The goal of this thesis is to study the ground or metastable state structure of nematic liquid crystal systems confined inside handled shapes such as a torus or double torus. We begin our work by introducing a new method to generate a toroidal droplet from a Newtonian liquid inside another, immiscible, Newtonian liquid. In this situation, a toroidal droplet is unstable and follows one of two routes in transforming into a spherical droplet: (i) its tube breaks in a way reminiscent to the breakup of a cylindrical jet, or (ii) its tube grows until it finally coalesces onto itself. However, to be able to probe the nematic structure, we need to address the issue of instabilities. This is done by replacing the outer liquid with a yield stress material, which ultimately leads to the stabilization of the toroidal droplet. Through the experimental investigation, we are able to establish the stabilization conditions. Finally, we generate and stabilize toroidal droplets with a nematic liquid crystal as the inner liquid and a yield stress material as the outer medium. Here we observe that in the ground state, the nematic liquid crystal exhibits an intriguing twisted structure irrespective of the aspect ratio of the torus. While there are no defects observed in a toroidal droplet case, two defects with -1 topological charge each emerge each time we increase the number of handles.

The Qweak experiment at Thomas Jefferson National Accelerator Facility (Jefferson Lab) will measure the proton's weak charge by measuring the parity violating asymmetry in elastic electron-proton scattering at very low momentum transfer, with the aim of determining the proton's weak charge with 4% combined statistical and systematic errors. The experimental apparatus includes a longitudinally polarized electron beam, a liquid hydrogen target, a room temperature toroidal magnetic spectrometer, and a set of precision detectors for the scattered electrons. The toroidal magnetic spectrometer, which will deflect away the inelastic scattered electrons and focus the elastic scattered electrons onto the detectors, plays a crucially important role in the experiment. In this thesis, in order to meet the requirements for the installation and calibration of the toroidal magnetic spectrometer, the numerical simulation of the spectrometer's magnetic field based on a realistic magnet model is discussed, a precise 3D field mapping is introduced, and some simulation results are provided. The zero-crossing analysis technique, which can be used to precisely infer the individual coil locations of the toroidal magnet, is presented and explored in detail.

La compréhension du transport d'impuretés dans le coeur des plasmas de tokamaks est un enjeu principal de la fusion par confinement magnétique. En effet les impuretés sont omni-présentes dans les tokamaks et leur présence dans le coeur a des effets négatifs sur le confinement du plasma (dilution, rayonnement). Récemment une attention particulière s'est portée sur le flux convectif turbulent dû au gradient de rotation toroïdale pour expliquer les profils plat/creux d'impuretés observés expérimentalement dans le coeur du plasma. Dans cette thèse une approche numérique a été adoptée avec l'utilisation entre autres de codes tels que NEO pour le transport néoclassique et GKW pour le transport turbulent, tout les deux incluant l'effet de la rotation toroïdale. Une comparaison du facteur de piquage du carbone (R/LnC) mesuré expérimentalement (dans le tokamak européen JET) et obtenu numériquement est faite pour un grand nombre de plasma en mode H (mode de confinement amélioré). La comparaison entre les mesures expérimentales de R/LnC et les résultats numériques donne lieu à deux constats. Premièrement la partie convective du flux correspondant au gradient de rotation toroïdale a un impact important sur R/LnC et principalement à valeurs élevées de ce gradient. Deuxièmement les simulations surestiment ce piquage dans le coeur du plasma où les profils expérimentaux sont creux. Ce désaccord, observé à haute collisionalité uniquement, est également obtenu pour le transport de moment ce qui pourrait être la signature d'un méchanisme de brisure de symmétrie (important pour le transport d'impureté et de moment) manquant. / Understanding impurity transport in the core of tokamak plasmas is central to achieving controlled fusion. Indeed impurities are ubiquitous in these devices and their presence in the core are detrimental to plasma confinement (fuel dilution, Bremsstrahlung). Recently, specific attention was given to the convective mechanism related to the gradient of the toroidal rotation to explain experimental flat/hollow impurity profiles in the plasma core. In this thesis, up-to-date modelling tools (NEO for neoclassical transport and GKW for turbulent transport) including the impact of toroidal rotation are used to study both the neoclassical and turbulent contributions to impurity fluxes. A comparison of the experimental and modelled carbon density peaking factor (R/LnC) is performed for a large number of baseline and hybrid H-mode plasmas (increased confinement regimes) with modest to high toroidal rotation from the European tokamak JET. Confrontation of experimental and modelled carbon peaking factor yields two main results. First roto-diffusion is found to have a nonnegligible impact on the carbon peaking factor at high values of the toroidal rotation frequency gradient. Second, there is a tendency to overpredict the experimental R/LnC in the core inner region where the carbon density profiles are hollow. This disagreement between experimental and modelled R/LnC, closely related to the collisionality, is also observed for the momentum transport channel which hints at a common parallel symmetry breaking mechanism lacking in the simulations.

