Relevant bibliographies by topics / Fractual

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  2. Dissertations / Theses
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Academic literature on the topic 'Fractual'

Author: Grafiati
Published: 4 June 2021
Last updated: 9 February 2022

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Journal articles on the topic "Fractual"

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AKIMOTO, Sho, Hiroshi ISODA, Masahiro MATSUDA, and Takahiro TSUCHIMOTO. "RESISTING PERFORMANCE AND FRACTUAL BEHAVIOR BY SILL EMBEDMENT DURING EARTHQUAKES." Journal of Structural and Construction Engineering (Transactions of AIJ) 81, no. 722 (2016): 747–55. http://dx.doi.org/10.3130/aijs.81.747.

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Hutton, D. M. "The (Mis)Behaviour of Markets: A Fractual View of Risk, Ruin and Reward20082Benoit B. Mandelbrot and Richard L. Hudson. The (Mis)Behaviour of Markets: A Fractual View of Risk, Ruin and Reward. Profile Books Ltd, 2006. 348 pp., ISBN: 1‐86‐197790‐5 Paperback £9.99." Kybernetes 37, no. 1 (2008): 190. http://dx.doi.org/10.1108/03684920810851087.

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Moreles Vázquez, Uriel Octavio. "Los fractales." Acta Universitaria 13 (September 1, 2003): 19–22. http://dx.doi.org/10.15174/au.2003.249.

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Knowles, Asante James. "Fractal Philosophy: Grounding the Nature of the Mind with Fractals." NeuroQuantology 17, no. 8 (2019): 19–23. http://dx.doi.org/10.14704/nq.2019.17.8.2799.

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Kertész, János. "Fractal fracture." Physica A: Statistical Mechanics and its Applications 191, no. 1-4 (1992): 208–12. http://dx.doi.org/10.1016/0378-4371(92)90529-y.

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COX, B. L., and J. S. Y. WANG. "FRACTAL ANALYSES OF ANISOTROPIC FRACTURE SURFACES." Fractals 01, no. 03 (1993): 547–59. http://dx.doi.org/10.1142/s0218348x93000575.

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Natural surfaces of rock fractures often have anisotropic asperity distributions, especially for shear fractures or faults. The asperity distributions could be treated as self-affine fractals with directional dependent scaling in the plane of the rock surfaces. Different fractal analyses (divider, slit-island, variogram) are applied to surface distributions of asperity data (topography): (1) a granitic fracture from the Stripa mine in Sweden; (2) a faulted and geothermally altered fracture from Dixie Valley, Nevada, USA. The cutoff patterns (indicator maps) of the granitic fracture show a radial pattern, while those of the faulted fracture show a very anisotropic stretched pattern of shapes. Different cutoff patterns of the same surface generally yield the same fractal dimension with the slit-island technique. The slit-island technique assumes that the cut-off patterns are self-similar in the plane of the surface, with the perimeter versus area analyzed for the entire population of contours, regardless of aspect ratio. We measure the variance in the two coordinate directions as a function of perimeter/area ratio for the anisotropic fracture from Dixie Valley to determine a self-affine scaling ratio for the slit-island analysis. We compare this ratio with anisotropy ratios obtained from simulated flow models based on channeling of flow through the largest openings. The possible applications of fractal analyses to both the geometry and flow are evaluated.
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Liu, Wei Fu, Shuang Long Liu, and Li Xin Sun. "Metamorphic Buried Hill Fracture Reservoir of Characterization and Evaluation." Applied Mechanics and Materials 522-524 (February 2014): 1303–6. http://dx.doi.org/10.4028/www.scientific.net/amm.522-524.1303.

