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Zaks, Michael. "Fractal Fourier spectra in dynamical systems." Thesis, [S.l.] : [s.n.], 2001. http://pub.ub.uni-potsdam.de/2002/0019/zaks.ps.
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Karavas, Costas. "Fractal chaotic systems : investigation of the geological system and its sedimentation behaviour." Thesis, McGill University, 1990. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=60052.
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Chaos theory has only recently been related to various phenomena in the earth sciences. Here, using systems theory in a description of geological processes, we study the chaotic development of sedimentary sequences.The geosystem is treated as a partially specified system in order to apply qualitative stability analysis in the investigation of sedimentation behaviour and interactions among geological processes. The analysis suggests that the sedimentary system is unstable. This instability in conjunction with the system's sensitive dependence to internal fluctuations (i.e., those generated within the system) provide supporting evidence to suggest a chaotic behaviour for the sedimentation system.
We suggest that chaos could act as the common underlying mechanism which is manifest as the fractal-flicker noise character observed in reflectivity well logs. Acoustic impedance variations--the geophysical measures of lithologic variability--represent the internal organization of the interacting geological processes. This organization under a chaotic regime is responsible for the common statistical character found in various sedimentary basins.
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Landais, François. "Lois d’échelles et propriétés statistiques multifractales de la topographie des planètes." Thesis, Université Paris-Saclay (ComUE), 2017. http://www.theses.fr/2017SACLS453/document.
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Au cours des 20 dernières années, le développement des méthodes de télédétection et le succès des missions spatiales ont considérablement enrichi nos connaissances sur les surfaces planétaires révélant une immense diversité de morphologies. Etant le reflet de l'interaction et de la compétition entre des processus géologiques dont les modalités sont variables d'un corps à l'autre, elles sont largement étudiées pour retracer l'histoire géologique des planètes telluriques. En particulier, des informations précieuses sur la nature des processus et sur les lois générales qui contrôlent la formation et l'évolution des paysages sont enregistrées dans le champ topographique qui peut être analysé en tant que champ statistique. Nous rapportons dans cette thèse les résultats d'une étude comparative des propriétés statistiques de la topographie des principaux corps du système solaire en nous appuyant sur le volume croissant de données altimétriques et photogrammétriques. Notre approche est centrée sur la notion de loi d'échelle qui vise à caractériser les symétries du champ en traduisant le caractère auto-similaire des surfaces naturelles : les détails d'une surface ressemblent en général à des versions réduites de l'ensemble. Nous mettons en oeuvre plusieurs méthodes d'analyse de données dites «multifractales» pour dégager le meilleur modèle statistique capable de décrire la topographie dans différents contexte et proposons de nouveaux indicateurs de rugosité à l'échelle globale, régionale et locale. Nous montrons qu'en dépit de leur diversité, les surfaces du système solaire respectent des lois statistiques similaires que nous explicitons. En particulier nous montrons que la distribution globale des pentes d'un corps respecte en général des lois multifractales pour les échelles supérieures à 10-20km et présente une structure statistique différente pour les échelles inférieures. Enfin nous proposons une méthode pour générer des topographies synthétique sphériques dont le propriétés statistiques sont similaires aux topographie planétaire du système solaireOver the past 20 years, the development of remote sensing methods and the success of space missions have considerably enriched our knowledge of planetary surfaces revealing an immense diversity of morphologies. Being the reflection of the interaction and the competition between geological processes whose modalities are variable from one body to the other, they are widely studied to trace the geological history of the telluric planets. In particular, precise information on the nature of processes and general laws controlling the formation and evolution of landscapes is recorded in the topographic field which can be analyzed as a statistical field. We report in this thesis the results of a comparative study of the statistical properties of the topography of the main bodies of the solar system based on the increasing volume of altimetric and photogrammetric data. Our approach focuses on the notion of scaling law which aims to characterize the symmetries of the field by translating the self-similar nature of natural surfaces: the details of a surface generally look like reduced versions of the whole. We use several methods of analyzing so-called "multifractal" to derive the best statistical model capable of describing the topography in different contexts and propose new indicators of roughness at the global, regional and local scale. We show that in spite of their diversity, the surface of the solar system respects similar statistical laws. In particular, we show that the overall distribution of the slopes of a body generally respects multifractal laws for scales greater than 10-20 km and presents a different statistical structure for the lower scales. Finally, we propose a method for generating spherical synthetic topographies whose statistical properties are similar to the topographies in the solar system
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Joanpere, Salvadó Meritxell. "Fractals and Computer Graphics." Thesis, Linköpings universitet, Matematiska institutionen, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-68876.
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Fractal geometry is a new branch of mathematics. This report presents the tools, methods and theory required to describe this geometry. The power of Iterated Function Systems (IFS) is introduced and applied to produce fractal images or approximate complex estructures found in nature. The focus of this thesis is on how fractal geometry can be used in applications to computer graphics or to model natural objects.
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Machado, Bruno Brandoli. "Texture analysis using complex system models: fractal dimension, swarm systems and non-linear diffusion." Universidade de São Paulo, 2016. http://www.teses.usp.br/teses/disponiveis/55/55134/tde-24112016-113253/.
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Texture is one of the primary visual attributes used to describe patterns found in nature. Several texture analysis methods have been used as powerful tools for real applications involving analysis and computer vision. However, existing methods do not successfully discriminate the complexity of texture patterns. Such methods disregard the possibility of describing image structures by means of measures such as the fractal dimension. Fractality-based measures allow a non-integer geometric interpretation with applications in areas such as mathematics, physics, and biology. With this gap in mind, the central hypothesis of this thesis is that textures can be described as irregular fractal surfaces due to their complex geometry; such geometry can be exploited for image analysis and computer vision. By exploring such possibilities, pushing the limits of the state-of-the-art, this thesis starts with an analysis of texture features achieved by means of agents on image surfaces. To do so, we used the Bouligand-Minkowski fractal dimension, swarm-system Artificial Crawlers, and non-linear diffusion of Perona-Malik, techniques that led to methodologies with efficacy and efficiency comparable to the state-of-the-art. Our first method combines fractal dimension with random walks on the surface of images. In a second approach, non-linear diffusion is used to represent texture images at different scales, which are described via their fractal dimension for image classification purposes. In a third proposal, we employ fractal dimension concepts over multiple scales derived from the same image for a richer texture description. One of the purposes is the automatic detection of diseases in soybean leaves. Finally, texture characteristics were exploited in a method based on complex networks used to analyze the agglomeration of particles in nanotechnology images. The results achieved in the four methodologies described in this thesis demonstrated the potential of using texture features in tasks of classification and pattern recognition. The contributions of this work shall support significant advances in materials engineering, computer vision, and agriculture.A textura é um dos principais atributos visuais para a descrição de padrões encontrados na natureza. Diversos métodos de análise de textura têm sido usados como uma poderosa ferramenta para aplicações reais que envolvem análise de imagens e visão computacional. Entretanto, os métodos existentes não conseguem discriminar com sucesso a complexidade dos padrões de textura. Tais métodos desconsideram a possibilidade de se descrever estruturas de imagens por meio de medidas como a dimensão fractal. Medidas baseadas em fractalidade permitem uma interpretação geométrica não-inteira que possui aplicações encontradas em áreas como matemática, física, e biologia. Sobre esta lacuna metodológica, a hipótese central desta tese é que texturas presentes na natureza podem ser medidas como superfícies fractais irregulares devido à sua geometria complexa, o que pode ser explorado para fins de análise de imagens e visão computacional. Para superar tais limitações, avançando o estado da arte, esta tese se inicia com uma análise das características de texturas baseada em caminhadas aleatórias de agentes sobre superfícies de imagens. Esta primeira análise leva a um método que combina dimensão fractal com caminhadas de agentes sobre a superfície de imagens. Em uma segunda abordagem, usa-se a difusão não-linear para representar imagens de texturas em diferentes escalas, as quais são descritas via dimensão fractal para fins de classificação de imagens. Em uma terceira proposta, emprega-se a dimensão fractal sobre múltiplas escalas derivadas de uma mesma imagem com o propósito de se realizar a descrição multi-escala de texturas. Um dos propósitos específicos foi a detecção automática de doenças em folhas de soja. Por último, as características de textura foram exploradas segundo uma metodologia baseada em redes complexas para análise de aglomeração de partículas em imagens de nanotecnologia. Os resultados alcançados nesta tese demonstraram o potencial do uso de características de textura. Para tanto foram usadas técnicas de dimensão fractal de Bouligand-Minkowski, multiagentes Artificial Crawlerse difusão não-linear de Perona-Malik, os quais alcançaram eficácia e eficiência comparáveis ao do estado da arte. As contribuições obtidas devem suportar avanços significativos nas áreas de engenharia de materiais, visão computacional, e agricultura.
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USUI, Shin'ichi, Masayuki TANIMOTO, Toshiaki FUJII, Tadahiko KIMOTO, and Hiroshi OHYAMA. "Fractal Image Coding Based on Classified Range Regions." Institute of Electronics, Information and Communication Engineers, 1998. http://hdl.handle.net/2237/14996.
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Fraser, Jonathan M. "Dimension theory and fractal constructions based on self-affine carpets." Thesis, University of St Andrews, 2013. http://hdl.handle.net/10023/3869.
