Índice de aromaticidade baseado na deslocalização, degenerescência e densidade (D3BIA) para acenos e moléculas homoaromáticas

The aromaticity index is an important tool for the investigation of aromatic molecules. This work consists on new applications of the aromaticity index developed by teacher Caio Lima Firme, so-called D3BIA (density, delocalization, degeneracy-based index of aromaticity). It was investigated its correlation with other well-known aromaticity indexes, such as HOMA (harmonic oscillator model of aromaticity), NICS (nucleus independent chemical shielding), PDI (para-delocalization index), magnetic susceptibility (), and energetic factor in the study of aromaticity of acenes and homoaromatic species based on bisnoradamantanyl cage. The density functional theory (DFT) was used for optimization calculations and for obtaining energetic factors associated with aromaticity and indexes HOMA and NICS. From quantum theory of atoms in molecules (QTAIM) it was obtained the indexes D3BIA, PDI and . For acenes, when the over-mentioned indexes were applied it was observed no correlation except for D3BIA and HOMA (R2=0.752). For bisnoradamantenyl dication and its derivatives, it was obtained a good correlation between D3BIA and NICS. Moreover, it was evaluated solely one of the factors used on D3BIA calculation, the delocalization index uniformity (DIU), so as to investigate its possible influence on stability of chemical species. Then, the DIU was compared with the formation Gibbs free energy of some pairs of carbocations, isomers or not, which each pair had small difference in point group symmetry and no difference among other well-known stability factors. The obtained results indicate that DIU is a new stability factor related to carbocations, that is, the more uniform the electron density delocalization, the more stable the is carbocation. The results of this work validate D3BIA and show its importance on the concept of aromaticity, indicating that it can be understood from degeneracy of atoms belonging the aromatic site, the electronic density in the aromatic site and the degree of uniformity of electron delocalization

Computabilidade no espaço dos intervalos reais: um modelo BSS intervalar

A matemática intervalar é uma teoria matemática originada na década de 60 com o objetivo de responder questões de exatidão e eficiência que surgem na prática da computação científica e na resolução de problemas numéricos. As abordagens clássicas para teoria da computabilidade tratam com problemas discretos (por exemplo, sobre os números naturais, números inteiros, strings sobre um alfabeto finito, grafos, etc.). No entanto, campos da matemática pura e aplicada tratam com problemas envolvendo números reais e números complexos. Isto acontece, por exemplo, em análise numérica, sistemas dinâmicos, geometria computacional e teoria da otimização. Assim, uma abordagem computacional para problemas contínuos é desejável, ou ainda necessária, para tratar formalmente com computações analógicas e computações científicas em geral. Na literatura existem diferentes abordagens para a computabilidade nos números reais, mas, uma importante diferença entre estas abordagens está na maneira como é representado o número real. Existem basicamente duas linhas de estudo da computabilidade no contínuo. Na primeira delas uma aproximação da saída com precisão arbitrária é computada a partir de uma aproximação razoável da entrada [Bra95]. A outra linha de pesquisa para computabilidade real foi desenvolvida por Blum, Shub e Smale [BSS89]. Nesta aproximação, as chamadas máquinas BSS, um número real é visto como uma entidade acabada e as funções computáveis são geradas a partir de uma classe de funções básicas (numa maneira similar às funções parciais recursivas). Nesta dissertação estudaremos o modelo BSS, usado para se caracterizar uma teoria da computabilidade sobre os números reais e estenderemos este para se modelar a computabilidade no espaço dos intervalos reais. Assim, aqui veremos uma aproximação para computabilidade intervalar epistemologicamente diferente da estudada por Bedregal e Acióly [Bed96, BA97a, BA97b], na qual um intervalo real é visto como o limite de intervalos racionais, e a computabilidade de uma função intervalar real depende da computabilidade de uma função sobre os intervalos racionais

Construção de mosaicos georreferenciados usando imagens aéreas de pequeno formato