The classical (proper) graph colouring problem asks for a colouring of the vertices of a graph with the minimum number of colours such that no two vertices with the same colour are adjacent. Equivalently the colouring is required to be such that the graph induced by the vertices coloured the same colour has the maximum degree equal to zero. The graph parameter associated with the minimum possible number of colours of a graph is called chromatic number of that graph. One generalization of this classical problem is to relax the requirement that the maximum degree of the graph induced by the vertices coloured the same colour be zero, and instead allow it to be some integer d. For d = 0, we are back at the classical proper colouring. For other values of d we say that the colouring has defect d. Another generalization of the classical graph colouring, is list colouring and its associated parameters: choosability and choice number. The main result of this thesis is to show that every graph G of Euler genus μ is ⌈2 + √(3μ + 3)⌉–choosable with defect 1 (equivalently, with clustering 2). Thus allowing any defect, even 1, reduces the choice number of surface embeddable graphs below the chromatic number of the surface. For example, the chromatic number of the family of toroidal graphs is known to be 7. The bound above implies that toroidal graphs are 5-choosable with defect 1. This strengthens the result of Cowen, Goddard and Jesurum (1997) who showed that toroidal graphs are 5-colourable with defect 1. In a graph embedded in a surface, two faces that share an edge are called adjacent. We improve the above bound for graphs that have embeddings without adjacent triangles. In particular, we show that every non-planar graph G that can be embedded in a surface of Euler genus μ without adjacent triangles, is ⌈(5+ √(24μ + 1)) /3⌉–choosable with defect 1. This result generalizes the result of Xu and Zhang (2007) to all the surfaces. They proved that toroidal graphs that have embeddings on the torus without two adjacent triangles are 4-choosable with defect 1.

This thesis analyses the singularities of toroidal compactifications. Motivated by a result of Shepherd-Barron about the first Voronoi compactification of the moduli space of principally polarised abelian varieties, the object taken into consideration consists of the perfect cone (also known as first Voroni) compactification of arithmetic quotients of type IV domains. These are of importance in the context of algebraic geometry because they are used to construct moduli spaces of polarised K3 surfaces and are strongly related to moduli spaces of hyperkähler varieties of higher dimension. The local analysis of singularities of a toroidal compactification reduces to that of finite quotients of toric varieties. The main result of this thesis gives a description of the singularities of the perfect cone compactification of the moduli space of pseudo-polarised K3 surfaces of square-free degree.

New ion trap mass spectrometry (ITMS) instrumentation, the toroidal IT and halo IT, were developed to meet the significant growth in on-site analysis applications. The miniature toroidal IT mass analyzer was operated with radio frequency (RF) trapping voltages of 3 kVp-p or less. Despite its reduced dimensions, it has roughly the same ion trapping capacity as conventional 3D quadrupole ITs. Unit-mass resolved spectra for n-butylbenzene, xenon, and naphthalene were obtained. The desired linear mass scale was obtained using conventional mass-selective instability scan combined with resonance ejection. The halo IT was also based on toroidal trapping geometry and microfabrication technology, consisting of two parallel ceramic plates, the facing surfaces of which were imprinted with sets of concentric ring electrodes. Unlike conventional ITs, in which hyperbolic metal electrodes establish equipotential boundary conditions, electric fields in the halo IT were established by applying different RF potentials to each ring. The potential on each ring could be independently optimized to provide the best trapping field. The halo IT featured an open structure, allowing easy access for in situ ionization. The toroidal geometry provided a large trapping volume. The photolithographic fabrication method avoided difficulty in meeting the required machining tolerances. Preliminary mass spectra showed resolution (m/δ m) of 60–75 when the trap was operated at 1.9 MHz and 500 Vp-p. Ion ejection through a hole in the center of the trap, and through slits machined in the ceramic plates were evaluated. The latter ejection method was done to mimic the design of the toroidal IT. The preferred electric fields containing higher order components were optimized by adjusting the potentials applied to the electrode rings of the halo IT without changing the original trapping plates and structure of the IT. The performance of the halo IT with 1% to 7% octopole field (A4/A2) components was determined. A best resolution of 280 (m/δ m) was obtained with 5% octopole field. SIMION simulations were used to demonstrate the toroidal trapping of ions and their mass analysis in both toroidal and halo ITs.

