"The present work is a study of the low inertia spreading dynamics of initially spherical viscous droplets on a planar interface. The droplets are affected by gravity, surface tension and viscous forces and are modeled as two-dimensional axisymmetric bodies. The main focus of this study is the examination of the dependence of droplet stability, equilibrium shape and fluid motion within the drop on the relative magnitude of these forces. The dynamics are modeled using the unsteady, non-linear Navier-Stokes equations for an incompressible fluid. The spreading of a droplet on a solid surface is modeled with both a no-slip and a partial-slip boundary condition. In addition, the spreading of a droplet on another identical drop (two-drop problem) is modeled to study the problem without the contact point singularity. The governing equations are solved numerically using the Mixed Galerkin Finite Element formulation, augmented by the use of the Newton-Raphson iteration scheme to effectively treat the non-linearities of the problem. The Generalized Eulerian Lagrangian formulation is adopted for the treatment of the moving free surface of the droplet. Computations are performed for capillary numbers ranging from 0.01 to 100 and for Reynolds numbers from 0.005 to 50, where the velocity scale is based on the droplet radius and the gravitational acceleration. For the droplet spreading on a solid surface, three distinct behaviors are observed~: for low Reynolds numbers and sufficiently high capillary numbers, droplets deform to a stable, equilibrium shape; for higher Reynolds numbers, an oscillatory droplet behavior occurs; at still higher Reynolds numbers, the droplets shatter. Very often, a recirculation is induced near the contact point just before the droplet shatters, which is also observed for the case of stable oscillating droplets. When a partial-slip boundary condition is applied, it is observed that the stability of the droplet and the rate at which the droplet attains the static contact angle depend strongly on the velocity of slip of the droplet with respect to the solid surface at the contact point. For the two-drop problem, only two distinct behaviors are observed: for low Reynolds numbers and high capillary numbers, the droplet retains a near-spherical shape and remains stable; while for higher Reynolds numbers, the droplet deforms to a high extent and becomes unstable."

This thesis presents results in two apparently disparate mathematical fields which can both be examined -- and even united -- by means of pure analysis. Fractional calculus is the study of differentiation and integration to non-integer orders. Dating back to Leibniz, this idea was considered by many great mathematical figures, and in recent decades it has been used to model many real-world systems and processes, but a full development of the mathematical theory remains incomplete. Many techniques for partial differential equations (PDEs) can be extended to fractional PDEs too. Three chapters below cover my results in this area: establishing the elliptic regularity theorem, Malgrange-Ehrenpreis theorem, and unified transform method for fractional PDEs. Each one is analogous to a known result for classical PDEs, but the proof in the general fractional scenario requires new ideas and modifications. Fractional derivatives and integrals are not uniquely defined: there are many different formulae, each of which has its own advantages and disadvantages. The most commonly used is the classical Riemann-Liouville model, but others may be preferred in different situations, and now new fractional models are being proposed and developed each year. This creates many opportunities for new research, since each time a model is proposed, its mathematical fundamentals need to be examined and developed. Two chapters below investigate some of these new models. My results on the Atangana-Baleanu model proposed in 2016 have already had a noticeable impact on research in this area. Furthermore, this model and the results concerning it can be extended to more general fractional models which also have certain desirable properties of their own. Fractional calculus and zeta functions have rarely been united in research, but one chapter below covers a new formula expressing the Lerch zeta function as a fractional derivative of an elementary function. This result could have many ramifications in both fields, which are yet to be explored fully. Zeta functions are very important in analytic number theory: the Riemann zeta function relates to the distribution of the primes, and this field contains some of the most persistent open problems in mathematics. Since 2012, novel asymptotic techniques have been applied to derive new results on the growth of the Riemann zeta function. One chapter below modifies some of these techniques to prove asymptotics to all orders for the Hurwitz zeta function. Many new ideas are required, but the end result is more elegant than the original one for Riemann zeta, because some of the new methodologies enable different parts of the argument to be presented in a more unified way. Several related problems involve asymptotics arbitrarily near a stationary point. Ideally it should be possible to find uniform asymptotics which provide a smooth transition between the integration by parts and stationary phase methods. One chapter below solves this problem for a particular integral which arises in the analysis of zeta functions.