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The aim of this thesis is to develop the dimension theory of self-affine carpets in several directions. Self-affine carpets are an important class of planar self-affine sets which have received a great deal of attention in the literature on fractal geometry over the last 30 years. These constructions are important for several reasons. In particular, they provide a bridge between the relatively well-understood world of self-similar sets and the far from understood world of general self-affine sets. These carpets are designed in such a way as to facilitate the computation of their dimensions, and they display many interesting and surprising features which the simpler self-similar constructions do not have. For example, they can have distinct Hausdorff and packing dimensions and the Hausdorff and packing measures are typically infinite in the critical dimensions. Furthermore, they often provide exceptions to the seminal result of Falconer from 1988 which gives the `generic' dimensions of self-affine sets in a natural setting. The work in this thesis will be based on five research papers I wrote during my time as a PhD student. The first contribution of this thesis will be to introduce a new class of self-affine carpets, which we call box-like self-affine sets, and compute their box and packing dimensions via a modified singular value function. This not only generalises current results on self-affine carpets, but also helps to reconcile the `exceptional constructions' with Falconer's singular value function approach in the generic case. This will appear in Chapter 2 and is based on a paper which appeared in 'Nonlinearity' in 2012. In Chapter 3 we continue studying the dimension theory of self-affine sets by computing the Assouad and lower dimensions of certain classes. The Assouad and lower dimensions have not received much attention in the literature on fractals to date and their importance has been more related to quasi-conformal maps and embeddability problems. This appears to be changing, however, and so our results constitute a timely and important contribution to a growing body of literature on the subject. The material in this Chapter will be based on a paper which has been accepted for publication in 'Transactions of the American Mathematical Society'. In Chapters 4-6 we move away from the classical setting of iterated function systems to consider two more exotic constructions, namely, inhomogeneous attractors and random 1-variable attractors, with the aim of developing the dimension theory of self-affine carpets in these directions. In order to put our work into context, in Chapter 4 we consider inhomogeneous self-similar sets and significantly generalise the results on box dimensions obtained by Olsen and Snigireva, answering several questions posed in the literature in the process. We then move to the self-affine setting and, in Chapter 5, investigate the dimensions of inhomogeneous self-affine carpets and prove that new phenomena can occur in this setting which do not occur in the setting of self-similar sets. The material in Chapter 4 will be based on a paper which appeared in 'Studia Mathematica' in 2012, and the material in Chapter 5 is based on a paper, which is in preparation. Finally, in Chapter 6 we consider random self-affine sets. The traditional approach to random iterated function systems is probabilistic, but here we allow the randomness in the construction to be provided by the topological structure of the sample space, employing ideas from Baire category. We are able to obtain very general results in this setting, relaxing the conditions on the maps from `affine' to `bi-Lipschitz'. In order to get precise results on the Hausdorff and packing measures of typical attractors, we need to specialise to the setting of random self-similar sets and we show again that several interesting and new phenomena can occur when we relax to the setting of random self-affine carpets. The material in this Chapter will be based on a paper which has been accepted for publication by 'Ergodic Theory and Dynamical Systems'.
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Sellami, Tarek. "Dynamique commune des fractals de rauzy de même matrice d' incidence." Thesis, Aix-Marseille, 2012. http://www.theses.fr/2012AIXM4030/document.
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On sait que la matrice d'incidence associée à une substitution ne suffit pas pour déterminer complètement le système dynamique associé, même dans des cas très simples, il existe plusieurs substitutions associées à une même matrice car il existe de nombreux mots ayant le même abélianisé. Dans cette thèse, on étudie les points communs de deux lignes brisées associées à deux substitutions $sigma_1$ et $sigma_2$ irréductibles unimodulaires de type Pisot qui ont la même matrice d'incidence. On identifie les points communs de ces deux lignes brisées à partir d'un algorithme. On montre ainsi que l'intersection de ces deux lignes brisées est aussi une ligne brisée associée au point fixe d'une nouvelle substitution. On montre plus précisément que si $sigma_1$ vérifie la conjecture Pisot et $0$ est un point intérieur à son fractal de Rauzy alors ces points communs peuvent être engendrés par une substitution définie sur un alphabet appelé alphabet des paires équilibrées. Cette substitution est obtenue à partir d'un algorithme, l'algorithme des paires équilibrées. On obtient ainsi l'intersection des intérieurs des deux fractals de Rauzy. En prenant la clôture de cet ensemble on obtient un ensemble substitutif. La condition que $0$ est un point intérieur au fractal de Rauzy associé à la substitution $sigma_1$ nous permet de montrer que l'intersection des deux fractals de Rauzy est de mesure positive. Dans une deuxième partie du travail on s'intéresse à l'étude de la frontière du fractal de Rauzy. Le fractal de Rauzy est dit fractal mais c'est en fait sa frontière qui est fractaleThe matrix of a substitution is not sufficient to completely determine the dynamics associated with it, even in the simplest cases since there are many words with the same abelianization. In this paper we study the common points of the canonical broken lines associated with two different irreducible Pisot unimodular substitutions σ1 and σ2 having the same incidence matrix. We prove that if σ1 verifies the Pisot conjecture and 0 is an inner point to the Rauzy fractal associated with the substitution σ1 then these common points can be generated with a substitution on an alphabet of so-called balanced pairs, and we obtain in this way the intersection of the interior of two Rauzy fractals
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Caputo, Jean-Guy. "Dimension et entropie des attracteurs associés à des écoulements réels : estimation et analyse de la méthode." Grenoble 1, 1986. http://www.theses.fr/1986GRE10057.
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On s'interesse a la caracterisation des regimes chaotiques par lesquels un ecoulement atteint la turbulence. On montre qu'un regime chaotique de convection de rayleigh-benard est decrit par un attracteur dont on determine la dimension et l'entropie. En vue de caracteriser des attracteurs de dimension plus elevee on determine les conditions d'obtention de resultats corrects sur des exemples precis
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Barreiras, Carmen da Piedade Maceiras. "O conjunto de cantor." Master's thesis, Universidade de Évora, 2011. http://hdl.handle.net/10174/15448.
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O objectivo deste trabalho é o estudo aprofundado de um dos fractais mais
conhecidos e estudados de sempre, o conjunto de Cantor.
É feita uma abordagem histórica, onde são apresentados os marcos principais da vida
e obra de Georg Cantor.
Faz-se uma abordagem rigorosa do Conjunto de Cantor clássico e demonstram-se as
suas principais propriedades, usando a de nição mais conhecida deste conjunto, como
intersecção numerável de conjuntos fechados e encaixados.
Estuda-se o conjunto de Cantor do ponto de vista dinâmico, isto é, como conjunto
prisioneiro do sistema dinâmico discreto das iteradas de certas funções no intervalo.
Fez-se o estudo do conjunto de Cantor enquanto fractal, estudando a sua dimensão de
Hausdor¤, dimensão de capacidade e as propriedades de auto-semelhança.
Finalmente propõem-se actividades de sala de aula no âmbito das matérias estudadas; ABSTRACT:The aim of this paper is a detailed study of one of the most known and
studied fractals of all time, the Cantor set.
It is made a historical approach, which presents the major landmarks of life and work
of Georg Cantor.
Is done a serious approach to the classical Cantor set and its main properties are
proven, using the better known de nition of this set as a countable intersection of closed
nested sets.
The Cantor set is studied from the dynamic point of view, that means, as the prisoner
set of a discrete dynamical system of the iterates of certain functions in the interval.
It is made the study of the Cantor set as a fractal, studying its Hausdor¤ dimension,
box-counting dimension and the properties of self-similarity.
Finally, are proposed classroom activities within the subject matter.
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Reis, Glauco dos Santos. "Uma abordagem de compressão de imagens através de sistemas de funções iteradas." Universidade Presbiteriana Mackenzie, 2011. http://tede.mackenzie.br/jspui/handle/tede/1408.
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Previous issue date: 2011-08-22Fundo Mackenzie de Pesquisa
A new image compression technique is proposed, based on the affine transformations (ATs) that define an iterated function system (IFS). Previous related research in the field has shown that an image may be approximated by iteratively subjecting a set of sub-regions to a group of ATs. In this case, the original image should be partitioned in regions, and each one of the active pixels are transformed by the AT. The new transformed set should be approximated to other image regions. This iterated execution to find ATs for the best set of areas might result in smaller storage space since the similar areas might be replaced by AT coefficients. Despite this advantage, the technique is computationally intensive, because both the sub-regions and the corresponding ATs that have to be searched for. Here, a new form of similarity is proposed, based on the successive points generated by the iteration of affine transformations. By understanding an AT as a discrete dynamical system, with each image point represented by an iteration of the AT, the method captures similarities between these points, namely, those with the same color in the image; by saving the starting point and the transformations coefficients, the points can be iterated back, to reconstruct the original image. This results in lighter computational effort, since the comparison is made point by point, instead of region by region. Experiments were made on a group of 10 images, representing a broad set of distinct features and resolutions. The proposed algorithm competes in terms of storage size, when compared to JPEG, mainly when the image size is small, and the number of colors are reduced, as currently happens for most images used in the Internet. Although the proposed method is faster than the traditional method for IFS compression, it is slower than common file formats like JPEG.
Uma nova técnica para compressão de imagens é proposta, baseada em conjuntos de transformações afins (affine transformations - ATs), normalmente conhecidos como sistemas de funções iteradas (iterated function system -IFS). Pesquisas anteriores mostraram que uma imagem poderia ser aproximada pela aplicação de um grupo de ATs em conjuntos de sub-regiões da imagem, de forma iterativa. Através deste processo, a imagem original seria subdividida em regiões e sobre a coordenada de cada ponto habilitado de cada região seria aplicada uma transformação afim. O resultado representaria um novo conjunto de pontos similares a outras regiões da imagem. A execução de forma iterada deste processo de identificação das ATs para o maior conjunto de regiões similares de uma determinada imagem permitiria uma redução no armazenamento, já que as regiões similares poderiam ser armazenadas como os coeficientes das transformações afins. Apesar desta vantagem em termos de compressão, a técnica é computacionalmente intensiva, pela busca exaustiva de sub-regiões e das ATs geradoras, de forma a proporcionar o melhor preenchimento em outras regiões da imagem. Esta pesquisa propõe uma nova forma de compressão baseada em ATs, utilizando a sequência de pontos gerada pela iteração das ATs. Entendendo uma AT como um sistema dinâmico em tempo discreto, cada novo ponto identificado é consequência direta da iteração da AT sobre o ponto anterior, permitindo a captura de similaridades nesta sequência de pontos. Através do salvamento dos coeficientes das ATs e das coordenadas iniciais, é possível a reconstrução da imagem pela iteração da AT a partir do ponto inicial. Isto pode resultar em menor esforço computacional, pois apenas comparações simples de pontos são necessárias, ao invés de comparações entre os pontos de regiões da imagem. Foram feitos experimentos em um conjunto de 10 classes de imagens, representando um espectro de diferentes características gerais e resoluções. O algoritmo proposto rivaliza em termos de armazenamento quando comparado ao formato JPEG, principalmente para imagens de pequeno tamanho e com número de cores reduzidas, como as utilizadas com frequência na Internet. Apesar de ser mais rápido para a compressão do que outros métodos baseados em IFS, ele é mais lento do que métodos clássicos como o JPEG.
