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 à 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 presents a computationally efficient cryptosystem based on chaotic continuous-interval cellular automata (CCA). This cryptosystem increases data protection as demonstrated by its flexibility to encrypt/decrypt information from distinct sources (e.g., text, sound, and images). This cryptosystem has the following enhancements over the previous chaos-based cryptosystems: (i) a mathematical model based on a new chaotic CCA strange attractor, (ii) integration of modules containing dynamical systems to generate complex sequences, (iii) generation of an unlimited number of keys due to the features of chaotic phenomena obtained through CCA, which is an improvement over previous symmetric cryptosystems, and (iv) a high-quality concealment of the cryptosystem strange attractor. Instead of using differential equations, a process of mixing chaotic sequences obtained from CCA is also introduced. As compared to other recent approaches, this mixing process provides a basis to achieve higher security by using a higher degree of complexity for the encryption/decryption processes. This cryptosystem is tested through the following three methods: (i) a stationarity test based on the invariance of the first ten statistical moments, (ii) a polyscale test based on the variance fractal dimension trajectory (VFDT) and the spectral fractal dimension (SFD), and (iii) a surrogate data test. This cryptosystem secures data from distinct sources, while leaving no patterns in the ciphertexts. This cryptosystem is robust in terms of resisting attacks that: (i) identify a chaotic system in the time domain, (ii) reconstruct the chaotic attractor by monitoring the system state variables, (iii) search the system synchronization parameters, (iv) statistical cryptanalysis, and (v) polyscale cryptanalysis.

This exploratory qualitative case study provides a description of the Glencree Centre for Peace and Reconciliation’s practice in addressing deep-rooted conflict, from the Republic of Ireland. This research grew out of practical problems from the field of conflict resolution in Canada, in particular interest-based mediation, in addressing deep-rooted conflict. Using an extended epistemology, data is harvested from praxis to create naturalistic generalizations: guidelines for addressing deep-rooted conflict. The research findings are the result of a synthesis of three data sources: interviews with facilitators from Glencree, textual data, and nearly five months of onsite observation. The main themes derived from the research include: Glencree’s Diverse Practice; Glencree’s Approach to Conflict; Glencree’s Identity; Glencree’s Approach to Deep-Rooted Conflict; and Implementing Glencree’s Approach. This study is intended as a snapshot in time of a set of dynamic and emergent ideas addressing conflict in practice. Through an inductive research design, findings from praxis are related to theory from the field of conflict resolution. In addition, implications for addressing deep-rooted conflict are identified, including Glencree’s emphasis on the need for flexibility as a characteristic for conflict work, and an underlying worldview incorporating aspects of dynamic systems theory and chaos theory.

Dans le but de clarifier les aspects dynamiques des modèles galactiques triaxiaux, le potentiel logarithmique est étudié a travers la méthode d'analyse en fréquence. Les caractéristiques dynamiques principales du système sont présentées en utilisant le formalisme hamiltonien approprié. Afin de comparer cette nouvelle approche avec des études précédentes, la méthode est appliquée a la version axisymétrique du potentiel. La précision de la méthode est démontrée a travers des techniques de perturbation et des transformations numériques en variables action-angle. En outre, la construction des applications fréquence pour plusieurs valeurs du paramètre de perturbation permet de fournir une vision globale de la dynamique du potentiel plan. Les zones chaotiques, les résonances importantes ainsi que les orbites périodiques sont détectées. La méthode est appliquée ensuite a la version tridimensionnelle du potentiel logarithmique. Les approximations quasi-périodiques fournies par la méthode permettent de clarifier la dynamique des types d'orbites principales et leur connexion avec des perturbations du hamiltonien général. Tous les détails fins de la dynamique, qui sont associés a l'addition du troisième degré de liberté, sont représentés dans les applications fréquence complètes, des images instantanées du réseau d'Arnold (''Arnol'd web'') du système. Ainsi, nous pouvons visualiser l'étendu des zones chaotiques et l'influence des lignes résonantes dans l'espace physique du système. Cette approche révèle plusieurs caractéristiques dynamiques inconnues des potentiels galactiques triaxiaux et indique que le chaos doit être une caractéristique importante des configurations triaxiales. Nous discutons finalement l'influence de ces résultats sur la construction des modèles galactiques auto-consistants.

