Mobiles is a composition for an ensemble consisting of 12 instruments. The piece, in one movement, incorporates intuition, chance, and twelve tone techniques and reflects the relationship between motion and rest or tension and release. The structure is modeled according to principles of growth and decay, starting off slowly, building, and then dying away. Much of the material is inspired by mental images invoked from modern theories concerning chaos. Mobiles' character stems from the principal use of two motives, the chaos motif and the echo motif. Primarily, the chaos motif is representative of a state of motion while the echo motif represents a state of rest. Mobile architecture is usually characteristic of symmetry, balance, and proportion, but because of uncertainty in a natural environment, this proportion often falls short of a perfect symmetrical balance as in the case of a crystal or a fractal design. It is this kind of architecture that Mobiles portrays in its form and developmental process.

Die vorliegende Arbeit beschäftigt sich mit der Chaossynchronisation in Netzwerken mit zeitverzögerten Kopplungen. Ein Netzwerk chaotischer Einheiten kann isochron und vollständig synchronisieren, auch wenn der Austausch der Signale einer oder mehreren Verzögerungszeiten unterliegt. In einem Netzwerk identischer Einheiten hat sich als Stabilitätsanalyse die Methode der Master Stability Funktion von Pecora und Carroll etabliert. Diese entspricht für ein Netzwerk gekoppelter iterativer Bernoulli-Abbildungen Polynomen vom Grade der größten Verzögerungszeit. Das Stabilitätsproblem reduziert sich somit auf die Untersuchung der Nullstellen dieser Polynome hinsichtlich ihrer Lage bezüglich des Einheitskreises. Eine solche Untersuchung kann beispielsweise numerisch mit dem Schur-Cohn-Theorem erfolgen, doch auch analytische Ergebnisse lassen sich erzielen. In der vorliegenden Arbeit werden Bernoulli-Netzwerke mit einer oder mehreren zeitverzögerten Kopplungen und/oder Rückkopplungen untersucht. Hierbei werden Aussagen über Teile des Stabilitätsgebietes getroffen, welche unabhängig von den Verzögerungszeiten sind. Des Weiteren werden Aussagen zu Systemen gemacht, welche sehr große Verzögerungszeiten aufweisen. Insbesondere wird gezeigt, dass in einem Bernoulli-Netzwerk keine stabile Chaossynchronisation möglich ist, wenn die vorhandene Verzögerungszeit sehr viel größer ist als die Zeitskala der lokalen Dynamik, bzw. der Lyapunovzeit. Außerdem wird in bestimmten Systemen mit mehreren Verzögerungszeiten anhand von Symmetriebetrachtungen stabile Chaossynchronisation ausgeschlossen, wenn die Verzögerungszeiten in bestimmten Verhältnissen zueinander stehen. So ist in einem doppelt bidirektional gekoppeltem Paar ohne Rückkopplung und mit zwei verschiedenen Verzögerungszeiten stabile Chaossynchronisation nicht möglich, wenn die Verzögerungszeiten in einem Verhältnis von teilerfremden ungeraden ganzen Zahlen zueinander stehen. Es kann zudem Chaossynchronisation ausgeschlossen werden, wenn in einem bipartiten Netzwerk mit zwei großen Verzögerungszeiten zwischen diesen eine kleine Differenz herrscht. Schließlich wird ein selbstkonsistentes Argument vorgestellt, das das Auftreten von Chaossynchronisation durch die Mischung der Signale der einzelnen Einheiten interpretiert und sich unter anderem auf die Teilerfremdheit der Zyklen eines Netzes stützt. Abschließend wird untersucht, ob einige der durch die Bernoulli-Netzwerke gefundenen Ergebnisse sich auf andere chaotische Netzwerke übertragen lassen. Hervorzuheben ist die sehr gute Übereinstimmung der Ergebnisse eines Bernoulli-Netzwerkes mit den Ergebnissen eines gleichartigen Netzwerkes gekoppelter Halbleiterlasergleichungen, sowie die Übereinstimmungen mit experimentellen Ergebnissen eines Systems von Halbleiterlasern. / A network consisting of chaotic units can exhibit isochronal and complete synchronisation even if the signals need certain delay times from one unit to another. A common method to analyze the stability of such a synchronization is the master stability function by Pecora and Carroll. For a network of coupled iterative Bernoulli maps the master stability function reduces to the solution of polynoms with degree of the largest delay time. Therefore analyzing the stability means analyzing the roots of these polynomials concerning their value with respect to the unit circle. This can be done numerically by using the Schur-Cohn theorem, but analytic results are possible, as well. In this work Bernoulli networks with one or more time-delayed couplings and/or self-feedbacks are analyzed. Parts of the stability region which are independent of the value of the delay times have been found. Furthermore systems with large time delays have been analyzed. There is no stable chaos synchronization if the delay time is much larger than the internal time scale or the Lyapunov time, respectively. Stable synchronization can be excluded for certain systems with several delay times due to symmetry arguments concerning the ratios between the delay times. For example, a pair which is bidirectionally coupled with two delay times cannot exhibit stable chaos synchronization if these two delay times are in a ratio of relatively prime, odd numbers. Furthermore, chaos synchronization can be excluded for a bipartite network in which two large delay times differ by a small amount. Finally, a self consistent argument is presented which interprets chaos synchronization as a result of mixing signals of each unit in the network and which is supported by results of non-negative matrices concerning relatively prime cycles in a network. The results of the Bernoulli networks are tested on several chaotic networks. There is a very good agreement of the analytic results of Bernoulli networks with networks of coupled semiconductor laser equations as well as a very good agreement with real life experiments of semiconductor laser systems.

