Metal oxides prepared through the nanocasting approach-mechanistic study, surface interactions and applications in separation

Mesoporous metal oxides are nowadays widely used in various technological applications, for instance in catalysis, biomolecular separations and drug delivery. A popular technique used to synthesize mesoporous metal oxides is the nanocasting process. Mesoporous metal oxide replicas are obtained from the impregnation of a porous template with a metal oxide precursor followed by thermal treatment and removal of the template by etching in NaOH or HF solutions. In a similar manner to the traditional casting wherein the product inherits the features of the mold, the metal oxide replicas are supposed to have an inverse structure of the starting porous template. This is however not the case, as broken or deformed particles and other structural defects have all been experienced during nanocasting experiments. Although the nanocasting technique is widely used, not all the processing steps are well understood. Questions over the fidelity of replication and morphology control are yet to be adequately answered. This work therefore attempts to answer some of these questions by elucidating the nanocasting process, pin pointing the crucial steps involved and how to harness this knowledge in making wholesome replicas which are a true replication of the starting templates. The rich surface chemistry of mesoporous metal oxides is an important reason why they are widely used in applications such as catalysis, biomolecular separation, etc. At times the surface is modified or functionalized with organic species for stability or for a particular application. In this work, nanocast metal oxides (TiO2, ZrO2 and SnO2) and SiO2 were modified with amino-containing molecules using four different approaches, namely (a) covalent bonding of 3-aminopropyltriethoxysilane (APTES), (b) adsorption of 2-aminoethyl dihydrogen phosphate (AEDP), (c) surface polymerization of aziridine and (d) adsorption of poly(ethylenimine) (PEI) through electrostatic interactions. Afterwards, the hydrolytic stability of each functionalization was investigated at pH 2 and 10 by zeta potential measurements. The modifications were successful except for the AEDP approach which was unable to produce efficient amino-modification on any of the metal oxides used. The APTES, aziridine and PEI amino-modifications were fairly stable at pH 10 for all the metal oxides tested while only AZ and PEI modified-SnO2 were stable at pH 2 after 40 h. Furthermore, the functionalized metal oxides (SiO2, Mn2O3, ZrO2 and SnO2) were packed into columns for capillary liquid chromatography (CLC) and capillary electrochromatography (CEC). Among the functionalized metal oxides, aziridinefunctionalized SiO2, (SiO2-AZ) showed good chemical stability, and was the most useful packing material in both CLC and CEC. Lastly, nanocast metal oxides were synthesized for phosphopeptide enrichment which is a technique used to enrich phosphorylated proteins in biological samples prior to mass spectrometry analysis. By using the nanocasting technique to prepare the metal oxides, the surface area was controlled within a range of 42-75 m2/g thereby enabling an objective comparison of the metal oxides. The binding characteristics of these metal oxides were compared by using samples with different levels of complexity such as synthetic peptides and cell lysates. The results show that nanocast TiO2, ZrO2, Fe2O3 and In2O3 have comparable binding characteristics. Furthermore, In2O3 which is a novel material in phosphopeptide enrichment applications performed comparably with standard TiO2 which is the benchmark for such phosphopeptide enrichment procedures. The performance of the metal oxides was explained by ranking the metal oxides according to their isoelectric points and acidity. Overall, the clarification of the nanocasting process provided in this work will aid the synthesis of metal oxides with true fidelity of replication. Also, the different applications of the metal oxides based on their surface interactions and binding characteristics show the versatility of metal oxide materials. Some of these results can form the basis from which further applications and protocols can be developed.

Structural studies and gabbro mylonitization within the Barton Bay Deformation Zone, Geraldton, Ontario /

Structures related to ductile siMple shear parallel to the Bankf ield-Tonbill Fault, define a 5km wide zone, the Barton Bay Deformation Zone. Structures present within this zone Include; simple shear fabrics S, C and C , asymmetric Z shaped folds with rotated axes, boudinage and pinch and swell structures and a subhorlzontal extension llneation. The most highly deformed rock is a gabbro mylonite which occurs in the fault zone. The deformation of this gabbro has been traced in stages from a protomylonite to an ultramylonite In which feldspar and chlorite grainslze has been reduced from over 100 microns to as little as 5 microns. Evidence from the mylonite and the surrounding structure indicates that deformation within the Barton Bay Deformation Zone is related to a regional simple shear zone, the Bankf ield-Tombill Fault. Movement along this shear zone was in a south over north oblique strike slip fashion with a dextral sense of displacement.

