Orientador : Ricardo Luiz Viana / Tese (doutorado) - Universidade Federal do Paraná / Resumo: Um oscilador linear por partes, carregado, amortecido e forçado é investigado numericamente. A não-linearidade é devida à rigidez assimétrica. A motivação física remete às ondulações de uma ponte pênsil, estimulada pelo fluxo lateral do vento. Um mapa de Poincaré bidimensional é obtido. Os parâmetros são introduzidos gradualmente, favorecendo uma abordagem fenomenológica. Retratos de fase revelam multi-estabilidade com estrutura de bacia muito intrincada, cujo expoente de incerteza resulta não-inteiro, apesar de argumentos geométricos demonstrarem que esta estrutura não é fractal. Um atrator caótico é destruído por uma crise de fronteira. Próximo ao parâmetro crítico, o tempo médio de transiente diminui com o amortecimento segundo uma lei de potência. Ocorre erosão da bacia de segurança quando é introduzido um limiar de ruptura para a mola unilateral. Atratores de períodos mais altos são destruídos pela adição de ruído. Movimento quasiperiódico, sincronização e caos são criados pelo acoplamento entre dois osciladores conectados por uma mola unilateral. / Abstract: A forced damped and preloaded piecewise-linear oscillator is numerically investigated. Nonlinearity is due to asymmetrical stiffness. Physical motivation alludes to the undulations of a suspension bridge, stimulated by transversal wind flow. A two-dimensional Poincare map is obtained. Parameters are gradually introduced, enhancing a phenomenological approach. Phase portraits reveal multistability with a highly entangled basin structure, which uncertainty exponent is non-integer, despite geometrical arguments demonstrate this structure is not fractal. A chaotic attractor is destroyed through boundary crisis. Close to critical parameter, average transient time decreases with damping as a power-law. Erosion of safe basin occurs as a rupture threshold for the one-sided spring is established. Periodic attractors with higher periods are destroyed by addition of noise. Quasiperiodic motion, synchronization and chaos are created by the coupling between two oscillators connected by a one-sided spring.

Les cellules vivantes peuvent être considérées comme des systèmes dynamiques. Ses propriétés dynamiques sont essentiellement régulées par des réseaux génétiques. Ce travail de thèse est motivé par l’existence de comportements dynamiques récurrents des réseaux génétiques tels que les oscillations, et s’articule autour de trois études. La première étude concerne le rôle des délais qui sont des ingrédients clés des oscillations. Dans la modélisation déterministe, le délai est modélisé comme délai explicite ou délai réactionnel. En étudiant un réseau génétique comprenant un gène auto-réprimé qui contient divers délais, nos résultats montrent analytiquement le principe de combinaison des divers délais et les influences différentes des délais explicites et réactionnels sur les oscillations. La seconde étude s’intéresse à l’impact des fluctuations moléculaires. Nous proposons un développement de cumulants de l’équation maîtresse et l’appliquons au circuit de gène auto-réprimé. Nous trouvons que les fluctuations modifient significativement les moyennes des quantités moléculaires prévues par les modèles déterministes, et induisent les oscillations. La troisième étude concerne les effets dynamiques de la pause des RNA Polymérases sur la transcription qui est modélisée par le modèle TASEP. Pour des durées des pauses intermédiaires et longues pour lesquelles l’approche de champ moyen n’est pas validée, nous parvenons néanmoins à une bonne compréhension des différents mécanismes qui contrôlent la dynamique de transcription et obtenons une description quantitative du taux de transcription en bon accord avec les simulations numériques. / Living cells can be viewed as dynamical systems and cellular dynamical properties essentially reply on genetic networks. This thesis work is motivated by one striking dynamical behavior of genetic networks, oscillation, and mainly includes three studies. The first study is about the delay that is one of key ingredients of biological oscillation. In mathematical modeling, delay is usually modeled as explicit delay or reaction delay. By studying a minimal genetic network, a self-repressing gene involving various delays, our analytical results reveal the combination principle of various delays and different dynamical influences of explicit and reaction delays on oscillations. The second study is to investigate the dynamical influences of molecular fluctuations on the oscillatory behavior. We develop a cumulant expansion of the master equation and apply it to the self-repressing gene circuit. We find that fluctuations shift significantly the averages of molecular quantities predicted by deterministic models and induce oscillations. In the third study, we investigate the dynamical effects of RNA Polymerase pausing on transcription in using TASEP model. In the limit case where pause duration is short, we can still construct a mean-field model to analyze the transcription rate and site occupation. In the general case where mean-field approach no long applies, we obtain a good understanding of various mechanisms driving the transcription dynamics over the entire range of pause duration, and in particular a theoretical prediction of transcription rate that agrees well with numerical simulations is given.