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Paleostress value, fractural porosity and fractural fractal dimension could be used to demonstrate the basement rock reservoir of buried hill in oilfields. The paleostress value determined the development of the reservoir fractures. Fractured types are recognized and fractural porosity is calculated by using bilateral logging data. Then the fractural fractal dimension is calculated by using seismic data to predict the distribution of fractured zone. Finally based on paleostress value, fractural porosity and fractural fractal dimension, fractured reservoir of buried hill is evaluated by using fuzzy mathematics.
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Pavičić, Ivica, Ivan Dragičević, Tatjana Vlahović, and Tonći Grgasović. "FRACTAL ANALYSIS OF FRACTURE SYSTEMS IN UPPER TRIASSIC DOLOMITES IN ŽUMBERAK MOUNTAIN, CROATIA." Rudarsko-geološko-naftni zbornik 32, no. 3 (2017): 1–13. http://dx.doi.org/10.17794/rgn.2017.3.1.

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Жихарев and L. Zhikharev. "Generalization to Three-Dimensional Space Fractals of Pythagoras and Koch. Part I." Geometry & Graphics 3, no. 3 (2015): 24–37. http://dx.doi.org/10.12737/14417.

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Fractals are geometric objects, each part of which is
 similar to the whole object, so that if we take a part and increase
 its size to the size of the whole object, it would be impossible to
 notice a difference. In other words, fractals are sets having scale
 invariance. In mathematics, they are associated primarily with
 non-differentiable functions. The concept of "fractal" (from the
 Latin "Fractus" meaning «broken») had been introduced by Benoit
 Mandelbrot (1924–2010), French and American mathematician,
 physicist, and economist. Mandelbrot had found that seemingly
 arbitrary fluctuations in price of goods have a certain tendency to
 change: it turned out that daily fluctuations are symmetrical with
 long-term price fluctuations. In fact, Benoit Mandelbrot applied
 his recursive (fractal) method to solve the problem. Since the last quarter of the nineteenth century, a large number
 of fractal curves and flat objects have been created; and methods
 for their application have been developed. From geometrical point
 of view, the most interesting fractals are "Koch snowflake" and
 "Pythagoras Tree". Two classes of analogues of the volumetric
 fractals were created with modern three-dimensional modeling
 program: "Fractals of growth” – like Pythagoras Tree, “Fractals of
 separation” – like Koch snowflake; the primary classification was
 developed, their properties were studied. Empiric data was processed
 with basic arithmetic calculations as well as with computer software.
 Among other things, for fractals of separation the task was to create
 an object with an infinite surface area, which in the future might
 acquire great importance for the development of the chemical and
 other industries.
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Guo, Li Hui, and Wan Qiang Hu. "Fractal Research in Metal Material Fracture Invalidation." Advanced Materials Research 703 (June 2013): 8–11. http://dx.doi.org/10.4028/www.scientific.net/amr.703.8.

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Though there are a lot of rules and models for metal material fracture, it makes lots of troubles for engineering application, because of the lacking of reasonable description of fracture principle and change law. This article discusses some basic problems of applying fractal geometry to fracture research, mainly including sectional fractal characteristics and measurement, the relationship of fractal dimension and fracture toughness, and some kinds of metal fractal models. At last, application of fractal theory in metal fracture is stated.
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Dissertations / Theses on the topic "Fractual"

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Antunes, Alex Francisco. "Evolu??o tectono-estrutural do Campo de Xar?u (Sub-bacia de Munda?, Bacia do Cear? - NE do Brasil: abordagem multiescala e pluriferramental." Universidade Federal do Rio Grande do Norte, 2004. http://repositorio.ufrn.br:8080/jspui/handle/123456789/18351.

