The quantitative description of rough fracture surfaces of concrete has been an important challenge for many years. Looking at the fracture surface of a concrete specimen, one realizes that the self-affine geometry of crack faces results from the stochastic nature of the crack growth. This is due to the heterogeneous nature of concrete that makes the crack tortuous leading its way through weak bonds, voids, mortar and getting arrested on encountering a hard aggregate forming crack face bridges. These mechanisms contribute to the tendency of the crack to follow a tortuous path. The self-similarity contained in the tortuous fracture surface of concrete makes it an ideal candidate to be considered as a fractal. Further, the softening response itself has been treated as a singular fractal function by earlier investigators. The very process of cracking and microcracking, could be considered very close to the stick and slip process and therefore as a fractal. Therefore modeling a crack as a fractal and characterizing it by a fractal dimension have become the focus of research in recent years. Due to randomly distributed discontinuous flaws and high heterogeneity of the internal structure of concrete, mechanical properties also randomly vary. Under the effect of the same external force, the stress intensity factors to which different points in the concrete are subjected are different. Hence the microcracks induced by the external force are distributed discontinuously and randomly. Therefore in the present study the effect of the random nature of the microcracks in the fracture process zone of concrete is investigated using both fractal and probabilistic approach. The most probable fractal dimension of a network of micro cracks is obtained as a function of the branching angle ‘α’ of the microcracks, considered as a random variable. Further, an ensemble of cracks is synthetically generated using Monte Carlo technique imposing a constraint that the random deviations do not exceed the maximum size of the aggregate. Such tortuous cracks are analyzed by extending Fictitious Crack Model (FCM) proposed by Hillerborg et al [37]. A numerical study is carried out to examine the influence of certain important fracture parameters on the beam response of plain concrete beams. The contents of this thesis are organized in seven chapters with references at the end. Chapter-1 summarizes the historical development of fracture mechanics. A brief review of the basic concepts of fracture mechanics theory is presented. In chapter-2 a brief review of literature on fracture mechanics of concrete is presented. An overview of the analytical models, numerical models and fractal models till date has been presented in a systematic way. In chapter-3 the fracture processs zone has been modeled as a fractal following the work of Ji et al [118]. The contribution here has been to improve the work of Ji et al [118] (which considers the region of microcracks as a fractal tree) by considering the branching angle as a random variable. Mean fractal dimension thus obtained is found to match well with the experimental results available in the literature. In chapter-4 FCM, as proposed by Hillerborg et al [37] has been modified to be applicable to cracks with varying inclined faces by considering both horizontal and vertical components of the closing forces. The theoretical aspects of the modified FCM have been described in detail. The procedure for the determination of influence co- efficient matrices for a random tortuous crack in mode-I and mixed-mode along with a fractal crack has been explained. In the subsequent chapters the study has been taken up in two parts. In the first part only one generator of the fractal tree considered by Ji et al [118] has been analyzed by FCM to obtain load-deformation responses and fracture energy. In part two, a random tortuous crack, as already defined earlier has been analyzed both in mode-I and mixed mode using FCM. In chapter-5 plain concrete beams with one generator of fractal tree has been analyzed. The influence of the branching angle on the post-peak response of (P-δ) curves and fracture energy has been obtained. In chapter-6 a random tortuous crack has been analyzed in mode-I by FCM. The analysis reveals the influence of maximum aggregate size upon the pre and post-peak behaviour in support of the experimental findings. The nominal stress at peak is found to depend on the characteristic dimension of the structure thereby confirming the size effect. Further fracture energy values have been obtained by the work of fracture method and the results show good agreement with the results obtained in the literature. In chapter-7 a random tortuous crack has been analyzed in mixed mode by FCM. While modeling, symmetry has been assumed only to facilitate computational work though it is known that loss of symmetry affects the peak load. However analysis of the whole beam can be handled by the code developed in the thesis In chapter-8 a summary of the research work is presented along with a list of major observations and references at the end.