In this work we propose a technique that uses uncontrolled small format aerial images, or SFAI, and stereohotogrammetry techniques to construct georeferenced mosaics. Images are obtained using a simple digital camera coupled with a radio controlled (RC) helicopter. Techniques for removing common distortions are applied and the relative orientation of the models are recovered using projective geometry. Ground truth points are used to get absolute orientation, plus a definition of scale and a coordinate system which relates image measures to the ground. The mosaic is read into a GIS system, providing useful information to different types of users, such as researchers, governmental agencies, employees, fishermen and tourism enterprises. Results are reported, illustrating the applicability of the system. The main contribution is the generation of georeferenced mosaics using SFAIs, which have not yet broadly explored in cartography projects. The proposed architecture presents a viable and much less expensive solution, when compared to systems using controlled pictures

Geração procedural de cenários orientada a objetivos

The game industry has been experiencing a consistent increase in production costs of games lately. Part of this increase refers to the current trend of having bigger, more interactive and replayable environments. This trend translates to an increase in both team size and development time, which makes game development a even more risky investment and may reduce innovation in the area. As a possible solution to this problem, the scientific community is focusing on the generation of procedural content and, more specifically, on procedurally generated levels. Given the great diversity and complexity of games, most works choose to deal with a specific genre, platform games being one of the most studied. This work aims at proposing a procedural level generation method for platform/adventure games, a fairly more complex genre than most classic platformers which so far has not been the subject of study from other works. The level generation process was divided in two steps, planning and viusal generation, respectively responsible for generating a compact representation of the level and determining its view. The planning stage was divided in game design and level design, and uses a goaloriented process to output a set of rooms. The visual generation step receives a set of rooms and fills its interior with the appropriate parts of previously authored geometry

Condicionamento estrutural das zonasa de cisalhamento da região de Forquilha, domínio Ceará Central: uma abordagem integrada de sensoriamento remoto e geologia estrutural

The studied region, named Forquilha and localized in northwestern Central Ceará domain (northern portion of Borborema Province), presents a lithostratigraphic framework constituted by paleoproterozoic metaplutonics, metasedimentary sequences and neoproterozoic granitoids. The metasedimentary rocks of Ceará group occupy most part of the area. This group is subdivided in two distinct units: Canindé and Independência. Canindé unit is represented basically by biotite paragneisses and muscovite paragneisses, with minor metabasic rocks (amphibolite lens). Independência sequence is composed by garnetiferous paragneisses, sillimanite-garnet-quartz-muscovite schists and quartz-muscovite schists, pure or muscovite quartzites and rare marbles. At least three ductile deformation events were recognized in both units of Ceará group, named D1, D2 and D3. The former one is interpreted as related to a low angle tangential tectonics which mass transport is southward. D2 event is marked by the development of close/isoclinal folds with a N-S oriented axis. Refolding patterns generated by F1 and F2 superposition are found in several places. The latest event (D3) corresponds to a transcurrent tectonics, which led to development of mega-folds and several shear zones, under a transpressional regime. The mapped shear zones are Humberto Monte (ZCHM), Poço Cercado (ZCPC) and Forquilha (ZCF). Digital image processing of enhanced Landsat 7-ETM+ satellite images, combined with field data, demonstrate that these penetrative structures are associated with positive and negative geomorphologic patterns, distributed in linear and curvilinear arrangements with tonal banding, corresponding to the ductile fabric and to crests. Diverse color composites were tested and RGB-531 and RGB-752 provided the best results for lineament analysis of the most prominent shear zones. Spatial filtering techniques (3x3 and 5x5 filters) were also used and the application of Prewitt filters generated the best products. The integrated analysis of morphological and textural aspects from filtered images, variation of tonalities related to the distribution of geologic units in color composites and the superposition over a digital elevation model, contributed to a characterization of the structural framework of the study area. Kinematic compatibility of ZCHM, ZCPC, ZCF shear zones, as well as Sobral-Pedro II (ZCSPII) shear zone, situated to the west of the study area, was one of the goal of this work. Two of these shear zones (ZCHM, ZCPC) display sinistral movements, while the others (ZCSPII, ZCF) exhibit dextral kinematics. 40Ar/39Ar ages obtained in this thesis for ZCSPII and ZCPC, associated with other 40Ar/39Ar data of adjacent areas, indicate that all these shear zones are related to Brasiliano orogeny. The trend of the structures, the opposite shear senses and the similar metamorphic conditions are fitted in a model based on the development of conjugate shear zones in an unconfined transpression area. A WNW-ESE bulk shortening direction is infered. The geometry and kinematic of the studied structures suggest that shortening was largely accommodated by lateral extrusion, with only minor amounts of vertical stretch

