La prédiction du bruit de roulement ferroviaire est en enjeu majeur pour la maitrise des nuisances sonores. Au point de contact roue/rail, la roue et la voie sont excités de manière dynamique, ce qui enclenche le rayonnement du bruit de roulement. Les réponses vibratoires au point de contact ainsi que les taux de décroissance des ondes sont des données primordiales pour simuler de manière précise le bruit de roulement. Or, la dimension infinie de la voie ferrée conduit bien souvent à des modèles éléments finis coûteux et non adaptés à la recherche de solutions innovantes. La thèse a pour objectifs de proposer un modèle vibratoire de voie en éléments finis qui prenne en compte la dimension infinie périodique de la voie, mais aussi d’inclure une portion de voie non-périodique sur laquelle des solutions anti-vibratiles peuvent être testées. La propagation des vibrations est exprimée sous la forme d’une décomposition en ondes par la méthode WFE (Wave Finite Element). Le calcul de la réponse vibratoire de la voie périodique infinie est obtenu à partir du déplacement d’une cellule physique longue d’environ 0.6 m. Pour réduire les temps de calcul nécessaires à sa condensation dynamique, une méthode de bi-périodisation est proposée. Le couplage entre les méthodes éléments finis et WFE est développé pour prendre en considération les supports élastiques dans cette cellule. Les comparaisons avec des mobilités expérimentales ainsi que des taux de décroissance montrent un très bon accord calculs-mesures. Enfin, le modèle développé dans cette thèse a permis de tester l’efficacité d’une solution anti-vibratile innovante développée au sein du projet CERVIFER. Celle-ci offre un comportement bi-mode, elle assouplit les supports autour de la roue préservant ainsi l’infrastructure, mais elle rigidifie les supports loin de la roue pour augmenter les taux de décroissance. Les résultats numériques se révèlent prometteurs en termes d’efficacité du dispositif et entrevoient une poursuite du développement de cette solution anti-vibratile. / Railway noise is a critical issue concerning environmental noise. At the wheel/rail contact point, both the wheel and the track are dynamically excited and vibrate together to emit the well known rolling noise. The point receptance of the rail and the track decay rates are important quantities to accurately predict wheel-rail noise emission. However, the infinite dimension of the track leads to cumbersome numerical finite-element (FE) models and not adapted to assist the research of innovative solutions. The goals of this thesis are to build an efficient numerical model for calculating the vibration from an infinite railway track, but also to include a central non-periodic part with the aim of testing anti-vibration solutions. The vibration propagation along the track is expressed as a sum of different waves using the WFEM (Wave Finite Element Method). The displacements of a 0.6 m unit cell lead to the computation of the whole track. To reduce the dynamic condensation of this cell, a bi-periodic method is proposed in this thesis. The FEM - WFEM coupling is proposed to easily include elastic supports inside the unit cell. Results show a good correlation between test and calculation. Finally, the model proposed in this thesis was used to test the efficiency of an innovative anti-vibration solution developed within the CERVIFER project. It is a dual mode device which makes the supports softer around the wheel to protect the infrastructure, and stiffer away from the wheel to increase the track decay rates. The numerical results revealed to be really promising, and they will permit to pursue the development of this anti-vibration solution.

In 1970, Raoul Bott published The Periodicity Theorem for the Classical Groups and Some of Its Applications, in which he uses this famous result as a guideline to present some important areas and tools of Algebraic Topology. This dissertation aims to use the path Bott presented in his article as a guideline to address certain topics on Algebraic Topology. We start this incursion developing important tools used in Homotopy Theory such as spectral sequences and Eilenberg-MacLane spaces, exploring how they can be combined to aid in computation of homotopy groups. We then study important results of Morse Theory, a tool which was in the centre of Botts proof of the Periodicity Theorem. We also develop two extensions: Morse-Bott Theory, and the applications of such results to the loopspace of a manifold. We end by giving an introduction to generalised cohomology theories and K-Theory. / Em 1970, Raoul Bott publicou o artigo The Periodicity Theorem for the Classical Groups and Some of Its Applications no qual usava esse famoso resultado como um guia para apresentar importantes áreas e ferramentas da Topologia Algébrica. O presente trabalho usa o mesmo caminho traçado por Bott em seu artigo como roteiro para explorar tópicos importantes da Topologia Algébrica. Começamos esta incursão desenvolvendo ferramentas importantes da Teoria de Homotopia como sequências espectrais e espaços de Eilenberg-MacLane, explorando como estes podem ser combinados para auxiliar em cálculos de grupos de homotopia. Passamos então a estudar resultados importantes de Teoria de Morse, uma ferramenta que estava no centro da demonstração de Bott do Teorema da Periodicidade. Desenvolvemos ainda, duas extensões: Teoria de Morse-Bott e aplicações destes resultados ao espaço de laços de uma variedade. Terminamos com uma introdução a teorias de cohomologia generalizadas e K-Teoria.

