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1
Rothacher, Markus. "Orbits of satellite systems in space geodesy /." Zürich : Institut für Geodäsie und Photogrammetrie, 1992. http://www.ub.unibe.ch/content/bibliotheken_sammlungen/sondersammlungen/dissen_bestellformular/index_ger.html.
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Belda, Santiago. "Contributions to the Earth Monitoring by Space Geodesy Methods." Doctoral thesis, Universidad de Alicante, 2015. http://hdl.handle.net/10045/50535.
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Kulkarni, Madhav Narayan. "A feasibility study of space VLBI for geodesy and geodynamics /." The Ohio State University, 1992. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487776210796273.
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Webb, T. L. "High resolution atmospheric modelling of a tropical island for space geodesy." Thesis, University of Reading, 2016. http://centaur.reading.ac.uk/66292/.
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Turbulent mixing processes over terrain cause local horizontal variations in water vapour from a variable vertically stratified profile. Temporal variations in water vapour distribution cause delays in phase used in the space geodetic InSAR technique. To correct for this, dynamic atmospheric models are used to simulate water vapour distribution and hence variable refractive phase delay over a small volcanic island in the humid tropics, Montserrat. Initialised by ECMWF analysis data at 16 km resolution, the Weather Research and Forecasting (WRF) model is nested to 300 m resolution. Synthetic simulations of trade window with the WRF Montserrat Model (WMM) demonstrate its ability to replicate gravity waves. WMM simulates atmospheric delay fields during the InSAR imaging of Montserrat by X-band radar (COSMO SkyMed) from two viewing geometries during December 2014. Field measurements during imaging and the recording of zenith wet delay (ZWD) by a 14-receiver GPS network are used for comparison with the radar data and atmospheric models. WMM and ZWD delay difference images appear to show two main influences: (static) topographic modulation and dynamic modulation due to the trade winds owing over and around the mountains. Mitigation of the unwanted delay field in COSMO-SkyMed interferograms using the WMM fields gives standard deviations of the residual delay field in the range 19-38 mm. Statistical calculations of pixel-wise delay estimates place model accuracy in the range 64-81%. The reasons for this level of mitigation may be truncation of initial conditions to WMM, the large amount of liquid water in the atmosphere and simulation of trade window across Montserrat.
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Hill, Christopher John. "Satellite laser ranging and some geophysical applications." Thesis, University of Nottingham, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.328388.
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Cruz, Jaime Y. "Disturbance vector in space from surface gravity anomalies using complementary models /." The Ohio State University, 1985. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487261553060066.
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Archinal, Brent Allen. "Determination of earth rotation by the combination of data from different space geodetic systems /." The Ohio State University, 1987. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487324944212785.
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Müller, Vitali [Verfasser]. "Design considerations for future geodesy missions and for space laser interferometry / Vitali Müller." Hannover : Technische Informationsbibliothek (TIB), 2018. http://d-nb.info/1169963056/34.
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Dumville, Mark. "Geo-referencing : Earth Observation imagery." Thesis, University of Nottingham, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.282598.
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Lindsey, Eric Ostrom. "Fault properties, rheology and interseismic deformation in Southern California from high-precision space geodesy." Thesis, University of California, San Diego, 2015. http://pqdtopen.proquest.com/#viewpdf?dispub=3721663.
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This dissertation presents the collection and processing of dense high-precision geode- tic data across major faults throughout Southern California. The results are used to inform numerical models of the long-term slip rate and interseismic behavior of these faults, as well as their frictional and rheological properties at shallow depths. The data include campaign surveys of dense networks of GPS monuments crossing the faults, and Interferometric Synthetic Aperture Radar (InSAR) observations from ENVISAT. Using a Bayesian framework, we first assess to what extent these data constrain relative fault slip rates on the San Andreas and San Jacinto faults, and show that the inferred parameters depend critically on the assumed fault geometry. We next look in detail at near-field observations of strain across the San Jacinto fault, and show that the source of this strain may be either deep anomalous creep or a new form of shallow, distributed yielding in the top few kilometers of the crust. On the San Andreas fault, we show that this type of shallow yielding does occur, and its presence or absence is controlled by variations in the local normal stress that result from subtle bends in the fault. Finally, we investigate shallow creep on the Imperial fault, and show that thanks to observations from all parts of the earthquake cycle it is now possible to obtain a strong constraint on the shallow frictional rheology and depth of the material responsible for creep. The results also suggest activity on a hidden fault to the West, whose existence has been previously suggested but never confirmed.
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Symons, Leighton James. "Global GPS networks and the determination of Earth Rotation Parameters." Thesis, University of Nottingham, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.263465.
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Van, Wyk Peter Ryan. "Rock mechanics for construction of the gravimeter vault at the Matjiesfontein Space Geodesy and Earth Observation Observatory." Thesis, Stellenbosch : Stellenbosch University, 2013. http://hdl.handle.net/10019.1/85638.
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Thesis (MEng)--Stellenbosch University, 2013.ENGLISH ABSTRACT: The suitability of local construction materials for construction purposes is governed by several rock mechanical properties. Strength, durability, performance and petrography of aggregates all influence the decisions engineers make in deciding if the aggregate is suitable and sustainable throughout the lifetime of a structure. This thesis investigates these properties by combining engineering, chemistry and geological disciplines to make informed decisions. The pertaining project for which the research was conducted is the construction of the gravimeter vault at the Matjiesfontein Geodesy and Earth Observation Observatory (MGO) although the research acquired can be used for other projects of a similar nature and other outbuildings at the MGO. Material at and around the site were tested for strength and durability according to certain South African National Standards (SANS). Slake durability was tested as certain rock types tend to slake when exposed to the atmosphere such as tillite of the Dwyka formation and shale of the Karoo Supergroup. Concrete cube strength was determined on cubes containing crushed rock from Matjiesfontein as well as river sand. Cube strength was conducted to analyse performance and to establish a mix design that would be sustainable throughout the lifetime of the project. Petrographic examination using Powder X-ray diffraction (PXRD), X-ray fluorescence (XRF), Scanning Electron Microscopy (SEM) and inspection under a petrographic microscope were conducted. These methods were used to determine if a risk exists for alkali-silica reactivity (ASR) in concrete when the rock types are used as aggregate, particularly if high quartz-bearing rock types such as quartzite of the Table Mountain group were to be used as coarse aggregate. Inspection of thin sections for strained quartz under a petrographic microscope and SEM imaging were important in determining if ASR may occur. The gravimeter vault was constructed using materials sourced mainly from Laingsburg. Tillite satisfied all tests and analyses conducted during the research, making it more suitable for construction than the other materials from Matjiesfontein. The slake durability test indicates that tillite is nearly as durable as quartzite, which is considered the most durable rock type at Matjiesfontein. This is due to atmospheric conditions in the Karoo being very dry with low humidity in comparison to the coast where slaking is known to occur. Slaking properties were most prominent for shale at Matjiesfontein and if excavated, it is recommended to cover the exposed shale with a layer of asphalt or cement to prevent slaking. The 10% fines aggregate crushing test (10%FACT) value for tillite was over the 210 kN prerequisite and the wet-to-dry ratio over 75% making it suitable for road construction according to the 10%FACT. All cube tests reached the desired 40 MPa prerequisite although the mixtures containing local river sand were unworkable. Unlike quartzite and quartzitic sandstone from Matjiesfontein, tillite is low in quartz and has minimal strained quartz. Therefore, no risk exists for ASR if tillite were to be used as aggregate in concrete.
AFRIKAANSE OPSOMMING: Die geskiktheid van plaaslike konstruksiemateriale vir konstruksiedoeleindes word deur sekere rots meganiese eienskappe beïnvloed. Sterkte, duursaamheid, volhoubaarheid en petrografie van aggregaat beïnvloed die besluite wat ingenieurs moet neem sodat die aggregaat aan standaarde voldoen en gedurende die leeftyd van ‘n struktuur volhoubaar is. Hierdie tesis ondersoek die genoemde eienskappe deur ingenieurs-, chemiese- en geologiese dissiplines te kombineer. Die voorgenome projek, waarvoor die navorsing ter sprake is, is vir die konstruksie van die gravimeterkluis by die “Matjiesfontein Geodesy and Earth Observation Observatory (MGO)”, alhoewel die navorsing ook gebruik kan word vir soortgelyke projekte, sowel as die konstruksie van die res van die geboue by die MGO. Materiale van die terrein en die omgewing is volgens sekere Suid-Afrikaanse kodes vir sterkte en duursaamheid getoets. Die blusbaarheid van materiale is getoets omdat sekere materiale, soos tilliet van die Dwyka-formasie en skalie van die Karoo Supergroep blus wanneer dit aan die atmosfeer blootgestel word. Die betonsterkte van kubusse, waarin plaaslike gesteentes en riviersand van Matjiesfontein vir aggregaat gebruik is, is bepaal. Die kubusse is getoets om die sterkte daarvan te analiseer en om ‘n betonmengsel, wat tydens die leeftyd van die projek volhoubaar is, daar te stel. Petrografiese eksaminering deur X-straal difraksie (XRD), X-straal fluoressensie (XRF), Skandeerelektronmikroskopie (SEM) en inspeksie onder ‘n petrografiese mikroskoop is gedoen. Met die doel om die petrografiese samestelling van materiale van Matjiesfontein te bepaal, is hierdie metodes gevolg om te uit te vind of daar ‘n risiko vir alkalie-silikaat reaksies (ASR) bestaan, as die gesteentes in beton gebruik word. Veral gesteentes met ‘n hoë hoeveelheid kwarts, soos kwartsiet van die Tafelberg-groep, is hier ter sprake. Inspeksie van dunsnitte vir gespanne kwarts onder ‘n petrografiese mikroskoop en SEM was belangrik om die risiko vir ASR te bepaal. Die gravimeterkluis is hoofsaaklik met materiale afkomstig van Laingsburg gebou. In vergelyking met die ander gesteentes by Matjiesfontein is tilliet, volgens alle toetsparameters, die mees geskikte gesteente vir konstruksiedoeleindes. Die blusbaarheid van tilliet vergelyk goed met kwartsiet, wat as die sterkste en duursaamste gesteente by Matjiesfontein, beskou word. Die rede hiervoor is die atmosferiese toestande wat baie droër is, asook die laer humiditeit in die Karoo, in vergelyking met gebiede nader aan die kus waar blusting meer algemeen voorkom. Die blusbaarheid van skalie by Matjiesfontein kom algemeen voor. As daar dus uitgrawing in hierdie gebied plaasvind, word dit aanbeveel dat ‘n laag sement of asfalt oorgegooi word om die blusting te verhoed. Die 10%FACT waarde vir tilliet was bo die vereiste 210 kN, asook bo die 75% nat-teenoor-droog-verhouding en daarom is dit volgens die 10%FACT-toets as padboumateriaal geskik. Alhoewel mengsels, wat plaaslike riviersand bevat het, onwerkbaar was, het alle toetsmonsters (kubusse) die vereiste 40 MPa- sterkte bereik. In vergelyking met kwartsiet en kwarsitiese sandsteen, bevat tilliet min kwarts en ook minimale gespanne kwarts. Daar bestaan dus geen risiko vir ASR indien tilliet van Matjiesfontien in die beton gebruik word nie.
