Caracterização de superfícies seletivas de freqüência e de antenas fractais para aplicações em redes sem fio

This work aims to investigate the behavior of fractal elements in planar microstrip structures. In particular, microstrip antennas and frequency selective surfaces (FSSs) had changed its conventional elements to fractal shapes. For microstrip antennas, was used as the radiating element of Minkowski fractal. The feeding method used was microstrip line. Some prototypes were built and the analysis revealed the possibility of miniaturization of structures, besides the multiband behavior, provided by the fractal element. In particular, the Minkowski fractal antenna level 3 was used to exploit the multiband feature, enabling simultaneous operation of two commercial tracks (Wi-Fi and WiMAX) regulated by ANATEL. After, we investigated the effect of switches that have been placed on the at the pre-fractal edges of radiating element. For the FSSs, the fractal used to elements of FSSs was Dürer s pentagon. Some prototypes were built and measured. The results showed a multiband behavior of the structure provided by fractal geometry. Then, a parametric analysis allowed the analysis of the variation of periodicity on the electromagnetic behavior of FSS, and its bandwidth and quality factor. For numerical and experimental characterization of the structures discussed was used, respectively, the commercial software Ansoft DesignerTM and a vector network analyzer, Agilent N5230A model

Pecolação em uma rede multifractal

In this work we present the principal fractals, their caracteristics, properties abd their classification, comparing them to Euclidean Geometry Elements. We show the importance of the Fractal Geometry in the analysis of several elements of our society. We emphasize the importance of an appropriate definition of dimension to these objects, because the definition we presently know doesn t see a satisfactory one. As an instrument to obtain these dimentions we present the Method to count boxes, of Hausdorff- Besicovich and the Scale Method. We also study the Percolation Process in the square lattice, comparing it to percolation in the multifractal subject Qmf, where we observe som differences between these two process. We analize the histogram grafic of the percolating lattices versus the site occupation probability p, and other numerical simulations. And finaly, we show that we can estimate the fractal dimension of the percolation cluster and that the percolatin in a multifractal suport is in the same universality class as standard percolation. We observe that the area of the blocks of Qmf is variable, pc is a function of p which is related to the anisotropy of Qmf

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

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

Structural characterization of a tin oxyhydroxide gel and its precursor sol

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Um estudo de fractais geométricos na formação de professores de matemática

Pós-graduação em Educação Matemática - IGCE

Um estudo de fractais geométricos através de caleidoscópios e softwares de geometria dinâmica

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Pano Kente: estrutura e estética africana

The fractal geometry of nature is seen in organizations and has set handcrafted artifacts, among them African Kente cloth traditionally produced by Ewe and Ashanti of West Africa. Incorporating parameters also classify products as carriers of fractal geometry, the Kente fabrics exhibit built from geometric shapes classified as seeds or unique architecture. This article aims to analyze examples of Kente cloths and establish the existence of geometric structures formed from a parent cell, exposing how this cell and how its architecture and formed patterns are maintained throughout the finished product.

Triboelectricity: Macroscopic Charge Patterns Formed by Self-Arraying Ions on Polymer Surfaces

Tribocharged polymers display macroscopically patterned positive and negative domains, verifying the fractal geometry of electrostatic mosaics previously detected by electric probe microscopy. Excess charge on contacting polyethylene (PE) and polytetrafluoroethylene (PTFE) follows the triboelectric series but with one caveat: net charge is the arithmetic sum of patterned positive and negative charges, as opposed to the usual assumption of uniform but opposite signal charging on each surface. Extraction with n-hexane preferentially removes positive charges from PTFE, while 1,1-difluoroethane and ethanol largely remove both positive and negative charges. Using suitable analytical techniques (electron energy-loss spectral imaging, infrared microspectrophotometry and carbonization/colorimetry) and theoretical calculations, the positive species were identified as hydrocarbocations and the negative species were identified as fluorocarbanions. A comprehensive model is presented for PTFE tribocharging with PE: mechanochemical chain homolytic rupture is followed by electron transfer from hydrocarbon free radicals to the more electronegative fluorocarbon radicals. Polymer ions self-assemble according to Flory-Huggins theory, thus forming the experimentally observed macroscopic patterns. These results show that tribocharging can only be understood by considering the complex chemical events triggered by mechanical action, coupled to well-established physicochemical concepts. Patterned polymers can be cut and mounted to make macroscopic electrets and multipoles.

