" The chemical engineering literature is dominated by physical and (bio)-chemical processes that exhibit complex nonlinear behavior, and as a consequence, the associated requirements of their analysis, optimization, control and monitoring pose considerable challenges in the face of emerging competitive pressures on the chemical, petrochemical and pharmaceutical industries. The above operational requirements are now increasingly imposed on processes that exhibit inherently nonlinear behavior over a wide range of operating conditions, rendering the employment of linear process control and monitoring methods rather inadequate. At the same time, increased research efforts are now concentrated on the development of new process control and supervisory systems that could be digitally implemented with the aid of powerful computer software codes. In particular, it is widely recognized that the important objective of process performance reliability can be met through a comprehensive framework for process control and monitoring. From: (i) a process safety point of view, the more reliable the process control and monitoring scheme employed and the earlier the detection of an operationally hazardous problem, the greater the intervening power of the process engineering team to correct it and restore operational order (ii) a product quality point of view, the earlier detection of an operational problem might prevent the unnecessary production of o-spec products, and subsequently minimize cost. The present work proposes a new methodological perspective and a novel set of systematic analytical tools aiming at the synthesis and tuning of well-performing digital controllers and the development of monitoring algorithms for nonlinear processes. In particular, the main thematic and research axis traced are: (i) The systematic integrated synthesis and tuning of advanced model-based digital controllers using techniques conceptually inspired by Zubov’s advanced stability theory. (ii) The rigorous quantitative characterization and monitoring of the asymptotic behavior of complex nonlinear processes using the notion of invariant manifolds and functional equations theory. (iii) The systematic design of nonlinear state observer-based process monitoring systems to accurately reconstruct unmeasurable process variables in the presence of time-scale multiplicity. (iv) The design of robust nonlinear digital observers for chemical reaction systems in the presence of model uncertainty. "

L'utilisation d'un matériau granulaire au sein de structures industrielles afin de diminuer les niveaux vibratoires est une solution alternative aux revêtements viscoélastiques, qui ont une dépendance forte aux conditions de température. Pour l'industrie navale et aéronautique l'enjeu est ainsi d'améliorer la fiabilité et le confort. Les niveaux d'interaction entre les grains dépendent des paramètres de contrôle (niveaud'accélération), mais aussi des caractéristiques des matériaux constitutifs des grains, du taux d'humidité dufluide environnant, de la géométrie et des dimensions des grains, ainsi que des conditions de confinement.Pour une accélération donnée, indépendante du point de la structure, la pertinence du choix d'unmatériau granulaire par rapport à une même masse indéformable est mise en évidence par l'étude de lavibration d'une cavité rigide montée sur un oscillateur partiellement remplie. La variation paramétrique destypes de confinements dans la cavité ainsi que le matériau constitutif des grains permet d'extraire lesparamètres influents dans la dissipation d'énergie. Le développement d'un modèle analytique à constanteslocalisées permet de simuler l'énergie dissipée par le système via un nombre réduit de coefficients représentantla dynamique vibratoire de la matière en grains. La confrontation de ce modèle avec différentesexpérimentations permet de valider son efficacité et son caractère prédictif dans la dissipation de l'énergievibratoire d'un système dynamique.Pour une structure modale en vibration, où le niveau d'accélération est dépendant du point de lastructure, l'optimisation du positionnement des amas de grain est montrée. / The use of granular material in industrial structures to reduce vibration levels is an alternative toviscoelastic surfacing, which is highly dependent on temperature conditions. For the naval and aeronauticalindustry, the challenge is to improve reliability and comfort. The levels of interaction between the grainsdepend on the control parameters (acceleration level), but also on the characteristics of the constituentmaterials of the grains, the moisture content of the surrounding fluid, the geometry and dimensions of thegrains, as well as their containment conditions.For a given acceleration, independent of the point of structure, the relevance of the choice of a granularmaterial with respect to the same non-deformable mass is demonstrated by the study of the vibration of a rigidcavity mounted on an oscillator partially filled. The parametric variations of the types of confinement in thecavity as well as the constituent material of the grains make it possible to extract the influent parameters inthe energy dissipation. The development of an analytical model with localized constants allows to simulate theenergy dissipated by the system via a reduced number of coefficients representing the vibratory dynamics ofthe granular matter. The comparison of this model with experiments makes it possible to validate itseffectiveness and its predictive character in the dissipation of the vibratory energy of a dynamic system.For a modal structure, where the acceleration level is dependent on the point of the structure, theoptimization of the grain cluster positioning is shown.

