Environmental regulation of nitrogen cycling processes, denitrification and nitrification, was studied in sediment of Hamilton Harbour, with particular emphasis on the role of CH$ sb4$ metabolism (production and consumption). Through extensive sediment sampling and numerical analysis, it was found that particulate carbon was the best predictor of potential for anaerobic production of CH$ sb4$ and CO$ sb2$. The only predictor of denitrification capacity was anaerobic CO$ sb2$ production, indicating that beside NO$ sb3 sp-$ and O$ sb2$, a biotic factor involved in carbon metabolism may be important in the control of this activity. / Suppression of aerobic N$ sb2$O production in sediment slurries by C$ rm sb2H sb2$ and correlation with NO$ sb3$-production indicated that it was dependent on chemolithotrophic nitrification. Although CH$ sb4$ (1 to 24 $ mu$M) stimulated production of NO$ sb3 sp-$ and N$ sb2$O, we found that CH$ sb4$ at 84 $ mu$M or greater suppressed nitrification. Following extensive studies of pore water chemistry, potential microbial activities, and counts of nitrifiers and methanotrophs, we found that CH$ sb4$ oxidation (i) is more likely to suppress nitrification by competition for O$ sb2$ and NH$ sb4 sp+$ between methanotrophs and nitrifiers, and (ii) may be more important than nitrification as a sink of hypolimnetic O$ sb2$ in Hamilton Harbour. / Amongst a number of inhibitors, allylsulfide was found to be a differential inhibitor with much less effect on CH$ sb4$ oxidation in sediment slurries or in axenic cultures of Methylosinus trichosporium OB3b than on nitrification in sediment slurries.

Orientador: Edmundo Capelas de Oliveira / Dissertação (mestrado profissional) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 2018-08-17T14:35:07Z (GMT). No. of bitstreams: 1 Rosa_EsterCristinaFontesdeAquino_M.pdf: 847998 bytes, checksum: d177526572b19cc1fdd5eeccdf511380 (MD5) Previous issue date: 2011 / Resumo: Este trabalho tem por objetivo modelar e resolver, matematicamente, um problema físico conhecido como pêndulo simples. Discutimos, como caso particular, as chamadas oscilações de pequena amplitude, isto é, uma aproximação que nos leva a mostrar que o período de oscilação é proporcional à raiz quadrada do quociente entre o comprimento do pêndulo e a aceleração da gravidade. Como vários outros problemas oriundos da Física, o pêndulo simples é representado através de equações diferenciais parciais. Assim, na busca de sua solução, aplicamos a metodologia de separação de variáveis que nos leva a um conjunto de equações ordinárias passíveis de simples integração. Escolhendo um sistema de coordenadas adequado, é conveniente usar o método de Hamilton-Jacobi, discutindo, antes, o problema do oscilador harmónico, apresentando, em seguida, o problema do pêndulo simples e impondo condições a fim de mostrar que as equações diferenciais associadas a esses dois sistemas são iguais, ou seja, suas soluções são equivalentes. Para tanto, estudamos o método de separação de variáveis associado às equações diferenciais parciais, lineares e de segunda ordem, com coeficientes constantes e três variáveis independentes, bem como a respectiva classificação quanto ao tipo. Posteriormente, estudamos as equações hipergeométricas, cujas soluções, as funções hipergeométricas. podem ser encontradas pelo método de Frobenius. Apresentamos o método de Hamilton-Jacobi, já mencionado, para o enfren-tamento do problema apresentado. Fizemos no capítulo final um apêndice sobre a função gama por sua presente importância no trato de funções hipergeométricas, em especial a integral elíptica completa de primeiro tipo que compõe a solução exata do período do pêndulo simples / Abstract: This work aims to present and solve, mathematically, the physics problem that is called simple pendulum. We reasoned, as an specific case, the so called low amplitude oscillation, that is, a convenient approximation that