L'objectif de la thèse est l'étude des propriétés géométriques des ensembles définissables dans les structures o-minimales et de ses applications. Il existe trois principaux résultats présentés dans cette thèse. Le premier est une preuve géométrique de l'existence de stratifications vérifiant les conditions (a) et (b) de Whitney d'ensembles définissables. Ce résultat fut d'abord prouvé par T. L. Loi en 1994 par une autre méthode. Le second est une preuve de l'existence de stratifications de Lipschitz (dans le sens de Mostowski) pour les ensembles définissables dans une structure o-minimale polynomialement bornée. Ceci est une généralisation de résultats de Parusin'ski en 1994 pour les ensembles sous-analytiques. Le troisième résultat est au sujet de la continuité des variations de géométrie intégrale appelées courbures de Lipschitz Killing locales, qui ont été introduites par A. Bernig et L. Broker en 2002. Nous prouvons que les courbures de Lipschitz Killing locales sont continues le long de strates de stratifications de Whitney d'ensembles définissable dans une structure o-minimale polynomialement bornée, et si les stratifications sont (w) régulières alors les courbures de Lipschitz Killing locales sont localement lipschitziennes le long des strates. / The thesis focus on study geometric properties of definable sets in o-minimal structures and its applications. There are three main results presented in this thesis. The first is a geometric proof of the existence of Whitney (a) and (b)-regular stratifications of definable sets. The result was initially proved by T. L. Loi in 1994 by using another method. The second is a proof of existence of Lipschitz stratifications (in the sense of Mostowski) of definable sets in a polynomially bounded o-minimal structure. This is a generalization of Parusinski's 1994 result for subanalytic sets. The third result is about the continuity of of variations of integral geometry called local Lipschitz Killing curvatures which were introduced by A. Bernig and L. Broker in 2002. We prove that Lipschitz Killing curvatures are continuous along strata of Whiney stratifications of definable sets in a polynomially bounded o-minimal structure. Moreover, if the stratifications are (w)-regular the Lipspchitz Killing curvatures are locally Lipschitz.

Internal waves are generated in a fluid if the density increases continuously with depth. The variation in density with depth, or stratification, defines the natural frequency of the fluid N. Two common examples of stratified fluids are the ocean and atmosphere; internal waves are generated continuously in both mediums. Although there are many internal wave generation mechanisms, one common and frequently studied method is tidal flow over oceanic bathymetry. If the local natural frequency of the water near the topography is greater than the tidal frequencyω, internal waves will be generated by the tidal flow over the topography. If N=ω, only evanescent waves will be formed. Unlike internal waves, evanescent waves decay rapidly as they move vertically away from their generation site. As evanescent waves pass from an evanescent region (N=ω),through a turning depth (N=ω) and into a propagating region (N=ω), they become propagating internal waves. Because internal waves can propagate energy across large distances, they play an important role in oceanic mixing and the overall energy budget of the ocean. Knowing where these waves are formed from evanescent waves and their corresponding energy improves understanding of the impact on their surrounding area.Kinetic energy density of evanescent and internal waves formed from oscillatory flow over topography in evanescent regions is first estimated using synthetic schlieren experiments and a novel linear theory model. Experiments were performed with two Gaussian topographies in an exponential density profile. The linear theory model, which uses a set of equations that links the evanescent and propagating regions with the Airy function to overcome the discontinuity inherent with a turning depth, was compared to the experiments. Both methods showed that increasing Fr1,the strength of the evanescent region relative to the excitation frequency, causes the propagating kinetic energy to decrease. In addition, kinetic energy decreased with increasing distance between the topography and the turning depth. Because the model does not account for non-linearities such as turbulence generation, it regularly overestimates propagating kinetic energy relative to the experiments. After comparing the model with synthetic schlieren experiments, it was used to estimate that 25% of the evanescent wave energy generated by an oceanic topography located at 15◦N, 130◦E can become propagating wave energy.The influence of topography shape and fluid density profile on kinetic energy density was also explored through a combination of experiments, a linear theory model, and numerical simulations. From numerical simulations, kinetic energy can be directly calculated with the velocity pro-file and indirectly with the density perturbation field, in the same manner as the synthetic schlieren experiments. Average propagating internal wave kinetic energy (KE∗ 2) as a function of Fr1D/H,which combines Fr1 with