Les structures composites sont souvent exposées à des ambiances dynamiques plus oumoins sévères. Ces vibrations peuvent développer différentes formes d’endommagement(fracture des fibres, délamination, fissuration de la matrice. . . ). Les défauts locaux sepropagent et affectent les propriétés mécaniques de la structure modifiant ainsi soncomportement dynamique global. Ces changements peuvent induire une dégradationrapide de la structure et une réduction de sa durée de vie. La thèse a pour objectif lamise en oeuvre de modèles de comportement pour le dimensionnement de structurescomplexes intégrant des sous-structures composites susceptibles d’être endommagées.La méthode des éléments finis est utilisée pour modéliser le comportement vibratoirelinéaire et non-linéaire de ces structures et l’endommagement est introduit via un modèlebilatéral, dans un premier temps. Durant le processus de résolution, une des difficultésrencontrées est le coût de calcul très élevé. Ainsi, un méta-modèle a été développé basésur les réseaux de neurones artificiels couplé avec la méthode de condensation par sousstructurationde Craig-Bampton. Les réseaux de neurones artificiels permettent d’estimer,à moindre cout numérique, le niveau d’endommagement sans avoir recours au calculexact. Le modèle d’endommagement bilatéral n’est pas adapté au cas de chargementsalternés ou périodiques. Par conséquent, la deuxième partie de la thèse est orientée versle développement d’un modèle d’endommagement unilatéral qui donne une meilleuredescription du comportement mécanique lorsque les micro-fissures sont fermées. De plus,dans plusieurs applications industrielles, les structures composites utilisées sont de faibleépaisseur. Par conséquent, elles peuvent avoir naturellement un comportement vibratoirenon-linéaire de type grands déplacements. Le modèle de comportement dynamique engrands déplacements et en présence de la non-linéarité matérielle d’endommagement estdéveloppé et validé. A l’issue de ces travaux de thèse, un outil numérique implémentésur MATLAB® a été développé intégrant deux modèles d’endommagement, bilatéralet unilatéral et une méta-modélisation permettant la localisation et l’estimation del’endommagement ainsi que la prédiction de la réponse dynamique des structures composites, totalement ou localement, endommagées. Le méta-modèle proposé permet deréduire significativement le coût de calcul tout en assurant une bonne précision en termesde localisation et d’estimation du niveau d’endommagement. Cet outil peut s’avérer utilepour diverses applications dans le domaine de surveillance de l’état de santé des structurescomposites. / Composite structures are often exposed to more or less severe dynamic perturbations.These vibrations can develop different forms of damage (fiber fracture, delamination,cracking of the matrix, etc.). Local defects propagate and affect the mechanical propertiesof the structure resulting to modify its global dynamic behavior. These changes can leadto the degradation of the structure and the reduction in its lifetime. This thesis focuseson the implementation of behavior models for the dimensioning of complex structuresintegrating damaged composite sub-structures. The finite element method is used tomodel the linear and nonlinear vibration behavior of these structures where the damageis introduced, initially, via a bilateral model. Since the high computational costs duringthe solving process, a meta-model was developed based on artificial neural networkscoupled with the condensation method of Craig-Bampton. Artificial neural networkspermit to estimate the damage severity at a lower numerical cost without resorting toexact calculation. The bilateral damage model is not adapted to the case of periodic loads.Consequently, the second part of the thesis is oriented towards the development of aunilateral damage model which gives a better description of the mechanical behaviorwhen the micro-cracks are closed. Moreover, in several industrial applications, the usedcomposite structures have small thickness. Therefore, they can naturally have a geometricnon-linear dynamic behavior. The model of dynamic behavior in large displacements andin the presence of material non-linearity of damage is developed and validated. At theend of this thesis, a numerical tool implemented on MATLAB® software was developedintegrating two models of damage, bilateral and unilateral, and a meta-modeling allowingthe localization and the estimation of the damage as well as the prediction of the linear andnon-linear dynamic responses of composite structures, totally or locally, damaged. Theproposed meta-model reduces significantly the computational cost and ensuring a goodaccuracy in terms of localization and estimation of the damage severity. Thereby, thistool can be useful in life-time estimation and monitoring strategies of composite structures.Thèse de

