Seja K um conjunto de Cantor. Neste trabalho apresentamos dois teoremas relacionados a densidade do conjunto das dinâmicas simbólicas. No caso de endomorfismos provamos que, dado uma dinâmica T : K K, existe uma T : K K próxima a T, tal que toda órbita é finalmente periódica. Já no caso de homeomorfismos, mostramos que, dado uma dinâmica T : K K, existe uma T : K K próxima a T, tal que o w-limite de toda órbita de T é uma órbita periódica. Em particular, mostramos que, em ambos os casos, todas as medidas ergódicas estão suportadas em órbitas periódicas. / Let K be a Cantor set. In this work we present two theorems related to the density of symbolic dynamics. We prove that given an endomorphism T : K K then there exists an endomorphism ~ T : K K close to T such that every orbit is finally periodic. We also prove that given a homeomorphism T : K K then there exists a homeomorphism ~ T : K K close to T such that the w-limit of every orbit is a periodic orbit. In particular, we have shown, in both cases, that all ergodic measures have support on periodic orbits.

Seja K um conjunto de Cantor. Neste trabalho apresentamos dois teoremas relacionados a densidade do conjunto das dinâmicas simbólicas. No caso de endomorfismos provamos que, dado uma dinâmica T : K K, existe uma T : K K próxima a T, tal que toda órbita é finalmente periódica. Já no caso de homeomorfismos, mostramos que, dado uma dinâmica T : K K, existe uma T : K K próxima a T, tal que o w-limite de toda órbita de T é uma órbita periódica. Em particular, mostramos que, em ambos os casos, todas as medidas ergódicas estão suportadas em órbitas periódicas. / Let K be a Cantor set. In this work we present two theorems related to the density of symbolic dynamics. We prove that given an endomorphism T : K K then there exists an endomorphism ~ T : K K close to T such that every orbit is finally periodic. We also prove that given a homeomorphism T : K K then there exists a homeomorphism ~ T : K K close to T such that the w-limit of every orbit is a periodic orbit. In particular, we have shown, in both cases, that all ergodic measures have support on periodic orbits.

Dans cette thèse, nous explorons des matériaux basés sur le bismuth qui peuvent présenter des propriétés topologiques. Bi est un composant d’Isolants Topologiques identifiés qui consistent en un volume isolant tout en présentant aussi des états électroniques conducteurs en surface topologiquement protégés. En particulier, ces états de surface sont polarisés en spin et sont protégés par la symétrie du renversement du temps. L’attrait des Isolants Topologiques découle non seulement de leur intérêt évident du point de vue de la physique fondamentale, mais aussi du fait qu’ils puissent trouver une application en spintronics et dans les ordinateurs quantiques.Dans ces systèmes, le couplage spin-orbit joue un rôle central. Le couplage spin-orbit peut aussi mener à la levée de dégénérescences de Rashba ou de Dresselhaus, phénomènes découlant de la brisure en symétrie respectivement engendrée par la surface/interface d’un système ou de l’inhérente structure cristalline atomique.L’interprétation de mesures de structures de bandes dépendantes du spin, comme observées par spectroscopie par photoemission résolue en angle (et en spin), est appuyée et complémentée par des calculs ab-initio Korringa-Kohn-Rostoker de la structure électronique qui incluent tous les aspects des systèmes examinés : en particulier le couplage spin-orbit, fondamentalement compris grâce à une approche entièrement relativiste.Nous avons d’abord déposé des couches minces de Bi sur un substrat d’InAs(111). Un cristal de Bi de très bonne qualité est obtenu, confirmé par la reproduction par étude théorique des bandes électroniques mesurées. En parallèle de la croissance de la couche de Bi, nous observons que l’In et le Bi forment des cristaux d’InBi, exposant des états de surface topologiques. Nos analyses théoriques confirment que ces états de surface sont polarisés en spin.Dans la seconde partie de la thèse, Bi est utilisé comme un dopant dans InAs, donnant un alliage d’InAsBi. L’intense couplage spin-orbit apporté par le Bi génère simultanément des effets Rashba et Dresselhaus mesurables, levant par conséquence la dégénérescence des états de surface de manière complètement atypique, donnant des états non-hélicoïdaux polarisés en spin. / In this thesis, we explore bismuth based materials that may exhibit topological properties. Bi is a parent compound of known Topological Insulators which consist of an insulating bulk while also presenting topologically protected conducting electronic surface states. In particular, these surface states are spin polarised and are protected by time-reversal symmetry. The dual appeal of topological insulators stems not only from their obvious interest from a fundamental physics point of view, but also from the fact that they may find use in spintronics and quantum computing.In those systems the spin-orbit coupling plays a central role. Spin-orbit coupling can also lead to the Rashba or Dresselhaus splitting, phenomena arising from the symmetry breaking respectively engendered by the surface/interface of a system or from the inherent atomic crystal structure.The interpretation of measured spin dependent band structure, as observed in (Spin-) and Angle-Resolved Photoemission Spectroscopy, was supported and completed by ab-initio Korringa-Kohn-Rostoker electronic structure calculations which account for all aspects of the investigated systems: in particular spin-orbit coupling, fundamentally included thanks to a fully relativistic approach.We first deposited Bi thin films onto a InAs(111) substrate. A crystal of Bi of very high quality was grown, confirmed by reproduction of the measured electronic bands by theoretical investigation. In parallel to Bi film growth, we observed that In and Bi form InBi crystals, exhibiting topological surface states. Our theoretical analyses confirm that these surface states are spin polarised.In the second part of the thesis, Bi was used as a dopant within InAs, forming an InAsBi alloy system. The strong spin-orbit coupling brought on by Bi generated simultaneously measurable Rashba and Dresselhaus effects, consequently splitting surface states in a completely atypical manner, giving non-helical spin polarised states.