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Stressler, Bryan James. "Characterization of stress changes in subduction zones from space- and ground-based geodetic observations." Thesis, University of Iowa, 2017. https://ir.uiowa.edu/etd/5648.
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Temporally and spatially clustered earthquake sequences along plate boundary zones indicate that patterns of seismicity may be influenced by earthquake-induced stress changes. Many studies invoke Coulomb stress change (CSC) as one possible geo-mechanical mechanism to explain stress interactions between earthquakes, their aftershocks, or large subsequent earthquakes; however, few address the statistical robustness of CSC triggering beyond spatial correlations. To address this, I evaluate the accuracy of CSC predictions in subduction zones where Earth’s largest earthquakes occur and generate voluminous and diverse aftershock sequences. A series of synthetic tests are implemented to investigate the accuracy of inferred stress changes predicted by slip distributions inverted from suites of geodetic observations (InSAR, GPS, seafloor geodetic observations) that are increasingly available for subduction zone earthquakes. Through these tests, I determine that inferred stress changes are accurately predicted at distances greater than a critical distance from modeled slip that is most dependent on earthquake magnitude and the proximity of observations to the earthquake itself. This methodology is then applied to the 2010 Mw 8.8 Maule, Chile earthquake sequence to identify aftershocks that may be used to perform statistically robust tests of CSC triggering; however, only 13 aftershocks from a population of 475 events occurred where confidence in CSC predictions is deemed to be high. The inferred CSC for these events exhibit large uncertainties owing to nodal plane uncertainties assigned to the aftershock mechanisms. Additionally, tests of multiple published slip distributions result in inconsistent stress change predictions resolved for the 13 candidate aftershocks. While these results suggest that CSC imparted by subduction megathrust earthquakes largely cannot be resolved with slip distributions inverted from terrestrial geodetic observations alone, the synthetic tests suggest that dramatic improvements can be made through the inclusion of near-source geodetic observations from seafloor geodetic networks. Furthermore, CSC uncertainties will likely improve with detailed earthquake moment tensor catalogs generated from dense regional seismic networks.
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König, Daniel [Verfasser], and B. [Akademischer Betreuer] Heck. "Determining a Terrestrial Geodetic Reference Frame Following the Integrated Approach of Space Geodesy / Daniel König. Betreuer: B. Heck." Karlsruhe : KIT-Bibliothek, 2013. http://d-nb.info/1044956119/34.
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Júnior, Edvaldo Simoes da Fonseca. "O sistema GPS como ferramenta para avaliação da refração ionosférica no Brasil." Universidade de São Paulo, 2002. http://www.teses.usp.br/teses/disponiveis/3/3138/tde-30102002-163432/.
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Após a desativação da disponibilidade seletiva, ocorrida em maio de 2000, a maior fonte de erro presente no sistema GPS passou a ser a refração ionosférica. Os seus efeitos provocam um avanço na fase de batimento da portadora e um atraso no código. Na região equatorial onde o Brasil está inserido, a refração ionosférica apresenta variações que decorrem de diversos fatores tais como: o ciclo solar, o movimento aparente do Sol, as estações do ano, o campo geomagnético, entre outras. Desta forma, a refração ionosférica é um fator limitante pois, degrada a determinação de posições, principalmente, se o usuário estiver utilizando um receptor de apenas uma freqüência. Para avaliar o efeito da refração ionosférica no Brasil, no período compreendido entre janeiro de 1997 a dezembro de 2001, foram utilizados dados coletados com receptores providos de duas freqüências e que integram a Rede Brasileira de Monitoramento Contínuo do Sistema GPS. Todos os dados foram preparados e inseridos em um programa científico de processamento das observáveis do sistema GPS. Devido à grande massa de dados foi necessário o desenvolvimento de um programa para verificar a integridade dos mesmos, converter as efemérides precisas e os dados para o formato de entrada do programa científico e preparar os arquivos de lote. Além das características apresentadas, este programa foi desenvolvido para automatizar o processo de cálculo do conteúdo total de elétrons. Ao final do processamento o programa exibe os parâmetros que representam a refração ionosférica ou seja, os valores calculados para o Conteúdo Total de Elétrons. Tais valores permitiram a criação de uma série histórica do comportamento da refração ionosférica abrangendo um intervalo de tempo que contempla um período em que o ciclo solar apresentava atividade mínima e um outro período em que o ciclo solar alcançou a máxima atividade. Estes dados indicam o comportamento da ionosfera para um período de cinco anos em uma das regiões do planeta que apresenta as maiores variações, comportamento este, que permitirá um melhor conhecimento da ionosfera e a melhoria ou desenvolvimento de modelos mais adequados. Foram gerados ainda, mapas da ionosfera que poderão auxiliar na melhoria da acurácia posicional.Since the US president decided to turn off the selective availability (SA) one of the biggest error in the GPS system has been the ionosphere refraction. The refraction effect on GPS signals are: delay for the code and an advance for the phase. In the equatorial region, where Brazil is, the refraction presents the biggest variations that are caused by the solar cycle, the time of the day, the season, the geomagnetic field and many others phenomena. In this case, the ionosphere refraction is a limitation because it increases the degradation of the position, specially if the user is using a single frequency receiver. To evaluate the ionospheric effects in Brazil, between January 1997 and December 2001, data from the Brazilian Continuous GPS Monitoring Network were used, provided by double frequency GPS receivers. All data were prepared and used by a scientific software to process the GPS observations. The volume of data was so big that it was necessary to write a software to manage the data integrity, to transform the precise ephemeris and the observations to scientific program format and to create batch files. Also, the program was used to process the data and to compute the total electron content automatically. At the end of the process, the software shows the TEC parameters. These parameters were used to create a historical series of the ionosphere refraction in Brazil. This series represents a period of minimal solar cycle, 1997, and a maximum period of the solar cycle, 2000 / 2001 in one of the most active regions of the planet. This series will improve the knowledge on the ionosphere and will allow to improve models or create new ones. Ionospheric maps that can be used to improve the positional accuracy, were also generated.
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Baek, Sang-Ho. "DEM generation and ocean tide modeling over Sulzberger Ice Shelf, West Antarctica, using synthetic aperture radar interferometry." Columbus, Ohio : Ohio State University, 2006. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1155745007.
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Luong, Ngoc-Dung. "Analyse d'erreurs de constellations de satellites en termes de positionnement global et d'orbitographie." Thesis, Nice, 2015. http://www.theses.fr/2015NICE4112/document.
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Grâce au développement des techniques spatiales (GNSS, DORIS, laser et le VLBI), la géodésie apporte quantité d’informations sur la forme de la Terre (sa géométrie et sa gravité), sa rotation et son orientation dans l’espace, aux échelles globales comme aux échelles régionales. L’étude des déformations de chaînes de montagne par GPS, des courants marins cartographiés par altimétrie satellitaire, des variations temporelles du champ de gravité, ainsi que l’établissement du repère de référence terrestre international, sont les exemples de l’apport de ces techniques à l’observation de la Terre et au changement global. Notre travail a pour but de faire un bilan des erreurs résiduelles de la géodésie spatiale, en séparant les causes des effets. Le but est de montrer comment les erreurs d’orbite se propagent d’abord dans la trajectoire, puis dans des produits globaux comme le repère de référence (via les mesures de poursuite de satellites) et la surface topographique (via les mesures altimétriques). Nous avons développé une approche analytique qui traite du transfert des erreurs d’origines géométrique et dynamique. En partant des équations du mouvement orbital, nous proposons une solution analytique d’ordre un du mouvement orbital circulaire, qui est appliquée pour propager les erreurs de modèle dynamique. Ensuite, les résultats sont transférés (ou projetés) sur plusieurs types de fonction de mesure : l’altimétrie, les mesures de distance et les mesures de vitesse radiale. L’originalité de ce travail tient pour beaucoup dans les méthodes purement analytiques qui ont été développées spécifiquement pour effectuer les analysesThanks to the development of space techniques (GNSS, DORIS, laser and VLBI) geodesy provides amount of information to determine and to study the shape of the Earth (its geometry and its gravity), its rotation and orientation in space at global scales as well as at regional scales. The study of crustal deformations by using GPS, the ocean topography by satellite altimetry, the temporal variations of the gravity field (mass transports) as well as the construction and monitoring of the International Terrestrial Reference Frame (ITRF), are some examples of the contribution of these techniques to the Earth observation including the current global change. Our work aims to separate causes and consequences. We developed a dedicated approach in which different source of errors, of geometrical and dynamical natures, are treated by analytical expressions. Starting from the dynamical satellite equation of motion, we propose to integrate and propagate the model errors and then to project the results into different measurement functions: altimetry, tracking distances and radial velocities. It results in a complex but comprehensive way that enables the propagation of prediction errors into some general geodetic products as the terrestrial reference frame or the ocean surface topography. The originality of this work lies in the development of a purely analytical method for circular orbits, which has been used to propagate errors from dynamical models. In addition, the resulting orbit errors were projected at the measurement level in order to deduce the impacts on some global geodetic products
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Machado, Wagner Carrupt. "Utilização de redes neurais artificiais na previsão do VTEC visando a geração de estações de referência virtuais em tempo-real." Universidade de São Paulo, 2012. http://www.teses.usp.br/teses/disponiveis/3/3138/tde-08022013-155136/.
