xix, 171 p. : ill. (some col.) A print copy of this thesis is available through the UO Libraries. Search the library catalog for the location and call number. / The field of quantum chaos investigates the quantum mechanical behavior of classically chaotic systems. This dissertation begins by describing an experiment conducted on an apparatus constructed to represent a three dimensional analog of a classically chaotic system. Patterns of reflected light are shown to produce fractals, and the behavior of the fractal dimension D F is shown to depend on the light's ability to escape the apparatus. The classically chaotic system is then used to investigate the conductance properties of semiconductor heterostructures engineered to produce a conducting plane relatively free of impurities and defects. Introducing walls that inhibit conduction to partition off sections considerably smaller than the mean distance between impurities defines devices called 'billiards'. Cooling to low temperatures enables the electrons traveling through the billiard to maintain quantum mechanical phase. Exposure to a changing electric or magnetic field alters the electron's phase, leading to fluctuations in the conductance through the billiard. Magnetoconductance fluctuations in billiards have previously been shown to be fractal. This behavior has been charted using an empirical parameter, Q , that is a measure of the resolution of the energy levels within the billiard. The relationship with Q is shown to extend beyond the ballistic regime into the 'quasi-ballistic' and 'diffusive' regimes, characterized by having defects within the conduction plane. A model analogous to the classically chaotic system is proposed as the origin of the fractal conductance fluctuations. This model is shown to be consistent with experiment and to account for changes of fine scale features in MCF known to occur when a billiard is brought to room temperature between low temperature measurements. An experiment is conducted in which fractal conductance fluctuations (FCF) are produced by exposing a billiard to a changing electric field. Comparison of D F values of FCF produced by electric fields is made to FCF produced by magnetic fields. FCF with high D F values are shown to de-correlate at smaller increments of field than the FCF with lower D F values. This indicates that FCF may be used as a novel sensor of external fields, so the response of FCF to high bias voltages is investigated. / Adviser: Stephen Kevan, Chairperson, Physics; Richard Taylor, Advisor, Physics; Robert Zimmerman, Member, Physics; Stephen Gregory, Member, Physics; David Johnson, Outside Member, Chemistry

Made available in DSpace on 2014-06-11T19:32:22Z (GMT). No. of bitstreams: 0 Previous issue date: 2011-03-15Bitstream added on 2014-06-13T21:04:11Z : No. of bitstreams: 1 uceda_ra_dr_sjrp.pdf: 905373 bytes, checksum: c2f0ae66c1c9b9621f826e692c6d9b4c (MD5) / Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) / Em 2000, Killeen e Taylor definiram a máquina de somar estocástica em base 2. Eles mostraram que o espectro do op erador de transi cão (agindo em l∞( N)), associado a essa máquina, e igual ao conjunto de Julia cheio de uma função quadrática. Nesse trabalho, estudamos outras propriedades espectrais e topológicass da máquina de Killeen e Taylor, e também das suas extensões à l∞(Z) e a outras bases não constantes. Esse estudo envolve conjuntos de Julia de funções quadráticas e também conjuntos de Julia cheios de endomor smos de C2 . Finalmente estudamos algumas propriedades aritméticas e topológicas de uma classe de fractais de Rauzy. Em particular estudamos o azulejamento periódico do plano complexo C induzido por eles. / In 2000, Killeen and Taylor de ned the sto hastic adding machine in base 2. They proved that the sp ectrum of the transition op erator (acting in l∞(N )) asso ciated to this machine is equal to the lled Julia set of a quadratic polynomial map. In this work, we study other sp ectral and top ological prop erties of Killeen and Taylor machine, and also of its extensions to l∞( Z) and to other non constant bases. This study envolves Julia sets of quadratic maps and also lled Julia sets of endomorphisms of C2 . Finally we study some arithmetical and topological prop erties of a class of Rauzy fractals. In particular we study the p erio dictiling of complex plane C induced by this class.