make us show that the period of oscillation is proportional to the quotient square root between the pendulum length and the gravity acceleration. Like several other problems arising from the physics, we are going to broach it through partial differential equations. Thus, in the search of its solution, we made use of the variable separation methodology that leads us to a body of ordinary equations susceptible of simple integration. Choosing an appropriate coordinate system, it is convenient to use the method Hamilton-Jacobi, arguing, first, the problem of the harmonic oscillator, with, then the problem of sf simple pendulum and imposing conditions to show that the differential equations associated with these two systems are equal, that is, their solutions are equivalent. With the purpose of reaching the objectives, we studied the variable separation method associated with partial differential equations, linear and of second order, with constant coefficient and three independent variables, as well as the respective classification about the type. Afterwards, we studied the hypergeometrical equations whose solutions, the hypergeometrical functions, are found by the Frobenius method. Introducing the Hamilton-Jacobi method, already mentioned, for addressing the problem presented. We made an appendix in the final chapter on the gamma function by its present importance in dealing with hypergeometric functions, in particular the elliptic integral of first kind consists of the exact period of sf simple pendulum / Mestrado / Fisica-Matematica / Mestre em Matemática

M.Sc. (Applied Mathematics) / Entanglement is a quantum resource with applications in quantum communication as well as quantum computing amongst others. Since quantum entanglement is such an abstract concept numerous mathematical measures exist. Some of these have a purely theoretic purpose whereas others play a role in describing the magnitude of entanglement of a system. In quantum systems energy level crossing may occur. Energy levels in quantum systems tend to repel each other so when any type of degeneracy occurs where the energy levels coalesce or cross it is of interest to us. Two such points of degeneracy are exceptional and diabolic points. When these occur it is useful to investigate these points in specific systems and observe level crossing. In this thesis we mainly investigate the relationship between entanglement, energy level crossing and symmetry as well as the exceptional and diabolic points of specific systems. We are especially interested in systems described by spin and Fermi operators.

Inthis degree project, a solution on a coarse grid is recovered by fitting apartial differential equation to a few known data points. The PDE to consideris the heat equation and the Dupire’s equation with their synthetic data,including synthetic data from the Black-Scholes formula. The approach to fit aPDE is by optimal control to derive discrete approximations to regularized Hamiltoncharacteristic equations to which discrete stepping schemes, and parameters forsmoothness, are examined. By non-parametric numerical implementation thedervied method is tested and then a few suggestions on possible improvementsare given / I detta examensarbete återskapas en lösning på ett glest rutnät genom att anpassa en partiell differentialekvation till några givna datapunkter. De partiella differentialekvationer med deras motsvarande syntetiska data som betraktas är värmeledningsekvationen och Dupires ekvation inklusive syntetiska data från Black-Scholes formel. Tillvägagångssättet att anpassa en PDE är att med hjälp av optimal styrning härleda diskreta approximationer på ett system av regulariserade Hamilton karakteristiska ekvationer till vilka olika diskreta stegmetoder och parametrar för släthet undersöks. Med en icke-parametrisk numerisk implementation prövas den härledda metoden och slutligen föreslås möjliga förbättringar till metoden.

