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.

Efeitos interfaciais em heteroestruturas quânticas nô-abruptas: GaAs/ALxGa1-xAs

Um minuncioso estudo das propriedades de confinamento em heterostructuras bidimensionais(poços quânticos) GaAs/AlxGa1_xAs, com interfaces graduais é realizado. Um modelo teórico que represente bem a variação da fração molar do alumínio nas interfaces, resultante do aparecimento de micro-rugosidades e ilhas durante os processos de crescimento e recozimento pós-crescimento da amostra, é elaborado. Vários perfis desta fração molar de alumínio nas interfaces são considerados. Soluções analíticas da equação de Schrodinger, na aproximação da massa efetiva constatne nas interfaces, resultando em equações transcendentais, que possibilitam a obtenção dos níveis de energia dos portadores, decorrentes do seu confinamento quântico, são apresentadas. Energias de ligação e de confinamento de excitons 2D, utilizando-se um método analítico e numerérico e a aproximação do potencial efetivo, são também calculadas. Resultados numéricos para os níveis de energia dos portadores e para as energias de ligação e de confinamento dos excitons 2D, em poços quânticos GaAs/Al0.35Ga0.65As não-abruptos, sem e com a presença de campo elétrico aplicado para vários perfis interfaciais da fração de molar, são mostrados. Para a obtenção desses resultados, faz-se uso do método dos degraus múltiplos e da técnica da matriz de transferência, e adota-se, como operador de energia cinética, o de Ben-Daniel e Duque para uma massa efetiva dependente da posição. Conclui-se que um modelo que leva em conta a existência de interfaces não-abruptas e seus diversos perfis é indispensável para uma melhor descrição das propriedades opto-eletrônicas de poços quânticos GaAs/AlxGa1-xAs, enquanto que a aproximação das interfaces abruptas apresenta-se bastante limitada

Evolução top-hat hidrodinâmica em campos de velocidades peculiares primordiais

We investigate the cosmology of the vacuum energy decaying into cold dark matter according to thermodynamics description of Alcaniz & Lima. We apply this model to analyze the evolution of primordial density perturbations in the matter that gave rise to the first generation of structures bounded by gravity in the Universe, called Population III Objects. The analysis of the dynamics of those systems will involve the calculation of a differential equation system governing the evolution of perturbations to the case of two coupled fluids (dark matter and baryonic matter), modeled with a Top-Hat profile based in the perturbation of the hydrodynamics equations, an efficient analytical tool to study the properties of dark energy models such as the behavior of the linear growth factor and the linear growth index, physical quantities closely related to the fields of peculiar velocities at any time, for different models of dark energy. The properties and the dynamics of current Universe are analyzed through the exact analytical form of the linear growth factor of density fluctuations, taking into account the influence of several physical cooling mechanisms acting on the density fluctuations of the baryonic component of matter during the evolution of the clouds of matter, studied from the primordial hydrogen recombination. This study is naturally extended to more general models of dark energy with constant equation of state parameter in a flat Universe

Criação da matéria em cosmologias com velocidade da luz variável e eletrônico não-linear

In this work we obtain the cosmological solutions and investigate the thermodynamics of matter creation in two diferent contexts. In the first we propose a cosmological model with a time varying speed of light c. We consider two diferent time dependence of c for a at Friedmann-Robertson- Walker (FRW) universe. We write the energy conservation law arising from Einstein equations and study how particles are created as c decreases with cosmic epoch. The variation of c is coupled to a cosmological Λ term and both singular and non-singular solutions are possible. We calculate the "adiabatic" particle creation rate and the total number of particles as a function of time and find the constrains imposed by the second law of thermodynamics upon the models. In the second scenario, we study the nonlinearity of the electrodynamics as a source of matter creation in the cosmological models with at FRW geometry. We write the energy conservation law arising from Einstein field equations with cosmological term Λ, solve the field equations and study how particles are created as the magnetic field B changes with cosmic epoch. We obtain solutions for the adiabatic particle creation rate, the total number of particles and the scale factor as a function of time in three cases: Λ = 0, Λ = constant and Λ α H2 (cosmological term proportional to the Hubble parameter). In all cases, the second law of thermodynamics demands that the universe is not contracting (H ≥ 0). The first two solutions are non-singular and exhibit in ationary periods. The third case studied allows an always in ationary universe for a suficiently large cosmological term