Η ποιότητα πολλών εκ των αποτελεσμάτων της σύγχρονης έρευνας εξαρτώνται άμεσα από την «ποιότητα» και την ποσότητα των τυχαίων αριθμών που χρησιμοποιούνται. Ειδικότερα σε τομείς όπως η στοχαστική μοντελοποίηση και προσομοίωση προτιμώνται οι ντετερμινιστικές γεννήτριες τυχαίων αριθμών, ή αλλιώς γεννήτριες ψευδοτυχαίων αριθμών λόγω της δυνατότητας αναπαραγωγής των αποτελεσμάτων και της μεταφερσιμότητας τους. Επομένως, μας είναι χρήσιμο να εντοπίσουμε ψευδοτυχαίες γεννήτριες αριθμών με αυξημένη φαινόμενη τυχαιότητα αποτελεσμάτων. Για το λόγο αυτό, στη διπλωματική εργασία προτείνεται και εξετάζεται η καταλληλότητα της θραυσματικής διάστασης (fractal dimension) για την αξιολόγηση ψευδοτυχαίων γεννητριών τυχαίων αριθμών (Pseudorandom Number Generators). Η θραυσματική διάσταση αποτελεί μία μετρική που δύναται να εκφράσει την τυχαιότητα των αποτελεσμάτων μιας γεννήτριας ψευδοτυχαίων αριθμών καθώς «ποσοτικοποιεί» την κατανομή των ψευδοτυχαίων αριθμών στον ευκλείδειο χώρο. Σε πρώτο στάδιο γίνεται μία επισκόπηση των υπαρχουσών μεθοδολογιών παραγωγής τυχαίων αριθμών καθώς και των προσεγγίσεων για την αξιολόγηση της απόδοσης των ψευδοτυχαίων γεννητριών τυχαίων αριθμών. Οι καθιερωμένες τεχνικές που εφαρμόζονται για την αξιολόγηση μιας γεννήτριας εστιάζουν σε στατιστικά χαρακτηριστικά που έχουν ως στόχο να μετρήσουν πόσο απρόβλεπτα είναι τα αποτελέσματά της, ή χαρακτηριστικά όπως η περίοδος μιας γεννήτριας. Ακολούθως, μελετάται η θραυσματική διάσταση και οι προτεινόμενες στη βιβλιογραφία μέθοδοι υπολογισμού της. Στο στάδιο αυτό επιλέγεται η κατάλληλη μέθοδος για τον υπολογισμό της θραυσματικής διάστασης. Στο τελευταίο πειραματικό στάδιο παρουσιάζονται τα αποτελέσματα της μέτρησης της μορφοκλασματικής διάστασης. Οι ψευδοτυχαίες γεννήτριες προς αξιολόγηση που μετείχαν στα υπολογιστικά πειράματα ήταν η Γραμμική Αναλογική γεννήτρια, η γεννήτρια Blum-Blum-Shub, η γεννήτρια που βασίζεται στο κρυπτοσύστημα RSA και η γεννήτρια που βασίζεται στο πρόβλημα του διακριτού λογαρίθμου. Τα υπολογιστικά πειράματα επιχειρούν να ανακαλύψουν την απόδοση των εξεταζόμενων γεννητριών αλλά και την ευαισθησία της συμπεριφοράς τους ως προς τις παραμέτρους εισόδου των γεννητριών. / Scientific experimental results are highly dependent on the "quality" and quantity of random numbers used for these experiments. Especially in areas such as stochastic modeling and simulation, deterministic random number generators, known as pseudorandom number generators are preferred because of reproducibility of the results and their portability. Trying to identify pseudorandom number generators sequences which appear to be random, we examine the suitability of Fractal Dimension measurement for assessing Pseudorandom Number Generators. The established techniques that are used to evaluate a generator are focused on statistical features that are designed to detect correlations into generated pseudorandom number sequences. On the other hand, Fractal Dimension is a metric that can express the randomness of the results of a pseudorandom number generator as it "quantifies" the distribution of pseudorandom numbers in Euclidean space. We attempt to evaluate some Pseudorandom Number Generators, like classical Linear Congruential generator, Blum-Blum-Shub generator, the generator based on RSA cryptosystem and the generator based on the Discrete Logarithm problem. The computational experiments presented in our work attempt to assess the performance and the sensitivity of the examined generators.

