Thesis (M.A.)--Bowling Green State University, 2007. / Document formatted into pages; contains v, 111 p. Includes bibliographical references.

L'objet de cette thèse est l'étude de l'asymptotique des collisions rasantes pour les équations de Kac et de Boltzmann ainsi que l'étude de la propagation du chaos pour l'équation de Keller-Segel dans un cadre sous-critique à l'aide d'équations différentielles stochastiques non linéaires. Le premier chapitre est consacré `a l'équation de Kac avec un potentiel Maxwellien. Nous commençons par donner une vitesse de convergence explicite (que l'on pense être optimale) dans le cadre de l'asymptotique des collisions rasantes. Puis nous approchons la solution de l'équation de Kac dans le cadre général, ce qui nous permet de montrer la propagation du chaos pour un système de particules vers cette dernière de manière quantitative. Dans le deuxième chapitre, nous étudions l'asymptotique des collisions rasantes pour l'équation de Boltzmann avec des potentiels mous et de Coulomb. Nous donnons là encore des vitesses de convergence explicites (mais non optimales).Enfin dans le troisième et dernier chapitre, nous montrons la propagation du chaos pour l'équation de Keller-Segel dans un cadre sous-critique. Pour cela, nous utilisons des arguments de compacité (tension du système de particules) / This thesis is devoted to the study of the asymptotic of grazing collisions for Kac's and Boltzmann's equations and to the study of the chaos propagation for some sub-critical Keller-Segel equation with non-linear Stochastic Differentials Equations. The first chapter is devoted to the Kac equation with a Maxwellian potential. We start by giving an explicit rate of convergence (than we believe to be optimal) for the asymptotic of grazing collisions. Then, we approximate the solution of Kac's equation in the general case, which allows us to show the chaos propagation for some particle system to this last one in a quantitative way. In the second chapter, we study the asymptotic of grazing collisions for the Boltzmann equation with soft and Coulomb potentials. We also give explicit rates of convergence (which are not optimal).Finally in the third and last chapter, we show the chaos propagation for some sub-critical Keller-Segel equation. To this aim, we use compactness arguments (tightness of the particle system)

This thesis is a narratological analysis of the poem “The Miracle” by Edith Södergran. The thesis uses narratological tools from Mieke Bal in order to investigate different themes mainly connected to Christological sacrificial mythology. The thesis furtermore offers a discussion that highlights the poem from a feminist theological point of view, mainly with the help of ideas developed by Catherine Keller and Anne-Sofie Eriksson. ”The Miracle” is a dialogue between a girl and a nun about a troublesome dream that the girl has. It is a dream, which the girl finds strange and it concerns the need for revenge to reach relief. The dialogue also shows the risk of a kind of oppressive forgiveness by covering unfairness, and how the girl finds her way with help from the nun. With the altar in the poem as a kind of stage, “The Miracle” offers a challenge for the church and the whole world about attitudes, and about how to be constructive and liberating. This includes questions about the need to be careful and realistic when it comes to danger as well. How can you aim for fairness and at the same time handle unfairness, at several levels? Both the girl and the nun keep progressing in their different situations, from a horizon including escatological expressions. It is not easy, but they are not tied to oppressive traditions in their way of thinking either. What makes “The Miracle” such an interesting poem is the way it directs the reader to pose several constructive questions, without offering preformed answers.