Soluções cosmológicas e locais para uma eletrodinâmica modificada

The present work investigates some consequences that arise from the use of a modifed lagrangean for the eletromagnetic feld in two diferent contexts: a spatially homogeneous and isotropic universe whose dynamics is driven by a magnetic feld plus a cosmological parameter A, and the problem of a static and charged point mass (charged black hole). In the cosmological case, three diferent general solutions were derived. The first, with a null cosmological parameter A, generalizes a particular solution obtained by Novello et al [gr-qc/9806076]. The second one admits a constant A and the third one allows A to be a time-dependent parameter that sustains a constant magnetic feld. The first two solutions are non-singular and exhibit in ationary periods. The third case studied shows an in ationary dynamics except for a short period of time. As for the problem of a charged point mass, the solutions of the Einstein-Maxwell equations are obtained and compared with the standard Reissner-Nordstrom solution. Contrary to what happens in the cosmological case, the physical singularity is not removed

Processos difusivos generalizados

We investigate several diffusion equations which extend the usual one by considering the presence of nonlinear terms or a memory effect on the diffusive term. We also considered a spatial time dependent diffusion coefficient. For these equations we have obtained a new classes of solutions and studied the connection of them with the anomalous diffusion process. We start by considering a nonlinear diffusion equation with a spatial time dependent diffusion coefficient. The solutions obtained for this case generalize the usual one and can be expressed in terms of the q-exponential and q-logarithm functions present in the generalized thermostatistics context (Tsallis formalism). After, a nonlinear external force is considered. For this case the solutions can be also expressed in terms of the q-exponential and q-logarithm functions. However, by a suitable choice of the nonlinear external force, we may have an exponential behavior, suggesting a connection with standard thermostatistics. This fact reveals that these solutions may present an anomalous relaxation process and then, reach an equilibrium state of the kind Boltzmann- Gibbs. Next, we investigate a nonmarkovian linear diffusion equation that presents a kernel leading to the anomalous diffusive process. Particularly, our first choice leads to both a the usual behavior and anomalous behavior obtained through a fractionalderivative equation. The results obtained, within this context, correspond to a change in the waiting-time distribution for jumps in the formalism of random walks. These modifications had direct influence in the solutions, that turned out to be expressed in terms of the Mittag-Leffler or H of Fox functions. In this way, the second moment associated to these distributions led to an anomalous spread of the distribution, in contrast to the usual situation where one finds a linear increase with time

Polaritons em materiais magnéticos nanoestruturados

In this work we present a theoretical study about the properties of magnetic polaritons in superlattices arranged in a periodic and quasiperiodic fashíons. In the periodic superlattice, in order to describe the behavior of the bulk and surface modes an effective medium approach, was used that simplify enormously the algebra involved. The quasi-periodic superlattice was described by a suitable theoretical model based on a transfer-matrix treatment, to derive the polariton's dispersion relation, using Maxwell's equations (including effect of retardation). Here, we find a fractal spectra characterized by a power law for the distribution of the energy bandwidths. The localization and scaling behavior of the quasiperiodic structure were studied for a geometry where the wave vector and the external applied magnetic field are in the same plane (Voigt geometry). Numerical results are presented for the ferromagnet Fe and for the metamagnets FeBr2 and FeCl2

Valores de referência para pressão inspiratória nasal SNIFF na população brasileira

The strength of respiratory muscle are frequently assessed by maximal inspiratory and expiratory pressure, however, the maneuvers to assess PImax and PEmax are difficult for many patients. The sniff nasal inspiratory pressure (SNIP) is a simple and noninvasive technique use to assess inspiratory muscles strength. Reference values have been previous established for SNIP in adults but no previous studies have provided reference values for SNIP in adult Brazilian population. The main objective of this study were propose reference values of SNIP for Brazilian population through establishment of relationship between anthropometric measurements, physical activity profile and SNIP and at the same time compare the values obtained with reference values previously published. We studied 117 subjects (59 male and 58 female) distributed in different age grouped 20-80 years old. The results showed on significant positive relationship between SNIP and height and negative correlation with age (p<0.05). In the multiple linear regression analysis only age continued to have an independent predictive role for the two dependent variables that correlated with SNIP. The values of SNIP found in Brazilian population were higher when compared with predict values of previous studies. The results of this study provide reference equations of SNIP for health Brazilian population from 20 to 80 years old