Made available in DSpace on 2014-06-11T19:33:38Z (GMT). No. of bitstreams: 0 Previous issue date: 2011-02-01Bitstream added on 2014-06-13T20:45:35Z : No. of bitstreams: 1 panosso_ar_dr_jabo.pdf: 805581 bytes, checksum: ae9e7cfe85602f581a11930028a83d72 (MD5) / Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) / Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) / Neste trabalho, foram avaliados aspectos diversos da emissão de CO2 (FCO2) em um Latossolo Vermelho em áreas de cana-de-açúcar sobre os sistemas de manejo de cana queimada (CQ) e cana crua (CC), no nordeste do Estado de São Paulo. No experimento 1 (ano de 2007), a média da FCO2 foi 39% superior na área de CQ (2,87 μmol m-2 s-1) quando compara à CC (2,06 μmol m-2 s-1) ao longo de um período de 70 dias de avaliação. Os modelos ajustados aos semivariogramas experimentais de FCO2 foram, na sua maioria, exponenciais em ambas as áreas. Os mapas de emissão foram homogêneos após um período de seca. O teor de matéria orgânica do solo e o estoque de carbono do solo (0-0,25 m) foram 13 e 20%, respectivamente, superiores em CQ quando comparados à CC. O grau de humificação da matéria orgânica do solo e a sua interação com a densidade do solo foi um importante fator, não somente na diferenciação da emissão de CO2 entre os diferentes sistemas de manejo. No experimento 2 (ano de 2008), foi conduzida a caracterização anisotrópica das variáveis estudadas por meio da dimensão fractal (DF), para diferentes direções (0o, 45o, 90o e 135o) em relação às linhas de plantio (0o). A propriedade porosidade livre de água (PLA) foi um dos principais fatores relacionados à variabilidade espacial de FCO2, independentemente das direções. Os valores de DF foram significativamente inferiores no sentido de plantio da cultura da cana-de-açúcar, indicando, além de anisotropia dessa propriedade, maior homogeneidade de FCO2 na direção de 0o. A PLA mostrou ser uma importante propriedade na compreensão da variabilidade espaçotemporal de FCO2, especialmente nas áreas de cana queimada / In this work was studied various aspects of soil CO2 emission (FCO2) of a bare Dark Red Latosol in sugarcane areas submitted to burned (B) and green (G) management systems in northeastern of São Paulo State. In the experiment 1 (year 2007), mean FCO2 emission was 39% higher in the B plot (2.87 μmol m-2 s-1) when compared to the G plot (2.06 μmol m-2 s-1) throughout the 70-day period after harvest. FCO2 Semivariogram models were mostly exponential in both areas. The emission maps are clearly more homogeneous after a drought period in both sites. Organic matter content and carbon stock (0-25 cm) were 13% and 20% higher in B, respectively, when compared to G. Regression analysis indicates that the humification index of soil organic matter, and its interaction with soil bulk density, is an important factor not just to differentiate emissions in each plot. In the experiment 2 (2008) the anisotropic characterization of the studied variables, was performed by deriving the fractal dimension (DF) calculated for different directions (0o, 45o, 90o and 135o) in relation to the crop line (0o). The air-filled pore space (AFPS) was the main factor affecting the spatial variability of FCO2 in all directions. The FCO2 DF values were significantly lower in the direction of planting of sugarcane crop, indicating anisotropy of this property and greater homogeneity in this direction. The AFPS was an important property in understanding the spatiotemporal variability of FCO2, especially in the areas submitted to burn

abstract: Dietary diversity is an important component of species’s ecology that often relates to species’s abundance and geographic distribution. Additionally, dietary diversity is involved in many hypotheses regarding the geographic distribution and evolutionary fate of fossil primates. However, in taxa such as primates with relatively generalized morphology and diets, a method for approximating dietary diversity in fossil species is lacking. One method that has shown promise in approximating dietary diversity is dental microwear analyses. Dental microwear variance has been used to infer dietary variation in fossil species, but a strong link between variation in microwear and variation in diet is lacking. This dissertation presents data testing the hypotheses that species with greater variation in dental microwear textures have greater annual, seasonal, or monthly dietary diversity. Dental microwear texture scans were collected from Phase II facets of first and second molars from 309 museum specimens of eight species of extant African Old World monkeys (Cercopithecidae; n = 9 to 74) with differing dietary