Made available in DSpace on 2017-07-10T19:24:32Z (GMT). No. of bitstreams: 1 Adilson Luiz Borssoi.pdf: 1394902 bytes, checksum: b878109433ce2676d97028180d5b56f4 (MD5) Previous issue date: 2009-07-10 / Irrigation by gravity is a technique applied to familiar farming that has been spread in Brazil. It is put into practice in social programs of some States or sold directly to producers. These sets of irrigation management have simplified and low costs, which improve the agricultural production, raise prospective life in countryside and therefore settle the small producer down on his farm. Based on this, the present study evaluated the coefficient of distribution uniformity (CDU) and coefficient of variation (CV), compared two methodologies to evaluate drip irrigation systems and determined the best height to set a tank that will provide pressure for the correct operation of all irrigation by gravity. The study was carried out at the Experimental Center of Agricultural Engineering of UNIOESTE, in Cascavel, Paraná. A set of irrigation, NetafimTM, was evaluated for familiar farming. It consists of a 1.7 Lh-1 drip tube as micro drip, screen filter, 12 mm connectors and a 20 mm diameter derivation line of polyethylene. Two experiments were carried out (irrigation and fertirrigation) and put under four pressures (1.2, 1.4, 1.6 and 1.8 mca) in a completely randomized design, according to two methodologies for flow collection: one proposed by Keller & Karmeli (1975) and the other by Deniculi et al. (1980), with 16 and 32 drippers that were evaluated respectively. Twenty flow collections were done with three replications, during 110 days. In the experiment fertirrigation, the first one was diluted directly into a 200 L tank, which supplied another 30 L container, adapted to control the pressurization according to its height. Fertilization was simulated for bean crop using urea, potassium chloride (KCl) and monoammonium phosphate (MAP). Data were statistically processed by comparison among treatments and each methodology, while the irrigation set was classified by the pattern by ASAE. For fertirrigation, the best pressure was 1.6 mca, classified as excellent for CDU (91.03%) and marginal for CV (7.47%). For the irrigation treatment, the best pressure was 1.6 mca, classified as excellent for CDU (91.2%) and marginal for CV (7.68%). Deniculi et al. (1980) methodology was more reliable for the evaluation of drip systems, since it evaluates a larger number of drippers. Treatments based on fertirrigation did not suffer any loss of distribution uniformity and can be adopted for such set. / A irrigação localizada por gravidade é uma técnica aplicada à agricultura familiar que está se difundindo no Brasil e é usada em programas sociais de alguns Estados ou comercializada diretamente aos produtores. Trata-se de conjuntos de irrigação que apresentam manejo simplificado e de baixo custo, os quais potencializam a produção agrícola, aumentam as perspectivas da vida no campo e, por conseguinte, fixam o pequeno produtor em sua propriedade. Diante disso, o presente trabalho teve como objetivo avaliar o coeficiente de uniformidade de distribuição (CUD) e o coeficiente de variação (CV), comparar duas metodologias para avaliação de sistemas de irrigação por gotejamento e determinar a melhor altura para instalação do reservatório que irá fornecer a pressão para o funcionamento do conjunto de irrigação por gravidade. O estudo foi implantado no Núcleo Experimental de Engenharia Agrícola da UNIOESTE em Cascavel, Paraná. Foi avaliado um conjunto de irrigação para a agricultura familiar da marca NetafimTM, o qual é constituído de tubo gotejador tipo micro drip de 1,7 Lh-1, filtro de tela, conectores de 12 mm e linha de derivação de polietileno de diâmetro de 20 mm. Foram realizados dois experimentos (irrigação e fertirrigação), submetidos a quatro pressões (1,2, 1,4, 1,6 e 1,8 mca) em um delineamento inteiramente casualizado, seguindo duas metodologias para coleta de vazões: a proposta por Keller & Karmeli (1975), e por Deniculi et al. (1980), com 16 e 32 gotejadores avaliados respectivamente. Foram feitas 20 coletas de vazões com três repetições no decorrer de 110 dias. Para o experimento de fertirrigação, o fertilizante foi diluído diretamente em um reservatório de 200 L, que abastecia outro recipiente de 30 L, adaptado para o controle da pressurização em função da altura do mesmo. A adubação foi simulada para a cultura do feijão utilizando Uréia, cloreto de potássio (KCl) e fosfato monoamônico (MAP). Os dados foram estatisticamente processados comparando-se entre os tratamentos e cada metodologia, classificando ainda o conjunto de irrigação pelas normas da ASAE. Para fertirrigação a melhor pressão foi de 1,6 mca e classificou-se como excelente para CUD (91,03%) e marginal para CV (7,47%). Para o tratamento irrigação, a melhor pressão foi de 1,6 mca e classificou-se como excelente para CUD (91,2%) e marginal para CV (7,68%). A metodologia de Deniculi et al. (1980) mostrou-se mais confiável para a avaliação de sistemas de gotejamento, por avaliar um número maior de emissores. Os tratamentos de fertirrigação não sofreram perda de uniformidade de distribuição e podem ser adotados para tal conjunto.