Geology of the Gander Group, Gander River Ultramafic Belt and Davidsville Group in the Jonathan's Pond - Weir's Pond Area, northeast Newfoundland /

The study area is situated in NE Newfoundland between Gander Lake and the north coast and on the boundary between the Gander and Botwood tectonostratigraphic zones (Williams et al., 1974). The area is underlain by three NE trending units; the Gander Group, the Gander River Ultramafic Belt (the GRUB) and the Davidsville Group. The easternmost Gander Group consists of a thick, psammitic unit composed predominantly of psammitic schist and a thinner, mixed unit of semipelitic and pelitic schist with minor psammite. The mixed unit may stratigraphically overlie the psammitic unit or be a lateral facies equivalent of the latter. No fossils have been recovered from the Gander Group. The GRUB is a terrain of mafic and ultramafic plutonic rocks with minor pillow lava and plagiogranite. It is interpreted to be a dismembered ophiolite in thrust contact with the Gander Group. The westernmost Davidsville Group consists of a basal conglomerate, believed deposited unconformably upon the GRUB from which it was derived, and an upper unit of greywacke and slate, mostly of turbidite origin, with minor limestone and calcareous sandstone. The limestone, which lies near the base of the unit, contains Upper Llanvirn to Lower Llandeilo fossils. The Gander and Davidsville Groups display distinctly different sedimentological , structural and metamorphic histories. The Gander Group consists of quartz-rich, relatively mature sediment. It has suffered three pre-Llanvirn deformations, of which the main deformation, Dp produced a major, NE-N-facing recumbent anticline in the southern part of the study area. Middle greenschist conditions existed from D^ to D- with growth of metamorphic minerals during each dynamic and static phase. In contrast, the mineralogically immature Davidsville Group sediment contains abundant mafic and ultramafic detritus which is absent from the Gander Group. The Davidsville Group displays the effects of a single penetrative deformation with localized D_ and D_ features, all of which can be shown to postdate D_ in the Gander Group. Rotation of the flat Gander S- into a subvertical orientation near the contact with the GRUB and the Davidsville Group is believed to be a Davidsville D^ feature. Regional metamorphism in the Davidsville Group is lower greenschist with a single growth phase, MS . These sedimentological, structural and metamorphic differences between the Gander and Davidsville Groups persist even where the GRUB is absent and the two units are in contact, indicating that the tectonic histories of the Gander and Davidsville Groups are distinctly different. Structural features in the GRUB, locally the result of multiple deformations, may be the result of Gander and/or Davidsville deformations. Metamorphism is in the greenschist facies. Geochemical analyses of the pillow lava suggest that these rocks were formed in a back-arc basin. Mafic intrusives in the Gander Group appear to be the result of magraatism separate from that producing the pillow lava. The Gander Group is interpreted to be a continental rise prism deposited on the eastern margin of the Late Precambrian-Lower Paleozoic lapetus Ocean. The GRUB, oceanic crust possibly formed in a marginal basin to the west, is believed to have been thrust eastward over the Gander Group, deforming the latter, during the pre-Llanvirnian, possibly Precambrian, Ganderian Orogeny. The Middle Ordovician and younger Davidsville Group was derived from, and deposited unconformably on, this deformed terrain. Deformation of the Davidsville Group occurred during the Middle Devonian Acadian Orogeny.