The thermal management of electric machines is investigated with the application of techniques to a Switched Reluctance Machine and a high-speed Switched Reluctance Machine. Two novel concepts for said management of a Switched Reluctance Machine are proposed and developed: Inter-Laminate Cooling and a Continuous Toroidal Winding. The Inter-Laminate Cooling concept is developed with application to an iron core inductor which serves as a proxy for the electric machine. The experimental results confirmed the capability of the method, expressed by the effectiveness, which defines the performance measure of the applied cooling method; a concept which itself is equally applicable to other cooling methods that may be applied to any electric machine. The effectiveness also describes the gain in allowable input power to the machine which is realized to reach the same thermal limit versus the case without Inter-Laminate Cooling. The Inter-Laminate Cooling was not applied in experimental test to a Switched Reluctance Machine due to the present economic and fabrication limitations. The Continuous Toroidal Winding concept, originally conceived to permit the consideration of a fluid capillary core type of winding to enhance machine cooling, is developed to allow for peripheral cooling of the machine windings and end windings. The Continuous Toroidal Winding version of the Switched Reluctance Machine is investigated for both its thermal and electrical performance in the context of a machine that is equivalent electromagnetically to its conventional counterpart. The Continuous Toroidal Winding Switched Reluctance Machine was found to perform thermally as tested, in a manner superior to that of the conventional machine where the Toroidal machine was simulated and researched at an equivalent level of operation to the conventional machine. The electrical performance of the Toroidal Switched Reluctance Machine although supportive of the simulation analysis used to develop the machine, was not fully conclusive. This may have been due to problematic iron cores used in the construction of the experimental machines. The application of the Inter-Laminate Cooling method to a Switched Reluctance Machine is considered on an analytical basis for the special case of a High Speed Switched Reluctance Machine and found to be of net positive benefit as the machine’s iron losses are dominant over its copper losses. Application of the Inter-Laminate Cooling method to a lower speed machine, whilst beneficial, is not sufficient to significantly impact the temperature of the machine’s windings such that it would offset the loss of specific torque and power. As such, Inter-Laminate Cooling is only applicable where the net benefit is positive overall; in that the gain in input power realized is sufficient to overcome the loss of specific power and torque which will occur due to the increased machine volume. The “effectiveness” and “gain” approach for the evaluation of cooling methods applied to electric machines is a concept which should be adopted to aid in the comparative understanding of the performance of myriad different cooling methods being applied to electric machines both in research and practice, of which there is only minimal understanding. / Thesis / Doctor of Philosophy (PhD)

No description available.

Switched reluctance machines (SRMs) are well known for their simple and robust structure, facilitating their increasing application in many sectors, for example vacuum cleaners, where domestic machines operate at high-speed, 50,000 RPM being typical. Conventional SRMs (CSRMs) use a decoupled concentrated phase winding so that torque is predominantly only generated due to the self-inductance, which limits utilization of the machine electrical circuits. In this thesis, the toroidal winding SRM (TSRM) is introduced, which operates based on the variation of mutual inductance between different phases. The toroidal winding introduces additional winding space, and the winding is practically easy to implement, both features that lead to a relatively higher copper filling factor. The toroidal winding also benefits the machine thermal performance, as the winding is directly exposed on the machine periphery and thus accessible to cooling. All these make TSRMs interesting and meaningful for further study. Following a comprehensive comparison of CSRM and TSRM characteristics, a general torque equation is presented that is applicable to both CSRM and TSRM. Two 12-switch converters are proposed to drive three-phase TSRMs. Moreover, sinusoidal current excitation with a commercial three-phase half-bridge converter has been suggested as an alternative converter solution for TSRMs. Accordingly, a three-phase six-stator-pole, four-rotor-pole CSRM is designed and optimized with a speed of up to 50,000 rpm in this thesis. A TSRM is resized to achieve the same envelope dimension as a benchmark CSRM. Thus, a comparative study between high-speed CSRM and TSRMs has been carried out. They have both been prototyped and tested. The findings suggest that the TSRM is superior, considering machine mass and wire temperature management. The TSRM has a better torque output at lower speeds because copper losses are dominant. However, the CSRM has more advantages at higher speeds due to lower iron losses and lower DC voltage requirements. / Thesis / Doctor of Philosophy (PhD)