Stars form from the collapse of molecular clouds and evolve in an environment rich in gas and dust before becoming Main Sequence stars. During this phase, characterised by the presence of a protoplanetary disc, stars manifest changes in the structure and luminosity. This thesis performs a multi-wavelength analysis, from optical to mm range, on a sample of young stars (YSOs), mainly Classical T Tauri (CTTS). The purpose is to study optical and infrared variability and its relation with the protoplanetary disc. Longer wavelength, in the mm range, are used instead to investigate the evolution of the disc, in terms of dust growth. In optical, an F-test on a sample of 39 CTTS reveals that 67\% of the stars are variable. The variability, quantified through pooled sigma, is visible both in magnitude amplitudes and changes over time. Time series analysis applied on the more variable stars finds the presence of quasi periodicity, with periods longer than two weeks, interpreted either as eclipsing material in the disc happening on a non-regular basis, or as a consequence of star-disc interaction via magnetic field lines. The variability of YSOs is confirmed also in infrared, even if with lower amplitude. No strong correlations are found between optical and infrared variability, which implies a different cause or a time shift in the two events. By using a toy model to explore their origin, I find that infrared variations are likely to stem from emissions in the inner disc. The evolution of discs in terms of dust growth is confirmed in most discs by the analysis of the slope of the spectral energy distribution (SED), after correcting for wind emission and optical depth effects. However, the comparison with a radiative transfer model highlights that a number of disc parameters, in particular disc masses and temperature, dust size distribution and composition, can also affect the slope of the SED.

Cette thèse concerne les phénomènes de propagation de certaines équations d'évolution dans des habitats périodiques. Dans la première partie, nous étudions les phénomènes d'expansion de certaines équations d'intégro-différence spatialement périodiques. Tout d'abord, nous établissons une théorie générale sur l'existence des vitesses de propagation pour des systèmes d'évolution noncompacts, sous l'hypothèse que les systèmes linéarisés ont des valeurs propres principales. Ensuite, nous introduisons la notion d'irréductibilité uniforme des mesures de Radon finies sur le cercle. On démontre que tout opérateur de convolution généré par une telle mesure admet une valeur propre principale. Enfin, nous prouvons l'existence de vitesses de propagation pour certains équations d'intégro-différence avec des noyaux de dispersion uniformément irréductibles. Dans la deuxième partie, nous étudions les phénomènes de propagation de front pour des équations de réaction-diffusion spatialement périodiques avec des non-linéarités bistables. Nous nous concentrons d'abord sur les solutions de type fronts pulsatoires. Sous diverses hypothèses, il est prouvé que les fronts pulsatoires existent lorsque la période spatiale est petite ou grande. Nous caractérisons aussi le signe des vitesses et nous montrons la stabilité exponentielle globale des fronts pulsatoires de vitesse non nulle. Nous étudions ensuite les solutions de type fronts de transition. Sous des hypothèses convenables, on prouve que les fronts de transition se ramènent aux fronts pulsatoires avec une vitesse non nulle. Mais nous montrons aussi l'existence de nouveaux types de fronts de transition qui ne sont pas des fronts pulsatoires. / This dissertation is concerned with propagation phenomena of some evolution equations in periodic habitats. The main results consist of the following two parts. In the first part, we investigate the spatial spreading phenomena of some spatially periodic integro-difference equations. Firstly, we establish a general theory on the existence of spreading speeds for noncompact evolution systems, under the hypothesis that the linearized systems have principal eigenvalues. Secondly, we introduce the notion of uniform irreducibility for finite Radon measures on the circle. It is shown that, any generalized convolution operator generated by such a measure admits a principal eigenvalue. Finally, applying the above general theories, we prove the existence of spreading speeds for some integro-difference equations with uniformly irreducible dispersal kernels. In the second part, we study the front propagation phenomena of spatially periodic reaction-diffusion equations with bistable nonlinearities. Firstly, we focus on the propagation solutions in the class of pulsating fronts. It is proved that, under various assumptions on the reaction terms, pulsating fronts exist when the spatial period is small or large. We also characterize the sign of the front speeds and we show the global exponential stability of the pulsating fronts with nonzero speed. Secondly, we investigate the propagation solutions in the larger class of transition fronts. It is shown that, under suitable assumptions, transition fronts are reduced to pulsating fronts with nonzero speed. But we also prove the existence of new types of transition fronts which are not pulsating fronts.

