This thesis is concerned with analysis of spectral and orbital stability of solitary wave solutions to discrete and continuous PT-symmetric nonlinear Schroedinger equations. The main tools of this analysis are inspired by Hamiltonian systems, where conserved quantities can be used for proving orbital stability and Krein signature can be computed for prediction of instabilities in the spectrum of linearization. The main results are obtained for the chain of coupled pendula represented by a discrete NLS model, and for the trapped atomic gas represented by a continuous NLS model. Analytical results are illustrated with various numerical examples. / Thesis / Doctor of Philosophy (PhD)

With the increase in space traffic, proliferation of inexpensive launch opportunities, and interest from many countries in utilizing the space domain, threats to existing space assets are likely to increase dramatically in the coming years. The development of a system that can identify potential threats and alert space operators is vital to maintaining asset resiliency and security. The focus of this thesis is the design and evaluation of such a system. The design is comprised of the development of a classification hierarchy and the selection of machine learning models that will enable the identification of anomalous object behavior. The hierarchy is based on previous examples applied to object classification while reconsidering the assumption that a satellite may perform only one mission. The selected machine learning models perform both supervised classification of actively maneuvering objects and unsupervised identification of anomalous behavior within large satellite constellations. The evaluation process considers the independent adjustment of model hyperparameters to achieve optimal model settings. The optimal models perform both classification functions and return moderate accuracy. The system is applied to several case studies examining edge cases and what factors constitute a threatening object and what factors do not. Suggestions for improvement of the system in the future are presented. / Master of Science / The increase in space traffic, proliferation of inexpensive launch opportunities, and interest from many countries in utilizing the space domain represent existential threats to existing spacecraft and operations in low-Earth orbit. Threats to the safe operation of spacecraft are likely to increase dramatically in the coming years. The development of a system that can identify potential threats and alert space operators is vital to maintaining asset resiliency and security. The focus of this thesis is the design and evaluation of such a system. This is accomplished by identifying a system architecture through evaluating current assumptions of what missions satellites are capable of performing. Following the system-level design, modules are proposed that utilize machine learning to identify satellite behavior that is abnormal. These modules are tested and tuned with optimal parameters to deliver improved identification performance. The system is applied to several case studies examining edge cases and what factors constitute a threatening object and what factors do not. Suggestions for improvement of the system in the future are presented.

The problem of developing a generalized impulse as a function of a set of parameters is investigated. The proposed generalized impulse alters an existing orbit by producing, over some period of time, a change in velocity, ΔV, as well as a change in position, Δr. The generalized impulse is described by parameters associated with an instantaneous change in velocity as well as parameters associated with an atmospheric skip trajectory. Closed form solutions are obtained through several changes of independent variable, the use of modified Chapman variables and the consequent analytical integration of the uncoupled equations. The closed form solutions contain between two and six parameters depending on the complexity of the desired skip trajectory. Fuel optimal transfer orbits are obtained using the generalized impulse along with Keplerian arcs and instantaneous changes in velocity. Families of coplanar and noncoplanar transfers for circular orbit to circular orbit are numerically generated. The generated transfer trajectories involve the rendezvous of two vehicles. The orbits are not globally optimal but rather optimal for the specified number and type of velocity impulses specified. The optimal solution to the nonlinear problem is determined via sequential quadratic programming which satisfies the Kuhn-Tucker optimality conditions for constrained minimization. It is found that for transfer between coplanar and noncoplanar orbits, solutions using the generalized impulse compare favorably with solutions obtained by optimal control theory. Numerical solution to complex problems involving transfer from general orbit to general orbit were not obtained. / Master of Science

A dual satellite system in a Low Earth Orbit, LEO, would be beneficial to study the electromagnetic occurrences in the magnetosphere and their contributions to the development of the aurora events in the Earth's lower atmosphere. An orbit configuration is sought that would increase the total time that both satellites are inside the auroral oval. Some additional objectives include minimizing the total fuel cost and the average angle between the satellites' radius vectors. This orbit configuration is developed using a series of instantaneous burns applied at each satellite's perigee. An analysis of the optimal solutions generated by a Particle Swarm Optimization method is completed using a cost function with different weights for the time, fuel, and angle terms. Three different scenarios are presented: a single burn case, a double burn case, and a four burn case. The results are calculated using two different orbital mechanics models: an unperturbed two-body simulation and a two-body simulation with added Earth's equatorial bulge effects. It is shown that the added perturbation reduces the total event time in the optimal solutions generated. Specific weights for the cost function are recommended for further studies. / Master of Science

Orbit propagation is the backbone of many problems in the space domain, such as uncertainty quantification, trajectory optimization, and guidance, navigation, and control of on orbit vehicles. Many of these techniques can rely on millions of orbit propagations, slowing computation, especially evident on low-powered satellite hardware. Past research has relied on the use of lookup tables or data streaming to enable on orbit solutions. These solutions prove inaccurate or ineffective when communication is interrupted. In this work, we introduce the use of physics-informed neural networks (PINNs) for orbit propagation to achieve fast and accurate on-board solutions, accelerated by GPU hardware solutions now available in satellite hardware. Physics-informed neural networks leverage the governing equations of motion in network training, allowing the network to optimize around the physical constraints of the system. This work leverages the use of unsupervised learning and introduces the concept of fundamental integrals of orbits to train PINNs to solve orbit problems with no knowledge of the true solution. Numerical experiments are conducted for both Earth orbits and cislunar space, being the first time a neural network integrator is implemented on flight-like hardware. The results show that the use of PINNs can decrease solution evaluation time by several order of magnitude while retaining accurate solutions to the perturbed two-body problem and the circular restricted three-body problem for deployment on spaceflight-like hardware. Implementation of these neural networks aim to reduce computational time to allow for real-time evaluation of complex algorithms on-board space vehicles.