Equacões preditivas para as pressões respiratórias estáticas máximas de adolescentes brasileiros

Introduction: The reference values and prediction equations for maximal respiratory pressures (MRP) differ significantly between the available studies. This large discrepancy can be attributed to the different methodologies proposed. Although the importance of MRP is widely recognized, there are no Brazilian studies that provide predictive equations and reference values for PRM adolescents. Objectives: The purpose of this study was to provide normal values and propose predictive equations for maximal static respiratory pressures of Brazilian adolescents. Methods: An observational cross-sectional study, which evaluated 182 adolescents of both sexes aged between 12 and 18 years, enrolled in schools of the state and private in the city of Natal / RN. The selection of schools and participants of the study was randomly through a lottery system. The spirometric evaluation was performed through the digital spirometer One Flow FVC prior to the assessment of respiratory muscle strength. The MICs were measured with MVD digital manometer 300. Statistical analysis was performed using the SPSS 17.0 software STATISTICS, assigning the significance level of 5%. The normality of data distribution was verified using the Kolmogorov-Smirnov (KS). The descriptive analysis was expressed as mean and standard deviation. We used one-way ANOVA test to verify the difference of the averages of MRPs between age and gender and comparing the averages of MRPs between levels of physical activity. The test t'Student unpaired compared the averages of MRPs being ages and sexes. The comparison of mean values obtained in this study PRM with the values predicted using the equations mentioned above was relizada by testing paired t'Student. To verify the correlation between the PRM and the independent variables (age, weight, height) was used Pearson correlation test. Levene's test evaluated the homogeneity of variance. To obtain predictive equations analysis was used stepwise multiple linear regression. Results: There was no significant difference in mean age between the PRM. The male adolescents, regardless of age, showed superiority in MRP values when compared to the opposite sex. Weight, height and sex correlated with the PRM. Regression analysis suggested in this study, pointed out that the weight and sex had an influence in MIP and MEP only in relation to sex influenced. The mean for each PRM adolescents classified as very active were superior to those observed in adolescents classified as irregularly active. Conclusion: This study provides reference values and two models of predictive equations for maximal inspiratory and expiratory pressures, and to establish the lower limits of normality that will serve as an indispensable condition for careful evaluation of respiratory muscle strength in Brazilian adolescents

Associação entre diferentes marcadores antropométricos com variáveis espirométricas e de força muscular respiratória em obesos mórbidos

A obesidade é uma epidemia global em alarmante ascensão. Caracterizada pelo excesso de gordura corporal subcutânea, de caráter multifatorial, está relacionada ao surgimento de diversas co-morbidades, entre elas, várias alterações respiratórias, estas se tornam mais intensas quanto maior o grau de obesidade. Não há consenso na relação entre os marcadores de adiposidade geral ou específicos e suas repercussões sobre a função ventilatória, especialmente em relação à sobrecarga muscular respiratória. Objetivo: Analisar a relação entre marcadores antropométricos e variáveis espirométricas e de força muscular respiratória em indivíduos com obesidade mórbida. Métodos: Estudo transversal entre setembro de 2007 e outubro de 2012. Participaram da pesquisa 163 obesos mórbidos (37.1±9.8 anos e IMC=49.0±5.88 Kg/m2) sem alterações espirométricas. Foram observadas as associações entre Índice de Massa Corporal-IMC, adiposidade localizada (Circunferências de Pescoço-CP, Cintura-CC e Quadril-CQ), percentual de gordura corporal através do Índice de Adiposidade Corporal-IAC, volumes e capacidades pulmonares (CVF, VEF1 e VRE) e pressões respiratória estática (PIM e PEM) e dinâmica (VVM). Resultados: O VRE foi o volume mais afetado pela obesidade (apenas 41%predito) e mostrou associação negativa nas relações com todos os marcadores de adiposidade (IMC: r=-0.52; IAC: r=-0.21; CC: r=-0.44; CP: r=-0.25 e CQ: r=-0.28). Há relação inversa entre o percentual de gordura corporal (IAC) com a CVF (r=-0.59), o VEF1(r=-0.56) e o VVM (r=-0.43). As pressões respiratórias são justificadas principalmente pela adiposidade ao redor do pescoço e o IAC. Nossos dados de força muscular respiratória foram melhores associados aos valores de referências sugeridos pelas equações de Harik-Klan et al (1998) para PIM (R²=0.72) e com a equação proposta por Neder et al (1999) para PEM (R²=0.52). Em um modelo de regressão linear, as variáveis de adiposidade não justificam a VVM, já o VEF1 explica 62% da variância da VVM em obesos mórbidos. Conclusão: O percentual da adiposidade corporal e a circunferência do pescoço estão associados com a força muscular e capacidade de gerar fluxo respiratório de obesos mórbidos. Sugerimos a equação elaborada por Harik-Klan et al (1998) para obtenção de valores preditos de PIM e a equação proposta por Neder et al (1999) para valores de normalidade da PEM em sujeitos com obesidade mórbida. Foi possível fornecer uma equação de referência específica para VVM em obesos mórbidos

