Given a hyperbolic surface, the set of all closed geodesics whose length is minimal form a graph on the surface, in fact a so called fat graph, which we call the systolic graph. The central question that we study in this thesis is: which fat graphs are systolic graphs for some surface -we call such graphs admissible. This is motivated in part by the observation that we can naturally decompose the moduli space of hyperbolic surfaces based on the associated systolic graphs. A systolic graph has a metric on it, so that all cycles on the graph that correspond to geodesics are of the same length and all other cycles have length greater than these. This can be formulated as a simple condition in terms of equations and inequations for sums of lengths of edges. We call this combinatorial admissibility. Our first main result is that admissibility is equivalent to combinatorial admissibility. This is proved using properties of negative curvature, specifically that polygonal curves with long enough sides, in terms of a lower bound on the angles, are close to geodesics. Using the above result, it is easy to see that a subgraph of an admissible graph is admissible. Hence it suffices to characterize minimal non-admissible fat graphs. Another major result of this thesis is that there are infinitely many minimal non-admissible fat graphs (in contrast, for instance, to the classical result that there are only two minimal non-planar graphs).

Physics in interactive environments, such as computer games, and simulations require well madeand accurate bounding volumes in order to act both realistically and fast. Today it is common to useeither inaccurate boxes or spheres as bounding volumes or to model the volume by hand. Thesemethods are either too inaccurate or require too much time to ever be able to be used in real-time,accurate virtual environments.This thesis presents a method to automatically generate collision hulls for both manifolds and nonmanifolds.This allows meshes to be used in a physical environment in just a few seconds and stillbeing able to behave realistically. The method performs Approximate Convex Decomposition byiteratively dividing the mesh into smaller, more convex parts. Every part is wrapped in a convexhull. Together the hulls make an accurate, but low cost, convex representation of the original mesh.The convex hulls are stored in a bounding volume hierarchy tree structure that enables fast testingfor collision with the mesh.

No description available.

Variable-speed Induction motor drives are nowadays used for various kinds of industrial processes, transportation systems, wind turbines and household appliances in the world. The majority of drives are for general purpose speed control applications where accurate speed control is not required for entire speed range. But for high dynamic drive application, very precise and fast control of induction motor drive is essential. For such applications, sophisticated and well-performing control design is a key issue. Precise and accurate torque control of the Induction Motor (IM) can only be accomplished by vector control and direct torque control. In terms of space vector theory, vector control implies that the instantaneous torque is controlled by way of the stator current vector that is orthogonal to the rotor flux vector. Precise knowledge of the rotor flux angle is therefore essential for a vector controlled IM. IMs do not allow the flux position to be easily measured, so most modern vector controlled IM drives rely on flux estimation. This means that the flux angle is derived from a flux estimator, using the dynamic model of the IM. Given that the rotor speed of the IM is measured by a mechanical shaft sensor. Flux estimation is a fairly easy task. However, vector control of IM without mechanical shaft speed sensor is of current interest in industrial environment. The driving motivations behind the development in sensorless control are lower cost, improved reliability and operating environment. In this thesis, a sensorless vector control scheme for rotor flux estimation using current error space phasor based hysteresis controller is proposed including the method for estimation of leakage inductance, Ls. For frequencies of operation less than 25 Hz, the rotor voltage and hence the rotor flux position is computed during the inverter zero voltage space vector using steady state model of IM. For above 25 Hz, active vector period and steady state model of IM is used. The whole rotor flux estimation scheme is dependent on current error space phasor and the steady state motor model, with rotor flux as a reference vector. Since no terminal voltage sensing is involved, dead time effects will not create problem in rotor flux sensing at low frequencies of operation. But appropriate