Le développement d'architectures moléculaires enchevêtrées (rotaxanes) est un sujet d'actualité en chimie supramoléculaire. Cette thèse examine la synthèse multi-étape de sous-unités de rotaxanes, notamment de composants macrocycliques électroactifs, et leur assemblage dans des structures moléculaires imbriquées. De nouveaux cycles à 31 et 35 chaînons à liaison hydrogène comprenant un motif récepteur bis (2,6-diamidopyridine) et une unité électroactive, à savoir du ferrocène ou de la triphénylamine, ont été synthétisés. Ces macrocycles ont été analysés par voltampérométrie cyclique, analyse par diffraction des rayons X sur cristal unique, ainsi que par spectroscopie RMN et spectrométrie de masse. Les interactions hôte-invité avec un acide complémentaire 5,5’-diéthylbarbiturique (Barbital) en tant qu’invité modèle ont également été étudiées par titrage spectroscopique par absorption électronique et RMN 1H. Les affinités de liaison étaient corrélées à la structure moléculaire. Des approches pour former des [2]rotaxanes, notamment en utilisant une réaction de matrice métallique active, où l'ion métallique joue le double rôle de matrice et de catalyseur, sont décrites. En particulier, les réactions de couplage de Huisgen ainsi que de Glaser catalysées au cuivre(I) ont été utilisées avec des bouchons de volumes variés. Dans une deuxième approche complémentaire de type "attache" de la formation de rotaxane, l'anneau électroactif a été formé directement entourant le composant de filetage servant de modèle. Cette méthodologie a permis d'obtenir deux [2] rotaxanes inédits via une réaction de "clipping" à cinq composants assistée par matrice, l'un des rotaxanes intégrant deux unités de ferrocène, tandis que l'autre comprenait deux unités de type triphénylamine. Les études de diffraction des rayons X sur cristal unique ont confirmé le caractère imbriqué des assemblages. / Development of interlocked molecular ring-on-thread architectures (rotaxanes) represents a central current topic in supramolecular chemistry. This thesis considers the multi-step synthesis of rotaxane subcomponents, notably electroactive macrocyclic components, and their assembly into interlocked molecular structures. Novel hydrogen-bonding 31- and 35-member rings comprising a bis(2,6-diamidopyridine) receptor motif and an electroactive unit, namely ferrocene or triphenylamine, were synthesized. These macrocycles were analyzed by cyclic voltammetry, single crystal X-ray diffraction analysis, as well as NMR spectroscopy and mass spectrometry. Host-guest interactions with a complementary 5,5’-diethylbarbituric acid (Barbital) as model guest were also studied by electronic absorption and 1H-NMR spectroscopic titrations. Binding affinities were correlated to molecular structure. Approaches to form 2rotaxanes, notably by employing an active metal template reaction, where the metal ion plays the dual role of template and catalyst, are described. In particular, the copper(I)-catalyzed Huisgen as well as Glaser coupling reactions were employed with a variety of bulky stopper groups. In a second complementary “clipping”-type approach to rotaxane formation, the electroactive ring was directly formed encircling the templating thread component. This methodology yielded two further novel [2]rotaxanes via a template-assisted five-component clipping reaction, one rotaxane integrating two ferrocene units while the other comprised two triphenylamine-like units. Single crystal X-ray diffraction studies confirmed the interlocked nature of the assemblies.

No description available.

No Abstract / Thesis / Bachelor of Arts (BA)

Cette thèse contient deux contributions à l’homogénéisation en espace-temps des équations de Hamilton-Jacobi du premier ordre. Ces équations sont en lien avec la modélisation du trafic routier. Enfin, sont présentés des résultats d’homogénéisation en milieu presque périodique. Le premier chapitre est consacré à l’homogénéisation d’un système infini d’équations différentielles couplées avec temps de retard. Ce système provient ici d’un modèle microscopique de trafic routier simple. Les conducteurs se suivent sur une route rectiligne infinie et l’on tient compte de leur temps de réaction. On suppose que la vitesse de chaque conducteur est une fonction de l’interdistance