In this work, we describe all the possible radiative processes occurring in a low temperature hydrogen plasma. Some of the fundamental concepts involving ionized gases and collision phenomena are presented, and a rigorous approach is used to show that classical mechanics is quite appropriate to our study. As an application to a laser engine, we investigate the effects of the maximum temperature, the temperature gradient, the stretching of the plasma shape, the engine pressure, and the equivalent sphere radius, on the total emitted power, including absorbing mechanisms through the equation of radiative transfer. Graphs related to spectral radiative exitances are included, and a complete set of graphs of the total power, permitting interpolations with respect to the above relevant parameters, are also provided. / Master of Science

- An Plasmaschweißbrennern treten starke thermomechanische Beanspruchungen aufgrund der ablaufenden thermophysikalischen Teilprozesse auf. Diese können durch funktionsgerechte werkstoffliche, konstruktive und fertigungstechnische Brennergestaltung bewerkstelligt und die Thermobilanz und Lebensdauer der Brenner verbessert werden. - Anhand des entwickelten strömungs-thermomechanischen/magneto-hydro-dynamischen Simulationsmodells wurden werkstofflich-konstruktive Lösungsansätze für Entwicklung von physikalischen Prozesswirkprinzipien der betrachteten Plasma-Schweißprozessvarianten erarbeitet. - Differente Einflussgrößen des Plasmaschweißprozesses wurden erfasst, analysiert und ihre Wirkung auf Prozessverhalten und Brennerkonstruktion ermittelt. - Die damit gewonnenen Erkenntnisse wurden für werkstoffliche, technisch-konstruktive Brennerentwicklung bzgl. der Ausführungsgeometrien, Prozessgaszuführung und Brennerkühlung genutzt.

La Théorie de la Fonctionnelle de la Densité (DFT) combinée avec le formalisme de la Symétrie Brisée (BS) est aujourd'hui très utilisée dans le domaine du magnétisme moléculaire pour le calcul des constantes d'échange magnétique. Dans le but d'améliorer la compréhension des contributions qui participe à l'interaction d'échange caractérisant les systèmes magnétiques, nous avons mené une étude théorique systématique basée sur l'étude de deux types de modèles. Ces complexes binucléaires de cuivre(II) reliés par divers groupements pontant de type hydroxo, azoture, et chloro, ainsi que des bis-nitroxydes modèles constitués de deux groupements nitroxydes reliés par un système conjugué sont caractérisés par des couplages ferro- et anti-ferromagnétiques variés. Nous avons développé une approche théorique basée sur l'utilisation d'orbitales gelées permettant d'étudier la décomposition de l'interaction d'échange magnétique en différentes contributions telles que l'échange direct, l'échange cinétique et le mécanisme de polarisation de spin. Dans un second temps, nous avons étendu ce travail de rationalisation aux effets de solvant à l'aide de modèles implicites ou explicites. Grâce à une analyse basée sur l'approche de Hoffmann, nous avons pu déterminer les paramètres caractérisant dans les mécanismes d'échange direct et d'échange cinétique. / Density Functional Theory (DFT) combined with the Broken Symmetry (BS) method is today widely used in the field of molecular magnetism for the computation of magnetic exchange coupling constants. In order to improve the understanding of the contributions involved in the exchange phenomena characterizing some magnetic systems, we propose a study based on two types of models. Copper(II) binuclear complexes connected with various bridging groups like hydroxo, azide, and chlorine, as well as small bis-nitroxide composed of two nitroxide moieties linked by a conjugated system show various ferro- and anti-ferromagnetic couplings. We have developed a theoretical approach based on the use of frozen orbitals to decompose the magnetic exchange interaction in different contributions such as the direct exchange, the kinetic exchange and mechanism of spin polarization. In a second part, we have extended this work to rationalize the solvent effects using implicit or explicit models. Through an analysis based on the Hoffmann's approach, we have determined some parameters characterizing the mechanisms of direct exchange and kinetic exchange.