Mythos und Mathematik : Hermann Brochs Roman "Die Schuldlosen" und seine Essays

„Natürlich habe ich mich [...] unausgesetzt mit Mathematik beschäftigt, umso mehr als ich sie für meine erkenntnistheoretisch-philosophischen Studien brauchte, denn ohne Mathematik lässt sich kaum mehr philosophieren.“, schreibt Hermann Broch 1948, ein Schriftsteller, der ca. zehn Jahre zuvor von sich selbst sogar behauptete, das Mathematische sei eine seiner stärksten Begabungen.rnDiesem Hinweis, die Bedeutung der Mathematik für das Brochsche Werk näher zu untersuchen, wurde bis jetzt in der Forschung kaum Folge geleistet. Besonders in Bezug auf sein Spätwerk Die Schuldlosen fehlen solche Betrachtungen ganz, sie scheinen jedoch unentbehrlich für die Entschlüsselung dieses Romans zu sein, der oft zu Unrecht als Nebenarbeit abgewertet wurde, weil ihm „mit gängigen literaturwissenschaftlichen Kategorien […] nicht beizukommen ist“ (Koopmann, 1994). rnDa dieser Aspekt insbesondere mit Blick auf Die Schuldlosen ein Forschungsdesiderat darstellt, war das Ziel der vorliegenden Arbeit, Brochs mathematische Studien genauer nachzuvollziehen und vor diesem Hintergrund eine Neuperspektivierung der Schuldlosen zu leisten. Damit wird eine Grundlage geschaffen, die einen adäquaten Zugang zur Struktur dieses Romans eröffnet.rnDie vorliegende Arbeit ist in zwei Teile gegliedert. Nach einer Untersuchung von Brochs theoretischen Betrachtungen anhand ausgewählter Essays folgt die Interpretation der Schuldlosen aus diesem mathematischen Blickwinkel. Es wird deutlich, dass Brochs Poetik eng mit seinen mathematischen Anschauungen verquickt ist, und somit nachgewiesen, dass sich die spezielle Bauform des Romans wie auch seine besondere Form des Erzählens tatsächlich aus dem mathematischen Denken des Autors ableiten lassen. Broch nutzt insbesondere die mathematische Annäherung an das Unendliche für seine Versuche einer literarischen Erfassung der komplexen Wirklichkeit seiner Zeit. Dabei spielen nicht nur Elemente der fraktalen Geometrie eine zentrale Rolle, sondern auch Brochs eigener Hinweis, es handele sich „um eine Art Novellenroman“ (KW 13/1, 243). Denn tatsächlich ergibt sich aus den poetologischen Forderungen Brochs und ihren Umsetzungen im Roman die Gattung des Novellenromans, wie gezeigt wird. Dabei ist von besonderer Bedeutung, dass Broch dem Mythos eine ähnliche Rolle in der Literatur zuspricht wie der Mathematik in den Wissenschaften allgemein.rnMit seinem Roman Die Schuldlosen hat Hermann Broch Neuland betreten, indem er versuchte, durch seine mathematische Poetik die komplexe Wirklichkeit seiner Epoche abzubilden. Denn „die Ganzheit der Welt ist nicht erfaßbar, indem man deren Atome einzelweise einfängt, sondern nur, indem man deren Grundzüge und deren wesentliche – ja, man möchte sagen, deren mathematische Struktur aufzeigt“ (Broch).