avec le conducteur qui le précède: on parle d’un modèle du type “follow-the-leader”. Grâce à un principe de comparaison strict, on montre la convergence vers un modèle macroscopique pour des temps de réaction inférieurs à une valeur critique. Dans un second temps, on exhibe un contre-exemple à l’homogénéisation pour un temps de réaction supérieur à cette valeur critique, pour des conditions initiales particulières. Pour cela, on perturbe la solution stationnaire dans laquelle les véhicules sont tous équidistants aux instants initiaux. Le second chapitre porte sur l’homogénéisation d’une équation de Hamilton-Jacobi dont l’Hamiltonien est discontinu en espace. Le modèle de trafic associé est une route rectiligne comportant une infinité de feux tricolores. Ces feux sont supposés identiques, équidistants et le déphasage entre deux feux successifs est supposé constant. On étudie l’influence à grande échelle de ce déphasage sur le trafic. On distingue la portion de route libre, qui sera représentée par un modèle macroscopique, et les feux, qui seront modélisés par des limiteurs de flux périodiques en temps. Le cadre théorique est celui par C. Imbert et R. Monneau (2017) pour les équations de Hamilton-Jacobi sur réseaux. L’étude se décompose en l’homogénéisation théorique, où l’Hamiltonien effectif dépend du déphasage, puis l’obtention de propriétés qualitatives de cet Hamiltonien à l’aide d’observations via des simulations numériques. Le troisième chapitre présente des résultats d’homogénéisation en milieu presque périodique. On étudie tout d’abord un problème d’évolution avec un Hamiltonien stationnaire, presque périodique en espace. À l’aide d’arguments presque périodiques, on effectue dans un second temps une nouvelle preuve du résultat d’homogénéisation du second chapitre. L’Hamiltonien est alors périodique en temps et presque périodique en espace. Sont également présentes des questions encore ouvertes, notamment dans le cas où l’Hamiltonien est presque périodique en temps-espace, et dans le cas d’un modèle de trafic où les feux sont assez proches, avec donc un modèle microscopique entre les feux / This thesis report deals with the homogenization in space and time of some first order Hamilton-Jacobi equations. It contains two contributions. The corresponding equations are derived from traffic flow modelling. We finally present some results of almost periodic homogenization. In the first chapter, we consider a one dimensional pursuit law with delay which is derived from traffic flow modelling. It takes the form of an infinite system of first order coupled delayed equations. Each equation describes the motion of a driver who interacts with the preceding one: such a model is referred to as a ``follow-the-leader" model. We take into account the reaction time of drivers. We derive a macroscopic model, namely a Hamilton-Jacobi equation, by a homogenization process for reaction times that are below an explicit threshold. The key idea is to show, that below this threshold, a strict comparison principle holds for the infinite system. Above this threshold, we show that collisions can occur. In a second time, for well-chosen dynamics and higher reaction times, we show that there exist some microscopic pursuit laws that do not lead to the previous macroscopic model. Such a law is here derived as a perturbation of the stationnary solution, for which all the vehicles are equally spaced at initial times. The second chapter is dedicated to the homogenization of a Hamilton-Jacobi equation for traffic lights. We consider an infinite road where lights are equally spaced and with a constant phase shift between two lights. This model takes the form of a first order Hamilton-Jacobi equation with an Hamiltonian that is discontinuous in the space variable and the notion of viscosity solution is the one introduced by C. Imbert and R. Monneau (2017). Each light is modelled as a time-periodic flux limiter and the traffic flow between two lights corresponds to the classical LWR model. The global Hamiltonian will be time-periodic but not periodic in space for a general phase shift. We first show that the rescaled solution converges toward the solution of the expected macroscopic model where the effective Hamiltonian depends on the phase shift. In a