This thesis is concerned with multigraphs and their complexity which is defined and quantified by the distribution of edge multiplicities. Two random multigraph models are considered.  The first model is random stub matching (RSM) where the edges are formed by randomly coupling pairs of stubs according to a fixed stub multiplicity sequence. The second model is obtained by independent edge assignments (IEA) according to a common probability distribution over the edge sites. Two different methods for obtaining an approximate IEA model from an RSM model are also presented. In Paper I, multigraphs are analyzed with respect to structure and complexity by using entropy and joint information. The main results include formulae for numbers of graphs of different kinds and their complexity. The local and global structure of multigraphs under RSM are analyzed in Paper II. The distribution of multigraphs under RSM is shown to depend on a single complexity statistic. The distributions under RSM and IEA are used for calculations of moments and entropies, and for comparisons by information divergence. The main results include new formulae for local edge probabilities and probability approximation for simplicity of an RSM multigraph. In Paper III, statistical tests of a simple or composite IEA hypothesis are performed using goodness-of-fit measures. The results indicate that even for very small number of edges, the null distributions of the test statistics under IEA have distributions that are  well approximated by their asymptotic χ2-distributions. Paper IV contains the multigraph algorithms that are used for numerical calculations in Papers I-III.

AC/DC adapters mostly employ two-stage topology: Power Factor Correction (PFC) pre-regulation stage followed by an isolated DC/DC converter stage. Low power AC/DC adapters require a small size to be competitive. Among their components, the bulk DC-link capacitor is one of the largest because it should keep the output voltage with low ripple. Also, the size of this capacitor is penalized due to the universal line voltage application. Synchronization through employing leading edge modulation for the first PFC stage and trailing edge modulation for the second DC/DC converter stage can significantly reduce the ripple current and ripple voltage of the DC-link capacitor. Thus, a smaller DC-link capacitance can be used, lowering the cost and size of the AC/DC adapter. Benefits of the synchronous switching scheme were already demonstrated experimentally. However, no mathematical analysis was presented. In this thesis, detailed mathematical analyses in per-unit quantity are given to facilitate the calculation of the DC-link capacitor ripple current reduction with Leading/Trailing Edge Modulation strategies. One of the limitations of leading/trailing edge modulation is that the switching frequencies of the two stages need to be equal to achieve the best reduction of the DC-link capacitor ripple current. The DC-link capacitor ripple current will become larger if the switching frequency of the DC/DC converter is larger than that of the PFC pre-regulator, which blocks us to employ higher frequency for isolated DC/DC converter to reduce its transformer size. This thesis proposed a new Leading/Trailing Edge Modulation strategy to further reduce the DC-link bulk capacitor ripple current when switching frequency of DC/DC converter stage is twice the switching frequency of PFC stage. This proposed pulse width modulation scheme was verified by simulation. Experimental results obtained through digital control based on FPGA are also presented in this thesis.

A graph is said to be 2-edge-connected if it remains connected after the deletion of any single edge. Given an unweighted bridgeless graph G with n vertices, the minimum size 2-edge-connected spanning subgraph problem (2EC) is that of finding a 2-edge-connected spanning subgraph of G with the minimum number of edges. This problem has important applications in the design of survivable networks. However, because the problem is NP-hard, it is unlikely that efficient methods exist for solving it. Thus efficient methods that find solutions that are provably close to optimal are sought. In this thesis, an approximation algorithm is presented for 2EC on bridgeless cubic graphs which guarantees to be within 5/4 of the optimal solution value, improving on the previous best proven approximation guarantee of 5/4+ε for this problem. We also focus on the linear programming (LP) relaxation of 2EC, which provides important lower bounds for 2EC in useful solution techniques like branch and bound. The “goodness” of this lower bound is measured by the integrality gap of the LP relaxation for 2EC, denoted by α2EC. Through a computational study, we find the exact value of α2EC for graphs with small n. Moreover, a significant improvement is found for the lower bound on the value of α2EC for bridgeless subcubic graphs, which improves the known best lower bound on α2EC from 9/8 to 8/7.

