Dans ce travail, nous nous sommes intéressés à l'étude asymptotique d'objets combinatoires aléatoires. Deux thèmes ont particulièrement retenu notre attention : les cartes planaires aléatoires et les modèles combinatoires liés à la théorie des fragmentations. La théorie mathématique des cartes planaires aléatoires est née à l'aube de notre millénaire avec les travaux pionniers de Benjamini & Schramm, Angel & Schramm et Chassaing & Schaeffer. Elle a ensuite beaucoup progressé, mais à l'heure où ces lignes sont écrites, de nombreux problèmes fondamentaux restent ouverts. Résumons en quelques mots clés nos principales contributions dans le domaine : l'introduction et l'étude du cactus brownien (avec J.F. Le Gall et G. Miermont), l'étude de la quadrangulation infinie uniforme vue de l'infini (avec L. Ménard et G. Miermont), ainsi que des travaux plus théoriques sur les graphes aléatoires stationnaires d'une part et les graphes empilables dans $\R^d$ d'autre part (avec I. Benjamini). La théorie des fragmentations est beaucoup plus ancienne et remonte à des travaux de Kolmogorov (1941) et de Filippov (1961). Elle est maintenant bien développée (voir par exemple l'excellent livre de J. Bertoin), et nous ne nous sommes pas focalisés sur cette théorie mais plutôt sur ses applications à des modèles combinatoires. Elle s'avère en effet très utile pour étudier différents modèles de triangulations récursives du disque (travail effectué avec J.F. Le Gall) et les recherches partielles dans les quadtrees (travail effectué avec A. Joseph). / The subject of this thesis is the asymptotic study of large random combinatorial objects. This is obviously very broad, and we focused particularly on two themes: random planar maps and their limits, and combinatorial models that are in a way linked to fragmentation theory. The mathematical theory of random planar maps is quite young and was triggered by works of Benjamini & Schramm, Angel & Schramm and Chassaing & Schaeffer. This fascinating field is still growing and fundamental problems remain unsolved. We present some new results in both the scaling limit and local limit theories by introducing and studying the Brownian Cactus (with J.F. Le Gall and G. Miermont), giving a new view point, a view from infinity, at the Uniform Infinite Planar Quadrangulation (UIPQ) and bringing more theoretical contributions on stationary random graphs and sphere packable graphs (with I. Benjamini). Fragmentation theory is much older and can be tracked back to Kolmogorov and Filippov. Our goal was not to give a new abstract contribution to this well-developed theory (see the beautiful book of J. Bertoin) but rather to apply it to random combinatorial objects. Indeed, fragmentation theory turned out to be useful in the study of the so-called random recursive triangulations of the disk (joint work with J.F. Le Gall) and partial match queries in random quadtrees (joint work with A. Joseph).

Cette thèse est consacrée aux systèmes dynamiques holomorphes en dimension complexe 2, et à la théorie des courants laminaires, qui en est issue. Nous étudions la dynamique d'une classe d'applications holomorphes, introduites par Hubbard et Oberste-Vorth, non nécessairement rationnelles, définies au voisinage du bidisque unité, qui sont aux applications de Hénon complexes ce que les applications d'allure polynomiale sont aux polynômes d' une variable. Nous montrons pour ces applications un certain nombre de propriétés dynamiques analogues à celles des difféomorphismes polynomiaux, établies notamment par Bedford, Lyubich, Smillie, Fornæ ss et Sibony: existence de courants positifs fermés invariants ``attractifs'', ainsi que d'une unique mesure d'entropie maximale, décrivant la répartition des points périodiques de type selle. Les courants laminaires, généralisation des ``cycles feuilletés'' de Sullivan, ont été introduits par Bedford, Lyubich et Smillie dans le cadre de l'étude des difféomorphismes polynomiaux de deux variables. Nous développons une théorie générale de ces courants. Premièrement nous donnons un critère géométrique portant sur une suite de courbes planes algébriques de degré tendant vers l'infini pour que ses valeurs d'adhérence au sens des courants soient laminaires, et en déduisons la laminarité du courant dynamique ``de Green'' pour une classe d'applications rationnelles du plan projectif, incluant celle des applications birationnelles. Pour les courants obtenus par ce procédé, nous montrons que l'on peut donner, sous une hypothèse de nature potentialiste, une interprétation géométrique au produit extérieur; nous montrons également que ces courants satisfont une propriété de ``prolongement analytique''. Ceci nous permet de réaliser ces courants comme cycles feuilletés sur une lamination abstraite.