device on-state drop are compensated at low frequencies (below 5 Hz) of operation to achieve a steady state operation up to less than 1 Hz. A constant switching frequency hysteresis current controller is used in inner current control loop for the PWM regulation, with smooth transition of operation to six-step mode operation. A simple Ls estimation based on current error space phasor is also proposed to nullify the deteriorating effect on rotor flux estimation. The parameter sensitivity of the control scheme to changes in the stator resistance Rs is also investigated. The drive scheme is tested up to a low frequency operation less than 1 Hz. The extensive simulation and experiment results are presented to show the proposed scheme’s good dynamic performance extending up to six-step operation. In contrast to vector control, direct torque control (DTC) method requires the knowledge of stator resistance only and thereby decreasing the associated sensitivity to parameters variation and the elimination of speed information. DTC as compared to vector control does not require co-ordinate transformation and PI controller. DTC is easy to implement because it needs only two hysteresis comparators and a lookup table for both flux and torque control. This thesis also investigates the possibilities in improvement of direct torque control scheme for high performance induction motor drive applications. Here, two schemes are proposed based on the direct torque control scheme for IM drive using 12-sided polygonal voltage space vectors for fast torque control. The torque control scheme based on DTC algorithm is proposed using 12-sided polygonal voltage space vector. The basic DTC scheme is used to control the torque. But the IM drive is open-end type. For torque control, the voltage space vectors orthogonal to stator flux vector in 12-sided polygonal space vector structure are used as hexagonal space vector based DTC scheme. The advantages achieved due to 12-sided polygonal space vector are mainly fast torque control and small torque ripple. The fast transient of torque with precise control is achieved using voltage space vector placed with a resolution of ±15. The torque ripple will be less as 6n±1 (n=odd) harmonic torque is totally eliminated from the whole range of PWM modulation. The comparative analysis of proposed 12-sided polygonal voltage space vector based DTC and conventional hexagonal space vector based DTC is also presented. Extensive simulation and experiment results are also presented to show the fast torque control at speeds of operation ranging from 5 Hz to the rated speed. The concept of 12-sided polygonal space vector based DTC is further extended for a variable speed control scheme using estimated fundamental stator voltage for sector identification. The conventional DTC scheme uses stator flux vector for identification of the sector and the switching vector are selected based on this sector information to control stator flux and torque. However, the proposed DTC scheme selects switching vectors based on the sector information of the estimated fundamental stator voltage vector and its relative position with respect to the stator flux vector. The fundamental stator voltage estimation is based on the steady state model of IM and information of synchronous frequency which is derived from computed stator flux using a low pass filter technique. The proposed DTC scheme utilizes the exact position of fundamental stator voltage vector and stator flux vector position to select optimal switching vector for fast control of torque with small variation of stator flux within hysteresis band. The present DTC scheme allows the full load torque control with fast transient response to very low speeds of operation below 5 Hz. The extensive simulation and experiment results are presented to show the fast torque control for speed of operation from zero speed to rated speed. However, the present scheme will have all the advantages of DTC scheme using stator flux vector for sector identification. All the above propositions are first simulated by MATLAB/Simulink and subsequently verified by an experimental laboratory prototype. The proposed control schemes are experimentally verified on a 3.7 kW IM drive. The control algorithms of the sensorless vector control using current error space phasor as well as DTC using 12-sided polygonal voltage space vector are completely implemented on a TI TMS320LF2812 DSP controller platform. These are some of the constituents for chapters 2, 3 and 4 in this thesis. Additionally, the first chapter also covers a brief survey on some of the recent progresses made in the field of sensorless vector control, direct torque control and current hysteresis controller. The thesis concludes with suggestion for further exploration.