Made available in DSpace on 2017-05-12T14:47:54Z (GMT). No. of bitstreams: 1 Adilson Luiz Borssoi.pdf: 1394902 bytes, checksum: b878109433ce2676d97028180d5b56f4 (MD5) Previous issue date: 2009-07-10 / Irrigation by gravity is a technique applied to familiar farming that has been spread in Brazil. It is put into practice in social programs of some States or sold directly to producers. These sets of irrigation management have simplified and low costs, which improve the agricultural production, raise prospective life in countryside and therefore settle the small producer down on his farm. Based on this, the present study evaluated the coefficient of distribution uniformity (CDU) and coefficient of variation (CV), compared two methodologies to evaluate drip irrigation systems and determined the best height to set a tank that will provide pressure for the correct operation of all irrigation by gravity. The study was carried out at the Experimental Center of Agricultural Engineering of UNIOESTE, in Cascavel, Paraná. A set of irrigation, NetafimTM, was evaluated for familiar farming. It consists of a 1.7 Lh-1 drip tube as micro drip, screen filter, 12 mm connectors and a 20 mm diameter derivation line of polyethylene. Two experiments were carried out (irrigation and fertirrigation) and put under four pressures (1.2, 1.4, 1.6 and 1.8 mca) in a completely randomized design, according to two methodologies for flow collection: one proposed by Keller & Karmeli (1975) and the other by Deniculi et al. (1980), with 16 and 32 drippers that were evaluated respectively. Twenty flow collections were done with three replications, during 110 days. In the experiment fertirrigation, the first one was diluted directly into a 200 L tank, which supplied another 30 L container, adapted to control the pressurization according to its height. Fertilization was simulated for bean crop using urea, potassium chloride (KCl) and monoammonium phosphate (MAP). Data were statistically processed by comparison among treatments and each methodology, while the irrigation set was classified by the pattern by ASAE. For fertirrigation, the best pressure was 1.6 mca, classified as excellent for CDU (91.03%) and marginal for CV (7.47%). For the irrigation treatment, the best pressure was 1.6 mca, classified as excellent for CDU (91.2%) and marginal for CV (7.68%). Deniculi et al. (1980) methodology was more reliable for the evaluation of drip systems, since it evaluates a larger number of drippers. Treatments based on fertirrigation did not suffer any loss of distribution uniformity and can be adopted for such set. / A irrigação localizada por gravidade é uma técnica aplicada à agricultura familiar que está se difundindo no Brasil e é usada em programas sociais de alguns Estados ou comercializada diretamente aos produtores. Trata-se de conjuntos de irrigação que apresentam manejo simplificado e de baixo custo, os quais potencializam a produção agrícola, aumentam as perspectivas da vida no campo e, por conseguinte, fixam o pequeno produtor em sua propriedade. Diante disso, o presente trabalho teve como objetivo avaliar o coeficiente de uniformidade de distribuição (CUD) e o coeficiente de variação (CV), comparar duas metodologias para avaliação de sistemas de irrigação por gotejamento e determinar a melhor altura para instalação do reservatório que irá fornecer a pressão para o funcionamento do conjunto de irrigação por gravidade. O estudo foi implantado no Núcleo Experimental de Engenharia Agrícola da UNIOESTE em Cascavel, Paraná. Foi avaliado um conjunto de irrigação para a agricultura familiar da marca NetafimTM, o qual é constituído de tubo gotejador tipo micro drip de 1,7 Lh-1, filtro de tela, conectores de 12 mm e linha de derivação de polietileno de diâmetro de 20 mm. Foram realizados dois experimentos (irrigação e fertirrigação), submetidos a quatro pressões (1,2, 1,4, 1,6 e 1,8 mca) em um delineamento inteiramente casualizado, seguindo duas metodologias para coleta de vazões: a proposta por Keller & Karmeli (1975), e por Deniculi et al. (1980), com 16 e 32 gotejadores avaliados respectivamente. Foram feitas 20 coletas de vazões com três repetições no decorrer de 110 dias. Para o experimento de fertirrigação, o fertilizante foi diluído diretamente em um reservatório de 200 L, que abastecia outro recipiente de 30 L, adaptado para o controle da pressurização em função da altura do mesmo. A adubação foi simulada para a cultura do feijão utilizando Uréia, cloreto de potássio (KCl) e fosfato monoamônico (MAP). Os dados foram estatisticamente processados comparando-se entre os tratamentos e cada metodologia, classificando ainda o conjunto de irrigação pelas normas da ASAE. Para fertirrigação a melhor pressão foi de 1,6 mca e classificou-se como excelente para CUD (91,03%) e marginal para CV (7,47%). Para o tratamento irrigação, a melhor pressão foi de 1,6 mca e classificou-se como excelente para CUD (91,2%) e marginal para CV (7,68%). A metodologia de Deniculi et al. (1980) mostrou-se mais confiável para a avaliação de sistemas de gotejamento, por avaliar um número maior de emissores. Os tratamentos de fertirrigação não sofreram perda de uniformidade de distribuição e podem ser adotados para tal conjunto.

