A difícil aceitação dos números negativos: um estudo da teoria dos números de Peter Barlow (1776-1862)

The present study seeks to present a historico-epistemological analysis of the development of the mathematical concept of negative number. In order to do so, we analyzed the different forms and conditions of the construction of mathematical knowledge in different mathematical communities and, thus, identified the characteristics in the establishment of this concept. By understanding the historically constructed barriers, especially, the ones having ontologicas significant, that made the concept of negative number incompatible with that of natural number, thereby hindering the development of the concept of negative, we were able to sketch the reasons for the rejection of negative numbers by the English author Peter Barlow (1776 -1862) in his An Elementary Investigation of the Theory of Numbers, published in 1811. We also show the continuity of his difficulties with the treatment of negative numbers in the middle of the nineteenth century

Um estudo sobre o ensino-aprendizagem das demonstrações matemáticas

Demonstrations are fundamental instruments for Mathematics and, as such, are frequently used by mathematicians, math teachers and students. In fact, demonstrations are part of every Mathematics teaching environment, because Mathematics considers something true when it can be demonstrated. This is in contrast to other fields of knowledge that employ observation and experimentation to validate truth. This dissertation presents a study of the teaching and learning of demonstrations in Mathematics, describing a Teaching Module applied in a course on the Theory of Numbers offered by the Mathematics Department of the Universidade Federal do Rio Grande do Norte for mathematics majors. The objective of the dissertation was to propose and test a Teaching Module that can serve as a model for teaching demonstrations. The Teaching Module consisted of the following five steps: the application of a survey to determine the students‟ profiles and their previous knowledge of mathematical language and techniques of demonstration; the analysis of a series of dialogues containing arguments in everyday language; the investigation and analysis of the structure of some important techniques of demonstration; a written assessment; and, finally, an interview to further verify the principal results of the Teaching Module. The analysis of the data obtained though the classroom activities, written assessments and interviews led to the conclusion that there was a significant amount of assimilation of the issue at the level of relational understanding, (SKEMP, 1980). These instruments verified that the students attained considerable improvement in their use of mathematical language and of the techniques of demonstration presented. Thus, the evidence supports the conclusion that the proposed Teaching Module is an effective means for the teaching/learning of mathematical demonstration and, as such, provides a methodological guide which may lay the foundations for a new approach to this important subject

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.

Polaritons de exciton em super-redes semicondutoras

In this work we study the spectrum (bulk and surface modes) of exciton-polaritons in infinite and semi-infinite binary superlattices (such as, ···ABABA···), where the semiconductor medium (A), whose dielectric function depends on the frequency and the wavevector, alternating with a standard dielectric medium B. Here the medium A will be modeled by a nitride III-V semiconductor whose main characteristic is a wide-direct energy gap Eg. In particular, we consider the numerical values of gallium nitride (GaN) with a crystal structure wurtzite type. The transfer-matrix formalism is used to find the exciton-polariton dispersion relation. The results are obtained for both s (TE mode: transverse electric) and p (TM mode: transverse magnetic) polarizations, using three diferent kind of additional boundary conditions (ABC1, 2 e 3) besides the standard Maxwell's boundary conditions. Moreover, we investigate the behavior of the exciton-polariton modes for diferent ratios of the thickness of the two alternating materials forming the superlattice. The spectrums shows a confinement of the exciton-polariton modes due to the geometry of the superlattice. The method of Attenuated Total Reflection (ATR) and Raman scattering are the most adequate for probing this excitations

Fermion localization on a split brane

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

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

Evolução tectono-estrutural do Campo de Xaréu (Sub-bacia de Mundaú, Bacia do Ceará - NE do Brasil: abordagem multiescala e pluriferramental