Pulsed-neutron borehole measurements involve a physical process in which a source emits energetic neutrons that lose energy upon collisions with formation nuclei, and are eventually captured by a nucleus to form a heavier, excited state. The excited nucleus decays to its ground state by the emission of gamma rays. Both thermal-neutron and gamma-ray populations decay with time at a rate defined by Sigma, which is a nuclear property that quantifies a material’s ability to capture thermal neutrons. The large contrast in Sigma between hydrocarbon and salty connate water enables calculations of water saturation directly from pulsed-neutron measurements. Sigma logs have proven useful in the assessment of thinly bedded formations because they exhibit a small volume of investigation, and have been deemed superior to resistivity logs in the petrophysical evaluation of carbonate formations. The recognized potential of Sigma logs in formation evaluation initiated the development of multi-detector Logging-While-Drilling (LWD) Sigma measurements. These measurements are acquired using one thermal-neutron and two gamma-ray detectors at different spacings from the source. Such a design is aimed at providing distinct radial depths of investigation to detect filtrate invasion in the near-wellbore zone. Despite their formation-evaluation potential, multi-detector time-decay measurements commonly remain affected by invasion, shoulder-bed, and well-deviation effects. The purpose of this dissertation is to develop a fast-forward simulation method to reproduce multi-detector time decays and combine the method with inversion techniques to improve the petrophysical interpretation of LWD Sigma measurements. First-order perturbation theory and a library of pre-calculated Monte Carlo detector-specific sensitivity functions and time decays are used to numerically simulate borehole Sigma measurements in realistic logging environments. The new simulation method is one hundred thousand times faster than rigorous Monte Carlo calculations and remains within two capture units of disparity. Next, the fast-forward simulation method is embedded within inversion algorithms to estimate layer-by-layer radial length of invasion and formation Sigma corrected for shallow invasion, shoulder-bed, and well-deviation effects. Both fast-forward and inverse modeling algorithms are benchmarked against laboratory and synthetic time decays. The improvement of formation Sigma obtained with inversion-based interpretation leads to an improvement in the estimation of Sigma-derived water saturation. Likewise, the estimated radial length of invasion is combined with neutron and density measurements to correct the latter for invasion effects. Results indicate that the inversion-based interpretation method is well suited for the evaluation of high-porosity formations invaded by salty mud filtrate. Inversion-based interpretation of field LWD time decays enables the estimation of lower values of water saturation when compared to conventional Sigma interpretation or resistivity methods. Estimated values of water saturation are as much as fifty percent lower than predicted by conventional interpretation of Sigma logs in the case of measurements affected by shoulder-bed effects, and as much as one hundred percent lower than predicted by the conventional interpretation method for measurements additionally affected by salty filtrate invasion. The key attributes of the combined petrophysical interpretation of multi-detector Sigma, neutron, and density measurements developed in this dissertation are that it explicitly enforces the physics of all nuclear measurements, honors the pressure and temperature dependency of reservoir fluid nuclear properties, and takes into account a-priori information such as mud-filtrate salinity, connate-water salinity, and bed-boundary locations. / text

Cette thèse est consacrée à l'étude de quelques problèmes en dynamique holomorphe discrete et continue à l'aide de la Théorie du Pluripotentiel. Le premier problème présenté concerne la description des paires d'endomorphismes holomorphes permutables du plan projectif complexe qui ne partagent pas une itérée. Nous nous intéressons au cas où les degrés des deux applications coïncident après un certain nombre d'itérations. Nous montrons que telles applications sont des exemples de Lattès ou bien des relèvements des exemples de Lattès unidimensionnels. Combiné avec un théorème de T.