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Made available in DSpace on 2015-02-24T19:48:39Z (GMT). No. of bitstreams: 1 AlexFA_ate_Cap4.pdf: 3915510 bytes, checksum: 709e53f554fdeeeefb4020512e95ef8b (MD5) Previous issue date: 2004-07-26<br>The Xar?u Oil Field, located in the center-southern portion of the Munda? Sub-Basin (eastern portion of the Cear? Basin), is characterized by a main Iramework of NW-trending and NE-dipping faults. The faults in the Xar?u Oil Field, among which the Xar?u Fautt stands out, are arranged according to an extensional-listriclan, rooted on a detachment surface corresponding to the Munda? Fault, the border fautt of Munda? Sub-Basin. During the tectonic-structural evolution of the Xar?u Oil Field and the Munda? Sub-Basin, the Munda? Fault played a crucial role on the control of the geometry of both compartments. The main carbonatic unit in the Xar?u Oil Field, named the Trair? Member(Paracuru Formation of Late Aptian to Early Albian age), contains the largest oil volume in the field, concentrated in structurally-controlled accumulations. The Trair? 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 Trair? Member in the Xar?u 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 Trair? 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 Xar?u Oil Field (and, consequently, in the Munda? 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 Munda? Sub-Basin, as part of the transcurrent to translormant opening of the Atlantic Equatorial Margin. The balancing of four struetural cross-sections ofthe Xar?u Oil Field indicates that the Munda? Fault was responsible for more than 50% of the total stretching (? factor) registered during the Early Aptian. At the initial stages of the "rifting", during Early Aptianuntil the Holocene, the Munda? Sub-Basin (and consequently the Xar?u 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 Munda? Sub-Basin. which reached actual values between 1.28 and 1.42. ln addnion to the tectonic-structural studies in the Xar?u Oil Field, the interpretation of remote sensing products, coupled wnh characterization of terrain analogues in seleeted areas along the northern Cear? State (continental margins of the Cear? 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 Xar?u 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 Cear? State and specilically in the Xar?u 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 l?eld (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 Cear? Basin
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Greenfield, Catherine. "Characterization of natural fracture networks using fractal methods." Thesis, Imperial College London, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.419182.

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Dougan, Lewis Thomas. "Fractal geometric analysis of spatially self-affine stochastic fracture." Thesis, Edinburgh Napier University, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.275458.

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Roach, Daniel Edward. "Fractal analyses and geometrical models of fracture surfaces in rock." Thesis, University of Ottawa (Canada), 1992. http://hdl.handle.net/10393/7844.

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Fracture propagation in rock often produces complex patterns, such as the branching patterns of fracture networks, or the irregular radiating patterns on fracture surfaces. These patterns often appear complex because they are unpredictable in detail, yet predictable in the sense that smaller pieces of the pattern, when suitably enlarged, are statistically similar to larger pieces of the pattern. This property of statistical self-similarity can be quantified using fractal geometry. The fractal nature of rock fracture patterns is related to lithological properties and to the dynamics of the fracturing processes. Joint surfaces in homogeneous rocks display rough radiating ridges. A "plumose joint" surface was analyzed using the slit island method and found to have a fractal dimension (D$\sb{\rm f}$) of 2.24 $\pm$.14 (95%). Surfaces with similar fractal dimensions (2.2-2.5) are produced by a three-dimensional computer simulation of jointing. In the simulation, randomly-distributed defects cause local mis-orientations of the stress field and local deflection of the propagating fracture front. After passing through the defect the joint surface is re-oriented relative to remote stresses, and a planar radial fracture segment (i.e. inclusion hackle) is formed. Collectively, the numerous inclusion hackle form the plumose surface pattern. For the simulation results, D$\sb{\rm f}$ increases (i.e. the surface gets rougher) in proportion to the log of the defect density. The simulation also demonstrates a complex relationship between D$\sb{\rm f}$ of the propagating fracture front and D$\sb{\rm f}$ of the fracture surface. Shatter cones are conical fracture surfaces produced during high energy events such as meteorite impact and nuclear explosion. These fractures also display radiating surface features. Using a modified version of the slit island method, the fractal dimension of a shatter cone surface in limestone is estimated to be 2.24 $\pm$ 0.09. The observation of shingled convex fracture surfaces within the conical envelope surrounding the shatter cone surface is demonstrated to support the genetic model of Johnson and Talbot (1964). Striations on these fracture surfaces are reinterpreted as micro-fracture intersections. The measured fractal dimensions of the joint and shatter cone surfaces (i.e 2.24) are within the range reported for most fracture surfaces in metals (i.e. 2.1 $\sim$ 2.3).
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Silva, Eloy de Macedo. "Fractal analysis of fracture surface of Duplex Stainless steel UNS S31803." Universidade Federal do CearÃ, 2002. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=7306.