The Xaréu Oil Field, located in the center-southern portion of the Mundaú Sub-Basin (eastern portion of the Ceará Basin), is characterized by a main Iramework of NW-trending and NE-dipping faults. The faults in the Xaréu Oil Field, among which the Xaréu Fautt stands out, are arranged according to an extensional-listriclan, rooted on a detachment surface corresponding to the Mundaú Fault, the border fautt of Mundaú Sub-Basin. During the tectonic-structural evolution of the Xaréu Oil Field and the Mundaú Sub-Basin, the Mundaú Fault played a crucial role on the control of the geometry of both compartments. The main carbonatic unit in the Xaréu Oil Field, named the Trairí Member(Paracuru Formation of Late Aptian to Early Albian age), contains the largest oil volume in the field, concentrated in structurally-controlled accumulations. The Trairí Member is composed by a variety of carbonatic rocks (massive, bedded or laminated calcilutites, ostracodites, calcarenites and carbonatic rudites, all of them presenting variable degrees of dolomitization). The carbonatic rocks are interbedded into thick packages of black shales and marls, besides local beds of siliciclastic conglomerates, sandstones, siltnes and argillites. From the spatial association and the genetic relationships between the carbonatic and siliciclastic units, it is possible to group them in three lithofacies associations (Marginal Plain, Ramp and Lacustrine Interior) that, together, were developed in a lacustrine system associated to a marginal sabkha. Structural studies based on drill coresthat sample the Trairí Member in the Xaréu Oil Field allowed to characterize two generations of meso- to microscale structures: the D1 group presents a typical hydroplastic character, being characterized by intra/interstratal to oblique-bedding shear zones. The hydroplastic character related to these structures allowed to infer their development at an early-lithilication stage of the Trairí Member, leading to infer an Early Cretaceous age to them. The second group of structures identified in the drill cores, nominated D2 and ascribed to a Neogene age, presents a strictly brttle character, being typilied by normal faults and slickenfibers of re-crystallized clayminerals, ali olthem displaying variable orientations. Although the present faults in the Xaréu Oil Field (and, consequently, in the Mundaú Sub-Basin) were classically relerred as struetures of essentially normal displacement, the kinematics analysis of the meso-to microscaie D1 struetures in the drill cores led to deline oblique displacements (normal with a clockwise strike-slip component) to these faults, indicating a main tectonic transport to ENE. These oblique movements would be responsible for the installation of a transtensive context in the Mundaú Sub-Basin, as part of the transcurrent to translormant opening of the Atlantic Equatorial Margin. The balancing of four struetural cross-sections ofthe Xaréu Oil Field indicates that the Mundaú Fault was responsible for more than 50% of the total stretching (ß factor) registered during the Early Aptian. At the initial stages of the "rifting", during Early Aptianuntil the Holocene, the Mundaú Sub-Basin (and consequently the Xaréu Oil Fleld) accumulated a total stretching between 1.21 and 1.23; in other words, the crust in this segment of the Atlantic Equatorial Margin was subjeeted to an elongation of about 20%. From estimates of oblique displacements related to the faults, it ws possible to construct diagrams that allow the determination of stretching factors related to these displacements. Using these diagrams and assuming the sense 01 dominant teetonictransport towards ENE, it was possible to calculate the real stretching lactors related to the oblique movement 0 of the faults in the Mundaú Sub-Basin. which reached actual values between 1.28 and 1.42. ln addnion to the tectonic-structural studies in the Xaréu Oil Field, the interpretation of remote sensing products, coupled wnh characterization of terrain analogues in seleeted areas along the northern Ceará State (continental margins of the Ceará and Potiguar basins), provided addnional data and constraints about the teetonic-structural evolution of the oil lield. The work at the analogue sites was particularly effective in the recognition and mapping, in semidetail scale, several generations of struetures originated under a brittle regime. Ali the obtained information (from the Xaréu Oil Field, the remote sensor data and the terrain analogues) were jointly interpreted, culminating with the proposnion of an evolutionary model lor this segment of the Atlantic Equatorial Margin; this model that can be applied to the whole Margin, as well. This segmentof the Atlantic Equatorial Margin was delormedin an early E-W (when considered lhe present-day position of the South American Plate) transcurrent to transform regime with dextral kinematics, started Irom, at least, the Early Aptian, which left its record in several outcrops along the continental margin of the Ceará State and specilically in the Xaréu off Field. The continuous operation of the regime, through the Albian and later periods, led to the definitive separation between the South American and African plates, with the formation of oceanic lithosphere between the two continental blocks, due to the emplacement off spreading centers. This process involved the subsequent transition of the transcurrent to a translorm dextral regime, creating lhe Equatorial Atlantic Oceano With the separation between the South American and African plates already completed and the increasing separation between lhe continental masses, other tecton ic mechanisms began to act during the Cenozoic (even though the Cretaceous tectonic regime lasted until the Neogene), like an E-W compressive stress líeld (related to the spreading olthe oceanic floor along lhe M id-Atlantic Ridge and to the compression of the Andean Chain) effective Irom the Late Cretaceous, and a state of general extension olthe horizontal surface (due to the thermal uplift ofthe central portion of Borborema Province), effective during the Neogene. The overlap of these mechanisms during the Cenozoic led to the imprint of a complex tectonic framework, which apparently influenced the migration and entrapment 01 hydrocarbon in the Ceará Basin