-C. Dinh et N. Sibony ce résultat complète la classification des paires permutables en dimension deux. Ensuite, nous nous intéressons à la dynamique des laminations par variétés complexes. Nous montrons que, dans une variété kählérienne compacte, le carré de la classe de cohomologie d'un cycle feuilleté dirigé par une lamination transversalement Lipschitz est toujours zéro. Parmi les conséquences nous montrons que l'espace projectif complexe $\pr^{n}$ n'admet pas de cycle feuilleté transversalement Lipschitz de dimension $q \leq \frac{n}{2}$. Cela généralise un résultat de J.E. Forn\ae ss et N. Sibony. Dans la dernière partie nous étudions les mesures de Monge-Ampère à potentiel höldérien. Nous montrons que ces mesures satisfont un analogue d'un théorème de H. Skoda concernant l'intégrabilité exponentielle d'une fonction plurisousharmonique en termes de ses nombres de Lelong. Ce résultat peut être vu comme une très forte compacité pour les fonctions plurisousharmoniques qui sont eux-mêmes un outil fondamental en dynamique holomorphe. / This thesis is devoted to the study of some problems in discrete and continuous holomorphic dynamics with the tools of Pluripotential Theory. The first problem we consider involves the description of commuting pairs of holomorphic endomorphisms of the complex projective plane that do not share an iterate. We consider the case when their degrees coincide after some number of iterations. We show that these maps are either Lattès maps or lifts of one-dimensional Lattès maps. Together with a theorem of T.-C. Dinh and N. Sibony this result completes the classification of commuting pairs in dimension two. Later on, we turn our attention to the dynamics of laminations by complex manifolds. We show that, on a compact Kähler manifold, the square of the cohomology class of a foliated cycle directed by a transversally Lipschitz lamination is always zero. As a corollary we show that the complex projective space $\pr^n$ do not carry any transversally Lipschitz foliated cycle of dimension $q \leq \frac{n}{2}$, generalizing a result by J.E. Forn\ae ss and N. Sibony. In the last part we study Monge-Ampère measures with Hölder continuous potential. We show that these measures satisfy an analogue of a theorem of H. Skoda concerning the exponential integrability of plurisubharmonic functions in terms of its Lelong numbers. This result can be viewed as a strong compactness property of plurisubharmonic functions, a class of functions of fundamental importance in holomorphic dynamics.

[pt] Automorfismos genéricos de cubos com alças (handlebodies) aparecem do estudo de classes the isotopia de automorfismos de variedades orientáveis de dimensão três. Automorfismos genéricos permanecem como uma das partes menos entendidas desse estudo.Dado um automorfismo genérico de um cubo com alças, é conhecida uma forma de se construir uma laminação bidimensional que é invariante pelo automorfismo. A essa laminação se associa um fator de crescimento. É sabido que, no caso de tal fator de crescimento ser minimal - uma característica importante, pois mede a complexidade essencial do automorfismo - a laminação deve gozar de uma certa propriedade de incompressibilidade. Nessa tese mostramos que o processo de se achar uma laminação com tal propriedade é algoritmico. Por outro lado, mostramos que tal propriedade não garante que o respectivo fator de crescimento seja minimal. Propomos uma outra propriedade, tensão transversal, mais forte que incompressibilidade, que conjecturamos também ser condição necessária para que o fator de crescimento seja minimal. Provamos a conjectura em alguns casos.Além dos resultados mencionados acima, desenvolvemos métodos para gerar automorfismos genéricos de cubos com alcas, que usamos para apresentar alguma variedade de exemplos. / [en] Generic automorphisms of handlebodies appear naturally in the study of isotopy classes of automophisms of orientable three-dimensional manifolds. Generic automorphisms remain as one of the least understood parts of this study. Given a generic automorphism of a handlebody one can construct a bidimensional lamination that is invariant under the automorphism. There is a growth rate associated to this lamination. It is known that, when this growth rate is minimal among all possible choices (an important property, for it measures the essential complexity of the automorphism), the lamination must have a certain incompressibility property. On this thesis we show that the process of finding a lamination with such a property is algorithmic. On the other hand, we show that this said incompressibility property is not sufficient for the minimality of the growth rate. We propose a stronger property, which we called transverse tightness, and conjecture that it is a necessary condition for the growth rate to be minimal. We prove the conjecture in some particular cases. In addition to the results mentioned above, we develop methods to generate generic automorphisms of handlebodies, which we use to present some variety of examples.