Submitted by Fabíola Silva (fabiola.silva@famerp.br) on 2018-02-27T14:13:48Z No. of bitstreams: 1 marciogatti_dissert.pdf: 2240052 bytes, checksum: 38cfe0f95ee7d8c6d51f09ffe75f33ba (MD5) / Made available in DSpace on 2018-02-27T14:13:48Z (GMT). No. of bitstreams: 1 marciogatti_dissert.pdf: 2240052 bytes, checksum: 38cfe0f95ee7d8c6d51f09ffe75f33ba (MD5) Previous issue date: 2015-11-17 / Introduction: Chronic Renal Failure (CRF) is a metabolic syndrome resulting in progressive loss of ability to renal excretion. In advanced stages dialysis is necessary. The introduction of new technological advances in hemodialysis made this procedure safe and able to maintain patients' lives for long periods. However, in 30% of the hemodialysis, may occur some kind of complication. The heart rate variability (HRV) reveals information on the functional state of the autonomic nervous system and reflects the balance between the sympathetic and parasympathetic branches of the same. HRV analysis have been proposed as a component of the clinical evaluation for risk stratification of patients. HRV can be studied by linear methods, time domain and frequency and nonlinear methods in the field of chaos. Objective: Assess whether or not there is an association between lower HRV immediately preceding the hemodialysis and the occurrence of complications during or after the same period. Casuistic and Method: 44 unselected patients were included in the study, regardless of sex and age being 15 (34.1%) were female and 29 patients (65.9%) males, with 61.7 ± 14.5 years. Inclusion criteria were considered just the fact of having IRC, be in regular program of performing hemodialysis in the dialysis unit at Hospital de Base (HB) of São José do Rio Preto. The methodology consisted of the assessment of HRV in the time, frequency and chaos, using registration electrocardiographic time series with the aid of equipment Polar RS800CX for 20 minutes moments before initiating hemodialysis session. The 44 patients were followed throughout the dialysis period by verifying the occurrence of complications. Results: 35 patients (NC) had no complications during hemodialysis, while 9 patients (C) had complications, such as hypotension, hypoglycemia, and cramps. The results showed no association between lower HRV with the occurrence of complications during or after hemodialysis. But it was evident that the diabetic patients had a higher probability of complications, because it was the only variable that showed a statistically significant difference. Comparing the results of HRV in diabetic patients with nondiabetic patients, we found lower values for the variables that represent the sympathetic autonomic activity, such as SDNN, LF, SD2 and alpha 1. Conclusions: HRV in the time, frequency and chaos was not characterized as a predictor of the occurrence of complications during or after hemodialysis. However, in diabetic patients there is a significant reduction in the sympathetic component associated with the occurrence of complications, highlighting the possibility of using a simple, noninvasive method for determining prognosis by studying HRV. / Introdução: Insuficiência Renal Crônica (IRC) é uma síndrome metabólica decorrente de perda progressiva da capacidade de excreção renal. Em fases avançadas é necessário o tratamento dialítico. A introdução de novos avanços tecnológicos no tratamento hemodialítico tornou esse procedimento seguro e capaz de manter a vida dos pacientes por longos períodos. Entretanto, em 30% das sessões de hemodiálise, pode ocorrer algum tipo de complicação. A variabilidade da freqüência cardíaca (VFC) revela informações do estado funcional do sistema nervoso autônomo e reflete o balanço entre os ramos parassimpático e simpático do mesmo. Análises da VFC têm sido propostas como um componente da avaliação clínica para a estratificação do risco dos pacientes. A VFC pode ser estudada por meio de métodos lineares, no domínio do tempo e da frequência e métodos não lineares, no domínio do caos. Objetivo: Avaliar se há ou não associação entre menor VFC no período imediatamente precedente à realização de hemodiálise e a ocorrência de complicações durante ou logo após a mesma. Casuística e Método: Foram incluídos no estudo 44 pacientes não selecionados, independente do sexo e idade sendo 15 (34,1%) do sexo feminino e 29 (65,9%) do sexo masculino, com 61,7±14,5 anos. Os critérios de inclusão foram considerados apenas o fato de ser portador de IRC, estar em programa regular de realização de hemodiálise na Unidade de Terapia Dialítica do HB de São José do Rio Preto. A metodologia consistiu na avaliação da VFC nos domínios do tempo, frequência e caos, utilizando-se de registro de series temporais eletrocardiográficas com auxilio do equipamento Polar RS800CX, por 20 minutos instantes antes de iniciarem a sessão de hemodiálise. Os 44 pacientes foram acompanhados durante todo o período dialítico com a verificação da ocorrência de complicações. Resultados: 35 pacientes (NC) não tiveram complicações durante a hemodiálise, enquanto que 9 pacientes (C) apresentaram complicações, como hipotensão, hipoglicemia e câimbras. Os resultados obtidos mostraram que não houve associação entre uma menor VFC com a ocorrência de complicações durante ou logo após a hemodiálise. Porém foi evidente que os pacientes diabéticos apresentaram maior probabilidade de complicações, pois foi a única variável que apresentou diferença estatisticamente significativa. Comparando os resultados da VFC nos pacientes diabéticos com os não diabéticos, encontramos menores valores para as variáveis que representam a atividade autonômica simpática, como SDNN, LF, SD2 e alfa 1. Conclusões: A VFC nos domínios do tempo, freqüência e caos não se caracterizou como preditivo da ocorrência de complicações durante ou logo após a hemodiálise. Entretanto, em pacientes diabéticos há uma redução significante do componente simpático associado à ocorrência de complicações, ressaltando-se a possibilidade de utilização de um método simples e não invasivo para determinação de prognóstico por meio do estudo da VFC.