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Inui, Kanji. "Study of the fractals generated by contractive mappings and their dimensions." Kyoto University, 2020. http://hdl.handle.net/2433/253370.
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Kyoto University (京都大学)0048
新制・課程博士
博士(人間・環境学)
甲第22534号
人博第937号
新制||人||223(附属図書館)
2019||人博||937(吉田南総合図書館)
京都大学大学院人間・環境学研究科共生人間学専攻
(主査)教授 角 大輝, 教授 上木 直昌, 准教授 木坂 正史
学位規則第4条第1項該当
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Thovert, Jean-François. "Phenomenes de transfert dans les milieux poreux fractals : l'empilement apollonien." Paris 6, 1987. http://www.theses.fr/1987PA066217.
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On definit un modele bidimensionnel de milieu poreux fractal. Ce modele utilise des empilements quasi-osculateurs de disques, eventuellement anisotropes et aleatoires. Description analytique complete des proprietes de transport par conduction. Etude numerique de la permeabilite de l'empilement vis-a-vis des fluides newtoniens et non newtoniens en loi puissance
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Gonschorowski, Juliano dos Santos. "Processamento de sinais e reconhecimento de padrões de resposta de sensores de gases através da geometria fractal." Universidade de São Paulo, 2007. http://www.teses.usp.br/teses/disponiveis/3/3140/tde-01082007-173551/.
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O objetivo do presente trabalho foi propor métodos de processamento de sinais e reconhecimento de padrões dos sinais de respostas de sensores de gás, utilizando técnicas e modelos da geometria fractal. Foram analisados e estudados os sinais de resposta de dois tipos de sensores. O primeiro sensor foi um dispositivo de óxido de estanho, cujo princípio de funcionamento baseia-se na mudança da resistividade do filme. Este forneceu sinais de respostas com características ruidosas como resposta à interação com as moléculas de gás. O segundo sensor foi um dispositivo Metal-Óxido-Semicondutor (MOS) com princípio de funcionamento baseado na geração de foto corrente, fornecendo respostas imagens bidimensionais. Para as análises dos sinais ruidosos do sensor de óxido de estanho, foi proposto um método de processamento baseado no modelo do movimento Browniano fracionário. Com este método foi possível a discriminação de gases combustíveis com uma taxa de acerto igual a 100%. Para as análises das respostas do tipo imagem do sensor MOS, foram propostos dois diferentes métodos. O primeiro foi embasado no princípio de compressão fractal de imagens e o segundo método proposto, foi baseado na análise e determinação da dimensão fractal multiescala. Ambos os métodos propostos mostram-se eficazes para a determinação da assinatura, como o reconhecimento, de todos os gases que foram utilizados nos experimentos. Os resultados obtidos no presente trabalho abrem novas fronteiras e perspectivas nos paradigmas de processamento de sinais e reconhecimento de padrões, quando utilizada a teoria da geometria fractal.The aim of the present work was to propose methods for signal possessing and pattern, recognition from the signals response of gas sensors using models and techniques from the fractal geometry. The data studied and analyzed were obtained from two kinds of sensors. The first sensor was the tin oxide device, which detection principle is based on the resistivity changes of the tin oxide film and it provides noisy signals as response to the gas interaction. The second sensor was a metal-oxide-semiconductor (MOS) device, which has as the working principle the photocurrent generation. This sensor provides two-dimensional images signals. A method using a fractional Brownian motion was proposed to analyze the noise signal from the tin oxide device. The fuel gases discrimination employing this model was 100% successful. Two different methods were proposed to analyze the signal response from the MOS device. The first method was based on the fractal image compression technique and the second one was based on the analysis and determination of the multiscale fractal dimension. Both proposed methods have shown to be efficient tools for signature determination as the pattern recognition of all gases that were used in the experiment. The results obtained in the present work open new frontiers and perspectives inside the paradigms of the signal processing and pattern recognition by using the fractal theory.
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Silva, Sandreane Poliana. "Comparação entre os métodos de compressão fractal e JPEG 2000 em um sistema de reconhecimento de íris." Universidade Federal de Uberlândia, 2008. https://repositorio.ufu.br/handle/123456789/14385.
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Currently living in the digital age, so the manipulation of data and images
is often all day. Due to the problem of space for storage of pictures and
time of transmission, many compression techniques had been developed, and
a great challenge is to make these techniques to bring good results in terms of
compression rate, picture quality and processing time. The Fractal Compression
technique developed by Fisher, was described, implemented and tested
in this work and it brought great results, and considerable improvement in
terms of execution time, which was rather low.
Another area that has been emphasizing is the use of biometric techniques
to the people recognition. A very used technique is the iris recognition that
has shown enough reliability. Thus, connecting the two technologies brings
great benefits. In this work, images of iris were compressed by the method
implemented here and were made simulations of the technique iris recognition
developed by Libor Maseck. The results show that it is possible to compress
fractally the images without damage the recognition system. Comparisons
were made and was possible realize that even with changes in pixels of images,
the system remains very reliable, bringing benefits to storage space.Atualmente vive-se na era digital, por isso a manipulação de dados e imagens é freqüente todos os dias. Devido ao problema de espaço para armazenamento dessas imagens e tempo de transmissão, foram desenvolvidas várias técnicas de compressão, e um grande desafio é fazer com que essas técnicas tragam bons resultados em termos de taxa de compressão, qualidade da imagem e tempo de processamento. A técnica de compressão Fractal desenvolvida por Fisher, foi descrita, implementada e testada neste trabalho e trouxe ótimos resultados, e melhoria considerável em termos de tempo de execução, que foi bastante reduzido. Outra área que vem se destacando é o uso de técnicas biométricas para reconhecimento de pessoas. Uma técnica muito usada é o reconhecimento de íris que tem mostrado bastante contabilidade. Assim, aliar as duas tecnologias traz grandes benefícios. No presente trabalho, imagens de íris foram comprimidas pelo método aqui implementado e foram realizadas simulações da técnica de reconhecimento de íris desenvolvida por Maseck. Os resultados mostram que é possível comprimir fractalmente as imagens sem prejudicar o sistema de reconhecimento. Comparações foram realizadas e foi possível perceber que mesmo havendo mudanças nos pixels das imagens, o sistema permanece bastante confiavel, trazendo vantagens em espaço de armazenamento.
Mestre em Ciências
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Janati, Idrissi Abderrazak. "Caractérisation physico-chimique des alumines par le concept d'objets fractals." Poitiers, 1988. http://www.theses.fr/1988POIT2305.
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Malý, Petr. "Návrh automatického obchodního systému s využitím fraktální geometrie." Master's thesis, Vysoké učení technické v Brně. Fakulta podnikatelská, 2015. http://www.nusl.cz/ntk/nusl-224844.
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This thesis deals with an analysis and prediction of foreign exchange markets. The thesis is based on the fractal market hypothesis and it uses tools based on fractal geometry for prediction of markets. The thesis also describes ways of using advanced methods of artificial intelligence for analyzing markets. The outcome is designed and implemented automatic trading system. The thesis also deals with testing of designed system on historical data and on the latest data as well.
18
Ould, Eleya Mohamed El Mustapha. "Analyse de la formation des gels acides de laits de vache, de chèvre et de brebis au moyen de la géométrie fractale : étude comparative." Vandoeuvre-les-Nancy, INPL, 1996. http://docnum.univ-lorraine.fr/public/INPL_T_1996_OULD_ELEYA_M_E_M.pdf.
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En se posant la question de l'universalité des mécanismes de la coagulation acide, on a choisi d'étudier l'influence de l'acidification et de la température sur trois types de lait: le lait de vache (Bos taurus), le lait de chèvre (Capra hircus) et le lait de brebis (Ovis aries), très différents par leur composition et par les propriétés et caractéristiques de leurs micelles. Le suivi de l'acidification des laits de vache, de chèvre et de brebis par hydrolyse de glucono-delta-lactone a permis de mettre en évidence deux comportements distincts, selon la température. Un comportement dit aux basses températures, observé pour les laits de vache et de brebis à 15 et 20°C et pour le lait de chèvre à 15, 20 et 30°C, et un comportement dit aux hautes températures, observé pour les laits de vache et de brebis à 30 et 40°C et pour le lait de chèvre à 40°C. Pour les trois types de lait, on montre que la structure des agrégats acides de micelles de caséines et celle des gels acides est de nature fractale. La diminution de la température entraine une densification de la structure des agrégats. Les différences entre les structures des agrégats caséiques des trois types de lait sont reliées aux différences de composition et de caractéristiques des micelles de caséines natives et leurs comportements vis-à-vis des modifications du pH et de la température. Ces résultats sont également discutés par rapport aux résultats des simulations numériques de l'agrégation colloïdale. À la fin de l'étude, on engage des réflexions nouvelles sur les aspects cinétiques de la coagulation acide, sur la structure des micelles caprine et ovine comparée avec la micelle bovine et enfin sur les relations entre phases d'agrégation et de gélification
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Nowotny, Thomas. "Phase transitions and multifractal properties of random field Ising models." Doctoral thesis, Universitätsbibliothek Leipzig, 2004. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-37023.