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

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

Mapeamento digital de análogos a reservatórios petrolíferos: exemplos para depósitos fluviais da Unidade Açu-3 - Bacia Potiguar

In the current work are presented the results about the study of digital mapping of analogs referents the fluvial oil reservoirs in the Açu Formation. With the regional recognizing in the south corner of Potiguar Basin was selected a area of 150 Km square in the west of Assu city. In this area was chosen the outcrops for the digital mapping and from the data fields and remote sensors were done the depositional architectural for the fluvial deposits, which it was named coarse meandering fluvial systems. In the deposits were individualized 3 (three) fluvial cycles, which they was separated by bounding surface of fifth order. Such cycles are preferentially sandy, with fining-upward sequence finished in flood plain deposits. Inner of the sandy levels of the filling channels were characterized least cycles, normaly incomplete, constituted by braided sandy bodies and bounding surfaces of fourth order. In the mapped area was chosen a outcrop with great exposition, where it was possible to see tipical deposits of filling channel and was in this outcrop that was done the digital mapping. In this outcrop was used diverse technics and tools, which they integrated sedimentological, altimetric (GPS, Total Station), LIDAR (Light Detection and Ranging), digital photomosaic of high resolution and of the inner geometries (Ground Penetration Radar) data sets. For the integrating, interpretation and visualization of data was used software GoCAD®. The final product of the outcrop digital mapping was the photorealistic model of part of the cliff (or slope) because the observed reflectors in the radargrams were absents. A part of bar oblique accretion was modeled according to GPR gride of 200x200 meters in the alluvial Assu river probable recent analog. With the data of inner geometries was developed the three-dimentional sedimentary architectural, where it was possible characterize sand sheet deposits and many hierarchy of braided channels. At last, simulations of sedimentary geometries and architectures of the Potiguar Basin Fluvial Reservoirs were done with PetBool software, in order to understand the capacity of this program in simulations with a lot of numbers of conditioning wells. In total, 45 simulations was acquired, where the time and the channel numbers increase in relation of the conditioning wells quantity. The deformation of the meanders was detected from the change of simulated dominion dimensions. The presence of this problem was because the relationship between the simulated dominion and the width of the meander

Estruturação do grupo Serra Grande região de Santana do Acaraú- CE e a reativação do lineamento Sobral Pedro II, integração com dados geofísicos

The study area is located in the NW portion of the Ceará state nearby the city of Santana do Acaraú. Geologically it lies along the Sobral-Pedro II lineament which limits the domains of Ceará Central and Noroeste do Ceará, both belonging to the Borborema Province.The object of study was a NE trending 30km long siliciclastic body (sandstone and conglomerate) bounded by transcurrent dextral faults. The sediments are correlated to the Ipú Formation (Serra Grande Group) from the Parnaiba basin, which age is thought to be Siluro-Devonian. Existing structural data shown that bedding has higher but variable dips (70-45) near the borders faults and much lower to subhorizontal inward the body. The brittle deformation was related to a reactivation, in lower crustal level, of the Sobral-Pedro II lineament (Destro (1987, 1999; Galvão, 2002).The study presented here was focused in applying geophysicals methods (gravimetry and seismic) to determine the geometry of the sandstone/conglomeratic body and together with the structural data, to propose a model to explain its deformation. The residual anomalies maps indicate the presence of two main graben-like structures. The sedimentary pile width was estimated from 2D gravimetric models to be about 500-600 meters. The 3D gravimetric model stressed the two maximum width regions where a good correlation is observed between the isopach geometry and the centripetal strike/dip pattern displayed by the sediments bedding. Two main directions (N-S and E-W) of block moving are interpreted from the distribution pattern of the maximum width regions of the sedimentary rock

Sistemas de dunas do parque das Dunas e Barreiras do Inferno/Natal (RN: levantamento geológico /geofísico, elaboração do modelo deterministico e avaliação da vulnerabilidade/suscetibilidade