The benefits of using feature-based CAD methodology and direct modelling are discussed inthe thesis. An experimental CAD study has been performed in which three different cases hasbeen modelled to get an overview of how direct modelling works in Solid Edge ST10 and to determine how the methodology could be integrated into product development. These two ways of modelling in Solid Edge are evaluated using previous research and data from thestudy to do a SWOT analysis and a Pugh matrix. Further on a comparison is made to find respective methodologies’ area of use.The experimental CAD study explores three cases in which each uses one type of product thatis investigated. The CAD models used as reference for the experiment are originally created using feature-based modelling, in the ordered module of Solid Edge. The intent is to recreate the models using direct modelling. The products of interest are created using different manufacturing processes which enables most tools in the Synchronous module to be put tothe test. Points of interests for the study is the workflow of direct modelling, to define the useand limits of Synchronous and investigate the synergy between the tools of the modules.It is concluded that direct modelling excels in certain area of operations where precision engineering can be ignored. When developing concepts for a new product, time could be savedby using the swift surface editing tool of direct modelling. When the CAD user does not need to rely on already set dimensions and is free to explore different shapes to create a 3D-model,direct modelling will come in handy due to its ability to model without taking history data into account. Direct modelling can also be used as a tool for creating redesigns of products containing complex feature trees. Cooperation between different CAD software could be strengthened using direct modelling where the need to redesign imported CAD files featuring “dead geometries” and empty history trees. These types of 3D-models, step, Parasolid’s etc can be easily modified using directmodelling in Solid Edge. Further research can be made to determine in which areas direct modeling can be applied and excel compared to the standard feature-based CAD methodology.

In the military arena there is an increase in demand for Low Observable (LO) flight vehicles. This drive for low observability imposes limits on Leading Edge (LE) sweep angles and prohibits the use of a tailplane/fin resulting in unconventional configurations; a typical example of which are Unmanned Combat Aerial Vehicles (UCAVs). This class of aircraft poses stability and control problems due to the early onset of flow separation. The focus of this project is on the on the use of Tangential Leading Edge Blowing (TLEB) as a means of separation suppression on such vehicles. This project is unique in that the TLEB slot is positioned on the wing lower surface facing the oncoming freestream. Also, the model in this project is representative of the outboard panel of a UCAV wing, a geometry on which TLEB has not been explored in the past. A swept wing model (LE sweep = 47 degrees, AR = 3) was designed. The model has a TLEB nozzle with a slot on the lower surface at approx. 1% yawed chord that spans 0.58 m (approx. 70% LE length). Baseline wing characteristics were obtained with the full slot exposed. The wing showed a variation in pitch between CL = 0 and 0.6 which from oil flow visualisation is believed to be due to laminar separation. At CL = 0.6 there is a positive pitch break which flow visualisation suggests is due to the occurrence of a LE vortex. Sensitivity studies for slot configuration, Re number and transition fixing were carried out. The blowing rates 0.0025, 0.005, 0.025, 0.05 were tested for two slot lengths; one full span (0.58 m) and another third span positioned at the midpoint of the full slot. All blowing rates show some suppression of the LE vortex and therefore reduction in severity of the pitch break at CL = 0.6. High blowing rates produce a negative shift in CM, which CFD suggests is due to a large amount of suction produced on the lower wing surface adjacent to the slot exit. This means the available trim power is less than for the lower blowing rates. Wool tuft results for high blowing rates from the middle slot show an increase in streamwise flow at the TE suggesting TLEB is capable of improving the effectiveness of TE devices. The effectiveness of TLEB at low blowing rates has been shown to be high compared to that found in literature. A 1st order analysis of the impact of TLEB on a full scale system shows realistic options.