Este trabalho apresenta um estudo sobre o transporte de partículas através da borda de um plasma confinado em tokamak. É introduzido um modelo, no qual infinitas ondas de deriva estão sobrepostas a um potencial eletrostático de equilíbrio, com campo magnético uniforme, que coloca o problema na forma de mapas. São analisados dois mapas, a saber, o mapa padrão e o mapa padrão não-twist. Resultados numéricos são apresentados para o transporte radial de partículas no mapa padrão. Para o mapa padrão não twist, além da análise do transporte, é realizado um estudo sobre variedades de pontos hiperbólicos e a relação da configuração destas com o transporte, mostrando alteração no transporte de partículas quando ocorre reconexão de variedades. / This work presents a study of the particle transport through the edge of a plasma cofined in a tokamak. A model, with an infinite number of drift waves superposed to an equilibrium electrostatic potential, in addition to an uniform magnetic field, is introduced, what puts the problem in the form of mappings. Two mappings are analysed, viz. the standard map and the standard non-twist map. Numerical results for the radial particle transport in the standard map are presented. For the standard non-twist map besides the transport analysis, a study of the manifolds of hyperbolic points and of the relation of their configuration with the transport is carried out, showing that the particle transport is changed when the manifold reconnection occurs.

Neste trabalho estuda-se a interação, através de choques, entre um oscilador harmônico e um carro de trilho de ar inclinado, análogo ao sistema descrito na literatura como \"bouncing-ball\". A análise teórica e a simulação prevêem estabilidade e bifurcação nas fases do oscilador em que ocorrem os choques, confirmados pela experiência. As simulações indicam a ocorrência de caos, fato que foi confirmado experimentalmente. O sistema experimental de aquisição de dados produzido permite a utilização no ensino de graduação. Os dados experimentais gerados pelo sistema são coletados por uma interface de aquisição, que trabalha acoplada a um microcomputador Apple II, e transferidos para um microcomputador tipo IBM-PC, possibilitando uma análise rápida dos resultados obtidos. Para a visualização das regiões de estabilidade, de bifurcação e do atrator estranho, que surge na região de caos, foram desenvolvidos programas gráficos e de cálculo, que permitem, também, realizar uma avaliação da dimensão do atrator. Os programas de simulação permitem ao aluno realizar cálculos e gerar gráficos, variando os parâmetros de controle do sistema. No experimento foi utilizado coeficiente de restituição E de 0,22 e a dimensão fractal encontrada para o atrator foi 1,2. / In the present dissertation the interaction between an harmonic oscillator and an air track\'s glider is studied, analogous to the system described in literature as the bouncing-ball. Theoretical analysis and simulation predict stability and bifurcation in the phases of the oscillator in which occur collisions. The simulations indicate the occurrence of chaos, a fact confirmed experimentally. The built up experimental data acquisition system can be used in undergraduate teaching. Experimental data generated by the system are collected by na acquisition interface, which works linked to an Apple II microcomputer, and are transferred to an IBM-PC type microcomputer, allowing quick analysis of the obtained results. To visualize the regions of stability, of bifurcation and of the strange attractor, graphic and calculation programs were developed, which also permit an evaluation of the attractor\'s dimension. The simulation programs allow the student to do calculations and generate graphs, while varying the system\'s control parameters. In the experiment a restitution coefficient E of 0.22 was used and the found fractal dimension for the attractor was 1.2.