This thesis addresses the orbit transfer optimization problem of a spacecraft. The optimal orbit transfer is the process of altering the orbit of a spacecraft with minimum propellant consumption. The spacecrafts are needed to realize orbit transfer to reach, change or keep its orbit. The spacecraft may be a satellite or the last stage of a launch vehicle that is operated at the exo-atmospheric region. In this study, a genetic algorithm based orbit transfer method has been developed. The applicability of genetic algorithm based orbit transfer method has been verified using orbit transfers which are optimal at specific cases. The solution to orbit transfer problem is also searched using steepest descent algorithm.While genetic algorithm can reach the optimal solution, steepest descent algorithm can reach optimal solution when a good initial prediction is provided. The effects of the initial orbital values on the orbit transfer solutions are also studied.

Dans cette thèse, nous présentons la conception et les performances de capteurs magnétiques basés sur les technologies AMR et GMR en vue d'une utilisation dans la navigation. Afin d'obtenir une sensibilité et une linéarité optimales à champ nul, le design des capteurs utilise des barberpoles et un pont de wheatstone pour l'un et prend avantage des différentes anisotropies et couplages pour l'autre. Les capteurs sont fabriqués par pulvérisations cathodiques et photolithographies et leurs performances en terme de sensibilité, de linéarité et de bruit sont testées et comparées. La conception de gradiomètres nécessaires à la navigation magnéto-inertielle repose sur l'utilisation de magnétorésistances placées aux extrémités du capteur reliées par un pont de WheatStone dont la sortie est proportionnelle au gradient du champ magnétique. Des concentrateurs de Flux destinés à amplifier le champ afin d'améliorer la sensibilité sont conçus et testés sur les capteurs. Un concentrateur de flux destiné à amplifier un champ ayant la forme du gradient est proposé comme amélioration des gradiomètres. Des solutions innovantes pour le swithching d'anisotropie et la compensation d'offset utilisant l'effet Hall de spin et le couplage spin-transfer sont étudiées. Dans cette optique, un dispositif de mesure du couplage spin-transfer appelé spin-torque-bridge est conçu et utilisé pour étudier l'effet Hall de spin et le spin transfer dans différentes multi-couches. / In this work, we present the conception and the performances of AMR and GMR-based sensors for navigation applications In order to obtain the best sensitivity and linearity at zero field, the design include barberpoles and a Wheatstone bridge for the first and takes advantage of the different anisotropies and coupling for the other. The sensor are fabricated by magnetron sputtering and photolithography and their performances in terms of sensitivity, linearity and noise are compared. The concept of gradiometers used for magneto-inertial navigation is based on the utilisation of magnetoresistances placed at each extremity of the sensor connected by a wheatstone bridge whose output is proportional to the gradient of the magnetic field. Flux concentrators designed to amplify the incoming field in order to improve the sensitivity are fabricated and tested on the sensors. A flux concentrator designed to amplify a magnetic gradient is proposed as an improvement of the gradiometers. Innovant solutions for low consumption anisotropy switching and offset compensation are being experimented using spin Hall effect and spin transfer torque with adjacent Pt and AuW layers. In that regard a spin torque measurement device: the spin-torque-bridge, is designed and used to study the spin hall effect and the spin transfer couplings in different multi layers.