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Dentre as técnicas de posicionamento utilizando os sistemas de navegação por satélite globais (GNSS - Global Navigation Satellite Systems), merece destaque a que utiliza dados de uma rede de estações GNSS para gerar estações de referência virtuais. Desde que as estações da rede não estejam separadas por mais de 100 km e o receptor do usuário esteja dentro da região interna à rede de referência, esta técnica de posicionamento pode proporcionar posicionamento com precisão melhor que 10 cm a usuários de receptores de uma frequência. No entanto, o posicionamento em tempo-real pode ser inviabilizado caso ocorra problema de comunicação com as estações da rede de referência. Tendo em vista a relação do conteúdo total de elétrons (TEC - Total Electron Content) com o atraso ionosférico de primeira ordem, esta pesquisa apresenta uma forma de se prever 72 horas do TEC na direção vertical (VTEC - Vertical Total Electron Content) regionalmente com a arquitetura de redes neurais artificiais (RNA) denominada perceptrons de múltiplas camadas (MLP MultiLayer Perceptrons). A metodologia de previsão do VTEC proposta foi empregada na geração de estações de referência virtuais, onde arquivos de previsão do atraso troposférico zenital, produzidos pelo Instituto Nacional de Pesquisas Espaciais (INPE), foram utilizados para considerar o atraso provocado pela atmosfera neutra e as efemérides preditas pelo serviço internacional do GNSS (IGS - International GNSS Service) foram empregadas para calcular a posição dos satélites. As RNA foram treinadas e avaliadas com dados de VTEC extraídos dos mapas da ionosfera globais (GIM - Global Ionospheric Map) produzidos pelo IGS e dos arquivos produzidos com o software Mod_Ion, ambos no formato IONEX (IONosphere Map EXchange), mostrando que o VTEC pode ser previsto por 72 horas com diferença média quadrática (RMS Root Mean Square) que varia de 1,2 unidades de TEC (TECU - TEC Units) a 12,5 TECU, em baixa e alta atividade solar, respectivamente. Dezoito linhas de base, localizadas no oeste do Estado de São Paulo, foram calculadas utilizando estações de referência virtuais e estações de referência reais, verificando-se que o posicionamento relativo tridimensional empregando a metodologia proposta apresentou RMS de aproximadamente 46 cm. Quando avaliada no posicionamento absoluto preciso (PPP Precise Point Positioning), o RMS relacionado com o posicionamento tridimensional foi de 26 cm.The positioning technique that uses data from a network of GNSS reference stations to generate virtual reference stations should be detached among the Global Navigation Satellite Systems (GNSS) positioning techniques. Since the inter reference station distances are up to 100 km and the user receiver is within the internal region of the network, this technique can provide single frequency receiver users positioning with better accuracy than 10 cm. However, real-time positioning can be impracticable if communication breakdown involving such reference stations occurs. Given the relation between the Total Electron Content (TEC) and the first-order ionospheric delay, this research presents a way to predict 72 hours of vertical TEC (VTEC) regionally using the Artificial Neural Networks (ANN) architecture called MultiLayer Perceptorns (MLP). The proposed VTEC prediction methodology was employed in the generation of virtual reference stations, where files of prediction of zenithal tropospheric delay, produced by the National Institute For Space Research (INPE Instituto de Pesquisas Espaciais), were used to take the neutral atmospheric delay into account and the precise ephemeris predicted by the GNSS International Service (GNSS) were employed to compute satellites positioning. ANN were trained and assessed using VTEC data from the Global Ionospheric Maps (GIM) produced by IGS and the files produced by Mod_Ion software, both in IONEX (IONosphere Map EXchange) format, showed VTEC can be predicted for 72 hours with Root Mean Square difference (RMS) of about 1.2 TEC units (TECU) and 12.5 TECU, respectively, in low solar activity and high solar activity. Eighteen baselines, in the west region of Sao Paulo State, were computed using virtual reference stations and real reference stations, verifying that the three-dimensional relative positioning using the proposed methodology showed RMS of 46 cm. When assessed by precise point positioning (PPP), the three-dimensional RMS positioning was of 26 cm.
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Belli, Alexandre. "Transfert de temps optique spatial (mission T2L2 / Jason-2) : applications et impacts en Géodésie." Thesis, Bourgogne Franche-Comté, 2017. http://www.theses.fr/2017UBFCD040/document.
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Mes travaux de thèse ont pour finalité la réalisation d’un transfert de temps intercontinentald’une stabilité meilleure que 2 ns sur 10 000 s, entre les observatoires géodésiquesde l’International Laser Ranging Service (ILRS). Ce transfert de temps est effectué à l’aide deliens spatiaux optiques obtenus par l’expérience de Transfert de Temps par Lien Laser (T2L2).T2L2 a été lancée le 20 Juin 2008 à 1336 km d’altitude à bord du satellite océanographiqueJason-2. Le principe de cette expérience est basé sur la datation, au sol dans les stations laseret à bord du satellite, d’impulsions laser très courtes (30 - 100 ps) aller - retour (2 voies) venantde 25 stations laser réparties sur le Globe. La performance du lien sol-bord (dont la stabilitéatteint des valeurs inférieures à 10 ps sur 100 s), procurée par la technologie laser d’une partet par la qualité de l’instrument spatial d’autre part permet de lire précisément les variationsde l’oscillateur bord (à quartz) développé pour le système d’orbitographie et de localisationDoppler Orbitography and Radiopositionning Integrated by Satellite (DORIS) du Centre Nationald’Études Spatiales (CNES). Nous montrons qu’il est possible de construire un modèle defréquence déterministe, à court terme (10 j) et moyen terme (plusieurs mois) d’évolution de lafréquence de l’oscillateur bord DORIS, avec une précision relative de 3 - 5·10≠13. Les variationsde fréquence sont induites par un environnement spatial complexe, où les radiations, la températureet le vieillissement du résonateur dégradent l’oscillateur. L’intégration de ce modèlenous permet la réalisation d’un temps à bord pour synchroniser le réseau ILRS complet et ainsiestimer les biais en temps des stations laser par rapport à l’Universal Time Coordinate (UTC).L’effet des biais en temps, estimé à l’aide de T2L2 sur l’orbite ainsi que sur les coordonnées desstations laser de l’International Terrestrial Reference Frame (ITRF) est déterminé précisémentau niveau de quelques millimètres. Enfin T2L2 étant également capable de dater le Pulse ParSeconde (PPS) du système Global Positionning System (GPS), nous étudions l’évolution sur lelong terme (plusieurs années) des horloges utilisées dans les stations laser et nous montrons lesproblèmes insoupçonnés de l’instabilité de leur système de temps/fréquence au solThe purpose of my Ph.D. works is the realization of a intercontinental time transfer,with a stability better than 2 ns over 10,000 s, between the International Laser RangingService (ILRS) geodetics observatories. This time transfer is performed thanks to optical spacelinks and the Time Transfer by Laser Link (T2L2) experiment. T2L2 is a passenger on-board theoceanographic satellite Jason-2, which was launched the 20th June 2008, at 1336 km of altitude.The principle of this experiment is based on the (two-way) short laser pulses (30 - 100 ps) timetagging, in laser station on ground and on-board the satellite, which come from 25 worldwidelaser stations. The high performance of the ground-to-space link (where the stability reach valuesbetter than 10 ps over 100 s), given by the laser technology in one hand, and the quality of thespace instrument in the other hand, allows to precisely read the frequency variations of the onboardoscillators (quartz) built for the orbitography and localization Doppler Orbitography andRadiopositionning Integrated by Satellite (DORIS) French system. We demonstrate the possibilityto build a deterministic frequency model, on the short term (10 days), mid-term (severalsmonth) for the on-board DORIS oscillator frequency evolution, with a relative precision at 3- 5·10≠13. Frequency variations are caused by a complex space environment, where radiations,temperature and device aging damage the oscillator. The integration of this model allows us tobuild an "on-orbit" time realization to synchronize the whole ILRS network and thus, estimatelaser station time biases in regard to the Universal Time Coordinate (UTC). The time bias effects,estimate thanks to T2L2, on the International Terrestrial Reference Frame (ITRF) stationcoordinates, is precisely determined at the level of a few millimeters. Finally, T2L2 is able totime tagged the Global Positionning System (GPS) Pulse Per Second (PPS) signal in order tostudy the clock long term (several years) behavior in laser station and we show the unexpectedproblems due to the instability of the station time and frequency system
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Blazquez, Alejandro. "Caractérisation par satellite des échanges d'eau entre l'océan et les continents aux échelles interannuelles à décennales." Thesis, Toulouse 3, 2020. http://www.theses.fr/2020TOU30074.