The lower and upper independent, domination and irredundant numbers of the graph G = (V, E) are denoted by i ( G) , f3 ( G), 'Y ( G), r ( G), ir ( G) and IR ( G) respectively. These six numbers are called the domination parameters. For each of these parameters n:, we define six types of criticality. The graph G is n:-critical (n:+ -critical) if the removal of any vertex of G causes n: (G) to decrease (increase), G is n:-edge-critical (n:+-edge-critical) if the addition of any missing edge causes n: (G) to decrease (increase), and G is Ir-ER-critical (n:- -ER-critical) if the removal of any edge causes n: (G) to increase (decrease). For all the above-mentioned parameters n: there exist graphs which are n:-critical, n:-edge-critical and n:-ER-critical. However, there do not exist any n:+-critical graphs for n: E {ir,"f,i,/3,IR}, no n:+-edge-critical graphs for n: E {ir,"f,i,/3} and non:--ER-critical graphs for: E {'Y,/3,r,IR}. Graphs which are "I-critical, i-critical, "I-edge-critical and i-edge-critical are well studied in the literature. In this thesis we explore the remaining types of criticality. We commence with the determination of the domination parameters of some wellknown classes of graphs. Each class of graphs we consider will turn out to contain a subclass consisting of graphs that are critical according to one or more of the definitions above. We present characterisations of "I-critical, i-critical, "I-edge-critical and i-edge-critical graphs, as well as ofn:-ER-critical graphs for n: E {/3,r,IR}. These characterisations are useful in deciding which graphs in a specific class are critical. Our main results concern n:-critical and n:-edge-critical graphs for n: E {/3, r, IR}. We show that the only /3-critical graphs are the edgeless graphs and that a graph is IRcritical if and only if it is r-critical, and proceed to investigate the r-critical graphs which are not /3-critical. We characterise /3-edge-critical and r-edge-critical graphs and show that the classes of IR-edge-critical and r-edge-critical graphs coincide. We also exhibit classes of r+ -critical, r+ -edge-critical and i- -ER-critical graphs. / Mathematical Sciences / D. Phil. (Mathematics)

Propostas de construção de dispositivos que unem a eletrônica com a spintrônica utilizando compostos semicondutores magnéticos diluídos (DMS) tem se tornado cada mais frequentes junto à comunidade científica em geral. Em particular, por suas propriedades magnéticas e de transporte hoje conhecidas, camadas de GaAs/GaMnAs pertencem a um grupo de DMS com grandes possibilidades de utilização prática. Nesse sentido, entender suas propriedades de transporte é essencial para o desenvolvimento dessa nova área. Investigamos o transporte spin polarizado em nanocamadas de GaAs/GaMnAs que exibem uma fase ferromagnética abaixo de certa temperatura de transição de fase. Como procedimento de pesquisa, nosso cálculo da resistividade considerou a existência de uma banda de impureza que determina a natureza do estado no nível de Fermi e dos estados próximos a ele como estendidos (condução "metálica") ou localizados (condução por excitação térmica). A ordem magnética e a resistividade são interligados devido à influência da polarização de spin da banda de impurezas e um efeito tipo separação Zeeman sobre a mobility edge (1). Obtivemos para um dado intervalo de concentração de manganês e de portadores, um comportamento metálico em que o transporte por estados estendidos domina em baixas temperaturas e é dominado por um processo de excitação térmica dos estados localizados para temperaturas próximas e acima da temperatura de transição. O resultado dessa combinação de canais de condução foi o aparecimento de uma lombada na resistividade, a qual tem sido observada experimentalmente, e traz esclarecimentos sobre a relação entre as propriedades de transporte e magnéticas desse material. (1) Embora a expressão possa ter uma tradução, é comumente usada na área em inglês. / Construction proposals of the contrivances that put together electronic with spintronic using diluted magnetic semiconducting compounds (DMS) are more and more frequent to the scientific community in general. In particular, because of its magnetic and transporting rightnesses that has been known today, GaMnAs stratums belongs to a DMS group with great possibilities of the practical utilization. In this sense, to understand its transporting rightnesses is essential to the development in this new area. We investigate the polarized spin transport in GaMnAs nanolayers that display an ferromagnetic stage below of the specific phase transition temperature. As a procedure research, our resistivity estimate has consider the existence of an impurity band that determine the state nature in the Fermi level and the states near to it like extended (metallicconduction) or located (thermic excitation conduction). The magnetic order and resistivity are interconnected due to the influence of the spin polarization of the band of the impurities and another efect as a Zeeman separation over the moblility edge. We aquire, for a certain interval of bearings and manganese concentration, a metallic behavior in which the transport to the extended states rules in low temperatures and is ruled by an process of thermic excitation of the states located to near and over temperatures of the transition temperature. The result of this transport channels combination was the appearance of an acclivity in the resistivity that has been observed experimentally and brings elucidations about the relation between the magnetic and transporting rightnesses of this material.