Caracterização geométrica e parametrização de depósitos transacionais recentes e sua aplicação na modelagem de reservatórios petrolíferos

In this beginning of the XXI century, the Geology moves for new ways that demand a capacity to work with different information and new tools. It is within this context that the analog characterization has important in the prediction and understanding the lateral changes in the geometry and facies distribution. In the present work was developed a methodology for integration the geological and geophysical data in transitional recent deposits, the modeling of petroliferous reservoirs, the volume calculation and the uncertainties associate with this volume. For this purpose it was carried planialtimetric and geophysics (Ground Penetrating Radar) surveys in three areas of the Parnaíba River. With this information, it was possible to visualize the overlap of different estuary channels and make the delimitation of the channel geometry (width and thickness). For three-dimensional visualization and modeling were used two of the main reservoirs modeling software. These studies were performed with the collected parameters and the data of two reservoirs. The first was created with the Potiguar Basin wells data existents in the literature and corresponding to Açu IV unit. In the second case was used a real database of the Northern Sea. In the procedures of reservoirs modeling different workflows were created and generated five study cases with their volume calculation. Afterwards an analysis was realized to quantify the uncertainties in the geological modeling and their influence in the volume. This analysis was oriented to test the generating see and the analogous data use in the model construction

Estruturas tectônicas cenozóicas na porção leste da Bacia Potiguar - RN

This thesis encompasses the integration of geological, geophysical, and seismological data in the east part of the Potiguar basin, northeastern Brazil. The northeastern region is located in South American passive margin, which exhibits important areas that present neotectonic activity. The definition of the chronology of events, geometry of structures generated by these events, and definition of which structures have been reactivated is a necessary task in the region. The aims of this thesis are the following: (1) to identify the geometry and kinematics of neotectonic faults in the east part of the Potiguar basin; (2) to date the tectonic events related to these structures and related them to paleoseismicity in the region; (3) to present evolutional models that could explain evolution of Neogene structures; (4) and to investigate the origin of the reactivation process, mainly the type of related structure associated with faulting. The main type of data used comprised structural field data, well and resistivity data, remote sensing imagery, chronology of sediments, morphotectonic analysis, x-ray analysis, seismological and aeromagnetic data. Paleostress analysis indicates that at least two tectonic stress fields occurred in the study area: NSoriented compression and EW-oriented extension from the late Campanian to the early Miocene and EW-oriented compression and NS-oriented extension from the early Miocene to the Holocene. These stress fields reactivated NE-SW- and NW-SE-trending faults. Both set of faults exhibit right-lateral strike-slip kinematics, associated with a minor normal component. It was possible to determine the en echelon geometry of the Samambaia fault, which is ~63 km long, 13 km deep, presents NE-SW trend and strong dip to NW. Sedimentfilled faults in granite rocks yielded Optically Stimulated Luminescence (OSL) and Single-Aliquot Regeneration (SAR) ages at 8.000 - 9.000, 11.000 - 15.000, 16.000 - 24.000, 37.000 - 45.500, 53.609 - 67.959 e 83.000 - 84.000 yr BP. The analysis of the ductile fabric in the João Câmara area indicate that the regional foliation is NE-SW-oriented (032o - 042o), which coincides with the orientation of the epicenters and Si-rich veins. The collective evidence points to reactivation of preexisting structures. Paleoseismological data suggest paleoseismic activity much higher than the one indicated by the short historical and instrumental record

Reavaliação de critérios estruturais na hidrogeologia de terrenos cristalinos, com ênfase na neotectônica e sensoriamento remoto