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CoordenaÃÃo de AperfeiÃoamento de Pessoal de NÃvel Superior<br>In the last years, the fractal geometry has become widely studied. Its application in several areas increased substantially, particularly in materials engineering and science, aiming the analysis of failures and the study of the mechanical properties of materials. Some studies have shown the relationship between the fracture surfaces and their mechanical properties using the fractal geometry and its properties of fractal dimension and selfsimilarity. In this research, the fracture surface of duplex stainless steel, which was obtained by the Charpy impact test, was studied applying the fractal geometry. Considering the 475ÂC embrittlement, the steel was submitted to thermal aging to obtain the fracture surfaces, whose images were captured by the scanning electron microscope (SEM). In the fractal analysis, a study was made applying the island method and profile analysis through the digitalization of the images and the application of image analyzing software. Emphasis was given on the calculation of the fractal dimension (FD) of the surface, on the energy absorbed during the impact test, on the involved fracture mechanisms and as well on the relationship between FD and thermal aging. In order to better understanding the subject, it was done the review about fracture mechanics, of duplex stainless steel and of fractal geometry. Finishing the research, the obtained fracture surface, the absorbed energy and the obtained values of FD were analyzed. The obtained results demonstrated a relationship between the fractal dimension, the size of the dimples in fracture surfaces and the impact energy to obtain them.<br>A geometria dos fractais nos Ãltimos anos tem se tornado bastante difundida no meio cientÃfico. O seu emprego em diversas Ãreas aumentou substancialmente, em particular na engenharia e ciÃncia dos materiais, com o objetivo de analisar falhas e estudar as propriedades mecÃnicas dos materiais. Alguns estudos tÃm mostrado a relaÃÃo entre as propriedades mecÃnicas de superfÃcies de fratura com a geometria dos fractais e suas propriedades de dimensÃo fractal e auto-similaridade. Nesta pesquisa, foi estudada, com base na geometria dos fractais, a superfÃcie de fratura do aÃo inoxidÃvel duplex obtida atravÃs do ensaio de impacto Charpy. Considerando a fragilizaÃÃo a 475&#61616;C, o aÃo foi submetido ao tratamento tÃrmico de envelhecimento para a obtenÃÃo das superfÃcies de fraturas cujas imagens foram captadas no microscÃpio eletrÃnico de varredura (MEV). Na anÃlise fractal foi feito um estudo aplicando os mÃtodos das ilhas e anÃlise de perfil atravÃs da digitalizaÃÃo das imagens e aplicaÃÃo de softwares de anÃlise de imagem. Foi dada Ãnfase na anÃlise do cÃlculo da dimensÃo fractal (Df) da superfÃcie, na energia absorvida no ensaio de impacto, nos mecanismos de fratura envolvidos, bem como na relaÃÃo entre Df e o tratamento tÃrmico de envelhecimento. Para o melhor entendimento do trabalho foi feita uma revisÃo bibliogrÃfica sobre a mecÃnica da fratura, o aÃo inoxidÃvel duplex e a geometria dos fractais. Para finalizar a pesquisa, foi feita a anÃlise da superfÃcie da fratura obtida, da energia absorvia e de valores de Df alcanÃados. Os resultados obtidos demonstraram uma relaÃÃo entre a dimensÃo fractal, o tamanho dos dimples em superfÃcies de fratura e a energia de impacto para a obtenÃÃo das mesmas.
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Kim, Tae Hyung. "Fracture characterization and estimation of fracture porosity of naturally fractured reservoirs with no matrix porosity using stochastic fractal models." [College Station, Tex. : Texas A&M University, 2007. http://hdl.handle.net/1969.1/ETD-TAMU-2570.