L’étage Valanginien est caractérisé dans le registre sédimentaire par une excursion positive des isotopes du carbone (amplitude 1,5-2‰), appelée « Episode Weissert ». Cet événement coïncide avec des changements paléoenvironnementaux et paléoclimatiques majeurs. La formation de la province volcanique ignée du Paraná-Etendeka a été proposée comme principal facteur forçant contrôlant ces changements. Cependant, de récentes études démontrent que l’Episode Weissert précède systématiquement l’activité volcanique. Ainsi, les facteurs déclenchant qui contrôlent ces changements sont encore source de débat. Dans cette étude des analyses cyclostratigraphique, biostratigraphique, minéralogique et géochimique ont été réalisés sur des sites de moyennes et hautes latitudes (coupes d’Orpierre et de La Charce/Arnayon dans le Bassin Vocontien, site 765C dans la plaine abyssale Argo) dans le but (i) d’explorer la dynamique des changements paléoenvironnementaux à l’échelle locale versus globale et (ii) de discuter des possibles facteurs forçant contrôlant l’épisode Weissert. Les processus diagénétiques et sédimentologiques locaux, qui pouvaient modifier le signal paléoclimatique, ont été discuté avant des interprétations paléoenvironnementales. La calibration astronomique de l’épisode Weissert, réalisée sur la coupe d’Orpierre, a permis pour la première fois le calcul de flux détritiques et de nutriments dans le Bassin Vocontien. Ces résultats indiquent de rapides changements climatiques aux moyennes latitudes, marqués par des conditions plus humides pendant l’Episode Weissert et des conditions plus sèches au Valanginien supérieur. En parallèle de nouvelles données géochimiques et minéralogiques, réalisés sur le site ODP 765C, ont été intégrées à une compilation globale de données géochimique et minéralogique sur 23 coupes répartie dans cinq grands environnements. Trois ceintures climatiques latitudinales majeures ont été identifié durant le Valanginien : (i) une ceinture aride dans l’océan proto Nord Atlantique (~15-17°N), (ii) une ceinture climatique subtropical dans la marge NW téthysienne (~25-30°N), et (iii) une ceinture climatique chaude et tempéré aux sites de hautes latitudes (~53°S et ~40 à ~70°N). Il apparaît que durant cette période, des facteurs orbitaux et tectoniques peuvent avoir contrôlé la distribution de ces ceintures et les principaux changements durant l’Episode Weissert. / The Valanginian stage witnesses a positive carbon isotope excursion (amplitude 1.5-2‰) in the sedimentary records, the so-called « Weissert Episode ». This event coincides with major palaeoenvironmental and palaeoclimatic changes. The formation of the Paraná-Etendeka large igneous province has widely been proposed as the major driving force behind these changes. However recent investigations demonstrate that the Weissert Episode precedes the volcanic activity. Thus the driving force(s) behind these changes are still under debate. In the herein study, cyclostratigraphic, biostratigraphic, mineralogical and geochemical analyses have been performed on mid- and high latitudes sites (the Orpierre and Arnayon/La Charce sections in the Vocontian Basin, and the ODP hole 765C in the Argo abyssal plain) in order (i) to explore the dynamic of the local versus global processes in the palaeoenvironmental changes and (ii) to discuss the possible forcing factors behind the Weissert Episode. Local diagenetic and sedimentological processes that might bias the palaeoclimatic signals are highlighted and discussed before any palaeoenvironmental interpretation. The astronomical calibration of the Weissert Episode performed at Orpierre, allowed for the first time, the calculation of detrital and nutrient influxes into the Vocontian basin. They highlight rapid climate changes at mid latitudes, characterized by pronounced humid conditions during the Weissert Event (Early–Late Valanginian transition) and drier conditions in the Late Valanginian. In parallel, new geochemical and mineralogical analyses performed on the ODP hole 765C have been integrated to a global compilation of published geochemical and mineralogical data from 23 sections, located in five depositional environments. Three latitudinal belts have been recognized during the Valanginian : (i) an arid palaeolatitudinal belt in the Proto North Atlantic Ocean (~15–17°N), (ii) a subtropical climatic belt in the Northwestern Tethyan margin (~25–30°N) ; and (iii) a warm temperate palaeoclimatic belt in the high latitudes site (~53°S and ~40 to 70°N). It appears that during this period, both tectonic and orbital factors might have controlled the distribution of the palaeoclimatic belts and the major palaeoenvironmental changes during the Weissert Episode.

Estudo das ressonâncias de três corpos na zona habitável (ZH), da estrela GJ 581 (Gliese 581), envolvendo dois planetas conhecidos e um terceiro planeta dentro da ZH. Séries de Lie são usadas para obter o Hamiltoniano médio (de segunda ordem nas massas) e teoria de Chirikov é usada para gerar um novo sistema de varáveis canônicas em que os momentos se orientam ao longo e através da ressonância. Um mapa de Hadjidemetriou é construido e permite o cálculo rápido da difusão das órbitas em uma extensa grade de condições iniciais. / Study of three-body resonances in the habitable zone (ZH), the star GJ 581 (Gliese 581), involving two known planets, and a third planet in the ZH. Lie series are used to obtain the average Hamiltonian (the second-order mass) and Chirikov theory is used to generate a new canonical variables system in which the moments are oriented along and across the resonance. A map of Hadjidemetriou is constructed and allows rapid calculation of the diffusion of orbits in an extensive grid of initial conditions.