The McTronX research group at the North–West University designs and develops Active Magnetic Bearings (AMBs). The group’s focus shifted to the design and development of AMB supported drive systems. This includes the electromagnetic and mechanical design of the electric machine, AMBs, auxiliary bearings as well as the development of the control system. The research group is currently developing an AMB supported high speed Induction Machine (IM) drive system that will facilitate tests in order to verify the design capability of the group. The research presented in this thesis describes the mechanical design and manufacturing of a high speed IM rotor section. The design includes; selecting the IM rotor topology, material selection, detail stress analysis and selecting appropriate manufacturing and assembly procedures. A comprehensive literature study identifies six main design considerations during the mechanical design of a high speed IM rotor section. These considerations include; magnetic core selection, rotor cage design, shaft design, shaft/magnetic core connection, stress due to operation at elevated temperatures and design for manufacture and assemble (DFMA). A critical overview of the literature leads to some design decisions being made and is used as a starting point for the detail design. The design choices include using a laminated cage rotor with a shrink fit for the shaft/magnetic core connection. Throughout the detail design an iterative process was followed incorporating both electromagnetic and mechanical considerations to deliver a good design solution. The first step of the iterative design process was, roughly calculating the material strengths required for first iteration material selection followed by more detailed interference fit calculations. From the detail stress analysis it became apparent that the stress in the IM rotor section cannot be calculated accurately using analytical methods. Consequently, a systematically verified and validated Finite Element Analysis (FEA) model was used to calculate the interferences required for each component. The detail stress analysis of the assembly also determined the allowable manufacturing dimensional tolerances. From the detail stress analysis it was found that the available lamination and squirrel cage material strengths were inadequate for the design speed specification of 27,000 r/min. The analysis showed that a maximum operating speed of 19,000 r/min can be achieved while complying with the minimum factor of safety (FOS) of 2. Each component was manufactured to the prescribed dimensional tolerances and the IM rotor section was assembled. With the failure of the first assembly process, machine experts were consulted and a revised process was implemented. The revised process entailed manufacturing five small lamination stacks and assembling the stack and squirrel cage afterwards. The end ring/conductive bar connection utilises interference fits due to the fact that the materials could not be welded. The process was successful and the IM rotor section was shrink fitted onto the shaft. However, after final machining of the rotor’s outer diameter (OD), inspections revealed axial displacement of the end rings and a revised FEA was implemented to simulate the effect. The results indicated a minimum FOS 0.6 at very small sections and with further analytical investigation it was shown that the minimum FOS was reduced to only 1.34. Although the calculations indicated the FOS was below the minimum prescribed FOS ? 2, the rotor spin tests were scheduled to continue as planned. The main reasons being that the lowest FOS is at very small areas and is located at non critical structural positions. The fact that the rotor speed was incrementally increased and multiple parameters were monitored, which could detect early signs of failure, further supported the decision. In testing the rotor was successfully spun up to 19,000 r/min and 27 rotor delevitation test were conducted at speeds of up to 10,000 r/min. After continuous testing a secondary rotor inspection was conducted and no visible changes could be detected. The lessons learnt leads to mechanical design and manufacturing recommendations and the research required to realise a 27,000 r/min rotor design. / Thesis (M.Ing. (Mechanical Engineering))--North-West University, Potchefstroom Campus, 2011.