Studies demonstrate localized neuro-retinal dysfunction in patients with diabetes and no visible diabetic retinopathy (DR). Poor glycemic control is a strong risk factor for DR. We hypothesized that poor glycemic control predicts increased areas of localized neuro-retinal dysfunction in patients with diabetes. Forty-eight adolescents with diabetes and 45 controls were tested using the standard (103 hexagons) multifocal electroretinogram (mfERG). Negative binomial regression analysis was conducted with number of abnormal hexagons (delayed responses) as the dependent variable and glycated hemoglobin (HbA1c), disease duration, age and sex as covariates. Results indicate that a one-unit increase in HbA1c predicts an 80% (p = 0.002) increase in the number of abnormal hexagons when controlling for age. Increased areas of neuro-retinal dysfunction are predicted by worsening glycemic control in patients with no visible DR. Standard mfERG may be useful in monitoring patients with diabetes and identifying those who may be at risk of developing DR.

Studies demonstrate localized neuro-retinal dysfunction in patients with diabetes and no visible diabetic retinopathy (DR). Poor glycemic control is a strong risk factor for DR. We hypothesized that poor glycemic control predicts increased areas of localized neuro-retinal dysfunction in patients with diabetes. Forty-eight adolescents with diabetes and 45 controls were tested using the standard (103 hexagons) multifocal electroretinogram (mfERG). Negative binomial regression analysis was conducted with number of abnormal hexagons (delayed responses) as the dependent variable and glycated hemoglobin (HbA1c), disease duration, age and sex as covariates. Results indicate that a one-unit increase in HbA1c predicts an 80% (p = 0.002) increase in the number of abnormal hexagons when controlling for age. Increased areas of neuro-retinal dysfunction are predicted by worsening glycemic control in patients with no visible DR. Standard mfERG may be useful in monitoring patients with diabetes and identifying those who may be at risk of developing DR.

Introduction: The use of high frequency oscillatory ventilation is increasing in treatment ofacute respiratory distress syndrome over the past decade. The technique of HFOV of ventilatingthe lungs at volumes less than the anatomical dead space calms the clinical concerns surroundingventilating stiff ARDS lungs with high pressures and volumes. This largely reduces theprobability of barotraumas and/or atelectrauma. Purpose: The study was on an in vitro bench model that answered the following researchquestions: 1. The effect of three inline closed suction adapters on delivered tidal volume duringHFOV with varying lung compliance 2. The effect of varying compliance on the amplitudedelivered by HFOV; and 3. The effect of compliance on tidal volume delivered by HFOV. Method: An in vitro bench model using high fidelity breathing simulator (ASL 5000, IngMarMedical) simulating an adult patient with ARDS was set up with 3100B SensorMedic highfrequency ventilator. The simulation included varying the compliance for each lung at 50, 40, 30and 20cmH2O while maintaining fixed resistance of 15 cmH2O/L/sec. The ventilator was set tothe following parameters: power of 6, frequency (f) of 5, inspiratory time (Ti) of 33%, bias flow(BF) of 30 LPM and oxygen concentration of 50%. The breathing simulator was connected withthe high frequency ventilator using a standard HFOV circuit and a size 8.0mm of endotrachealtube. Fourteen French Kimberly Clark suction catheters (with T and Elbow adapters) and Air-Life suction catheters (Y adapter) were placed in-line with the circuit successively to carry outthe study. Each run lasted for 1 minute after achieving stable state conditions. Thisapproximated to 300 breaths. The data was collected from the stimulator and stored by the hostcomputer. Data Analysis: The data was analyzed using SPSS v.11 to determine the statistical significance.A probability value (P value) of ≤ 0.001 was considered to be statistically significant. Results: The data analysis showed that Air-Life Y-adapter suction catheters caused the least lostin tidal volume when placed in line with HFOV and hence proved to be the most efficient. Thestudy also showed a direct relationship between amplitude and lung compliance i.e. an increasein lung compliance caused an associated increase in amplitude (power setting remainingunaltered). Lastly, the study did not show a statistically significant change in tidal volume withchanges in lung compliance. Future studies may be required to further evaluate the clinicalsignificance of the same. Conclusion:1. Many factors affect delivery of tidal volume during high frequency ventilation and thus it isnot constant. Choice of in-line suction system to be placed in line is one of the determinants ofthe same.2. Lung compliance changes lead to associated changes in amplitude delivery by HFOV. Thisshould be adjusted as patient condition improves by altering the power settings to ensure optimalventilation and to avoid trauma to the lungs.