Petrography and geochemistry of the McArthur Township area, Ontario /

The McArthur Township area in the Archean Abitibi Belt of northeast Ontario contains northwesterly trending volcanic rocks which are located on a limb of a large syncline. The axial trace of the syncline passes through the adjacent Douglas Township. The Archean volcanic rocks and associated sedimentary rocks are intruded and deformed by two large plutons and a few smaller hypabyssal intrusions. A petrographic and geochemical study of the Precambrian rocks exposed 1n the study area was undertaken in order to investigate the metamorphic grade and geochemical characteristics of the rocks. All the samples were studied with the microscope and analysis of 20 major and trace elements were determined on a selection of the less altered specimens by x-ray fluorescence. Three different periods of igneous activity have occurred in the study area. The first two periods were dominated by volcanic extrusive rocks accompanied by gabbroic sills. The third cycle is the diapiric intrusion of the granitic plutons and subsequent metamorphism of the older rocks to the low to medium grade. Two periods of sedimentation are also recognized in the study area which occurred after the first and second cycle of volcanism. Chemically, the lavas are subdivided into three main associations: (1) The komatiitic association is characterized by high MgO, high Ni, low Ti02 and a low FeO*/(FeO* + MgO) ratio. They occupy the base of each volcanic cycle and some of the flows exhibit spinifex textures. (2) The tholeiitic association displays distinct iron and titanium enrichment trends in the intermediate membersor -i r (3) The calc-alkaline association contains low FeO* and TI02 and high Ni contents relative to modern calc-alkaline types. They are formed at the end of each cycle of volcanism and overlie the tholeiitic flows. All three associations of the first volcanic cycle are exposed in the study area, while the second cycle is represented by a komatiltic sequence. The volcanic rocks were possibly formed by multiple partial melting of the Archean mantle to produce parental magmas under various P - T conditions.

Confocal and two-photon microscopy : image enhancement /

Confocal and two-photon microcopy have become essential tools in biological research and today many investigations are not possible without their help. The valuable advantage that these two techniques offer is the ability of optical sectioning. Optical sectioning makes it possible to obtain 3D visuahzation of the structiu-es, and hence, valuable information of the structural relationships, the geometrical, and the morphological aspects of the specimen. The achievable lateral and axial resolutions by confocal and two-photon microscopy, similar to other optical imaging systems, are both defined by the diffraction theorem. Any aberration and imperfection present during the imaging results in broadening of the calculated theoretical resolution, blurring, geometrical distortions in the acquired images that interfere with the analysis of the structures, and lower the collected fluorescence from the specimen. The aberrations may have different causes and they can be classified by their sources such as specimen-induced aberrations, optics-induced aberrations, illumination aberrations, and misalignment aberrations. This thesis presents an investigation and study of image enhancement. The goal of this thesis was approached in two different directions. Initially, we investigated the sources of the imperfections. We propose methods to eliminate or minimize aberrations introduced during the image acquisition by optimizing the acquisition conditions. The impact on the resolution as a result of using a coverslip the thickness of which is mismatched with the one that the objective lens is designed for was shown and a novel technique was introduced in order to define the proper value on the correction collar of the lens. The amoimt of spherical aberration with regard to t he numerical aperture of the objective lens was investigated and it was shown that, based on the purpose of our imaging tasks, different numerical apertures must be used. The deformed beam cross section of the single-photon excitation source was corrected and the enhancement of the resolution and image quaUty was shown. Furthermore, the dependency of the scattered light on the excitation wavelength was shown empirically. In the second part, we continued the study of the image enhancement process by deconvolution techniques. Although deconvolution algorithms are used widely to improve the quality of the images, how well a deconvolution algorithm responds highly depends on the point spread function (PSF) of the imaging system applied to the algorithm and the level of its accuracy. We investigated approaches that can be done in order to obtain more precise PSF. Novel methods to improve the pattern of the PSF and reduce the noise are proposed. Furthermore, multiple soiu'ces to extract the PSFs of the imaging system are introduced and the empirical deconvolution results by using each of these PSFs are compared together. The results confirm that a greater improvement attained by applying the in situ PSF during the deconvolution process.