Two-dimensional electron gases (2DEG) located at GaAs/Al0.33Ga0.67As heterojunctions are modulated by a periodic magnetic field generated by a magnetic grating fabricated at the surface of the heterostructure and are irradiated by microwaves. The devices were investigated for the detection of excitations of both paramagnetic and ferromagnetic spins in the magnetoresistance. Electron spin antiresonance was electrically detected, where spin flips are propelled by two transitions: one activated by snake orbit oscillations in the slanted magnetic field, the other by the microwaves. The double resonance forms a dark state which blocks spin flips, decreases Overhauser shift and freezes snake orbit drift, therefore changing the conduction in the 2DEG. The antiresonance is quantitatively described in the coherent population trapping framework. Collective and localised spin wave modes in dysprosium and cobalt gratings were detected as well in the 2DEG. Such effects were investigated as a function of microwave power, temperature, tilt angle of the applied magnetic field, and by varying the structural and material parameters to change the strength of dipolar interactions. The data reveal two types of spin waves. Dipolar magnetisation waves propagate across the grating through the magnetostatic interaction between stripes. An analytical expression of their dispersion curve was derived and a good fit of the ferromagnetic resonance broadening was obtained. The second type are dipolar edge spin waves which manifest through a series of sharp resonances at lower magnetic field. These waves are confined near the pole surfaces in spin wave ”wells”. The eigenfrequencies of the quantised modes were calculated and a qualitative explanation of the low field resonances was obtained. The experiments show that photovoltage measurements in hybrid semiconductor-ferromagnetic structures provide a sensitive and non-invasive tool for probing the spin waves of small magnets

Στην παρούσα διατριβή διερευνήθηκε η δυνατότητα του GPS-RTS στη μελέτη ταλαντώσεων ως προς την ακρίβεια προσδιορισμού του εύρους και της συχνότητας ταλάντωσης και το διάστημα των συχνοτήτων που μπορούν να καταγραφούν, με βάση συσκευή παραγωγής ελεγχόμενων εξαναγκασμένων ταλαντώσεων και ακολουθήθηκε στατιστική ανάλυση δεδομένων. Τα πειράματα βασίστηκαν στην σύγκριση των καταγραφών ταλαντώσεων γνωστών χαρακτηριστικών που δημιούργησε η συσκευή και την σύγχρονη καταγραφή τους με τα όργανα GPS και RTS και εν μέρη άμεση οπτική παρατήρηση. Κατά την φάση των πειραμάτων αντιμετωπίστηκαν προβλήματα απώλειας των μετρήσεων τα οποία εκτιμάται ότι μπορούν να αντιμετωπιστούν με κατάλληλη συνδεσμολογία για το GPS και κατάλληλο λογισμικό για το RTS Οι χρονοσειρές που προέκυψαν από περισσότερα από 100 πειράματα αναλύθηκαν με συμβατικές στατιστικές μεθόδους (π.χ. έλεγχο χονδροειδών σφαλμάτων) και φασματική ανάλυση με βάση τις μεθόδους: FFT, το περιοδόγραμμα Lomb και την Φασματική Ανάλυση Ελαχίστων Τετραγώνων (LSSA). Με βάση τις προτεινόμενες μεθόδους αναλύσεων προέκυψαν τα παρακάτω: • το GPS μπορεί να καταγράψει με ακρίβεια ταλαντώσεις με συνολικό εύρος ≥4cm για συχνότητες διέγερσης ≤4 Hz ενώ μπορεί να προσδιορίσει την συχνότητα ταλάντωσης ακόμα για διέγερση των 4 Hz και • το RTS μπορεί να καταγράψει με ακρίβεια ταλάντωσης με συνολικό εύρος ταλάντωσης της τάξης του 1 cm και μπορεί να προσδιορίσει με ακρίβεια την συχνότητα διέγερσης για χαμηλόσυχνές ταλαντώσεις (μέχρι