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Depuis 2002, GRACE fourni des estimations des échanges d'eau entre l'océan et les continents. Cependant, ces estimations sont incertaines car elles montrent des écarts lorsque différentes approches et différents paramètres sont utilisés pour traiter les données GRACE. Je revois le traitement des données GRACE, en accordant une attention particulière aux différentes sources d'erreurs et d'incertitudes. L'incertitude dans le bilan global de l'eau, à des échelles annuelles à interannuelles est due à la corrections du mouvement du géocentre ainsi qu'à l'incertitude dans la correction du GIA. Cela est particulièrement vrai pour l'estimation de la masse de l'océan et les eaux continentales dont l'incertitude liée à la tendance pour la période 2005 à 2015 est de ±0.33mmSLE/yrSince 2002, GRACE provides estimates of the transfers of water-mass from land to the ocean. However, these estimates are uncertain as they show discrepancies when different approaches and different parameters are used to process the GRACE data. I revisit the treatment of GRACE data, paying a special attention to the different sources of errors and uncertainties. The main sources of uncertainty in the global water budget, at annual to interannual time scales, are the spread in the geocenter corrections and the uncertainty in the GIA correction. This is particularly true for the ocean mass and glacier and TWS mass change estimates for which the uncertainty in trends for the period from 2005 to 2015 is ±0.33mmSLE/yr
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Cavalletti, Fabio. "Optimal transportation in geodesic spaces." Doctoral thesis, SISSA, 2011. http://hdl.handle.net/20.500.11767/4213.
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Nurul, Huda Ibnu. "Etude des propriétés rhéologiques globales de la Terre à l'aune des observations VLBI." Thesis, Paris Sciences et Lettres (ComUE), 2019. http://www.theses.fr/2019PSLEO007.
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Depuis le début du vingtième siècle, l’observation des variations de rotation de la Terre par les techniques astro-géodésiques permet de dévoiler les propriétés rhéologiques globales de la Terre. En particulier, les paramètres des modes d'oscillation libre de l'axe de rotation, qui sont aussi des paramètres de résonance - reflètent les défauts d'élasticité de la Terre solide, la réponse de l’océan au forçage externe et les propriétés de la graine fluide, éventuellement du noyau solide. On peut obtenir de meilleures contraintes sur ces paramètres de résonance en confrontant le mouvement terrestre du pôle de rotation observé (mouvement du pôle) – et aussi la nutation en tant que mouvement du pôle en rétrograde diurne - à l’excitation modélisée qui le produit. Les propriétés rhéologiques de la Terre sont d'autant mieux déterminées que le mouvement du pôle (y compris dans la bande diurne) est observé précisément et l’excitation modélisée correctement. A l'heure actuelle, si la précision du mouvement du pôle est légèrement meilleure au delà de 2 jours, la meilleure reconstitution du forçage concerne la bande de nutation (la bande rétrograde diurne), car il est procède alors des marées gravimétriques luni-solaires, lesquelles sont modélisées avec une grande précision). C'est pourquoi notre travail est d'abord consacré à l'ajustement direct des composantes luni-solaires périodiques de la nutation à partir des retards du VLBI, puis à l'estimation des paramètres de résonances dans la fonction de transfert entre ces termes de nutation observés et ceux modélisés pour une terre rigide, lesquels reflètent le forçage luni-solaire. Les résultats obtenus confirme notamment le raccourcissement d’environ 40-50 jours de la période de résonance du mouvement du pôle dans la bande rétrograde diurne. Nous montrons comment cette diminution s'explique par la réponse dynamique des océans à la marée du pôle, laquelle est étudiée à l'aune des modèles de marées océaniques diurnes . Nous prédisons également un changement des paramètres de résonance du mouvement du pôle à proximité de la fréquence de résonance de la nutation libre du noyau; cette modification semble confirmée par la détermination de ces paramètres à partir des termes de nutation. Notre étude des paramètres de résonance s'étend au delà de la bande de nutation. D'une part, nous réexaminons l’estimation des paramètres de résonance du mouvement du pôle dans la bande saisonnière, dominée par l’oscillation de Chandler, en utilisant les derniers modèles hydro-atmosphériques. D'autre part, nous étudions la résonance du mouvement du pôle à la bande prograde diurne, où l’excitation est dominée par la marée océanique. Nous obtenons une période de résonance de l’ordre de 393 jours, corroboré par notre modélisation fondée sur les modèles de marée océanique. L'ensemble des résultats obtenus permet d'apporter des contraintes sur la dépendance en fréquence du nombre de Love et du nombre de Love océanique caractérisant respectivement la réponse de la Terre solide et des océans à un potentiel externe de degré 2Since the beginning of the 20th century, the observation of the Earth rotation variations through astro-geodetic techniques enables to investigate the global rheological properties of the Earth, in particular, the resonance parameters of the free rotation modes reflect the solid Earth anelasticity, the ocean response to an external forcing, and the properties of the fluid inner core, eventually of the solid inner core. Better constraints on these resonance parameters can be obtained by confronting the observed terrestrial motion of the rotation pole (the so-called polar motion) - including nutation as a retrograde diurnal polar motion - to the modelled excitation producing it. The more precise the modelled excitation and the observed polar motion are, the better the Earth rheological properties will be determined. For now, the best precision are reached in the nutation band. So, our work is first dedicated to a direct adjustment of the nutation components from VLBI delays, then the adjustment of the resonance parameters in the transfer function between the observed nutation terms and the corresponding rigid nutation terms that reflects the luni-solar forcing. The obtained resonance parameters confirms in particular the shortening of the polar motion resonance period of about 40 - 50 day in the retrograde diurnal band. Then, we show that the dynamical behaviour of the oceans in the diurnal band is mostly responsible for that. We also predicted a supplementary change of the resonance parameters in the vicinity of the free core nutation resonance, as expected from the solid Earth response, and confirmed by the adjustment of these parameters through the nutation terms. In addition to the nutation band, we revisit the estimation of the polar motion resonance parameters in the seasonal band, dominated by the Chandler wobble, in light of the most recent global circulation models of the hydro-atmospheric layers. Finally, we extend the investigation of polar motion resonance to the prograde diurnal polar motion, where the excitations mostly result from the ocean tides. We obtain a resonance period of about 393 days, and confirmed by our prediction based on the ocean tidal models. These results allow us to impose constraints on the frequency dependence of the body Love number and the Love number oceanic, characterizing respectively the response of the solid Earth and the oceans to an external potential of degree 2
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Eissa, Leila. "Utilisation de méthodes de l'astrogéodésie et de la géodésie spatiale pour des études de déformations de l’écorce terrestre : représentations de déformations et de leur degré de signification par des tenseurs régulièrement répartis." Thesis, Paris Est, 2011. http://www.theses.fr/2011PEST1018/document.
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Les outils de la géodésie spatiale sont aujourd'hui très fortement impliqués dans les études géophysiques. Le champ de déformations horizontales d'un site d'étude est fourni par les vecteurs déplacement ou par un champ tensoriel. Ce dernier possède l'avantage d'être indépendant de tout référentiel, contrairement à ce qui est nécessaire pour exprimer les vecteurs vitesse. Néanmoins, les méthodes de calcul de tenseurs dépendent souvent d'une décomposition arbitraire en figures élémentaires à partir des points de mesures géodésiques. De plus, la représentation de ces tenseurs selon leurs axes principaux est d'une lecture et d'une interprétation assez difficiles et nécessitent un certain entraînement. Cette thèse traite, dans un premier temps, le problème de fournir un champ continu de déformations sous la forme des tenseurs régulièrement répartis, de façon peu dépendante des points de mesure, et dans un deuxième temps, de fournir une représentation cartographique intuitive de ces tenseurs avec, pour la première fois, une représentation simultanée de leur degré de significativité. L'estimation des incertitudes de la déformation obtenue est analysée selon deux points de vue : d'une part, une méthode de Monte Carlo est appliquée pour la détermination des barres d'erreurs liées aux mesures, son résultat permet le calcul de degré de significativité des tenseurs par comparaison des valeurs de tenseurs par rapport à leurs incertitudes, et d'autre part, une estimation des contraintes imposées par la géométrie de distribution des points de mesures qui est ensuite combinée avec la première source d'erreur. La nouvelle approche de représentation a été analysée via une enquête auprès d'un groupe de géophysiciens, en leur fournissant plusieurs possibilités de représentations. En se basant sur les résultats de cette enquête, nous avons pu valider la nouvelle représentation qui permet de mettre en évidence certains aspects mal mis en évidence par la représentation classique, et donc le choix des éléments graphiques de la carte permettant de fournir la représentation la plus intuitive possibleSpace geodesy tools are now strongly involved in geophysical studies. The horizontal deformation field for a region of interest is provided by two main methods : a velocity field and a strain tensor field. A strain tensors field solution has the advantage of being independent of the reference frame in which the velocities are expressed. Nevertheless, the current methods of calculation of a strain tensors field depend on the positioning of geodetic points. Furthermore, the current mapping method of tensors by their mains axis is not easy to read and to interpret, needing some training. This thesis is devoted to the problem of calculating a continuous field of regularly spaced strain tensors, and providing an intuitive mapping method of these tensors with a simultaneous representation of their significance level on the same map. The estimation of uncertainties related to the deformation field is made in two steps : firstly, a Monte Carlo method is applied for the calculation of uncertainties related to the measurements, its results allow to define the significance level of tensors by normalizing tensor's values with respect to their related uncertainties, then, the constraints coming from the distribution of the network of measurement points are calculated and combined with the first source of error. The new approach of mapping tensors was analyzed through an opinion survey by providing several possibilities of representation. The results of this opinion survey allowed us to validate this new mapping method by geophysicists for representing a deformation field, because it allows highlighting some aspects not well illustrated by the classical mapping method of tensors, and therefore choosing the graphical elements of the map which provide the best intuitive method of mapping a strain tensors field
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Khalafalla, Eltayeb Elrayah. "Computer aided processing of geodesic structural forms." Thesis, University of Surrey, 1994. http://epubs.surrey.ac.uk/845/.
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Draper, Christopher Peter William. "The geodesic Gauss map of spheres and complex projective space." Thesis, University of York, 2015. http://etheses.whiterose.ac.uk/11542/.
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For an isometrically immersed submanifold, the spherical Gauss map is the induced immersion of the unit normal bundle into the unit tangent bundle. Compact rank one symmetric spaces have the distinguishing feature that their geodesics are closed with the same period, and so we can define the manifold of geodesics as the quotient of the unit tangent bundle by geodesic flow. Through this quotient we define the geodesic Gauss map to be the Lagrangian immersion given by the projection of the spherical Gauss map. In this thesis we establish relationships between the minimality of isometrically immersed submanifolds of the sphere and complex projective space and the minimality of the geodesic Gauss map with respect to the Kähler-Einstein metric on the manifold of geodesics. In particular, we establish that for an isometrically immersed holomorphic submanifold of complex projective space, its geodesic Gauss map is minimal Lagrangian if it has conformal shape form.