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第21598号 / 理博第4505号 / 新制||理||1647(附属図書館) / 京都大学大学院理学研究科化学専攻 / (主査)教授 小野 輝男, 教授 吉村 一良, 教授 島川 祐一 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DGAM

In the globally collaborative effort of maintaining an accurate space catalog, it is of utmost importance for ground tracking stations to provide observations which can be used to update and improve the catalog. However, each tracking station is responsible for viewing thousands of objects in a limited window of time. Limitations in sensor capabilities, human error, and other circumstances inevitably result in erroneous, or unusable, data, but when receiving information from a tracking station, it may be difficult for the end-user to determine a data set's usability. Variables in equipment, environment, and processing create uncertainties when computing the positions and orbits of the satellites. Firstly, this research provides a reference frame for what degrees of errors or biases in equipment translate to different levels of orbital errors after a least squares orbit determination. Secondly, using just an incoming data set's angle error distribution compared to the newly determined orbit, statistical distribution testing is used to determine the validity and usability of the newly received data set. In the context of orbit position uncertainty, users are then able to communicate and relay the uncertainties in the data they share while assessing incoming data for potential sources of error.

Nous avons étudié par des méthodes numériques et en théorie k.p avancée les propriétés tunnel d’électrons et de trous dans des systèmes modèles et hétérostructures composés de semi-conducteurs impliquant des interactions spin-orbite de volume. Nous démontrons que le couplage entre les interactions spin-orbite et d’échange à l’interface de jonctions tunnel résulte en un fort contraste de transmission de porteurs selon le signe de la composante de leur vecteur d’onde dans le plan de la jonction. Cet effet conduit à un effet tunnel anormal d’interface que nous appelons « Effet Hall Tunnel Anormal » (ATHE). De façon similaire, des processus tunnel non-conventionnels se manifestant sur des isolants topologiques ont été prédits par d’autres auteurs. Alors que l’ensemble de ces effets Hall anormaux sont liés aux interactions spin-orbite, les effets tunnel anormaux diffèrent des effets Hall tunnel, des effets Hall et des effets Hall de spin par la forte amplitude prédite ainsi que par des phénomènes de chiralité. Ces propriétés possèdent un lien nontrivial avec la symétrie du système. L’ensemble de ces résultats démontre l’existence d’une nouvelle classe d’effets tunnel qui devaient être étudiés expérimentalement dans un futur proche. En ce qui concerne la bande de valence, nous démontrons, en utilisant un Hamiltonien 14x14 prolongeant un modèle 2x2, que le calcul décrivant l’ATHE repose sur un traitement subtil des états dits « spurious » (états non-physiques) et nous donnons quelques éléments d’amélioration et de compréhension. Dans ce mémoire de thèse, nous développons deux méthodes numériques pour résoudre le problème des états spurious en développant en parallèle des méthodes k.p respectivement à 14 bandes et 30 bandes afin de décrire des matériaux semiconducteurs à gap indirect. Les calculs menés dans la bande de valence d’hétérostructures semiconductrice incluant interfaces et barrières tunnel (approches 6x6 et 14x14) sans centre de symétrie d’inversion mettent en évidence des propriétés d’asymétrie équivalente à celles obtenues dans la bande de conduction. De tels effets sont interprétés, dans le cadre de calculs de perturbation en transport basés sur des techniques de fonctions de Green, par des effets chiraux orbitaux lors du branchement tunnel des fonctions évanescentes dans la barrière. / We report on theoretical, analytical and computational investigations and k.p calculations of electron and hole tunneling, in model systems and heterostructures composed of exchange-split III-V semiconductors involving spin-orbit interaction (SOI). We show that the interplay of SOI and exchange interactions at interfaces and tunnel junctions results in a large difference of transmission for carriers, depending on the sign of their incident in-plane wave vector (k//): this leads to interfacial skew-tunneling effects that we refer to as Anomalous Tunnel Hall Effect (ATHE). In a 2x2 exchange-split band model, the transmission asymmetry (A) between incidence angles related to +k// and -k// wave vector components, is shown to be maximal at peculiar points of the Brillouin zone corresponding to a totally quenched transmission (A = 100%). More generally, we demonstrate the universal character of the transmission asymmetry A vs. in-plane wavevector component, for given reduced kinetic energy and exchange parameter, A being universally scaled by a unique function, independent of the spin-orbit strength and of the material parameters. Similarly, striking tunneling phenomena arising in topological insulators have just been predicted. While they all are related to the spin-orbit directional anisotropy, ATHE differs from the tunneling Hall effect, spontaneous anomalous, and spin Hall effects, or spin-galvanic effect, previously reported for electron transport, by its giant forward asymmetry and chiral nature. These features have non-trivial connection with the symmetry properties of the system. All these results show that a new class of tunneling phenomena can now be investigated and experimentally probed.When valence bands are involved, we show (using 14x14 Hamiltonian and within a 2x2 toy model) that ATHE accurate calculations rely on a subtle treatment of the spurious (unphysical) states and we give an insight into the topology of the complex band structure. We introduce two numerical methods to remove spurious states and successfully, include them in 30-band codes able to describe indirect bandgap group-IV semiconductors. Calculations performed in the valence bands of model heterostructures including tunnel barriers, in both 6x6 and 14x14 k.p Hamiltonians without inversion asymmetry, more astonishingly highlight the same trends in the transmission asymmetry which appears to be related to the difference of orbital chirality and to the related branching (overlap) of the corresponding evanescent wave functions responsible for the tunneling current. Besides, we built an analytical model and developed scattering perturbative techniques based on Green’s function method to analytically deal with electrons and holes and to compare these results with numerical calculations. The agreement between the different approaches is very good. In the case of holes, the asymmetry appears to be robust and persists even when a single electrode is magnetic.

