Cette thèse comporte trois parties essentiellement indépendantes, dont chacune est consacrée à l'étude d'un système de particules, suivant une dynamique déterministe ou aléatoire, et à l'intérieur duquel les interactions se font uniquement aux collisions entre les particules.La Partie I propose une étude numérique et théorique des états stationnaires hors de l'équilibre du Modèle d'Échange Complet, introduit en physique pour comprendre le transport de la chaleur dans certains matériaux poreux.La Partie II est consacrée à un système de particules browniennes évoluant sur la droite réelle et interagissant à travers leur rang. Le comportement limite de ce système, en temps long et à grand nombre de particules, est décrit, puis les résultats sont appliqués à l'étude d'un modèle de marché financier dit modèle d'Atlas en champ moyen.La Partie III introduit une version multitype du système de particules étudié dans la partie précédente, qui permet d'approcher des systèmes paraboliques d'équations aux dérivées partielles non-linéaires. La limite petit bruit de ce système est appelée dynamique des particules collantes multitype et approche cette fois des systèmes hyperboliques. Une étude détaillée de cette dynamique donne des estimations de stabilité en distance de Wasserstein sur les solutions de ces systèmes. / This thesis contains three independent parts, each one of which is dedicated to the study of a particle system, following either a deterministic or a stochastic dynamics, and in which interactions only occur at collisions. Part I contains a numerical and theoretical study of nonequilibrium steady states of the Complete Exchange Model, which was introduced by physicists in order to understand heat transfer in some porous materials. Part II is dedicated to a system of Brownian particles evolving on the real line and interacting through their ranks. The long time and mean-field behaviour of this system is described, then the results are applied to the study of a model of equity market called the mean-field Atlas model. Part III introduces a multitype version of the particle system studied in the previous part, which allows to approximate parabolic systems of nonlinear partial differential equations. The small noise limit of of this system is called multitype sticky particle dynamics and now approximates hyperbolic systems. A detailed study of this dynamics provides stability estimates in Wasserstein distance for the solutions of these systems.

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Please note: creative writing theses are permanently embargoed in OpenBU. No public access is forecasted for these. To request private access, please click on the lock icon and filled out the appropriate web form. / BEASTS is a character driven play that explores the chaos of American womanhood through the dark underbelly of a relationship between Fran, a pregnant suburbanite and her older sister Judy, an irreverent artist with a propensity for disruption. When Judy hears that Fran’s husband, Jim is on a business trip she decides to pay Fran a visit. The friction between these siblings is palpable and continues to intensify as Judy unearths confounding secrets and infringes upon the relationship that Fran has with her Doula, Amelia, an elitist earth mama who’s been Fran’s only female friend since relocating back East. The world of the play begins in realism and ends in magical realism; as their environment starts to mirror the anarchy of their psychological labyrinthine world: a giant tree falls in the middle of the living room, the walls of the house cave in, raging wolves howl in the distance. Form and logic disintegrate into another realm as Fran and Judy unwittingly fight through pain to arrive at a moment of love which is devitalized when Jim returns home. / 2999-01-01T00:00:00Z

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Genetic and home chaos influences in early childhood have been independently associated with externalizing problems, characterized by inattentive, hyperactive, and aggressive behaviors. However, the Behavioral Genetics approach indicates that genetic and environmental influences, although independently effective, interact to produce behavior throughout development. Thus, this thesis uses two samples, the Early Growth and Development study (EGDS), n= 564, and the Avon Longitudinal Study of Parents and Children (ALSPAC), n= 8,952, and two genetically-sensitive approaches, a parent-child adoption approach and a polygenic scoring approach, to examine how genetic influences and home chaos interact in early childhood (age 3-4) to predict externalizing problems later in childhood (age 7). Results indicate that, although home chaos is correlated with later externalizing problems, the effect is reduced in the context of earlier externalizing, possibly suggesting that home chaos is most salient for concurrent, not later, externalizing problems. In addition, genetic influences were not predictive of externalizing problems in either study, nor was the interaction of home chaos and genetic influences. This pattern of results suggests that, although home chaos may be an important factor for concurrent externalizing problems, other factors, e.g., parenting style and prenatal risk, may be more salient than home chaos, especially in interaction with genetic effects. Further, failure to find genetic influence in this thesis suggest that accounting for the broad scope of genetic influences on complex traits like externalizing and the specific genetic risk for individual externalizing phenotypes is important in attempts to find genetic influence and interaction.