The current work was developed on the dune systems of the Parque das Dunas and Barreira do Inferno. These places are located in the cities of Natal and Parnamirim (RN, Brazil), respectively. This project has the purpose of developing the deterministic model on a specific blowout at Parque das Dunas, based in the geophysical interpretations of the lines gotten with the Ground Penetration Radar and the planialtimetric acquisitions of the topographical surface of the land. Also analyses of the vulnerability/susceptibility of these dune systems had been done in relation to the human pressures. To develop its deterministic model, it is necessary to acquire inner and outer geometries of the cited blowout. In order to depict inner geometries underneath the surface are used the GPR observing the altimetric control for topographical correction of the GPR lines. As for the outer geometries, the geodesic GPS gives us the planialtimetric points (x, y and z points) with milimetric precision, resulting in high-resolution surfaces. Using interpolation methods of the planialtimetric points was possible create Digital Elevations Models (DEM´s) of these surfaces. As a result, 1,161.4 meters of GPR lines were acquired on the blowout at the Parque das Dunas and 3,735.27 meters on the blowout at the Barreira do Inferno. These lines had been acquired with a 200 MHz antenna, except the 7 and 8 lines, for which we had been used a 100 MHz antenna. The gotten data had been processed and interpreted, being possible to identify boundary surfaces of first, second and third order. The first order boundary surface is related with the contact of the rocks of the Barreiras Group with the aeolian deposits. These deposits had been divided in two groups (Group 1 and Group 2) which are related with the geometry of stratum and the dip of its stratifications. Group 1 presented stratum of sigmoidal and irregular geometries and involved bodies where the reflectors had presented dips that had varied of 20 to the 28 degrees for the Parque das Dunas blowout and of 22 to the 29 degrees for the Barreira do Inferno blowout. Usually, it was limited in the base for the first order surface and in the top for the second order surface. Group 2 presented stratum of trough, wedge or lens geometries, limited in the base for the second order vi surface, where the corresponding deposits had more shown smoothed reflectors or with dips of low angle. The Deterministic and Digital Elevation Models had been developed from the integration and interpretation of the 2D data with the GOCAD® program. In Digital Elevations Models it was possible to see, for the localities, corridor or trough-shaped blowouts. In Deterministic Model it was possible to see first and second order boundary surfaces. For the vulnerability/susceptibility of the dune systems it was applied the methodology proposal by Boderè al (1991); however the same one did not show adequate because it evaluates actual coastal dunes. Actual coastal dunes are dunes that are presented in balance with the current environmental conditions. Therefore, a new methodology was proposal which characterizes the supplying and activity sedimentary, as well as the human pressures. For the methodology developed in this work, both the localities had presented a good management. The Parque das Dunas was characterized as a relic dune system and the Barreira do Inferno was characterized as a palimpsestic dune system. Also two Thematic Maps had been elaborated for the environmental characterization of the studied dune systems, with software ArcGis 8.3, and its respective data bases

Desenvolvimento de dobras e falhas em ambiente distensional: Aplicação da modelagem física

