This thesis encompasses a body of experimental work on the use of structured light in quantum cryptographic protocols. In particular, we investigate the ability to perform quantum key distribution through various quantum channels (fibre, free-space, underwater) in laboratory and realistic conditions. We first demonstrate that a special type of optical fibre (vortex fibre) capable of coherently transmitting vector vortex modes is a viable quantum channel. Next, we describe the first demonstration of high-dimensional quantum cryptography using structured photons in an urban setting. In particular, the prevalence of atmospheric turbulence can introduce many errors to a transmitted key; however, we are still able to transmit more information per carrier using a 4-dimensional scheme in comparison to a 2-dimensional one. Lastly, we investigate the possibility of performing secure quantum communication with twisted photons in an uncontrolled underwater channel. We find that though it is possible for low-dimensional schemes, high-dimensional schemes suffer from underwater turbulence without the use of corrective wavefront techniques.

<p>Generating and stabilizing periodic motions in nonlinear systems is a challenging task. In the control system community this topic is also known as limit cycle control. In recent years a framework known as Virtual Holonomic Constraints (VHC) has been developed as one of the solutions to this problem. The aim of this thesis is to give an insight into this approach and its practical application.</p><p>The contribution of this work is primarily the experimental validation of the theory. A step by step procedure of this methodology is given for motion planning, as well as for controller design. Three particular setups were chosen for experiments: the inertia wheel pendulum, the Furuta pendulum and the two-link planar pendulum. These under-actuated mechanical systems are well known benchmarking setups for testing advanced control design methods.</p><p>Further application is intended for cases such as biped robot walking/running, human and animal locomotion analysis, etc.</p>

Accurate electronic structure calculations are becoming more and more important because of the increasing need for information about systems which are hard to perform experiments on. Databases compiled from theoretical results are also being used more than ever for applications, and the reliability of the theoretical methods are of utmost importance. In this thesis, the present limits on theoretical alloy calculations are investigated and improvements on the methods are presented. A short introduction to electronic structure theory is included as well as a chapter on Density Functional Theory, which is the underlying method behind all calculations presented in the accompanying papers. Multiple Scattering Theory is also discussed, both in more general terms as well as how it is used in the methods employed to solve the electronic structure problem. One of the methods, the Exact Muffin-Tin Orbital method, is described extensively, with special emphasis on the slope matrix, which energy dependence is investigated together with possible ways to parameterize this dependence. Furthermore, a chapter which discusses different ways to perform calculations for disordered systems is presented, including a description of the Coherent Potential Approximation and the Screened Generalized Perturbation Method. A comparison between the Exact Muffin-Tin Orbital method and the Projector Augmented-Wave method in the case of systems exhibiting both compositional and magnetic disordered is included as well as a case study of the MoRu alloy, where the theoretical and experimental discrepancies are discussed. The thesis is concluded with a short discussion on magnetism, with emphasis on its computational aspects. I further discuss a generalized Heisenberg model and its applications, especially to fcc Fe, and also present an investigation of the competing magnetic structures of FeNi alloys at different concentrations, where both collinear and non-collinear magnetic structures are included. For Invar-concentrations, a spin-flip transition is found and discussed. Lastly, I discuss so-called quantum corrals and possible ways of calculating properties, especially non-collinear magnetism, of such systems within perturbation theory using the force theorem and the Lloyd’s formula.

Several methods are presented for the design of satellite formations for science missions in high-eccentricity reference orbits with quantifiable performance criteria specified throughout only a portion the orbit, called the Region of Interest (RoI). A modified form of the traditional average along-track drift minimization condition is introduced to account for the fact that performance criteria are only specified within the RoI, and a robust formation design algorithm (FDA) is defined to improve performance in the presence of formation initialization errors. Initial differential mean orbital elements are taken as the design variables and the Gim-Alfriend state transition matrix (G-A STM) is used for relative motion propagation. Using mean elements and the G-A STM allows for explicit inclusion of J2 perturbation effects in the design process. The methods are applied to the complete formation design problem of the NASA Magnetospheric Multiscale (MMS) mission and results are verified using the NASA General Mission Analysis Tool (GMAT). Since satellite formations in high-eccentricity orbits will spend long times at high altitude, third-body perturbations are an important design consideration as well. A detailed analytical analysis of third-body perturbation effects on satellite formations is also performed and averaged dynamics are derived for the particular case of the lunar perturbation. Numerical results of the lunar perturbation analysis are obtained for the example application of the MMS mission and verified in GMAT.