MESCH / Department of Hydrology and Water Resources

We present an efficient method to compute the electrostatic fields, torques and forces in dipolar systems, which is based on the fast Fourier transform for nonequispaced data (NFFT). We consider 3d-periodic, 2d-periodic, 1d-periodic as well as 0d-periodic (open) boundary conditions. The method is based on the corresponding Ewald formulas, which immediately lead to an efficient algorithm only in the 3d-periodic case. In the other cases we apply the NFFT based fast summation in order to approximate the contributions of the nonperiodic dimensions in Fourier space. This is done by regularizing or periodizing the involved functions, which depend on the distances of the particles regarding the nonperiodic dimensions. The final algorithm enables a unified treatment of all types of periodic boundary conditions, for which only the precomputation step has to be adjusted.

This dissertation is devoted to study of complex systems in human physiology particularly heartbeats and brain dynamics. We have studied the dynamics of heartbeats that has been a subject of investigation of two independent groups. The first group emphasized the multifractal nature of the heartbeat dynamics of healthy subjects, whereas the second group had established a close connection between healthy subjects and the occurrence of crucial events. We have analyzed the same set of data and established that in fact the heartbeats are characterized by the occurrence of crucial and Poisson events. An increase in the percentage of crucial events makes the multifractal spectrum broader, thereby bridging the results of the former group with the results of the latter group. The crucial events are characterized by a power index that signals the occurrence of 1/f noise for complex systems in the best physiological condition. These results led us to focus our analysis on the statistical properties of crucial events. We have adopted the same statistical analysis to study the statistical properties of the heartbeat dynamics of subjects practicing meditation. The heartbeats of people doing meditation are known to produce coherent fluctuations. In addition to this effect, we made the surprising discovery that meditation makes the heartbeat depart from the ideal condition of 1/f noise. We also discussed how to combine the wave-like nature of the dynamics of the brain with the existence of crucial events that are responsible for the 1/f noise. We showed that the anomalous scaling generated by the crucial events could be established by means of a direct analysis of raw data. The efficiency of the direct analysis procedure is made possible by the fact that periodicity and crucial events is the product of a spontaneous process of self-organization. We argue that the results of this study can be used to shed light into the nature of this process of self-organization.

No description available.

We compute the Hilbert-Kunz functions of two-dimensional rings of type ADE by using representations of their indecomposable, maximal Cohen-Macaulay modules in terms of matrix factorizations, and as first syzygy modules of homogeneous ideals.