Structure function and Multifractal spectrum applied to Digital Elevation Model

A Digital Elevation Model (DEM) provides the information basis used for many geographic applications such as topographic and geomorphologic studies, landscape through GIS (Geographic Information Systems) among others. The DEM capacity to represent Earth?s surface depends on the surface roughness and the resolution used. Each DEM pixel depends on the scale used characterized by two variables: resolution and extension of the area studied. DEMs can vary in resolution and accuracy by the production method, although there are statistical characteristics that keep constant or very similar in a wide range of scales. Based on this property, several techniques have been applied to characterize DEM through multiscale analysis directly related to fractal geometry: multifractal spectrum and the structure function. The comparison of the results by both methods is discussed. The study area is represented by a 1024 x 1024 data matrix obtained from a DEM with a resolution of 10 x 10 m each point, which correspond with a region known as ?Monte de El Pardo? a property of Spanish National Heritage (Patrimonio Nacional Español) of 15820 Ha located to a short distance from the center of Madrid. Manzanares River goes through this area from North to South. In the southern area a reservoir is found with a capacity of 43 hm3, with an altitude of 603.3 m till 632 m when it is at the highest capacity. In the middle of the reservoir the minimum altitude of this area is achieved.

Geometrical characterization of undisturbed soil samples using X-ray computed tomography image analysis. Effect of soil management on soil structure

El estudio de la estructura del suelo es de vital importancia en diferentes campos de la ciencia y la tecnología. La estructura del suelo controla procesos físicos y biológicos importantes en los sistemas suelo-planta-microorganismos. Estos procesos están dominados por la geometría de la estructura del suelo, y una caracterización cuantitativa de la heterogeneidad de la geometría del espacio poroso es beneficiosa para la predicción de propiedades físicas del suelo. La tecnología de la tomografía computerizada de rayos-X (CT) nos permite obtener imágenes digitales tridimensionales del interior de una muestra de suelo, proporcionando información de la geometría de los poros del suelo y permitiendo el estudio de los poros sin destruir las muestras. Las técnicas de la geometría fractal y de la morfología matemática se han propuesto como una poderosa herramienta para analizar y cuantificar características geométricas. Las dimensiones fractales del espacio poroso, de la interfaz poro-sólido y de la distribución de tamaños de poros son indicadores de la complejidad de la estructura del suelo. Los funcionales de Minkowski y las funciones morfológicas proporcionan medios para medir características geométricas fundamentales de los objetos geométricos tridimensionales. Esto es, volumen, superficie, curvatura media de la superficie y conectividad. Las características del suelo como la distribución de tamaños de poros, el volumen del espacio poroso o la superficie poro-solido pueden ser alteradas por diferentes practicas de manejo de suelo. En este trabajo analizamos imágenes tomográficas de muestras de suelo de dos zonas cercanas con practicas de manejo diferentes. Obtenemos un conjunto de medidas geométricas, para evaluar y cuantificar posibles diferencias que el laboreo pueda haber causado en el suelo. ABSTRACT The study of soil structure is of vital importance in different fields of science and technology. Soil structure controls important physical and biological processes in soil-plant-microbial systems. Those processes are dominated by the geometry of soil pore structure, and a quantitative characterization of the spatial heterogeneity of the pore space geometry is beneficial for prediction of soil physical properties. The technology of X-ray computed tomography (CT) allows us to obtain three-dimensional digital images of the inside of a soil sample providing information on soil pore geometry and enabling the study of the pores without disturbing the samples. Fractal geometry and mathematical morphological techniques have been proposed as powerful tools to analyze and quantify geometrical features. Fractal dimensions of pore space, pore-solid interface and pore size distribution are indicators of soil structure complexity. Minkowski functionals and morphological functions provide means to measure fundamental geometrical features of three-dimensional geometrical objects, that is, volume, boundary surface, mean boundary surface curvature, and connectivity. Soil features such as pore-size distribution, pore space volume or pore-solid surface can be altered by different soil management practices. In this work we analyze CT images of soil samples from two nearby areas with contrasting management practices. We performed a set of geometrical measures, some of them from mathematical morphology, to assess and quantify any possible difference that tillage may have caused on the soil.