Hydrogeological prospecting in Northeast Brazil and in other crystalline terrains has been developed on the basis of structural and regional geology concepts that date back to the 50-60 decades and, as such, demand a natural re-evaluation and update. In this kind of terrain, the percolation and accumulation of ground water are controlled by fractures and other types of discontinuities, such as foliations and geological contacts that, through weathering, impart porosity and permeability to the rocks, allowing water flow and storage. Several factors should be considered in the process of locating water wells, as discussed in the literature. Among these, the kind of structures, fracture geometry (including aperture and connectivity) and their geological and chronological context. It is important to correlate fracture systems with the regional neotectonic framework. Fractures at low angle (sub parallel) with the principal stress axis (s1) are those which tend to open (actually they work as tension joints) and, in principle, would present major hydric potential; in the opposite side, fractures at high angle to s1 would behave as closed by a compressional component. Fractures diagonal to the compression and tension axes correspond to shear fractures and, due to their connectivity with second fractures, are also important in terms of hydric potential. Uplift followed by terrain denudation leads to decompression and a general tendency to open (aided by weathering processes) fractures and other rock discontinuities, at different orientations. Low angle fractures, formed in this context, are equally important to increase connectivity, collection of water and recharge of the aquifer systems. In a general way, an opening component (neotectonic or by terrain decompression) and several models to increase fracture connectivity correlate with a greater hydric potential of these structures. Together with parallel research, this thesis addresses models of ground water occurrence in crystalline terrains, either improving well established concepts like the (Riacho-Fenda model), but also stressing other possibilities, like the role of alluvium and paleo-regoliths (the Calha Elúvio-Aluvionar model) and of strongly altered, permo-porous zones placed at variable depths below the present surface, flanking several types of discontinuities, especially interconnected fracture arrays (the Bolsões de Intemperismo model). Different methodological approaches are also discussed in order to improve success rates in the location of water wells in crystalline terrains. In this methodological review, a number of case studies were selected in the eastern domain of the State of Rio Grande do Norte, involving the localities of Santa Cruz, Santo Antônio, Serrinha, Nova Cruz, Montanhas, Lagoa de Pedras and Lagoa Salgada. Besides the neotectonic analysis of brittle structures, this Thesis addresses the validation of remote sensing as a tool for ground water prospecting. Several techniques were tested in order to detect and select areas with higher potential for ground water accumulation, using Landsat 5-TM and RADARSAT images, besides conventional aerial photos. A number of filters were tested to emphasize lineaments in the images, improving their discrimination, to identify areas with higher overburden humidity, which could reflect subsurface water accumulation, as well as alluvium and other sedimentary covers that might act as recharge zones. The work started with a regional analysis with the orbital images, followed by analysis of aerial photos, up to a detailed structural study of rock exposures in the terrain. This last step involved the analysis of outcrops surrounding wells (in a ray of approximately 10 to 100 m) with distinct productivities, including dry examples. At the level required for detail, it was not possible to accomplish a statistical approach using the available well data catalogs, which lack the desired specific information. The methodology worked out in this Thesis must undergo a testing phase through location of new water wells. An increase in the success rates as desired will led to a further consolidation step with wider divulgation of the methodology to private companies and governmental agencies involved in ground water prospecting in crystalline terrains

Litoestratigrafia e deformação cenzóica na região de Icapuí, Ceará, e implicações para a estruturação de campos de petróleo na borda ocidental da bacia Potiguar(NE do Brasil)