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Andresen, Christian André. "Properties of fracture networks and other network systems." Doctoral thesis, Norges teknisk-naturvitenskapelige universitet, Institutt for fysikk, 2009. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-5074.

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Smith, Robert Lee. "Determining the role of fractal geometry and fracture energy in brittle bilayer materials." [Gainesville, Fla.] : University of Florida, 2009. http://purl.fcla.edu/fcla/etd/UFE0014623.

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Mattos, Sergio Henrique Vannucchi Leme de. "Complexidade dos padrões espaciais e espectrais de fitofisionomias de cerrado no estado de São Paulo." [s.n.], 2010. http://repositorio.unicamp.br/jspui/handle/REPOSIP/287400.

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Orientador: Archimedes Perez Filho<br>Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Geociências<br>Made available in DSpace on 2018-08-16T22:58:04Z (GMT). No. of bitstreams: 1 Mattos_SergioHenriqueVannucchiLemede_D.pdf: 6600919 bytes, checksum: bfd36ba151a1b9a681d89be124b67670 (MD5) Previous issue date: 2010<br>Resumo: O Cerrado se constitui em um mosaico de fitofisionomias que se distinguem entre si pelos padrões espaciais que apresentam. Apesar das características e dinâmica do Cerrado apontarem que ele deve ser compreendido como um sistema complexo, o paradigma da complexidade e os métodos dele derivados ainda são pouco aproveitados no estudo do Cerrado. O objetivo geral da presente pesquisa foi avaliar a complexidade dos padrões espaciais (texturais) e espectrais de fitofisionomias de Cerrado a fim de verificar quais propriedades relativas à sua organização e dinâmica tais padrões podem revelar. Para tanto, foram usadas imagens do sensor multi-espectral Aster relativas a unidades de conservação do estado de São Paulo situadas nos municípios de Assis, Itirapina e Luiz Antônio. Medidas de complexidade baseadas na entropia informacional e de dimensão fractal foram aplicadas às imagens e respectivas curvas de respostas espectrais de fisionomias de Cerrado presentes nas localidades estudadas. Uma área-teste foi selecionada para se avaliar as correlações entre fisionomias, seus padrões texturais e espectrais e fatores pedológicos e geomorfológicos. Os resultados obtidos para as análises textural e espectral de imagens do sensor mostram que cada fisionomia apresenta valores estatisticamente iguais nas diferentes extensões avaliadas, revelando a auto-similaridade dos padrões em várias escalas. Houve também uma forte tendência de cada fisionomia obter os mesmos valores em diferentes localidades, o que permite estabelecer intervalos de valores típicos para cada uma, independentemente da área estudada. Por outro lado, nenhuma medida foi totalmente eficiente em distinguir as diferentes fisionomias de Cerrado de uma mesma localidade, principalmente aquelas com padrões mais semelhantes. Quanto às correlações, foram encontradas associações significativas entre fisionomias e fatores pedogeomorfológicos, porém não houve nenhum fator que respondesse exclusivamente pelas características vegetacionais de determinada fisionomia e nem pela configuração de seus padrões, apontando que elas dependem das inter-relações de vários fatores. Pelos resultados alcançados na presente pesquisa, confirma-se que o Cerrado é um sistema dinâmico complexo e que, portanto, o entendimento de sua organização e dinâmica deve-se pautar nos conceitos, modelos e métodos próprios do paradigma da complexidade. Uma característica marcante aqui revelada é a invariância escalar dos padrões, a qual é indicativa de que o Cerrado apresentaria criticalidade autoorganizada, sendo algumas de suas fisionomias representativas de estados próximos a pontos críticos. Conforme apontam os resultados, fisionomias intermediárias, como cerrado denso, cerrado ss e campo cerrado, apresentariam esse tipo de organização, enquanto fisionomias situadas próximas aos extremos do gradiente vegetacional do Cerrado (como campo sujo e cerradão) representariam estados mais estáveis do sistema<br>Abstract: Brazilian Cerrado is characterized as a mosaic of phytophysiognomies with different spatial patterns. Despite of its characteristics and dynamics suggest that the Cerrado should be understood as a complex system, the complexity paradigm and methodologies are not widely used in Cerrado studies yet. The general objective of this research has been to evaluate the complexity of spatial (textural) and spectral patterns of Cerrado's phytophysiognomies with the purpose of verifying which properties related to organization and dynamic those patterns could show. For this, images from Aster multispectral sensor were used to study Cerrado areas in conservation reserves at São Paulo State (Brazil). Complexity measures based on information entropy and fractal dimension were applied to physiognomies images and to the correspondent spectral response curves. A test-area was selected to evaluate correlations between physiognomies, their textural and spectral patterns, and pedological-geomorphological factors. Textural and spectral image analysis pointed out that each physiognomy presents statistically equal values for different extents considered, showing self-similarity patterns in several scales. There was also a strong tendency that each physiognomy presents the same values at different localities, attributing a typical range of values for each one, independent of its localization. However, no measure was totally efficient to distinguish different Cerrado's physiognomies, especially those with similar patterns. For correlations, significant associations between physiognomies and pedological-geomorphological factors were founded, but here there was no factor responding exclusively for vegetation characteristics of a given physiognomy and for pattern configurations as well, suggesting that they depend on interrelations of many factors. Results obtained in this work confirm that Cerrado is a complex dynamical system and, therefore, comprehension of its organization and dynamics demands concepts, models, and methods related to complexity paradigm. A remarkable characteristic that was revealed here is about scale-invariance of patterns, which indicates that Cerrado presents self-organization criticality. As results show, this type of organization occurs in intermediary physiognomies, while grassland and forest physiognomies are more stable<br>Doutorado<br>Análise Ambiental e Dinâmica Territorial<br>Doutor em Ciências
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Wang, JingLing. "Topics in Fractal Geometry." Thesis, University of North Texas, 1994. https://digital.library.unt.edu/ark:/67531/metadc279332/.