[pt] Neste trabalho, são apresentadas algumas aplicações da otimização topológica para problemas de autovalor onde o principal objetivo é maximizar um determinado autovalor, como por exemplo uma frequência natural de vibração ou uma carga crítica linearizada, usando elementos finitos poligonais em domínios bidimensionais arbitrários. A otimização topológica tem sido comumente utilizada para minimizar a flexibilidade de estruturas sujeitas a restrições de volume. A ideia desta técnica é distribuir uma certa quantidade de material em uma estrutura, sujeita a carregamentos e condições de contorno, visando maximizar a sua rigidez. Neste trabalho, o objetivo é obter uma distribuição ótima de material de maneira a maximizar uma determinada frequência natural (para mantê-la afastada da frequência de excitação externa, por exemplo) ou maximizar a menor carga crítica linearizada (para garantir um nível mais elevado de estabilidade da estrutura). Malhas poligonais construídas usando diagramas de Voronoi são empregadas na solução do problema de otimização topológica. As variáveis de projeto, i.e. as densidades do material, utilizadas no processo de otimização, são associadas a cada elemento poligonal da malha. Vários exemplos de otimização topológica, tanto para problemas de frequências naturais de vibração quanto para cargas críticas linearizadas, são apresentados para demonstrar a funcionalidade e a aplicabilidade da metodologia proposta. / [en] In this work, we present some applications of topology optimization for eigenvalue problems where the main goal is to maximize a specified eigenvalue, such as a natural frequency or a linearized buckling load using polygonal finite elements in arbitrary two-dimensional domains. Topology optimization has commonly been used to minimize the compliance of structures subjected to volume constraints. The idea is to distribute a certain amount of material in a given design domain subjected to a set of loads and boundary conditions such that to maximize its stiffness. In this work, the objective is to obtain the optimal material distribution in order to maximize the fundamental natural frequency (e.g. to keep it away from an external excitation frequency) or to maximize the lowest critical buckling load (e.g. to ensure a higher level of stability of the structures). We employ unstructured polygonal meshes constructed using Voronoi tessellations for the solution of the structural topology optimization problems. The design variables, i.e. material densities, used in the optimization scheme, are associated with each polygonal element in the mesh. We present several topology optimization examples for both eigenfrequency and buckling problems in order to demonstrate the functionality and applicability of the proposed methodology.

The Discrete element method (DEM) is a methodology to investigatethe interactions among granular materials. It analyzes the behavior of par-ticulate environments by solving force-displacement equations that adhereto Newton’s second law of motion. Despite its usefulness, the DEM is notwithout limitations, and researchers are still facing certain challenges thatrestrict them from performing detailed analyses of granular materials. Thisstudy addresses two issues in DEM modeling of granular materials in rail-way embankments. Firstly, the long computational time required by theDEM for modeling fine angular particles in granular materials is addressedby exploring the effects of particle scaling on the shear behavior of granularmaterial. This study investigates the impact of particle size distribution,particle angularity, and the amount of scaling on the accuracy and compu-tational efficiency of DEM. Secondly, the limitations of DEM in includingthe continuous rail beam structure in the track are addressed by verifyinga DEM model against physical measurements of a full-scale ballasted trackand investigating the influence of including the rail beam structure on high-speed railway ballasted tracks. The results show that the use of particlescaling in the first study significantly improves the computational efficiencyof the DEM while maintaining accuracy, and this method is used in thesecond study to investigate the influence of the rail beam structure on thebehavior of railway tracks. / Diskreta elementmetoden (DEM) är en effektiv metod för att undersö-ka interaktioner i granulära material. Metoden analyserar samverkan mellanpartiklar genom att lösa kraft-deformationsekvationer som följer Newtonsandra lag. Trots dess användbarhet har DEM vissa begränsningar och fors-kare stöter fortfarande på vissa utmaningar som hindrar dem från att ge-nomföra detaljerade analyser av granulära material. Denna studie tar upptvå frågeställningar vid DEM-modellering av granulära material i järnvägs-bankar. För det första behandlas den långa beräkningstiden som krävs föratt modellera granulära material genom att utforska effekterna av parti-kelskalning på skjuvbeteendet. Studien undersöker effekten av partikelstor-leksfördelning och spetsighet på noggrannheten och beräkningseffektivite-ten. För det andra behandlas begränsningarna hos DEM när det gäller attinkludera den kontinuerliga rälsstrukturen i spåret genom att verifiera enDEM-modell mot fysiska mätningar av ett ballasterat spår i full skala ochundersöka inverkan av att inkludera rälsstrukturen. Resultaten i den förstastudien visar att tillämpningen av partikelskalning avsevärt förbättrar be-räkningseffektiviteten samtidigt som noggrannheten bibehålls. Partikelskal-ning används i den andra studien för att undersöka inverkan av rälsstruk-turen på beteendet hos järnvägsspår. / <p>QC 230508</p>