The McTronX research group at the North–West University designs and develops Active Magnetic Bearings (AMBs). The group’s focus shifted to the design and development of AMB supported drive systems. This includes the electromagnetic and mechanical design of the electric machine, AMBs, auxiliary bearings as well as the development of the control system. The research group is currently developing an AMB supported high speed Induction Machine (IM) drive system that will facilitate tests in order to verify the design capability of the group. The research presented in this thesis describes the mechanical design and manufacturing of a high speed IM rotor section. The design includes; selecting the IM rotor topology, material selection, detail stress analysis and selecting appropriate manufacturing and assembly procedures. A comprehensive literature study identifies six main design considerations during the mechanical design of a high speed IM rotor section. These considerations include; magnetic core selection, rotor cage design, shaft design, shaft/magnetic core connection, stress due to operation at elevated temperatures and design for manufacture and assemble (DFMA). A critical overview of the literature leads to some design decisions being made and is used as a starting point for the detail design. The design choices include using a laminated cage rotor with a shrink fit for the shaft/magnetic core connection. Throughout the detail design an iterative process was followed incorporating both electromagnetic and mechanical considerations to deliver a good design solution. The first step of the iterative design process was, roughly calculating the material strengths required for first iteration material selection followed by more detailed interference fit calculations. From the detail stress analysis it became apparent that the stress in the IM rotor section cannot be calculated accurately using analytical methods. Consequently, a systematically verified and validated Finite Element Analysis (FEA) model was used to calculate the interferences required for each component. The detail stress analysis of the assembly also determined the allowable manufacturing dimensional tolerances. From the detail stress analysis it was found that the available lamination and squirrel cage material strengths were inadequate for the design speed specification of 27,000 r/min. The analysis showed that a maximum operating speed of 19,000 r/min can be achieved while complying with the minimum factor of safety (FOS) of 2. Each component was manufactured to the prescribed dimensional tolerances and the IM rotor section was assembled. With the failure of the first assembly process, machine experts were consulted and a revised process was implemented. The revised process entailed manufacturing five small lamination stacks and assembling the stack and squirrel cage afterwards. The end ring/conductive bar connection utilises interference fits due to the fact that the materials could not be welded. The process was successful and the IM rotor section was shrink fitted onto the shaft. However, after final machining of the rotor’s outer diameter (OD), inspections revealed axial displacement of the end rings and a revised FEA was implemented to simulate the effect. The results indicated a minimum FOS 0.6 at very small sections and with further analytical investigation it was shown that the minimum FOS was reduced to only 1.34. Although the calculations indicated the FOS was below the minimum prescribed FOS ? 2, the rotor spin tests were scheduled to continue as planned. The main reasons being that the lowest FOS is at very small areas and is located at non critical structural positions. The fact that the rotor speed was incrementally increased and multiple parameters were monitored, which could detect early signs of failure, further supported the decision. In testing the rotor was successfully spun up to 19,000 r/min and 27 rotor delevitation test were conducted at speeds of up to 10,000 r/min. After continuous testing a secondary rotor inspection was conducted and no visible changes could be detected. The lessons learnt leads to mechanical design and manufacturing recommendations and the research required to realise a 27,000 r/min rotor design. / Thesis (M.Ing. (Mechanical Engineering))--North-West University, Potchefstroom Campus, 2011.