A geochemical and petrological study of volcanic rocks in the Beardmore-Geraldton Archaean Greenstone Belt, Northwestern Ontario

Three repetitive sequences of northward youngIng, east striking, linear, volcano-sedimentary units are found in the late Archaean BeardmoreGeraldton greenstone belt, situated within the Wabigoon subprovince of the Superior Province of northwestern Ontario. The volcanic components are characterised by basaltic flows that are pillowed at the top and underlain by variably deformed massive flows which may In part be intrusive. Petrographic examination of the volcanic units indicates regional metamorphism up to greenschist facies (T=3250 C - 4500 C, P=2kbars) overprinted by a lower amphibolite facies thermal event (T=5750 C, P=2kbars) confined to the south-eastern portion of the belt. Chemical element results suggest olivine, plagioclase and pyroxene are the main fractionating mineral phases. Mobility studies on the varIOUS chemical elements indicate that K, Ca, Na and Sr are relatively mobile, while P, Zr, Ti, Fet (total iron = Fe203) and Mg are relatively immobile. Discriminant diagrams employing immobile element suggests that the majority of the samples are of oceanic affinity with a minor proportion displaying an island arc affinity. Such a transitional tectonic setting IS also refle.cted in REE data where two groups of volcanic samples are recognised. Oceanic tholeiites are LREE depleted with [La/Sm] N = 0.65 and a relatively flat HREE profile with [Sm/Yb] N = 1.2. Island arc type basalts (calc-alkaline) are LREE enriched, with a [La/Sm] N = 1.6, and a relatively higher fractionated HREE profile with [Sm/Yb] N = 1.9. Petrogenetic modelling performed on oceanIC tholeiites suggests derivation from a depleted spinel lherzolite source which undergoes 20% partial melting. Island arc type basalts can be derived by 10% partial melting of a hypothetical amphibolitised oceanic tholeiite source. The majority of the volcanic rocks in the Beardmore-Geraldton Belt are interpreted to represent fragments of oceanic crust trapped at a consuming plate margin. Subsequent post accretionary intrusion of gabbroic rocks (sensu lato) with calc-alkaline affinity is considered to result in the apparent hybrid tectonic setting recognized for the BGB.

Micromorphology of Last Glacial Maximum Grounding line sediments around the Antarctic Peninsula

Sediments recovered from seven Last Glacial Maximum grounding lines sites, around the Antarctic Peninsula, were analyzed using micromorphology. This is the first evidence that grounding line sediments from around the Antarctic Peninsula have complex deformational histories and subglacial origins. It was determined that grounding zone wedge contain multiple units, or diamicton layers, with homogenized boundaries. The multiple diamicton units / layers are due to the accretionary formation of a grounding line wedge. All the sediments were deposited via deformation, and continual reincorporation, homogenization of lower diamicton layers by upper diamicton layers produced what macroscopically appeared to be a single massive diamicton unit. The morainal ridge that was sampled, alternatively, is composed of a single unit, or diamicton layer, that was subglacial in origin and believed to have been pushed out to form a ridge that was subsequently deformed via glacial push.

Determining rotational direction of rotation structures using prolate shaped grains within till

Micromorphology is used to analyze a wide range of sediments. Many microstructures have, as yet, not been analyzed. Rotation structures are the least understood of microstructures: their origin and development forms the basis of this thesis. Direction of rotational movement helps understand formative deformational and depositional processes. Twenty-eight rotation structures were analyzed through two methods of data extraction: (a) angle of grain rotation measured from Nikon NIS software, and (b) visual analyses of grain orientation, neighbouring grainstacks, lineations, and obstructions. Data indicates antithetic rotation is promoted by lubrication, accounting for 79% of counter-clockwise rotation structures while 21 % had clockwise rotation. Rotation structures are formed due to velocity gradients in sediment. Subglacial sediments are sheared due to overlying ice mass stresses. The grains in the sediment are differentially deformed. Research suggests rotation structures are formed under ductile conditions under low shear, low water content, and grain numbers inducing grain-to-grain interaction.