the relative distance between the topography and the turning depth D/H,was compared for all methods. KE∗ 2 decreases with increasing Fr1D/H for all methods. Also, far from the turning depth, the direct and indirect simulations indicate similar kinetic energy when in the propagating region, where a distance from the turning depth can be quantified based on N and ω. This work was expanded to include a medium Gaussian, steep Gaussian, sinusoidal, and complex topography with two layer linear, parabolic, cubic, and exponential density profiles to investigate the validity of assuming an average natural frequency in the evanescent region and the impact of the topographic slope on KE∗ 2. A comparison of the density profiles indicated that using a two layer linear density profile has similar results compared to the other density profiles for estimating KE∗ 2 as a function of Fr1D/H. Also, KE∗ 2 is non-negligible for Fr1D/H<4. Increasing the maximum slope of a topography shape decreases the kinetic energy of the generated internal waves, though it was found that the energy is dependent upon the actual shape of the topography as well.Particle image velocimetry (PIV) experiments were performed and compared to synthetic schlieren (SS). While SS experiments generally resulted in an overestimate of kinetic energy relative to the PIV results, the trends from each experimental method matched well. It is recommended that SS be used in regions away from turning depths, but that either are valid in the evanescent and propagating regions. PIV methods should be used when results near the turning depth or the topography are desired.

This thesis is on moduli spaces of complexes of sheaves and diagrams of such moduli spaces. The objects in these diagrams are constructed as geometric invariant theory quotients and the points in these quotients correspond to certain equivalence classes of complexes. The morphisms in these diagrams are constructed by taking direct sums with acyclic complexes. We then study the colimit of such a diagram and in particular are interested in studying the images of quasi-isomorphic complexes in the colimit. As part of this thesis we construct categorical quotients of a group action on unstable strata appearing in a stratification associated to a complex projective scheme with a reductive group action linearised by an ample line bundle. We study this stratification for a closed subscheme of a quot scheme parametrising quotient sheaves over a complex projective scheme and relate the Harder-Narasimhan types of unstable sheaves with the unstable strata in the associated stratification. We also study the stratification of a parameter space for complexes with respect to a linearisation determined by certain stability parameters and show that a similar result holds in this case. The objects in these diagrams are indexed by different Harder-Narasimhan types for complexes and are quotients of parameter schemes for complexes of this fixed Harder-Narasimhan type. This quotient is given by a choice of linearisation of the action and so the diagrams depend on these choices. We conjecture that these choices can be made so that for any quasi-isomorphism between complexes representing points in this diagram both complexes are identified in the colimit of this diagram.

This thesis traces the etymology of 'materialism' using a Foucauldian discourse analysis to bring to the fore the word's use as discursive mode of power. Through examining over 5000 texts, spanning across 400 years, I trace a line from the origins of materialism in philosophical thought of the Renaissance and Enlightenment eras to its uptake in American rhetoric and integration into the consumer behaviour literature. This approach leads to a reconceptualization of materialism. Commonly viewed in consumer studies as a measurable value, trait, or motive inherent in the consumer, I situate materialism as external to the consumer. The word's history, especially in consumer studies, demonstrates that it embodies moral condemnations. I find that accusations of materialism rise in discourses during moments of intense social dislocations. It is wielded by social groups as part of a play for status. In this analysis, concepts of power as per Foucault and social distinctions as per Bourdieu, are used to explain the motives residing behind the use of the word. These motives, which reflect sociocultural dynamics and geo-political agendas, manifest in the meanings attributed to 'materialism', and the directionality of the allegation. Thus I argue that 'materialism', at its essence, is an epithet used to advance or demobilise a set of interests. This is what I term, delegitimizing discourse - words used to debase other social groups. Studying 'materialism' as a case in point, I note that groups use delegitimizing discourse either an assimilative measure - rhetoric geared towards indoctrination - or as a defensive mechanism - rhetoric used to debase threatening elements and behaviours. It is hoped that this new perspective will encourage academics to be rethink their approach to studying materialism, or in the least, to be aware of what is being measured, and what moral judgements and interests they are perpetuating through their continued studies.