Ce manuscrit porte sur certaines extensions à des séries temporelles prenant des valeurs entières du modèle paramétrique périodique autorégressif établi pour des séries prenant des valeurs réelles. Les modèles que nous considérons sont basés sur l'utilisation de l'opérateur de Steutel et Van Harn (1979) et généralisent le processus autorégressif stationnaire à valeurs entières (INAR) introduit par Al-Osh & Alzaid (1987) à des séries de comptage périodiquement corrélées. Ces généralisations incluent l'introduction d'un opérateur périodique, la prise en compte d'une structure d’autocorrélation plus complexe dont l’ordre est supérieur à un, l'apparition d'innovations de variances périodiques mais aussi à inflation de zéro par rapport à une loi discrète donnée dans la famille des distributions exponentielles, ainsi que l’utilisation de covariables explicatives. Ces extensions enrichissent considérablement le domaine d'applicabilité des modèles de type INAR. Sur le plan théorique, nous établissons des propriétés mathématiques de nos modèles telles que l'existence, l'unicité, la stationnarité périodique de solutions aux équations définissant les modèles. Nous proposons trois méthodes d'estimation des paramètres des modèles dont une méthode des moments basée sur des équations du type Yule-Walker, une méthode des moindres carrés conditionnels, et une méthode du quasi maximum de vraisemblance (QML) basée sur la maximisation d'une vraisemblance gaussienne. Nous établissons la consistance et la normalité asymptotique de ces procédures d'estimation. Des simulations de type Monte Carlo illustrent leur comportement pour différentes tailles finies d'échantillon. Les modèles sont ensuite ajustés à des données réelles et utilisés à des fins de prédiction. La première extension du modèle INAR que nous proposons consiste à introduire deux opérateurs de Steutel et Van Harn périodiques, l'un modélisant les autocorrélations partielles d'ordre un sur chaque période et l'autre captant la saisonnalité périodique des données. Grâce à une représentation vectorielle du processus, nous établissons les conditions l'existence et d'unicité d'une solution périodiquement corrélées aux équations définissant le modèle. Dans le cas où les innovations suivent des lois de Poisson, nous étudions la loi marginale du processus. Á titre d'exemple d'application sur des données réelles, nous ajustons ce modèle à des données de comptage journalières du nombre de personnes ayant reçu des antibiotiques pour le traitement de maladies respiratoires dans la région de Vitória au Brésil. Comme les affections respiratoires sont fortement corrélées au niveau de pollution atmosphérique et aux conditions climatiques, la structure de corrélation des nombres quotidiens de personnes recevant des antibiotiques montre, entre autres caractéristiques, une périodicité et un caractère saisonnier hebdomadaire. Nous étendons ensuite ce modèle à des données présentant des autocorrélations partielles périodiques d'ordre supérieur à un. Nous étudions les propriétés statistiques du modèle, telles que la moyenne, la variance, les distributions marginales et jointes. Nous ajustons ce modèle au nombre quotidien de personnes recevant du service d'urgence de l'hôpital public de Vitória un traitement pour l'asthme. Enfin, notre dernière extension porte sur l'introduction d'innovations suivant une loi de Poisson à inflation de zéro dont les paramètres varient périodiquement, et sur l’ajout de covariables expliquant le logarithme de l'intensité de la loi de Poisson. Nous établissons certaines propriétés statistiques du modèle et nous mettons en oeuvre la méthode du QML pour estimer ses paramètres. Enfin, nous appliquons cette modélisation à des données journalières du nombre de personnes qui se sont rendues dans le service d'urgence d'un hôpital pour des problèmes respiratoires, et nous utilisons comme covariable la concentration de polluant dans la même zone géographique. / This manuscript deals with some extensions to time series taking integer values of the autoregressive periodic parametric model established for series taking real values. The models we consider are based on the use of the operator of Steutel and Van Harn (1979) and generalize the stationary integer autoregressive process (INAR) introduced by Al-Osh & Alzaid (1987) to periodically correlated counting series. These generalizations include the introduction of a periodic operator, the taking into account of a more complex autocorrelation structure whose order is higher than one, the appearance of innovations of periodic variances but also at zero inflation by relation to a discrete law given in the family of exponential distributions, as well as the use of explanatory covariates. These extensions greatly enrich the applicability domain of INAR type models. On the theoretical level, we establish mathematical properties of our models such as the existence, the uniqueness, the periodic stationarity of solutions to the equations defining the models. We propose different methods for estimating model parameters, including a method of moments based on Yule-Walker equations, a conditional least squares method, and a quasi-maximum likelihood method based on the maximization of a Gaussian likelihood. We establish the consistency and asymptotic normality of these estimation procedures. Monte Carlo simulations illustrate their behavior for different finite sample sizes. The models are then adjusted to real data and used for prediction purposes.The first extension of the INAR model