Structures quantiques de certaines sous-variétés lagrangiennes non-monotones

Soit (M,ω) un variété symplectique fermée et connexe.On considère des sous-variétés lagrangiennes α : L → (M,ω). Si α est monotone, c.- à-d. s’il existe η > 0 tel que ημ = ω, Paul Biran et Octav Conea ont défini une version relative de l’homologie quantique. Dans ce contexte ils ont déformé l’opérateur de bord du complexe de Morse ainsi que le produit d’intersection à l’aide de disques pseudo-holomorphes. On note (QH(L), ∗), l’homologie quantique de L munie du produit quantique. Le principal objectif de cette dissertation est de généraliser leur construction à un classe plus large d’espaces. Plus précisément on considère soit des sous-variétés presque monotone, c.-à-d. α est C1-proche d’un plongement lagrangian monotone ; soit les fibres toriques de variétés toriques Fano. Dans ces cas non nécessairement monotones, QH(L) va dépendre de certains choix, mais cela sera irrelevant pour les applications présentées ici. Dans le cas presque monotone, on s’intéresse principalement à des questions de déplaçabilité, d’uniréglage et d’estimation d’énergie de difféomorphismes hamiltoniens. Enfin nous terminons par une application combinant les deux approches, concernant la dynamique d’un hamiltonien déplaçant toutes les fibres toriques non-monotones dans CPn.

Anéantir l’Autre monstrueux : entreprise narrative et corporelle de disparition dans Moi, l’interdite d’Ananda Devi

Le récit Moi, l’interdite, se présente comme une exception parmi les œuvres d’Ananda Devi en ce qu’il n’aborde pas de front ni implicitement le thème de la dissidence féminine, comme nous pouvons l’observer dans la plus grande majorité des œuvres de l’auteure mauricienne. Au contraire, le récit s’évertue à mettre en place un processus singulier : celui d’une disparition, perpétré contre la narratrice et protagoniste principale, condamnée à être l’éternel Autre à cause de son physique monstrueux. La présente étude se donne pour objectif d’exposer les rouages à la fois narratifs, thématiques, corporels et relationnels de cet anéantissement de l’Autre à travers une approche essentiellement narratologique. Dans un premier temps, l’entreprise de disparition est observée à travers plusieurs procédés narratifs : complexité chronologique, enchâssement de plusieurs niveaux de récit, abondance de narrataires. Dans un second temps, le thème de la disparition est questionné dans les relations aliénantes nouées par la narratrice, dont le corps difforme est le principal enjeu. De cette volonté de destruction (re)nait et (re)meurt une narratrice, malade de folie, dont les séquelles incurables l’empêcheront de réaliser son désir d’appartenance à un Même fantasmé.

Création interactive de mondes virtuels : combiner génération procédurale et contrôle utilisateur intuitif

Réalisé en cotutelle avec l'Université de Grenoble.

Mechanical simulation of the endovascular repair of abdominal aortic aneurysms

Ce travail de thèse porte sur la simulation du déploiement des prothèses vasculaires de type stent-graft (SG) lors de la réparation endovasculaire (EVAR) des anévrismes de l’aorte abdominale (AAA). Cette étude se présente en trois parties: (i) tests mécaniques en flexion et compression de SG couramment utilisés (corps et jambage de marque Cook) ainsi que la simulation numérique desdits tests, (ii) développement d’un modèle numérique d’anévrisme, (iii) stratégie de simulation du déploiement des SG. La méthode numérique employée est celle des éléments finis. Dans un premier temps, une vérification du modèle éléments finis (MEF) des SG est realisée par comparaison des différents cas de charge avec leur pendant expérimental. Ensuite, le MEF vasculaire (AAA) est lui aussi vérifié lors d’une comparaison des niveaux de contraintes maximales principales dans la paroi avec des valeurs de la littérature. Enfin, le déploiement est abordé tout en intégrant les cathéters. Les tests mécaniques menés sur les SG ont été simulés avec une différence maximale de 5,93%, tout en tenant compte de la pré-charge des stents. Le MEF de la structure vasculaire a montré des contraintes maximales principales éloignées de 4,41% par rapport à un modèle similaire précédemment publié. Quant à la simulation du déploiement, un jeu complet de SG a pu être déployé avec un bon contrôle de la position relative et globale, dans un AAA spécifique pré-déformé, sans toutefois inclure de thrombus intra-luminal (TIL). La paroi du AAA a été modélisée avec une loi de comportement isotropique hyperélastique. Étant donné que la différence maximale tolérée en milieu clinique entre réalité et simulation est de 5%, notre approche semble acceptable et pourrait donner suite à de futurs développements. Cela dit, le petit nombre de SG testés justifie pleinement une vaste campagne de tests mécaniques et simulations supplémentaires à des fins de validation.