We study the dynamics of time-like geodesics in the field of black holes perturbed by a circular ring or disc, restricting to static and axisymmetric class of space-times. Two analytical methods are tested which do not require solving the equations of motion: (i) the so-called geometric criterion of chaos based on eigenvalues of the Riemann tensor, and (ii) the method of Melnikov which detects the chaotic layer arising by break-up of a homoclinic orbit. Predictions of both methods are compared with numerical results in order to learn how accurate and reliable they are.

Physical systems are usually not closed and insight about their internal structure is experimentally derived by scattering. This is efficiently described by resonance eigenfunctions of non-Hermitian quantum systems with a corresponding classical dynamics that allows for the escape of particles. For the phase-space distribution of resonance eigenfunctions in chaotic systems with partial and full escape we obtain a universal description of their semiclassical limit in terms of classical conditional invariant measures with the same decay rate. For partial escape, we introduce a family of conditionally invariant measures with arbitrary decay rates based on the hyperbolic dynamics and the natural measures of forward and backward dynamics. These measures explain the multifractal phase-space structure of resonance eigenfunctions and their dependence on the decay rate. Additionally, for the nontrivial limit of full escape we motivate the hypothesis that resonance eigenfunctions are described by conditionally invariant measures that are uniformly distributed on sets with the same temporal distance to the quantum resolved chaotic saddle. Overall we confirm quantum-to-classical correspondence for the phase-space densities, for their fractal dimensions, and by evaluating their Jensen–Shannon distance in a generic chaotic map with partial and full escape, respectively. / Typische physikalische Systeme sind nicht geschlossen, sodass ihre innere Struktur mit Hilfe von Streuexperimenten untersucht werden kann. Diese werden mit Hilfe einer nicht-Hermiteschen Quantendynamik und deren Resonanzeigenzuständen beschrieben. Die dabei zugrunde liegende klassische Dynamik berücksichtigt den Verlust von Teilchen. Für die semiklassische Phasenraumverteilung solcher Resonanzeigenzustände in chaotischen Systemen mit partieller und voller Öffnung entwickeln wir eine universelle Beschreibung mittels bedingt invarianter Maße gleicher Zerfallsrate. Für partiellen Zerfall stellen wir eine Familie bedingt invarianter Maße mit beliebiger Zerfallsrate vor, welche auf der hyperbolischen Dynamik und den natürlichen Maßen der vorwärts gerichteten und der invertierten Dynamik aufbauen. Diese Maße erklären die multifraktale Phasenraumstruktur der Resonanzzustände und deren Abhängigkeit von der Zerfallsrate. Darüber hinaus motivieren wir für den nicht trivialen Grenzfall voll geöffneter Systeme die Hypothese, dass Resonanzeigenzustände durch ein bedingt invariantes Maß beschrieben werden, welches gleichverteilt auf solchen Mengen ist, die den gleichen zeitlichen Abstand zum quantenunscharfen chaotischen Sattel haben. Insgesamt bestätigen wir die quantenklassische Korrespondenz für die Phasenraumdichten, deren fraktale Dimensionen und durch Auswertung ihres Jensen–Shannon Abstandes in einer generischen chaotischen Abbildung sowohl für partielle als auch für volle Öffnung.