that we propose consists of introducing two periodic operators of Steutel and Van Harn, one modeling the partial autocorrelations of order one on each period and the other capturing the periodic seasonality of the data. Through a vector representation of the process, we establish the conditions of existence and uniqueness of a solution periodically correlated to the equations defining the model. In the case where the innovations follow Poisson's laws, we study the marginal law of the process. As an example of real-world application, we are adjusting this model to daily count data on the number of people who received antibiotics for the treatment of respiratory diseases in the Vitória region in Brazil. Because respiratory conditions are strongly correlated with air pollution and weather, the correlation pattern of the daily numbers of people receiving antibiotics shows, among other characteristics, weekly periodicity and seasonality. We then extend this model to data with periodic partial autocorrelations of order higher than one. We study the statistical properties of the model, such as mean, variance, marginal and joined distributions. We are adjusting this model to the daily number of people receiving emergency service from the public hospital of the municipality of Vitória for treatment of asthma. Finally, our last extension deals with the introduction of innovations according to a Poisson law with zero inflation whose parameters vary periodically, and on the addition of covariates explaining the logarithm of the intensity of the Poisson's law. We establish some statistical properties of the model, and we use the conditional maximum likelihood method to estimate its parameters. Finally, we apply this modeling to daily data of the number of people who have visited a hospital's emergency department for respiratory problems, and we use the concentration of a pollutant in the same geographical area as a covariate. / Este manuscrito trata de algumas extensões para séries temporais de valores inteiros domodelo paramétrico periódico autorregressivo estabelecido séries temporais de valores reais. Osmodelos considerados baseiam-se no uso do operadorde Steutel e Van Harn (1979) e generalizamo processo autorregressivo depara números inteiros estacionários (INAR) introduzidos por Al-Osh & Alzaid(1987) para séries de contagem periodicamente correlacionadas. Essas generalizações incluem aintrodução de um operador periódico, a consideração de uma estrutura de autocorrelação mais complexa,cuja ordem é maior do que um, o aparecimentode inovações de variâncias periódicas, e também ainflação zero em relação a uma lei discreta dadana família de distribuições exponenciais, bem comoo uso de covariáveis explicativas. Essas extensões enriquecem muito o domínio de aplicabilidade dosmodelos do tipo INAR. No nível teórico, estabelecemospropriedades matemáticas de nossos modeloscomo a existência, a unicidade, e a estacionariedadeperiódica de soluções para as equações que definemos modelos. Propomos três métodos para estimarparâmetros de modelos, incluindo um métodode momentos baseado nas equações de Yule-Walker,um método de mínimos quadrados condicionais e ummétodo de quasi-máxima verossimilhança (QML) baseadona maximização de uma probabilidade Gaussiana. Estabelecemos a consistência e a normalidadeassintótica desses procedimentos de estimativa. Assimulações de Monte Carlo ilustram seus comportamentospara diferentes tamanhos de amostras finitas.Os modelos são então ajustados para dados reais eusados para fins de previsão. A primeira extensão domodelo INAR que propomos consiste na introdução de dois operadores periódicos de Steutel e VanHarn, o primeiro atua modelando as autocorrelações parciais de ordem um em cada período e o outro capturando a sazonalidade periódica dos dados.Através de uma representação vetorial do processo,estabelecemos as condições existência e unicidadede uma solução periodicamente correlacionada às equações que definem o modelo. No casoem que as inovações seguem as leis de Poisson,estudamos a lei marginal do processo. Como umexemplo de aplicação no mundo real, estamos ajustandoeste modelo aos dados diários de contagemdo número de pessoas que receberam antibióticos para o tratamento de doenças respiratórias na região de Vitória, Brasil. Como as condições respiratórias estão fortemente correlacionadas com a poluição doar e o clima, o padrão de correlação dos números diários de pessoas que recebem antibióticos mostra,entre outras características, a periodicidade semanale a sazonalidade. Em seguida, estendemosesse modelo para dados com autocorrelações parciaisperiódicas de ordem maior que um. Estudamosas propriedades estatísticas do modelo, como média,variância, distribuições marginais e conjuntas. Ajustamosesse modelo ao número diário de pessoascom problema respiratório que receberam atendimentode emergência no pronto-atendimento da redepública do município de Vitória. Finalmente, nossa última extensão trata da introdução de inovações de acordo com uma lei de Poisson com inflação zero cujos parâmetros variam periodicamente, e daadição de covariáveis explicando o logaritmo da intensidadeda lei de Poisson. Estabelecemos algumaspropriedades estatísticas do modelo e usamoso método QML para estimar seus parâmetros. Porfim, aplicamos essa modelagem aos dados diários sobre o número de pessoas que visitaram o departamentode emergência de um hospital por problemasrespiratórios e usamos como covariável a sérieconcentrações diárias e um poluente medido namesma área geográfica.