Structures algébriques, systèmes superintégrables et polynômes orthogonaux

Cette thèse est divisée en cinq parties portant sur les thèmes suivants: l’interprétation physique et algébrique de familles de fonctions orthogonales multivariées et leurs applications, les systèmes quantiques superintégrables en deux et trois dimensions faisant intervenir des opérateurs de réflexion, la caractérisation de familles de polynômes orthogonaux appartenant au tableau de Bannai-Ito et l’examen des structures algébriques qui leurs sont associées, l’étude de la relation entre le recouplage de représentations irréductibles d’algèbres et de superalgèbres et les systèmes superintégrables, ainsi que l’interprétation algébrique de familles de polynômes multi-orthogonaux matriciels. Dans la première partie, on développe l’interprétation physico-algébrique des familles de polynômes orthogonaux multivariés de Krawtchouk, de Meixner et de Charlier en tant qu’éléments de matrice des représentations unitaires des groupes SO(d+1), SO(d,1) et E(d) sur les états d’oscillateurs. On détermine les amplitudes de transition entre les états de l’oscillateur singulier associés aux bases cartésienne et polysphérique en termes des polynômes multivariés de Hahn. On examine les coefficients 9j de su(1,1) par le biais du système superintégrable générique sur la 3-sphère. On caractérise les polynômes de q-Krawtchouk comme éléments de matrices des «q-rotations» de U_q(sl_2). On conçoit un réseau de spin bidimensionnel qui permet le transfert parfait d’états quantiques à l’aide des polynômes de Krawtchouk à deux variables et on construit un modèle discret de l’oscillateur quantique dans le plan à l’aide des polynômes de Meixner bivariés. Dans la seconde partie, on étudie les systèmes superintégrables de type Dunkl, qui font intervenir des opérateurs de réflexion. On examine l’oscillateur de Dunkl en deux et trois dimensions, l’oscillateur singulier de Dunkl dans le plan et le système générique sur la 2-sphère avec réflexions. On démontre la superintégrabilité de chacun de ces systèmes. On obtient leurs constantes du mouvement, on détermine leurs algèbres de symétrie et leurs représentations, on donne leurs solutions exactes et on détaille leurs liens avec les polynômes orthogonaux du tableau de Bannai-Ito. Dans la troisième partie, on caractérise deux familles de polynômes du tableau de Bannai-Ito: les polynômes de Bannai-Ito complémentaires et les polynômes de Chihara. On montre également que les polynômes de Bannai-Ito sont les coefficients de Racah de la superalgèbre osp(1,2). On détermine l’algèbre de symétrie des polynômes duaux -1 de Hahn dans le cadre du problème de Clebsch-Gordan de osp(1,2). On propose une q - généralisation des polynômes de Bannai-Ito en examinant le problème de Racah pour la superalgèbre quantique osp_q(1,2). Finalement, on montre que la q -algèbre de Bannai-Ito sert d’algèbre de covariance à osp_q(1,2). Dans la quatrième partie, on détermine le lien entre le recouplage de représentations des algèbres su(1,1) et osp(1,2) et les systèmes superintégrables du deuxième ordre avec ou sans réflexions. On étudie également les représentations des algèbres de Racah-Wilson et de Bannai-Ito. On montre aussi que l’algèbre de Racah-Wilson sert d’algèbre de covariance quadratique à l’algèbre de Lie sl(2). Dans la cinquième partie, on construit deux familles explicites de polynômes d-orthogonaux basées sur su(2). On étudie les états cohérents et comprimés de l’oscillateur fini et on caractérise une famille de polynômes multi-orthogonaux matriciels.