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In dieser Arbeit werden Zufallsfeld-Ising-Modelle mit einem eingefrorenen dichotomen symmetrischen Zufallsfeld für den eindimensionalen Fall und das Bethe-Gitter untersucht. Dabei wird die kanonische Zustandssumme zu der eines einzelnen Spins in einem effektiven Feld umformuliert. Im ersten Teil der Arbeit werden das mulktifraktale Spektrum dieses effektiven Feldes untersucht, Übergänge im Spektrum erklärt und Ungleichungen zwischen lokalen und globalen Dimensionsbegriffen bewiesen, die eine weitgehend vollständige Charakterisierung des multifraktalen Spektrums durch eine Reihe von Schranken erlauben. Ein weiterer Teil der Arbeit beschäftigt sich mit einer ähnlichen Charakterisierung des Maßes der lokalen Magnetisierung, das aus dem Maß des effektiven Feldes durch Faltung hervorgeht. In diesem Zusammenhang wird die Faltung von Multifraktalen in einem allgemeineren Rahmen behandelt und Zusammenhänge zwischen den multifraktalen Eigenschaften der Faltung und denen der gefalteten Maße bewiesen. Im dritten Teil der Dissertation wird der Phasenübergang von Ferro- zu Paramagnetismus im Modell auf dem Bethe Gitter untersucht. Neben verbesserten exakten Schranken für die Eindeutigkeit des paramagnetischen Zustands werden im wesentlichen drei Kriterien für die tatsächliche Lage des Übergangs angegeben und numerisch ausgewertet. Die multifraktalen Eigenschaften des effektiven Felds im Modell auf dem Bethe-Gitter schließlich erweisen sich als trivial, da die interessanten Dimensionen nicht existierenIn this work random field Ising models with quenched dichotomous symmetric random field are considered for the one-dimensional case and on the Bethe lattice. To this end the canonical partition function is reformulated to the partition function of one spin in an effective field. In the first part of the work the multifractal spectrum of this effective field is investigated, transitions in the spectrum are explained and inequalities between local and global generalized fractal dimensions are proven which allow to characterize the multifractal spectrum bei various bounds. A further part of the work is dedicated to the characterization of the measure of the local magnetization which is obtained by convolution of the measure of the effective field with itself. In this context the convolution of multifractals is investigated in a more general setup and relations between the multifractal properties of the convolution and the multifractal properties of the convoluted measures are proven. The phase transition from ferro- to paramagnetismus for the model on the Bethe lattice is investigated in the third part of the thesis. Apart from improved exact bounds for the uniqueness of the paramagnetic state essentially three criteria for the transition are developped and numerically evaluated to determine the transition line. The multifractal properties of the effective field for the model on the Bethe lattice finally turn out to be trivial because the interesting dimensions do not exist
20
Korabel, Nickolay. "Deterministic transport: from normal to anomalous diffusion." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2004. http://nbn-resolving.de/urn:nbn:de:swb:14-1101988907015-56546.
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The way in which macroscopic transport results from microscopic dynamics is one of the important questions in statistical physics. Dynamical systems theory play a key role in a resent advance in this direction. Offering relatively simple models which are easy to study, dynamical systems theory became a standard branch of modern nonequilibrium statistical physics. In the present work the deterministic diffusion generated by simple dynamical systems is considered. The deterministic nature of these systems is more clearly expressed through the dependencies of the transport quantities as functions of systems parameters. For fully hyperbolic dynamical systems these dependencies were found to be highly irregular and, in fact, fractal. The main focus in this work is on nonhyperbolic and on intermittent dynamical systems. First, the climbing sine map is considered which is a nonhyperbolic system with many physical applications. Then we treat anomalous dynamics generated by a paradigmatic subdiffusive map. In both cases these systems display deterministic transport which, under variation of control parameters, is fractal. For both systems we give an explanation of the observed phenomena. The third part of the thesis is devoted to the relation between chaotic and transport properties of dynamical systems. This question lies at the heart of dynamical systems theory. For closed hyperbolic dynamical systems the Pesin theorem links the sum of positive Lyapunov exponents to the Kolmogorov-Sinai entropy. For open hyperbolic systems the escape rate formula is valid. In this work we have formulated generalizations of these formulas for a class of intermittent dynamical systems where the chaotic properties are weaker.
21
Piché, Daniel G. "Complex Bases, Number Systems and Their Application to Fractal-Wavelet Image Coding." Thesis, University of Waterloo, 2002. http://hdl.handle.net/10012/1057.
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This thesis explores new approaches to the analysis of functions by combining tools from the fields of complex bases, number systems, iterated function systems (IFS) and wavelet multiresolution analyses (MRA). The foundation of this work is grounded in the identification of a link between two-dimensional non-separable Haar wavelets and complex bases. The theory of complex bases and this link are generalized to higher dimensional number systems. Tilings generated by number systems are typically fractal in nature. This often yields asymmetry in the wavelet trees of functions during wavelet decomposition. To acknowledge this situation, a class of extensions of functions is developed. These are shown to be consistent with the Mallat algorithm. A formal definition of local IFS on wavelet trees (LIFSW) is constructed for MRA associated with number systems, along with an application to the inverse problem. From these investigations, a series of algorithms emerge, namely the Mallat algorithm using addressing in number systems, an algorithm for extending functions and a method for constructing LIFSW operators in higher dimensions. Applications to image coding are given and ideas for further study are also proposed. Background material is included to assist readers less familiar with the varied topics considered. In addition, an appendix provides a more detailed exposition of the fundamentals of IFS theory.
22
Pich??, Daniel G. "Complex Bases, Number Systems and Their Application to Fractal-Wavelet Image Coding." Thesis, University of Waterloo, 2002. http://hdl.handle.net/10012/1057.
Full textAbstract:
This thesis explores new approaches to the analysis of functions by combining tools from the fields of complex bases, number systems, iterated function systems (IFS) and wavelet multiresolution analyses (MRA). The foundation of this work is grounded in the identification of a link between two-dimensional non-separable Haar wavelets and complex bases. The theory of complex bases and this link are generalized to higher dimensional number systems. Tilings generated by number systems are typically fractal in nature. This often yields asymmetry in the wavelet trees of functions during wavelet decomposition. To acknowledge this situation, a class of extensions of functions is developed. These are shown to be consistent with the Mallat algorithm. A formal definition of local IFS on wavelet trees (LIFSW) is constructed for MRA associated with number systems, along with an application to the inverse problem. From these investigations, a series of algorithms emerge, namely the Mallat algorithm using addressing in number systems, an algorithm for extending functions and a method for constructing LIFSW operators in higher dimensions. Applications to image coding are given and ideas for further study are also proposed. Background material is included to assist readers less familiar with the varied topics considered. In addition, an appendix provides a more detailed exposition of the fundamentals of IFS theory.
23
Fernandes, Nelson Pires dos Santos Neto. "Fractais clássicos - Aplicações à sala de aulas em São Tomé." Master's thesis, Universidade de Évora, 2020. http://hdl.handle.net/10174/28661.
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A ideia deste trabalho, é o de abordar o estudo dos fractais, evidenciando a sua beleza e
importância matemática. Posteriormente, pretendemos mostrar que os fractais são um
assunto relevante, estruturante e que o seu estudo deveria ser incorporado no ensino
secundário de São Tomé e, nesse sentido, é importante os devidos contactos com as
autoridades educativas do país para a possibilidade de introdução ao destes conceitos
matemáticos nos programas de Matemática de S. Tomé e Príncipe.
Nesta perspectiva, ao longo do trabalho vamos apresentar os conceitos matemáticos
relativos aos fractais, com vista a específicar actividades pedagógicas a decorrer na sala
de aula com o devido apoio do corpo docente, actividades essas a realizar pelos alunos
em grupo ou de forma individual, consolidando assim o tema em estudo, ou seja, os
fractais. O trabalho está organizado em três capítulos, estruturados da seguinte forma:
− No primeiro capítulo, apresentamos uma breve nota histórica, de modo a preparar o
leitor para uma acessível compreensão da geometria fractal e suas propriedades;
− No segundo capítulo, descrevemos, de forma breve, mas rigorosa, alguns dos mais
conhecidos fractais que ao longo de vários anos têm fascinado alunos dos vários
níveis de ensino permitindo, assim, uma melhor compreensão de certos conteúdos
matemáticos;
− No terceiro capítulo, apresentamos algumas sugestões e/ou orientações, no sentido
de proporcionar uma melhor identificação de aspectos essenciais do tema, e ajudar
na seleção e implementação de estratégias que melhor rentabilizam o trabalho
na sala de aula;
− Por fim, no quarto capítulo apresentaremos as conclusões desta dissertação.
De referir que este trabalho tem por base os trabalhos mencionados na bibliografia
[1, 24]; Abstract:
Classic Fractals-Applications to the Classroom in S˜ao Tom´e
The idea of this work is to approach the study of fractals, highlighting their beauty
and mathematical importance. Subsequently, we intend to show that fractals are a
relevant, structuring subject and that their study should be incorporated into secondary
education in S˜ao Tom´e and, in this sense, it is important to have the necessary
contacts with the country’s educational authorities for the possibility of introducing
these concepts mathematicians in the Mathematics programs of S. Tom´e and Pr´ıncipe.
In this perspective, throughout the work we will present the mathematical concepts
related to Fractals, with a view to specific pedagogical activities taking place in the
classroom with the proper support of the teaching staff, activities to be carried out by
students in groups or individually, consolidating thus the subject under study, that is,
fractals. The work is organized in three chapters, structured as follows:
− In the first chapter, we present a brief historical note, in order to prepare the reader
for an accessible understanding of fractal geometry and its properties;
− In the second chapter, we describe, briefly but rigorously, some of the most wellknown
fractals that over the years have fascinated students at various levels of
education, thus allowing a better understanding of certain mathematical content;
− In the third chapter, we present some suggestions and/or guidelines, in order to
provide a better identification of essential aspects of the theme, and to help in
the selection and implementation of strategies that better profit the work in the
classroom;
− Finally, in the fourth chapter we will present the conclusions of this dissertation.
It should be noted that this work is based on the works mentioned in the bibliography
[1, 24].
24
Tuel, Alain. "Caracterisation de la structure de silices de precipitation par resonance magnetique nucleaire de solide et de leur morphologie." Paris 6, 1987. http://www.theses.fr/1987PA066653.
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Etude par rmn en phase solide et par analyses d'images de microscopie electronique. Evaluation du pourcentage des differentes especes, de la densite en hydroxyles et de leur evolution en fonction d'un traitement thermique determine. Etude de la structure geometrique des surfaces apres griffage de petites molecules (diols et alcools). Proposition d'un modele ou la surface des silices de precipitation est constitue d'une couche tres desorganisee d'epaisseur donnee. Caracterisation des projections bidimensionnelles des agregats de silice par des exposants fractals, a partir des micrographies electroniques
25
Nassar, Alaa S. N. "A Hybrid Multibiometric System for Personal Identification Based on Face and Iris Traits. The Development of an automated computer system for the identification of humans by integrating facial and iris features using Localization, Feature Extraction, Handcrafted and Deep learning Techniques." Thesis, University of Bradford, 2018. http://hdl.handle.net/10454/16917.