This exploratory qualitative case study provides a description of the Glencree Centre for Peace and Reconciliation’s practice in addressing deep-rooted conflict, from the Republic of Ireland. This research grew out of practical problems from the field of conflict resolution in Canada, in particular interest-based mediation, in addressing deep-rooted conflict. Using an extended epistemology, data is harvested from praxis to create naturalistic generalizations: guidelines for addressing deep-rooted conflict. The research findings are the result of a synthesis of three data sources: interviews with facilitators from Glencree, textual data, and nearly five months of onsite observation. The main themes derived from the research include: Glencree’s Diverse Practice; Glencree’s Approach to Conflict; Glencree’s Identity; Glencree’s Approach to Deep-Rooted Conflict; and Implementing Glencree’s Approach. This study is intended as a snapshot in time of a set of dynamic and emergent ideas addressing conflict in practice. Through an inductive research design, findings from praxis are related to theory from the field of conflict resolution. In addition, implications for addressing deep-rooted conflict are identified, including Glencree’s emphasis on the need for flexibility as a characteristic for conflict work, and an underlying worldview incorporating aspects of dynamic systems theory and chaos theory.

Ao passar por uma fina camada magnética uma corrente spin polarizada pode produzir um efeito de torque clássico atuando na camada, sendo capaz de gerar precessão e reversão da magnetização. Esse efeito tem sido alvo de inúmeras pesquisas, em especial pela possibilidade de aplicações em memórias magnéticas não voláteis e em nano-osciladores de alta frequência, entretanto outras características podem ser exploradas. Em particular, devido ao seu caráter não-linear, torques de spin aplicados em camadas magnéticas podem fornecer condições para aparecimento de caos determinístico e ressonância estocástica. Caos determinístico pode ocorrer em sistemas dinâmicos contínuos que tenham ao menos três graus de liberdade. Nesse caso, mesmo que apenas termos determinísticos sejam considerados, a combinação de termos não-lineares e alta sensibilidade em relação a condições iniciais ou pequenas perturbações pode gerar irregularidade e imprevisibilidade no sistema. Ressonância estocástica é o nome que se dá para fenômenos em que a adição de ruído a um sistema pode melhorar a resposta do mesmo, existindo um nível ótimo de ruído. Esse fenômeno pode ser usado para detecção e amplificação de sinais de baixa intensidade, por exemplo. Aqui analisamos a dinâmica da magnetização da camada livre de junções magnéticas em geometrias do tipo nanopilar, com o estudo dividido em dinâmicas determinísticas e estocásticas. Dentro da análise apenas com termos determinísticos, buscamos verificar comportamentos regulares, irregulares e caóticos, caracterizando o sistema através da geração de diagramas com as fases dinâmicas para diferentes valores de parâmetros. Foram vistas duas geometrias diferentes, sendo que em uma delas foi possível fazer a caracterização completa das fases dinâmicas do sistema. No caso de dinâmicas estocásticas, buscamos explorar efeitos não-lineares e flutuações térmicas, analisando ressonância estocástica e sincronização facilitada por ruído em uma junção túnel magnética, além de estudar as respostas dinâmicas quando há apenas o torque de Slonczewski e quando também está presente o torque tipo campo. Foi possível observar a influência de diversos parâmetros, como a amplitude da corrente aplicada e a frequência de entrada, na resposta magnética e na sincronização de dispositivos estocásticos. Além disso, vimos que com a inclusão do torque tipo campo aparece um possível novo comportamento, similar à ressonância, em alta frequência, ainda não detectado experimentalmente. Esses resultados são importantes pela possibilidade de uso desses dispositivos spintrônicos em transmissão segura de dados, comunicação em alta frequência e em uma nova geração de dispositivos bio-inspirados e eficientes energeticamente. / When passing through a fine magnetic layer a spin polarized electric current may result in a classical torque acting on the layer, being capable of causing magnetization precession and reversal. This effect has been object of numerous researches, specially because of possible applications in non-volatile magnetic memories and high frequency nanooscillators. However, other characteristics can be exploited. In particular, because of its non-linear features, spin torques acting on magnetic layers can generate the conditions for deterministic chaos and stochastic resonance to arise. Deterministic chaos may happen in continuous nonlinear dynamical systems with at least three degrees of freedom. In this case, even if only deterministic terms are considered, the combination of nonlinearities with high