This thesis deals with the sedimentological/stratigraphic and structural evolution of the sedimentary rocks that occur in the NW continental border of the Potiguar Basin. These rocks are well exposed along coastal cliffs between the localities of Lagoa do Mato and Icapuí, Ceará State (NE Brazil). The sedimentological/stratigraphic study involved, at the outcrop scale, detailed facies descriptions, profile mapping of the vertical succession of different beds, and columnar sections displaying inferred lateral relationships. The approach was complemented by granulometric and petrographic analyses, including the characterization of heavy mineral assemblages. The data set allowed to recognize two kinds of lithological units, a carbonate one of very restricted occurrence at the base of the cliffs, and three younger, distinct siliciclastic units, that predominate along the cliffs, in vertical and lateral extent. The carbonate rocks were correlated to the late Cretaceous Jandaíra Formation, which is covered by the siliciclastic Barreiras Formation. The Barreiras Formation occurs in two distinct structural settings, the usual one with nondeformed, subhorizontal strata, or as tilted beds, affected by strong deformation. Two lithofacies were recognized, vertically arranged or in fault contacts. The lower facies is characterized by silty-argillaceous sandstones with low-angle cross bedding; the upper facies comprises medium to coarse grained sandstones, with conglomeratic layers. The Tibau Formation (medium to coarse-grained sandstones with argillite intercalations) occurs at the NW side of the studied area, laterally interlayered with the Barreiras Formation. Eolic sediments correlated to the Potengi Formation overly the former units, either displaying an angular unconformity, or simply an erosional contact (stratigraphic unconformity). Outstanding structural features, identified in the Barreiras Formation, led to characterize a neocenozoic stress field, which generated faults and folds and/or reactivated older structures in the subjacent late cretaceous (to paleogene, in the offshore basin) section. The structures recognized in the Barreiras Formation comprise two distinct assemblages, namely a main extensional deformation between the localities of Ponta Grossa and Redonda, and a contractional style (succeeded by oblique extensional structures) at Vila Nova. In the first case, the structural assemblage is dominated by N-S (N±20°Az) steep to gently-dipping extensional faults, displaying a domino-style or listric geometry with associated roll-over structures. This deformation pattern is explained by an E-W/WNW extension, contemporaneous with deposition of the upper facies of the Barreiras Formation, during the time interval Miocene to Pleistocene. Strong rotation of blocks and faults generated low-angle distensional faults and, locally, subvertical bedding, allowing to estimate very high strain states, with extension estimates varying between 40% up to 200%. Numerous detachment zones, parallel to bedding, help to acommodate this intense deformation. The detachment surfaces and a large number of faults display mesoscopic features analoguous to the ones of ductile shear zones, with development of S-C fabrics, shear bands, sigmoidal clasts and others, pointing to a hydroplastic deformation regime in these cases. Local occurrences of the Jandaíra limestone are controled by extensional faults that exhume the pre-Barreiras section, including an earlier event with N-S extension. Finally, WNWtrending extensional shear zones and faults are compatible with the Holocene stress field along the present continental margin. In the Vila Nova region, close to Icapuí, gentle normal folds with fold hinges shallowly pluging to SSW affect the lower facies of the Barreiras Formation, displaying an incipient dissolution cleavage associated with an extension lineation at high rake (a S>L fabric). Deposition of the upper facies siliciclastics is controlled by pull-apart graben structures, bordered by N-NE-trending sinistral-normal shear zones and faults, characterizing an structural inversion. Microstructures are compatible with tectonic deformation of the sedimentary pile, burried at shallow depths. The observed features point to high pore fluid pressures during deformation of the sediments, producing hydroplastic structures through mechanisms of granular flow. Such structures are overprinted by microfractures and microfaults (an essentially brittle regime), tracking the change to microfracturing and frictional shear mechanisms accompanying progressive dewatering and sediment lithification. Correlation of the structures observed at the surface with those present at depth was tested through geophysical data (Ground Penetrating Radar, seismics and a magnetic map). EW and NE-trending lineaments are observed in the magnetic map. The seismic sections display several examples of positive flower structures which affect the base of the cretaceous sediments; at higher stratigraphic levels, normal components/slips are compatible with the negative structural inversion characterized at the surface. Such correlations assisted in proposing a structural model compatible with the regional tectonic framework. The strong neogenepleistocene deformation is necessarily propagated in the subsurface, affecting the late cretaceous section (Açu and Jandaíra formations), wich host the hydrocarbon reservoirs in this portion of the Potiguar Basin. The proposed structural model is related to the dextral transcurrent/transform deformation along the Equatorial Margin, associated with transpressive terminations of E-W fault zones, or at their intersections with NE-trending lineaments, such as the Ponta Grossa-Fazenda Belém one (the LPGFB, itself controlled by a Brasiliano-age strike-slip shear zone). In a first step (and possibly during the late Cretaceous to Paleogene), this lineament was activated under a sinistral transpressional regime (antithetic to the main dextral deformation in the E-W zones), giving way to the folds in the lower facies of the Barreiras Formation, as well as the positive flower structures mapped through the seismic sections, at depth. This stage was succeeded (or was penecontemporaneous) by the extensional structures related to a (also sinistral) transtensional movement stage, associated to volcanism (Macau, Messejana) and thermal doming processes during the Neogene-Pleistocene time interval. This structural model has direct implications to hydrocarbon exploration and exploitation activities at this sector of the Potiguar Basin and its offshore continuation. The structure of the reservoirs at depth (Açu Formation sandstones of the post-rift section) may be controlled (or at least, strongly influenced) by the deformation geometry and kinematics characterized at the surface. In addition, the deformation event recognized in the Barreiras Formation has an age close to the one postulated for the oil maturation and migration in the basin, between the Oligocene to the Miocene. In this way, the described structural cenario represents a valid model to understand the conditions of hydrocarbon transport and acummulation through space openings, trap formation and destruction. This model is potentially applicable to the NW region of the Potiguar Basin and other sectors with a similar structural setting, along the brazilian Equatorial Atlantic Margin