Propostas de construção de dispositivos que unem a eletrônica com a spintrônica utilizando compostos semicondutores magnéticos diluídos (DMS) tem se tornado cada mais frequentes junto à comunidade científica em geral. Em particular, por suas propriedades magnéticas e de transporte hoje conhecidas, camadas de GaAs/GaMnAs pertencem a um grupo de DMS com grandes possibilidades de utilização prática. Nesse sentido, entender suas propriedades de transporte é essencial para o desenvolvimento dessa nova área. Investigamos o transporte spin polarizado em nanocamadas de GaAs/GaMnAs que exibem uma fase ferromagnética abaixo de certa temperatura de transição de fase. Como procedimento de pesquisa, nosso cálculo da resistividade considerou a existência de uma banda de impureza que determina a natureza do estado no nível de Fermi e dos estados próximos a ele como estendidos (condução "metálica") ou localizados (condução por excitação térmica). A ordem magnética e a resistividade são interligados devido à influência da polarização de spin da banda de impurezas e um efeito tipo separação Zeeman sobre a mobility edge (1). Obtivemos para um dado intervalo de concentração de manganês e de portadores, um comportamento metálico em que o transporte por estados estendidos domina em baixas temperaturas e é dominado por um processo de excitação térmica dos estados localizados para temperaturas próximas e acima da temperatura de transição. O resultado dessa combinação de canais de condução foi o aparecimento de uma lombada na resistividade, a qual tem sido observada experimentalmente, e traz esclarecimentos sobre a relação entre as propriedades de transporte e magnéticas desse material. (1) Embora a expressão possa ter uma tradução, é comumente usada na área em inglês. / Construction proposals of the contrivances that put together electronic with spintronic using diluted magnetic semiconducting compounds (DMS) are more and more frequent to the scientific community in general. In particular, because of its magnetic and transporting rightnesses that has been known today, GaMnAs stratums belongs to a DMS group with great possibilities of the practical utilization. In this sense, to understand its transporting rightnesses is essential to the development in this new area. We investigate the polarized spin transport in GaMnAs nanolayers that display an ferromagnetic stage below of the specific phase transition temperature. As a procedure research, our resistivity estimate has consider the existence of an impurity band that determine the state nature in the Fermi level and the states near to it like extended (metallicconduction) or located (thermic excitation conduction). The magnetic order and resistivity are interconnected due to the influence of the spin polarization of the band of the impurities and another efect as a Zeeman separation over the moblility edge. We aquire, for a certain interval of bearings and manganese concentration, a metallic behavior in which the transport to the extended states rules in low temperatures and is ruled by an process of thermic excitation of the states located to near and over temperatures of the transition temperature. The result of this transport channels combination was the appearance of an acclivity in the resistivity that has been observed experimentally and brings elucidations about the relation between the magnetic and transporting rightnesses of this material.