sensitivity on initial conditions or small perturbations can produce irregularity and unpredictability in the dynamical behaviour. Stochastic resonance is the phenomenon in which the addition of noise in a system can produce a better output, or system response, existing an optimal noise level. This effect can be used as a way to detect and amplify low intensity signal, for example. In this PhD Thesis we study the magnetization dynamics on the free layer of magnetic junctions in nanopillar geometries. The work is divided into two parts: deterministic and stochastic dynamics. When analysing the deterministic case we tried to characterize regular, irregular and chaotic behaviours, producing dynamical phases diagrams for different system parameters. Two different geometries were analysed, being possible to generate a complete characterization of the dynamical phases in one of them. For the stochastic case we tried to explore nonlinear effects and thermal fluctuations, analysing stochastic resonance and noise-enhanced synchronization in a magnetic tunnel junction and studying the dynamical response when only one spin torque is considered, the Slonczewski torque, and also when a perpendicular torque, the field-like torque, is present. We were able to see the influence of several system parameters, such as the amplitude of the applied electric current and the input frequency, on the system response and on the synchronization of stochastic systems. Also, we noticed that with the inclusion of the field-like torque a possibly new high frequency resonance-like behaviour appears. These results are important because of the possibility of using new spintronic devices for secure data transmission, high frequency communications and on a new generation of bio-inspired devices.

This thesis constitutes a narrative that explores an alternative meaning construction for the experience of loss. During the telling of this story, I consider the appropriateness of adopting the 'new paradigm' approach for this particular thesis, and the constructivist and social constructionist epistemological assumptions underlying such an approach. I delve into the use of 'self as researcher under this epistemological umbrella. This is followed by an exploration of 'chaos theory' and its application to social systems. And finally, I consider the usefulness of this theory in constructing meanings for loss experiences on various systemic levels within my own family system. / Psychology / M.A.(Clinical Psychology)

Response of flexible structures — such as cable-supported bridges and aircraft wings — is associated with a number of uncertainties in structural and flow parameters. This thesis is aimed at efficient uncertainty quantification in a few such flow and flow-induced structural response problems. First, the uncertainty quantification in the lift force exerted on a submerged body in a potential flow is considered. To this end, a new method — termed here as semi-intrusive stochastic perturbation (SISP) — is proposed. A sensitivity analysis is also performed, where for the global sensitivity analysis (GSA) the Sobol’ indices are used. The polynomial chaos expansion (PCE) is used for estimating these indices. Next, two stability problems —divergence and flutter — in the aeroelasticity are studied in the context of reliability based design optimization (RBDO). Two modifications are proposed to an existing PCE-based metamodel to reduce the computational cost, where the chaos coefficients are estimated using Gauss quadrature to gain computational speed and GSA is used to create nonuniform grid to reduce the cost even further. The proposed method is applied on a rectangular unswept cantilever wing model. Next, reliability computation in limit cycle oscillations (LCOs) is considered. While the metamodel performs poorly in this case due to bimodality in the distribution, a new simulation-based scheme proposed to this end. Accordingly, first a reduced-order model (ROM) is used to identify the critical region in the random parameter space. Then the full-scale expensive model is run only over a this critical region. This is applied to the rectangular unswept cantilever wing with cubic and fifth order stiffness terms in its equation of motion. Next, the wind speed is modeled as a spatio-temporal process, and accordingly new representations of spatio-temporal random processes are proposed based on tensor decompositions of the covariance kernel. These are applied to three problems: a heat equation, a vibration, and a readily available covariance model for wind speed. Finally, to assimilate available field measurement data on wind speed and to predict based on this assimilation, a new framework based on the tensor decompositions is proposed. The framework is successfully applied to a set of measured data on wind speed in Ireland, where the prediction based on simulation is found to be consistent with the observed data.

