Time-periodic perturbation of a Lienard equation with an unbounded homoclinic loop

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Efeitos não-gaussianos em astrofísica e cosmologia

The recent astronomical observations indicate that the universe has null spatial curvature, is accelerating and its matter-energy content is composed by circa 30% of matter (baryons + dark matter) and 70% of dark energy, a relativistic component with negative pressure. However, in order to built more realistic models it is necessary to consider the evolution of small density perturbations for explaining the richness of observed structures in the scale of galaxies and clusters of galaxies. The structure formation process was pioneering described by Press and Schechter (PS) in 1974, by means of the galaxy cluster mass function. The PS formalism establishes a Gaussian distribution for the primordial density perturbation field. Besides a serious normalization problem, such an approach does not explain the recent cluster X-ray data, and it is also in disagreement with the most up-to-date computational simulations. In this thesis, we discuss several applications of the nonextensive q-statistics (non-Gaussian), proposed in 1988 by C. Tsallis, with special emphasis in the cosmological process of the large structure formation. Initially, we investigate the statistics of the primordial fluctuation field of the density contrast, since the most recent data from the Wilkinson Microwave Anisotropy Probe (WMAP) indicates a deviation from gaussianity. We assume that such deviations may be described by the nonextensive statistics, because it reduces to the Gaussian distribution in the limit of the free parameter q = 1, thereby allowing a direct comparison with the standard theory. We study its application for a galaxy cluster catalog based on the ROSAT All-Sky Survey (hereafter HIFLUGCS). We conclude that the standard Gaussian model applied to HIFLUGCS does not agree with the most recent data independently obtained by WMAP. Using the nonextensive statistics, we obtain values much more aligned with WMAP results. We also demonstrate that the Burr distribution corrects the normalization problem. The cluster mass function formalism was also investigated in the presence of the dark energy. In this case, constraints over several cosmic parameters was also obtained. The nonextensive statistics was implemented yet in 2 distinct problems: (i) the plasma probe and (ii) in the Bremsstrahlung radiation description (the primary radiation from X-ray clusters); a problem of considerable interest in astrophysics. In another line of development, by using supernova data and the gas mass fraction from galaxy clusters, we discuss a redshift variation of the equation of state parameter, by considering two distinct expansions. An interesting aspect of this work is that the results do not need a prior in the mass parameter, as usually occurs in analyzes involving only supernovae data.Finally, we obtain a new estimate of the Hubble parameter, through a joint analysis involving the Sunyaev-Zeldovich effect (SZE), the X-ray data from galaxy clusters and the baryon acoustic oscillations. We show that the degeneracy of the observational data with respect to the mass parameter is broken when the signature of the baryon acoustic oscillations as given by the Sloan Digital Sky Survey (SDSS) catalog is considered. Our analysis, based on the SZE/X-ray data for a sample of 25 galaxy clusters with triaxial morphology, yields a Hubble parameter in good agreement with the independent studies, provided by the Hubble Space Telescope project and the recent estimates of the WMAP

Extension of PT-symmetric quantum mechanics to the Dirac theory with position-dependent mass

We present a new method to construct the exactly solvable PT-symmetric potentials within the framework of the position-dependent effective mass Dirac equation with the vector potential coupling scheme in 1 + 1 dimensions. In order to illustrate the procedure, we produce three PT-symmetric potentials as examples, which are PT-symmetric harmonic oscillator-like potential, PT-symmetric potential with the form of a linear potential plus an inversely linear potential, and PT-symmetric kink-like potential, respectively. The real relativistic energy levels and corresponding spinor components for the bound states are obtained by using the basic concepts of the supersymmetric quantum mechanics formalism and function analysis method. (C) 2007 Elsevier B.V. All rights reserved.

Some orbital characteristics of lunar artificial satellites

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Third-body perturbation in the case of elliptic orbits for the disturbing body

This work presents a semi-analytical and numerical study of the perturbation caused in a spacecraft by a third-body using a double averaged analytical model with the disturbing function expanded in Legendre polynomials up to the second order. The important reason for this procedure is to eliminate terms due to the short periodic motion of the spacecraft and to show smooth curves for the evolution of the mean orbital elements for a long-time period. The aim of this study is to calculate the effect of lunar perturbations on the orbits of spacecrafts that are traveling around the Earth. An analysis of the stability of near-circular orbits is made, and a study to know under which conditions this orbit remains near circular completes this analysis. A study of the equatorial orbits is also performed. Copyright (C) 2008 R. C. Domingos et al.

