O estudo de caos na propagação do raio de som em um guia de onda no oceano

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Estudo de ciclos limites em uma classe de equações diferenciais descontínuas

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Sobre a estabilidade estrutural e regularizações de campos de vetores descontínuos

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Aumento da atividade dos sistemas antioxidantes modula o estresse oxidativo na saliva de crianças com cárie precoce severa

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Equações de diferenças: aplicações no ensino médio

Pós-graduação em Matemática em Rede Nacional - IBILCE

Localização de descargas parciais em transformadores de potência por meio de sensores piezelétricos de baixo custo e sistemas inteligentes

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Localização de descargas parciais em transformadores de potência por meio de sensores piezelétricos de baixo custo e sistemas inteligentes

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Continuity of Lyapunov functions and of energy level for generalized gradient semigroup

The global attractor of a gradient-like semigroup has a Morse decomposition. Associated to this Morse decomposition there is a Lyapunov function (differentiable along solutions)-defined on the whole phase space- which proves relevant information on the structure of the attractor. In this paper we prove the continuity of these Lyapunov functions under perturbation. On the other hand, the attractor of a gradient-like semigroup also has an energy level decomposition which is again a Morse decomposition but with a total order between any two components. We claim that, from a dynamical point of view, this is the optimal decomposition of a global attractor; that is, if we start from the finest Morse decomposition, the energy level decomposition is the coarsest Morse decomposition that still produces a Lyapunov function which gives the same information about the structure of the attractor. We also establish sufficient conditions which ensure the stability of this kind of decomposition under perturbation. In particular, if connections between different isolated invariant sets inside the attractor remain under perturbation, we show the continuity of the energy level Morse decomposition. The class of Morse-Smale systems illustrates our results.

Evaluation of physiologic complexity in time series using generalized sample entropy and surrogate data analysis

Complexity in time series is an intriguing feature of living dynamical systems, with potential use for identification of system state. Although various methods have been proposed for measuring physiologic complexity, uncorrelated time series are often assigned high values of complexity, errouneously classifying them as a complex physiological signals. Here, we propose and discuss a method for complex system analysis based on generalized statistical formalism and surrogate time series. Sample entropy (SampEn) was rewritten inspired in Tsallis generalized entropy, as function of q parameter (qSampEn). qSDiff curves were calculated, which consist of differences between original and surrogate series qSampEn. We evaluated qSDiff for 125 real heart rate variability (HRV) dynamics, divided into groups of 70 healthy, 44 congestive heart failure (CHF), and 11 atrial fibrillation (AF) subjects, and for simulated series of stochastic and chaotic process. The evaluations showed that, for nonperiodic signals, qSDiff curves have a maximum point (qSDiff(max)) for q not equal 1. Values of q where the maximum point occurs and where qSDiff is zero were also evaluated. Only qSDiff(max) values were capable of distinguish HRV groups (p-values 5.10 x 10(-3); 1.11 x 10(-7), and 5.50 x 10(-7) for healthy vs. CHF, healthy vs. AF, and CHF vs. AF, respectively), consistently with the concept of physiologic complexity, and suggests a potential use for chaotic system analysis. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4758815]

Thermodynamics of Ising model with infinite-range interactions by generalized canonical ensemble

In this work we present the idea of how generalized ensembles can be used to simplify the operational study of non-additive physical systems. As alternative of the usual methods of direct integration or mean-field theory, we show how the solution of the Ising model with infinite-range interactions is obtained by using a generalized canonical ensemble. We describe how the thermodynamical properties of this model in the presence of an external magnetic field are founded by simple parametric equations. Without impairing the usual interpretation, we obtain an identical critical behaviour as observed in traditional approaches.

Magnetic flux transport by turbulent reconnection in astrophysical flows

The role of magnetohydrodynamics (MHD) turbulence in astrophysical environments is still highly debated. An important question that permeates this debate is the transport of magnetic flux. This is particularly important, for instance, in the context of star formation. When clouds collapse gravitationally to form stars, there must be some magnetic flux transport. Otherwise, the newborn stars would have magnetic fields several orders of magnitude larger than the observed ones. Also, the magnetic flux that is dragged in the late stages of the formation of a star can remove all the rotational support from the accretion disc that grows around the protostar. The efficiency of the mechanism that is often invoked to allow transport of magnetic fields at different stages of star formation, namely ambipolar diffusion, has recently been put in check. We discuss here an alternative mechanism for magnetic flux transport which is based on turbulent fast magnetic reconnection. We review recent results from three-dimensional MHD numerical simulations that indicate that this mechanism is very efficient in decoupling and transporting magnetic flux from the inner denser regions to the outskirts of collapsing clouds at different stages of star formation. We discuss this mechanism also in the context of dynamo processes and speculate that it can play a role both in solar dynamo and in accretion disc dynamo processes.