Cette thèse consiste en une étude théorique et expérimentale de la dynamique d'une diode laser à émission latérale (850 nm) avec rétroaction optique à conjugaison de phase. Le dispositif expérimental est conçu afin de voir la diversité dynamique du laser à travers l'analyse temporelle et spectrale alors que le taux de rétroaction varie. La rétroaction à conjugaison de phase est effectuée par mélange à quatre ondes dans un cristal photoréfractif. Le temps de propagation du faisceau laser dans la cavité externe est appelé retard. Sous l’effet de la rétroaction, le système montre une grande richesse dynamique qui varie du chaos total à des régimes auto-pulsés aux fréquences déterminés par le longueur de la cavité externe pour la première fois mis en évidence ici. Des simulations menées en parallèle basées sur les équations de Lang-Kobayashi couramment utilisées apportent des confirmations théoriques aux observations expérimentales. Les principaux points traités sont la crise chaotique et bistabilité de solutions pulsées, les régimes auto-pulsés (stabilisation et déstabilisation) ainsi que les transitions entre eux, la caractérisation d’événements extrêmes de différentes natures avec la distribution statistique associée ainsi qu’une résonance cohérente déterministe de fluctuations à basse fréquence induite par le retard. Au-delà de l’intérêt fondamental de ces résultats et des comparaisons qui peuvent être établies avec d’autres systèmes laser, des applications dans la génération de signaux tout-optique ainsi que le contrôle du chaos sont des débouchés potentiels de cette étude. / This thesis is a theoretical and experimental study of the dynamics of an edge-emitting laser diode (850 nm) with phase-conjugate feedback. The experimental device is designed to see the dynamical range of the laser through the temporal and spectral properties while the feedback rate varies. Phase-conjugate feedback is performed through four-wave mixing in a photorefractive crystal. The propagation time of the laser beam in the external cavity is termed external time delay. Under the effect of the feedback, the system shows a wide dynamical range including chaos and self-pulsing states which characteristic properties are determined by the length of the external cavity. For the first time self-pulsing states at frequencies multiples of the fundamental frequency of the external cavity are evidenced. Simulations carried out based on the commonly-used Lang-Kobayashi laser rate equations provide theoretical confirmations to the experimental observations. The main topics tackled here are chaos crisis and bistability of pulsing solutions, self-pulsing regimes (through their stabilization and destabilization) and the transitions between them, characterization of extreme events of two kinds along with their statistical distribution and delay-induced deterministic coherence resonance of low frequency fluctuations. Beyond the fundamental interest of these results and the many comparisons that can be made with other laser systems, applications in the field of all-optical signal generation and control of chaos are direct consequences of this study.

