An integral part of NASA's vision for the coming years is a sustained infrastructure in cislunar space. The current baseline trajectory for this facility is a Near Rectilinear Halo Orbit (NRHO), a periodic orbit in the Circular Restricted Three-Body Problem. One of the goals of the facility is to serve as a proving ground for human spaceflight operations in deep space. Thus, this investigation focuses on transfers between the baseline NRHO and a family of periodic orbits that originate from a period-doubling bifurcation along the halo family. This new family of orbits has been termed the ``butterfly" family. This investigation also provides an overview of the evolution for a large subset of the butterfly family. Transfers to multiple subsets of the family are found by leveraging different design strategies and techniques from dynamical systems theory. The different design strategies are discussed in detail, and the transfers to each of these regions are compared in terms of propellant costs and times of flight.

In 1992 Du and Hwang published a paper confirming the correctness of a well known 1968 conjecture of Gilbert and Pollak suggesting that the Euclidean Steiner ratio for the plane is 2/3. The original objective of this thesis was to adapt the technique used in this proof to obtain results for other Minkowski spaces. In an attempt to create a rigorous and complete version of the proof, some known results were given new proofs (results for hexagonal trees and for the rectilinear Steiner ratio) and some new results were obtained (on approximation of Steiner ratios and on transforming Steiner trees). The most surprising result, however, was the discovery of a fundamental gap in the proof of Du and Hwang. We give counter examples demonstrating that a statement made about inner spanning trees, which plays an important role in the proof, is not correct. There seems to be no simple way out of this dilemma, and whether the Gilbert-Pollak conjecture is true or not for any number of points seems once again to be an open question. Finally we consider the question of whether Du and Hwang's strategy can be used for cases where the number of points is restricted. After introducing some extra lemmas, we are able to show that the Gilbert-Pollak conjecture is true for 7 or fewer points. This is an improvement on the 1991 proof for 6 points of Rubinstein and Thomas. / Mathematical Sciences / Ph. D. (Mathematics)

Made available in DSpace on 2015-05-14T12:36:55Z (GMT). No. of bitstreams: 1 parte1.pdf: 1169586 bytes, checksum: 685986454ee5e2cc58d709e7d646732f (MD5) Previous issue date: 2009-08-28 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / This work presents a new heuristic, called Heurística 1, and the implementations of the GRASP, Simulated Annealing and Genetic Algorithms metaheuristics for the rectilinear Steiner minimum tree problem (RSMTP), talking about its theoretical aspects, like computational complexity, and practical ones, like pseudo-codes and implementation strategies. The new techniques for RSMTP presented, especially the Genetic Algorithms, have computational results of superior quality in comparison to the best heuristics in present litera / Este trabalho apresenta uma nova heurística, denominada Heurística 1, e a implementação das metaheurísticas GRASP, Simulated Annealing e Algoritmos Genéticos para o problema da árvore retilínea mínima de Steiner (RSMTP), discorrendo sobre seus aspectos teóricos, como a complexidade computacional; e práticos, como pseudocódigos e estratégias de implementação. As novas abordagens para o RSMTP apresentadas, em especial os Algoritmos Genéticos, ostentam resultados computacionais de qualidade superior às apresentadas pelas melhores heurísticas da literatura atual.