second time, numerical simulations are used to analyse the effect of the phase shift on the effective Hamiltonian and to reveal some properties of the effective Hamiltonian from the numerical observations. In the third chapter, we are interested in some homogenization problems of Hamilton-Jacobi equations within the almost periodic setting which generalizes the usual periodic one. The first problem is the evolutionary version of the work cite {ishii2000almost}, with the same stationary Hamiltonian. The second problem has already been solved in the second chapter but we use here almost periodic arguments for the time periodic and space almost periodic Hamiltonian. We only study the ergodicity of the associated cell problems. We finally discuss open problems, the first one concerning a space and time almost periodic Hamiltonian and the second one being a microscopic model for traffic flow modelling where the Hamiltonian is almost periodic in space

A reação de Fenton é o nome dado à oxidação de ferro(II) a ferro(III) pela água oxigenada, uma reação que produz espécies com alto poder oxidante como o radical hidroxila. Neste trabalho, foi desenvolvida uma metodologia espectrofotométrica para o acompanhamento da formação de ferro(III) nos momentos iniciais da reação de Fenton. Esta metodologia foi aplicada a quatro conjuntos de reações: (A) o sistema Fenton simples, contendo apenas ferro(II) e H2O2; (B) o sistema A contendo isopropanol, um substrato orgânico simples que sofre principalmente oxidação a acetona; (C) o sistema A contendo o catalisador 3,5-di-terc-butil-catecol (H2DTBCat); (D) o sistema C mais isopropanol, que corresponde ao sistema catalítico completo. Em cada conjunto, variou-se as concentrações de ferro(II) e H2O2. Um modelo cinético, baseado num conjunto de reações explícitas e as respectivas constantes de velocidade, foi desenvolvido para simular a velocidade de formação de ferro(III) para estes quatro conjuntos de reações. Utilizando reações relatadas na literatura, o modelo forneceu simulações que reproduziram satisfatoriamente os dados experimentais dos conjuntos A e B. No caso dos conjuntos C e D, porém, foi necessário propor uma etapa envolvendo a formação de ferro(IV) ou ferril, estabilizado por complexação com o H2DTBCat. Entretanto, mesmo com a inclusão desta espécie, o modelo não captou a complexidade do sistema em altas concentrações de peróxido e ferro. Esta falha foi atribuída à rápida degradação competitiva do H2DTBCat nestas condições, com a subseqüente participação destes produtos de degradação na reação ou como co-catalisadores ou como inibidores. / The Fenton reaction is the name given to the oxidation of iron(II) to iron(III) by hydrogen peroxide, a reaction that produces highly oxidizing species like the hydroxyl radical. In this work, a spectrophotometric methodology is developed to accompany the formation of iron(III) during the initial moments of the Fenton reaction. This methodology was applied to four sets of reactions: (A) the simple Fenton system, containing only iron(II) and H2O2; (B) system A containing isopropanol, a simple substrate that undergoes principally oxidation to acetone; (C) system A containing the catalyst 3,5-di-tert-butyl-catechol (H2DTBCat); (D) system C plus isopropanol, corresponding to the complete catalytic system. For each set of reactions, the concentrations of iron(II) and H2O2 were varied. A kinetic model, based on explicit chemical reactions and their respective rate constants, was developed to simulate the the rate of formation of iron(III) for these four sets of reactions above. Using reactions described in the literature, the model produced simulations that satisfactorily reproduced the experimental data of sets A and B. In the case of sets C and D, however, it was necessary to propose an additional step involving the formation of iron(IV) or ferril, stabilized by complexation with H2DTBCat. Nonetheless, even with the inclusion of this species, the model failed to capture the complexity of the system at high concentrations of peroxide and iron. This failure was attributed to the rapid competitive degradation of H2DTBCat under these conditions, with the subsequent participation of the degradation products in the reaction as either co-catalysts or inhibitors.