Rapid technological development and the emerging necessity to insert this reality in the school environment demand Brazilian government\'s efforts to develop new educational policies. One of the latest initiatives is the One Computer per Student Program (PROUCA), whose goal is to provide a netbook for each student of some selected schools. This research aims to analyze what kind of influence is exerted by these netbooks in English classes of elementary school, from a regular public school of Uberaba/MG. This is a qualitative ethnographic research, guided by the Paradigm of Complexity and theories on the process of language teaching and learning mediated by technology. Participants are students from two classes of sixth grade and three classes of eighth grade, two English teachers, the school principal and the director of the Department of Information and Communication Technology from Uberaba s Board of Education. Data were collected through argumentative texts produced by the students and the English teachers, besides semi-structured interviews performed with some selected students and with the mentioned directors and field notes. The generated results show that students perceive the use of netbooks as a positive aspect in English classes, but they point out the problems with the Internet link as one of the main weaknesses of the program. These inconveniences let students become demotivated and demand preparation and creativity for teachers to deal with a system on the edge of chaos. In addition, the data reflect the possibility to develop dynamic, fun and productive classes without the use of digital technologies. Motivation to learn depends, essentially, on the pedagogy adopted by the teacher to conduct their classes. / O rápido desenvolvimento tecnológico e a emergente necessidade de inserção dessa realidade no ambiente escolar exigem esforços do governo brasileiro na elaboração de novas políticas educacionais. Uma das iniciativas mais recentes é o Programa Um Computador por Aluno (PROUCA), cujo objetivo é disponibilizar um netbook para cada aluno das escolas contempladas. Esta pesquisa objetiva analisar qual o tipo de influência exercida por esses netbooks nas aulas de língua inglesa, do Ensino Fundamental, de uma escola municipal regular de Uberaba/MG. Trata-se de uma pesquisa qualitativa, de cunho etnográfico, orientada pelo Paradigma da Complexidade e por teorias sobre o processo de ensino e aprendizagem de línguas mediado por tecnologias. Os participantes são alunos de duas turmas de sexto ano e três turmas de oitavo ano, além de dois professores de inglês, a diretora da escola e o diretor do Departamento de Tecnologias de Informação e Comunicação da Secretaria de Educação de Uberaba. Os dados foram coletados através de textos argumentativos produzidos pelos alunos e pelos professores de inglês, entrevistas semiestruturadas realizadas com alguns alunos selecionados e com os diretores mencionados e notas de campo. Os resultados gerados revelam que os alunos percebem a utilização dos netbooks como um aspecto positivo nas aulas de inglês, mas apontam os problemas de conexão com a Internet como um dos principais pontos negativos do programa. Esses transtornos causam desmotivação nos alunos e demandam preparação e criatividade dos professores, para lidar com um sistema no limite do caos. Além disso, os dados refletem a possibilidade de se desenvolver aulas dinâmicas, divertidas e produtivas sem o uso de tecnologias digitais. A motivação para aprender depende, essencialmente, da pedagogia adotada pelo professor ao ministrar suas aulas. / Mestre em Estudos Linguísticos

Ao passar por uma fina camada magnética uma corrente spin polarizada pode produzir um efeito de torque clássico atuando na camada, sendo capaz de gerar precessão e reversão da magnetização. Esse efeito tem sido alvo de inúmeras pesquisas, em especial pela possibilidade de aplicações em memórias magnéticas não voláteis e em nano-osciladores de alta frequência, entretanto outras características podem ser exploradas. Em particular, devido ao seu caráter não-linear, torques de spin aplicados em camadas magnéticas podem fornecer condições para aparecimento de caos determinístico e ressonância estocástica. Caos determinístico pode ocorrer em sistemas dinâmicos contínuos que tenham ao menos três graus de liberdade. Nesse caso, mesmo que apenas termos determinísticos sejam considerados, a combinação de termos não-lineares e alta sensibilidade