In the mid-1920s, the great Albert Einstein proposed that at extremely low temperatures, a gas of bosonic particles will enter a new phase where a large fraction of them occupy the same quantum state. This state would bring many of the peculiar features of quantum mechanics, previously reserved for small samples consisting only of a few atoms or molecules, up to a macroscopic scale. This is what we today call a Bose-Einstein condensate. It would take physicists almost 70 years to realize Einstein's idea, but in 1995 this was finally achieved. The research on Bose-Einstein condensates has since taken many directions, one of the most exciting being to study their behavior when they are placed in optical lattices generated by laser beams. This has already produced a number of fascinating results, but it has also proven to be an ideal test-ground for predictions from certain nonlinear lattice models. Because on the other hand, nonlinear science, the study of generic nonlinear phenomena, has in the last half century grown out to a research field in its own right, influencing almost all areas of science and physics. Nonlinear localization is one of these phenomena, where localized structures, such as solitons and discrete breathers, can appear even in translationally invariant systems. Another one is the (in)famous chaos, where deterministic systems can be so sensitive to perturbations that they in practice become completely unpredictable. Related to this is the study of different types of instabilities; what their behavior are and how they arise. In this thesis we compare classical and quantum mechanical nonlinear lattice models which can be applied to BECs in optical lattices, and also examine how classical nonlinear concepts, such as localization, chaos and instabilities, can be transfered to the quantum world.

Orientador: José Roberto Fioretto / Resumo: A Síndrome do Desconforto Respiratório Agudo (SDRA) cursa com alta morbi-mortalidade apesar dos avanços no entendimento de sua fisiopatologia e tratamento. A terapia ventilatória baseia-se na proteção pulmonar, sendo a ventilação oscilatória de alta frequência (VOAF) uma opção de método protetor. A posição prona (PP) é terapia adjuvante que possibilita homogeneização da distribuição do volume corrente (VC) e promove recrutamento alveolar. O objetivo do estudo foi investigar o efeito da posição prona associada à VOAF e ventilação mecânica convencional (VMC) protetora sobre a oxigenação, inflamação, dano oxidativo e histologia pulmonares, comparando-a à posição supina em ambos os modos ventilatórios. Foram instrumentados 75 coelhos com traqueostomia e acessos vasculares. A lesão pulmonar aguda (LPA) foi induzida por lavagem traqueal de salina aquecida (30mL/Kg, 38°C). Os animais foram então aleatorizados em cinco grupos (n=15): 1) GC (Controle): animais sadios em VMC protetora basal; 2) GVMS: animais com LPA em VMC protetora e posição supina; 3) GVMP: animais com LPA em VMC protetora e posição prona; 4) GVAFS: animais com LPA em VOAF e posição supina; 5) GVAFP: animais com LPA em VOAF e posição prona. Após, foram submetidos a quatro horas de VMC protetora (modo pressão regulada-volume controlado, PEEP 10 cmH2O, VC 6mL/kg, Ti 0,5s, FR 40 rpm e FiO2 1) ou VOAF (MAP 15 mmHg, FR 10Hz, amplitude 22 e FiO2 1). O nível de significância foi de 5%. Após a indução, os grupos apresentaram... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: Acute Respiratory Distress Syndrome (ARDS) presents with high morbidity and mortality despite advances in the understanding of its pathophysiology and treatment. Ventilatory therapy is based on the intention of injuring less, with high frequency oscillatory ventilation (HFOV) being a protective method option. Prone position (PP) is an adjuvant therapy that enables homogenization of volume tidal (VT) distribution and promotes alveolar recruitment. The aim of this study was to investigate the effects of prone position associated with HFOV and protective conventional mechanical ventilation (CMV) on oxygenation and lung inflammation, oxidative damage and histology, comparing it with the supine position in both ventilatory modes. Seventy five rabbits were submitted to tracheostomy and vascular accesses. ALI was induced by tracheal infusion of heated saline (30mL/kg, 38° C). The subjects were then ramdomized in five groups (n=15): 1) CG (Control): healthy animals in basal protective CMV; 2) MVSG: animals with ALI in protective CMV and supine position; 3) MVPG animals with ALI in protective CMV and prone position; 4) HFSG: animals with ALI in HFOV and supine position; 5) HFPG: animals with ALI in HFOV and prone position. After that, they were submitted to four hours of protective VMC (PRV mode, PEEP 10 cmH2O, VC 6ml/kg, Ti 0,5s, FR=40 rpm and FiO2 1) or HFOV (MAP 15 mmHg, FR 10 Hz, amplitude 22 and FiO2 1). The level of significance was 5%. After induction, the groups presented simi... (Complete abstract click electronic access below) / Doutor