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Donner, Ralf. "Die visuelle Interpretation von Fernerkundungsdaten." Doctoral thesis, Technische Universitaet Bergakademie Freiberg Universitaetsbibliothek "Georgius Agricola", 2009. http://nbn-resolving.de/urn:nbn:de:bsz:105-095192.
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Die Fähigkeit, in Luft- und Satellitenbildern Objekte wiederzuerkennen, kann folgendermaßen erklärt werden: Aus der Kenntnis einer Landschaft und ihrer Abbildung im Bild werden Interpretationsregeln entwickelt, die bestimmten Kombinationen von Bildmerkmalen wie Farbe, Form, Größe, Textur oder Kontext festgelegte Bedeutungen zuordnen. Kommt es nicht auf das Wiedererkennen mit festen Wahrnehmungsmustern an, stellt sich die bislang offene Frage nach einer wissenschaftlichen Kriterien genügenden Methode, wie der gedankliche Zusammenhang zwischen den Sinneswahrnehmungen erfasst werden kann. Die Erfahrung von Umkehrbildern und optischen Täuschungen führt zur Frage nach dem festen Element bei der visuellen Interpretation von Fernerkundungsdaten. Galileis Antwort, Messwerte als Ausgangspunkt naturwissenschaftlicher Erkenntnis zu nehmen, löst die Mehrdeutigkeiten und Unsicherheiten gedanklicher Interpretationen nicht auf, denn zu jeder Zahl gehört bereits eine gedankliche Bestimmung darüber, was sie bedeutet: Äpfel, Birnen, Höhendifferenzen … Daher muss für die begriffliche Interpretation der Wahrnehmungen ein anderer Ausgangspunkt bestimmt werden: Weder kann der Mensch beobachten oder wahrnehmen, ohne seine Erlebnisse gedanklich zu fassen und zu ordnen, noch ist die Sinnesempfindung ein subjektives, vom Gegenstand abgespaltenes, nur persönliches Erlebnis. Wahrnehmung realisiert sich als Einheit von Wahrnehmendem und Wahrgenommenen. Demzufolge gibt es keine binäre Unterscheidung von objektiver Tatsache und subjektiver Interpretation. Wahrnehmung findet zwischen den Polen reiner Empfindung eines gegebenen und sinnlichkeitsfreien Denkens statt. Die reinen Erlebnisqualitäten der Sinnesempfindungen (warm, kalt, hell, rau) stellen sich als die am wenigsten von der subjektiven gedanklichen Interpretation abhängigen Elemente des Erkenntnisprozesses dar. Diesem Verhältnis von Beobachtung und gedanklicher Deutung entspricht ein phänomenologischer Untersuchungsansatz. Mit ihm bekommen Erfahrungen als absolute Elemente der Wahrnehmung primäre Bedeutung, gedankliche Interpretationen werden zu Abhängigen. Daher werden in der Untersuchung Ergebnisse phänomenologischer Arbeiten bevorzugt. Auch die eigene Bearbeitung des Themas geht von einer konsequent empirischen Position aus. Um einen Sachverhalt zu verstehen, genügt es nicht, bei den Sinnesempfindungen stehen zu bleiben, denn zu ihrem Verständnis fehlt der gedankliche Zusammenhang, die Erlebnisse müssen begrifflich interpretiert werden. Dabei ist die Doppelrolle der Begriffe von entscheidender Bedeutung: In der Analyse grenzen sie innerhalb des Erfahrungsfeldes Teilaspekte gegeneinander ab, welche in der Synthese durch dieselben Begriffe gedanklich verbunden werden. Diese Funktion der Begriffe wird ausgenutzt, um Wiedererkennen und Bildung von Verständnis zu differenzieren: Die Interpretation der Erfahrung nach a priori vorgegebenen Mustern zielt auf das Wiedererkennen. Im Gegensatz dazu emergiert Verständnis im Prozess der Begriffsbildung aus den Beobachtungen: Man sucht erst nach einer Gliederung, welche eine gedankliche Synthese plausibel erscheinen lässt. Das Konzept der Selbstorganisation hat in der Ökologie mechanistische Vorstellungen weitgehend abgelöst und im letzten Jahrzehnt auch in die Technik Eingang gefunden. Mit den Worten dieses Konzeptes kann die Begriffsbildung als Erkenntnisprozess beschrieben werden, in welchem sich gedankliche und nichtgedankliche Wahrnehmungen selbst organisieren. Sinnesempfindungen haben auch in anderen Zugangsweisen zur Natur eine dominierende Stellung. Daher können Goetheanismus, wissenschaftliche Ästhetik und Kunst zu einer voraussetzungslosen Naturerkundung beitragen. Die nahe Verwandtschaft von Phänomenologie, Ästhetik und Kunst lässt künstlerisches Schaffen als Vervollkommnung des in der Natur Veranlagten erscheinen. Weitere Querbeziehungen ergeben sich aus der Interpretation topografischer oder thematischer Karten oder sonstiger visualisierter raumbezogener Daten. Parallelen und Unterschiede werden herausgearbeitet. Moderne Naturwissenschaft ist quantitativ. Daher ist zu klären, was mathematische Modellierung zur Verständnisbildung beiträgt. In diesem Teil der Arbeit ist es der folgende Gedanke, welcher über die hinlänglich bekannte Nützlichkeit mathematischer Modellierungen, Vorausberechnungen und Simulationen hinausgeht: Die Mathematik überzeugt durch ihre logische Strenge in der Ableitung und Beweisführung: Aus Obersatz und Untersatz folgt die Konklusion. Eine Beobachtungsmethode, bei welcher eine Beobachtung an die nächste gereiht wird, so dass sich das Eine aus dem Anderen ergibt, wobei kein Sprung die Folge unterbricht, käme der Notwendigkeit eines mathematischen Beweises gleich. Diese strenge Folge des Einen aus dem Anderen tritt in der wissenschaftlichen Argumentation an die Stelle der spontanen Intuition mit Verifikation, Falsifikation und bestätigendem Beispiel. Auf diese Weise kann durch die Anwendung der mathematischen Methode eine realitätsnahe Begriffsbildung erreicht werden. Die bis hierher dargelegten Aspekte der Wahrnehmung, der Ästhetik, der Kunst und der Mathematik werden in der Methode einer voraussetzungslosen Begriffsentwicklung zusammengefasst. Damit ist das Hauptziel der Untersuchung, die Entwicklung einer auf das Verständnis gerichteten erfahrungsbasierten Beobachtungsmethode, erreicht. Die Abhandlung wird mit der Anwendung der entwickelten Methode auf einen Grundbegriff der Geoinformatik in folgender Weise fortgesetzt: Für die Geoinformatik ist der Raumbegriff von grundlegender Bedeutung. Daher bietet es sich an, diesen Begriff unter Anwendung der entwickelten Methode zu untersuchen. Unter phänomenologischen Gesichtspunkten stehen Raum und Zeit in einem engen Zusammenhang. Beide werden in der Bewegung erfahren. Interpretiert man Bewegung mit den Begriffen des Nebeneinander und des Nacheinander, entsteht Wissen von Raum und Zeit. Mit anderen Worten: Die am Leib erfahrene Bewegung wird durch Interpretation mit dem Raumbegriff zur Vorstellung durchlaufener Orte. Je nachdem, welche Sinneserfahrungen, allgemeiner: Beobachtungen, zugrunde gelegt werden, hat der Raum unterschiedliche geometrische Eigenschaften. Die Erfahrungen des Tastsinnes begründen euklidische Beobachtungen. Die Begriffe Raum und Zeit haben für die Verständnisbildung eine fundamentale Bedeutung. Mit ihrer Hilfe können die Erlebnisse als zugleich und nebeneinander oder als nacheinander geordnet werden. Sie ermöglichen Erkenntnis durch Analyse und Synthese. Wesentliches Motiv der Untersuchung ist die Frage nach der Bildung von Verständnis im Rahmen der visuellen Interpretation. Das Erkennen von Objekten stellt sich als synästhetische Synthese der Sinnesempfindungen und gedanklicher Inhalte dar. Unterschiedliche Gewichtungen der Gedankeninhalte lassen zwei Vorgehensweisen unterscheiden: 1, Für das Erkennen von Neuem ist es von grundlegender Bedeutung, dass die gedanklichen Inhalte den nichtgedanklichen Sinnesempfindungen untergeordnet sind, das heißt von diesen modifiziert werden können. Vorgewussten Begriffen kommt die Rolle von Hypothesen zu. 2, Beim Wiedererkennen haben gedankliche Inhalte eine dominierende Rolle – anhand von Interpretationsmerkmalen sollen Bildinhalten Bedeutungen zugewiesen werden. Das Bild wird hierzu nach Bildflächen mit solchen Kombinationen von Farben, Formen, Mustern, Texturen und räumlichen Anordnungen durchsucht, die dem zu suchenden Begriff entsprechen können. Oder das Bild wird, bei Verwendung einer Art Beispielschlüssel, nach Übereinstimmungen mit kompletten Bildmustern durchsucht. Auch das ist eine Form des Wiedererkennens. Um ein Phänomen zu verstehen, kommt es darauf an, in der Regelmäßigkeit der äußeren Form den Zusammenhang zu entdecken, der den verschiedenartigen Ausgestaltungen als regelndes Element zugrunde liegt. Dazu muss über eine Klassifizierung von Interpretationsmerkmalen hinausgegangen werden. Die gedankliche Auseinandersetzung mit den visualisierten Repräsentanzen der Phänomene unterstützt die Bildung eines solchen ideellen Zusammenhangs, welcher das in aller Mannigfaltigkeit der natürlichen Erscheinungen Gleichbleibende, Ruhende darstellt, aus welchem die Einzelphänomene hervorgegangen sein könnten. Die Funktionen beschreiben die Wechselwirkungen zwischen den räumlichen Elementen, welche sich in Austauschprozessen von Energie, Material und Stoffen ausdrücken. Überall dort, wo räumliche Anordnung ein Ausdruck funktionaler Beziehungen ist, unterstützt die visuelle Wahrnehmung der räumlichen Beziehungen die Einsicht in die sachlichen. In den Schlussfolgerungen wird die Visualisierung von Geodaten als Mittel zur Sichtbarmachung des Zusammenhanges zwischen den Erscheinungen charakterisiert. Die Bezugnahme zur Fernerkundung führt zu der Feststellung, dass die Anwendung der vorgeschlagenen Forschungsstrategie im Bereich der Geofernerkundung nur eingeschränkt möglich ist.