Gromov’s compactness theorem for metric spaces, a compactness theorem for the space of compact metric spaces equipped with the Gromov-Hausdorff distance, is a theorem with many applications. In this thesis, we give a generalisation of this landmark result, more precisely, we give a compactness theorem for the space of distance measure spaces equipped with the generalised Gromov-Hausdorff-Levi-Prokhorov distance. A distance measure space is a triple (X, d,µ), where (X, d) forms a distance space (a generalisation of a metric space where, we allow the distance between two points to be infinity) and µ is a finite Borel measure. Using this result we prove that the Deligne-Mumford compactification is the completion of the moduli space of Riemann surfaces under the generalised Gromov-Hausdorff-Levi-Prokhorov distance. The Deligne-Mumford compactification, a compactification of the moduli space of Riemann surfaces with explicit description of the limit points, and the closely related Gromov compactness theorem for J-holomorphic curves in symplectic manifolds (in particular curves in an algebraic variety) are important results for many areas of mathematics. While Gromov compactness theorem for J-holomorphic curves in symplectic manifolds, is an important tool in symplectic topology, its applicability is limited by the lack of general methods to construct pseudo-holomorphic curves. One hopes that considering a more general class of objects in place of pseudo-holomorphic curves will be useful. Generalising the domain of pseudo-holomorphic curves from Riemann surfaces to Riemann surface laminations is a natural choice. Theorems such as the uniformisation theorem for surface laminations by Alberto Candel (which is a partial generalisation of the uniformisation theorem for surfaces), generalisations of the Gauss-Bonnet theorem proved for some special cases, and topological classification of “almost all" leaves using harmonic measures reinforces the usefulness of this line on enquiry. Also, the success of essential laminations, as generalised incompressible surfaces, in the study of 3-manifolds suggests that a similar approach may be useful in symplectic topology. With this motivation, we prove a compactness theorem analogous to the Deligne-Mumford compactification for the space of Riemann surface laminations.

Despite their sudden growth in popularity, the role-playing actual-play podcasts have either been ignored or grouped with the genre of audio drama in prior scholarly works. Examination using frame analysis shows, however, that these podcasts are distinct in their engagement of the audience on multiple, simultaneous levels; levels which correspond with well-known media genres such as Documentary, Fiction, and Game Play. Each frame has its own layer of identities, conduct, and avenue for appealing to audiences just as these genres have their own distinct appeals. Through the combinations of these frames, familiar tropes and techniques such as Short-Form Improv and Campbell's monomyth are broadened and challenged, and identities become entangled in this post-modern medium. Delineating the features of these frames and exploring their interactions and interconnectivity not only helps to distinguish the actual-play podcast as its own distinct podcast genre, but also highlights the potential for using such frames or frame analysis in other media forms.

Cette thèse s’inscrit dans le cadre des études des phénomènes électromagnétiques dansles régions frontales des grands turbo-générateurs. L’objectif de la thèse est d’estimer apriori le champ magnétique axial en fonction du point de fonctionnement afin d’éviterles possibles dégradations du circuit magnétique (dus aux points chauds et tensions entretôles, qui sont liés à la composante axiale du champ).Une maquette à échelle réelle a été spécialement conçue et réalisée dans le but d’améliorerla compréhension physique des phénomènes : les pertes, la pénétration du champ magnétiqueet les tensions entre tôles sont analysés.Les simulations par éléments finis sont ensuite utilisées : les avantages et inconvénientsseront discutés, ainsi qu’une comparaison critique des résultats par rapport aux mesuresexpérimentales sur la maquette. La région frontale d’un turbo-alternateur est aussi entièrementmodélisée.Enfin, un modèle simple du flux axial est développé. Ses coefficients sont déterminés àl’aide de simulations par éléments finis, mais il peut ensuite être utilisé en temps réel afind’estimer le flux axial correspondant à un point de fonctionnement quelconque. / This work aims to improve the knowledge of electromagnetic phenomena that occurin the end region of large turbo-generators. The goal of this work is to evaluate theaxial magnetic flux density with regard to the operating conditions (such as active orreactive power) in order to prevent potential deterioration of the stator. Indeed, the axialmagnetic field is known to induce hot points or voltages between laminations that maycause insulation breakdown and thus stator faults.An experimental apparatus in real scale has been designed and built. Its purpose is tostudy precisely the following phenomena: losses, axial magnetic flux density penetration,voltage across adjacent voltages.Finite element simulations (FEM) are also used: their advantages and drawbacks arediscussed, and the results are compared with the experimental measures. The wholeend-region of a turbo-generator is also simulated.Finally, a simple model of the axial magnetic flux is proposed. Its parameters are basedon the results of the FEM model, but it may be used in real time to evaluate the axialmagnetic flux density of any operating point.