Aktuell unterliegt unsere Stromversorgung mit der Energiewende einer Transformation, welche letzten Endes auch Änderungen der Struktur des Stromnetzes bedingt. Jenes ist ein hochkomplexes System aus unzähligen Erzeugern und Verbrauchern die miteinander wechselwirken. Im Lichte dessen leiten sich, (nicht nur) für zukünftige Stromnetze, einige methodischen Fragen ab. Wie kann die Stabilität verschiedener Betriebszustände oder Szenarien miteinander verglichen werdem? Welches sind die neuralgischen Punkte eines Stromnetzes? Zu welchem Grad bestimmt die Netzwerkstruktur die Systemstabilität? Im Zentrum der vorliegenden Dissertation steht dabei das emergente Phänomen der Synchronisation in Oszillatornetzwerken sowie dessen Stabilität. Im Bezug auf Stromnetze ist die Synchronisation dadurch gekennzeichnet, dass alle Erzeuger und Verbraucher mit der Netzfrequenz im Takt schwingen. Mit probabilistischen Stabilitätsmaßen lässt sich die Systemstabilität auf verschiedene Art quantifizieren. Neben einer Untersuchung möglicher Beschränkungen werden zwei neue probabilistische Maße entwickelt. Dabei spielen insbesondere die Häufigkeit und Dauer von Störungen sowie die Einhaltung der Betriebsgrenzen eine Rolle. Weiterhin wird der Einfluss kleiner Netzwerkstrukturen, sogenannter Motive, auf die Stabilität herausgearbeitet. Hierzu werden die Stabilitätsmaße in statistischen Verfahren mit charakteristischen Größen aus der Netzwerktheorie verknüpft. Es zeigt sich dann, dass das Auftreten spezieller Motive die Systemstabilität erhöht, wohingegen andere diese herabsetzen. Diese Zusammenhänge zwischen Netzwerkmotiven und Stabilität der Synchronisation erweitern die Kenntnisse über Zusammenhänge zwischen Struktur und Stabilität komplexer Systeme. Darüber hinaus erweitern die neu entwickelten probabilistischen Stabilitätsmaße das Methodenspektrum der nichtlinearen Dynamik zur Stabilitätsanalyse, insbesondere für Systeme auf komplexen Netzwerken mit vielen Freiheitsgraden. / In the light of the energy transition, power systems undergo a major transformation enabled by appropriate modifications of the grid’s underlying structure. This network constitutes the complex interaction of numerous producers and consumers. The power grid is additionally subject to intermittent disturbances that also include large deviations. These aspects prompt methodological problems for (future) power grids in particular and complex systems in general. How can the stability of different operating points or scenarios be compared? What are the critical components of the network? To which extent is the stability of an operating point determined by the network structure? This dissertation focusses on the emergent phenomenon of synchronisation on networks. In power grids, this corresponds to all units working at the same rhythm – the rated grid frequency. Regarding an analysis with so-called probabilistic stability measures, important limitations are discussed and novel approaches are developed. In particular, the new measures consider repeated perturbations as well as operational bounds on transient deviations. Moreover, the influence of small network structures, so-called motifs, on the stability is investigated. For this purpose, the stability measures are paired with network characteristics using statistical approaches. On this basis, it turns out that, while the abundance of special motifs enhances stability, others typically diminish it. In conclusion, the development of analysis methods and their comparison with network characteristics uncovers relationships between network motifs and the stability of synchronisation. These results are general to a large class of complex systems and build a foundation to future research in this direction. In addition to that, the novel probabilistic stability measures extend the range of methods in nonlinear dynamics by important aspects, especially for high-dimensional complex systems.

In welcher Weise hängt die Dynamik eines neuronalen Systems von den Eigenschaften seiner Netzwerkstruktur ab? Diese wichtige Fragestellung der Neurowissenschaft untersuchen wir in dieser Dissertation anhand einer analytischen und numerischen Modellierung der Aktivität großer neuronaler Netzwerke mit komplexer Struktur. Im Fokus steht die Relevanz zweier bestimmter Merkmale für die Dynamik: strukturelle Heterogenität und Gradkorrelationen. Ein zentraler Bestandteil der Dissertation ist die Entwicklung einer Molekularfeldnäherung, mit der die mittlere Aktivität heterogener, gradkorrelierter neuronaler Netzwerke berechnet werden kann, ohne dass einzelne Neuronen explizit simuliert werden müssen. Die Netzwerkstruktur wird von einer reduzierten Matrix erfasst, welche die Verbindungsstärke zwischen den Neuronengruppen beschreibt. Für einige generische Zufallsnetzwerke kann diese Matrix analytisch berechnet werden, was eine effiziente Analyse der Dynamik dieser Systeme erlaubt. Mit der Molekularfeldnäherung und numerischen Simulationen zeigen wir, dass assortative Gradkorrelationen einem neuronalen System ermöglichen, seine Aktivität bei geringer externer Anregung aufrecht zu erhalten und somit besonders sensitiv auf schwache Stimuli zu reagieren. / An important question in neuroscience is how the structure and dynamics of a neuronal network relate to each other. We approach this problem by modeling the spiking activity of large-scale neuronal networks that exhibit several complex network properties. Our main focus lies on the relevance of two particular attributes for the dynamics, namely structural heterogeneity and degree correlations. As a central result, we introduce a novel mean-field method that makes it possible to calculate the average activity of heterogeneous, degree-correlated neuronal networks without having to simulate each neuron explicitly. We find that the connectivity structure is sufficiently captured by a reduced matrix that contains only the coupling between the populations. With the mean-field method and numerical simulations we demonstrate that assortative degree correlations enhance the network’s ability to sustain activity for low external excitation, thus making it more sensitive to small input signals.