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Kuhlmann, Sally Malinda. "Geodesic knots in hyperbolic 3 manifolds." Connect to thesis, 2005. http://repository.unimelb.edu.au/10187/916.
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This thesis is an investigation of simple closed geodesics, or geodesic knots, in hyperbolic 3-manifolds.Adams, Hass and Scott have shown that every orientable finite volume hyperbolic 3-manifold contains at least one geodesic knot. The first part of this thesis is devoted to extending this result. We show that all cusped and many closed orientable finite volume hyperbolic 3-manifolds contain infinitely many geodesic knots. This is achieved by studying infinite families of closed geodesics limiting to an infinite length geodesic in the manifold. In the cusped manifold case the limiting geodesic runs cusp-to-cusp, while in the closed manifold case its ends spiral around a short geodesic in the manifold. We show that in the above manifolds infinitely many of the closed geodesics in these families are embedded.
The second part of the thesis is an investigation into the topology of geodesic knots, and is motivated by Thurston’s Geometrization Conjecture relating the topology and geometry of 3-manifolds.We ask whether the isotopy class of a geodesic knot can be distinguished topologically within its homotopy class. We derive a purely topological description for infinite subfamilies of the closed geodesics studied previously in cusped manifolds, and draw explicit projection diagrams for these geodesics in the figure-eight knot complement. This leads to the result that the figure-eight knot complement contains geodesics of infinitely many different knot types in the3-sphere when the figure-eight cusp is filled trivially.
We conclude with a more direct investigation into geodesic knots in the figure-eight knot complement. We discuss methods of locating closed geodesics in this manifold including ways of identifying their isotopy class within a free homotopy class of closed curves. We also investigate a specially chosen class of knots in the figure-eight knot complement, namely those arising as closed orbits in its suspension flow. Interesting examples uncovered here indicate that geodesics of small tube radii may be difficult to distinguish topologically in their free homotopy class.
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Salazar, Malpartida Johan Renzo. "Geodesic deviation equation in locally de Sitter spacetimes." Universidade Estadual Paulista (UNESP), 2018. http://hdl.handle.net/11449/157153.
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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
Como é bem conhecido, a relatividade especial de Einstein, cuja cinemática é governada pelo grupo de Poincaré, deixa de valer na escala de Planck devido à existência de uma escala de comprimento invariante, dada pelo comprimento de Planck. Por essa razão, ela é incapaz de descrever a cinemática naquela escala. Uma solução possível para esse problema, a qual preserva a simetria de Lorentz — e consequentemente a causalidade — é substituir a relatividade especial de Einstein por uma relatividade especial na qual a cinemática é governada pelo grupo de de Sitter. Claro que uma mudança na relatividade especial irá pruduzir mudanças concomitantes na relatividade geral, a qual se torna o que chamamos de relatividade geral modificada por de Sitter. Trabalhando no contexto dessa teoria, o objetivo desse trabalho é deduzir a fórmula geral da aceleração relativa entre duas geodésicas próximas, a qual leva à equação do desvio geodésico modificada por de Sitter. Uma análise simples dos efeitos adicionais induzidos pela cinemática local de de Sitter é apresentada.
As is well-known, the Poincaré invariant Einstein special relativity breaks down at the Planck scale due to the presence of an invariant length, given by the Planck length. For this reason, it is unable to describe the spacetime kinematics at that scale. A possible solution to this problem that preserves Lorentz symmetry — and consequently causality — is arguably to replace the Poincaré invariant Einstein special relativity by a de Sitter invariant special relativity. Of course, a change in special relativity produces concomitant changes in general relativity, which becomes what we have called de Sitter modified general relativity. By working in the context of this theory, the purpose of this work is to deduce the general relative acceleration between nearby geodesics, which leads to the de Sitter modified geodesic deviation equation. A simple analysis of the additional effects induced by the local de Sitter kinematics is presented.
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Del, Bonifro Francesca. "Geodesics motion in fuzzy black hole space-times." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2017. http://amslaurea.unibo.it/13512/.
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Classical General Relativity predicts the existence of space-times with non-trivial casual structures known as Black Holes. A classical black hole could form by the gravitational collapse of a compact object, which should end into a singularity covered by a (sharply defined) horizon, with a size equal to the gravitational radius of the matter source. In a quantum theory, the matter source is described by a quantum state, and one can correspondingly describe its gravitational radius by means of a Horizon Wave-Function. The resulting space-time is therefore expected to be "fuzzy", and so will be the geodesic motion of test particles. Orbits of massive particles as well as trajectories of light rays around such fuzzy gravitational sources are here analysed in details using both analytical approximations and numerical calculations. The uncertainty in the time of radial free fall and the effects on the out-going radiation emitted by the collapsing matter will also be presented.
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TAMBORINI, CAROLINA. "On totally geodesic subvarieties in the Torelli locus and their uniformizing symmetric spaces." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2022. http://hdl.handle.net/10281/371476.
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Oggetto di questa tesi sono le sottovarietà totalmente geodetiche dello spazio dei moduli A_g di varietà abeliane principalmente polarizzate e la loro relazione con il luogo di Torelli. Questo è definito come la chiusura in A_g dell'immagine dello spazio dei moduli M_g di curve algebriche complesse lisce di genere g tramite la mappa di Torelli j: M_g-->A_g. Lo spazio dei moduli A_g è un quoziente dello spazio di Siegel, che è uno spazio simmetrico. Una sottovarietà algebrica di A_g è totalmente geodetica se è l'immagine, tramite la naturale mappa di proiezione, di una qualche sottovarietà totalmente geodetica dello spazio di Siegel. Ci si aspetta che j(M_g) contenga poche sottovarietà totalmente geodetiche di A_g. Questo è anche in accordo con la congettura di Coleman-Oort. La geometria differenziale degli spazi simmetrici si può descrivere attraverso la teoria di gruppi e algebre di Lie. In particolare, le sottovarietà totalmente geodetiche di spazi simmetrici possono essere caratterizzate in termini di algebre di Lie. Queste considerazioni sono alla base della trattazione svolta in questa tesi, in cui utilizziamo alcuni strumenti della teoria di Lie per indagare alcuni aspetti geometrici dell'inclusione di j(M_g) in A_g. I principali risultati presentati sono i seguenti. Nel Capitolo 2, consideriamo il pull-back dell'operazione di Lie-bracket sullo spazio tangente ad A_g tramite la mappa di Torelli e lo caratterizziamo in termini della geometria della curva. Per farlo usiamo il nucleo di Bergman associato alla curva. Inoltre, colleghiamo il nucleo di Bergman alla seconda forma fondamentale della mappa Torelli. Nel Capitolo 3, determiniamo quale spazio simmetrico uniforma ciascuno dei controesempi noti alla congettura di Coleman-Oort attraverso il calcolo della decomposizione dell'algebra di Lie associata. Questi esempi noti erano stati ottenuti studiando famiglie di rivestimenti di Galois. Nel capitolo 4 ci concentriamo sullo studio di queste famiglie e descriviamo una nuova costruzione topologica di famiglie di G-rivestimenti di P^1.This thesis deals with totally geodesic subvarieties of the moduli space A_g of principally polarized abelian varieties and their relation with the Torelli locus. This is the closure in A_g of the image of the moduli space M_g of smooth, complex algebraic curves of genus g via the Torelli map j: M_g-->A_g. The moduli space A_g is a quotient of the Siegel space, which is a Riemannian symmetric space. An algebraic subvariety of A_g is totally geodesic if it is the image, under the natural projection map, of some totally geodesic submanifold of the Siegel space. Geometric considerations lead to the expectation that j(M_g) should contain very few totally geodesic subvarieties of A_g. This expectation also agrees with the Coleman-Oort conjecture. The differential geometry of symmetric spaces is described through Lie theory. In particular, totally geodesic submanifolds can be characterized via Lie algebras. This motivates the discussion carried out in this thesis, in which we use some Lie-theoretic tools to investigate geometric aspects of the inclusion of j(M_g) in A_g. The main results presented are the following. In Chapter 2, we consider the pull-back of the Lie bracket operation on the tangent space of A_g via the Torelli map, and we characterize it in terms of the geometry of the curve. We use the Bergman kernel form associated with the curve. Also, we link the Bergman kernel form to the second fundamental form of the Torelli map. In Chapter 3, we determine which symmetric space uniformizes each of the known counterexamples to the Coleman-Oort conjecture via the computation of the associated Lie algebra decomposition. These known examples were obtained studying families of Galois coverings of curves. Chapter 4 focuses on these families for their own sake, and we describe a new topological construction of families of G-coverings of the line.
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Lévy, Hugo. "Towards well-posed and versatile numerical solutions of scalar-tensor theories of gravity with screening mechanisms : applications at sub-Solar system scales." Electronic Thesis or Diss., université Paris-Saclay, 2024. http://www.theses.fr/2024UPASP119.