Fibonacci Series, Golden Proportions, and the Human Biology

Pythagoras, Plato and Euclid’s paved the way for Classical Geometry. The idea of shapes that can be mathematically defined by equations led to the creation of great structures of modern and ancient civilizations, and milestones in mathematics and science. However, classical geometry fails to explain the complexity of non-linear shapes replete in nature such as the curvature of a flower or the wings of a Butterfly. Such non-linearity can be explained by fractal geometry which creates shapes that emulate those found in nature with remarkable accuracy. Such phenomenon begs the question of architectural origin for biological existence within the universe. While the concept of a unifying equation of life has yet to be discovered, the Fibonacci sequence may establish an origin for such a development. The observation of the Fibonacci sequence is existent in almost all aspects of life ranging from the leaves of a fern tree, architecture, and even paintings, makes it highly unlikely to be a stochastic phenomenon. Despite its wide-spread occurrence and existence, the Fibonacci series and the Rule of Golden Proportions has not been widely documented in the human body. This paper serves to review the observed documentation of the Fibonacci sequence in the human body.

Análise de superfícies seletivas em frequência com geometria multifractal

Frequency Selective surfaces are increasingly common structures in telecommunication systems due to their geometric and electromagnetic advantages. As a matter of fact, the frequency selective surfaces with fractal geometry type would allow an even bigger reduction of the electrical length which provided greater flexibility in the design of these structures. In this work, we investigated the use of multifractal geometry in frequency selective surfaces. Three structures with different multifractal geometries have been proposed and analyzed. The first structure allowed the design of multiband structures with greater flexibility in controlling the resonant frequencies and bandwidth. The second structure provided a bandwidth increase even with the rising of the fractal level. The third structure showed response with angle stability, dual polarization and provided room for a bandwidth increase with the rising of the structural multifractality. Furthermore, the proposed structures increased the degree of freedom in the multiband designs because they have multiple resonant frequencies ratios between adjacent bands and are easy to deploy. The validation of the proposed structures was initially verified through simulations in Ansoft Designer software and then the structures were constructed and the experimental results obtained

Estudo da variação da periodicidade e do acoplamento entre superfícies seletivas de frequência com elementos fractais e helicoidais em estruturas de multicamadas

This work aims to investigate the behavior of fractal and helical elements structures in planar microstrip. In particular, the frequency selective surfaces (FSSs) had changed its conventional elements to fractal and helical formats. The dielectric substrate used was fiberglass (FR-4) and has a thickness of 1.5 mm, a relative permittivity 4.4 and tangent loss equal to 0.02. For FSSs, was adopting the Dürer’s fractal geometry and helical geometry. To make the measurements, we used two antennas horns in direct line of sight, connected by coaxial cable to the vector network analyzer. Some prototypes were select for built and measured. From preliminary results, it was aimed to find practical applications for structures from the cascading between them. For FSSs with Dürer’s fractal elements was observed behavior provided by the multiband fractal geometry, while the bandwidth has become narrow as the level of iteration fractal increased, making it a more selective frequency with a higher quality factor. A parametric analysis allowed the analysis of the variation of the air layer between them. The cascading between fractal elements structure were considered, presented a tri-band behavior for certain values of the layer of air between them, and find applications in the licensed 2.5GHz band (2.3-2.7) and 3.5GHz band (3.3-3.8). For FSSs with helical elements, six structures were considered, namely H0, H1, H2, H3, H4 and H5. The electromagnetic behavior of them was analyzed separately and cascaded. From preliminary results obtained from the separate analysis of structures, including the cascade, the higher the bandwidth, in that the thickness of the air layer increases. In order to find practical applications for helical structures cascaded, the helical elements structure has been cascaded find applications in the X-band (8.0-12.0) and unlicensed band (5.25-5.85). For numerical and experimental characterization of the structures discussed was used, respectively, the commercial software Ansoft Designer and a vector network analyzer, Agilent N5230A model.