Aerial recovery of autonomous micro air vehicles (MAVs) presents many unique challenges due to the difference in size and speed of the recovery vehicle and MAV. This thesis presents algorithms to enable an autonomous MAV to estimate the orbit of a recovery vehicle and track the orbit until the final docking phase. Methods for estimating ellipses that are rotated out of the x − y plane are developed and demonstrated through simulation. These algorithms are shown to be robust to noise and stable numerically. Parameter update methods that are computationally inexpensive, such as recursive least squares and Kalman filtering, are discussed and simulated. A discussion is given of orbit tracking algorithms for circular orbits, and these methods are expanded to include elliptical orbits. These algorithms enable the MAV to track the recovery vehicle's orbit, based on a vector field approach. The tracking algorithms are divided into lateral and longitudinal controllers that allow for tracking of inclined orbits. Finally, the hardware and software setup for live flight tests is discussed. Flight test results are given that validate the functionality of the orbit estimation and orbit tracking algorithms.

Engineering and technical challenges exist with the material transport of natural resources in space. One aspect of this transport problem is the design of an orbit architecture in the Earth-Moon system (EMS) that facilitates these resources through the mining cycle. In this thesis, it is proposed to use the Circular Restricted 3-Body Problem (CR3BP) to design an orbit architecture composed of L3 Lyapunov orbits, hyperbolic invariant stable and unstable manifolds, and geosynchronous (GEO) orbits. A single shooting method (SSM) and natural parameter continuation (NPC) numerical algorithm is used to compute a family of L3 Lyapunov orbits. Invariant Manifold Theory (IMT) is leveraged to find the set of feasible hyperbolic invariant stable and unstable manifolds associated with a L3 Lyapunov orbit. Ideal L3 Lyapunov orbits are chosen to construct an orbit architecture based off favorable metrics like orbital period, Jacobi Constant, and stability index. Manifolds that enter the GEO and xGEO (beyond GEO) volumes are identified. Finally, a ∆V analysis for GEO to manifold transfer is conducted. An achievement of this study is the computation of stable L3 Lyapunov orbits. The primary contribution of this paper lies in its modeling of a L3 Lyapunov orbit architecture using the CR3BP. / Master of Science / Engineering and technical challenges exist with the material transport of natural resources in space. One aspect of this transport problem is the design of an orbit architecture in the Earth-Moon system (EMS) that facilitates these resources through the mining cycle. In this thesis, it is proposed to use the Circular Restricted 3-Body Problem (CR3BP) to design an orbit architecture composed of L3 Lyapunov orbits, hyperbolic invariant stable and unstable manifolds, and geosynchronous (GEO) orbits. L3 is a unique point in space in a rotating frame of reference where the gravity of the Earth and Moon create a dynamical equilibrium point. Due to its location in a rotating frame of reference relative to the Earth and the Moon, orbits around L3 tend to greater stability than L1 or L2. A single shooting method (SSM) and natural parameter continuation (NPC), which are computational methods for finding solutions that connect discrete boundary conditions, numerical algorithm is used to compute a family of L3 Lyapunov orbits. Invariant Manifold Theory (IMT), which is a dynamical system structure that is invariant throughout the action of the system, is leveraged to find the set of feasible hyperbolic invariant stable and unstable manifolds associated with L3 Lyapunov orbits. Ideal L3 Lyapunov orbits and manifolds are chosen to construct an orbit architecture based off favorable metrics like orbital period, Jacobi Constant, and stability index. Manifolds that enter the GEO and xGEO (beyond GEO) volumes are identified. Finally, a ∆V analysis for GEO to manifold transfer is conducted. An achievement of this study is the computation of stable L3 Lyapunov orbits. The primary contribution of this paper lies in its modeling of a L3 Lyapunov orbit architecture using the CR3BP.