Despite the success of modern quantum chemistry in predicting properties of organic molecules, the treatment of inorganic systems, which have many close lying states, remains out of quantitative reach for current methods. To treat non-dynamic correlation, we take advantage of the density matrix renormalization group (DMRG) method that has become very successful in the field of solid state physics. We present a detailed study of the DMRG method, and we pay special attention to the evolution of the understanding behind the mathematical structure of the DMRG wave function. Our primary goal is to develop a density matrix renormalization group self--consistent--field (DMRG-SCF) approach, analogous to the complete active space self--consistent field (CASSCF) method, but dealing with large active spaces that are too demanding for the full configuration interaction (FCI) method. As a first step towards such a DMRG-SCF procedure, we present a spin-adapted DMRG algorithm designed to target spin- and spatial-symmetry states that are hard to obtain while using an unrestricted algorithm. Our next step is a modification of the DMRG algorithm to obtain decreasing energy at every step during the sweep. This monotonically convergent DMRG scheme lets us obtain the two-body density matrix as a by--product of the existing procedure without any additional cost in storage. Additionally, the two-body density matrix produced at convergence using this scheme is free from the N-representability problem that is present when the two--body density matrix is produced with the two-site DMRG scheme without additional storage cost. Finally, taking advantage of the modifications developed herein, we present results obtained from our DMRG-SCF method. Lastly, we discuss possible ways of incorporating dynamical correlation into the DMRG scheme, in order to obtain a modern multireference approach.

Over the past half century, multiplicity studies have provided a foundation for the theories of stellar formation and evolution through understanding how likely it is that stars form alone or with companions. If spectroscopic orbits are combined with techniques that can determine visual orbits, we can access the most fundamental parameter of stellar evolution, stellar mass. This dissertation is composed of two main sections. The first involves the investigation of the seminal multiplicity study of Duquennoy & Mayor (1991b) which has been the ``gold standard" for solar-type stars for nearly 20 years. Improvements in technology in the intervening years have improved the measurement accuracy for radial velocities and distances on which the study was based. Using Georgia State University's CHARA Array to search the systems in Duquennoy & Mayor's multiplicity survey for overlooked companions along with a literature search covering regimes unreachable by the CHARA Array, we have found that more than 40% of the Duquennoy & Mayor's sample was further than originally believed and the uncorrected multiplicity percentages change from 57:38:4:1:0% (single:double:triple:quad:quint%) to 48:42.5:7.5:1:1% with the discoveries of multiple previously undiscovered companions. The second part of this project describes the application of separated fringe packets for resolving the astrometric position of secondaries with small angular separations on long-baseline optical interferometers. The longest baselines of the CHARA Array allow access to a previously inaccessible range of separations compared with other techniques (<40 milliarcseconds) and the ability to very accurately angularly resolve a large number of single- and double-lined spectroscopic binaries. Combining astrometric and spectroscopic orbits provides assumption-free stellar masses and using the CHARA Array allows access to many previously unreachable systems available for high-accuracy mass determinations. We report the first angular separation measurements of seven spectroscopic binary systems, five additional separated fringe packet detections, ten systems with probably overlapping fringe packets, four systems with new data on pre-existing orbits, one completely new visual orbit for a SB2 system previously unresolved, and the detection of two previously unknown companions.

The self-calibration method, a new interferometric technique using measurements in the K′-band (2.1 μm) at the CHARA Array, has been used to derive orbits for several spectroscopic binaries. This method uses the wide component of a hierarchical triple system to calibrate visibility measurements of the triple’s close binary system through quasi-simultaneous observations of the separated fringe packets of both. Prior to the onset of this project, the reduction of separated fringe packet data had never included the goal of deriving visibilities for both fringe packets, so new data reduction software has been written. Visibilities obtained with separated fringe packet data for the target close binary are run through both Monte Carlo simulations and grid search programs in order to determine the best-fit orbital elements of the close binary. Several targets, with spectral types ranging from O to G and luminosity classesfrom III to V, have been observed in this fashion, and orbits have been derived for the close binaries of eight targets (V819 Her B, Kappa Peg B, Eta Vir A, Eta Ori Aab, 55 UMa A, 13 Ceti A, CHARA 96 Ab, HD 129132 Aa). The derivation of an orbit has allowed for the calculation of the masses of the components in these systems. The magnitude differences between the components can also be derived, provided that the components of the close binary have a magnitude difference of Delta K < 2.5 (CHARA’s limit). Derivation of the orbit also allows for the calculation of the mutual inclination (Phi), which is the angle between the planes of the wide and close orbits. According to data from the Multiple Star Catalog, there are 34 triple systems other than the 8 studied here for which the wide and close systems both have visual orbits. Early formation scenarios for multiple systems predict coplanarity (Phi < 15 degrees), but only 6 of these 42 systems are possibly coplanar. This tendency against coplanarity may suggest that the capture method of multiple system formation is more important than previously believed.