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Les théories tenseur-scalaires de la gravité font partie des alternatives à la Relativité Générale les plus convaincantes, résilientes, et riches en termes de phénoménologie. Les modèles encore viables aujourd'hui reposent sur des mécanismes d'écrantage afin d'être compatibles avec les tests locaux de la gravité, tout en conservant une certaine pertinence physique. La recherche de ces champs scalaires hypothétiques dépend alors de notre capacité à concevoir des expériences adaptées à leur phénoménologie. Hélas, cette tâche est grandement entravée par la difficulté de modéliser suffisamment précisément les effets de cinquième force dans des configurations réalistes. En effet, cela nécessite de résoudre des équations aux dérivées partielles semi-linéaires en présence de distributions de masse non-triviales, ce pour quoi les méthodes purement analytiques ne sont que d'un usage limité. Dans cette perspective, le présent travail de thèse traite ce problème via le développement d'un outil numérique polyvalent visant à obtenir des solutions bien posées aux équations de Klein-Gordon non-linéaires qui apparaissent dans de tels modèles de gravité modifiée. L'outil en question, nommé femtoscope, s'appuie sur la méthode des éléments finis. Celle-ci permet de représenter des géométries arbitrairement complexes et des problèmes multi-échelles par le biais de raffinement locaux du maillage. Les non-linéarités sont quant à elles traitées par la méthode de Newton. La nouveauté majeure apportée par femtoscope est sa gestion des conditions aux limites asymptotiques — i.e. lorsque le comportement du champ n'est connu qu'infiniment loin des sources — dont la prise en compte de manière appropriée est souvent essentielle en vue d'obtenir des solutions numériques pourvues de sens physique. Pour ce faire, nous utilisons la méthode des éléments finis inversés. Nous nous appuyons ensuite sur femtoscope pour étudier la gravité tenseur-scalaire aux échelles sub-système Solaire. En utilisant un modèle réaliste de la Terre, nous traitons la question relative à la détectabilité d'une cinquième force de type caméléon, au moyen de missions de géodésie spatiale telles que GRACE-FO. L'influence de l'atmosphère terrestre ainsi que la rétroaction d'un satellite sur le champ scalaire sont toutes deux prises en compte. Nous constatons que la cinquième force a un effet supposément mesurable sur la dynamique orbitale d'un point matériel, mais que la connaissance imparfaite de la distribution de masse à l'intérieur de la Terre donne lieu à des dégénérescences qui réduisent considérablement le pouvoir contraignant de ce type de mission. Ces dégénérescences peuvent en principe être levées en réalisant l'expérience à deux altitudes différentes. Enfin, nous ouvrons de nouvelles perspectives en explorant la possibilité de tester les théories tenseur-scalaires avec écrantage en se servant d'horloges atomiques. L'idée des expériences que nous décrivons est d'exploiter la contribution du champ scalaire sur le décalage vers le rouge gravitationnel, cette dernière étant absente en Relativité Générale. On souligne le fait que de telles expériences sont de nature profondément différente des recherches de cinquième forceScalar-tensor theories of gravity are among the most compelling, resilient and phenomenologically-rich alternatives to General Relativity. Viable models make use of screening mechanisms in order to be consistent with local tests of gravity whilst still retaining physical relevance. The hunt for such hypothetical scalar fields therefore hinges on the design of sophisticated model-dependent experiments. Alas, this task is greatly hampered by the difficulty of accurately modeling fifth force effects in realistic setups. Indeed, the latter requires solving semi-linear partial differential equations in the presence of complex matter distributions, for which analytical approaches are clearly insufficient. In this perspective, the present PhD work tackles this issue by developing a versatile numerical tool devoted to obtaining well-posed solutions to the nonlinear Klein-Gordon equations arising in such modified gravity models. The tool, called femtoscope, builds on the finite element method which allows one to deal with arbitrarily complex geometries and multi-scale problems through local mesh refinement. Nonlinearities, on the other hand, are handled via Newton's method. The novelty and most important feature of femtoscope is its careful treatment of asymptotic boundary conditions — i.e. when the field's behavior is only known infinitely far away from the sources — which is often essential to obtain physically meaningful numerical solutions. This is achieved by employing the inverted finite element method. We then make use of femtoscope to investigate screened scalar-tensor gravity at sub-Solar system scales. Using a realistic model of the Earth, we address the question of the detectability of a putative chameleon fifth force in orbit by means of GRACE-FO-like space geodesy missions. The influence of the atmosphere as well as the backreaction of spacecraft on the scalar field are both considered. We find that, although the fifth force has a supposedly measurable effect on the dynamics of a point-like spacecraft, the imperfect knowledge of the mass distribution inside the Earth gives rise to degeneracies, which in turn severely limit the constraining power of such space missions. These degeneracies can in principle be lifted by performing the experiment at two different altitudes. Finally, we open up new perspectives by exploring the possibility of testing screened scalar-tensor theories with atomic clocks, exploiting the distinctive imprint of the scalar field on the gravitational redshift with respect to General Relativity. It is emphasized that such experiments are profoundly different in nature from fifth force searches
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Howarth, Laura. "The existence and structure of constants of geodesic motion admitted by spherically symmetric static space-times." Thesis, University of Hull, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.310318.
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Sebastianutti, Marco. "Geodesic motion and Raychaudhuri equations." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2019. http://amslaurea.unibo.it/18755/.
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The work presented in this thesis is devoted to the study of geodesic motion in the context of General Relativity. The motion of a single test particle is governed by the geodesic equations of the given space-time, nevertheless one can be interested in the collective behavior of a family (congruence) of test particles, whose dynamics is controlled by the Raychaudhuri equations. In this thesis, both the aspects have been considered, with great interest in the latter issue. Geometric quantities appear in these evolution equations, therefore, it goes without saying that the features of a given space-time must necessarily arise. In this way, through the study of these quantities, one is able to analyze the given space-time. In the first part of this dissertation, we study the relation between geodesic motion and gravity. In fact, the geodesic equations are a useful tool for detecting a gravitational field. While, in the second part, after the derivation of Raychaudhuri equations, we focus on their applications to cosmology. Using these equations, as we mentioned above, one can show how geometric quantities linked to the given space-time, like expansion, shear and twist parameters govern the focusing or de-focusing of geodesic congruences. Physical requirements on matter stress-energy (i.e., positivity of energy density in any frame of reference), lead to the various energy conditions, which must hold, at least in a classical context. Therefore, under these suitable conditions, the focusing of a geodesics "bundle", in the FLRW metric, bring us to the idea of an initial (big bang) singularity in the model of a homogeneous isotropic universe. The geodesic focusing theorem derived from both, the Raychaudhuri equations and the energy conditions acts as an important tool in understanding the Hawking-Penrose singularity theorems.
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Marshall, Joseph. "Computation in hyperbolic groups." Thesis, University of Warwick, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.369403.
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Fama, Christopher J., and -. "Non-smooth differential geometry of pseudo-Riemannian manifolds: Boundary and geodesic structure of gravitational wave space-times in mathematical relativity." The Australian National University. School of Mathematical Sciences, 1998. http://thesis.anu.edu.au./public/adt-ANU20010907.161849.
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[No abstract supplied with this thesis - The first page (of three) of the Introduction follows]
¶
This thesis is largely concerned with the changing representations of 'boundary' or 'ideal' points of a
pseudo-Riemannian manifold -- and our primary interest is in the space-times of general relativity. In particular, we are interested in the following question: What assumptions about the 'nature' of 'portions' of a certain 'ideal boundary' construction (essentially the 'abstract boundary' of Scott and Szekeres (1994)) allow us to define precisely the topological type of these 'portions', i.e., to show that different representations of this ideal boundary, corresponding to different embeddings of the manifold into others, have corresponding 'portions' that are homeomorphic?
¶
Certain topological properties of these 'portions' are preserved, even allowing for quite unpleasant properties of the metric (Fama and Scott 1995). These results are given in Appendix D, since they are not used elsewhere and, as well as representing the main portion of work undertaken under the supervision of Scott, which deserves recognition, may serve as an interesting example of the relative ease with which certain simple results about the abstract boundary can be obtained.
¶
An answer to a more precisely formulated version of this question appears very diffcult in general. However, we can give a rather complete answer in certain cases, where we dictate certain 'generalised regularity' requirements for our embeddings, but make no demands on the precise functional form of our metrics apart from these. For example, we get a complete answer to our question for abstract boundary sets which do not 'wiggle about' too much -- i.e., they satisfy a certain Lipschitz condition -- and through which the metric can be extended in a manner which is not required to be differentiable (C[superscript1]), but is continuous and non--degenerate. We allow similar freedoms on the interior of the manifold, thereby bringing gravitational wave space-times within our sphere of discussion. In fact, in the course of developing these results in progressively greater generality, we get, almost 'free', certain abilities to begin looking at geodesic structure on quite general pseudo-Riemannian manifolds.
¶
It is possible to delineate most of this work cleanly into two major parts. Firstly, there are results which use classical geometric constructs and can be given for the original abstract boundary construction, which requires differentiability of both manifolds and metrics, and which we summarise below. The second -- and significantly longer -- part involves extensions of those constructs and results to more general metrics.
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Chappa, Eduardo. "The x-ray transform of tensor fields /." Thesis, Connect to this title online; UW restricted, 2002. http://hdl.handle.net/1773/5750.
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Vignotto, Davide. "Analysis of the in-Flight Performance of a Critical Space Mechanism." Doctoral thesis, Università degli studi di Trento, 2021. http://hdl.handle.net/11572/323575.
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Gravitational waves detection is a challenging scientific objective, faced by scientist in the last 100 years, when Einstein theorized their existence. Despite multiple attempts, it was only in 2016 that the first observation of a gravitational wave was officially announced. The observation, worth a Nobel Prize, was made possible thanks to a worldwide collaboration of three large ground-based detectors. When detecting gravitational waves from ground, the noisy environment limits the frequency bandwidth of the measurement. Thus, the type of cosmic events that are observable is also limited. For this reason, scientists are developing the first gravitational waves detector based in space, which is a much quieter environment, especially in the sub-Hertz bandwidth. The space-based detector is named laser interferometer space antenna (LISA) and its launch is planned for 2034. Due to the extreme complexity of the mission, involving several new technologies, a demonstrator of LISA was launched and operated between 2015 and 2017. The demonstrator mission, called LISA Pathfinder (LPF), had the objective to show the feasibility of the gravitational waves observation directly from space, by characterizing the noise affecting the relative acceleration of two free falling bodies in the milli-Hertz bandwidth. The mission was a success, proving the expected noise level is well below the minimum requirement.
