. The special case of three axial creep under axial loading is also presented. The “transversal creep” relevant for the compression strength of masonry was discussed and numerical examples have been added to show the effect of changed time-dependent Poisson’s ratio. In another chapter, many examples are presented showing the application of the suggested material models and discontinuous numerical method named eXtended finite element method. Conclusions and recommendations are given in the last chapter.

Cette thèse est dédiée à l’étude du phénomène d’explosion en temps fini pour les équations semi-linéaires des ondes. On traite deux modèles dans ce travail.Dans une première direction, on considère l’équation semi-linéaire des ondes à valeurs complexes avec une nonlinéarité en puissance. On caractérise d’abord toutes les solutions du problème stationnaire comme une famille à deux paramètres.Ensuite, on utilise une approche de système dynamique pour montrer que la solution en transformation auto-similaire s’approche d’une solution stationnaire particulière dans l’espace d’énergie, dans le cas des points non caractéristiques.Ceci donne le profil à l’explosion pour l’équation originale dans le cas non-caractéristique.Dans une seconde direction, on étudie l’exemple de l’équation des ondes avec source exponentielle critique en dimension 1. On généralise les résultats de Godin pour une classe de données initiales beaucoup plus grandes. On prouve des estimations à l’explosion pour tout point de l’espace et on donne une estimation optimale du taux d’explosion pour les points non-caractéristiques. / This thesis is devoted to the study of the finite time blow-up phenomena for the semilinear waves equations. We treat two models in this work.In the first part, we consider a complex-valued solution for the semilinear wave equation with power nonlinearity. We first characterize all the solutions of the associated stationary problem as a two-parameter family. Then, weuse a dynamical system formulation to show that the solution in self-similar variables approaches some particular stationary one in the energy norm, in the non-characteristic case. This gives the blow-up profile for the original equation in the non-characteristic case.The second part is dedicated to the study of the semilinear wave equation with exponential nonlinearity in one space dimension. We generalize the results of Godin to a much larger class of initial data. We prove blow-up estimates near any point and give an optimal bound on the blow-up rate near the non characteristic points.

Cette thèse est consacrée à l'étude de systèmes d'équations aux dérivées partielles. En particulier nous nous intéressons à des systèmes issus de la mécanique des fluides avec contraintes qui permettent de décrire de manière continue en temps et en espace des quantités physiques telles que la densité ou la vitesse. Dans ce cadre nous construisons des modèles pour la biologie : modélisation de la croissance d'un biofilm de micro-algues et modélisation du gros intestin et de sa couche de mucus. Ces modèles sont ensuite testés numériquement à l'aide de schémas numériques spécifiquement élaborés pour ces modèles. Cette thèse est complétée par une étude numérique du modèle d'Aw-Rascle avec contrainte pour le trafic routier / This thesis is devoted to the study of partial differential equation systems. In particular, we are interested in constrained systems coming from the fluid mechanics field which allow to describe, in time and space, physical quantities such as density or speed. In this context we build models for biology: modeling of the growth of micro-algae biofilms and modeling of the large intestine and its mucus layer. These models are then tested numerically using numerical schemes specifically developed for these models. This thesis is supplemented with a numerical study of Aw-Rascle model with constraint for road traffic

In this work the compression behavior of masonry was investigated. After a detailed review of code approaches and different research works, a new formula was suggested to describe the compression strength of masonry, based on the mechanical and geometrical properties of its components, when deformation properties of units are larger than the ones of mortar. Later on, a new model, Extended Drucker-Prager Cap Yielding Function, is suggested to describe the three axial compression stress state of mortar in masonry in case deformation properties of mortar are larger than the ones of mortar, and to describe the three axial compression stress state of brick in the other case. This includes defining its parameters based on test diagrams of the mortar material, implementing the model in the numerical software ANSYS, and the numerical results are evaluated for simple cube example. The controlling equations of creep based on the visco-elastic creep theory are presented in the general case of three axial creep under three axial loading conditions. The special case of three axial creep under axial loading is also presented. The “transversal creep” relevant for the compression strength of masonry was discussed and numerical examples have been added to show the effect of changed time-dependent Poisson’s ratio. In another chapter, many examples are presented showing the application of the suggested material models and discontinuous numerical method named eXtended finite element method. Conclusions and recommendations are given in the last chapter.