Les contextes toujours plus variés et dynamiques dans lesquels les logiciels actuels s'exécutent leurs imposent de s'adapter de façon autonome à ces changements. L'objectif de cette thèse est de faciliter le développement de telles applications adaptatives, en considérant l'adaptation comme un aspect qui doit être développé séparément du reste de l'application a fin de pouvoir y être intégré et modifié dynamiquement. Pour cela nous proposons Safran, une extension du modèle de composants Fractal permettant d'associer dynamiquement des politiques d'adaptation aux composants d'une application. Ces politiques sont programmées dans un langage dédié sous la forme de règles réactives. Leur exécution repose d'une part sur WildCAT, un système permettant de détecter les évolutions du contexte d'exécution (quand adapter ?), et d'autre part sur FScript, un langage dédié pour la reconfiguration dynamique consistante de composants Fractal (comment adapter ?).

Mémoire numérisé par la Division de la gestion de documents et des archives de l'Université de Montréal

This dissertation analyzes the spatial distribution and kinematics of the Late Cenozoic Basin and Range (BR) and cross normal fault (CF) systems and their related graben basins around the Snake River Plain (SRP), and investigates the spatio-temporal patterns of lavas that were erupted by the migrating Yellowstone hotspot along the SRP, applying a diverse set of GIS-based spatial statistical techniques. The spatial distribution patterns of the normal fault systems, revealed by the Ripley's K-function, display clustered patterns that correlate with a high linear density, maximum azimuthal variation, and high box-counting fractal dimensions of the fault traces. The extension direction for normal faulting is determined along the major axis of the fractal dimension anisotropy ellipse measured by the modified Cantor dust method and the minor axis of the autocorrelation anisotropy ellipse measured by Ordinary Kriging, and across the linear directional mean (LDM) of the fault traces. Trajectories of the LDMs for the cross faults around each caldera define asymmetric sub-parabolic patterns similar to the reported parabolic distribution of the epicenters, and indicate sub-elliptical extension about each caldera that may mark the shape of hotspot’s thermal doming that formed each generation of cross faults. The decrease in the spatial density of the CFs as a function of distance from the axis of the track of the hotspot (SRP) also suggests the role of the hotspot for the formation of the cross faults. The parallelism of the trend of the exposures of the graben filling Sixmile Creek Formation with the LDM of their bounding cross faults indicates that the grabens were filled during or after the CF event. The global and local Moran’s I analyses of Neogene lava in each caldera along the SRP reveal a higher spatial autocorrelation and clustering of rhyolitic lava than the coeval basaltic lava in the same caldera. The alignment of the major axis of the standard deviational ellipses of lavas with the trend of the eastern SRP, and the successive spatial overlap of older lavas by progressively younger mafic lava, indicate the migration of the centers of eruption as the hotspot moved to the northeast.

This thesis introduces efficient numerical techniques for the analysis of novel electromagnetic metamaterials. The modelling is based on a Method of Moments modal analysis in conjunction with an interpolation scheme, which significantly accelerates the computations. Triangular basis functions are used that allow for modelling of arbitrary shaped metallic elements. Unlike the conventional methods, impedance interpolation is applied to derive the dispersion characteristics of planar periodic structures. With these techniques, the plane wave and the surface wave responses of fractal structures have been studied by means of transmission coefficients and dispersion diagrams. The multiband properties and the compactness of the proposed structures are presented. Based on this method, novel planar left-handed metamaterials are also proposed. Verifications of the left-handedness are presented by means of full wave simulation of finite planar arrays using commercial software and lab measurement. The structures are simple, readily scalable to higher frequencies and compatible with low-cost fabrication techniques.

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 existieren. / In 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.