Proposta metodológica para o imageamento, caracterização, parametrização e geração de modelos virtuais de afloramentos

The aim of this work was to describe the methodological procedures that were mandatory to develop a 3D digital imaging of the external and internal geometry of the analogue outcrops from reservoirs and to build a Virtual Outcrop Model (VOM). The imaging process of the external geometry was acquired by using the Laser Scanner, the Geodesic GPS and the Total Station procedures. On the other hand, the imaging of the internal geometry was evaluated by GPR (Ground Penetrating Radar).The produced VOMs were adapted with much more detailed data with addition of the geological data and the gamma ray and permeability profiles. As a model for the use of the methodological procedures used on this work, the adapted VOM, two outcrops, located at the east part of the Parnaiba Basin, were selected. On the first one, rocks from the aeolian deposit of the Piaui Formation (Neo-carboniferous) and tidal flat deposits from the Pedra de Fogo Formation (Permian), which arises in a large outcrops located between Floriano and Teresina (Piauí), are present. The second area, located at the National Park of Sete Cidades, also at the Piauí, presents rocks from the Cabeças Formation deposited in fluvial-deltaic systems during the Late Devonian. From the data of the adapted VOMs it was possible to identify lines, surfaces and 3D geometry, and therefore, quantify the geometry of interest. Among the found parameterization values, a table containing the thickness and width, obtained in canal and lobes deposits at the outcrop Paredão and Biblioteca were the more relevant ones. In fact, this table can be used as an input for stochastic simulation of reservoirs. An example of the direct use of such table and their predicted radargrams was the identification of the bounding surface at the aeolian sites from the Piauí Formation. In spite of such radargrams supply only bi-dimensional data, the acquired lines followed of a mesh profile were used to add a third dimension to the imaging of the internal geometry. This phenomenon appears to be valid for all studied outcrops. As a conclusion, the tool here presented can became a new methodology in which the advantages of the digital imaging acquired from the Laser Scanner (precision, accuracy and speed of acquisition) were combined with the Total Station procedure (precision) using the classical digital photomosaic technique

Simulação de Fluxo no Meio Poroso Utilizando o Fluent

The complexity of the Phenomenon of fluid flow in porous way causes a difficulty in its explicit description. Different in the cases where the flow is given through a pipe, where it is possible to measure the length and diameter of the pipe and to determine their ability to flow as a function of pressure, which is a complicated task in porous way. However, we try to approach clearly the equations used to conjecture the behavior of fluid flow in porous way. We made use of the Gambit to create a fractal geometry with the fluent we give the contour´s conditions we would want to analyze the data. The triangular mesh was created; it makes interactions with the discs of different rays, as barriers putted in the geometry. This work presents the results of a simulation with a flow of viscous fluids (oilliquid). The oil flows in a porous way constructed in 2D. The behavior evaluation of the fluid flow inside the porous way was realized with graphics, images and numerical results used for different datas analysis. The study was aimed in relation at the behavior of permeability (k) for different fractal dimensions. Taking into account the preservation of porosity and increasing the fractal distribution of the discs. The results showed that k decreases when we increase the numbers of discs, although the porosity is the same for all generations of the first simulation, in other words, the permeability decreases when we increase the fractality. Well, there are strong turbulence in the flow each time we increase the number of discs and this hinders the passage of the same to the exit. These results permitted to put in evidence how the permeability (k) is affected in a porous way with obstacles distributed in a diversified form. We also note that k decreases when we increase the pressure variation (P) within geometry. So, in front of the results and the absence of bibliographic subsidies about other theories, the work realized here can possibly by considered the unpublished form to explain and reflect on how the permeability is changed when increasing the fractal dimension in a porous way