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Multimodal biometric systems have been widely applied in many real-world applications due to its ability to deal with a number of significant limitations of unimodal biometric systems, including sensitivity to noise, population coverage, intra-class variability, non-universality, and vulnerability to spoofing. This PhD thesis is focused on the combination of both the face and the left and right irises, in a unified hybrid multimodal biometric identification system using different fusion approaches at the score and rank level.
Firstly, the facial features are extracted using a novel multimodal local feature extraction approach, termed as the Curvelet-Fractal approach, which based on merging the advantages of the Curvelet transform with Fractal dimension. Secondly, a novel framework based on merging the advantages of the local handcrafted feature descriptors with the deep learning approaches is proposed, Multimodal Deep Face Recognition (MDFR) framework, to address the face recognition problem in unconstrained conditions. Thirdly, an efficient deep learning system is employed, termed as IrisConvNet, whose architecture is based on a combination of Convolutional Neural Network (CNN) and Softmax classifier to extract discriminative features from an iris image.
Finally, The performance of the unimodal and multimodal systems has been evaluated by conducting a number of extensive experiments on large-scale unimodal databases: FERET, CAS-PEAL-R1, LFW, CASIA-Iris-V1, CASIA-Iris-V3 Interval, MMU1 and IITD and MMU1, and SDUMLA-HMT multimodal dataset. The results obtained have demonstrated the superiority of the proposed systems compared to the previous works by achieving new state-of-the-art recognition rates on all the employed datasets with less time required to recognize the person’s identity.Multimodal biometric systems have been widely applied in many real-world applications due to its ability to deal with a number of significant limitations of unimodal biometric systems, including sensitivity to noise, population coverage, intra-class variability, non-universality, and vulnerability to spoofing. This PhD thesis is focused on the combination of both the face and the left and right irises, in a unified hybrid multimodal biometric identification system using different fusion approaches at the score and rank level.
Firstly, the facial features are extracted using a novel multimodal local feature extraction approach, termed as the Curvelet-Fractal approach, which based on merging the advantages of the Curvelet transform with Fractal dimension. Secondly, a novel framework based on merging the advantages of the local handcrafted feature descriptors with the deep learning approaches is proposed, Multimodal Deep Face Recognition (MDFR) framework, to address the face recognition problem in unconstrained conditions. Thirdly, an efficient deep learning system is employed, termed as IrisConvNet, whose architecture is based on a combination of Convolutional Neural Network (CNN) and Softmax classifier to extract discriminative features from an iris image.
Finally, The performance of the unimodal and multimodal systems has been evaluated by conducting a number of extensive experiments on large-scale unimodal databases: FERET, CAS-PEAL-R1, LFW, CASIA-Iris-V1, CASIA-Iris-V3 Interval, MMU1 and IITD and MMU1, and SDUMLA-HMT multimodal dataset. The results obtained have demonstrated the superiority of the proposed systems compared to the previous works by achieving new state-of-the-art recognition rates on all the employed datasets with less time required to recognize the person’s identity.Higher Committee for Education Development in Iraq
26
Baier, Tânia [UNESP]. "O nexo geometria fractal - produção da ciência contemporânea tomado como núcleo do currículo de matemática do ensino básico." Universidade Estadual Paulista (UNESP), 2005. http://hdl.handle.net/11449/102079.
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baier_t_dr_rcla.pdf: 3138210 bytes, checksum: 6a3b90ff257e39970340d208660ea724 (MD5)Nesta tese é desenvolvida a proposta de trabalhar a Matemática no Ensino Básico segundo as concepções da ciência contemporânea. Tomou-se a Física Clássica e a Moderna e as respectivas teorias matemáticas por elas utilizadas, buscando-se explicitar as visões de homem, de mundo, de conhecimento e de ciência por elas assumidas. Privilegiou-se, nesta análise, a contraposição da ciência mecanicista em relação à sistêmica. Na primeira, o destaque sendo dado à separação sujeito/objeto, à representação do espaço físico como sendo apenas o euclidiano, ao cálculo exato, priorizando, portanto, os aspectos quantitativos da Matemática. A metáfora que diz dessa concepção é a da máquina. Na sistêmica, a metáfora que a expressa é a da rede, que diz da impossibilidade de separar o sujeito que conhece do objeto conhecido e da inexistência de uma hierarquia de a prioris. Nesta abordagem, foi destacada a importância dos padrões que emergem pelos processos iterativos, os quais geram, também, objetos fractais. O tratamento matemático estende-se do quantitativo ao qualitativo. Com a emergência do pensamento sistêmico, dá-se conta da ameaça que se anuncia à permanência da vida no planeta. Nesta investigação buscou-se trabalhar o núcleo do que está na ameaça, entendida como decorrente de praticar-se a postura mecanicista à exaustão, mostrando-se uma possibilidade de neutralizá-la por meio da adoção da postura fenomenológica, pela realização de ser-se cuidado. Ele foi tomado como central à atividade educadora articulada com a visão sistêmica da ciência.
This thesis develops a proposition about working with Mathematics in Basic Teaching (Elementary and High School), according to the conceptions of contemporary science. Classical and Modern Physics, as the mathematical theories used by those, were taken, searching to explain the visions of man, of world, of knowledge and science assumed by them. This analysis priviledges the confrontation of mechanicist science in relation to the systemic science. In the first one, the emphasis is given to the separation subject/object, to the representation of physical space as only being the Euclidian one, to the exact calculation, thus priorizing the quantitatives aspects of Mathematics. The metaphor which talks about this conception is the machine. In the systemic science, the metaphor which express it is the web, which talks about the impossibility of separating the knowing subject from the known object and the inexistence of a hierarchy of a priori. This approach has emphasized the importance of patterns emerged by the iterative processes which generate, also, fractal objects. The Mathematical treatment extend from quantitative to qualitative. With the emergency of systemic thought, one take into account the threat announced to the permanence of life on the planet. This research aimed to work over what lays in that threat, understood as a result of practicing the mechanicist attitude to the exhaustion, showing a possibility of neutralize it by the adoption of the phenomenological posture, by the achievement of one-self-being care. It was taken as central to the educational activity, articulated with the science systemic vision.
27
Baier, Tânia. "O nexo "geometria fractal - produção da ciência contemporânea" tomado como núcleo do currículo de matemática do ensino básico /." Rio Claro : [s.n.], 2005. http://hdl.handle.net/11449/102079.
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Orientador: Maria Aparecida Viggiani BicudoBanca: Maria Inês Fini
Banca: Silvio Donizetti de Oliveira Gallo
Banca: Suzinei Aparecida Siqueira Marconato
Banca: Ubiratan D'Ambrósio
Nesta tese é desenvolvida a proposta de trabalhar a Matemática no Ensino Básico segundo as concepções da ciência contemporânea. Tomou-se a Física Clássica e a Moderna e as respectivas teorias matemáticas por elas utilizadas, buscando-se explicitar as visões de homem, de mundo, de conhecimento e de ciência por elas assumidas. Privilegiou-se, nesta análise, a contraposição da ciência mecanicista em relação à sistêmica. Na primeira, o destaque sendo dado à separação sujeito/objeto, à representação do espaço físico como sendo apenas o euclidiano, ao cálculo exato, priorizando, portanto, os aspectos quantitativos da Matemática. A metáfora que diz dessa concepção é a da máquina. Na sistêmica, a metáfora que a expressa é a da rede, que diz da impossibilidade de separar o sujeito que conhece do objeto conhecido e da inexistência de uma hierarquia de a prioris. Nesta abordagem, foi destacada a importância dos padrões que emergem pelos processos iterativos, os quais geram, também, objetos fractais. O tratamento matemático estende-se do quantitativo ao qualitativo. Com a emergência do pensamento sistêmico, dá-se conta da ameaça que se anuncia à permanência da vida no planeta. Nesta investigação buscou-se trabalhar o núcleo do que está na ameaça, entendida como decorrente de praticar-se a postura mecanicista à exaustão, mostrando-se uma possibilidade de neutralizá-la por meio da adoção da postura fenomenológica, pela realização de ser-se cuidado. Ele foi tomado como central à atividade educadora articulada com a visão sistêmica da ciência.
This thesis develops a proposition about working with Mathematics in Basic Teaching (Elementary and High School), according to the conceptions of contemporary science. Classical and Modern Physics, as the mathematical theories used by those, were taken, searching to explain the visions of man, of world, of knowledge and science assumed by them. This analysis priviledges the confrontation of mechanicist science in relation to the systemic science. In the first one, the emphasis is given to the separation subject/object, to the representation of physical space as only being the Euclidian one, to the exact calculation, thus priorizing the quantitatives aspects of Mathematics. The metaphor which talks about this conception is the machine. In the systemic science, the metaphor which express it is the web, which talks about the impossibility of separating the knowing subject from the known object and the inexistence of a hierarchy of a priori. This approach has emphasized the importance of patterns emerged by the iterative processes which generate, also, fractal objects. The Mathematical treatment extend from quantitative to qualitative. With the emergency of systemic thought, one take into account the threat announced to the permanence of life on the planet. This research aimed to work over what lays in that threat, understood as a result of practicing the mechanicist attitude to the exhaustion, showing a possibility of neutralize it by the adoption of the phenomenological posture, by the achievement of one-self-being care. It was taken as central to the educational activity, articulated with the science systemic vision.
Doutor
28
Boattin, Boisdon Madeleine. "Approximation en coordonnées barycentriques généralisées." Toulouse 3, 1988. http://www.theses.fr/1988TOU30005.
Full textAbstract:
Les coordonnées barycentriques généralisées permettent la construction d'une nouvelle catégorie d'approximants et d'espaces fonctionnels associes parmi lesquels les fonctions éléments finis, les fonctions splines d'interpolation, Les approximants fractals sont des cas particuliers. Les courbes fractales ont alors une écriture globale, voire algorithmique et pour un paramétrage intrinsèque appartiennent à des espaces de Sobolev d'ordre non entier
29
Wu, Shi-Ching. "Fractal analyses of some natural systems." Thesis, University of Hull, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.322455.