Mutual Information Rate and Bounds for It

The amount of information exchanged per unit of time between two nodes in a dynamical network or between two data sets is a powerful concept for analysing complex systems. This quantity, known as the mutual information rate (MIR), is calculated from the mutual information, which is rigorously defined only for random systems. Moreover, the definition of mutual information is based on probabilities of significant events. This work offers a simple alternative way to calculate the MIR in dynamical (deterministic) networks or between two time series (not fully deterministic), and to calculate its upper and lower bounds without having to calculate probabilities, but rather in terms of well known and well defined quantities in dynamical systems. As possible applications of our bounds, we study the relationship between synchronisation and the exchange of information in a system of two coupled maps and in experimental networks of coupled oscillators.

Records of migration in the exoplanet configurations

When compared to our Solar System, many exoplanet systems exhibit quite unusual planet configurations; some of these are hot Jupiters, which orbit their central stars with periods of a few days, others are resonant systems composed of two or more planets with commensurable orbital periods. It has been suggested that these configurations can be the result of a migration processes originated by tidal interactions of the planets with disks and central stars. The process known as planet migration occurs due to dissipative forces which affect the planetary semi-major axes and cause the planets to move towards to, or away from, the central star. In this talk, we present possible signatures of planet migration in the distribution of the hot Jupiters and resonant exoplanet pairs. For this task, we develop a semi-analytical model to describe the evolution of the migrating planetary pair, based on the fundamental concepts of conservative and dissipative dynamics of the three-body problem. Our approach is based on an analysis of the energy and the orbital angular momentum exchange between the two-planet system and an external medium; thus no specific kind of dissipative forces needs to be invoked. We show that, under assumption that dissipation is weak and slow, the evolutionary routes of the migrating planets are traced by the stationary solutions of the conservative problem (Birkhoff, Dynamical systems, 1966). The ultimate convergence and the evolution of the system along one of these modes of motion are determined uniquely by the condition that the dissipation rate is sufficiently smaller than the roper frequencies of the system. We show that it is possible to reassemble the starting configurations and migration history of the systems on the basis of their final states, and consequently to constrain the parameters of the physical processes involved.

The effects of hypocalcemia on spatial alternans and ventricular fibrillation studied with the optical mapping technique

The heart is a wonderful but complex organ: it uses electrochemical mechanisms in order to produce mechanical energy to pump the blood throughout the body and allow the life of humans and animals. This organ can be subject to several diseases and sudden cardiac death (SCD) is the most catastrophic manifestation of these diseases, responsible for the death of a large number of people throughout the world. It is estimated that 325000 Americans annually die for SCD. SCD most commonly occurs as a result of reentrant tachyarrhythmias (ventricular tachycardia (VT) and ventricular fibrillation (VF)) and the identification of those patients at higher risk for the development of SCD has been a difficult clinical challenge. Nowadays, a particular electrocardiogram (ECG) abnormality, “T-wave alternans” (TWA), is considered a precursor of lethal cardiac arrhythmias and sudden death, a sensitive indicator of risk for SCD. TWA is defined as a beat-to-beat alternation in the shape, amplitude, or timing of the T-wave on the ECG, indicative of the underlying repolarization of cardiac cells [5]. In other words TWA is the macroscopic effect of subcellular and celluar mechanisms involving ionic kinetics and the consequent depolarization and repolarization of the myocytes. Experimental activities have shown that TWA on the ECG is a manifestation of an underlying alternation of long and short action potential durations (APDs), the so called APD-alternans, of cardiac myocytes in the myocardium. Understanding the mechanism of APDs-alternans is the first step for preventing them to occur. In order to investigate these mechanisms it’s very important to understand that the biological systems are complex systems and their macroscopic properties arise from the nonlinear interactions among the parts. The whole is greater than the sum of the parts, and it cannot be understood only by studying the single parts. In this sense the heart is a complex nonlinear system and its way of working follows nonlinear dynamics; alternans also, they are a manifestation of a phenomenon typical in nonlinear dynamical systems, called “period-dubling bifurcation”. Over the past decade, it has been demonstrated that electrical alternans in cardiac tissue is an important marker for the development of ventricular fibrillation and a significant predictor for mortality. It has been observed that acute exposure to low concentration of calcium does not decrease the magnitude of alternans and sustained ventricular Fibrillation (VF) is still easily induced under these condition. However with prolonged exposure to low concentration of calcium, alternans disappears, but VF is still inducible. This work is based on this observation and tries to make it clearer. The aim of this thesis is investigate the effect of hypocalcemia spatial alternans and VF doing experiments with canine hearts and perfusing them with a solution with physiological ionic concentration and with a solution with low calcium concentration (hypocalcemia); in order to investigate the so called memory effect, the experimental activity was modified during the way. The experiments were performed with the optical mapping technique, using voltage-sensitive dye, and a custom made Java code was used in post-processing. Finding the Nolasco and Dahlen’s criterion [8] inadequate for the prediction of alternans, and takin into account the experimental results, another criterion, which consider the memory effect, has been implemented. The implementation of this criterion could be the first step in the creation of a method, AP-based, discriminating who is at risk if developing VF. This work is divided into four chapters: the first is a brief presentation of the physiology of the heart; the second is a review of the major theories and discovers in the study of cardiac dynamics; the third chapter presents an overview on the experimental activity and the optical mapping technique; the forth chapter contains the presentation of the results and the conclusions.