Processo de difusão com agregação e reorganização espontânea em uma rede 2D

Difusive processes are extremely common in Nature. Many complex systems, such as microbial colonies, colloidal aggregates, difusion of fluids, and migration of populations, involve a large number of similar units that form fractal structures. A new model of difusive agregation was proposed recently by Filoche and Sapoval [68]. Based on their work, we develop a model called Difusion with Aggregation and Spontaneous Reorganization . This model consists of a set of particles with excluded volume interactions, which perform random walks on a square lattice. Initially, the lattice is occupied with a density p = N/L2 of particles occupying distinct, randomly chosen positions. One of the particles is selected at random as the active particle. This particle executes a random walk until it visits a site occupied by another particle, j. When this happens, the active particle is rejected back to its previous position (neighboring particle j), and a new active particle is selected at random from the set of N particles. Following an initial transient, the system attains a stationary regime. In this work we study the stationary regime, focusing on scaling properties of the particle distribution, as characterized by the pair correlation function ø(r). The latter is calculated by averaging over a long sequence of configurations generated in the stationary regime, using systems of size 50, 75, 100, 150, . . . , 700. The pair correlation function exhibits distinct behaviors in three diferent density ranges, which we term subcritical, critical, and supercritical. We show that in the subcritical regime, the particle distribution is characterized by a fractal dimension. We also analyze the decay of temporal correlations

Teorias f(R) de gravidade na formulação de Palatini

In this dissertation, after a brief review on the Einstein s General Relativity Theory and its application to the Friedmann-Lemaitre-Robertson-Walker (FLRW) cosmological models, we present and discuss the alternative theories of gravity dubbed f(R) gravity. These theories come about when one substitute in the Einstein-Hilbert action the Ricci curvature R by some well behaved nonlinear function f(R). They provide an alternative way to explain the current cosmic acceleration with no need of invoking neither a dark energy component, nor the existence of extra spatial dimensions. In dealing with f(R) gravity, two different variational approaches may be followed, namely the metric and the Palatini formalisms, which lead to very different equations of motion. We briefly describe the metric formalism and then concentrate on the Palatini variational approach to the gravity action. We make a systematic and detailed derivation of the field equations for Palatini f(R) gravity, which generalize the Einsteins equations of General Relativity, and obtain also the generalized Friedmann equations, which can be used for cosmological tests. As an example, using recent compilations of type Ia Supernovae observations, we show how the f(R) = R − fi/Rn class of gravity theories explain the recent observed acceleration of the universe by placing reasonable constraints on the free parameters fi and n. We also examine the question as to whether Palatini f(R) gravity theories permit space-times in which causality, a fundamental issue in any physical theory [22], is violated. As is well known, in General Relativity there are solutions to the viii field equations that have causal anomalies in the form of closed time-like curves, the renowned Gödel model being the best known example of such a solution. Here we show that every perfect-fluid Gödel-type solution of Palatini f(R) gravity with density and pressure p that satisfy the weak energy condition + p 0 is necessarily isometric to the Gödel geometry, demonstrating, therefore, that these theories present causal anomalies in the form of closed time-like curves. This result extends a theorem on Gödel-type models to the framework of Palatini f(R) gravity theory. We derive an expression for a critical radius rc (beyond which causality is violated) for an arbitrary Palatini f(R) theory. The expression makes apparent that the violation of causality depends on the form of f(R) and on the matter content components. We concretely examine the Gödel-type perfect-fluid solutions in the f(R) = R−fi/Rn class of Palatini gravity theories, and show that for positive matter density and for fi and n in the range permitted by the observations, these theories do not admit the Gödel geometry as a perfect-fluid solution of its field equations. In this sense, f(R) gravity theory remedies the causal pathology in the form of closed timelike curves which is allowed in General Relativity. We also examine the violation of causality of Gödel-type by considering a single scalar field as the matter content. For this source, we show that Palatini f(R) gravity gives rise to a unique Gödeltype solution with no violation of causality. Finally, we show that by combining a perfect fluid plus a scalar field as sources of Gödel-type geometries, we obtain both solutions in the form of closed time-like curves, as well as solutions with no violation of causality