L’étude des vortex trouve sa justification dans le rôle que ces derniers jouent dans la turbulence quantique. L’équation de Gross-Pitaevskii ne peut pas nous permettre de modéliser convenablement l’Hélium superfluide, mais on peut l’utiliser pour obtenir le paramètre d'ordre d’un superfluide modèle, ayant le maximum de propriétés en commun avec l’Hélium, notamment une courbe de dispersion identique, par la modification du terme d’interactions.En supposant que le minimum roton influence l’essentiel de la physique, on détermine la forme du paramètre d’ordre loin de la perturbation créée par le vortex rectilinéaire axisymétrique par deux approches différentes - il apparaît alors que seuls deux paramètres sont nécessaires pour caractériser entièrement le profil.Le modèle proposé par Pomeau-Rica, qui offre la possibilité d’étudier le superfluide près de la cristallisation, met en lumière l’impact de la profondeur du minimum roton sur l’amplitude des oscillations. Par comparaison avec les résultats obtenus ab initio par Reatto, les résultats donnés par le modèle de Berloff-Roberts exhibent un déphasage marqué, qui semble être une conséquence non-physique de la forme du spectre d’excitation. Les calculs énergétiques laissent à penser que les oscillations portent une faible fraction de l’énergie du vortex, l'énergie cinétique dominant.Le calcul du paramètre d’ordre est effectué pour un anneau de grande taille par rapport à la distance interatomique, à vitesse nulle et à vitesse non-nulle. La détermination des énergies potentielle et cinétique permet d’accéder à la vitesse maximale atteinte par l’anneau en fonction de son rayon et de la comparer à la vitesse critique de Landau. / Vortices study's justification lays in the fact that those former play an important part in quantum turbulence. The Gross-Pitaevskii equation can't be a proper model for superfluid helium, but we can still use it to determine the order parameter of a theoretical superfluid, which has then the maximum amount of properties in common with liquid helium, and in particular, the same dispersion relation, thus gained by modifying the interaction terms.We then make the assumption that all the physical properties of the superfluid are triggered by the existence of the roton minimum, which allows us to calculate the order parameter far from the perturbation created by an axisymmetric rectilinear vortex, using two different methods. At that point, it appears that only two parameters are needed to fully characterize vortex profil.Pomeau-Rica's model offers the possibility to study the superfluid near crystallization and reveals the influence of the roton minimum's shape and depth on oscillations' amplitude. Results are subsequently compared to those given by Reatto's ab initio calculations. In Berloff-Roberts' model, profil displays a strong phase shift, which seems to be a non-physical consequence of the dispersion relation's shape at high frequencies. Energies reckoning leads us to think that oscillations carry a small fraction of the total vortex' energy, meaning that the kinetic energy is dominant.The order parameter for a vortex ring, whose radius is much larger than the interatomic distance, is calculated at zero and nonzero speed. Potential and kinetic energies are estimated and help us obtain the maximal speed reached by such a ring, depending on its radius and finally discussed this speed in regard to the Landau critical speed.

Ion traps used in mass spectrometers are of two classes. One class consists of traps having three electrode geometries which have rotational symmetry about central axis. They are called axially symmetric ion traps. Paul trap, Cylindrical Ion Trap(CIT) are examples in this class. Other class of traps contain 2D electric field inside them which has same profile along the central axis due to translational symmetry. Linear Ion Trap(LIT) and Rectilinear Ion Trap(RIT) are examples in this class. In the ideal hyperbolic geometries of Paul trap and LIT, electric field is a perfectly linear function of distance from the center of the trap. But when these ideal geometries are simplified in to simpler geometries of the CIT and the RIT for ease in machining, linearity of field, which is a specialty of Paul trap and LIT is lost. In this thesis, an effort is made to optimize the field within the traps by using split electrodes. The ring electrode of the CIT and both pairs of electrodes in the RIT are divided into more number of parts. Suitable voltages are applied on these parts to improve the linearity of the field. This thesis contains six chapters. Chapter 1 contains a background information about mass spectrometry. Chapter 2 discusses the Boundary Element Method (BEM) used to calculate charge distribution and Nelder-Mead method used for optimization. It also shows the calculation of multipoles. In Chapter 3, two new geometries namely split-electrode RIT and split-electrode CIT are considered with the objective of improving the linearity of electric field inside them. It is shown here that by applying certain external potential on various parts of split electrodes of these geometries, it is possible to improve the linearity of electric field inside them. In Chapter 4, capacitor models of new geometries proposed in chapter 3 are discussed. The use of external capacitors as a replacement to external power supply is also discussed in this chapter. InChapter5, study similar to that ofChapter3is carried out by splitting the geometries in more number of parts. The possibility of improved field profile is investigated by applying full potential to some of these parts and keeping other parts at ground potential. In Chapter 6, concluding remarks are discussed.

Given a finite set K of terminals in the plane. A rectilinear Steiner minimum tree for K (RST) is a tree which interconnects among these terminals using only horizontal and vertical lines of shortest possible length containing Steiner point. We show the complexity of RST i.e. belongs to NP-complete. Moreover we present an approximative method of determining the solution of RST problem proposed by Sanjeev Arora in 1996, Arora's Approximation Scheme. This algorithm has time complexity polynomial in the number of terminals for a fixed performance ratio 1 + Epsilon.