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30
Schönwetter, Moritz. "Fractal Dimensions in Classical and Quantum Mechanical Open Chaotic Systems." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2017. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-215747.
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Fractals have long been recognized to be a characteristic feature arising from chaotic dynamics; be it in the form of strange attractors, of fractal boundaries around basins of attraction, or of fractal and multifractal distributions of asymptotic measures in open systems. In this thesis we study fractal and multifractal measure distributions in leaky Hamiltonian systems. Leaky systems are created by introducing a fully or partially transparent hole in an otherwise closed system, allowing trajectories to escape or lose some of their intensity. This dynamics results in intricate (multi)fractal distributions of the surviving trajectories. These systems are suitable models for experimental setups such as optical microcavities or microwave resonators. In this thesis we perform an improved investigation of the fractality in these systems using the concept of effective dimensions. They are defined as the dimensions far from the usually considered asymptotics of infinite evolution time $t$, infinite sample size $S$, and infinite resolution (infinitesimal box-size $varepsilon$). Yet, as we show, effective dimensions can be considered as intrinsic to the dynamics of the system. We present a detailed discussion of the behaviour of the numerically observed dimension $D_mathrm{obs}(S,t,varepsilon)$. We show that the three parameters can be expressed in terms of limiting length scales that define the parameter ranges in which $D_mathrm{obs}(S,t,varepsilon)$ is an effective dimension of the system. We provide dynamical and statistical arguments for the dependence of these scales on $S$, $t$, and $varepsilon$ in strongly chaotic systems and show that the knowledge of the scales allows us to define meaningful effective dimensions. We apply our results to three main fields. In the context of numerical algorithms to calculate dimensions, we show that our findings help to numerically find the range of box sizes leading to accurate results. We further show that they allow us to minimize the computational cost by providing estimates of the required sample-size and iteration time needed. A second application field of our results is systems exhibiting non-trivial dependencies of the effective dimension $D_mathrm{eff}$ on $t$ and $varepsilon$. We numerically explore this in weakly chaotic leaky systems. There, our findings provide insight into the dynamics of the systems, since deviations from our predictions based on strongly chaotic systems at a given parameter range are a sign that the stickiness inherent to such systems needs to be taken into account in that range. Lastly, we show that in quantum analogues of chaotic maps with a partial leak, a related effective dimension can be used to explain the numerically observed deviation from the predictions provided by the fractal Weyl law for systems with fully absorbing leaks. Here, we provide an analytical description of the expected scaling based on the classical dynamics of the system and compare it with numerical results obtained in the studied quantum mapsEs ist seit langem bekannt, dass Fraktale eine charakteristische Begleiterscheinung chaotischer Dynamik sind. Sie treten in Form von seltsamen Attraktoren, von fraktalen Begrenzungen der Einzugsbereiche von Attraktoren oder von fraktalen und multifraktalen Verteilungen asymptotischer Maße in offenen Systemen auf. In dieser Arbeit betrachten wir fraktal und multifraktal verteilte Maße in geöffneten hamiltonschen Systemen. Geöffnete Systeme werden dadurch erzeugt, dass man ein völlig oder teilweise transparentes Loch im Phasenraum definiert, durch das Trajektorien entkommen können oder in dem sie einen Teil ihrer Intensität verlieren. Die Dynamik in solchen Systemen erzeugt komplexe (multi)fraktale Verteilungen der verbleibenden Trajektorien, beziehungsweise ihrer Intensitäten. Diese Systeme sind zur Modellierung experimenteller Aufbauten, wie zum Beispiel optischer Mikrokavitäten oder Mikrowellenresonatoren, geeignet. In dieser Arbeit führen wir eine verbesserte Untersuchung der Fraktalität in derartigen Systemen durch, die auf dem Konzept der effektiven Dimensionen beruht. Diese sind als die Dimensionen definiert, die weit weg von den üblicherweise betrachteten Limites unendlicher Iterationszeit $t$, unendlicher Stichprobengröße $S$ und unendlicher Auflösung, also infinitesimaler Boxgröße $varepsilon$ auftreten. Dennoch können effektive Dimensionen, wie wir zeigen, als der Dynamik des Systems inhärent angesehen werden. Wir führen eine detaillierte Diskussion der numerisch beobachteten Dimension $D_mathrm{obs}(S,t,varepsilon)$ durch und zeigen, dass die drei Parameter $S$, $t$ und $varepsilon$ in Form grenzwertiger Längenskalen ausgedrückt werden können, die die Parameterbereiche definieren, in denen $D_mathrm{obs}(S,t,varepsilon)$ den Wert einer effektiven Dimension des Systems annimmt. Wir beschreiben das Verhalten dieser Längenskalen in stark chaotischen Systemen als Funktionen von $S$, $t$ und $varepsilon$ anhand statistischer Überlegungen und anhand von auf der Dynamik basierenden Aussagen. Weiterhin zeigen wir, dass das Wissen um diese Längenskalen die Definition aussagekräftiger effektiver Dimensionen ermöglicht. Wir wenden unsere Ergebnisse hauptsächlich in drei Bereichen an: Im Kontext numerischer Algorithmen zur Dimensionsberechnung zeigen wir, dass unsere Ergebnisse es erlauben, diejenigen $varepsilon$-Bereiche zu finden, die zu korrekten Ergebnissen führen. Weiterhin zeigen wir, dass sie es uns erlauben, den Rechenaufwand zu minimieren, indem sie uns eine Abschätzung der benötigten Stichprobengröße und Iterationszeit ermöglichen. Ein zweiter Anwendungsbereich sind Systeme, die sich durch eine nichttriviale Abhängigkeit von $D_mathrm{eff}$ von $t$ und $varepsilon$ auszeichnen. Hier ermöglichen unsere Ergebnisse ein besseres Verständnis der Systeme, da Abweichungen von den Vorhersagen basierend auf der Annahme von starker Chaotizität ein Anzeichen dafür sind, dass im entsprechenden Parameterbereich die Eigenschaft dieser Systeme, dass Bereiche in ihrem Phasenraum Trajektorien für eine begrenzte Zeit einfangen können, relevant ist. Zuletzt zeigen wir, dass in quantenmechanischen Analoga chaotischer Abbildungen mit partiellen Öffnungen eine verwandte effektive Dimension genutzt werden kann, um die numerisch beobachteten Abweichungen vom fraktalen weyl'schen Gesetz für völlig transparente Öffnungen zu erklären. In diesem Zusammenhang zeigen wir eine analytische Beschreibung des erwarteten Skalierungsverhaltens auf, die auf der klassischen Dynamik des Systems basiert, und vergleichen sie mit numerischen Erkenntnissen, die wir über die Quantenabbildungen gewonnen haben
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Knight, Georgie Samuel. "Fractal diffusion coefficients in simple dynamical systems." Thesis, Queen Mary, University of London, 2012. http://qmro.qmul.ac.uk/xmlui/handle/123456789/15044.
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Deterministic diffusion is studied in simple, parameter-dependent dynamical systems. The diffusion coefficient is often a fractal function of the control parameter, exhibiting regions of scaling and self-similarity. Firstly, the concepts of chaos and deterministic diffusion are introduced in the context of dynamical systems. The link between deterministic diffusion and physical diffusion is made via random walk theory. Secondly, parameter-dependent diffusion coefficients are analytically derived by solving the Taylor-Green-Kubo formula. This is done via a recursion relation solution of fractal 'generalised Takagi functions'. This method is applied to simple one-dimensional maps and for the first time worked out fully analytically. The fractal parameter dependence of the diffusion coefficient is explained via Markov partitions. Linear parameter dependence is observed which in some cases is due to ergodicity breaking. However, other cases are due to a previously unobserved phenomenon called the 'dominating-branch' effect. A numerical investigation of the two-dimensional 'sawtooth map' yields evidence for a possible fractal structure. Thirdly, a study of different techniques for approximating the diffusion coefficient of a parameter-dependent dynamical system is then performed. The practicability of these methods, as well as their capability in exposing a fractal structure is compared. Fourthly, an analytical investigation into the dependence of the diffusion coefficient on the size and position of the escape holes is then undertaken. It is shown that varying the position has a strong effect on diffusion, whilst the asymptotic regime of small-hole size is dependent on the limiting behaviour of the escape holes. Finally, an exploration of a method which involves evaluating the zeros of a system's dynamical zeta function via the weighted Milnor-Thurston kneading determinant is performed. It is shown how to relate the diffusion coefficient to a zero of the dynamical zeta function before analytically deriving the diffusion coefficient via the kneading determinant.
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Pavani, Gustavo Antonio [UNESP]. "Propriedades topológicas e aritméticas dos fractais de Rauzy." Universidade Estadual Paulista (UNESP), 2010. http://hdl.handle.net/11449/94227.
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O objetivo deste trabalho é estudar propriedades topológicas e aritméticas dos fractais de Rauzy. Em particular provamos que o fractal de Rauzy é um subconjunto compacto de C, conexo, com interior simplesmente conexo e que ele induz um azulejamento periódico do plano complexo. Além disso, construimos um autômato finito capaz de gerar a fronteira do fractal de Rauzy. Com isto demos uma parametrização para a fronteira e claculamos sus dimensão de Hausdorff. Estudamos também os pontos extremos do fractal de Rauzy.
The aim of this work is to study some topological and arithmetical properties of the Rauzy fractals. In particular we proved that the Rauzy fractal is a compact subset of C, connected, its interior is simply connected, and it induces a periodic tiling of the complex pane. Furthermore, we studied the construction of a finite automaton able to generate the boundary of the Rauzy fractal, allowing us to provide a parametrization for its boundary, and claculate its Hausdorff dimension. We also studied the extremal points of the Rauzy fractal.
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Bortolan, Matheus Cheque. "Atratores para sistemas dinâmicos discretos: dimensão fractal e continuidade da estrutura por perturbações." Universidade de São Paulo, 2009. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-20052009-090139/.