diversity. Dietary diversity was calculated based on food category consumption frequency at study sites of wild populations. Variation in the individual microwear variables complexity (Asfc) and scale of maximum complexity (Smc) distinguished groups that were consistent with differences in annual dietary diversity, but other variables did not distinguish such groups. The overall variance in microwear variables for each species in this sample was also significantly correlated with the species’s annual dietary diversity. However, the overall variance in microwear variables was more strongly correlated with annual frequencies of fruit and foliage consumption. Although some variation due to seasonal and geographic differences among individuals was present, this variation was small in comparison to the variation among species. Finally, no association was found between short-term monthly dietary variation and variation in microwear textures. These results suggest that greater variation in microwear textures is correlated with greater annual dietary diversity in Cercopithecidae, but that variation may be more closely related to the frequencies of fruit and foliage in the diet. / Dissertation/Thesis / Doctoral Dissertation Anthropology 2015

Depuis Ruelle, puis Rugh, Baladi, Tsujii, Liverani et d'autres, on sait que la fuite vers l'équilibre statistique dans de nombreux systèmes dynamiques chaotiques est gouvernée par le spectre de résonances de Ruelle de l'opérateur de transfert. A la suite de récents travaux de Faure, Sjöstrand et Roy, cette thèse propose une approche semiclassique de systèmes dynamiques chaotiques de type partiellement expansifs. Une partie du mémoire est consacrée aux extensions d'applications expansives vers des groupes de Lie compacts, en se reistreignant essentiellement aux extensions vers le groupe spécial unitaire SU(2). On se sert de la théorie des états cohérents pour les groupes de Lie, développée dans les années 70 par Perelomov et Gilmore, pour mettre en oeuvre les outils semiclassiques et la théorie des résonances de Helfer et Sjöstrand. On en déduira une estimation de Weyl et un gap spectral pour les résonances de Ruelle prouvant que la fuite vers l'équilibre statistique dans ces modèles est gouvernée par un opérateur de rang fini (en accord avec les résultats obtenus par Tsujii pour les semi-flots partiellement expansifs). On étend ensuite cette approche aux modèles "ouverts" pour lesquels la dynamique présente un ensemble captif de Cantor. On montrera l'existence d'un spectre discret de résonances de Ruelle et on prouve une loi de Weyl fractale, analogue classique du théorème de Lin-Guillopé-Zworski pour les résonances du laplacien hyperbolique sur les surfaces à courbure négative constante. On montre aussi un gap spectral asymptotique. On expliquera pourquoi ces modèles semblent être des objets d'étude adaptés pour approcher des questions importantes et difficiles du chaos classique ou quantique. On pense en particulier au problème de la minoration du nombre de résonances, étudié dans le contexte des applications quantiques par Nonnenmacher et Zworski. / Since the work of Ruelle, then Rugh, Baladi, Tsujii, Liverani and others, it is kown that the convergence towards statistical equilibrium in many chaotic dynamical systems is gouverned by the Ruelle spectrum of resonances of the so-called transfer operator. Following recent works from Faure, Sjöstrand and Roy, this thesis gives a semiclassical approach for partially expanding chaotic dynamical systems. The first part of the thesis is devoted to compact Lie groups extenstions of expanding maps, essentially restricting to SU(2) extensions. Using Perlomov's coherent state theory for Lie groups, we apply the semiclassical theory of resonances of Helfer and Sjöstrand. We deduce Weyl type estimations and a spectral gap for the Ruelle resonances, showing that the convergence towards equilibrium is controled by a finite rank operator (as Tsujii already showed for partially expanding semi-flows). We then extend this approach to "open" models, for which the dynamics exhibits a fractal invariant reppeler. We show the existence of a discrete spectrum of resonances and we prove a fractal Weyl law, the classical analogue of Lin-Guillopé-Zworski's theorem on resonances of non-compact hyperbolic surfaces. We also show an asymptotic spectral gap. Finally we breifly explain why these models are interseting "toy models" to explore important questions of classical and quantum chaos. In particular, we have in mind the problem of proving lower bounds on the number of resonances, studied in the context of open quantum maps by Nonnenmacher and Zworski.