[pt] Nessa pesquisa, desenvolvemos uma nova metodologia para analizar materiais nos regimes oscilatórios linear e quasilinear. Foi mostrado que poucos experimentos reológicos são necessários. Além disso, a análise de dados apresentada é objetiva já apenas processamentos simples são necessários para avaliar as funções materiais. Esse fato contrasta com grande parte das análises de escoamento oscilatório de alta amplitude, tendo em vista que essas metodologias requerem manipulação matemática complexa dos dados. Por fim, a metodologia desenvolvida também apresenta grande evolução com relação às metodologias utilizadas anteriormente para analisar materiais no regime QL-LAOS. / [en] In this research, we developed a novel methodology to analyze materials in the linear and quasilinear oscillatory regimes (constant structure motions). It was shown that very few rheometric experiments are necessary. Furthermore, data analysis presented on this thesis is straightforward as raw data obtained from the rheometer requires simple data processing before being input into the equations that evaluate the material functions. This fact is in contrast with most large amplitude oscillatory shear analysis methods since they aim to analyze structure-changing motions and this requires complex mathematical manipulation of data. At last, both experimental methodology and data analysis presented in this research are much simpler than the previous methodologies used to analyze materials in the QL-LAOS regime.

Cette thèse concerne l'ingénierie des systèmes complexes à partir d'une dynamique souhaitée. En particulier, nous nous intéressons aux populations d'oscillateurs et aux réseaux de régulation génétique. Dans une première partie, nous nous fondons sur une hypothèse, introduite en neurosciences, qui souligne le rôle de la synchronisation neuronale dans le traitement de l'information cognitive. Nous proposons de l'utiliser sur un plan plus large pour étudier le traitement de l'information par des populations d'oscillateurs. Nous discutons des isochrons de quelques oscillateurs classés selon leurs symétries dans l'espace des états. Cela nous permet d'avoir un critère qualitatif pour choisir un oscillateur. Par la suite, nous définissons des procédures d'impression, de lecture et de réorganisation de l'information sur une population d'oscillateurs. En perspective, nous proposons un système à couches d'oscillateurs de Wilson-Cowan. Ce système juxtapose convenablement synchronisation et désynchronisation à travers l'utilisation de deux formes de couplage: un couplage continu et un couplage par pulsation. Nous finissons en proposant une application de ce système: la détection de contours dans une image. En deuxième partie, nous proposons d'utiliser une approche par contraintes pour identifier des réseaux de régulation génétique à partir de connaissances partielles sur leur dynamique et leur structure. Le formalisme que nous utilisons est connu sous le nom de réseaux d'automates booléens à seuil ou réseaux Hopfield-semblables. Nous appliquons cette méthode, afin de déterminer le réseau de régulation de la morphogenèse florale d'Arabidopsis thaliana. Nous montrons l'absence d'unicité des solutions dans l'ensemble des modèles valides (ici, 532 modèles). Nous montrons le potentiel de cette approche dans la détermination et la classification de modèles de réseaux de régulation génétique. L'ensemble de ces travaux mène à un certain nombre d'applications, en particulier dans le développement de nouvelles méthodes de stockage de l'information et dans le design de systèmes de calcul non conventionnel. / This thesis is concerned by the engineering of complex systems from a desired dynamics. Particularly, we are interested by populations of oscillators and genetical regulatory networks. In a first part, we start from a hypothesis introduced in neuroscience, which highlight the role of neural synchronization in the cognitive processing. We propose to use this hypothesis in a more general panorama to investigate the computing with populations of oscillators. We discuss about the isochrons of few oscillators selected according to their symmetry in the state space. Therefore, we define procedures for making footprints, for reading and for reorganizing information by a population of oscillators. As a perspective, we propose a system of lattices of Wilson-Cowan oscillators organized in several interconnected layers. This system properly mixes synchronization and desynchronization by using two types of coupling : pulsed and continuous coupling. At the end of this part, we propose to use this system in order to detect the edges of an image. In the second part, we propose a constraint-based approach to determine the structure of genetic regulatory networks starting from incomplete knowledge on their structure and their dynamics. The formalism we use is widely called thresholded Boolean automata networks or Hopfield-like networks. As an proof of concept, we apply this method to determine the regulatory network of Arabidopsis thaliana flower morphogenesis. We obtain 532 valid models instead of one unique solution and then classify them by using structural robustness criteria. By this way, we showed the potential of this approach in determining and classifying thresholded Boolean automata networks like genetic regulatory networks or neural networks. This works leads to many applications, in particular the developpement and the design of new methods for processing information and the design of systems of unconventional computing.