Este trabalho apresenta um estudo sobre o transporte de partículas através da borda de um plasma confinado em tokamak. É introduzido um modelo, no qual infinitas ondas de deriva estão sobrepostas a um potencial eletrostático de equilíbrio, com campo magnético uniforme, que coloca o problema na forma de mapas. São analisados dois mapas, a saber, o mapa padrão e o mapa padrão não-twist. Resultados numéricos são apresentados para o transporte radial de partículas no mapa padrão. Para o mapa padrão não twist, além da análise do transporte, é realizado um estudo sobre variedades de pontos hiperbólicos e a relação da configuração destas com o transporte, mostrando alteração no transporte de partículas quando ocorre reconexão de variedades. / This work presents a study of the particle transport through the edge of a plasma cofined in a tokamak. A model, with an infinite number of drift waves superposed to an equilibrium electrostatic potential, in addition to an uniform magnetic field, is introduced, what puts the problem in the form of mappings. Two mappings are analysed, viz. the standard map and the standard non-twist map. Numerical results for the radial particle transport in the standard map are presented. For the standard non-twist map besides the transport analysis, a study of the manifolds of hyperbolic points and of the relation of their configuration with the transport is carried out, showing that the particle transport is changed when the manifold reconnection occurs.

A millimetric droplet may bounce and self-propel on the surface of a vertically vibrating bath, where its horizontal `walking' motion is induced by repeated impacts with its accompanying Faraday wave field. This hydrodynamic pilot-wave system exhibits many features that were previously thought to be exclusive to the quantum realm, including quantized dynamics and emergent wavelike statistics. We develop a discrete-time iterative map to analyse the pilot-wave dynamics in a number of settings, employing a sophisticated fluid model to capture the intricacies of the Faraday wave evolution neglected by previous works. We first study the stability of bouncing and walking dynamics, and elucidate further features of the droplet's wave-induced added mass. We also explore the periodic and chaotic dynamics arising when the droplet is subjected to a harmonic potential, a Coriolis force, or the interaction with a seconddroplet. Finally, we modify our fluid model to account for interactions with submerged boundaries, allowing us to rationalise the pilot-wave dynamics in a circular corral.

Nesta tese, investigamos o transporte caótico de partículas por ondas de deriva ressonantes na borda do plasma em tokamaks com fluxo poloidal de deriva do tipo ~E × ~B, um problema crítico para compreender, na fusão, as propriedades de confinamento dos plasmas. Usamos, para tokamaks com grande razão de aspecto, um modelo hamiltoniano não integrável (proposto por Horton) para descrever a contribuição dinâmica não linear ao transporte. Assim, embora o fluxo total, composto pelo fluxo de equilíbrio e por duas ondas de deriva ressonantes, não seja turbulento na descrição euleriana, as trajetórias lagrangianas das partículas são caóticas. Foi estudada a influência do perfil radial do campo elétrico nas barreiras de transporte e nas células convectivas criadas pela interação não linear entre o fluxo de equilíbrio e as ondas ressonantes. Para equilíbrios com fluxo reverso, nossos resultados mostram que o transporte de partículas pode ser reduzido pela alteração do perfil do campo elétrico. Finalmente, nossos resultados são aplicados para propor uma interpretação das experiências recentes em tokamaks que mostram uma redução do transporte quando um eletrodo polarizado é inserido na borda do plasma. Como um exemplo, usamos valores experimentais obtidos no TCABR para os perfis radiais do campo elétrico de equilíbrio e suas flutuações, durante o regime ôhmico padrão e durante o regime de confinamento melhorado. / We investigate the chaotic particle transport by resonant drift waves propagating in tokamaks plasma edges with ~E × ~B poloidal zonal flow, a critical problem for the understanding of the confinement properties of fusion plasmas. We assume, for large aspect ratio tokamaks, a non integrable hamiltonian model (proposed by Horton) to describe the non linear dynamical contribution to the transport. Thus, although the total flow, formed by the equilibrium flow and two dominant resonant drift waves, is not turbulent in the eulerian point of view, the lagrangian particle trajectories are chaotic. We study the influence of the electric field radial profile on the transport barriers and convective cells created by the non linear interaction between the poloidal flow and the resonant waves. For equilibria with reverse shear flows, our results show that the particle transport can be reduced by modifying the electric field profile. Futhermore, our results are applied to propose an interpretation of recent tokamak experiments developed for studying the transport reduction when a biased electrode is inserted into the plasma edge or the Scrape-Off-Layer. As an example, we use the equilibrium and fluctuating electric field radial profiles measured in the TCABR tokamak to calculate the transport during the standard ohmic and improved confinement regimes obtained in this tokamak.