Made available in DSpace on 2016-06-02T19:19:55Z (GMT). No. of bitstreams: 1 ALBUQUERQUE_Diego_2012.pdf: 2909594 bytes, checksum: 91148b3e77351d9e01e62932373d67a6 (MD5) Previous issue date: 2012-03-30 / Financiadora de Estudos e Projetos / This work studied ultrathin films of titanium oxide deposited by the technique r. f. reactive sputtering with different oxygen flows and different deposition times. Optical properties were studied (ultra-violeta/Visível) and the surface morphology (Atomic Force Microscopy). The composition and structural properties of the films were analyzed by X-ray diffraction and Rutherford Backscattering Spectroscopy. The films are amorphous and rough (fractal dimension around 2.6 to 2.7 and roughness around 1.6 to 2.5 nm). The stoichiometry was fairly close to the titanium dioxide (TiO2). The optical energy Gap obtained by three different models presented values between 3.0 to 3.5 eV. / Neste trabalho foram estudados filmes ultrafinos de óxido de titânio depositados pela técnica sputtering reativo r.f., com diferentes fluxos de oxigênio e diferentes tempos de deposição. Foram estudadas as propriedades ópticas (Ultra-Violeta/Visível), bem como a morfologia da superfície (Microscopia de Força Atômica). As propriedades estruturais e a composição dos filmes foram estudadas por Difração de raios-X e por Rutherford Backscattering Spectroscopy. Os filmes são amorfos e com superfície rugosa (dimensão fractal em torno de 2,6 - 2,7 e rugosidade em torno de 1,6 - 2,5 nm). A estequiometria ficou bastante próxima do dióxido de titânio (TiO2). A energia do Gap óptico obtido por três modelos distintos apresentou valores entre 3,0 3,5 eV.

Made available in DSpace on 2016-06-02T19:29:56Z (GMT). No. of bitstreams: 1 5136.pdf: 1469178 bytes, checksum: a0809686f5333526f7e5eb0a69d193b3 (MD5) Previous issue date: 2013-03-15 / Financiadora de Estudos e Projetos / With the purpose of elucidating some aspects concerning the importance of substrate spatial complexity to the ecology of Chironomidae (Diptera) family in Cerrado streams, three field experiments were carried out in Ipameri and Mimoso de Goiás Municipalities, Goiás State, Brazil. These experiments are described in three chapters that compose this thesis i) Temporal dynamics of Chironomidae (Diptera) larvae on substrates with different levels of spatial complexity and roughness in a Central Brazil stream; ii) Is substrate complexity important for Chironomidae (Diptera) larvae to resist hydrological disturbance?; iii) Influence of spatial complexity and roughness on Chironomidae (Diptera) assemblages. Artificial substrates with different complexity and roughness levels were fixed in bed streams for colonization of Chironomidae larvae. Samplings were taken after a period of 30 days. Results indicated that: i) Colonization of substrates by larvae was not influenced by substrate spatial complexity and no patterns of colonization were observed, considering the various ecological guilds; ii) Both complexity and roughness were not sufficient to maintain the abundance of these organisms, evidencing their sensibility to sudden rain events; iii) Spatial complexity and roughness of substrate influenced the structure of Chironomidade assemblages and were two important aspects to the diversity of these organisms. / Buscando esclarecer alguns aspectos a respeito da importância da complexidade espacial do substrato sobre a ecologia de Chironomidae (Diptera) em córregos de baixa ordem do Cerrado brasileiro, foram realizados três experimentos aqui apresentados em três capítulos: i) Dinâmica temporal de Chironomidae (Diptera) em substratos com diferentes complexidades e rugosidades em um riacho do Brasil Central; ii) A complexidade do substrato é importante para as larvas de Chironomidae (Diptera) resistirem à perturbação hídrica?; iii) Influência da complexidade espacial e da rugosidade na assembleia de Chironomidae (Diptera). Os experimentos foram realizados nos municípios de Ipameri e Mimoso de Goiás, ambos situados no Estado de Goiás. Para amostragem das larvas de Chironomidae foram utilizados substratos artificiais com diferentes níveis de complexidade e rugosidade fixados no leito dos riachos para colonização. De forma geral os resultados obtidos indicaram que: i) A colonização dos substratos pelas larvas não foi influenciada pela complexidade espacial do substrato, não sendo observados padrões de colonização, considerando as diferentes guildas ecológicas; ii) Tanto a complexidade quanto a rugosidade do substrato não foram suficientes para a manutenção da abundância das larvas de Chironomidae, evidenciando sua sensibilidade a eventos inesperados de chuva; iii) A complexidade espacial e a rugosidade do substrato afetam a estrutura da assembleia de Chironomidae, sendo dois importantes aspectos para a diversidade destes organismos.