Complex systems are those which exhibit one or more of the following inter-related behaviours: 1. Nonlinear behaviour: the component parts do not act in linear ways, that is the superposition of the actions of the parts is not the output of the system. 2. Emergent behaviour: the output of the system may be inexpressible in terms of the rules or equations of the component parts. 3. Self-organisation: order appears from the chaotic interactions of individuals and the rules they obey. 4. Layers of description: in which a rule may apply at some higher levels of description but not at lower layers. 5. Adaptation: in which the environment becomes encoded in the rules governing the structure and/or behaviour of the parts (in this case strictly agents) that undergo selection in which those that are by some measure better become more numerous than those that are not as “fit”. A single cell is a complex system: we cannot explain all of its behaviour as simply the sum of its parts. Similarly, DNA structures, social networks, cancers, the brain, and living beings are intricate complex systems. This thesis tackles all of these topics from a complex systems approach. I have skirted some of the philosophical issues of complex systems and mainly focussed on appropriate tools to analyse these systems, addressing important questions such as: • What is the best way to extract information from DNA? • How can we model and analyse mutations in DNA? • Can we determine the likely spread of both viruses and ideas in social networks? • How can we model the growth of cancer? • How can we model and analyse interactions between genes in such living systems as the fruit fly, cancers, and humans? • Can complex systems techniques give us some insight into the human brain? / http://proxy.library.adelaide.edu.au/login?url= http://library.adelaide.edu.au/cgi-bin/Pwebrecon.cgi?BBID=1290759 / Thesis (Ph.D.)-- School of Electrical and Electronic Engineering, 2007

Les interactions gravitationnelles et électrostatiques sont deux exemples fondamentaux de systèmes en interaction de longue portée. Les propriétés d'équilibre de modèles simples en interaction de longue portée sont bien comprises et révèlent des comportemens exotiques: capacité spécifique négative et inéquivalence des ensembles statistiques par exemple. La compréhension de l'évolution dynamique dans le cas de systèmes en interaction de longue portée représente encore actuellement un défi théorique. Des modèles simples présentent des propriétés telles que des transitions de phase hors d'équilibre ou des états quasi-stationnaires. Le but de la présente thèse est d'étudier les propriétés dynamiques de systèmes en interaction de longue portée pour des modèles à une dimension. La description cinétique adéquate est donnée par l'équation de Vlasov. Une théorie statistique proposée par D. Lynden-Bell est appropriée pour prédire dans certaines situations l'aboutissement de la dynamique. Un outil de simulation pour l'équation de Vlasov complète cette approche. Une étude détaillée de la transition de phase dans le Laser à Electrons Libres est présentée et la transition est analysée à l'aide de la théorie de Lynden-Bell. Ensuite, la présence d'étirement et de repliement est étudiée dans le modèle Hamiltonian Mean-Field en analogie avec la dynamique des fluides. Enfin, un système de pendules découplés dont les états asymptotiques sont similaires à ceux du modèle Hamiltonian Mean-Field est introduit. Son évolution asymptotique est prédite par la théorie de Lynden-Bell et par une approche exacte. Ce système présente une évolution initiale rapide similaire à la relaxation violente présente dans des modèles plus compliqués. De plus, une transition de phase hors d'équilibre est trouvée si une condition d'auto-consistence est imposée. En résumé, la présente thèse comporte des résultats originaux liés à la présence d'états quasi-stationnaires et de transitions de phase hors d'équilibre dans des modèles unidimensionnels en interaction de longue portée. Les résultats concernant le Laser à Electrons Libres offrent une perspective de réalisation expérimentale des phénomènes décrits dans cette thèse. / Gravitational and electrostatic interactions are fundamental examples of systems with long-range interactions. Equilibrium properties of simple models with long-range interactions are well understood and exhibit exotic behaviors: negative specific heat and inequivalence of statistical ensembles for instance. The understanding of the dynamical evolution in the case of long-range interacting systems still represents a theoretical challenge. Phenomena such as out-of-equilibrium phase transitions or quasi-stationary states have been found even in simple models. The purpose of the present thesis is to investigate the dynamical properties of systems with long-range interactions, specializing on one-dimensional models. The appropriate kinetic description for these systems is the Vlasov equation. A statistical theory devised by D. Lynden-Bell is adequate to predict in some situations the outcome of the dynamics. A complementary numerical simulation tool for the Vlasov equation is developed. A detailed study of the out-of-equilibrium phase transition occuring in the Free-Electron Laser is performed and the transition is analyzed with the help of Lynden-Bell's theory. Then, the presence of stretching and folding in phase space for the Hamiltonian Mean-Field model is studied and quantified from the point of view of fluid dynamics. Finally, a system of uncoupled pendula for which the asymptotic states are similar to the ones of the Hamiltonian Mean-Field model is introduced. Its asymptotic evolution is predicted via both Lynden-Bell's theory and an exact computation. This system displays a fast initial evolution similar to the violent relaxation found for interacting systems. Moreover, an out-of-equilibrium phase transition is found if one imposes a self-consistent condition on the system. In summary, the present thesis discusses original results related to the occurence of quasi-stationary states and out-of-equilibrium phase transitions in 1D models with long-range interaction. The findings regarding the Free-Electron Laser are of importance in the perspective of experimental realizations of the aforementioned phenomena.

