The focus of this thesis is the numerical study of subcritical transition to turbulence in boundary-layer flows. For the most part, boundary layers with uniform suction are considered. Constant homogeneous suction counteracts the spatial growth of the boundary layer, rendering the flow parallel. This enables research approaches which are not feasible in the context of spatially developing flows. In the first part, the laminar–turbulent separatrix of the asymptotic suction boundary layer (ASBL) is investigated numerically by means of an edge-tracking algorithm. The obtained edge states experience recurrent dynamics, going through calm and bursting phases. The self-sustaining mechanism bears many similarities with the classical regeneration cycle of near-wall turbulence. The recurrent simple structure active during calm phases is compared to the nucleation of turbulence events in bypass transition originating from delocalised initial conditions. The implications on the understanding of the bypass-transition process and the edge state's role are discussed. Based on this understanding, a model is constructed which predicts the position of the nucleation of turbulent spots during free-stream turbulence induced transition in spatially developing boundary-layer flow. This model is used together with a probabilistic cellular automaton (PCA), which captures the spatial spreading of the spots, correctly reproducing the main statistical characteristics of the transition process. The last part of the thesis is concerned with the spatio-temporal aspects of turbulent ASBL in extended numerical domains near the onset of sustained turbulence. The different behaviour observed in ASBL, i.e. absence of sustained laminar–turbulent patterns, which have been reported in other wall-bounded flows, is associated with different character of the large-scale flow. In addition, an accurate quantitative estimate for the lowest Reynolds number with sustained turbulence is obtained / <p>QC 20160429</p>

Made available in DSpace on 2016-03-15T19:38:04Z (GMT). No. of bitstreams: 1 ANA LEDA SILVA MORAES.pdf: 1708515 bytes, checksum: 8e07dd190f9a5fd165c14e35c2c626b0 (MD5) Previous issue date: 2016-02-01 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Epidemiology is the science that studies the occurrence of diseases in a population. The results of these studies allow a comprehension of a disease propagation and enable actions in order to control epidemics. There are many mathematical models used in epidemiological studies; in which SIR-like models are the most used. In this model, the population is divided into three groups: S - susceptible individuals to infection, I - infected individuals, and R - recovered individuals. The proposal of this thesis is, based on a new SIR model, taking into consideration the effect of recovered individuals on the propagation of contagious diseases and on the recovery of sick individuals. This can be relevant to the study of propagation of typical diseases in children, since immune individuals can catalyze the encounters among susceptible children and infected children, as well as to contribute to the recovery of sick individuals. The predictive ability of the proposed model is evaluated from the records refering to the incidence of chickenpox in Belgium, Germany and Italy, in a pre-vaccination era. / Epidemiologia é a ciência que estuda as ocorrências de doenças numa população. Os resultados desses estudos permitem uma compreensão do comportamento da incidência da doença e possibilita ações a fim de controlar epidemias. Há vários modelos matemáticos que são utilizados para estudos epidemiológicos, sendo modelos do tipo SIR os mais empregados. Nesse modelo, divide-se a população em três classes: &#119878; - indivíduos suscetíveis à infecção, &#119868; - indivíduos infectados, e &#119877; - indivíduos recuperados. A proposta desta dissertação é, a partir de um novo modelo SIR, levar em consideração o efeito de indivíduos recuperados na propagação de doenças contagiosas e na recuperação de indivíduos doentes. Isso pode ser relevante no estudo da propagação de infecções típicas de crianças, já que indivíduos imunes podem servir como catalisador de encontros entre crianças suscetíveis e crianças infectadas, bem como contribuir para a recuperação de indivíduos doentes. A capacidade preditiva do modelo proposto é avaliada a partir dos registros referentes à incidência de varicela na Alemanha, Bélgica e Itália, numa era pré-vacinação.

Made available in DSpace on 2016-03-15T19:38:51Z (GMT). No. of bitstreams: 1 Pericles do Prado Turnes Junior.pdf: 1375255 bytes, checksum: 24dc630ef135368b840995d533e161e8 (MD5) Previous issue date: 2014-07-29 / Instituto Presbiteriano Mackenzie / There are many epidemiological models written in terms of ordinary differential equations (ODE). This approach is based on the homogeneous mixing assumption; that is, the topological structure of the network of social contacts, established by the individuals in the population, is not relevant to forecast the propagation of the studied pathogen. In this work, an epidemiological model formulated in terms of ODE and probabilistic cellular automata (PCA) is proposed to study the spread of contagious diseases that do not conferimmunity. The state variables of this model are the percentages of susceptible individuals, infected individuals and empty space. It is shown that this dynamical system can experience Hopf and transcritical bifurcations. Then, this model is used to evaluate the validity of the homogeneous mixing assumption, by using real data related to the transmission of gonorrhea, hepatitis C virus, human immunodeficiency virus and obesity. / Muitos modelos epidemiológicos são escritos em termos de equações diferenciais ordinárias (EDO). Essa abordagem baseia-se no pressuposto de mistura homogênea; ou seja, a estrutura topológica da rede de contatos sociais, estabelecida pelos indivíduos da população, não é relevante para prever o avanço do patógeno em estudo. Neste trabalho, é proposto um modelo epidemiológico formulado em termos de EDO e de autômato celular probabilista (ACP) para estudar a propagação de doenças contagiosas que não conferem imunidade. As variáveis de estado desse modelo são as porcentagens de indivíduos suscetíveis, de indivíduos infectados e de espaço vazio. Mostra-se que esse sistema dinâmico pode apresentar bifurcações de Hopf e transcrítica. O modelo é , então, usado para avaliar a validade da hipótese de mistura homogênea, usando dados relacionados à transmissão de gonorreia, vírus da hepatite C, vírus da imunodeficiência humana e obesidade.

La première partie de cette thèse porte sur les automates cellulaires probabilistes (ACP) sur la ligne et à deux voisins. Pour un ACP donné, nous cherchons l'ensemble de ces lois invariantes. Pour des raisons expliquées en détail dans la thèse, ceci est à l'heure actuelle inenvisageable de toutes les obtenir et nous nous concentrons, dans cette thèse, surles lois invariantes markoviennes. Nous établissons, tout d'abord, un théorème de nature algébrique qui donne des conditions nécessaires et suffisantes pour qu'un ACP admette une ou plusieurs lois invariantes markoviennes dans le cas où l'alphabet E est fini. Par la suite, nous généralisons ce résultat au cas d'un alphabet E polonais après avoir clarifié les difficultés topologiques rencontrées. Enfin, nous calculons la fonction de corrélation du modèleà 8 sommets pour certaines valeurs des paramètres du modèle en utilisant une partie desrésultats précédents. / The first part of this thesis is about probabilistic cellular automata (PCA) on the line and with two neighbors. For a given PCA, we look for the set of its invariant distributions. Due to reasons explained in detail in this thesis, it is nowadays unthinkable to get all of them and we concentrate our reections on the invariant Markovian distributions. We establish, first, an algebraic theorem that gives a necessary and sufficient condition for a PCA to have one or more invariant Markovian distributions when the alphabet E is finite. Then, we generalize this result to the case of a polish alphabet E once we have clarified the encountered topological difficulties. Finally, we calculate the 8-vertex model's correlation function for some parameters values using previous results.The second part of this thesis is about infinite iterations of stochastic processes. We establish the convergence of the finite dimensional distributions of the α-stable processes iterated n times, when n goes to infinite, according to parameter of stability and to drift r. Then, we describe the limit distributions. In the iterated Brownian motion case, we show that the limit distributions are linked with iterated functions system.