Flow induced self-oscillations cause acoustic pressure oscillations of large amplitude in pipe flows. If Reynolds number is treated as a parameter, these floinduced oscillations occur only at discrete and critical values of Reynolds number. However, for a small range of Reynolds numbers around such a critical value, such periodic oscillations may appear intermittently. If intermittency, which is a precursor to these self-oscillations, can be detected, prediction of an impending instability may be possible. In experiments done by Vineeth and Sujith (Int. J. Aeroacoustics, 2016) on flow in a duct orifice arrangement, where flow enters through the duct inlet, and leaves into the atmosphere through the orifice exit, “whistling” was observed at a Reynolds number of 4200 (based on the orifice thickness and flow speed within the orifice), where large amplitude pressure oscillations were observed. At slightly lower Reynolds numbers, bursts of relatively smaller amplitudes of pressure oscillations were observed to appear intermittently. For a similar configuration, Large Eddy Simulations (LES) have been carried out with explicit filtering as a sub­ grid scale model here. Both whistling and intermittency are observed in the simulations. As air flows from the duct into the orifice, it turns sharply around the corner at the duct­ orifice interface. Due to this sharp turn, flow separation occurs, and hence, a shear layer is formed at the mouth of the orifice. The mechanism of whistling is found to be this shear layer within the orifice flapping about and hitting the trailing edge of the orifice periodically, thus causing the shear layer to break and roll up into a vortex. At Reynolds numbers where intermittency is observed, the shear layer is found to very mildly come in contact with the edges of the orifice walls, thus disturbing it. In the simulations, time series data of pressure are recorded at various probe locations. In a given time series, if scale invariance behaviour exists, it can be quantified by measuring the Hurst exponent. The numerical value of the Hurst exponent is an index of “long range or short range dependence” in a time series. Hurst exponent is measured in the time series data obtained. It is found to drop to zero as the flow approaches the state of a self-sustained oscillation, since the growth rates of all the long term as well as short term trends in the time series vanish. A loss of multifractality in the time series is also observed as the flow approaches whistling. As a part of the this thesis, new, split high resolution schemes of high order are designed following the Hixon Turmel Proposal.

Submitted by Automa??o e Estat?stica (sst@bczm.ufrn.br) on 2016-04-22T21:41:53Z No. of bitstreams: 1 JoseIdifranseAguiarTrindade_TESE.pdf: 3433912 bytes, checksum: cc18488777701871fa15bf7410b660d3 (MD5) / Approved for entry into archive by Arlan Eloi Leite Silva (eloihistoriador@yahoo.com.br) on 2016-04-22T22:05:27Z (GMT) No. of bitstreams: 1 JoseIdifranseAguiarTrindade_TESE.pdf: 3433912 bytes, checksum: cc18488777701871fa15bf7410b660d3 (MD5) / Made available in DSpace on 2016-04-22T22:05:27Z (GMT). No. of bitstreams: 1 JoseIdifranseAguiarTrindade_TESE.pdf: 3433912 bytes, checksum: cc18488777701871fa15bf7410b660d3 (MD5) Previous issue date: 2015-01-30 / Conselho Nacional de Desenvolvimento Cient?fico e Tecnol?gico (CNPq) / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior (CAPES) / Este trabalho tem como objetivo investigar o comportamento de elementos fractais e elementos helicoidais em estruturas planares de microfita. Em particular, as superf?cies seletivas de frequ?ncia (FSS) tiveram seus elementos convencionais alterados para formatos fractais e para o formato helicoidal. O substrato diel?trico usado ? de fibra de vidro (FR-4) e tem espessura de 1,5 mm, permissividade el?trica relativa de 4,4 e tangente de perdas igual a 0,02. Para as FSS, adotou-se a geometria fractal pentagonal de D?rer e a geometria helicoidal. Para efetuar as medi??es, foram utilizadas duas antenas cornetas em visada direta, conectadas por cabo coaxial a um analisador de redes vetorial. Alguns prot?tipos foram selecionados para fabrica??o e medi??o. A partir dos resultados preliminares obtidos, objetivou-se encontrar aplica??es pr?ticas para as