High strength low alloy (HSLA) steels have been developed to simultaneously have high yield strength and high fracture toughness. However, in practical applications steel must be welded. Traditional arc welding has proven detrimental to the fracture toughness of HSLA steels. Friction stir welding has recently shown mixed results in welding HSLA steels. The range of welding parameters used in these recent studies however has been very limited. With only a few welding parameters tested, the effect of spindle speed, travel speed, and heat input on the fracture toughness of friction stir welded HSLA steel remains unknown. To understand how the friction stir welding process parameters affect fracture toughness, double sided welds in API X80 were performed and analyzed. Results show that at room temperature friction stir welded API X80 exceeded industry minimum fracture toughness requirements in both the API Standard 1104 and DNV-OS-F101 by 143% and 62%, respectively. The process parameters of spindle speed and HI have been shown to effectively control the fracture toughness of the stir zone. Relationships have been established that show that fracture toughness increased by 85% when spindle speed decreased by 59% and heat input decreased by 46%.

<p>This thesis is devoted to introducing new problem formulations and exact solution methods for a class of continuous covering location models. The manuscript includes three self-contained studies which are organized as in the following. </p> <p> In the first study, we introduce the planar expropriation problem with non-rigid rectangular facilities which has many applications in regional planning and undesirable facility location domains. This model is proposed for determining the locations and formations of two-dimensional rectangular facilities. Based on the geometric properties of such facilities, we developed a new formulation which does not require employing distance measures. The resulting model is a mixed integer nonlinear program. For solving this new model, we derived a continuous branch-and-bound framework utilizing linear approximations for the tradeoff curve associated with the facility formation alternatives. Further, we developed new problem generation and bounding strategies suitable for this particular branch-and-bound procedure. We designed a computational study where we compared this algorithm with two well-known mixed integer nonlinear programming solvers. Computational experience showed that the branch-and-bound procedure we developed performs better than BARON and SBB both in terms of processing time and size of the branching tree.</p> <p> The second study is referred to as the planar maximal covering problem with single convex polygonal shapes and it has ample applications in transmitter location, inspection of geometric shapes and directional antenna location. In this study, we investigated maximal point containment by any convex polygonal shape in the Euclidean plane. Using a fundamental separation property of convex sets, we derived a mixed integer linear formulation for this problem. We were able to identify two types of special cuts based on the geometric properties of the shapes under study, which were later employed for developing a branch-and-cut procedure for solving this particular location model. We also evaluated the resultant bound quality after employing the afore-mentioned cuts. </p> <p> In the third study, we discuss the dynamic planar expropriation problem with single convex polygonal shapes. We showed how the basic problem formulations discussed in the first two studies extend to their diametric opposites, and further to models in higher dimensions. Subsequently, we allowed a dynamic setting where the shape under study is expected to function over a finite planning horizon and the system parameters such as the fixed point locations and expropriation costs are subject to change. The shape was permitted to relocate at the beginning of each time period according to particular relocation costs. We showed that this dynamic problem structure can be decomposed into a set of static problems under a particular vector of relocations. We discussed the solution of this model by two enumeration procedures. Subsequently, we derived an incomplete dynamic programming procedure which is suitable for this distinct problem structure. In this method, there is no need to evaluate all the branches of the branching tree and one proceeds with keeping the minimum stage cost. The evaluation of a branch is postponed until relocation takes place in the lower-level problems. With this postponing structure, the procedure turned out to be superior to the two enumeration procedures in terms of tree size. </p> / Thesis / Doctor of Philosophy (PhD)