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Books on the topic "Fractual"

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author, Yanovskii Yurii Grigorevich, ed. Fractal mechanics of polymers: Chemistry and physics of complex polymeric materials. Apple Academic Press, 2014.

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Uribe, Diego. Fractal cuts: Exploring the magic of fractals with pop-up designs. 2nd ed. Tarquin, 1995.

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Uribe, Diego. Fractal cuts: Exploring the magic of fractals with pop-up designs. Tarquin, 1998.

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Kozlov, G. V. Fractal analysis and synergetics of catalysis in nanosystems. Nova Science Publishers, 2008.

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Fractaal. Querido, 1986.

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Fractal. Ático Ediciones, 2008.

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Benítez, Luis. Fractal. Ediciones Correo Latino, 1992.

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Fernández-Martínez, Manuel, Juan Luis García Guirao, Miguel Ángel Sánchez-Granero, and Juan Evangelista Trinidad Segovia. Fractal Dimension for Fractal Structures. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-16645-8.

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Mark, Peterson, and Waite Group, eds. The Waite Group's fractal creations: Explore the magic of fractals on your PC. Waite Group Press, 1991.

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Massopust, Peter Robert. Fractal functions, fractal surfaces, and wavelets. Academic Press, 1994.

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Book chapters on the topic "Fractual"

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Borodich, Feodor M. "Fractals and fractal scaling in fracture mechanics." In Fracture Scaling. Springer Netherlands, 1999. http://dx.doi.org/10.1007/978-94-011-4659-3_13.

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Janahmadov, Ahad Kh, and Maksim Y. Javadov. "Fractal Kinetics of Fracture." In Materials Forming, Machining and Tribology. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-28189-6_4.