Despite the success of modern quantum chemistry in predicting properties of organic molecules, the treatment of inorganic systems, which have many close lying states, remains out of quantitative reach for current methods. To treat non-dynamic correlation, we take advantage of the density matrix renormalization group (DMRG) method that has become very successful in the field of solid state physics. We present a detailed study of the DMRG method, and we pay special attention to the evolution of the understanding behind the mathematical structure of the DMRG wave function. Our primary goal is to develop a density matrix renormalization group self--consistent--field (DMRG-SCF) approach, analogous to the complete active space self--consistent field (CASSCF) method, but dealing with large active spaces that are too demanding for the full configuration interaction (FCI) method. As a first step towards such a DMRG-SCF procedure, we present a spin-adapted DMRG algorithm designed to target spin- and spatial-symmetry states that are hard to obtain while using an unrestricted algorithm. Our next step is a modification of the DMRG algorithm to obtain decreasing energy at every step during the sweep. This monotonically convergent DMRG scheme lets us obtain the two-body density matrix as a by--product of the existing procedure without any additional cost in storage. Additionally, the two-body density matrix produced at convergence using this scheme is free from the N-representability problem that is present when the two--body density matrix is produced with the two-site DMRG scheme without additional storage cost. Finally, taking advantage of the modifications developed herein, we present results obtained from our DMRG-SCF method. Lastly, we discuss possible ways of incorporating dynamical correlation into the DMRG scheme, in order to obtain a modern multireference approach.

The ability to observe resident space objects (RSOs) is a necessary requirement for space situational awareness. While objects in a Low-Earth Orbit are easily ob- servable by ground-based sensors, diffculties arise when trying to monitor objects with larger orbits far above the Earth's surface, e.g. a Geostationary Orbit. Camera systems mounted on satellites can provide an eff ective way to observe these objects. Using a satellite with a speci c orbit relative to the RSO's orbit, one can passively observe all the objects that share the RSO's orbit over a given time without active maneuvering. An orbit can be defi ned by ve parameters: semi-major axis, eccentricity, right ascension of ascending node, inclination, and argument of perigee (a; e; ; i; !). Using these parameters, one can create an orbit that will surround the target orbit allowing the satellite in the Rock-Around Orbit (RAO) orbit to have a 360 degree view of RSOs in the target orbit. The RAO orbit can be applied to any circular or elliptical target orbit; and for any target orbit, there are many possible RAO orbits. Therefore, diff erent methods are required to narrow down the selection of RAO orbits. These methods use distance limitations, time requirements, orbit perturbations, and other factors to limit the orbit selections. The first step is to determine the range of RAO semi-major axes for any given target orbit by ensuring the RAO orbit does not exceed a prescribed maximum al- lowable distance, dmax from the target orbit. It is then necessary to determine the eccentricity range for each possible RAO semi-major axis. This is done by ensuring the RAO still does not exceed dmax but also ensuring that the RAO orbit travels inside and outside of the target orbit. This comprises one half of the rock-around motion. The final step is to determine the inclination of the RAO orbit. Only a small inclination different from that of the target orbit is required to complete the rock-around motion while the maximum inclination is found by making sure the RAO orbit does not exceed dmax. It is then important to consider orbit perturbations, since they can destroy the synchronization between the RAO and target orbit. By examining the e ffects of the linear J2 perturbations on the right ascension of ascending node and argument of perigee, the correct semi-major axis, eccentricity, and inclination can be chosen to minimize the amount of fuel required for station keeping. The optimal values can be found by finding the Delta v needed for di fferent combinations of the variables and then choosing the values that provide the minimum Delta v. For any target orbit, there are multiple RAO orbit possibilities that can provide 360 degree coverage of a target orbit. Even after eliminating some of them based on the methods already described, there are still many possibilities. The rest of the elimination process would then be based on the mission requirements which could be the range of an on-board sensor, the thruster or reaction wheel controls, or any other number of possibilities.

Le problème considéré est celui du contrôle optimal des transferts orbitaux (problème proposé par le Centre National d'Études Spatiales). Le modèle retenu est l'équation de Kepler contrôlée, la loi de commande étant la poussée d'un engin spatial en orbite autour de la Terre. Les contributions concernent d'une part le temps minimal, d'autre part la moyennation du problème de la minimisation de l'energie. L'action du contrôle peut être considérée comme la perturbation d'un système intégrable, perturbation dont la moyennation fournit une approximation dont on vérifie qu'elle est encore intégrable. Un objet fondamental dans l'étude est l'application exponentielle définie par le flot extrémal du problème de contrôle. Ses propriétés renseignent sur l'existence de solution, ainsi que sur l'optimalité locale ou globale des extrémales du problème. Parmi les résultats obtenus, on peut citer la mise en évidence de l'existence de Pi-singularités et de points conjugués en temps minimal, la platitude de la métrique associée par la moyennation au transfert à énergie minimale vers les orbites circulaires (les trajectoires optimales sont des droites), ainsi que la caractérisation du lieu de coupure du moyenné par comparaison avec la restriction de la métrique plate à un ellipso\"\i de de révolution.