και 1 Hz). Συμπερασματικά, οι μέθοδοι επίγειων αλλά και δορυφορικών μεθόδων μπορούν να χρησιμοποιηθούν για την παρακολούθηση των ταλαντώσεων/μετακινήσεων των εύκαμπτων κατασκευών, ενώ με βελτίωση των διατάξεών τους και των λογισμικών τους με στόχο να αντιμετωπιστούν τα προβλήματα που παρουσιάστηκαν, αναμένεται ακόμα καλύτερη ακρίβεια. / At the present study, the ability of GPS-RTS was examined for the oscillation monitoring.At the present thesis, the performance of the modern geodetic methods, GPS and RTS, for the oscillation monitoring was examined. In order to assess the performance of the two methods the study was based on known oscillations which were produced by a special oscillation device and the records of GPS and RTS which were monitoring the oscillations. The estimate of the performance was based on the comparison of the known oscillation characteristics (displacement and frequency) and those which were arose by the analysis of the GPS-RTS records. During the oscillation experiments many problems were faced and especially with interruptions at the GPS and RTS records, which can be solved by a more appropriate connection between the antenna and the receiver of the GPS system and the use of a more advanced software for the RTS. Time series, based on the GPS-RTS records of more than 100 oscillations experiments, were analysed with compatible statistical and frequency domain analysis methods: FFT, LSSA (Least Square Spectrum Analysis) and Lomb. According to the analysis: • GPS can define accurately the total oscillation displacement when it is ≥4cm and the frequency when it is ≤4 Hz and • RTS can define accurately the total oscillation displacement when it is ≥1cm and the frequency when it is ≤1 Hz. According to the analysis, the two geodetic methods proved to be very accurate for the oscillation monitoring of flexible structures and their performance can be improved with the use of more sophisticated software for the RTS and connections for the GPS.

Orientador: Sergio Roberto Lopes / Dissertação (mestrado) - Universidade Federal do Paraná / Resumo: Neste trabalho nos analisamos um modelo simplificado da dinâmica cardíaca, apresentado por dois osciladores de van der Pol acoplados assimetricamente. Neste caso, os osciladores e os acoplamentos entre eles, modelam o comportamento dos dois marcapassos cardíacos (os nodos sinoatrial e o atrioventricular) e das fibras nervosas que transmitem os impulsos nervosos. Estudamos as condições necessárias para a ocorrência de sincronização entre os osciladores além de outras dinâmicas do sistema que demonstram como seu comportamento evolui. Para este estudo utilizamos a análise dos expoentes de Lyapunov, expoentes de Lyapunov condicionais, diagramas de parâmetros, diagramas de bifurcações, entre outros. / Abstract: In this work, we analyze a simplified model of cardiac dynamics. The model is composed by two asymmetric coupled van der Pol oscillators. In this case the oscillators and the coupling between them model the behavior of the two cardiac pacemaker (the sinus and atriventricular nodes) and the fibers nervous that transmit the nervous impulse. We study here the necessary conditions to get synchronization between the oscillators as well as the dynamics of system that shows how it evolves. This study is made analyzing the Lyapunov exponent, conditional transverse Lyapunov exponents, parameters diagrams, bifurcations diagrams and others.

