Wall-bounded turbulent dispersed multiphase flows occur in a variety of industrial, biological and environmental applications. The complex nature of the carrier and the particulate phase is elevated to a higher level when introducing geometrical complexities such as curved walls. Realising such flows and dispersed phases poses challenging problems both from computational and also physical point of view. The present thesis addresses some of these issues by studying a coupled Eulerian–Lagrangian computational framework. The content of the thesis addresses both turbulent wall flows and coupled particle motion. In the first part, turbulent flow in straight pipes is simulated by means of direct numerical simulation (DNS) with the spectrally accurate code nek5000  to examine the Reynolds-number effect on turbulence statistics. The effect of the curvature to these canonical turbulent pipe flows is then added to generate Prandtl’s secondary motion of first kind. These configurations, as primary complex geometries in this study, are examined by means of statistical analysis to unfold the evolution of turbulence characteristics from a straight pipe. A fundamentally different Prandtl’s secondary motion of the second kind is also put to test by adding side-walls to a canonical turbulent channel flow and analysing the evolution of various statistical quantities with varying the duct width-to-height aspect ratios. Having obtained a characterisation of the turbulent flow in the geometries of bent pipes and ducts, the dispersion of small heavy particles is modelled in these configurations by means of point particles which are one-way coupled to the flow. For this purpose a parallel Lagrangian Particle Tracking (LPT) scheme is implemented in the spectral-element code nek5000 . Its numerical accuracy, parallel scalability and general performance in realistic situations is scrutinised. The analysis of the resulting particle fields shows that even a small amount of secondary motion has a profound impact on the particle phase dynamics and its concentration maps. For each of the aforementioned turbulent flow cases new and challenging questions have arisen to be addressed in the present research works. The goal of extending understanding of the particle dispersion in turbulent bent pipes and rectangular ducts are also achieved. / <p>QC 20151118</p>

This thesis studies the geometry of hyperbolic monopoles using supersymmetry in four and six dimensions. On the one hand, we show that starting with a four dimensional supersymmetric Yang-Mills theory provides the necessary information to study the geometry of the complex moduli space of hyperbolic monopoles. On the other hand, we require to start with a six dimensional supersymmetric Yang-Mills theory to study the geometry of the real moduli space of hyperbolic monopoles. In chapter two, we construct an off-shell supersymmetric Yang-Mills-Higgs theory with complex fields on three-dimensional hyperbolic space starting from an on-shell supersymmetric Yang-Mills theory on four-dimensional Euclidean space. We, then, show that hyperbolic monopoles coincide precisely with the configurations that preserve one half of the supersymmetry. In chapter three, we explore the geometry of the moduli space of hyperbolic monopoles using the low energy linearization of the field equations. We find that the complexified tangent bundle to the hyperbolic moduli space has a 2-sphere worth of integrable structures that act complex linearly and behave like unit imaginary quaternions. Moreover, we show that these complex structures are parallel with respect to the Obata connection, which implies that the geometry of the complexified moduli space of hyperbolic monopoles is hypercomplex. We also show, as a requirement of analysing the geometry, that there is a one-to-one correspondence between the number of solutions of the linearized Bogomol’nyi equation on hyperbolic space and the number of solutions of the Dirac equation in the presence of hyperbolic monopole. In chapter four and five, we shift the focus to supersymmetric Yang-Mills theories in six dimensional Minkowskian spacetime. Via dimensional reduction we construct a supersymmetric Yang-Mills Higgs theory on R3 with real fields which we then promote to H3. Under certain supersymmetric constraints, we show that hyperbolic monopoles configurations of this theory preserve, again, one half of the supersymmetry. Then, through investigating the geometry of the moduli space we showthat the moduli space is described by real coordinate functions (zero modes), and we construct two sets of 2-sphere of real complex structures that act linearly on the tangent bundle of the moduli space, but don’t behave like unit quaternions. This result coincides with the result of Bielawski and Schwachhöfer, who called this new type of geometry pluricomplex geometry. Finally, we show that in the limiting case, when the radius of curvature H3 is set to infinity, the geometry becomes hyperkähler which is the geometry of the moduli space of Euclidian monopoles.

Noncommutative Riemannian geometry is an area that has seen intense activity over the past 25 years. Despite this, noncommutative complex geometry is only now beginning to receive serious attention. The theory of quantum groups provides a large family of very interesting potential examples, namely the quantum flag manifolds. Thus far, only the irreducible quantum flag manifolds have been investigated as noncommutative complex spaces. In a series of papers, Heckenberger and Kolb showed that for each of these spaces, there exists a q-deformed Dolbeault double complex. In this thesis a comprehensive framework for noncommutative complex geometry on quantum homogeneous spaces is introduced. The main ingredients used are covariant differential calculi and Takeuchi's categorical equivalence for faithfully at quantum homogeneous spaces. A number of basic results are established, producing a simple set of necessary and sufficient conditions for noncommutative complex structures to exist. It is shown that when applied to the quantum projective spaces, this theory reproduces the q-Dolbeault double complexes of Heckenberger and Kolb. Furthermore, the framework is used to q-deform results from Borel{Bott{ Weil theory, and to produce the beginnings of a theory of noncommutative Kahler geometry.