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Hergarten, Stefan. "Fractals and Fractal Distributions." In Self-Organized Criticality in Earth Systems. Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/978-3-662-04390-5_1.

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Janahmadov, Ahad Kh, and Maksim Javadov. "Fractal Kinetics of Fracture." In Materials Forming, Machining and Tribology. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-93861-5_3.

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Davydova, M. "Fractal Aspects of Fracture Simulation." In IUTAM Symposium on Analytical and Computational Fracture Mechanics of Non-Homogeneous Materials. Springer Netherlands, 2002. http://dx.doi.org/10.1007/978-94-017-0081-8_11.

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Cherepanov, G. P. "Fractals in Fracture of Solids." In Methods of Fracture Mechanics: Solid Matter Physics. Springer Netherlands, 1997. http://dx.doi.org/10.1007/978-94-017-2262-9_8.

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Wnuk, Michael P. "Fractals and Mechanics of Fracture." In Handbook of Damage Mechanics. Springer New York, 2014. http://dx.doi.org/10.1007/978-1-4614-8968-9_18-1.

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Wnuk, Michael P. "Fractals and Mechanics of Fracture." In Handbook of Damage Mechanics. Springer New York, 2014. http://dx.doi.org/10.1007/978-1-4614-5589-9_18.

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Yavari, Arash, and Michael P. Wnuk. "Finite Fracture Mechanics for Fractal Cracks." In IUTAM Symposium on Scaling in Solid Mechanics. Springer Netherlands, 2009. http://dx.doi.org/10.1007/978-1-4020-9033-2_21.

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Li, J. M., Li Lü, M. O. Lai, and B. Ralph. "Fractal-based Study of Fracture Surfaces." In Image-Based Fractal Description of Microstructures. Springer US, 2003. http://dx.doi.org/10.1007/978-1-4757-3773-8_11.

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Conference papers on the topic "Fractual"

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Chavka, G. G. "Beauty of fractals design of fractal antennas." In 2007 6th International Conference on Antenna Theory and Techniques. IEEE, 2007. http://dx.doi.org/10.1109/icatt.2007.4425120.

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Reddy, R. M., and B. N. Rao. "Probabilistic Fracture Mechanics Using Fractal Finite Element Method." In ASME 2008 Pressure Vessels and Piping Conference. ASMEDC, 2008. http://dx.doi.org/10.1115/pvp2008-61109.

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Abstract:
This paper presents probabilistic fracture-mechanics analysis of linear-elastic cracked structures subjected to mixed-mode (modes I and II) loading conditions using fractal finite element method (FFEM). The method involves FFEM for calculating fracture response characteristics; statistical models of uncertainties in load, material properties, and crack geometry; and the first-order reliability method for predicting probabilistic fracture response and reliability of cracked structures. The sensitivity of fracture parameters with respect to crack size, required for probabilistic analysis, is calculated using continuum shape sensitivity analysis. Numerical examples based on mode-I and mixed-mode problems are presented to illustrate the proposed method. The results show that the predicted failure probability based on the proposed formulation of the sensitivity of fracture parameter is accurate in comparison with the Monte Carlo simulation results. Since all gradients are calculated analytically, reliability analysis of cracks can be performed efficiently using FFEM.
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Acuña, Jorge A. "Rate Transient Analysis of Fracture Swarm Fractal Networks." In Unconventional Resources Technology Conference. American Association of Petroleum Geologists, 2020. http://dx.doi.org/10.15530/urtec-2020-2118.

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Murata, S., H. Mitsuishi, and T. Saito. "Characterization of Fracture Permeability by Using a Fractal Model." In SPE Asia Pacific Oil and Gas Conference and Exhibition. Society of Petroleum Engineers, 2002. http://dx.doi.org/10.2118/77881-ms.

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Riollet, B., C. J. Bean, and S. S. Dolan. "Seismic Wave Scattering in Fractal Fracture Populations - Numerical Simulations." In 59th EAGE Conference & Exhibition. European Association of Geoscientists & Engineers, 1997. http://dx.doi.org/10.3997/2214-4609-pdb.131.gen1997_p012.