Orientador: Gastão Inácio Krein / Banca: Iberê Luiz Caldas / Banca: Felipe Barbedo Rizzato / Resumo: Uma das características mais importantes das teorias de gauge não-Abelianas é a não-linearidade das equações de campo clássicas. Mostra-se no contexto da teoria de Yang-Mills que essa característica pode fazer com que o campo de gauge apresente comportamento caótico. Isso pode acontecer mesmo quando estivermos considerando a dinâmica do campo na ausência de fontes, isto é, o vácuo da teoria de Yang-Mills. Discutimos a relação entre os comportamentos caótico e ergódico. Em seguida, introduzimos a formulação de Berdichevsky da Mecânica Estatística Clássica para sistemas dinâmicos Hamiltonianos que são ergódicos e possuem poucos graus de liberdade. A Mecânica Estatística de Berdichevsky é usada para estudar a situação mais simples numa teoria de gauge não-Abeliana onde as variáveis de campo são caóticas e o espaço de fase correspondente tem a propriedade geométrica necessária. Mostramos que, para os propósitos desse estudo, um par de campos escalares complexos deve ser incluído no problema. Mais precisamente, analisamos o modelo de Higgs não-Abeliano; a Lagrangiana da teoria considerada possui uma simetria SU(2). A transição de uma descrição dinâmica do sistema de YangMills-Higgs (fora do equilíbrio termodinâmico) para uma descrição termodinâmica (quando ele atingiu o equilíbrio) é investigada numericamente. Mostra-se que depois de um tempo suficientemente longo as soluções numéricas se comportam de tal maneira que o sistema pode ser descrito de um jeito mais simples através de grandezas como a temperatura, calculadas de acordo com as prescriçõees da Mecânica Estatística de equilíbrio. Estas são previstas analiticamente para comparção com os resultados numéricos... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: One of the most important features of non-Abelian gauge theories is the non-linearity of the classical field equations. In the context of Yang-Mills theory it is shown that this feature can cause the gauge field to show chaotic behavior. That can happen even when we are considering the field dynamics in the absence of sources, i.e., the vacuum of the Yang-Mills theory. We discuss the connection between chaotic and ergodic behaviors. Then we introduce Berdichevsky's formulation of Classical Statistical Mechanics for Hamiltonian dynamical systems that are both ergodic and low-dimensional. Berdichevsky's theory of Statistical Mechanics is used to study the simplest situation in a non-Abelian gauge theory where the field variables are chaotic and the corresponding phase space has the necessary geometric property. We show that, for the purposes of this study, a pair of complex scalar fields must be introduced in the problem. More precisely, we analyse the so-called non-Abelian Higgs model; the Lagrangian of the theory we are considering has a SU(2) symmetry. The transition from a non-equilibrium dynamical description of the Yang-Mills-Higgs system to a thermodynamical description when it reaches equilibrium is numerically investigated. It is shown that after a sufficiently long time the numerical solutions behave in such a manner that the system can be described by quantities like the temperature, determined in accordance with the prescriptions of equilibrium Statistical Mechanics. These are predicted analytically for comparison with the numerical results. It is verified that there is agreement between analytical and numerical predictions so that the thermalization of the Yang-Mills-Higgs system can be explained with the aid of Berdichevsky's Statistical Mechanics. A dynamical approach to the study... (Complete abstract click electronic access below) / Mestre