Cette thèse est consacrée à l’exploitation des propriétés de non-circularité et de non-gaussianité des signaux d’intérêt (SOI) et/ou des interférences pour les transmissions sans fil et l’écoute passive. Dans une première partie de cette thèse, nous nous intéressons à l’extension des récepteurs SIMO-MLSE conventionnels vers de nouvelles architectures exploitant la potentielle non-circularité au second ordre des interférences co-canal (CCI), pour la démodulation de signaux rectilignes (BPSK, ASK), quasi-rectilignes (MSK, GMSK et OQAM) et à symboles complexes (QAM). L’architecture générale des récepteurs développés est basée sur un prétraitement avec une extension widely linear (WL) du filtre adapté spatio-temporel, ramenant le traitement de démodulation à un problème scalaire, un échantillonnage au rythme symbole et ensuite un organe de décision basé sur une version modifiée de l’algorithme de Viterbi. Pour le cas particulier des signaux quasi-rectiligne, on intercale un traitement de dérotation entre l’échantillonneur et l’organe de décision. Un travail de modélisation à temps discret des SOI, brouilleurs et du bruit de fond a été mené afin de créer des modèles de simulations pour la validation des expressions SINR analytiques interprétables, via l’évaluation des probabilités d’erreur symboles. Dans une deuxième partie, nous nous intéressons à la formation de voies (Beamforming) non-linéaire à travers des structures de Volterra complexe du troisième ordre. Ces dernières permettent l’exploitation de la non-circularité jusqu’au sixième ordre ainsi que du caractère non-gaussien des SOI et/ou des interférences. Dans le contexte de l’écoute passive, nous avons introduit un beamformer MVDR de Volterra du troisième ordre utilisant la seule information a priori du vecteur directionnel du SOI et implémentable grâce à une structure équivalente GSC. Nous avons étudié ses performances en particulier par l’évaluation analytique des expressions du SINR en fonction des statistiques de l’interférence, et par sa vitesse d’apprentissage, démontrant ainsi sa supériorité par rapport aux beamformers MVDR linéaire et WL classiques. Dans un contexte de radiocommunications, nous avons étudié une version MMSE de ce beamformer de Volterra complexe du troisième ordre qui prend lui en compte les propriétés statistiques de non-circularité jusqu’au sixième ordre et de non-gaussianité du SOI et du CCI. La dernière partie de cette thèse est consacrée à la robustesse de tests de détection de rectilinéarité de signaux en présente d’offsets de fréquence. Ces tests sont importants pour ajuster la nature du traitement (linéaire ou WL) en fonction de la rectilinéarité des signaux, afin de garantir le meilleur rapport performance/temps de convergence des algorithmes / This thesis is devoted to exploit the non-circularity and non-gaussianity properties of signals of interest (SOI) and/or interference for wireless transmissions and passive listening. In the first part of this thesis, we are interested in the extension of conventional SIMO-MLSE receivers to new architectures exploiting the potential second order non-circularity of co-channel interference (CCI), for the demodulation of rectilinear signals (BPSK, ASK), quasi-rectilinear (MSK, GMSK and OQAM) and quadrature amplitude modulation (QAM). The general architecture of the developed receivers is based on a pre-processing with a widely linear (WL) extension of the spatio-temporal matched filter, bringing the demodulation processing back to a scalar problem, a sampling at the symbol rate and then a decision block based on a modified version of the Viterbi algorithm. For the particular case of the quasi-rectilinear signals, a derotation processing is interposed between the sampler and the decision block. A work on equivalent discrete time modeling of SOI, interferers and background noise has been carried out in order to create simulation models as for the validation of the interpretable analytic SINR expressions, by the evaluation of the symbol error rates. In a second part, we are interested to the beamforming through complex Volterra structures of the third order. These structures allow us the exploitation of the non-circularity up to the sixth order as well as the non-gaussian nature of the SOI and/or the interferences. For passive listening applications, we have introduced a third-order Volterra MVDR beamformer using only a priori information of SOI steering vector and implemented by an equivalent GSC structure. We have studied its performance, in particular by interpretable closed-form expressions as functions of statistics of the interference, and by its speed of learning, thus proving its advantages with respect to the conventional linear and WL MVDR beamformers. For wireless communications applications, we have studied an MMSE version of this complex Volterra beamformer of the third order that takes into account of the non-circularity up to the sixth order as well as the non-gaussian nature of the SOI and interference. The last part of this thesis is devoted to the robustness of rectilinearity tests in the presence of frequency offset. These tests are important for adjusting the processing (linear or WL) as a function of the rectilinearity of the signals in order to guarantee the best performance/convergence rate ratio of algorithms