Reactive Control for Transmission Overload Relief Based on Sensitivity Analysis and Cooperative Game Theory

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Termodinâmica de um gás de fótons no contexto de eletrodinâmicas não-lineares

The objective of this dissertation is the development of a general formalism to analyze the thermodynamical properties of a photon gas under the context of nonlinear electrodynamics (NLED). To this end it is obtained, through the systematic analysis of Maxwell s electromagnetism (EM) properties, the general dependence of the Lagrangian that describes this kind of theories. From this Lagrangian and in the background of classical field theory, we derive the general dispersion relation that photons must obey in terms of a background field and the NLED properties. It is important to note that, in order to achieve this result, an aproximation has been made in order to allow the separation of the total electromagnetic field into a strong background electromagnetic field and a perturbation. Once the dispersion relation is in hand, the usual Bose-Einstein statistical procedure is followed through which the thermodynamical properties, energy density and pressure relations are obtained. An important result of this work is the fact that equation of state remains identical to the one obtained under EM. Then, two examples are made where the thermodynamic properties are explicitly derived in the context of two NLED, Born-Infelds and a quadratic approximation. The choice of the first one is due to the vast appearance in literature and, the second one, because it is a first order approximation of a large class of NLED. Ultimately, both are chosen because of their simplicity. Finally, the results are compared to EM and interpreted, suggesting possible tests to verify the internal consistency of NLED and motivating further developement into the formalism s quantum case

A Grounded Theory como abordagem metodológica para pesquisas qualitativas em odontologia

Este trabalho consiste na proposta de utilização, em Odontologia, de uma abordagem metodológica usada em pesquisas qualitativas, denominada Grounded Theory, quando se objetiva compreender fenômenos ou se pretende descrevê-los de acordo com o ponto de vista do sujeito. Pesquisas em saúde, utilizando abordagens qualitativas, estão sendo, cada vez mais, empregadas entre pesquisadores e, na Odontologia, esta abordagem metodológica proposta torna-se fundamental, no sentido de propiciar a exploração de assuntos ainda pouco trabalhados nesta perspectiva metodológica, possibilitando que as pesquisas adquiriram contribuições originais e, assim, ampliando nosso conhecimento. São apresentadas as etapas a serem seguidas nesta abordagem, elucidando-as com alguns exemplos de parte de entrevistas realizadas numa pesquisa que teve como objetivos: compreender a experiência do idoso com a saúde bucal ao longo da vida e desenvolver e validar um modelo teórico representativo dessa experiência.

Game theory in sugarcane crop residue and available energy optimization

This work proposes a mathematical model to aid variety selection and planting quantity of sugarcane in order to reduce crop residues, maximize energy generated by this residue, and satisfy all the supply of the mill. We propose Linear Programming with two objective. The conflict between these objectives allows the use of the Nonzero-sum Game Theory. (C) 2003 Elsevier B.V. Ltd. All rights reserved.

Regularization and singular perturbation techniques for non-smooth systems

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Teleparallel equivalent of non-Abelian Kaluza-Klein theory

Based on the equivalence between a gauge theory for the translation group and general relativity, a teleparallel version of the non-Abelian Kaluza-Klein theory is constructed. In this theory, only the fiber-space turns out to be higher dimensional, spacetime being kept always four dimensional. The resulting model is a gauge theory that unifies, in the Kaluza-Klein sense, gravitational and gauge fields. In contrast with the ordinary Kaluza-Klein models, this theory defines a natural length scale for the compact submanifold of the fiber space, which is shown to be of the order of the Planck length.

Electromagnetic field at finite temperature: A first order approach

In this work we study the electromagnetic field at finite temperature via the massless DKP formalism. The constraint analysis is performed and the partition function for the theory is constructed and computed. When it is specialized to the spin 1 sector we obtain the well-known result for the thermodynamic equilibrium of the electromagnetic field. (c) 2006 Elsevier B.V. All rights reserved.

Quantum state density and critical temperature in M-theory

We discuss the asymptotic properties of quantum states density for fundamental p-branes which can yield a microscopic interpretation of the thermodynamic quantities in M-theory. The matching of the BPS part of spectrum for superstring and supermembrane gives the possibility of getting membrane's results via string calculations. In the weak coupling limit of M-theory, the critical behavior coincides with the first-order phase transition in the standard string theory at temperature less than the Hagedorn's temperature T-H. The critical temperature at large coupling constant is computed by considering M-theory on manifold with topology R-9 circle times T-2. Alternatively we argue that any finite temperature can be introduced in the framework of membrane thermodynamics.

Charges and fluxes in Maxwell theory on compact manifolds with boundary

We investigate the charges and fluxes that can occur in higher-order Abelian gauge theories defined on compact space-time manifolds with boundary. The boundary is necessary to supply a destination to the electric lines of force emanating from brane sources, thus allowing non-zero net electric charges, but it also introduces new types of electric and magnetic flux. The resulting structure of currents, charges, and fluxes is studied and expressed in the language of relative homology and de Rham cohomology and the corresponding abelian groups. These can be organised in terms of a pair of exact sequences related by the Poincare-Lefschetz isomorphism and by a weaker flip symmetry exchanging the ends of the sequences. It is shown how all this structure is brought into play by the imposition of the appropriately generalised Maxwell's equations. The requirement that these equations be integrable restricts the world-volume of a permitted brane (assumed closed) to be homologous to a cycle on the boundary of space-time. All electric charges and magnetic fluxes are quantised and satisfy the Dirac quantisation condition. But through some boundary cycles there may be unquantised electric fluxes associated with quantised magnetic fluxes and so dyonic in nature.

Duffin-Kemmer-Petiau theory in the causal approach

In this paper we consider the scalar sector of Duffin-Kemmer-Petiau theory in the framework of Epstein-Glaser causal method. We calculate the lowest order distributions for Compton scattering, vacuum polarization, self-energy and vertex corrections. By requiring gauge invariance of the theory we recover, in a natural way, the scalar propagator of the usual effective theory.