[Formulae and special characters can only be approximated here. Please see the pdf version of the abstract for an accurate reproduction.] The formation of world-class Archean orogenic gold deposits in the Eastern Goldfields Province of Western Australia was the result of a critical combination of physical and chemical processes that modified a single and widespread ore-fluid along fluid pathways and at the sites of gold deposition. Increased gold endowment in these deposits is associated with efficient regional-scale fluid focusing mechanisms and the influence of multiple ore-depositional processes at the deposit-scale. Measurement of the complexity of geologic features, as displayed in high-quality geologic maps of uniform data density, can be used to highlight areas that influence regional-scale hydrothermal fluid flow. Useful measurements of geological complexity include fractal dimensions of map patterns, density and orientation of faults and lithologic contacts, and proportions of rock types. Fractal dimensions of map patterns of lithologic contacts and faults highlight complexity gradients. Steep complexity gradients, between domains of high and low fractal dimensions within a greenstone belt, correspond to district-scale regions that have the potential to focus the flow of large volumes of hydrothermal fluid, which is critical for the formation of significant orogenic gold mineralization. Steep complexity gradients commonly occur in greenstone belts where thick sedimentary units overly more complex patterns of lithologic contacts, associated with mafic intrusive and mafic volcanic units. The sedimentary units in these areas potentially acted as seals to the hydrothermal Mineral Systems, which resulted in fluid-pressure gradients and increased fluid flow. The largest gold deposits in the Kalgoorlie Terrane and the Laverton Tectonic Zone occur at steep complexity gradients adjacent to thick sedimentary units, indicating the significance of these structural settings to gold endowment. Complexity gradients, as displayed in surface map patterns, are an indication of three-dimensional connectivity along fluid pathways, between fluid source areas and deposit locations. Systematic changes in the orientation of crustal-scale shear zones are also significant and measurable map features. The largest gold deposits along the Bardoc Tectonic Zone and Boulder-Lefroy Shear Zone, in the Eastern Goldfields Province, occur where there are counter-clockwise changes in shear zone orientation, compared to the average orientation of the shear zone along its entire length. Sinistral movement along these shear zones resulted in the formation of district-scale dilational jogs and focused hydrothermal fluid-flow at the Golden Mile, New Celebration and Victory-Defiance deposits. Faults and lithologic contacts are the dominant fluid pathways in orogenic gold Mineral Systems, and measurements of the density of faults and contacts are also a method of quantifying the complexity of geologic map patterns on high-quality maps. Significantly higher densities of pathways in areas surrounding larger gold deposits are measurable within 20- and 5-kilometer search radii around them. Large variations in the sulfur isotopic composition of ore-related pyrites in orogenic gold deposits in the Eastern Goldfields Province are the result of different golddepositional mechanisms and the in-situ oxidation of a primary ore fluid in specific structural settings. Phase separation and wall-rock carbonation are potentially the most common mechanisms of ore-fluid oxidation and gold precipitation. The influence of multiple gold-depositional mechanisms increases the potential for significant ore-fluid oxidation, and more importantly, provides an effective means of increasing gold endowment. This explains the occurrence of negative δ34S values in ore-related pyrites in some world-class orogenic gold deposits. Sulfur isotopic compositions alone cannot uniquely define potential gold endowment. However, in combination with structural, hydrothermal alteration and fluid inclusion studies that also seek to identify multiple ore-forming processes, they can be a useful indicator. The structural setting of a deposit is also a potentially important factor controlling ore-fluid oxidation and the distribution of δ34S values in ore-related pyrites. At Victory-Defiance, the occurrence of negative δ34S(py) values in gently-dipping dilational structures, compared to more positive δ34S(py) values in steeply-dipping compressional structures, is potentially associated with different gold-depositional mechanisms that developed as a result of fluid-pressure fluctuations during different stages of the fault-valve cycle. During the pre-failure stage, when fluids are discharging from faults, fluid-rock interaction is the dominant gold-depositional mechanism. Phase separation and back-mixing of modified ore-fluid components are dominant during and immediately after faulting. Under appropriate conditions, any, or all, of these three mechanisms can oxidize orogenic gold fluids and cause gold deposition. The influence of multiple gold-depositional mechanisms during fault-valve cycles at dilational jogs, where fluid pressure fluctuations are interpreted to be most severe, can potentially explain both the large gold endowment of the giant to world-class Golden Mile, New Celebration and Victory-Defiance deposits along the Boulder-Lefroy Shear Zone, and the presence of gold-related pyrites with negative δ34S values in these deposits. This study highlights the interplay that exists between physical and chemical processes in orogenic gold Mineral Systems, during the transport of ore fluids in pathways from original fluid reservoirs to deposit sites. Potentially, a single and widespread orogenic ore-fluid could become oxidized, and lead to the formation of ore-related sulfides with variable sulfur isotopic compositions, depending on the nature and orientation of major fluid pathways, the nature of wall-rocks through which it circulates, and the precise ore-depositional processes that develop during fault-valve cycles.