<p dir="ltr">The Global Navigation Satellite System (GNSS) is heavily relied on for the navigation of Earth satellites. For satellites in cislunar space and beyond, GNSS is not readily available. As a result, other sources such as NASA's Deep Space Network (DSN) must be relied on for navigation. However, DSN is overburdened and can only support a small number of satellites at a time. Furthermore, communication with external sources can become interrupted or deprived in these environments. Given NASA's current efforts towards cislunar space operations and the expected increase in cislunar satellite traffic, there will be a need for more autonomous navigation options in cislunar space and beyond.</p><p dir="ltr">In this thesis, a navigation system capable of accurate and computationally efficient orbit determination in these communication-deprived environments is proposed and investigated. The emphasis on computational efficiency is in support of cubesats which are constrained in size, cost, and mass; this makes navigation even more challenging when resources such as GNSS signals or ground station tracking become unavailable.</p><p dir="ltr">The proposed navigation system, which is called GRAVNAV in this thesis, involves a two-satellite formation orbiting a planet. The primary satellite hosts an Extended Kalman Filter (EKF) and is capable of measuring the relative position of the secondary satellite; accurate attitude estimates are also available to the primary satellite. The relative position measurements allow the EKF to estimate the absolute position and velocity of both satellites. In this thesis, the proposed navigation system is investigated in the two-body and three-body problems.</p><p dir="ltr">The two-body analysis illuminates the effect of the gravity model error on orbit determination performance. High-fidelity gravity models can be computationally expensive for cubesats; however, celestial bodies such as the Earth and Moon have non-uniform and highly-irregular gravity fields that require complex models to describe the motion of satellites orbiting in their gravity field. Initial results show that when a second-order zonal harmonic gravity model is used, the orbit determination accuracy is poor at low altitudes due to large gravity model errors while high-altitude orbits yield good accuracy due to small gravity model errors. To remedy the poor performance for low-altitude orbits, a Gravity Model Error Compensation (GMEC) technique is proposed and investigated. Along with a special tuning model developed specifically for GRAVNAV, this technique is demonstrated to work well for various geocentric and lunar orbits.</p><p><br></p><p dir="ltr">In addition to the gravity model error, other variables affecting the state estimation accuracy are also explored in the two-body analysis. These variables include the six Keplerian orbital elements, measurement accuracy, intersatellite range, and satellite formation shape. The GRAVNAV analysis shows that a smaller intersatellite range results in increased state estimation error. Despite the intersatellite range bounds, semimajor axis, measurement model, and measurement errors being identical for both orbits, the satellite formation shape also has a strong influence on orbit determination accuracy. Formations that place both satellites in different orbits significantly outperform those that place both satellites in the same orbit.</p><p dir="ltr">The three-body analysis primarily focuses on characterizing the unique behavior of GRAVNAV in Near Rectilinear Halo Orbits (NRHOs). Like the two-body analysis, the effect of the satellite formation shape is also characterized and shown to have a similar impact on the orbit determination performance. Unlike the two-body problem, however, different orbits possess different stability properties which are shown to significantly affect orbit determination performance. The more stable NRHOs yield better GRAVNAV performance and are also less sensitive to factors that negatively impact performance such as measurement error, process noise, and decreased intersatellite range.</p><p dir="ltr">Overall, the analyses in this thesis show that GRAVNAV yields accurate and computationally efficient orbit determination when GMEC is used. This, along with the independence of GRAVNAV from GNSS signals and ground-station tracking, shows that GRAVNAV has good potential for navigation in cislunar space and beyond.</p>