Nicht-wässrige Emulsionspolymerisationen

Die vorliegende Arbeit beschäftigt sich mit der Darstellung von Latexpartikeln in nicht-wässrigen Emulsionssystemen. Hintergrund der Untersuchungen war die Frage, ob es durch die Anwendung von nicht-wässrigen Emulsionen ermöglicht werden kann, sowohl wassersensitive Monomere als auch feuchtigkeitsempfindliche Polymerisationen zur Darstellung von Polymer-Latexpartikeln und deren Primärdispersionen einzusetzen. Das Basiskonzept der Arbeit bestand darin, nicht-wässrige Emulsionen auf der Basis zweier nicht mischbarer organischer Lösungsmittel unterschiedlicher Polarität auszubilden und anschließend die dispergierte Phase der Emulsion zur Synthese der Latexpartikel auszunutzen. Hierzu wurden verschiedene nicht-wässrige Emulsionssysteme erarbeitet, welche als dispergierte Phase ein polares und als kontinuierliche Phase ein unpolares Lösungsmittel enthielten. Auf Basis dieser Ergebnisse wurde in den nachfolgenden Untersuchungen zunächst die Anwendbarkeit solcher Emulsionen zur Darstellung verschiedener Acrylat- und Methacrylatpolymerdispersionen mittels radikalischer Polymerisation studiert. Um zu zeigen, dass die hier entwickelten nicht-wässrigen Emulsionen auch zur Durchführung von Stufenwachstumsreaktionen geeignet sind, wurden ebenfalls Polyester-, Polyamid- und Polyurethan-Latexpartikel dargestellt. Die Molekulargewichte der erhaltenen Polymere lagen bei bis zu 40 000 g/mol, im Vergleich zu wässrigen Emulsions- und Miniemulsions¬polymerisationssystemen sind diese um den Faktor fünf bis 30 höher. Es kann davon ausgegangen werden, dass hauptsächlich zwei Faktoren für die hohen Molekulargewichte verantwortlich sind: Zum einen die wasserfreien Bedingungen, welche die Hydrolyse der reaktiven Gruppen verhindern, und zum anderen die teilweise erfüllten Schotten-Baumann-Bedingungen, welche an der Grenzfläche zwischen dispergierter und kontinuierlicher Phase eine durch Diffusion kontrollierte ausgeglichene Stöchiometrie der Reaktionspartner gewährleisten. Somit ist es erstmals möglich, hochmolekulare Polyester, -amide und -urethane in nur einem Syntheseschritt als Primär¬dispersion darzustellen. Die Variabilität der nicht-wässrigen Emulsionen wurde zudem in weiteren Beispielen durch die Synthese von verschiedenen elektrisch leitfähigen Latices, wie z.B. Polyacetylen-Latexpartikeln, aufgezeigt. In dieser Arbeit konnte gezeigt werden, dass die entwickelten nicht-wässrigen Emulsionen eine äußerst breite Anwendbarkeit zur Darstellung von Polymer-Latexpartikeln aufweisen. Durch die wasserfreien Bedingungen erlauben die beschriebenen Emulsionsprozesse, Latexpartikel und entsprechende nicht-wässrige Dispersionen nicht nur traditionell radikalisch, sondern auch mittels weiterer Polymerisationsmechanismen (katalytisch, oxidativ oder mittels Polykondensation bzw. -addition) darzustellen.