This thesis describes the fabrication and characterization of ex situ magnesium diboride (MgB<sub>2<) bulk material to study its sintering behaviour. Since the discovery of superconductivity in magnesium diboride in 2001, many research studies have identified the attractive properties of this easy-to-fabricate, low cost superconductor which can attain high critical current density even without heat-treatment. However there is little consensus in the literature on the processing requirements to produce high quality MgB<sub>2< material with low impurity content and high density. In this work, the key parameters in the production of dense ex situ MgB<sub>2< produced from Alfa Aesar MgB<sub>2< powder are established by examining the effect of modifying the characteristics of the starting material and the processing parameters during pressureless and pressure assisted heat-treatment. The particle size distribution, impurity content and particle morphology of Alfa Aesar MgB<sub>2< powder were determined using laser dffraction, X-ray diffraction, X-ray photoelectron spectroscopy, electron dispersive spectroscopy, scanning electron microscopy and transmission electron microscopy. This powder was also modified by separation (sieving and sedimentation) and milling (ball milling and attrition milling), with changes made to the powder determined by the same techniques. A pressureless heat-treatment method using a magnesium diboride powder bed was developed. This minimised MgO formation in samples produced from as-purchased MgB<sub>2< powder to less than 8 wt.% for heat-treatment at 1100°C. MgO content was determined by X-ray diffraction using calibrated standards. MgB<sub>2< bulk material was produced from as-purchased and modified powders by pressureless heat-treatment under Ar gas, and characterized using Archimedes' density method, X-ray diffraction, Vickers hardness testing, scanning electron microscopy, and magnetization measurements. Very limited densification was observed for all samples prepared by pressureless heat-treatment, with only limited increases in connectivity observed for some samples heat-treated at 1100°C. Pressure-assisted bulk samples were prepared from as-purchased MgB<sub>2< and selected modified powders using resistive sintering, spark plasma sintering, and hot pressing. These were characterized using the same techniques, which indicated much more extensive densification with similar levels of impurity formation as for pressureless heat-treatment at 1100°C. The results indicate that densification and applied pressure are strongly correlated, while the effect of temperature is less significant. The optimum processing environment (inert gas or vacuum) was dependent on the technique used. These results indicate that pressure-assisted heat-treatment is required in order to produce dense bulk MgB<sub>2<.

: Les travaux présentés dans cette thèse traitent du contrôle de systèmes dynamiques soumis à des excitations harmoniques et transitoires en utilisant des absorbeurs de type Nonlinear Energy Sink (NES). Plusieurs aspects ont été développés : la conception et la réalisation d'un nouveau design pour le NES cubique, l'étude de la location et du transfert irréversible d'énergie sur un NES bistable et le développement d'un critère de conception pour un NES à Vibro-Impact (VI). Dans un premier temps, un critère de conception est proposé pour le NES à raideur cubique. Le design proposé est basé sur des ressorts coniques ou des ressorts à pas variable. Un mécanisme à raideur négative est aussi introduit pour supprimer la partie linéaire et avoir une raideur cubique pure. Dans un deuxième temps, le concept du NES est validé expérimentalement par des essais statiques et des essais dynamiques. Une analyse de sensibilité est aussi menée sur la longueur des ressorts précontraints, elle dénote parfois un état bistable de l'oscillateur. Ensuite, le NES bistable ainsi obtenu est étudié plus en détail. Ce type d'absorbeur s'avère être très robuste pour différents types d’excitation. Des études expérimentales sont aussi menées afin d'explorer le comportement dynamique. Enfin, un critère de conception est proposé pour le NES à Vibro-Impact. Des calculs analytiques détaillés sont proposés pour contrôler les vibrations sous différentes excitations. L'étude expérimentale montre une bonne cohérence avec les résultats théoriques. / The work presented in this thesis deals with the passive control of dynamics systems subjected to harmonic and transient excitations using a Nonlinear Energy Sink (NES). Several research aspects have been developed: design theory and experimental study of a novel NES, efficient Targeted Energy Transfer (TET) of bistable NES and design criteria for optimally tuned Vibro-Impact (VI) NES. Firstly, a design criterion intended to provide optimal nonlinear stiffness is proposed. Then a novel design of NES system yielding cubic stiffness with conical springs or variable pitch springs and negative stiffness mechanism is developed. Secondly, the experimental procedures for static and dynamic test are presented and applied to validate the concept of NES system. Then a sensitivity analysis is performed with respect to the pre-compressed length of springs. Thirdly, the optimal design of the above device with negative stiffness (termed as bistable NES) is studied. This type of NES is proved to work robustly for different types of excitation, and experimental study of semi-active control are explored. Finally, design criteria for optimally tuned VI NES are studied. Detailed analytical calculations of clearance to control the vibration under different excitations are proposed. A good correspondence between theoretical and experimental results is observed.