Contribuição ao estudo de redes complexas: modelo de afinidade com métrica

Currently the interest in large-scale systems with a high degree of complexity has been much discussed in the scientific community in various areas of knowledge. As an example, the Internet, protein interaction, collaboration of film actors, among others. To better understand the behavior of interconnected systems, several models in the area of complex networks have been proposed. Barabási and Albert proposed a model in which the connection between the constituents of the system could dynamically and which favors older sites, reproducing a characteristic behavior in some real systems: connectivity distribution of scale invariant. However, this model neglects two factors, among others, observed in real systems: homophily and metrics. Given the importance of these two terms in the global behavior of networks, we propose in this dissertation study a dynamic model of preferential binding to three essential factors that are responsible for competition for links: (i) connectivity (the more connected sites are privileged in the choice of links) (ii) homophily (similar connections between sites are more attractive), (iii) metric (the link is favored by the proximity of the sites). Within this proposal, we analyze the behavior of the distribution of connectivity and dynamic evolution of the network are affected by the metric by A parameter that controls the importance of distance in the preferential binding) and homophily by (characteristic intrinsic site). We realized that the increased importance as the distance in the preferred connection, the connections between sites and become local connectivity distribution is characterized by a typical range. In parallel, we adjust the curves of connectivity distribution, for different values of A, the equation P(k) = P0e

Estudo de Fractalidade e Evolução Dinâmica de Sistemas Complexos

In this work, the study of some complex systems is done with use of two distinct procedures. In the first part, we have studied the usage of Wavelet transform on analysis and characterization of (multi)fractal time series. We have test the reliability of Wavelet Transform Modulus Maxima method (WTMM) in respect to the multifractal formalism, trough the calculation of the singularity spectrum of time series whose fractality is well known a priori. Next, we have use the Wavelet Transform Modulus Maxima method to study the fractality of lungs crackles sounds, a biological time series. Since the crackles sounds are due to the opening of a pulmonary airway bronchi, bronchioles and alveoli which was initially closed, we can get information on the phenomenon of the airway opening cascade of the whole lung. Once this phenomenon is associated with the pulmonar tree architecture, which displays fractal geometry, the analysis and fractal characterization of this noise may provide us with important parameters for comparison between healthy lungs and those affected by disorders that affect the geometry of the tree lung, such as the obstructive and parenchymal degenerative diseases, which occurs, for example, in pulmonary emphysema. In the second part, we study a site percolation model for square lattices, where the percolating cluster grows governed by a control rule, corresponding to a method of automatic search. In this model of percolation, which have characteristics of self-organized criticality, the method does not use the automated search on Leaths algorithm. It uses the following control rule: pt+1 = pt + k(Rc − Rt), where p is the probability of percolation, k is a kinetic parameter where 0 < k < 1 and R is the fraction of percolating finite square lattices with side L, LxL. This rule provides a time series corresponding to the dynamical evolution of the system, in particular the likelihood of percolation p. We proceed an analysis of scaling of the signal obtained in this way. The model used here enables the study of the automatic search method used for site percolation in square lattices, evaluating the dynamics of their parameters when the system goes to the critical point. It shows that the scaling of , the time elapsed until the system reaches the critical point, and tcor, the time required for the system loses its correlations, are both inversely proportional to k, the kinetic parameter of the control rule. We verify yet that the system has two different time scales after: one in which the system shows noise of type 1 f , indicating to be strongly correlated. Another in which it shows white noise, indicating that the correlation is lost. For large intervals of time the dynamics of the system shows ergodicity