O paradoxo da superdifusão de uma caminhada aleatória com memória exponencial

The random walk models with temporal correlation (i.e. memory) are of interest in the study of anomalous diffusion phenomena. The random walk and its generalizations are of prominent place in the characterization of various physical, chemical and biological phenomena. The temporal correlation is an essential feature in anomalous diffusion models. These temporal long-range correlation models can be called non-Markovian models, otherwise, the short-range time correlation counterparts are Markovian ones. Within this context, we reviewed the existing models with temporal correlation, i.e. entire memory, the elephant walk model, or partial memory, alzheimer walk model and walk model with a gaussian memory with profile. It is noticed that these models shows superdiffusion with a Hurst exponent H > 1/2. We study in this work a superdiffusive random walk model with exponentially decaying memory. This seems to be a self-contradictory statement, since it is well known that random walks with exponentially decaying temporal correlations can be approximated arbitrarily well by Markov processes and that central limit theorems prohibit superdiffusion for Markovian walks with finite variance of step sizes. The solution to the apparent paradox is that the model is genuinely non-Markovian, due to a time-dependent decay constant associated with the exponential behavior. In the end, we discuss ideas for future investigations.

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.

Avaliação da adição de Nanosílica e silicato de sódio em pastas de cimento para poços de petróleo com baixo gradiente de fratura

The oil wells cementing is a critical step during the phase of well drilling, because problems during the operation of slurry pumping and an incomplete filling of the annular space between the metal casing and the formation can cause the slurry loss. Therefore, the slurry adopted in primary cementing an oil well must be properly dosed so that these problems are avoided during its pumping. When you drill a well in a weak rock formation requires even more careful, because should be a limit of hydrostatic pressure exerted during cementation, that does not occur rock collapse. With the objective of performing the cementing of a well whose formation is weak or unconsolidated are employed lighter slurries. Thus, this study used slurries with sodium silicate and nano silica in concentrations of 0,1; 0,4; 0,7 e 1,0 gpc, in which the slurries with nano silica showed the rheological parameters higher concentrations of up to 0.7 gpc and for concentration of 1.0 the slurry with sodium silicate obtained the highest values, remaining above the limits for application in fields, mainly wells with low fracture gradient, because a significant increase in viscosity may result in an increase in pressure pumping in operations of secondary cementations. Furthermore, there was no decrease in strength with increasing concentration of additive. Then, it is possible use of these additives to formulate Lighter slurry

Ergodicidade em cadeias de Markov não-homogêneas e cadeias de Markov com transições raras

The central objective of a study Non-Homogeneous Markov Chains is the concept of weak and strong ergodicity. A chain is weak ergodic if the dependence on the initial distribution vanishes with time, and it is strong ergodic if it is weak ergodic and converges in distribution. Most theoretical results on strong ergodicity assume some knowledge of the limit behavior of the stationary distributions. In this work, we collect some general results on weak and strong ergodicity for chains with space enumerable states, and also study the asymptotic behavior of the stationary distributions of a particular type of Markov Chains with finite state space, called Markov Chains with Rare Transitions

Avaliação da adição de Nanosílica e silicato de sódio em pastas de cimento para poços de petróleo com baixo gradiente de fratura

The oil wells cementing is a critical step during the phase of well drilling, because problems during the operation of slurry pumping and an incomplete filling of the annular space between the metal casing and the formation can cause the slurry loss. Therefore, the slurry adopted in primary cementing an oil well must be properly dosed so that these problems are avoided during its pumping. When you drill a well in a weak rock formation requires even more careful, because should be a limit of hydrostatic pressure exerted during cementation, that does not occur rock collapse. With the objective of performing the cementing of a well whose formation is weak or unconsolidated are employed lighter slurries. Thus, this study used slurries with sodium silicate and nano silica in concentrations of 0,1; 0,4; 0,7 e 1,0 gpc, in which the slurries with nano silica showed the rheological parameters higher concentrations of up to 0.7 gpc and for concentration of 1.0 the slurry with sodium silicate obtained the highest values, remaining above the limits for application in fields, mainly wells with low fracture gradient, because a significant increase in viscosity may result in an increase in pressure pumping in operations of secondary cementations. Furthermore, there was no decrease in strength with increasing concentration of additive. Then, it is possible use of these additives to formulate Lighter slurry