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

Buraco negros, correspondência AdS/BCFT e fluido/gravidade

Einstein’s equations with negative cosmological constant possess the so-called anti de Sitter space, AdSd+1, as one of its solutions. We will later refer to this space as to the "bulk". The holographic principle states that quantum gravity in the AdSd+1 space can be encoded by a d−dimensional quantum field theory on the boundary of AdSd+1 space, invariant under conformal transformations, a CFTd. In the most famous example, the precise statement is the duality of the type IIB string theory in the space AdS5 × S 5 and the 4−dimensional N = 4 supersymmetric Yang-Mills theory. Another example is provided by a relation between Einstein’s equations in the bulk and hydrodynamic equations describing the effective theory on the boundary, the so-called fluid/gravity correspondence. An extension of the "AdS/CFT duality"for the CFT’s with boundary was proposed by Takayanagi, which was dubbed the AdS/BCFT correspondence. The boundary of a CFT extends to the bulk and restricts a region of the AdSd+1. Neumann conditions imposed on the extension of the boundary yield a dynamic equation that determines the shape of the extension. From the perspective of fluid/gravity correspondence, the shape of the Neumann boundary, and the geometry of the bulk is sourced by the energy-momentum tensor Tµν of a fluid residing on this boundary. Clarifying the relation of the Takayanagi’s proposal to the fluid/gravity correspondence, we will study the consistence of the AdS/BCFT with finite temperature CFT’s, or equivalently black hole geometries in the bulk.

Construtivismo de marco teórico-pedagógico a grife: um estudo a partir das mensagens veiculadas na internet

This thesis is resulted of a research on propagated the social representations of constructivism in the Internet, which as had estimated basic the idea of Moscovici (1961) of that the media it has determinative paper in the popularization of the scientific theories, in formation e propagation of the social representations and in the construction of behaviors human beings. Understanding the Internet as latest space of circulation of social communications, therefore, privileged field (and still not explored) for studies of social representations, we choose this half midiático as investigative field of our research, it if it constitutes in the "great ocean of the new informational planet" (LEVY, 2000, p. 126), besides making possible the interaction with different forms of images, different individuals, different ' world ', configuring itself as important space of symbolic production e of analysis of the representational process in the world contemporary. Based in these questions, we trace as objective to analyze the circulating speech propagated on-line on the constructivism, searching to apprehend the social representations shared the respect. This objective was constructed in face of the insertion of the theory constructivist in the educational way has two decades more than, as well as of its consolidation as reference in different social contexts, mainly in midiático. The question that directed the research was: as this theory obtains to penetrate in some layers of our society, to influence the world readings e the behaviors of different people? That modifications it suffers in this trajectory and which the paper of the Internet in this process? The corpus of the research was constituted of the substances on the theory found in the Internet, in pages in Portuguese of Google, in the period of 27 of July of 2004 the 17 of August of 2004. The data they had been analyzed on the basis of the project of analysis of content elaborated for Moscovici (1961) and in the estimated theoreticians of the social communication, in special of the hypermedia. The results had disclosed that the Internet participates of determinative form in the process of popularization of the constructivism theory, not only spreading out its estimated theoretician- methodological for the domain public (diffusion), but propagating positive beliefs and images of its postulates (propagation) and using them it service of interests politicians e financiers (propaganda). The popularization of the constructivism in the Internet and social representations of this theory propagated configure one process in which the theory passes of pedagogical theoretical landmark for grief, assuming a commercial character extremely and the status of solution for problems of the education and the society, stirring up attitudes and behaviors in public, most general possible, that comes to take care of to the interests politicians e marketing. Recognizing the diversity, the permanent renewal of information and the negotiation of directions gifts in the Internet, as well as the innumerable ones forms of access to the information found by it, we consider results of the research as fruits of the inherent characteristics to this way midiático, to the time where we call the attention for relativity these results, for the plasticity of knowing them and sensible propagated on-line e for the great challenge that the hypermedia imposes to the study of communication phenomena, of the social representations and in educational quarrels and for the necessity of new research that they investigate the forms of socialization of the information and communication propitiated by hypermedia and its implications in the construction of the symbolic universes and in practical social

Conexão entre as redes complexas e estatística de Kaniadakis e busca eficiente das propriedades críticas do processo epidêmico difusivo 1D

In this work we study a connection between a non-Gaussian statistics, the Kaniadakis statistics, and Complex Networks. We show that the degree distribution P(k)of a scale free-network, can be calculated using a maximization of information entropy in the context of non-gaussian statistics. As an example, a numerical analysis based on the preferential attachment growth model is discussed, as well as a numerical behavior of the Kaniadakis and Tsallis degree distribution is compared. We also analyze the diffusive epidemic process (DEP) on a regular lattice one-dimensional. The model is composed of A (healthy) and B (sick) species that independently diffusive on lattice with diffusion rates DA and DB for which the probabilistic dynamical rule A + B → 2B and B → A. This model belongs to the category of non-equilibrium systems with an absorbing state and a phase transition between active an inactive states. We investigate the critical behavior of the DEP using an auto-adaptive algorithm to find critical points: the method of automatic searching for critical points (MASCP). We compare our results with the literature and we find that the MASCP successfully finds the critical exponents 1/ѵ and 1/zѵ in all the cases DA =DB, DA DB. The simulations show that the DEP has the same critical exponents as are expected from field-theoretical arguments. Moreover, we find that, contrary to a renormalization group prediction, the system does not show a discontinuous phase transition in the regime o DA >DB.

Não-extensividade em percolação por ligações de longo - alcance

A linear chain do not present phase transition at any finite temperature in a one dimensional system considering only first neighbors interaction. An example is the Ising ferromagnet in which his critical temperature lies at zero degree. Analogously, in percolation like disordered geometrical systems, the critical point is given by the critical probability equals to one. However, this situation can be drastically changed if we consider long-range bonds, replacing the probability distribution by a function like . In this kind of distribution the limit α → ∞ corresponds to the usual first neighbor bond case. In the other hand α = 0 corresponds to the well know "molecular field" situation. In this thesis we studied the behavior of Pc as a function of a to the bond percolation specially in d = 1. Our goal was to check a conjecture proposed by Tsallis in the context of his Generalized Statistics (a generalization to the Boltzmann-Gibbs statistics). By this conjecture, the scaling laws that depend with the size of the system N, vary in fact with the quantitie