Freie Univ., Diss.--Berlin, 2001. / Literaturverz. S. 227 - 236.

Diss. Northwestern Univ., 2007.

Diss. Northwestern Univ., 2007.

Cette thèse porte sur deux équations aux dérivées partielles qui modélisent les phénomènes biologiques de l'évolution génétique et mouvement dans l'espace d'une population de cellules. Le premier problème (Partie I, Chapitre 1), il est sur l'évolution phénotypique d'une population de cellules, nous avons réussi à démontrer que la limite asymptotique des solutions de l'équation différentielle partielle proposée est une masse de Dirac. Pour modéliser ce phénomène, nous avons étudié une équation de transport sur le mouvement génétique, y compris des éléments classiques de l'écologie mathématique et ajouter un transport terme dans la variable génétique x pour modéliser le phénomène de sélection naturelle. Nous intégrons un paramètre approprié dans notre modèle, qui a un problème associé normalisée. Ensuite, nous faisons quelques estimations pour donner des propriétés des solutions et obtenir sa limite. Pour ce faire, nous définissons une sous-solution et sur-solution, qui délimitent la solution du problème en appliquant un principe du maximum.Le deuxième problème (Partie II, Chapitre 2), résume les principaux résultats obtenus dans l'étude d'un système d'équations aux dérivées partielles paraboliques inspiré par l'équation Keller-Segel. C'est pourquoi le résultat principal est d'obtenir des conditions optimales sur la masse initiale pour l'existence globale et blow-up des solutions du système étudié, utilisé la méthode des moments et des inégalités de Hardy-Littlewood-Sobolev pour systèmes. / In Chapter 1, we consider a cell population where the individuals live in the same environmental conditions for some fixed period of time where they compete for nutrients among themselves, considering that offspring has the same trait as their parents, we were defining a fitness function that is trait and density dependent, assuming there were a unique trait best adapted at fixed environmental conditions. We modeled this phenomenon using a Transport Equation. The main result have been obtaining a Dirac mass concentration like solutions for the asymptotic behavior, incorporating a parameter, which is biologically sustained. We applied the classical framework to obtain this result. First, we give the apriori estimates and existence result to the simplified problem, next we add terms to have a more realistic model, then we study an approximate problem given some regularity and properties at solutions, finally we obtain this limit. We used tools as BV convergence properties, Anzats, sub and super solutions, maximum principle, etc.Chapter 2 had been publishing in the following papers (see part II):- E. ESPEJO, K. VILCHES, C. CONCA (2012), Sharp conditon for blow-up and global existence in a two species chemotactic Keller-Segel system in R^2, European J. Appl. Math- C. CONCA, E. ESPEJO, K. VILCHES (2011), Remarks on the blow-up and global existence for a two species chemotactic Keller-Segel system in R^2. European J. Appl. Math.In this chapter, we give the main results obtained in these two publications. We have been studying the sharp condition to global existence and Blow-up in time to the parabolic PDE system in R^2, inspired by the studies were done in the one species case. We model the movement for two chemotactic populations produced by one chemical substance. The main result is to extend the result obtained to classical simplified Keller-Segel model in one species case to the multispecies case, using the adequately tools for PDE’s systems. We used the moment method to prove Blow-up and have been bounding the entropy to show global existence.