Sur une classe de structures kählériennes généralisées toriques

Cette thèse concerne le problème de trouver une notion naturelle de «courbure scalaire» en géométrie kählérienne généralisée. L'approche utilisée consiste à calculer l'application moment pour l'action du groupe des difféomorphismes hamiltoniens sur l'espace des structures kählériennes généralisées de type symplectique. En effet, il est bien connu que l'application moment pour la restriction de cette action aux structures kählériennes s'identifie à la courbure scalaire riemannienne. On se limite à une certaine classe de structure kählériennes généralisées sur les variétés toriques notée $DGK_{\omega}^{\mathbb{T}}(M)$ que l'on reconnaît comme étant classifiées par la donnée d'une matrice antisymétrique $C$ et d'une fonction réelle strictement convexe $\tau$ (ayant un comportement adéquat au voisinage de la frontière du polytope moment). Ce point de vue rend évident le fait que toute structure kählérienne torique peut être déformée en un élément non kählérien de $DGK_{\omega}^{\mathbb{T}}(M)$, et on note que cette déformation à lieu le long d'une des classes que R. Goto a démontré comme étant libre d'obstruction. On identifie des conditions suffisantes sur une paire $(\tau,C)$ pour qu'elle donne lieu à un élément de $DGK_{\omega}^{\mathbb{T}}(M)$ et on montre qu'en dimension 4, ces conditions sont également nécessaires. Suivant l'adage «l'application moment est la courbure» mentionné ci-haut, des formules pour des notions de «courbure scalaire hermitienne généralisée» et de «courbure scalaire riemannienne généralisée» (en dimension 4) sont obtenues en termes de la fonction $\tau$. Enfin, une expression de la courbure scalaire riemannienne généralisée en termes de la structure bihermitienne sous-jacente est dégagée en dimension 4. Lorsque comparée avec le résultat des physiciens Coimbra et al., notre formule suggère un choix canonique pour le dilaton de leur théorie.

Analytical Investigations 0n Collapse of Cylindrical Submarine Shells

Submarine hull structure is a watertight envelope, under hydrostatic pressure when in operation. Stiffened cylindrical shells constitute the major portion of these submarine hulls and these thin shells under compression are susceptible to buckling failure. Normally loss of stability occurs at the limit point rather than at the bifurcation point and the stability analysis has to consider the change in geometry at each load step. Hence geometric nonlinear analysis of the shell forms becomes. a necessity. External hydrostatic pressure will follow the deformed configuration of the shell and hence follower force effect has to be accounted for. Computer codes have been developed based on all-cubic axisymmetric cylindrical shell finite element and discrete ring stiffener element for linear elastic, linear buckling and geometric nonIinear analysis of stiffened cylindrical shells. These analysis programs have the capability to treat hydrostatic pressure as a radial load and as a follower force. Analytical investigations are carried out on two attack submarine cylindrical hull models besides standard benchmark problems. In each case, the analysis has been carried out for interstiffener, interdeepframe and interbulkhead configurations. The shell stiffener attachment in each of this configuration has been represented by the simply supported-simply supported, clamped-clamped and fixed-fixed boundary conditions in this study. The results of the analytical investigations have been discussed and the observations and conclusions are described. Rotation restraint at the ends is influential for interstiffener and interbulkhead configurations and the significance of axial restraint becomes predominant in the interbulkhead configuration. The follower force effect of hydrostatic pressure is not significant in interstiffener and interdeepframe configurations where as it has very high detrimental effect on buckling pressure on interbulkhead configuration. The geometric nonlinear interbulkhead analysis incorporating follower force effect gives the critical value of buckling pressure and this analysis is recommended for the determination of collapse pressure of stiffened cylindrical submarine shells.