Fatores de influência na produção de leite bovino sobre os níveis da contagem bacteriana total

The objective of this study was to evaluate the influence of milking procedures on the levels of total bacterial count (TBC) in bovine milk. In the first study the influences of procedures for hygienic milking, cleaning of milking equipment and milk cooling tanks on the TBC levels were evaluated. Four bulk samples of milk were collected from each tank in eight properties for TBC analysis, employing the flow cytometry method. A questionnaire was applied in each property to assess the current situation of milking procedures on each production system that took part on this research, followed by training of employees in good agricultural practices in the production of milk and monitoring of the TBC measurements. The methodology for analysis of longitudinal data was considered, focusing on random effects models. The results showed that the handling procedures for milking and the cleanliness of the cooling tank contributed to a further reduction in the levels of TBC raw milk cooling tanks. The second study aimed to describe the percentage of the properties that comply with the Normative Instruction Nº 51 (Brazil s IN 51) with regard to total bacterial count (TBC) in bovine milk. The study was conducted from January 2010 to July 2011. Milk samples were collected from the eight properties selected for TBC analysis by the flow cytometry method. Again, on each property a questionnaire was applied to assess the current situation of milking procedures on each production system that took part on this research, followed by training of employees in good agricultural practices in the production of milk and monitoring of the TBC measurements. The methodology of marginal models based on Generalized Estimate Equations (GEEs) was followed in the statistical analysis. The results showed that the handling procedures of the milking and the cleanliness of the cooling tanks contributed to a considerable percentage of the properties that reached the limits of TBC established by IN 51

Dinâmica populacional e alimentar de Stegastes fuscus, (Osteichthyes:pomacentridae) em arrecifes da praia de Búzius, no Rio Grande do Norte

The damselfish, Stegastes fuscus Cuvier, 1830 (Osteichthyes: Perciformes: Pomacentridae), is abundant in the coastal reefs of Búzios Beach, Rio Grande do Norte, Brazil and they play an important role in the reef community ecology. The present study investigated the feeding strategy of this species considering the food habits and morfo-histology of the digestive tract. Influence of the environmental correlates such as temperature, rainfall and luminosity in the tidal rock pools were studied. The fish were captured on a monthly basis from September 2004 to August 2005, during which period 842 individuals of S. fuscus were captured, 125 males, 437 females and 280 individuals without sex identification. The sex ratio observed was 1 M : 3,5 F. The total body length of males varied from 3.6 to 11.3 cm, with a mean of 7.77 cm; that of females varied from 2.9 to 11.4 cm, with a mean of 7.85 cm, and that of sex grouped individuals varied from 2.9 to 11.4 cm, with a mean of 7.83. However, there was no difference between males and females in total body length. This species presented a positive alometric growth and the equations obtained for the relation between body mass and total body length were: Wt =0,0174Lt 3,1123 for males; Wt =0,0137Lt 3,2294 for females and Wt = 0,0148Lt 3.1928 for sex grouped individuals. The relation between total body length and standard length was L t = 1 ,3223Ls + 0,1527 for sex grouped individual s. February to August was associated to a long period of gonadal resting. The fish spawned during January and in September -October. The frequency of fish with empty stomachs occurred during August to December, whereas frequency of fish with food contents i n stomachs occurred during January to July. This species is considered as a preferential herbivore based on the volume of macroalgae in its diet composition. The morfo -histological aspects of S. fuscus confirm herbivory. Among the environmental factors con sidered only rainfall showed a correlation with the feeding habits of this species