O problema da matéria escura e o teorema do virial na teoria de gravidade Eddington-Born-Infeld

Dark matter is a fundamental ingredient of the modern Cosmology. It is necessary in order to explain the process of structures formation in the Universe, rotation curves of galaxies and the mass discrepancy in clusters of galaxies. However, although many efforts, in both aspects, theoretical and experimental, have been made, the nature of dark matter is still unknown and the only convincing evidence for its existence is gravitational. This rises doubts about its existence and, in turn, opens the possibility that the Einstein’s gravity needs to be modified at some scale. We study, in this work, the possibility that the Eddington-Born-Infeld (EBI) modified gravity provides en alternative explanation for the mass discrepancy in clusters of galaxies. For this purpose we derive the modified Einstein field equations and find their solutions to a spherical system of identical and collisionless point particles. Then, we took into account the collisionless relativistic Boltzmann equation and using some approximations and assumptions for weak gravitational field, we derived the generalized virial theorem in the framework of EBI gravity. In order to compare the predictions of EBI gravity with astrophysical observations we estimated the order of magnitude of the geometric mass, showing that it is compatible with present observations. Finally, considering a power law for the density of galaxies in the cluster, we derived expressions for the radial velocity dispersion of the galaxies, which can be used for testing some features of the EBI gravity.

Estatística não-extensiva aplicada ao cálculo do calor específico eletrônico em estruturas quasiperiódicas

Systems whose spectra are fractals or multifractals have received a lot of attention in recent years. The complete understanding of the behavior of many physical properties of these systems is still far from being complete because of the complexity of such systems. Thus, new applications and new methods of study of their spectra have been proposed and consequently a light has been thrown on their properties, enabling a better understanding of these systems. We present in this work initially the basic and necessary theoretical framework regarding the calculation of energy spectrum of elementary excitations in some systems, especially in quasiperiodic ones. Later we show, by using the Schr¨odinger equation in tight-binding approximation, the results for the specific heat of electrons within the statistical mechanics of Boltzmann-Gibbs for one-dimensional quasiperiodic systems, growth by following the Fibonacci and Double Period rules. Structures of this type have already been exploited enough, however the use of non-extensive statistical mechanics proposed by Constantino Tsallis is well suited to systems that have a fractal profile, and therefore our main objective was to apply it to the calculation of thermodynamical quantities, by extending a little more the understanding of the properties of these systems. Accordingly, we calculate, analytical and numerically, the generalized specific heat of electrons in one-dimensional quasiperiodic systems (quasicrystals) generated by the Fibonacci and Double Period sequences. The electronic spectra were obtained by solving the Schr¨odinger equation in the tight-binding approach. Numerical results are presented for the two types of systems with different values of the parameter of nonextensivity q

Confinamento de fónons ópticos em estruturas piezoelétricas periódicas e quasiperiódicas

We study the optical-phonon spectra in periodic and quasiperiodic (Fibonacci type) superlattices made up from III-V nitride materials (GaN and AlN) intercalated by a dielectric material (silica - SiO2). Due to the misalignments between the silica and the GaN, AlN layers that can lead to threading dislocation of densities as high as 1010 cm−1, and a significant lattice mismatch (_ 14%), the phonon dynamics is described by a coupled elastic and electromagnetic equations beyond the continuum dielectric model, stressing the importance of the piezoelectric polarization field in a strained condition. We use a transfer-matrix treatment to simplify the algebra, which would be otherwise quite complicated, allowing a neat analytical expressions for the phonon dispersion relation. Furthermore, a quantitative analysis of the localization and magnitude of the allowed band widths in the optical phonon s spectra, as well as their scale law are presented and discussed