This thesis explores aspects of generalized geometry, a geometric framework introduced by Hitchin and Gualtieri in the early 2000s. In the first part, we introduce a new class of submanifolds in stable generalized complex manifolds, so-called Lagrangian branes with boundary. We establish a correspondence between stable generalized complex geometry and log symplectic geometry, which allows us to prove results on local neighbourhoods and small deformations of this new type of submanifold. We further investigate Lefschetz thimbles in stable generalized complex Lefschetz fibrations and show that Lagrangian branes with boundary arise in this context. Stable generalized complex geometry provides the simplest examples of generalized complex manifolds which are neither complex nor symplectic, but it is sufficiently similar to symplectic geometry for a multitude of symplectic results to generalize. Our results on Lefschetz thimbles in stable generalized complex geometry indicate that Lagrangian branes with boundary are part of a potential generalisation of the Wrapped Fukaya category to stable generalized complex manifolds. The work presented in this thesis should be seen as a first step towards the extension of Floer theory techniques to stable generalized complex geometry, which we hope to develop in future work. The second part of this thesis studies Dorfman brackets, a generalisation of the Courant- Dorfman bracket, within the framework of double vector bundles. We prove that every Dorfman bracket can be viewed as a restriction of the Courant-Dorfman bracket on the standard VB-Courant algebroid, which is in this sense universal. Dorfman brackets have previously not been considered in this context, but the results presented here are reminiscent of similar results on Lie and Dull algebroids: All three structures seem to fit into a more general duality between subspaces of sections of the standard VB-Courant algebroid and brackets on vector bundles of the form T M ⊕ E ∗ , E → M a vector bundle. We establish a correspondence between certain properties of the brackets on one, and the subspaces on the other side.

No description available.

La cavitation est un phénomène de changement de phase dans les zones de basses pressions des machines hydrauliques. Ses conséquences sont souvent néfastes : pertes de performances, génération de bruit et de vibrations, abrasion des matériaux... Ces effets deviennent une préoccupation importante dans la conception des machines hydrauliques. Ce travail a pour objectif principal de développer un modèle de simulation numérique pour la simulation de la cavitation à haut ordre de précision, pour des écoulements compressibles visqueux, et pour des géométries complexes. Le modèle adopté pour la modélisation de la cavitation est le modèle de mélange homogène. Cette formulation ne dépend d'aucun paramètre empirique et peut être aisément étendu à du multi-espèce. Nous utilisons un code de volumes finis, dont le haut ordre de reconstruction est assuré par la méthode des moindres carrés mobiles. / Cavitation is a phase change phenomenon, wich occurs in low pressure areas in hydraulic systems. Its consequences are often harmful and undesired : it causes loss of efficiency, noise and vibration generation, and structural abrasion... These effects become a major preoccupation in the conception of hydraulic systems. The main objective of this work is to develop a numerical tool for the numerical modelisation of cavitation at high orders of accuracy, for compressible and viscous flows, in complex geometries. The model used for the modelisation of the cavitation is the homogeneous mixture model, wich formulation is independent of empirical parameters, and is easily extendable for multi-spieces flows. We use a finite volume developped in the DynFluid laboratory, in wich the high accuracy order of reconstruction is obtained using the Moving Least Square approximation.

The continual advance in manufacturing processes has resulted in significantly more compact, high performance, devices. Consequently, heat extraction has become the limiting factor, and of primary concern. Therefore, a substantial amount of research has been done regarding high efficiency micro heat exchangers, employing novel working fluids. This dissertation numerically investigated the thermal behaviour of microchannel elements cooled by Newtonian and non-Newtonian fluids, with the objective of maximising thermal conductance subject to constraints. This was done, firstly, for a two-dimensional simple microchannel, and secondly, for a three-dimensional complex microchannel. A numerical model was used to solve the governing equations relating to the flow and temperature fields for both cases. The geometric configuration of each cooling channel was optimised for Newtonian and non-Newtonian fluids, at a fixed inlet velocity and heat transfer rate. In addition, the effect of porosity on thermal conductance was investigated. Geometric optimisation was employed to the simple and complex microchannels, whereby an optimal geometric ratio (height versus length) was found to maximise thermal conductance. Moreover, analysis indicated that the bifurcation point of the complex microchannel could be manipulated to achieve a higher thermal conductance. In both cases, it was found that the non-Newtonian fluid characteristics resulted in a significant variation in thermal conductance as inlet velocity was increased. The ii characteristics of a dilatant fluid greatly reduced thermal conductance on account of shear-thickening on the boundary surface. In contrast, a pseudoplastic fluid showed increased thermal conductance. A comparison of the simple and complex microchannel showed an improved thermal conductance resulting from greater flow access to the conductive area, achieved by the complex microchannel. Therefore, it could be concluded that a complex microchannel, in combination with a pseudoplastic working fluid, substantially increased the thermal conductance and efficiency, as opposed to a conventional methodology. / Dissertation (MEng)--University of Pretoria, 2012. / gm2014 / Mechanical and Aeronautical Engineering / unrestricted