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Neste trabalho, estudamos uma generalização dos semigrupos gradientes, os semigrupos gradiente-like, algumas de suas propriedades e a sua invariância por pequenas perturbações; isto é, pequenas perturbações de sistemas gradiente-like continuam sendo gradiente-like. Como consequência da caracterização dos atratores para este tipo de sistema, estudamos a atração exponencial de atratores. Por fim, estudamos o concetio de dimensão de Hausdorff e dimensão fractal de atratores e apresentamos alguns resultados sobre este assunto, e estudamos a construção de uma nova classe de atratores, os atratores exponenciais fractaisIn this work, we study a generalization of gradient discrete semigroups, the gradientlike semigroups, some of its properties and its invariance under small perturbations; that is, small perturbations of gradient-like semigroups are still gradient-like semigroups. As a consequence of the characterization of the attractors for this sort of semigroups, we study the exponential attraction of attractors. Finally, we study some concepts of Hausdorff dimension and fractal dimension and present some results about this subject, and we studied the construction of a new class of attractors, the exponential fractal attractors
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Constantine, William L. B. "Wavelet techniques for chaotic and fractal dynamics /." Thesis, Connect to this title online; UW restricted, 1999. http://hdl.handle.net/1773/7124.
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Rai, Durgesh K. "Quantification of Fractal Systems using Small Angle Scattering." University of Cincinnati / OhioLINK, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1377870724.
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Pavani, Gustavo Antonio. "Propriedades topológicas e aritméticas dos fractais de Rauzy /." São José do Rio Preto : [s.n.], 2010. http://hdl.handle.net/11449/94227.
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Orientador: Ali MessaoudiBanca: Daniel Smania Brandão
Banca: Vanderlei Minori Horita
Resumo: O objetivo deste trabalho é estudar propriedades topológicas e aritméticas dos fractais de Rauzy. Em particular provamos que o fractal de Rauzy é um subconjunto compacto de C, conexo, com interior simplesmente conexo e que ele induz um azulejamento periódico do plano complexo. Além disso, construimos um autômato finito capaz de gerar a fronteira do fractal de Rauzy. Com isto demos uma parametrização para a fronteira e claculamos sus dimensão de Hausdorff. Estudamos também os pontos extremos do fractal de Rauzy.
Abstract: The aim of this work is to study some topological and arithmetical properties of the Rauzy fractals. In particular we proved that the Rauzy fractal is a compact subset of C, connected, its interior is simply connected, and it induces a periodic tiling of the complex pane. Furthermore, we studied the construction of a finite automaton able to generate the boundary of the Rauzy fractal, allowing us to provide a parametrization for its boundary, and claculate its Hausdorff dimension. We also studied the extremal points of the Rauzy fractal.
Mestre
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Pesquet-Popescu, Béatrice. "Modélisation bidimensionnelle de processus non stationnaires et application à l'étude du fond sous-marin." Cachan, Ecole normale supérieure, 1998. http://www.theses.fr/1998DENS0021.
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Dans cette thèse, nous proposons des généralisations anisotropes des champs 2D de type fractal. Tout d'abord, nous introduisons les champs 2D à accroissements stationnaires fractionnaires et nous montrons que le mouvement brownien fractionnaire appartient à cette classe de processus. L'intérêt d'une analyse multi résolution de ces champs est démontré théoriquement et sur un exemple d'application à la localisation sous-marine. Pour la modélisation de données, un moyen efficace pour caractériser les textures à accroissements stationnaires est fourni par la fonction de structure. Nous soulignons la possibilité de contrôler l'anisotropie de ces champs par le biais de cette fonction, dont nous proposons également plusieurs modèles. La fonction de structure est aussi employée pour l'interpolation des champs non stationnaires à accroissements stationnaires. Un autre aspect de ce travail concerne les extensions bidimensionnelles des processus ARIMA fractionnaires et leurs liens avec les champs continus présentés. Finalement, nous considérons des processus auto-similaires non-gaussiens et étudions les statistiques de leurs coefficients d'ondelettes.
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Bon, Jérôme. "Etude des propriétés acoustiques basse fréquence des aérogels de silice à basse température." Grenoble 1, 1988. http://www.theses.fr/1988GRE10056.
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Le frottement interne et le module d'young a basse frequence d'aerogels de silice de faible densite sont mesures par la methode de la lame vibrante encastree entre 100 mk et 80 k. Les resultats sont proches de ceux de la silicice vitreuse, en l'absence d'helium adsorbe, et sont interpretes en termes de systeme a deux niveaux. L'adsorption d'helium modidie notablement les resultats
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Babič, Vojtěch. "Návrh automatického obchodního systému na devizových trzích s využitím fraktální geometrie." Master's thesis, Vysoké učení technické v Brně. Fakulta podnikatelská, 2016. http://www.nusl.cz/ntk/nusl-254205.
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The main focus of the thesis are approaches to technical analysis, trading systems and it summarizes interesting findings, according to which a FOREX automated trading system was designed and implemented. Optimization and testing were a prerequisite for a real-world deployment, so the automated trading system was tested on historical data and some of its input parameters were optimized for maximum stability and profit.
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Batelková, Andrea. "Srovnávací analýzy progresivních struktur řízení podniku." Master's thesis, Vysoké učení technické v Brně. Ústav soudního inženýrství, 2014. http://www.nusl.cz/ntk/nusl-232920.
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The thesis is created in order to conduct a comparative analysis of organizational structure of the company. The parameters for comparison are determined. The first one is the comparative analysis of the Amoeba Management System with a Divisional Structure. The second one is the comparative analysis of Fractal and Matrix Organizational Structure. The conslusions of these analyzes determine the key parameters for management on the basis of the suggested organizational structure for effective management.
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Mizutani, Masahiro. "Dynamical systems on fractals = Furakutarujo ̄no rikigakukei /." Electronic version of summary, 1986. http://www.wul.waseda.ac.jp/gakui/gaiyo/1268.pdf.
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Dubarry, Blandine. "Comportement asymptotique des systèmes de fonctions itérées et applications aux chaines de Markov d'ordre variable." Thesis, Rennes 1, 2017. http://www.theses.fr/2017REN1S114/document.
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L'objet de cette thèse est l'étude du comportement asymptotique des systèmes de fonctions itérées (IFS). Dans un premier chapitre, nous présenterons les notions liées à l'étude de tels systèmes et nous rappellerons différentes applications possibles des IFS telles que les marches aléatoires sur des graphes ou des pavages apériodiques, les systèmes dynamiques aléatoires, la classification de protéines ou encore les mesures quantiques répétées. Nous nous attarderons sur deux autres applications : les chaînes de Markov d'ordre infini et d'ordre variable. Nous donnerons aussi les principaux résultats de la littérature concernant l'étude des mesures invariantes pour des IFS ainsi que ceux pour le calcul de la dimension de Hausdorff. Le deuxième chapitre sera consacré à l'étude d'une classe d'IFS composés de contractions sur des intervalles réels fermés dont les images se chevauchent au plus en un point et telles que les probabilités de transition sont constantes par morceaux. Nous donnerons un critère pour l'existence et pour l'unicité d'une mesure invariante pour l'IFS ainsi que pour la stabilité asymptotique en termes de bornes sur les probabilités de transition. De plus, quand il existe une unique mesure invariante et sous quelques hypothèses techniques supplémentaires, on peut montrer que la mesure invariante admet une dimension de Hausdorff exacte qui est égale au rapport de l'entropie sur l'exposant de Lyapunov. Ce résultat étend la formule, établie dans la littérature pour des probabilités de transition continues, au cas considéré ici des probabilités de transition constantes par morceaux. Le dernier chapitre de cette thèse est, quant à lui, consacré à un cas particulier d'IFS : les chaînes de Markov de longueur variable (VLMC). On démontrera que sous une condition de non-nullité faible et de continuité pour la distance ultramétrique des probabilités de transitions, elles admettent une unique mesure invariante qui est attractive pour la convergence faibleThe purpose of this thesis is the study of the asymptotic behaviour of iterated function systems (IFS). In a first part, we will introduce the notions related to the study of such systems and we will remind different applications of IFS such as random walks on graphs or aperiodic tilings, random dynamical systems, proteins classification or else $q$-repeated measures. We will focus on two other applications : the chains of infinite order and the variable length Markov chains. We will give the main results in the literature concerning the study of invariant measures for IFS and those for the calculus of the Hausdorff dimension. The second part will be dedicated to the study of a class of iterated function systems (IFSs) with non-overlapping or just-touching contractions on closed real intervals and adapted piecewise constant transition probabilities. We give criteria for the existence and the uniqueness of an invariant probability measure for the IFSs and for the asymptotic stability of the system in terms of bounds of transition probabilities. Additionally, in case there exists a unique invariant measure and under some technical assumptions, we obtain its exact Hausdorff dimension as the ratio of the entropy over the Lyapunov exponent. This result extends the formula, established in the literature for continuous transition probabilities, to the case considered here of piecewise constant probabilities. The last part is dedicated to a special case of IFS : Variable Length Markov Chains (VLMC). We will show that under a weak non-nullness condition and continuity for the ultrametric distance of the transition probabilities, they admit a unique invariant measure which is attractive for the weak convergence
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Boore, Graeme C. "Directed graph iterated function systems." Thesis, University of St Andrews, 2011. http://hdl.handle.net/10023/2109.
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This thesis concerns an active research area within fractal geometry. In the first part, in Chapters 2 and 3, for directed graph iterated function systems (IFSs) defined on ℝ, we prove that a class of 2-vertex directed graph IFSs have attractors that cannot be the attractors of standard (1-vertex directed graph) IFSs, with or without separation conditions. We also calculate their exact Hausdorff measure. Thus we are able to identify a new class of attractors for which the exact Hausdorff measure is known. We give a constructive algorithm for calculating the set of gap lengths of any attractor as a finite union of cosets of finitely generated semigroups of positive real numbers. The generators of these semigroups are contracting similarity ratios of simple cycles in the directed graph. The algorithm works for any IFS defined on ℝ with no limit on the number of vertices in the directed graph, provided a separation condition holds. The second part, in Chapter 4, applies to directed graph IFSs defined on ℝⁿ . We obtain an explicit calculable value for the power law behaviour as r → 0⁺ , of the qth packing moment of μ[subscript(u)], the self-similar measure at a vertex u, for the non-lattice case, with a corresponding limit for the lattice case. We do this (i) for any q ∈ ℝ if the strong separation condition holds, (ii) for q ≥ 0 if the weaker open set condition holds and a specified non-negative matrix associated with the system is irreducible. In the non-lattice case this enables the rate of convergence of the packing L[superscript(q)]-spectrum of μ[subscript(u)] to be determined. We also show, for (ii) but allowing q ∈ ℝ, that the upper multifractal q box-dimension with respect to μ[subscript(u)], of the set consisting of all the intersections of the components of F[subscript(u)], is strictly less than the multifractal q Hausdorff dimension with respect to μ[subscript(u)] of F[subscript(u)].