Implementação da técnica de difração de elétrons de baixa energia

The purpose of this study is to describe the implementation of the Low Energy Electron Diffaction (LEED) technique in the Laboratory of Magnetic Nanostructures and Semiconductors of the Department of Theoretical and Experimental Physics of the Universidade Federal do Rio Grande do Norte (UFRN), Natal, Brazil. During this work experimental apparatus were implemented for a complete LEED set-up. A new vacuum system was also set up. This was composed of a mechanical pump, turbomolecular pump and ionic pump for ultra-high vacuum and their respective pressure measurement sensors (Pirani gauge for low vacuum measures and the wide range gauge -WRG); ion cannon maintenance, which is basically mini-sputtering, whose function is sample cleaning; and set-up, maintenance and handling of the quadrupole mass spectrometer, whose main purpose is to investigate gas contamination inside the ultra-high vacuum chamber. It should be pointed out that the main contribution of this Master's thesis was the set-up of the sample heating system; that is, a new sample holder. In addition to the function of sample holder and heater, it was necessary to implement the function of sustaining the ultra-high vacuum environment. This set of actions is essential for the complete functioning of the LEED technique

Condições de energia de hawking e ellis e a equação de raychaudhuri

In the Einstein s theory of General Relativity the field equations relate the geometry of space-time with the content of matter and energy, sources of the gravitational field. This content is described by a second order tensor, known as energy-momentum tensor. On the other hand, the energy-momentum tensors that have physical meaning are not specified by this theory. In the 700s, Hawking and Ellis set a couple of conditions, considered feasible from a physical point of view, in order to limit the arbitrariness of these tensors. These conditions, which became known as Hawking-Ellis energy conditions, play important roles in the gravitation scenario. They are widely used as powerful tools for analysis; from the demonstration of important theorems concerning to the behavior of gravitational fields and geometries associated, the gravity quantum behavior, to the analysis of cosmological models. In this dissertation we present a rigorous deduction of the several energy conditions currently in vogue in the scientific literature, such as: the Null Energy Condition (NEC), Weak Energy Condition (WEC), the Strong Energy Condition (SEC), the Dominant Energy Condition (DEC) and Null Dominant Energy Condition (NDEC). Bearing in mind the most trivial applications in Cosmology and Gravitation, the deductions were initially made for an energy-momentum tensor of a generalized perfect fluid and then extended to scalar fields with minimal and non-minimal coupling to the gravitational field. We also present a study about the possible violations of some of these energy conditions. Aiming the study of the single nature of some exact solutions of Einstein s General Relativity, in 1955 the Indian physicist Raychaudhuri derived an equation that is today considered fundamental to the study of the gravitational attraction of matter, which became known as the Raychaudhuri equation. This famous equation is fundamental for to understanding of gravitational attraction in Astrophysics and Cosmology and for the comprehension of the singularity theorems, such as, the Hawking and Penrose theorem about the singularity of the gravitational collapse. In this dissertation we derive the Raychaudhuri equation, the Frobenius theorem and the Focusing theorem for congruences time-like and null congruences of a pseudo-riemannian manifold. We discuss the geometric and physical meaning of this equation, its connections with the energy conditions, and some of its several aplications.

Teoria cinética não extensiva: efeitos físicos em gases e plasmas

The standard kinetic theory for a nonrelativistic diluted gas is generalized in the spirit of the nonextensive statistic distribution introduced by Tsallis. The new formalism depends on an arbitrary q parameter measuring the degree of nonextensivity. In the limit q = 1, the extensive Maxwell-Boltzmann theory is recovered. Starting from a purely kinetic deduction of the velocity q-distribution function, the Boltzmann H-teorem is generalized for including the possibility of nonextensive out of equilibrium effects. Based on this investigation, it is proved that Tsallis' distribution is the necessary and sufficient condition defining a thermodynamic equilibrium state in the nonextensive context. This result follows naturally from the generalized transport equation and also from the extended H-theorem. Two physical applications of the nonextensive effects have been considered. Closed analytic expressions were obtained for the Doppler broadening of spectral lines from an excited gas, as well as, for the dispersion relations describing the eletrostatic oscillations in a diluted electronic plasma. In the later case, a comparison with the experimental results strongly suggests a Tsallis distribution with the q parameter smaller than unity. A complementary study is related to the thermodynamic behavior of a relativistic imperfect simple fluid. Using nonequilibrium thermodynamics, we show how the basic primary variables, namely: the energy momentum tensor, the particle and entropy fluxes depend on the several dissipative processes present in the fluid. The temperature variation law for this moving imperfect fluid is also obtained, and the Eckart and Landau-Lifshitz formulations are recovered as particular cases