Cette thèse porte sur l'étude d'équation de Hamilton-Jacobi-Bellman associées à des problèmes de contrôle optimal et de jeux à champ moyen avec la particularité qu'on se place sur un réseau (c'est-à-dire, des ensembles constitués d'arêtes connectées par des jonctions) dans les deux problèmes, pour lesquels on autorise différentes dynamiques et différents coûts dans chaque bord d'un réseau. Dans la première partie de cette thèse, on considère un problème de contrôle optimal sur les réseaux dans l'esprit des travaux d'Achdou, Camilli, Cutrì & Tchou (2013) et Imbert, Moneau & Zidani (2013). La principale nouveauté est qu'on rajoute des coûts d'entrée (ou de sortie) aux sommets du réseau conduisant à une éventuelle discontinuité de la fonction valeur. Celle-ci est caractérisée comme l'unique solution de viscosité d'une équation Hamilton-Jacobi pour laquelle une condition de jonction adéquate est établie. L'unicité est une conséquence d'un principe de comparaison pour lequel nous donnons deux preuves différentes, l'une avec des arguments tirés de la théorie du contrôle optimal, inspirée par Achdou, Oudet & Tchou (2015) et l'autre basée sur les équations aux dérivées partielles, d'après Lions & Souganidis (2017). La deuxième partie concerne les jeux à champ moyen stochastiques sur les réseaux. Dans le cas ergodique, ils sont décrits par un système couplant une équation de Hamilton-Jacobi-Bellman et une équation de Fokker- Planck, dont les inconnues sont la densité m de la mesure invariante qui représente la distribution des joueurs, la fonction valeur v qui provient d'un problème de contrôle optimal "moyen" et la constante ergodique ρ. La fonction valeur v est continue et satisfait dans notre problème des conditions de Kirchhoff aux sommets très générales. La fonction m satisfait deux conditions de transmission aux sommets. En particulier, due à la généralité des conditions de Kirchhoff, m est en général discontinue aux sommets. L'existence et l'unicité d'une solution faible sont prouvées pour des Hamiltoniens sous-quadratiques et des hypothèses très générales sur le couplage. Enfin, dans la dernière partie, nous étudions les jeux à champ moyen stochastiques non stationnaires sur les réseaux. Les conditions de transition pour la fonction de valeur v et la densité m sont similaires à celles données dans la deuxième partie. Là aussi, nous prouvons l'existence et l'unicité d'une solution faible pour des Hamiltoniens sous-linéaires et des couplages et dans le cas d'un couplage non-local régularisant et borné inférieurement. La principale difficulté supplémentaire par rapport au cas stationnaire, qui nous impose des hypothèses plus restrictives, est d'établir la régularité des solutions du système posé sur un réseau. Notre approche consiste à étudier la solution de l'équation de Hamilton-Jacobi dérivée pour gagner de la régularité sur la solution de l'équation initiale. / The dissertation focuses on the study of Hamilton-Jacobi-Bellman equations associated with optimal control problems and mean field games problems in the case when the state space is a network. Different dynamics and running costs are allowed in each edge of the network. In the first part of this thesis, we consider an optimal control on networks in the spirit of the works of Achdou, Camilli, Cutrì & Tchou (2013) and Imbert, Monneau & Zidani (2013). The main new feature is that there are entry (or exit) costs at the edges of the network leading to a possible discontinuous value function. The value function is characterized as the unique viscosity solution of a Hamilton-Jacobi equation for which an adequate junction condition is established. The uniqueness is a consequence of a comparison principle for which we give two different proofs. One uses some arguments from the theory of optimal control and is inspired by Achdou, Oudet & Tchou (2015). The other one is based on partial differential equations techniques and is inspired by a recent work of Lions & Souganidis (2017). The second part is about stochastic mean field games for which the state space is a network. In the ergodic case, they are described by a system coupling a Hamilton- Jacobi-Bellman equation and a Fokker-Planck equation, whose unknowns are the density m of the invariant measure which represents the distribution of the players, the value function v which comes from an "average" optimal control problem and the ergodic constant ρ. The function v is continuous and satisfies general Kirchhoff conditions at the vertices. The density m satisfies dual transmission conditions. In particular, due to the generality of Kirchhoff’s conditions, m is in general discontinuous at the vertices. Existence and uniqueness are proven for subquadratic Hamiltonian and very general assumptions about the coupling term. Finally, in the last part, we study non-stationary stochastic mean field games on networks. The transition conditions for value function v and the density m are similar to the ones given in second part. Here again, we prove the existence and uniqueness of a weak solution for sublinear Hamiltonian and bounded non-local regularizing coupling term. The main additional difficulty compared to the stationary case, which imposes us more restrictive hypotheses, is to establish the regularity of the solutions of the system placed on a network. Our approach is to study the solution of the derived Hamilton-Jacobi equation to gain regularity over the initial equation.