The geological modeling allows, at laboratory scaling, the simulation of the geometric and kinematic evolution of geological structures. The importance of the knowledge of these structures grows when we consider their role in the creation of traps or conduits to oil and water. In the present work we simulated the formation of folds and faults in extensional environment, through physical and numerical modeling, using a sandbox apparatus and MOVE2010 software. The physical modeling of structures developed in the hangingwall of a listric fault, showed the formation of active and inactive axial zones. In consonance with the literature, we verified the formation of a rollover between these two axial zones. The crestal collapse of the anticline formed grabens, limited by secondary faults, perpendicular to the extension, with a curvilinear aspect. Adjacent to these faults we registered the formation of transversal folds, parallel to the extension, characterized by a syncline in the fault hangingwall. We also observed drag folds near the faults surfaces, these faults are parallel to the fault surface and presented an anticline in the footwall and a syncline hangingwall. To observe the influence of geometrical variations (dip and width) in the flat of a flat-ramp fault, we made two experimental series, being the first with the flat varying in dip and width and the second maintaining the flat variation in width but horizontal. These experiments developed secondary faults, perpendicular to the extension, that were grouped in three sets: i) antithetic faults with a curvilinear geometry and synthetic faults, with a more rectilinear geometry, both nucleated in the base of sedimentary pile. The normal antithetic faults can rotate, during the extension, presenting a pseudo-inverse kinematics. ii) Faults nucleated at the top of the sedimentary pile. The propagation of these faults is made through coalescence of segments, originating, sometimes, the formation of relay ramps. iii) Reverse faults, are nucleated in the flat-ramp interface. Comparing the two models we verified that the dip of the flat favors a differentiated nucleation of the faults at the two extremities of the mater fault. V These two flat-ramp models also generated an anticline-syncline pair, drag and transversal folds. The anticline was formed above the flat being sub-parallel to the master fault plane, while the syncline was formed in more distal areas of the fault. Due the geometrical variation of these two folds we can define three structural domains. Using the physical experiments as a template, we also made numerical modeling experiments, with flat-ramp faults presenting variation in the flat. Secondary antithetic, synthetic and reverse faults were generated in both models. The numerical modeling formed two folds, and anticline above the flat and a syncline further away of the master fault. The geometric variation of these two folds allowed the definition of three structural domains parallel to the extension. These data reinforce the physical models. The comparisons between natural data of a flat-ramp fault in the Potiguar basin with the data of physical and numerical simulations, showed that, in both cases, the variation of the geometry of the flat produces, variation in the hangingwall geometry

Dinâmica da paisagem no litoral oriental do Rio Grande do Norte: geocartografia e padrões espaciais dos campos de dunas móveis

This study shows the results of a research developed in the coastal regions of the Maxaranguape and Touros municipalities, more specific in the mobile dune fields of the Rio Grande do Norte's eastern coast. Although the coastal zones, represent a small percentage of the earth's surface it concentrates a great part of the world's population. The Rio Grande do Norte's state coastal landscape mosaic composed by the dune fields suggest a dynamic scene of changes in the spatial and temporal arranges, with significant changes in the geometry of the sedimentary cover. Following this perspective this research has the objective to map the emerged coastal zone of the Rio Grande do Norte's eastern coast under the perspective of the time-space evolution of the mobile dune fields using geoprocessing techniques, which includes remote sensing, digital images processing and geographic information system (GIS). The results imply the issue of thematic maps: Geologic map; multitemporal evolution map of the mobile dune fields; quantification of the mobile dune fields differences map; temporal evolution of the mobile dune fields surrounds map. The El Niño episodes have directly affected the atmospheric circulation, what have enhanced the sedimentary input in the sand dune, what can justify the relative area growth between the years of 1993 and 2001. The dynamic of the landscape transition were higher than the stability of the spatial pattern of the dune and it's surrounds, as a result the Rio Grande do Norte eastern coast dune fields, specially the mobile dunes from Touros, Zumbi and Maracajau have shown a decrease on the sedimentary cover without vegetation area from 1970 to 2007. Therefore, the data acquired and the techniques used, can be, eventually applied to the mobile dune fields monitoring in order to preserve the dune ecosystems in the Rio Grande do Norte coast

Modelagem estrutural física de semigrábens ortogonais e oblíquos à distenção regional: influência da trama do embasamento e comparação com analógicos no nordeste brasileiro

The physical structural modeling tool is being increasingly used in geology to provide information about the evolutionary stages (nucleation, growth) and geometry of geological structures at various scales. During the simulations of extensional tectonics, modeling provides a better understanding of fault geometry and evolution of the tectonic-stratigraphic architecture of rift basins. In this study a sandbox type apparatus was used to study the nucleation and development of basins influenced by previous structures within the basement, variably oriented as regards to the main extensional axis. Two types of experiments were conducted in order to: (i) simulate the individual (independent) development of half-grabens oriented orthogonal or oblique to the extension direction; (ii) simulate the simultaneous development of such half-grabens, orthogonal or oblique to the extension direction. In both cases the same materials (sand mixed with gypsum) were used and the same boundary conditions were maintained. The results were compared with a natural analogue represented by the Rio do Peixe Basin (one of the eocretaceous interior basins of Northeast Brazil). The obtained models allowed to observe the development of segmented border faults with listric geometry, often forming relay ramps, and the development of inner basins faults that affect only the basal strata, like the ones observed in the seismic sections of the natural analogue. The results confirm the importance of basement tectonic heritage in the geometry of rift depocenters