Testes cinemáticos em cosmologia com decaimento do vácuo

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior

Fraturas e caminhos ótimos na rede de Barabasi-Albert

Following the study of Andrade et al. (2009) on regular square lattices, here we investigate the problem of optimal path cracks (OPC) in Complex Networks. In this problem we associate to each site a determined energy. The optimum path is defined as the one among all possible paths that crosses the system which has the minimum cost, namely the sum of the energies along the path. Once the optimum path is determined, at each step, one blocks its site with highest energy, and then a new optimal path is calculated. This procedure is repeated until there is a set of blocked sites forming a macroscopic fracture which connects the opposite sides of the system. The method is applied to a lattice of size L and the density of removed sites is computed. As observed in the work by Andrade et al. (2009), the fractured system studied here also presents different behaviors depending on the level of disorder, namely weak, moderated and strong disorder intensities. In the regime of weak and moderated disorder, while the density of removed sites in the system does not depend of the size L in the case of regular lattices, in the regime of high disorder the density becomes substantially dependent on L. We did the same type of study for Complex Networks. In this case, each new site is connected with m previous ones. As in the previous work, we observe that the density of removed sites presents a similar behavior. Moreover, a new result is obtained, i.e., we analyze the dependency of the disorder with the attachment parameter m

Modelos cosmológicos com velocidade da luz variável

Conselho Nacional de Desenvolvimento Científico e Tecnológico

Caracterização infravermelho e distribuição espectral de energia para as estrelas com planetas

Neste trabalho estudamos o comportamento das estrelas pertencentes a sistemas planetários no que diz respeito às suas características infravermelho e à distribuição espectral de energia (SED). Nosso estudo tem como base uma análise detalhada do comportamento da emissão no infravermelho de 48 estrelas com planetas, classificadas como estrelas da seqüência principal, subgigantes ou gigantes. Foram analisados dados de fotometria infravermelho nas bandas 12, 25 e 60µm do catálogo de fontes IRAS puntiformes (IPSC) e nas bandas JHK do projeto 2 Micron All Sky Survey (2MASS). A partir do cálculo da discrepância na posição de apontamento da fonte e do cálculo do índice de cor, selecionamos e localizamos os objetos no diagrama de cor-cor do IRAS. Este diagrama permite-nos identificar possíveis objetos detentores de disco de poeira. Fizemos também uma análise da distribuição espectral de energia onde observamos também traços de excesso de fluxo no infravermelho, com isso, confirmarmos a presença do disco de poeira nos objetos identificados no diagrama de cor. Apesar da atual amostra de estrelas com planetas incluir apenas um subconjunto de estrelas com planetas detectadas na vizinhança solar, a presente análise do fluxo infravermelho nesses objetos oferecem uma possibilidade única de estudar as características infravermelho das estrelas pertencentes aos sistemas planetários extra-solar. Neste contexto, nosso estudo aponta resultados interessantes, entre outros destacamos o fato de algumas estrelas com planetas apresentarem um peculiar fluxo IRAS [60-25], indicando a co-existência de poeira juntamente com os planetas destes sistemas extra solar

Estudo das variáveis de processamento das matérias-primas da região do crato - ce na fabricação de produtos cerâmicos por extrusão e por prensagem

The limits to inform is about the character stico of basic, quimica, mineralogical and mechaniques of matlaughed material used in the manufacturing process the product certified in economic region the Cariri, specifically in the city of Crato, Ceará state, motivated the development of this work, since in this region the exist ing economic context that a general appear as important in the production chains. Were made twentyfive soils-test specimen collection and the study was performed to differentiate the mat laugh materials of variaveis processing of mathing raw materials in the factory The product mica monkeys by extrusion and pressing. The results were obtained ap s as analyzes: grain size, index of plasticity, fluoresce incidence X-ray difration the X-ray, and analyzes thermicals and properties technological. through s of curves gresifica returned to was a comparison between the retro the linear, absorb to water, porosity and bulk density. the results show that the excellent distribution and character acceptable available for the processing of the structure color dark red. needing, therefore, of the mixture of a less plastic clay with thick granulation, that works as plasticity reducer. In spite of the different resignation forms for prensagem and extrusion, the characteristics of absorption of water and rupture tension the flexing was shown inside of the patterns of ABNT