This work proposes to address the computation of flow-generated noise, including the high frequency components in an acceptable computational time, relative to industrial applications. In this framework, hybrid methods based on aeroacoustic analogies are relevant to predict the corresponding sound, in term of computational time and easy implementation, and are separating the sources of sound computation from the sound propagation itself. Both parts of the hybrid method are then investigated.<p><p>Firstly, the sources of sound should be computed accurately, reproducing most of the energy content of the turbulent flow. The present study is mainly based on LES computations, that are a good compromise between the accuracy and the time required to obtain the sources, especially for low Mach number application, where incompressible flow computations can be used. The influence of the computational parameters is then studied through the investigation of the influence of the boundary conditions, flow solver, mesh refinement, LES subgrid-scale model and computational domain definition. <p><p>Secondly, the sound sources propagation is computed using classical analogies based most of the time on free field Green's functions. They are limited to the low frequency range of the emitted sound spectrum, where the source is compact, if incompressible acoustic sources are used. They are then proposed to be combined with Amiet's theory for airfoil noise to cover the remaining high frequency part of the sound spectrum. The limitations of Amiet's theory are analysed through the geometrical and acoustical far-field assumptions. Furthermore, an inverse strip method is proposed to extend Amiet's theory to spanwise varying flow conditions and taking correctly into account the spanwise wave number effects. <p><p>The leading-edge noise mechanism is studied through the interaction of the turbulent region of a jet with a NACA0012 airfoil. The hybrid method, consisting in an incompressible LES computation combined with Curle's analogy, showed its limitation to the low frequency range of the sound spectrum when low-order CFD are used. The Amiet's theory, based on the modelisation of the upstream velocity spectrum, provides a good sound prediction at high frequency, as far as the airfoil thickness is accounted for. <p><p>The Trailing-edge noise mechanism is studied through the flow around a mid-span cut of a blade (CD airfoil) of an automotive cooling fan. <p>Three different acoustic methods are used :Curle's analogy is using wall-pressure fluctuations over the airfoil surface, Ffowcs-Williams and Hall's analogy is using volumetric velocity informations around the trailing-edge and Amiet's theory for trailing-edge noise is using the wall-pressure spectrum around the trailing-edge and the corresponding spanwise correlation. The methods using wall-pressure informations are shown to directly transfer the informations of the wall-pressure spectrum to the sound spectrum. Differences are appearing in the higher frequency range where the airfoil starts to be non compact, invalidating the use of Curle's analogy at such frequencies compared to the other methods, taking scattering effects into account implicitly in their formulations. <p><p>Finally, in order to reduce the computational cost, Amiet's theory for trailing-edge noise is proposed to be driven from steady RANS computations. Two methods to compute the wall-pressure spectrum from boundary-layer informations are studied. Their respective robustness and reliability are analysed in an uncertainty quantification framework, in case of varying velocity profiles upstream the airfoil. Both models showed similar results and tendency compared to the wall-pressure LES spectrum, as far as the flow topology remains similar. / Doctorat en Sciences de l'ingénieur / info:eu-repo/semantics/nonPublished

A graph is said to be 2-edge-connected if it remains connected after the deletion of any single edge. Given an unweighted bridgeless graph G with n vertices, the minimum size 2-edge-connected spanning subgraph problem (2EC) is that of finding a 2-edge-connected spanning subgraph of G with the minimum number of edges. This problem has important applications in the design of survivable networks. However, because the problem is NP-hard, it is unlikely that efficient methods exist for solving it. Thus efficient methods that find solutions that are provably close to optimal are sought. In this thesis, an approximation algorithm is presented for 2EC on bridgeless cubic graphs which guarantees to be within 5/4 of the optimal solution value, improving on the previous best proven approximation guarantee of 5/4+ε for this problem. We also focus on the linear programming (LP) relaxation of 2EC, which provides important lower bounds for 2EC in useful solution techniques like branch and bound. The “goodness” of this lower bound is measured by the integrality gap of the LP relaxation for 2EC, denoted by α2EC. Through a computational study, we find the exact value of α2EC for graphs with small n. Moreover, a significant improvement is found for the lower bound on the value of α2EC for bridgeless subcubic graphs, which improves the known best lower bound on α2EC from 9/8 to 8/7.