Thesis (MScEng)--Stellenbosch University, 2013. / ENGLISH ABSTRACT: An accurate description of the atmospheric boundary layer (ABL) is a prerequisite for computational fluid dynamic (CFD) wind studies. This includes taking into account the thermal stability of the atmosphere, which can be stable, neutral or unstable, depending on the nature of the surface fluxes of momentum and heat. The diurnal variation between stable and unstable conditions in the Namib Desert interdune was measured and quantified using the wind velocity and temperature profiles that describe the thermally stratified atmosphere, as derived by Monin- Obukhov similarity theory. The implementation of this thermally stratified atmosphere into CFD has been examined in this study by using Reynoldsaveraged Navier-Stokes (RANS) turbulence models. The maintenance of the temperature, velocity and turbulence profiles along an extensive computational domain length was required, while simultaneously allowing for full variation in pressure and density through the ideal gas law. This included the implementation of zero heat transfer from the surface, through the boundary layer, under neutral conditions so that the adiabatic lapse rate could be sustained. Buoyancy effects were included by adding weight to the fluid, leading to the emergence of the hydrostatic pressure field and the resultant density changes expected in the real atmosphere. The CFD model was validated against measured data, from literature, for the flow over a cosine hill in a wind tunnel. The standard k-ε and SST k-ω turbulence models, modified for gravity effects, represented the data most accurately. The flow over an idealised transverse dune immersed in the thermally stratified ABL was also investigated. It was found that the flow recovery was enhanced and re-attachment occurred earlier in unstable conditions, while flow recovery and re-attachment took longer in stable conditions. It was also found that flow acceleration over the crest of the dune was greater under unstable conditions. The effect of the dune on the flow higher up in the atmosphere was also felt at much higher distances for unstable conditions, through enhanced vertical velocities. Under stable conditions, vertical velocities were reduced, and the influence on the flow higher up in the atmosphere was much less than for unstable or neutral conditions. This showed that the assumption of neutral conditions could lead to an incomplete picture of the flow conditions that influence any particular case of interest. / AFRIKAANSE OPSOMMING: 'n Akkurate beskrywing van die atmosferiese grenslaag (ABL) is 'n voorvereiste vir wind studies met berekenings-vloeimeganika (CFD). Dit sluit in die inagneming van die termiese stabiliteit van die atmosfeer, wat stabiel, neutraal of onstabiel kan wees, afhangende van die aard van die oppervlak vloed van momentum en warmte. Die daaglikse variasie tussen stabiele en onstabiele toestande in die Namib Woestyn interduin is gemeet en gekwantifiseer deur gebruik te maak van die wind snelheid en temperatuur profiele wat die termies gestratifiseerde atmosfeer, soos afgelei deur Monin-Obukhov teorie, beskryf. Die implementering van hierdie termies gestratifiseerde atmosfeer in CFD is in hierdie studie aangespreek deur gebruik te maak van RANS turbulensie modelle. Die handhawing van die temperatuur, snelheid en turbulensie profiele in die lengte van 'n uitgebreide berekenings domein is nodig, en terselfdertyd moet toegelaat word vir volledige variasie in die druk en digtheid, deur die ideale gaswet. Dit sluit in die implementering van zero hitte-oordrag vanaf die grond onder neutrale toestande sodat die adiabatiese vervaltempo volgehou kan word. Drykrag effekte is ingesluit deur die toevoeging van gewig na die vloeistof, wat lei tot die ontwikkeling van die hidrostatiese druk veld, en die gevolglike digtheid veranderinge, wat in die werklike atmosfeer verwag word. Die CFD-model is gevalideer teen gemete data, vanaf die literatuur, vir die vloei oor 'n kosinus heuwel in 'n windtonnel. Die standaard k-ε en SST k-ω turbulensie modelle, met veranderinge vir swaartekrag effekte, het die data mees akkuraat voorgestel. Die vloei oor 'n geïdealiseerde transversale duin gedompel in die termies gestratifiseerde ABL is ook ondersoek. Daar is bevind dat die vloei herstel is versterk en terug-aanhegging het vroeër plaasgevind in onstabiele toestande, terwyl vloei herstel en terug-aanhegging langer gevat het in stabiele toestande. Daar is ook bevind dat vloei versnelling oor die kruin van die duin groter was onder onstabiele toestande. Die effek van die duin op die vloei hoër op in die atmosfeer is ook op hoër afstande onder onstabiele toestande gevoel, deur middel van verhoogte vertikale snelhede. Onder stabiele toestande, is vertikale snelhede verminder, en die invloed op die vloei hoër op in die atmosfeer was veel minder as vir onstabiel of neutrale toestande. Dit het getoon dat die aanname van neutrale toestande kan lei tot 'n onvolledige beeld van die vloei toestande wat 'n invloed op 'n bepaalde geval kan hê.