Erkenntnisse aus paläoklimatologischen Studien, theoretischen Betrachtungen und Modellsimulationen deuten darauf hin, dass anthropogene Emissionen von Treibhausgasen und Aerosolen zu großskaligen, singulären Klimaereignissen führen könnten. Diese bezeichnen stark nichtlineare, abrupte Klimaänderungen, mit regionalen bis hin zu globalen Auswirkungen. Ziel dieser Arbeit ist die Entwicklung von Modellen zweier maßgeblicher Komponenten des Klimasystems, die singuläres Verhalten aufweisen könnten: die atlantische thermohaline Zirkulation (THC) und der indische Monsun. Diese Modelle sind so konzipiert, dass sie den Anforderungen der "Integrated Assessment"-Modellierung genügen, d.h., sie sind realistisch, recheneffizient, transparent und flexibel. <br /> <br /> Das THC-Modell ist ein einfaches, interhemisphärisches Boxmodell, das anhand von Daten kalibriert wird, die mit einem gekoppelten Klimamodell mittlerer Komplexität erzeugt wurden. Das Modell wird durch die globale Mitteltemperatur angetrieben, die mit Hilfe eines linearen Downscaling-Verfahrens in regionale Wärme- und Süßwasserflüsse übersetzt wird. Die Ergebnisse einer Vielzahl von zeitabhängigen Simulationen zeigen, dass das Modell in der Lage ist, maßgebliche Eigenschaften des Verhaltens komplexer Klimamodelle wiederzugeben, wie die Sensitivität bezüglich des Ausmaßes, der regionalen Verteilung und der Rate der Klimaänderung. <br /> <br /> Der indische Monsun wird anhand eines neuartigen eindimensionalen Boxmodells der tropischen Atmosphäre beschrieben. Dieses enthält Parmetrisierungen der Oberflächen- und Strahlungsflüsse, des hydrologischen Kreislaufs und derHydrologie der Landoberfläche. Trotz des hohen Idealisierungsgrades ist das Modell in der Lage, relevante Aspekte der beobachteten Monsundynamik, wie z.B. den Jahresgang des Niederschlags und das Eintritts- sowie Rückzugsdatum des Sommermonsuns, zufrieden stellend zu simulieren. Außerdem erfasst das Modell die Sensitivitätdes Monsuns bezüglich Änderungen der Treibhausgas- und Aerosolkonzentrationen, die aus komplexeren Modellen bekannt sind. <br /> <br /> Eine vereinfachte Version des Monsunmodells wird für die Untersuchung des qualitativen Systemverhaltens in Abhängigkeit von Änderungen der Randbedingungen eingesetzt. Das bemerkenswerteste Ergebnis ist das Auftreten einer Sattelknotenbifurkation des Sommermonsuns für kritische Werte der Albedo oder der Sonneneinstrahlung. Darüber hinaus weist das Modell zwei stabile Zustände auf: neben dem niederschlagsreichen Sommermonsun besteht ein Zustand, der sich durch einen schwachen hydrologischen Kreislauf auszeichnet. Das Beachtliche an diesen Ergebnissen ist, dass anthropogene Störungen der plantetaren Albedo, wie Schwefelemissionen und/oder Landnutzungsänderungen, zu einer Destabilisierung des indischen Monsuns führen könnten. <br /> <br /> Das THC-Boxmodell findet exemplarische Anwendung in einem "Integrated Assessment" von Klimaschutzstrategien. Basierend auf dem konzeptionellen und methodischen Gerüst des Leitplankenansatzes werden Emissionskorridore (d.h. zulässige Spannen an CO2-Emissionen) berechnet, die das Risiko eines THC-Zusammenbruchs begrenzen sowie sozioökonomische Randbedingungen berücksichtigen. Die Ergebnisse zeigen u.a. eine starke Abhängigkeit der Breite der Emissionskorridore von der Klima- und hydrologischen Sensitivität. Für kleine Werte einer oder beider Sensitivitäten liegt der obere Korridorrand bei weit höheren Emissionswerten als jene, die von plausiblen Emissionsszenarien für das 21. Jahrhundert erreicht werden. Für große Werte der Sensitivitäten hingegen, verlassen schon niedrige Emissionsszenarien den Korridor in den frühen Jahrzehnten des 21. Jahrhunderts. Dies impliziert eine Abkehr von den gegenwärtigen Emissionstrends innherhalb der kommenden Jahrzehnte, wenn das Risko eines THC Zusammenbruchs gering gehalten werden soll. <br /> <br /> Anhand einer Vielzahl von Anwendungen - von Sensitivitäts- über Bifurkationsanalysen hin zu integrierter Modellierung - zeigt diese Arbeit den Wert reduzierter Modelle auf. Die Ergebnisse und die daraus zu ziehenden Schlussfolgerungen liefern einen wertvollen Beitrag zu der wissenschaftlichen und politischen Diskussion bezüglich der Folgen des