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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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Kjøll, Per Kristian. "Integration of a Fractal Generator with Mali GPU." Thesis, Norges teknisk-naturvitenskapelige universitet, Institutt for elektronikk og telekommunikasjon, 2012. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-18810.
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The Mandelbrot set is a well-known fractal with mathematical propertiesthat can be exploited to create 3D-landscapes. The operations required tocalculate a heightmap using the Mandelbrot set are highly parallelizableand is thus suitable for a hardware implementation. Generation of 3D-landscapes,on-the-y, using the Mandelbrot set is desirable since the Mandel-brot set is innitely complex[4] and deterministic. This makes possible thecreation of many dierent landscapes with complex patters in, for example,computer games.A previous master thesis[4] presents a vertex array generator(VAG) thatgenerates the vertices of a 3D-landscape based on an area of the Mandelbrotset. This thesis explores dierent architectures that connect this vertex arraygenerator with the Mali-400 graphics processing unit(GPU). The result isthat the VAG in its current state is not suitable for integration, mostly sinceit does not support random access to vertices. Thus, a new fractal generatorarchitecture is presented, reusing parts of the VAG.The new fractal generator is implemented in Verilog and its functionalityis veried using the Universal Verication Methodology(UVM). Then, thefractal generator is integrated with the Mali-400 GPU in an FPGA frame-work and synthesized on FPGA. Tests are also performed at each step ofintegration.An OpenGL for Embedded Systems 2.0 demo is written to showcase thefunctionality of the fractal generator. Changes have been made to the Mali-400 drivers to automatically congure and set-up the fractal generator whilethe demo is running.The fractal generator is shown to be working as intended with a scalableperformance based on a number of internal cores. Using 64 cores the fractalgenerator has a worst-case frame time of 51.1 ms at 400Mhz which equals aframe rate of 450 frames pr second, vastly outperforming a software imple-mentation.The fractal generator is currently limited to creating landscapes of 128x128points, the intention was to use the demo and driver to increase the resolutionbut this has not been solved.Increasing the resolution and optimizing the cache size of the fractal generatorhas been left for future work.
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Black, Robert D. (Robert Douglas) Carleton University Dissertation Computer Science. "On fractals, chaos and the Hailstone numbers." Ottawa, 1992.
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Werner, Ivan. "Contractive Markov systems." Thesis, University of St Andrews, 2004. http://hdl.handle.net/10023/15173.
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We introduce a theory of contractive Markov systems (CMS) which provides a unifying framework in so-called "fractal" geometry. It extends the known theory of iterated function systems (IFS) with place dependent probabilities [1][8] in a way that it also covers graph directed constructions of "fractal" sets [18]. Such systems naturally extend finite Markov chains and inherit some of their properties. In Chapter 1, we consider iterations of a Markov system and show that they preserve the essential structure of it. In Chapter 2, we show that the Markov operator defined by such a system has a unique invariant probability measure in the irreducible case and an attractive probability measure in the aperiodic case if the restrictions of the probability functions on their vertex sets are Dini-continuous and bounded away from zero, and the system satisfies a condition of a contractiveness on average. This generalizes a result from [1]. Furthermore, we show that the rate of convergence to the stationary state is exponential in the aperiodic case with constant probabilities and a compact state space. In Chapter 3, we construct a coding map for a contractive Markov system. In Chapter 4, we calculate Kolmogorov-Sinai entropy of the generalized Markov shift. In Chapter 5, we prove an ergodic theorem for Markov chains associated with the contractive Markov systems. It generalizes the ergodic theorem of Elton [8].
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Callaghan, Sarah Anne. "Fractal analysis and synthesis of rain fields for radio communication systems." Thesis, University of Portsmouth, 2004. https://researchportal.port.ac.uk/portal/en/theses/fractal-analysis-and-synthesis-of-rain-fields-for-radio-communication-systems(038a2dbf-4464-40fd-ab6e-fe9d3a21101a).html.
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This thesis has the aim of introducing fractal methods for the analysis and synthesis of rain fields into the field of radio communication systems. To this end, the fractal nature of rain rate contours as measured by meteorological radar was verified, using different techniques including the area-perimeter relationship, the box-counting dimension, and power spectral density function analysis. The fractal dimension of these contours was found to be -1.2, and the different methods of calculation agreed with each other. Scaling results were also exhibited by the distribution of number of contours with respect to their enclosed area. Multifractal analysis of the radar measured rain fields showed that rain rate fields display multifractal behaviour, as described in the literature. However, log rain rate fields have a straight line K(q) function, indicating that for these fields mono fractal methods of analysis and synthesis may be used. This is of particular interest to the communications engineering community, who are not concerned with the extreme events that require multi fractals to correctly categorise them, and are already accustomed to dealing with observables on a logarithmic basis. A study of the physical and phenomenological aspects of rain was conducted, with particular emphasis on the impact of measuring device resolution and scaling limits on the calculation of the fractal dimension of rain fields. Also investigated were the differences between stratiform, convective and frontal rain events, the results of which led to the inclusion of climatologically based parameters into the rain field simulator proposed. The simulator uses a discrete additive cascade process to produce simulated mono fractal log rain rate fields, which are visually and statistically realistic. The calculated value for one of the parameters, H = 1/3, related to the power spectral density function exponent, shows that log rain rate is antipersistent, and that log rain rate has long range anticorrelation. The procedure required to convert from rain rate fields R(x,y,z,t) (mm/hr) to attenuation along a path AdB (p,t) (dB) was detailed. It was found that the Met Office's Nimrod rain radar database does not have a spatial resolution high enough to be able to accurately use radar derived attenuation data as a substitute for measurements made on site diversity links -1 Okm apart. The fractal rain field simulator can scale the data in space to any size resolution required, without adversely affecting the statistics and spatial behaviour of the simulated field. Attenuation time series derived from the simulated rain fields were created. In order to compare them statistically with measured attenuation time series, cumulative distribution functions were calculated from a database of measured and simulated events. The results give reasonable agreement, but emphasise the need for more measured data in order to more accurately characterise the wide range of variability present in attenuation events. Similar conclusions were drawn from the results of the diversity gain comparison performed between the measured and simulated data. The time series were also applied to the case study of a switching algorithm for an Earthspace radio system using site diversity as a fade mitigation technique. The inputs into such a switching algorithm were defined and discussed, including a simple short-term attenuation predictor. The behaviour of the switching algorithm with the simulated data was contrasted with the behaviour with measured site diversity data, with similar results. Finally, potential areas of improvement and further work were identified.
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Klages, Rainer. "Microscopic Chaos, Fractals, and Transport in Nonequilibrium Steady States. - (Die Veröffentlichung einer ergänzten und überarbeiteten Version bei "World Scientific Publishing" ist für 2005/06 geplant.)." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2004. http://nbn-resolving.de/urn:nbn:de:swb:14-1107426004665-22819.
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A fundamental challenge is to understand nonequilibrium statistical mechanics starting from microscopic chaos in the equations of motion of a many-particle system. In this thesis we summarize recent theoretical advances along these lines. We focus on two different approaches to nonequilibrium transport: One considers Hamiltonian dynamical systems under nonequilibrium boundary conditions, another one suggests a non-Hamiltonian approach to nonequilibrium situations created by external electric fields and by temperature or velocity gradients. A surprising result related to the former approach is that in simple low-dimensional periodic models the deterministic transport coefficients are typically fractal functions of control parameters. These fractal transport coefficients yield the first central theme of this thesis. We exemplify this phenomenon by deterministic diffusion in a simple chaotic map. We then construct an arsenal of analytical and numerical methods for computing further transport coefficients such as electrical conductivities andchemical reaction rates. These methods are applied to hierarchies of chaotic dynamical systems that are successively getting more complex, starting from abstract one-dimensional maps generalizing a simple random walk on the line up to particle billiards that should be directly accessible in experiments. In all cases, the resulting transport coefficients turn out to be either strictly fractal, or at least to be profoundly irregular. The impact of random perturbations on these quantities is also investigated. We furthermore provide some access roads towards a physical understanding of these fractalities. The second central theme is formed by a critical assessment of the non-Hamiltonian approach to nonequilibrium transport. Here we consider situations where the nonequilibrium constraints pump energy into a system, hence there must be some thermal reservoir that prevents the system from heating up. For this purpose a deterministic and time-reversible modeling of thermal reservoirs was proposed in form of Gaussian and Nose-Hoover thermostats. This approach yielded simple relations between fundamental quantities of nonequilibrium statistical mechanics and of dynamical systems theory. Our goal is to critically assesses the universality of these results. As a vehicle of demonstration we employ the driven periodic Lorentz gas, a toy model for the classical dynamics of an electron in a metal under application of an electric field. Applying different types of thermal reservoirs to this system we compare the resulting nonequilibrium steady states with each other. Along the same lines we discuss an interacting many-particle system under shear and heat. Finally, we outline an unexpected relationship between deterministic thermostats and active Brownian particles modeling biophysical cell motility.
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Huang, Jungang. "Spontaneous optical fractals in linear & nonlinear systems." Thesis, University of Salford, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.491053.
Full textAbstract:
This thesis concerns the generation and characterisation of optical fractals. Chapter 1 presents a brief introduction to fractals and fractal dimensions, and then a review of contexts where fractal concepts have arisen in optics. These contexts are classified in terms of whether the fractal-generating mechanisms at work are linear or nonlinear.