Dans le milieu automobile, les règlementations visant à limiter l’émission de particules fines et de gaz à effet de serre sont devenues de plus en plus sévères au cours des dernières années. Cette tendance ne va pas s’inverser et des solutions doivent être trouvées pour améliorer le rendement des moteurs à combustion interne (ICE) qui propulsent la majorité des véhicules de tourisme dans le monde.Une des solutions permettant d’améliorer le rendement thermodynamique de l’ICE est d’utiliser un turbocompresseur. Cet organe de suralimentation permet d’accroître le couple du moteur en augmentant la pression d’air dans les cylindres et par conséquent la quantité de comburant. Le turbocompresseur présente cependant un inconvénient pour l’agrément de conduite. Selon la technologie employée, un temps de latence (turbo lag) plus ou moins important apparait entre le moment ou le conducteur appui sur la pédale d’accélérateur et le moment ou le couple est disponible sur les roues.Pour pallier ce problème, on peut utiliser une machine électrique venant assister le turbocompresseur durant la phase de montée en vitesse. Cette machine peut faire partie d’un système indépendant de compression d’air et placée en amont du turbocompresseur, on parlera alors de turbo assisté électriquement. Cette machine peut aussi être intégrée directement au turbocompresseur, on parlera alors de turbo électrique. Dans les deux cas, le temps de réponse du turbocompresseur est amélioré ce qui impacte directement la dynamique du véhicule et le plaisir de conduite. Dans le cas du turbo électrique, l’intégration de la machine électrique directement sur le turbocompresseur permet son fonctionnement en génératrice en offrant ainsi une amélioration du rendement global de l’ICE.Le sujet de la thèse est la modélisation et la conception des machines électriques haute vitesse pour ces applications. Les principales qualités recherchées pour ces machines seront :-leurs capacités à pouvoir fonctionner à haute vitesse : les vitesses recherchées se situe typiquement entre 70 000 et 150 000 tr/min pour des vitesses périphériques de l’ordre de 150 m/s ;-leurs densités de puissance : on recherche des puissances de 3 à 15 kW pour des machines compactes qui devront être intégrées sous le capot du véhicule ;-des rendements élevés de l’ordre de 95 % ;-une conception adaptée à la production en grande série pour l’automobile.Pour répondre à cette problématique, les travaux suivants ont été entrepris :Dans un premier temps, nous avons modélisé finement les phénomènes électromagnétiques et mécaniques liées aux machines électriques haute vitesse à encoches et aimants permanents positionnés en surface. Pour cela, nous avons développé un modèle de calcul en sous-domaines pour la partie électromagnétique et un modèle multicouches de résistance des matériaux pour le calcul de la tenue du rotor à haute vitesse.Dans un deuxième temps, pour pouvoir explorer des topologies de machines très différentes, nous avons eu recourt aux méthodes de calcul par éléments finis. Nous avons pu identifier et de comparer plusieurs topologies de machines à encoches, sans encoches, à bobinage dentaire ou toroïdal. Cette étude paramétrique a permis de comparer la densité de couple et le rendement de ces machines.Enfin, dans une dernière partie, nous avons traité le cas du prototypage et des mesures de ces machines. Pour cela, sur la base des études réalisées, nous avons prototypé trois machines aux performances prometteuses. La conception mécanique des différentes machines est abordée ainsi que les méthodes de mesures et les difficultés liées aux caractérisations à haute vitesse.Au cours de ce travail de thèse, d’autres aspects ont aussi été abordés tel que la modélisation des pertes du système machine électrique et convertisseur de puissance, la dynamique des rotors ou encore les émissions acoustiques. / In the automotive industry, regulations to limit the emission of greenhouse gases have become more and more severe. This trend is not going to change and solutions must be found to improve the efficiency of internal combustion engines (ICE) that drive the majority of passenger cars in the world.Turbochargers are a clever solution to improve the thermodynamic efficiency of the ICE. This forced induction device increases the air pressure in the cylinders and therefore the engine torque. However, turbochargers have a major disadvantage for the driver experience: a lag time (turbo lag) between the moment when the driver steps on the accelerator and the moment when torque is available.To overcome this problem, an electric machine can be used to assist the turbocharger during the speed up phase. This machine can be a part of an independent system of air compression and placed upstream of the turbocharger or it can be integrated directly into the turbocharger. In both cases, the response time of the turbocharger is greatly reduced which directly impacts the dynamic of the vehicle and the driving pleasure. The integration of the electric machine directly on the turbocharger allows its operation as a generator to improve the overall efficiency of the ICE.The subject of this thesis is the modeling and design of high speed electric machines for these applications. The main requirements are:-High-speed operation: between 70,000 and 150,000 rpm and peripheral speeds around 150 m/s.-Power density: from 3 to 15 kW for compact machines that will have to be integrated under the hood of the vehicle.-High efficiency: around 95 % and above.-A design adapted to mass production for the automotive industry.To cope with this requirements, the following tasks were undertaken:Firstly, we modeled the electromagnetic and mechanical behaviors of high-speed slotted electric machines with surface-mounted permanent magnets. For the electromagnetic part, we developed a subdomain calculation model. For the mechanical part, we worked on a multilayer model to evaluate the rotor strength at high speed.Secondly, we used finite element analysis methods to explore different machine structures. We compared several topologies of slotted and slotless machines, with tooth-coil winding and toroidal winding. This parametric study allowed us to compare the torque density and efficiency of these machines.Finally, we dealt with the case of prototyping and measurements of these machines. Based on the previous studies, we prototyped three machines with promising performances. The mechanical design of the different machines is discussed as well as the measurement methods and the difficulties associated with high speed characterization.During this thesis work, other aspects were also discussed such as the losses in power converters driving high-speed electric machines, rotor dynamics and acoustic emissions.