[pt] A otimização topológica tem como objetivo encontrar a distribuição mais eficiente de material (ótima topologia) em uma determinada região, satisfazendo as restrições de projeto estabelecidas pelo usuário. Na abordagem tradicional atribui-se uma variável de projeto, constante, denominada densidade, para cada elemento finito da malha. Dessa forma, a qualidade da representação dos novos contornos da estrutura depende do nível de discretização da malha: quanto maior a quantidade de elementos, mais bem definida será a topologia da estrutura otimizada. No entanto, a utilização de malhas super-refinadas implica em um elevado custo computacional, principalmente na etapa de solução numérica das equações de equilíbrio pelo método dos elementos finitos. Este trabalho propõe uma nova estratégia computacional para o refinamento adaptativo local de malhas utilizando elementos finitos poligonais em domínios bidimensionais arbitrários. A ideia consiste em realizar um refinamento da malha nas regiões de concentração de material, sobretudo nos contornos internos e externos, e um desrefinamento nas regiões de baixa concentração de material, como por exemplo, nos furos internos. Desta forma, é possível obter topologias ótimas, com alta resolução e relativamente baixo custo computacional. Exemplos representativos são apresentados para demonstrar a robustez e a eficiência da metodologia proposta por meio de comparações com resultados obtidos com malhas super-refinadas e mantidas constantes durante todo o processo de otimização topológica. / [en] Topology optimization aims to find the most efficient distribution of material (optimal topology) in a given domain, subjected to design constraints defined by the user. The quality of the new boundary representation depends on the level of mesh refinement: the greater the number of elements in the mesh, the better will be the representation of the optimized structure. However, the use of super refined meshes implies in a high computational cost, especially regarding the numerical solution of the linear systems of equations that arise from the finite element method. This work proposes a new computational strategy for adaptive local mesh refinement using polygonal finite elements in arbitrary two-dimensional domains. The idea is to perform a mesh refinement in regions of material concentration, mostly in inner and outer boundaries, and a mesh derefinement in regions of low material concentration such as the internal holes. Thus, it is possible to obtain optimal topologies with high resolution and relatively low computational cost. Representative examples are presented to demonstrate the robustness and efficiency of the proposed methodology by comparing the results obtained herein with the ones from the literature where super refined meshes are held constant throughout all topology optimization process.

Multilevel converters are finding increased attention in industry and academia as the preferred choice of electronic power conversion for high power applications. They have a wide application area in a variety of industries involving transportation and energy management, a significant portion of which comprises of multilevel inverter fed induction motor drives. Multilevel inverters are ideally suitable for high power drives, since the switching frequency of the devices is limited for high power applications. In low power drives, the switching frequency is often in the range of tens of kHz, so that switching frequency harmonics are pushed higher in the frequency spectrum thereby the size and cost of the filter are reduced. But higher switching frequency has its own drawbacks, in particular for high voltage, high power applications. They cause large dv/dt stress on the motor and the devices, increased EMI problems and higher switching losses. An engineering trade-o is thus needed to select the minimum switching frequency without compromising on the output voltage quality. The present work is an alternate approach in this direction. Here, new inverter topologies and PWM strategies are developed that can eliminate a set of harmonics in the phase voltage using 12-sided polygonal space vector diagrams, also called dodecagonal space vector diagrams. A dodecagonal space vector diagram has many advantages over a hexagonal one. Switching space vectors on a dodecagon will not produce any harmonics of the order 6n 1, (n=odd) in the phase voltage. The next set of harmonics thus reside at 12n 1, (n=integer). By increasing the number of samples in a sector, it is also possible to suppress the lower order harmonics and a nearly sinusoidal voltage can be obtained. This is possible to achieve at a low switching frequency of the inverters. At the same time, a dodecagon is closer to