This study comprises three parts. First, to validate the Oral Individualized Classroom Environment Questionnaire (OICEQ) which is used to assess students perceptions of the learning environment in secondary chemistry classes in the U.S.A. The OICEQ is a modified version of the actual and preferred versions of the Individualized Classroom Environment Questionnaire (ICEQ) (Fraser, 1990). Second, to investigate associations between three types of science educational assessments; predictors of performance, perceptions of the classroom environment, and chemistry academic performance. Third, to address the following two questions:1. Are chaos and constructivism allies of adversaries to assessments (predictors, perceptions, and performance)?2. Is action research a valid process of evaluating a constructivist chemistry classroom (examining associations between chaos and constructivism)?A sample of 473 students from 21 chemistry classes took the Test of Logical Thinking (TOLT), the Myers-Briggs Type Indicator (MBTI), the Individualized Classroom Environment Questionnaire (OICEQ), pretests, post-tests, and final examinations. The statistical analyses confirmed the reliability and validity of the OICEQ and ICEQ when used with senior chemistry students. Investigation of associations between predictors, perceptions, and performances revealed 29 significant associations with OICEQ and 21 significant associations with the ICEQ. Findings from the study indicated that: (1) chaos is an adversary to social assessment and personal constructivism is an ally to personal assessment; (2) action research is a valid process for evaluating a constructivist chemistry classroom it is a unifying concept for constructivism, chaos, and assessment; (3) through an action research-constructivist process and a cyberchaos research perspective, the impact of a constructivist teaching paradigm and chaos ++ / distort the assessment of data in a chemistry classroom.

In today's climate of increased criminal attacks on the privacy of personal or confidential data over digital communication systems, a more secure physical communication link is required. Chaotic signals which have bifurcation behavior (depending on some initial condition) can readily be exploited to enhance the security of communication systems. A chaotic generator produces disordered sequences that provide very good auto- and cross- correlation properties similar to those of random white noise. This would be an important feature in multiple access environments. These sequences are used to scramble data in spread spectrum systems as they can produce low co-channel interference, hence improve the system capacity and performance. The chaotic signal can be created from only a single mathematical relationship and is neither restricted in length nor is repetitive/ cyclic. On the other hand, with the progress in digital signal processing and digital hardware, there has been an increased interest in using adaptive algorithms to improve the performance of digital systems. Adaptive algorithms provide the system with the ability to self-adjust its coefficients according to the signal condition, and can be used with linear or non-linear systems; hence, they might find application in chaos communication. There has been a lot of literature that proposed the use of LMS adaptive algorithm in the communication arena for a variety of applications such as (but not limited to): channel estimation, channel equalization, demodulation, de-noising, and beamforming. In this thesis, we conducted a study on the application of chaos theory in communication systems as well as the application of adaptive algorithms in chaos communication. The First Part of the thesis tackled the application of chaos theory in com- munication. We examined different types of communication techniques utilizing chaos theory. In particular, we considered chaos shift keying (CSK) and mod- ified kind of logistic map. Then, we applied space-time processing and eigen- beamforming technique to enhance the performance of chaos communication. Following on, we conducted a study on CSK and Chaos-CDMA in conjunction with multi-carrier modulation (MCM) techniques such as OFDM (FFT/ IFFT) and wavelet-OFDM. In the Second Part of the thesis, we tried to apply adaptivity to chaos com- munication. Initially, we presented a study of multi-user detection utilizing an adaptive algorithm in a chaotic CDMA multi-user environment, followed by a study of adaptive beamforming and modified weight-vector adaptive beam- forming over CSK communication. At last, a study of modified time-varying adaptive filtering is presented and a conventional adaptive filtering technique is applied in chaotic signal environment. Twelve papers have been published during the PhD candidature, include two journal papers and ten refereed conference papers.