Cette thèse est consacrée à l’étude d’une classe d’équations de réaction-diffusion avec advection non-locale. La motivation vient du mouvement cellulaire avec le phénomène de ségrégation observé dans des expérimentations de co-culture cellulaire. La première partie de la thèse développe principalement le cadre théorique de notre modèle, à savoir le caractère bien posé du problème et le comportement asymptotique des solutions dans les cas d'une ou plusieurs espèces.Dans le Chapitre 1, nous montrons qu'une équation scalaire avec un noyau non-local ayant la forme d'une fonction étagée, peut induire des bifurcations de Turing et de Turing-Hopf avec le nombre d’ondes dominant aussi grand que souhaité. Nous montrons que les propriétés de bifurcation de l'état stable homogène sont intimement liées aux coefficients de Fourier du noyau non-local.Dans le Chapitre 2, nous étudions un modèle d'advection non-local à deux espèces avec inhibition de contact lorsque la viscosité est égale à zéro. En employant la notion de solution intégrée le long des caractéristiques, nous pouvons rigoureusement démontrer le caractère bien posé du problème ainsi que la propriété de ségrégation d'un tel système. Par ailleurs, dans le cadre de la théorie des mesures de Young, nous étudions le comportement asymptotique des solutions. D'un point de vue numérique, nous constatons que sous l'effet de la ségrégation, le modèle d'advection non-locale admet un principe d'exclusion.Dans le dernier Chapitre de la thèse, nous nous intéressons à l'application de nos modèles aux expérimentations de co-culture cellulaire. Pour cela, nous choisissons un modèle hyperbolique de Keller-Segel sur un domaine borné. En utilisant les données expérimentales, nous simulons un processus de croissance cellulaire durant 6 jours dans une boîte de pétri circulaire et nous discutons de l’impact de la propriété de ségrégation et des distributions initiales sur les proportions de la population finale. / This thesis is devoted to the study for a class of reaction-diffusion equations with nonlocal advection. The motivation comes from the cell movement with segregation phenomenon observed in cell co-culture experiments. The first part of the thesis mainly develops the theoretical framework of our model, namely the well-posedness and asymptotic behavior of solutions in both single-species and multi-species cases.In Chapter 1, we show a single scalar equation with a step function kernel may display Turing and Turing-Hopf bifurcations with the dominant wavenumber as large as we want. We find the bifurcation properties of the homogeneous steady state is closed related to the Fourier coefficients of the nonlocal kernel.In Chapter 2, we study a two-species nonlocal advection model with contact inhibition when the viscosity equals zero. By employing the notion of the solution integrated along the characteristics, we rigorously prove the well-posedness and segregation property of such a hyperbolic nonlocal advection system. Besides, under the framework of Young measure theory, we investigate the asymptotic behavior of solutions. From a numerical perspective, we find that under the effect of segregation, the nonlocal advection model admits a competitive exclusion principle.In the last Chapter, we are interested in applying our models to a cell co-culturing experiment. To that aim, we choose a hyperbolic Keller-Segel model on a bounded domain. By utilizing the experimental data, we simulate a 6-day process of cell growth in a circular petri dish and discuss the impact of both the segregation property and initial distributions on the finial population proportions.