Palma forrageira (Opuntia ficus indica e Nopalea cochenillifera) como matéria-prima para produção de etanol celulósico e enzimas celulolíticas

The need for new sources of energy and the concern about the environment have pushed the search for renewable energy sources such as ethanol. The use of lignocellulosic biomass as substrate appears as an important alternative because of the abundance of this raw material and for it does not compete with food production. However, the process still meets difficulties of implementation, including the cost for production of enzymes that degrade cellulose to fermentable sugars. The aim of this study was to evaluate the behavior of the species of cactus pear Opuntia ficus indica and Nopalea cochenillifera, commonly found in northeastern Brazil, as raw materials for the production of: 1) cellulosic ethanol by simultaneous saccharification and fermentation (SSF) process, using two different strains of Saccharomyces cerevisiae (PE-2 and LNF CA-11), and 2) cellulolytic enzymes by semi-solid state fermentation (SSSF) using the filamentous fungus Penicillium chrysogenum. Before alcoholic fermentation process, the material was conditioned and pretreated by three different strategies: alkaline hydrogen peroxide, alkaline using NaOH and acid using H2SO4 followed by alkaline delignification with NaOH. Analysis of composition, crystallinity and enzymatic digestibility were carried out with the material before and after pretreatment. In addition, scanning electron microscopy images were used to compare qualitatively the material and observe the effects of pretreatments. An experimental design 2² with triplicate at the central point was used to evaluate the influence of temperature (30, 40 and 45 °C) and the initial charge of substrate (3, 4 and 5% cellulose) in the SSF process using the material obtained through the best condition and testing both strains of S. cerevisiae, one of them flocculent (LNF CA-11). For cellulase production, the filamentous fungus P. chrysogenum was tested with N. cochenillifera in the raw condition (without pretreatment) and pretrated hydrothermically, varying the pH of the fermentative medium (3, 5 and 7). The characterization of cactus pear resulted in 31.55% cellulose, 17.12% hemicellulose and 10.25% lignin for N. cochenillifera and 34.86% cellulose, 19.97% hemicellulose and 15.72% lignin for O. ficus indica. It has also been determined, to N. cochenillifera and O. ficus indica, the content of pectin (5.44% and 5.55% of calcium pectate, respectively), extractives (26.90% and 9.69%, respectively) and ashes (5.40% and 5.95%). Pretreatment using alkaline hydrogen peroxide resulted in the best cellulose recovery results (86.16% for N. cochenillifera and 93.59% for O. ficus indica) and delignification (48.79% and 23.84% for N. cochenillifera and O. ficus indica, respectively). This pretreatment was also the only one which did not increase the crystallinity index of the samples, in the case of O. ficus indica. However, when analyzing the enzymatic digestibility of cellulose, alkali pretreatment was the one which showed the best yields and therefore it was chosen for the tests in SSF. The experiments showed higher yield of conversion of cellulose to ethanol by PE-2 strain using the pretreated N. cochenillifera (93.81%) at 40 °C using 4% initial charge of cellulose. N. cochenillifera gave better yields than O. ficus indica and PE-2 strain showed better performance than CA-11. N. cochenillifera proved to be a substrate that can be used in the SSSF for enzymes production, reaching values of 1.00 U/g of CMCase and 0.85 FPU/g. The pretreatment was not effective to increase the enzymatic activity values

Influência da intensidade de aeração na formação do floco de lodo ativado e na eficiência de remoção de matéria orgânica