Submitted by Ronildo Prado (ronisp@ufscar.br) on 2017-08-10T20:03:05Z No. of bitstreams: 1 DissVCZ.pdf: 2645955 bytes, checksum: 705c14ce02c3cbf785699b4d10919a28 (MD5) / Approved for entry into archive by Ronildo Prado (ronisp@ufscar.br) on 2017-08-10T20:03:12Z (GMT) No. of bitstreams: 1 DissVCZ.pdf: 2645955 bytes, checksum: 705c14ce02c3cbf785699b4d10919a28 (MD5) / Approved for entry into archive by Ronildo Prado (ronisp@ufscar.br) on 2017-08-10T20:03:18Z (GMT) No. of bitstreams: 1 DissVCZ.pdf: 2645955 bytes, checksum: 705c14ce02c3cbf785699b4d10919a28 (MD5) / Made available in DSpace on 2017-08-10T20:03:29Z (GMT). No. of bitstreams: 1 DissVCZ.pdf: 2645955 bytes, checksum: 705c14ce02c3cbf785699b4d10919a28 (MD5) Previous issue date: 2017-01-23 / Não recebi financiamento / The aim of this paper is to develop a didactic sequence exploring practical activities that will help students in the teaching-learning process of the concepts of sequences, geometric progressions and logarithms, which are included in the school curriculum of the first year of high school. In this sequence we will propose practical activities in the teacher's lesson plan and will work on the mathematics contained in them. We will also report how the activities were applied, how the students participated, the concerns that arose and some considerations that can be made for improving the activity. Subsequently, we chose some questions that have appeared in the OBMEP and ENEM tests in previous years that involve content included in the activities and which may complement the activities. / O objetivo principal deste trabalho é desenvolver uma sequência didática explorando atividades práticas que auxilie os alunos no processo de ensino-aprendizagem dos conceitos de sequências, progressões geométricas e logaritmos, que constam no currículo da 1ª Série do Ensino Médio. Nesta sequência propomos atividades práticas em Fichas do Aluno e trabalhamos a matemática presente nelas. Relatamos como foi a aplicação das atividades, como foi a participação dos alunos, quais as dúvidas que surgiram e algumas considerações que podem ser feitas para aprimorar a atividade. Posteriormente selecionamos algumas questões que constam nas provas da OBMEP e do Enem nos anos anteriores que envolvem conteúdos que constam nas atividades e podem complementar as atividades.

Orientador: Ali Messaoudi / Banca: Vanderlei Minori Horita / Banca: Daniel Smania Brandão / Banca: Christian Mauduit / Banca: Glauco Valle da Silva Coelho / Resumo: Em 2000, Killeen e Taylor definiram a máquina de somar estocástica em base 2. Eles mostraram que o espectro do op erador de transi cão (agindo em l∞( N)), associado a essa máquina, e igual ao conjunto de Julia cheio de uma função quadrática. Nesse trabalho, estudamos outras propriedades espectrais e topológicass da máquina de Killeen e Taylor, e também das suas extensões à l∞(Z) e a outras bases não constantes. Esse estudo envolve conjuntos de Julia de funções quadráticas e também conjuntos de Julia cheios de endomor smos de C2 . Finalmente estudamos algumas propriedades aritméticas e topológicas de uma classe de fractais de Rauzy. Em particular estudamos o azulejamento periódico do plano complexo C induzido por eles. / Abstract: In 2000, Killeen and Taylor de ned the sto hastic adding machine in base 2. They proved that the sp ectrum of the transition op erator (acting in l∞(N )) asso ciated to this machine is equal to the lled Julia set of a quadratic polynomial map. In this work, we study other sp ectral and top ological prop erties of Killeen and Taylor machine, and also of its extensions to l∞( Z) and to other non constant bases. This study envolves Julia sets of quadratic maps and also lled Julia sets of endomorphisms of C2 . Finally we study some arithmetical and topological prop erties of a class of Rauzy fractals. In particular we study the p erio dictiling of complex plane C induced by this class. / Doutor