Made available in DSpace on 2016-04-27T16:58:23Z (GMT). No. of bitstreams: 1 Renan Faria.pdf: 1138485 bytes, checksum: b2c93fff6bcbf6153741e12f671cadc2 (MD5) Previous issue date: 2007-08-29 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / The purpose of this research was to investigate and analyze the meaning production for 10th graders of a school from the state network in Minas Gerais, about cartesian graphs that represent the rectilinear movement. The aspects favored in the understanding and elaboration of the graph using pencils and paper, a sensor, the graphic calculator, the teacher s paper and the activities in this environment were particularly analyzed, besides the interventions that occurred. The starting point was based in a story, in which the students were incited to build their cartesian graphic representation, using pencils and paper. After that, they used the sensor with the graphic calculator. The students were instructed by the teachers and they should move accordingly in order to reproduce a d x t graph, corresponding to the one offered in the calculator screen. Thus, it was tried to contemplate student-student, teacher-student and student technology. The speeches and the actions were recorded and transcribed. As a theoretical reference the researcher used the Embodiment Cognition Theory, based on Lakoff and Núñes, especially in the role of the cultural metaphors and in the Model of Argumentative Strategies (MEA) for the analysis of the speeches and gestures organized in episodes, which aimed at the understanding of the meanings produced. The ideas from Mobile et al. about the visualization aspects were applied, contemplating the implications that different dispositions of symbols and graphs have in the meaning production by the students. It was concluded that the adequate use of the technology enabled an immediate feedback to the students and that this interferes in the kind of relation that the teacher has with his/her students, modifying, also, the understanding about the use of technology in the classroom / Esta pesquisa teve como objetivo investigar e analisar a produção de significados, para alunos do primeiro ano do Ensino Médio de uma escola da rede estadual de Minas Gerais, para gráficos cartesianos que representam o movimento retilíneo. Em particular, foram analisados os aspectos favorecidos na compreensão e elaboração do gráfico com lápis e papel e com o uso do sensor e calculadora gráfica e também o papel do professor e das atividades nesse ambiente além das interações ocorridas. O ponto de partida baseou-se em uma história, na qual os alunos foram instigados a construir sua representação gráfica cartesiana, utilizandose de lápis e papel. Em seguida, empregaram o sensor com a calculadora gráfica. Os alunos foram instruídos pelos professores e deveriam se movimentar de modo a reproduzir um gráfico d x t, correspondente ao oferecido na tela da calculadora. Assim, procurou-se contemplar a interação aluno-aluno, professor-aluno e alunotecnologia. As falas e as ações foram gravadas e transcritas. Como referencial teórico, o pesquisador valeu-se da Teoria da Cognição Corporificada, baseada e Lakoff e Nunes, em particular no papel das metáforas conceituais e no Modelo de Estratégia Argumentativa (MEA) para análise das falas e gestos organizadas em episódios que visavam a compreensão dos significados produzidos. As idéias de Nobile et al. Sobre aspectos de visualização foram empregadas, contemplando-se as implicações que distintas disposições de símbolos e gráficos acarretam na produção de significados pelos alunos. Concluiu-se que o uso adequado da tecnologia propiciou um feedback imediato aos estudantes e que isso interfere no tipo de relação que o professor tem com seus alunos, modificando, também, a compreensão sobre o uso de tecnologia em sala de aula

Squeeze Film Dampers (SFD) provide viscous damping in rotor bearing systems to reduce lateral vibration amplitudes and to isolate mechanical components. Aircraft engine shafts, often supported on roller bearings, operate at high rotational speeds and are susceptible to large amplitude shaft whirl due to rotor imbalance. SFDs aid to reduce such large whirl amplitudes while also eliminating rotor instabilities. he current work quantifies experimentally the forced performance of two parallel squeeze SFDs separated by a central groove. Force coefficients are identified in a specialized SFD test rig constructed to undergo similar operating and loading conditions as in jet engines. Of interest is to quantify the effect of a central feed groove on the forced performance of SFDs and to validate predictions from a computational tool. The test rig comprises of an elastically supported bearing structure and one of two journals. Tests are conducted on two open ends SFDs, both with diameter D and nominal radial clearance c; each damper with two parallel film land lengths L= 1/5 D and 2L, separated by a feed groove of width L and depth 3/4 L. ISO VG 2 grade lubricant oil flows into the central groove via 3 orifices, 120 degrees apart, and then through the film lands to finally exit to ambient. In operation, a static loader pulls the bearing to various static off center positions with respect to the stationary journal, and electromagnetic shakers (2,200 N) excite the test system with single frequency loads over a frequency range to generate rectilinear, circular and elliptical orbits with specified motion amplitudes. A frequency domain method identifies the SFD mechanical parameters, viz., stiffness, damping, and added mass coefficients. The long damper generates 7 times more direct damping and 2 times more added mass compared to the short length damper. The damping coefficients are sensitive to the static eccentricity (up to 50 percent c) while showing lesser dependency on the amplitude of whirl motion (up to 20 percent c). On the other hand, added mass coefficients are nearly constant with static eccentricity and decrease with higher amplitudes of motion. The magnitudes of identified cross-coupled coefficients are insignificant for all imposed operating conditions for either damper. Large dynamic pressures recorded in the central groove demonstrate the groove does not isolate the film lands by merely acting as a source of lubricant, but contributes to the generation of large added mass coefficients. The recorded dynamic pressures in the film lands and central groove do not evidence lubricant vapor or gas cavitation for the tested static eccentricities and amplitudes of motion. The direct damping coefficients for both dampers are independent of excitation frequency over the frequency range of the tests. Predictions derived from a novel SFD computational tool that includes flow interactions in the central groove and oil supply orifices agree well with the experimental force coefficients for both dampers. The current work advances the state of the art in SFDs for jet engines.