Yes / Fused deposition modelling (FDM) 3D printing has shown the most immediate potential for on-demand dose personalisation to suit particular patient's needs. However, FDM 3D printing often involves employing a relatively large molecular weight thermoplastic polymer and results in extended release pattern. It is therefore essential to fast-track drug release from the 3D printed objects. This work employed an innovative design approach of tablets with unique built-in gaps (Gaplets) with the aim of accelerating drug release. The novel tablet design is composed of 9 repeating units (blocks) connected with 3 bridges to allow the generation of 8 gaps. The impact of size of the block, the number of bridges and the spacing between different blocks was investigated. Increasing the inter-block space reduced mechanical resistance of the unit, however, tablets continued to meet pharmacopeial standards for friability. Upon introduction into gastric medium, the 1 mm spaces gaplet broke into mini-structures within 4 min and met the USP criteria of immediate release products (86.7% drug release at 30 min). Real-time ultraviolet (UV) imaging indicated that the cellulosic matrix expanded due to swelling of hydroxypropyl cellulose (HPC) upon introduction to the dissolution medium. This was followed by a steady erosion of the polymeric matrix at a rate of 8 μm/min. The design approach was more efficient than a comparison conventional formulation approach of adding disintegrants to accelerate tablet disintegration and drug release. This work provides a novel example where computer-aided design was instrumental at modifying the performance of solid dosage forms. Such an example may serve as the foundation for a new generation of dosage forms with complicated geometric structures to achieve functionality that is usually achieved by a sophisticated formulation approach.

Generalized geometry of type B_n is the study of geometric structures in T+T^&ast;+1, the sum of the tangent and cotangent bundles of a manifold and a trivial rank 1 bundle. The symmetries of this theory include, apart from B-fields, the novel A-fields. The relation between B_n-geometry and usual generalized geometry is stated via generalized reduction. We show that it is possible to twist T+T^&ast;+1 by choosing a closed 2-form F and a 3-form H such that dH+F²=0. This motivates the definition of an odd exact Courant algebroid. When twisting, the differential on forms gets twisted by d+F&tau;+H. We compute the cohomology of this differential, give some examples, and state its relation with T-duality when F is integral. We define B_n-generalized complex structures (B_n-gcs), which exist both in even and odd dimensional manifolds. We show that complex, symplectic, cosymplectic and normal almost contact structures are examples of B_n-gcs. A B_n-gcs is equivalent to a decomposition (T+T^&ast;+1)_&Copf;= L + L + U. We show that there is a differential operator on the exterior bundle of L+U, which turns L+U into a Lie algebroid by considering the derived bracket. We state and prove the Maurer-Cartan equation for a B_n-gcs. We then work on surfaces. By the irreducibility of the spinor representations for signature (n+1,n), there is no distinction between even and odd B_n-gcs, so the type change phenomenon already occurs on surfaces. We deal with normal forms and L+U-cohomology. We finish by defining G²₂-structures on 3-manifolds, a structure with no analogue in usual generalized geometry. We prove an analogue of the Moser argument and describe the cone of G²₂-structures in cohomology.

The most general AdS$_5 imes Y$ solutions of type IIB string theory that are AdS/CFT dual to superconformal field theories in four dimensions can be fruitfully described in the language of generalized geometry, a powerful hybrid of complex and symplectic geometry. We show that the cone over the compact five-manifold $Y$ is generalized Calabi-Yau and carries a generalized holomorphic Killing vector field $xi$, dual to the R-symmetry. Remarkably, this cone always admits a symplectic structure, which descends to a contact structure on $Y$, with $xi$ as Reeb vector field. Moreover, the contact volumes of $Y$, which can be computed by localization, encode essential properties of the dual CFT, such as the central charge and the conformal dimensions of BPS operators corresponding to wrapped D3-branes. We then define a notion of ``generalized Sasakian geometry'', which can be characterized by a simple differential system of three symplectic forms on a four-dimensional transverse space. The correct Reeb vector field for an AdS$_5$ solution within a given family of generalized Sasakian manifolds can be determined---without the need of the explicit metric---by a variational procedure. The relevant functional to minimize is the type IIB supergravity action restricted to the space of generalized Sasakian manifolds, which turns out to be just the contact volume. We conjecture that this contact volume is equal to the inverse of the trial central charge whose maximization determines the R-symmetry of the dual superconformal field theory. The power of this volume minimization is illustrated by the calculation of the contact volumes for a new infinite family of solutions, in perfect agreement with the results of $a$-maximization in the dual mass-deformed generalized conifold theories.