Orientador: Antônio Carlos Mazzeo / Banca: Marcos Tadeu Del Roio / Banca: Adilson Marques Gennari / Resumo: O Partido Comunista Brasileiro, desde o seu surgimento em 1922, entendeu que para se conquistar a democracia seria preciso construir uma aliança operária camponesa, e este entendimento foi ampliado a partir do final da década de vinte, quando os comunistas visualizaram a burguesia como participe da aliança juntamente com o operariado e o campesinato. Por esta época, começou a se forjar entre os comunistas do Brasil - em consonância com o acordo manifestado pelos comunistas russos --, a concretização da estratégia política nacional-democrática, cujo processo revolucionário estaria calcado no etapismo. Quando se deu a cisão em 1962 surgiu o PCdoB, este partido manteve a mesma estratégia política durante as décadas de setenta e oitenta. Cabe destacar que apesar de em seus documentos o partido afirme com veemência que a burguesia representa a classe social a ser varrida da historia, não raras vezes esta mesma classe foi lembrada pelo PCdoB como necessária ao processo de democratização. Assim, foi devido a essa pendularidade, que compreendemos que o PCdoB poderia ser denominado de pêndulo vermelho. Durante o processo de democratização brasileira, cujo pano de fundo foi o projeto de auto-reforma perpetrado pelo regime militar, o PCdoB não economizou esforços para manter as amplas alianças, que nos estertores do governo do Gal. Figueiredo ficou conhecida como Aliança Democrática. Algum tempo depois, quando a burguesia se certificou de que a sua dominação e direção sobre o conjunto da nação estava assegurada, tratou aprofundar a sua política conservadora, não restando alternativa ao PCdoB, a não a ser a sua saída desta mesma aliança. Portanto, consideramos que o PCdoB (por nós denominado de pêndulo vermelho) manteve a mesma estratégia política de buscar alianças - mesmo que conjunturais - com a burguesia, outrora denominada nacional, mesmo... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: The Brazilian Communist Party, since its inception in 1922, understood that to achieve the democracy would have to build a working peasant alliance, and this understanding was expanded from the late twenties, when the communists viewed the bourgeoisie as a participant in the alliance with the working class and peasantry. By this time, began to forge between the Communists in Brazil - in line with the agreement expressed by the Russian Communists - the achievement of national policy strategy-democratic revolutionary process which would be trampled in steps. When the split occurred in 1962 came the YNA, the party maintained the same political strategy during the seventies and eighties. It should be noted that although in their documents the party asserting strongly that the bourgeoisie is the class to be wiped out of history, often the same class was remembered by YNA as necessary to the process of democratization. Thus, it was due to this oscillatory, we understand that PCdoB could be called red pendulum. During the process of democratization in Brazil, whose background was the project of self-reform perpetrated by the military regime, the YNA was hard at work to keep the broad alliances that in the throes of the government of Gal. Figueiredo was known as the Democratic Alliance. Some time later, when the bourgeoisie is satisfied that its domination and direction for the whole nation was assured, tried to deepen their political conservative, and there is an alternative to YNA, not to their departure of that alliance. Therefore, we consider the YNA (we called pendulum red) remained the same political strategy of seeking alliances - even if short-term - with the bourgeoisie, once called national, even at the expense of subordinate communist during the term of the same political alliance with the bourgeoisie to the establishment of the National Constituent Assembly in 1987 / Mestre