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Buyakov, A. S., and S. N. Kulkov. "Fractal dimension studies of porous ZrO2-MgO fracture surface." In PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON ADVANCED MATERIALS WITH HIERARCHICAL STRUCTURE FOR NEW TECHNOLOGIES AND RELIABLE STRUCTURES 2019. AIP Publishing, 2019. http://dx.doi.org/10.1063/1.5131912.

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Ait Aouit, D., and A. Ouahabi. "Fractal and spectral analysis of fracture surfaces of elastomeric materials." In MATERIALS CHARACTERISATION 2007. WIT Press, 2007. http://dx.doi.org/10.2495/mc070191.

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Rok, Vladimir, Alexander Druzhinin, Russ Evans, and Xiang‐Yang Li. "Multi‐scale fracture characterization using fractal frequency‐power‐law attenuation models." In SEG Technical Program Expanded Abstracts 2003. Society of Exploration Geophysicists, 2003. http://dx.doi.org/10.1190/1.1817611.

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Horta Rangel, Jaime, J. Gomez Sanchez, and V. Castano Meneses. "Dynamic behavior of bones under fracture: fractal dimension vs. applied loads." In Second International Conference on Experimental Mechanics, edited by Fook S. Chau and Chenggen Quan. SPIE, 2001. http://dx.doi.org/10.1117/12.429624.

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Kim, Tae Hyung, and David Stuart Schechter. "Estimation of Fracture Porosity of Naturally Fractured Reservoirs with No Matrix Porosity Using Fractal Discrete Fracture Networks." In SPE Annual Technical Conference and Exhibition. Society of Petroleum Engineers, 2007. http://dx.doi.org/10.2118/110720-ms.

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Reports on the topic "Fractual"

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Ferer, M., B. Dean, and C. Mick. Fractal modeling of natural fracture networks. Office of Scientific and Technical Information (OSTI), 1995. http://dx.doi.org/10.2172/72907.

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Kendall, Gay, P. J. Cote, and L. V. Meisel. Perimeter-Yardstick Technique for Fracture Surface Fractal Analysis. Defense Technical Information Center, 1994. http://dx.doi.org/10.21236/ada286240.

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Wilson, T. Fractal Analysis of Fracture Systems: Topical report, September 3, 1996. Office of Scientific and Technical Information (OSTI), 1997. http://dx.doi.org/10.2172/620973.

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Ferer, M. V., B. H. Dean, and C. Mick. Fractal modeling of natural fracture networks. Final report, June 1994--June 1995. Office of Scientific and Technical Information (OSTI), 1996. http://dx.doi.org/10.2172/251345.

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Fisher, Yuval, and Albert Lawrence. Fractal Image Encoding. Defense Technical Information Center, 1992. http://dx.doi.org/10.21236/ada253892.

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Fisher, Yuval, and Albert Lawrence. Fractal Image Encoding. Defense Technical Information Center, 1992. http://dx.doi.org/10.21236/ada248003.

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NETROLOGIC INC SAN DIEGO CA. Fractal Image Encoding. Defense Technical Information Center, 1991. http://dx.doi.org/10.21236/ada243620.

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Fisher, Yuval, and Albert Lawrence. Fractal Image Encoding. Defense Technical Information Center, 1990. http://dx.doi.org/10.21236/ada229910.

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Lorimer, Nancy D., Robert G. Haight, and Rolfe A. Leary. The fractal forest: fractal geometry and applications in forest science. U.S. Department of Agriculture, Forest Service, North Central Forest Experiment Station, 1994. http://dx.doi.org/10.2737/nc-gtr-170.

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Bak, P., and K. Chen. Fractal dynamics of earthquakes. Office of Scientific and Technical Information (OSTI), 1995. http://dx.doi.org/10.2172/80934.

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