En 1979, Trotman a démontré que les stratifications réelles lisses qui satisfont la condition de (a)-régularité sont précisément celles pour lesquelles la transversalité aux strates des applications est une condition stable dans la topologie forte. C'était un résultat surprenant puisque la (t)-régularité semblait être plus appropriée pour la stabilité de la transversalité, une erreur qui a été faite dans plusieurs articles avant que ce résultat soit montré par Trotman. Notre premier résultat est un analogue au résultat de Trotman pour la topologie faible.Il y a une dizaine d'années Trotman a demandé si le même résultat est valable pour les stratifications analytiques complexes. Dans ce travail on démontre un analogue du résultat de Trotman dans le cas complexe, en utilisant la notion de variété de Oka introduite par Forstneric et on montre que la conjecture n'est pas vraie en général en donnant des contre-exemples.Dans sa thèse, Trotman a formulé une conjecture pour généraliser son résultat pour les stratifications (a_f)-régulières de Thom. Dans une tentative de résolution de cette conjecture on a observé que la transversalité par rapport à un feuilletage est une condition stable, cependant ce n'est pas une condition générique. Donc, en voulant imiter la preuve de Trotman on ne pourra pas obtenir cette généralisation. Néanmoins, on donne ici une preuve de cette conjecture. Ce résultat peut être résumé en disant que les (a_f)-défauts dans une stratification peuvent être détectés en perturbant les applications transverses au feuilletage induit par f. Certaines techniques pour détecter (a_f)-défauts sont aussi données vers la fin. / Trotman in 1979 proved that real smooth stratifications which satisfy the condition of $(a)$-regularity are precisely those stratifications for which transversality to the strata of smooth mappings is a stable condition in the strong topology. This was a surprising result since $(t)$-regularity seemed to be more appropriate for stability of transversality, a mistake that was made in several articles before this result of Trotman. Our first result is an analogue of this result of Trotman for the weak topology.Trotman asked more than ten years ago whether a similar result holds for complex analytic stratifications. We will give an analogue of Trotman's result in the complex setting using Forstneriv c's notion of Oka manifolds and show that the result is not true in general by giving counterexamples.In his Ph.D. thesis Trotman conjectured a generalization of his result for Thom $(a_f)$-regular stratifications. In an attempt to prove this conjecture we noticed that while transversality to a foliation is a stable condition, it is not generic in general. Thus, mimicking the proof of the result of Trotman would not suffice to obtain this generalization. Nevertheless, we will present a proof of this conjecture in this work. This result can be summarized by saying that Thom $(a_f)$-faults in a stratification can be detected by perturbation of maps transverse to the foliation induced by $f$. Some other techniques of detecting $(a_f)$-faults are also given towards the end.