In wastewater treatment, activated sludge systems have been a technology widely applied as secondary treatment. During this step, which has a strong biological aspect, it is necessary to introduce oxygen supply for the maintenance of metabolic activity of the bacteria through the aerators. Aeration devices are responsible for most of the energy consumption in this stage. In this background, the influence of three aeration intensities (atmospheric air flow 3.5, 7.0 and 10.5 L.min-1) and the concentration of dissolved oxygen (DO) on the dimension of activated sludge flocs as well as on the efficiency of organic matter removal were assessed using a traditional activated sludge system which was fed with synthetic domestic wastewater. Samples were taken weekly from the three units that make up the system feed, aeration and storage tank in order to verify the Chemical Oxygen Demand (COD). It was established the process efficiency through a comparison between the initial and final COD. Besides the parameters already mentioned, this monitoring work on activated sludge batch system was also observed by Mixed Liquor Suspend Solids (MLSS), Volatile Suspend Solids (VSS), pH and temperature measures. The results have showed a maximum removal efficiency around 75% in the first aeration sequence and approximately 85% for the second and third one. For the first aeration, the DO concentration remained higher than 3.0 mg.L-1 and a diameter range from 10 to 60 μm was observed. In the second e third sequence, the DO concentration remained higher than 4.0 mg.L-1 with a diameter range of 10 until 200 μm. Although the sequence 1 and 2 have presented similar performances for organic matter removal, the sequence 2 promoted a regular floc size distribution and with lower values of Sludge Volumetric Index (SVI) meaning a better flocculating ability. In addition, the results reaffirmed what the literature has reported: higher DO concentrations produce flocs with greater dimensions

Incorporação do lodo de tanque séptico como matéria-prima de uma mistura asfáltica

In Natal/RN, 68% of the population uses some kind of individual system for their domestic sewers treatment, being that the most used it is septic tank, followed by sumidouro. Every treatment system of sewers, usually used, generates a by-product denominated sludge. That residue presents some components, in its constitution, undesirable under the environmental and sanitary point of view. In such case, to assure that the system treatment has satisfactory results, it is necessary to do the adjusted disposition of the sludge sewage. Several countries are looking for technical alternatives for the use and disposition of residues. Under technical and environmental conditions appropriate, these materials can be used, decreasing the consumption of the natural resources and the treatment need, storage or elimination of the wastes, what decrease the risks created. Some of the alternatives of recycling of the sludge sewage are: the application in the agriculture, in the production of energy and as raw material in the civil construction. This study evaluated asphalt mixtures behavior that partially substituted conventional aggregates by septic tank sludge. The septic tank sludge gave origin to two raw materials called raw sludge and sludge ash. The raw sludge was put as a small aggregate and the sludge ash as filler. In the first experiment it was made a comparison between the mixture with conventional aggregates and the mixtures that replaced sand by raw sludge in the proportions from 5% to 40%. In the second experiment, it was made comparison between mixtures with 1%, 2% and 3% of sludge ash and cement. The stages developed along the study were: physical characterization of the conventional materials; physical, chemistry, thermal, mineralogical characterizations and analysis of environmental risk of the raw sludge; physical characterization and analysis of environmental risk of the sludge ash; analysis of the mixtures performance through its volumetric and mechanical characteristics; forecast of the mixtures susceptibility in the moisture presence. For the grain size composition used and with the percentage asphalt adopted, the mixtures with up to 7,5% of raw sludge in his composition attend to the National Department of Transports Infrastructure (DNIT) specifications. However, in agreement with the mixtures susceptibility in the moisture presence, the mixtures with addition of raw sludge don't present satisfactory acting. In such case, they could be used in arid and semi-arid areas. The raw sludge application in mixtures increased their voids volume and their stability. However, it damaged mixtures adhesiveness. Mixtures with sludge ash and with cement presented similar behavior. However, mixtures with sludge ash presented a better performance than mixtures with cement as for their stability and their tensile strength ratio. The mixture with 1% of sludge ash is better. The wastes studied don't represent environmental risk

Modelos analíticos para rádio fontes extragalácticas

The great majority of analytical models for extragalactic radio sources suppose self-similarity and can be classified into three types: I, II and III. We have developed a model that represents a generalization of most models found in the literature and showed that these three types are particular cases. The model assumes that the area of the head of the jet varies with the jet size according to a power law and the jet luminosity is a function of time. As it is usually done, the basic hypothesis is that there is an equilibrium between the pressure exerted both by the head of the jet and the cocoon walls and the ram pressure of the ambient medium. The equilibrium equations and energy conservation equation allow us to express the size and width of the source and the pressure in the cocoon as a power law and find the respective exponents. All these assumptions can be used to calculate the evolution of the source size, width and radio luminosity. This can then be compared with the observed width-size relation for radio lobes and the power-size (P-D) diagram of both compact (GPS and CSS) and extended sources from the 3CR catalogue. In this work we introduce two important improvement as compared with a previous work: (1)We have put together a larger sample of both compact and extended radio sources