Tunneling is a central result of quantum mechanics. It allows quantum particles to enter regions which are inaccessible by classical dynamics. Consequences of the tunneling process are most relevant. For example it causes the alpha-decay of radioactive nuclei and it is argued that proton tunneling is decisive for the emergence of DNA mutations. The theoretical prediction of corresponding tunneling rates is explained in standard textbooks on quantum mechanics for regular systems. Typical physical systems such as atoms or molecules, however, also show chaotic motion. Here the calculation of tunneling rates is more demanding. In this text a selection of articles on the prediction of tunneling rates in systems which allow for regular and chaotic motion is summarized. The presented approach is then used to explain consequences of tunneling on the quantum spectrum, such as the universal power-law behavior of small energy spacings and the flooding of regular states.

Orientador: Weber Flávio Pereira / Resumo: A Teoria dos Sistemas Dinâmicos pode ser aplicada em diversas áreas da ciência, para, por exemplo, modelar fenômenos e problemas: Biológicos, da Física, Mecânica, Eletrônica, Economia, etc. Um sistema pode ser definido como um conjunto de elementos agrupados que mantêm alguma interação, de modo que existam relações de causa e efeito. Dizemos que é dinâmico quando algumas grandezas que compõem os elementos variam no tempo, sendo o tempo discreto quando a variável tempo é um número inteiro. Na busca de uma compreensão qualitativa e/ou topológica de um sistema, revela-se uma gama muito grande de movimentos que podem ser tanto regulares quanto caóticos. O termo “caos” só foi introduzido por James Yorke e TienYien Li em 1975, num artigo que simplificava um dos resultados da escola russa: o Teorema de Sharkovskii de 1964. Esporadicamente, antes e depois da introdução do termo, os sistemas caóticos apareciam na literatura aplicada, o mais famoso deles foi por Edward Norton Lorenz em 1963, que se propôs a modelar a convecção atmosférica. Em seus estudos ele descobriu que, para o seu modelo matemático, ínfimas modificações nas coordenadas iniciais mudavam de forma significativa os resultados finais, daí originou o termo popular do fenômeno (Efeito Borboleta). Mais tarde, em 1989, Robert Luke Devaney no seu livro: “An Introduction to Chaotic Dynamical Systems” [11], definiu um sistema como caótico se ele tem uma dependência sensível das condições iniciais, é topologicamente transitivo e suas ... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: Dynamical Systems Theory can be applied in various areas of science, for example, to model phenomena and problems: biology, physics, mechanics, electronics, economics, etc. A system can be defined as a set of grouped elements that maintain someinteraction. Wesaythatitisdynamicwhensomemagnitudesthatmakeupthe elementsvaryintime,beingdiscretetimewhenthevariabletimeisaninteger. Inthe pursuit of a qualitative and/or topological understanding of a system, a wide range of movements that can be both regular or chaotic is revealed. The term “chaos” was only introduced by James Yorke and TienYien Li in 1975, in an article that simplified one of the results of the Russian school: the 1964 Sharkovskii’s Theorem. Sporadically, before and after the introduction of the term, chaotic systems appeared in applied literature, the most famous of which was by Edward Norton Lorenz in 1963, who set out to model atmospheric convection. In his studies he found that for his created system, minor modifications to the initial coordinates significantly changed the final results, hence the popular term of the phenomenon (Butterfly Effect). Later, in 1989, Robert Luke Devaney in his book, “An Introduction to Chaotic Dynamical Systems” [11], defined a system as chaotic if it has a sensitive dependence on initial conditions, is topologically transitive, and its periodic orbits form a dense set. The main objective of this work is to study and present the evolution of the definition of discrete time Chaotic Dynamic Sy... (Complete abstract click electronic access below) / Mestre

This thesis advances the theory of network specialization by characterizing the effect of network specialization on the eigenvectors of a network. We prove and provide explicit formulas for the eigenvectors of specialized graphs based on the eigenvectors of their parent graphs. The second portion of this thesis applies network specialization to learning problems. Our work focuses on training reservoir computers to mimic the Lorentz equations. We experiment with random graph, preferential attachment and small world topologies and demonstrate that the random removal of directed edges increases predictive capability of a reservoir topology. We then create a new network model by growing networks via targeted application of the specialization model. This is accomplished iteratively by selecting top preforming nodes within the reservoir computer and specializing them. Our generated topology out-preforms all other topologies on average.