Cette thèse se propose d'étudier les Miracles de Nostre Dame par personnages en tant que corpus de réécritures dramatiques d'un répertoire assez important de contes hagiographiques et romanesques. La recherche, fondée sur une démarche essentiellement intertextuelle qui fait référence ponctuellement à un vaste corpus de textes de comparaison, est centrée sur deux axes. Il s'agit d'abord de vérifier si les réminiscences mythiques que les textes recèlent sont les simples résidus inertes d'une longue stratification ou s'ils s'organisent, au-delà de l'agencement rationnel de chaque récit, en faisant appel à une mémoire littéraire et mythico-folklorique et en se disposant dans des configurations assez cohérentes. Ensuite, il s'agit d'étudier le contexte de la mise en scène des Miracles, les éléments intrinsèque de l'écriture dramatique, et, par le biais de l'étude de quelques exemples significatifs, les formes de la représentation, qui semblent calquer et réadapter des formes de la théâtralité diffuse liées à des rites préchrétiens. Produits d'un imaginaire chrétien qu'ils contribuent à leur tour à façonner, les Miracles sont des pièces qui exemplifient le rôle de médiatrice universelle de la Vierge tout en évoquant une vision du monde lié au calendrier ancestral d'une culture « autre », qui fait surface dans l'écriture dramatique et dans la mise en scène, en renforçant et en amplifiant, en général, la portée du message édifiant. / This thesis propose to studying the Miracles de Nostre Dame par personnages as corpus of dramatic rewritings of a rather important directory of hagiographic and romantic tales. The research, based on an essentially intertextual approach which makes punctual references to a vast corpus of texts of comparison, is centered on two axes. It is a question at first of verifying if the mythical recollections which texts contain are the simple residues empty of meaning of a long stratification or if they get organized, beyond the rational plot of every narrative, by calling into play a literary and mythical-folk memory and arranging themselves in rather coherent configurations. Then, it is a question of studying the context of the staging and the intrinsic elements of the dramatic writing, and, by means of the study of some significant examples, the forms of the representation, which seem to trace and to readjust forms of the diffuse theatricality bound up pagan rites. Produced by a Christian imagination which they contribute in their turn to shape, the Miracles are plays which exemplify the role of universal mediator of the Virgin while evoking a vision of the world connected to the ancestral calendar of an "other" culture, which makes surface in the dramatic writing and in the staging, by strengthening and by amplifying, generally, the influence of the edifying message.

Les tourbillons et les écoulements méso-échelles océaniques contribuent de façon importante au transport de masses d'eau et de chaleur dans l'océan. La compréhension de leurs dynamiques, et de leurs interactions avec la topographie, est primordiale, pour caractériser les échanges thermohalins, le déplacements d'espèces biologiques ou de polluants. En particulier, les courants et tourbillons de surface, situés dans les cent ou deux cents premiers mètres de profondeur, jouent un rôle capital dans les échanges entre la zone côtière et la zone hauturière. Cette thèse porte sur la modélisation expérimentale idéalisée de deux phénomènes pouvant participer activement aux échanges horizontaux et verticaux dans la couche supérieure océanique. Les sillages d'îles peuvent être le lieu d'instabilités fortes dans les zones anticycloniques de l'écoulement. Des expériences ont été réalisées sur la Plateforme Coriolis (LEGI) à Grenoble, pour identifier les régimes dynamiques de ces instabilités. Ce dispositif (13 mètres de diamètre) a permis d'atteindre de faibles rapports d'aspects géométriques, tout en travaillant avec un dispositif couche-mince. Des visualisations avec colorants et des mesures du champ de vitesse horizontal par intercorrélation de particules ont été réalisées, afin d'étudier la sensibilité des instabilités dans les anticyclones pour différentes gammes de nombres de Reynolds et de Rossby. Nous montrons que ces instabilités sont présentes dès la couche limite anticyclonique, autour de l'île. L'autre partie de ce travail concerne la dynamique d'un tourbillon de surface, en interaction avec la côte ou le talus océanique. Des mesures récentes (campagne EGYPT-1) nous ont permis de mesurer la dérive particulière d'un anticyclone de surface le long de la côte libyenne. Cette dérive vers l'est ne peut s'expliquer par la simple prise en compte de l'effet beta ou de l'effet miroir le long de la côte. Des expériences idéalisées sont menées sur la table tournante de l'ENSTA, afin de modéliser de façon simple l'interaction d'une côte ou d'un talus sur la dynamique d'un anticyclone, à la surface d'un dispositif bi-couche. La vitesse de ce tourbillon de surface voit notamment sa dérive doubler lorsqu'il se trouve initialement à la base de la pente, montrant ainsi l'existence d'une rétroaction possible de la couche du fond sur la dynamique de la couche de surface.