em relação a condições iniciais ou pequenas perturbações pode gerar irregularidade e imprevisibilidade no sistema. Ressonância estocástica é o nome que se dá para fenômenos em que a adição de ruído a um sistema pode melhorar a resposta do mesmo, existindo um nível ótimo de ruído. Esse fenômeno pode ser usado para detecção e amplificação de sinais de baixa intensidade, por exemplo. Aqui analisamos a dinâmica da magnetização da camada livre de junções magnéticas em geometrias do tipo nanopilar, com o estudo dividido em dinâmicas determinísticas e estocásticas. Dentro da análise apenas com termos determinísticos, buscamos verificar comportamentos regulares, irregulares e caóticos, caracterizando o sistema através da geração de diagramas com as fases dinâmicas para diferentes valores de parâmetros. Foram vistas duas geometrias diferentes, sendo que em uma delas foi possível fazer a caracterização completa das fases dinâmicas do sistema. No caso de dinâmicas estocásticas, buscamos explorar efeitos não-lineares e flutuações térmicas, analisando ressonância estocástica e sincronização facilitada por ruído em uma junção túnel magnética, além de estudar as respostas dinâmicas quando há apenas o torque de Slonczewski e quando também está presente o torque tipo campo. Foi possível observar a influência de diversos parâmetros, como a amplitude da corrente aplicada e a frequência de entrada, na resposta magnética e na sincronização de dispositivos estocásticos. Além disso, vimos que com a inclusão do torque tipo campo aparece um possível novo comportamento, similar à ressonância, em alta frequência, ainda não detectado experimentalmente. Esses resultados são importantes pela possibilidade de uso desses dispositivos spintrônicos em transmissão segura de dados, comunicação em alta frequência e em uma nova geração de dispositivos bio-inspirados e eficientes energeticamente. / When passing through a fine magnetic layer a spin polarized electric current may result in a classical torque acting on the layer, being capable of causing magnetization precession and reversal. This effect has been object of numerous researches, specially because of possible applications in non-volatile magnetic memories and high frequency nanooscillators. However, other characteristics can be exploited. In particular, because of its non-linear features, spin torques acting on magnetic layers can generate the conditions for deterministic chaos and stochastic resonance to arise. Deterministic chaos may happen in continuous nonlinear dynamical systems with at least three degrees of freedom. In this case, even if only deterministic terms are considered, the combination of nonlinearities with high sensitivity on initial conditions or small perturbations can produce irregularity and unpredictability in the dynamical behaviour. Stochastic resonance is the phenomenon in which the addition of noise in a system can produce a better output, or system response, existing an optimal noise level. This effect can be used as a way to detect and amplify low intensity signal, for example. In this PhD Thesis we study the magnetization dynamics on the free layer of magnetic junctions in nanopillar geometries. The work is divided into two parts: deterministic and stochastic dynamics. When analysing the deterministic case we tried to characterize regular, irregular and chaotic behaviours, producing dynamical phases diagrams for different system parameters. Two different geometries were analysed, being possible to generate a complete characterization of the dynamical phases in one of them. For the stochastic case we tried to explore nonlinear effects and thermal fluctuations, analysing stochastic resonance and noise-enhanced synchronization in a magnetic tunnel junction and studying the dynamical response when only one spin torque is considered, the Slonczewski torque, and also when a perpendicular torque, the field-like torque, is present. We were able to see the influence of several system parameters, such as the amplitude of the applied electric current and the input frequency, on the system response and on the synchronization of stochastic systems. Also, we noticed that with the inclusion of the field-like torque a possibly new high frequency resonance-like behaviour appears. These results are important because of the possibility of using new spintronic devices for secure data transmission, high frequency communications and on a new generation of bio-inspired devices.