anthropogenen Klimawandels und der langfristigen Klimaschutzziele. / Concerns have been raised that anthropogenic climate change could lead to large-scale singular climate events, i.e., abrupt nonlinear climate changes with repercussions on regional to global scales. One central goal of this thesis is the development of models of two representative components of the climate system that could exhibit singular behavior: the Atlantic thermohaline circulation (THC) and the Indian monsoon. These models are conceived so as to fulfill the main requirements of integrated assessment modeling, i.e., reliability, computational efficiency, transparency and flexibility. <br /> <br /> The model of the THC is an interhemispheric four-box model calibrated against data generated with a coupled climate model of intermediate complexity. It is designed to be driven by global mean temperature change which is translated into regional fluxes of heat and freshwater through a linear down-scaling procedure. Results of a large number of transient climate change simulations indicate that the reduced-form THC model is able to emulate key features of the behavior of comprehensive climate models such as the sensitivity of the THC to the amount, regional distribution and rate of change in the heat and freshwater fluxes. <br /> <br /> The Indian monsoon is described by a novel one-dimensional box model of the tropical atmosphere. It includes representations of the radiative and surface fluxes, the hydrological cycle and surface hydrology. Despite its high degree of idealization, the model satisfactorily captures relevant aspects of the observed monsoon dynamics, such as the annual course of precipitation and the onset and withdrawal of the summer monsoon. Also, the model exhibits the sensitivity to changes in greenhouse gas and sulfate aerosol concentrations that are known from comprehensive models. <br /> <br /> A simplified version of the monsoon model is employed for the identification of changes in the qualitative system behavior against changes in boundary conditions. The most notable result is that under summer conditions a saddle-node bifurcation occurs at critical values of the planetary albedo or insolation. Furthermore, the system exhibits two stable equilibria: besides the wet summer monsoon, a stable state exists which is characterized by a weak hydrological cycle. These results are remarkable insofar, as they indicate that anthropogenic perturbations of the planetary albedo such as sulfur emissions and/or land-use changes could destabilize the Indian summer monsoon. <br /> <br /> The reduced-form THC model is employed in an exemplary integrated assessment application. Drawing on the conceptual and methodological framework of the tolerable windows approach, emissions corridors (i.e., admissible ranges of CO2- emissions) are derived that limit the risk of a THC collapse while considering expectations about the socio-economically acceptable pace of emissions reductions. Results indicate, for example, a large dependency of the width of the emissions corridor on climate and hydrological sensitivity: for low values of climate and/or hydrological sensitivity, the corridor boundaries are far from being transgressed by any plausible emissions scenario for the 21st century. In contrast, for high values of both quantities low non-intervention scenarios leave the corridor already in the early decades of the 21st century. This implies that if the risk of a THC collapse is to be kept low, business-as-usual paths would need to be abandoned within the next two decades. <br /> <br /> All in all, this thesis highlights the value of reduced-form modeling by presenting a number of applications of this class of models, ranging from sensitivity and bifurcation analysis to integrated assessment. The results achieved and conclusions drawn provide a useful contribution to the scientific and policy debate about the consequences of anthropogenic climate change and the long-term goals of climate protection. <br><br>--- <br> Anmerkung:<br> Die Autorin ist Trägerin des von der Mathematisch-Naturwissenschaftlichen Fakultät der Universität Potsdam vergebenen Michelson-Preises für die beste Promotion des Jahres 2003/2004.