a circle than a hexagon; so the linear modulation range is extended by about 6.6% compared to the hexagonal case. For a 50 Hz rated frequency operation, under constant V/f ratio, the linear modulation can be achieved upto a frequency of 48.3 Hz. Also, the harmonics of the order 6n 1, (n=odd) are absent in the over-modulation region. Maximum fundamental voltage is obtained from this inverter at the end of over-modulation region, where the phase voltage becomes a 12-step waveform. The present work is developed on dodecagonal space vector diagrams. The entire work can be summarized and explained through Fig. 1. This figure shows the development of hexagonal and dodecagonal space vector diagrams. It is known that, 3-level and 5-level space vector diagrams have been developed as an improvement over 2-level ones. They Figure 1: Development of hexagonal and dodecagonal space vector diagrams have better harmonic performance, reduced dv/dt stress on the motor and devices, better electromagnetic compatibility and improvement of efficiency over 2-level space vector diagrams. This happens because the instantaneous error between the reference vector and the switching vectors reduces, as the space vector density increases in the diagram. This is shown at the top of the figure. In the bottom part, the development of the dodecagonal space vector diagram is shown, which is the contribution of this thesis work. This is explained in brief in the following lines. Initially, a space vector diagram is proposed which switches on hexagonal space vectors in lower-modulation region and dodecagonal space vectors in the higher modulation region. As the reference vector length increases, voltage vectors at the vertices of the outer dodecagon and the vertices from the outer most hexagon is used for PWM control. This results in highly suppressed 5th and 7th order harmonics thereby improving the harmonic profile of the motor current. This leads to the 12-step operation at rated voltage where all the 5th and 7th order harmonics are completely eliminated. At the same time, the linear range of modulation extends upto 96.6% of base speed. Because of this, and the high degree of suppression of lower order harmonics, smooth acceleration of the motor upto rated speed is possible. The presence of multilevel space vector structure also limits the switching frequency of the inverters. In the next work, the single dodecagonal space vector diagram is improved upon to form two concentric dodecagons spanning the space vector plane (Fig. 1). The radius of the outer dodecagon is double the inner one. It reduces the device rating and the dv/dt stress on the devices to half compared to existing 12-sided schemes. The entire space vector diagram is divided into smaller sized isosceles triangles. PWM switching on these smaller triangles reduces the inverter switching frequency without compromising on the output voltage quality. The space vector diagram is further refined to accommodate six concentric dodecagons in the space vector plane (Fig. 1). Here the space vector diagram is characterized by alternately placed dodecagons which become closer to each other at higher radii. As such the harmonics in the phase voltage are reduced, in particular at higher modulation indices. At the same time, because of the dodecagonal space vector structure, all the 6n ± 1, (n=odd) harmonics are eliminated from the phase voltage. A nearly sinusoidal phase voltage can be generated without resorting to high frequency switching of the inverters. The above space vector diagrams are developed using different inverter circuits. The first work is developed from cascaded combination of three 2-level inverters, while the second and third works use 3-level NPC inverters feeding an open end induction motor drive. The circuit topologies are explained in detail in the respective chapters. Apart from this, PWM switching schemes and detailed analysis on duty cycle calculations using the concept of volt-second balance are also presented. They show that with proper switching schemes, the proposed configurations can substantially reduce the overall loss of the inverter. Other operational issues like capacitor voltage balancing of 3-level NPC inverters and improvement of input current drawn from the grid are also covered. All the above propositions are first simulated by MATLAB and subsequently verified by an experimental laboratory prototype. Motor current waveforms both at steady state and transient conditions during motor acceleration show that the induction motor can be fed from nearly sinusoidal voltage at all operating conditions. Simplified comparative studies are also made with the proposed converters and higher level inverters in terms of output voltage quality and losses. These are some of the constituents for chapters 2, 3 and 4 in this thesis. Additionally, the first chapter also covers a brief survey on some of the recent progresses made in the field of multilevel inverter. The thesis concludes with some interesting ideas for further thought and exploration.