estruturas a partir do cascateamento entre elas. Para as FSSs com elementos fractais de D?rer, observou-se um comportamento multibanda proporcionado pela geometria fractal, ao mesmo tempo em que a largura de banda se tornou estreita na medida em que o n?vel de itera??o fractal aumentou, tornando-a uma estrutura mais seletiva em frequ?ncia, com um maior fator de qualidade. Uma an?lise param?trica possibilitou a an?lise da influ?ncia da varia??o da camada de ar entre elas. As estruturas fractais pentagonais foram consideradas e cascateadas. O cascateamento entre determinadas estruturas pentagonais apresentou um comportamento tri-band para determinados valores da camada de ar entre elas, com aplica??es na banda licenciada 2,5 GHz (2,3 ~ 2,7 GHz), e 3,5 GHz (3,3 ~ 3,8 GHz). Para as FSSs com elementos helicoidais, seis estruturas foram consideradas. A partir de resultados preliminares obtidos com a an?lise isolada das estruturas, o cascateamento entre elas proporcionou o aumento da largura de banda, na medida em que a espessura da camada de ar aumenta. Com a finalidade de encontrar aplica??es pr?ticas para as estruturas helicoidais cascateadas, as estruturas propostas foram cascateadas e as mesmas encontraram aplica??es na banda-X (8,0 ~ 12,0 GHz), e na banda n?o licenciada que compreende a faixa de 5,25 a 5,85 GHz. Na caracteriza??o num?rica e experimental das estruturas abordadas, utilizou-se, respectivamente, o software comercial Ansoft Designere um analisador de redes vetorial, modelo N5230A da Agilent. / 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 D?rer?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 D?rer?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.

Submitted by Automa??o e Estat?stica (sst@bczm.ufrn.br) on 2017-01-27T13:40:52Z No. of bitstreams: 1 DanielEcco_TESE.pdf: 15819405 bytes, checksum: 00c65d8e05776036ef4d17fa23f04e68 (MD5) / Approved for entry into archive by Arlan Eloi Leite Silva (eloihistoriador@yahoo.com.br) on 2017-01-31T14:21:06Z (GMT) No. of bitstreams: 1 DanielEcco_TESE.pdf: 15819405 bytes, checksum: 00c65d8e05776036ef4d17fa23f04e68 (MD5) / Made available in DSpace on 2017-01-31T14:21:06Z (GMT). No. of bitstreams: 1 DanielEcco_TESE.pdf: 15819405 bytes, checksum: 00c65d8e05776036ef4d17fa23f04e68 (MD5) Previous issue date: 2016-07-29 / Atrav?s de estudos sobre percola??o, pode-se determinar se uma rede bidimensional percola, percorrendo apenas parte das fronteiras dos aglomerados, verificando se existem dois s?tios da fronteira conectados em lados opostos da rede, isto ?, sem a necessidade de preencher todos os s?tios que formam os aglomerados. O objeto desta tese ? um algoritmo para tal fim. Diante da velocidade que este algoritmo ter?, percorrendo apenas parte das fronteiras dos aglomerados, vimos que seria poss?vel estudar redes de tamanhos jamais alcan?ados (superiores a um trilh?o de s?tios), com complexidade menor que 1 e um baixo custo computacional em rela??o aos algoritmos j? desenvolvidos sobre o tema percola??o. Passamos, com isso, a querer estudar o comportamento do limiar de percola??o e da dimens?o fractal da fronteira em redes dos mais diversos tamanhos e com uma grande quantidade de simula??es, as quais os resultados permitiram fazer compara??es e confirmar as previs?es feitas atrav?s de leis de escalas j? conhecidas na literatura. / Through studies on percolation, can determine if a percolates dimensional network, covering only part of the borders of the agglomerates by checking if there are two border sites connected on opposite sides of the net, i.e. without the need to fill all the sites form agglomerates. The object of this thesis is an algorithm for this purpose. Given the speed that this algorithm will, covering only part of the borders of the clusters, we saw that it would be possible to study never reached sizes of networks (more than one trillion websites), with less complexity than 1 and a low computational cost compared to the algorithms already developed on the theme percolation. We pass, therefore, to want to study the behavior of percolation threshold and the fractal dimension of the border into networks of different sizes and with a lot of simulations, which results allowed comparisons and confirm the predictions made by laws scales known in the literature.