The free-falling bodies of LPF, called test masses (TMs), were hosted inside dedicated electrode housings (EH), located approximately 30 cm apart inside the spacecraft. When free falling, each TM stays approximately in the center of the EH, thus having milli-meter wide gaps within the housing walls. Due to the presence of such large gaps, the TMs were mechanically constrained by dedicated mechanisms (named CVM and GPRM) in order to avoid damaging the payload during the launch phase and were released into free fall once the spacecraft was in orbit. Prior to the start of the science phase, the injection procedure of the TMs into free-fall was started. Such a procedure brought each TM from being mechanically constrained to a state where it was electro-statically controlled in the center of the EH. Surprisingly, the mechanical separation of the release mechanism from the TM caused unexpected residual velocities, which were not controllable by the electrostatic control force responsible for capturing the TM once released. Therefore, both the TMs collided with either the surrounding housing walls or the release mechanism end effectors. It was possible to start the science phase by manually controlling the release mechanism adopting non-nominal injection strategies, which should not be applicable in LISA, due to the larger time lag. So, since any release mechanism malfunctioning may preclude the initialization of LISA science phase, the GPRM was extensively tested at the end of LPF, by means of a dedicated campaign of releases, involving several modifications to the nominal injection procedure. The data of the extended campaign are analyzed in this work and the main conclusion is that no optimal automated release strategy is found for the GPRM flight model as-built configuration that works reliably for both the TMs producing a nominal injection procedure. The analysis of the in-flight data is difficult since the gravitational referencesensor of LPF is not designed for such type of analysis. In particular, the low sampling frequency (i.e., 10 Hz) constitutes a limiting factor when detecting instantaneous events such as collisions of the TM. Despite the difficulties of extracting useful information on the TM residual velocity from the in-flight data, it is found that the main cause of the uncontrollable state of the released TM is the collision of the TM with the plunger, i.e., one of the end-effectors of the GPRM. It is shown that the impact is caused by the oscillation of the plunger or by the elastic relaxation of the initial preload force that holds the TM. At the end of the analysis, some improvements to the design of the release mechanism are brie y discussed, aimed at maximizing the probability of performing a successful injection procedure for the six TMs that will be used as sensing bodies in the LISA experiment.
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Safsten, Clarke Alexander. "Busemann G-Spaces, CAT(k) Curvature, and the Disjoint (0, n)-Cells Property." BYU ScholarsArchive, 2017. https://scholarsarchive.byu.edu/etd/6486.
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A review of geodesics and Busemann G-spaces is given. Aleksandrov curvature and the disjoint (0, n)-cells property are defined. We show how these properties are applied to and strengthened in Busemann G-spaces. We examine the relationship between manifolds and Busemann G-spaces and prove that all Riemannian manifolds are Busemann G-spaces, though not all metric manifolds are Busemann G-spaces. We show how Busemann G-spaces that also have bounded Aleksandrov curvature admit local closest-point projections to geodesic segments. Finally, we expound local properties of Busemann G-spaces and define a new property which we call the symmetric property. We show that Busemann G-spaces which have the disjoint (0,n)-cells property for every value of n cannot have the symmetric property.
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Yang, Lei. "HAUSDORFF DIMENSION OF DIVERGENT GEODESICS ON PRODUCT OF HYPERBOLIC SPACES." The Ohio State University, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=osu1401466357.
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Bearse, Tim. "Sub, Counter and Someothers." VCU Scholars Compass, 2010. http://scholarscompass.vcu.edu/etd/2202.
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Shchur, Vladimir. "Quasi-isometries between hyperbolic metric spaces, quantitative aspects." Phd thesis, Université Paris Sud - Paris XI, 2013. http://tel.archives-ouvertes.fr/tel-00867709.
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In this thesis we discuss possible ways to give quantitative measurement for two spaces not being quasi-isometric. From this quantitative point of view, we reconsider the definition of quasi-isometries and propose a notion of ''quasi-isometric distortion growth'' between two metric spaces. We revise our article [32] where an optimal upper-bound for Morse Lemma is given, together with the dual variant which we call Anti-Morse Lemma, and their applications.Next, we focus on lower bounds on quasi-isometric distortion growth for hyperbolic metric spaces. In this class, $L^p$-cohomology spaces provides useful quasi-isometry invariants and Poincaré constants of balls are their quantitative incarnation. We study how Poincaré constants are transported by quasi-isometries. For this, we introduce the notion of a cross-kernel. We calculate Poincaré constants for locally homogeneous metrics of the form $dt^2+\sum_ie^{2\mu_it}dx_i^2$, and give a lower bound on quasi-isometric distortion growth among such spaces.This allows us to give examples of different quasi-isometric distortion growths, including a sublinear one (logarithmic).
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Trin, Marie. "Application de courants géodésiques à la géométrie des surfaces." Electronic Thesis or Diss., Université de Rennes (2023-....), 2024. http://www.theses.fr/2024URENS025.
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Soit Z une surface de type fini et de caractéristique d'Euler strictement négative. Un courant géodésique sur Z est une mesure de Radon, stable par l'action du groupe fondamentale, sur les géodésiques non- orientées et bi-infinies du revêtement universel de Z. Cette notion a été introduite par F.Bonhaon en 1986 et a depuis eu de nombreuses applications à l'étude de la géométrie des surfaces. On s'intéresse ici à deux applications de cette notion: l'étude de la compactification de l'espace de Teichmüller et les problèmes de comptage de courbes. Le premier chapitre de ce manuscrit est dédié aux définitions et propriétés fondamentales nécessaires. Le chapitre 2 traite de la compactification de Thurston de l'espace de Teichmüller, en particulier, on prouve que la méthode de Bonahon par les courants géodésiques peut être adaptée aux surfaces non-compactes d'aire finie. Ce chapitre démontre aussi des résultats sur les suites de géodésiques aléatoires. Les deux chapitres suivant sont dédiés à des problèmes de comptage de géodésiques. Dans le chapitre 3 on montre que l'on peut compter les arcs d'une surface à bords à l'aide de suites convergentes de mesures sur les courants géodésiques. Puis, le chapitre 4 est dédié aux différentes ouvertures qu'offrent ce manuscrit. La principale étant le comptage des orbites pour l'action des sous-groupes du mapping class group sur les courbesLet Z be a finite surface with negative Euler characteristic. A geodesic current on Z is a Radon measure on the set of bi-infinite unoriented geodesics of the universal cover of Z which is stable by the action of the fundamental group. This notion has been introduced by F.Bonahon in 1986 and has since proven to be a fertile concept in the study of geometry of surfaces. In this thesis we are interested in two main applications of geodesic currents: the compactification of Teichmüller space and counting problems in surfaces. The first chapter is dedicated to the necessary definitions and properties. Chapter 2 deals with Thurston compactification of Teichmüller space. Especially, we will prove that the method developed by Bonahon using geodesic currents can be extended for non-compact surfaces of finite area. This chapter also contains some results about sequences of random geodesics. The last two chapters focus on counting problems. In chapter 3 we prove that arcs in surfaces with boundary can be counted thanks to sequences of measures on geodesic currents. Hence, chapter 4 is dedicated to the different perspectives associated to this manuscipt. The main one being to count elements in the orbits for the action of subgroups of mapping class groups on curves
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Gorine, Mohammed. "Influence de la courbure sur la taille du barycentre convexe dans les variétés différentiables." Thesis, Strasbourg, 2015. http://www.theses.fr/2015STRAD001/document.
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Si µ est une mesure de probabilité à support compact dans uns espace vectoriel ou affine de dimension finie, le barycentre (ou centre de gravité) de µ est un point bien défini de l’espace. Mais des difficultés surgissent lorsque l’espace est remplacé par une variété riemannienne M ; dans ce cas, même en se restreignant aux variétés convexes (c’est-à-dire deux dont points quelconques sont toujours joints par une géodésique et une seule) et aux mesures à support fini, il est en général impossible d'assigner à chaque probabilité un barycentre de façon que, d'une part,pour tous λϵ [0; 1] et x et y dans M, le barycentre de µ = (1- λ ) δˣ+ λ δy soit toujours le point γ(λ), sur la géodésique telle que γ (0) = x et γ (1) = y, et que, d'autre part, soit préservée la propriété d'associativité (pour faire une moyenne, on peut commencer par faire des moyennes partielles). Dés que la mesure µ est portée par au moins trois points non tous situées sur une même géodésique, il y a de multiples façons différentes de définir son barycentre comme barycentre de barycentres partiels de barycentres partiels etc., chaque opération élémentaire ne faisant intervenir que deux points. On obtient ainsi tout un ensemble de points de M, les barycentres itérés de µ . Pour des probabilités plus générales, on appelle barycentre convexe de µ l'ensemble b(µ) des points x de M qui sont limites d'une suite (xn), ou chaque xn est un barycentre itéré d'une probabilité µn à support fini, les mesures µn tendant vers µIf μ is a probability measure carried on a small in a finite-dimension vectorial or affine space, the μ- barycenter (center of gravity) is a well-defined point in space. Nevertheless, difficulties arise when space is changed by Riemannian manifold M. In this case, even if we limit to convex manifolds (i.e : when any two points are joined by one geodesic and just one) and to finite-support measures, it’s, in general impossible to attribute a barycenter to each probability, in such a way, on one hand, whetever λϵ [0; 1] and x and y in M, the barycenter of µ = (1- λ ) δˣ+ λ δy will be always the point γ(λ) of the geodesic such that γ (0) = x et γ (1) =y, and on another hand, the associative property will be maintained (to make a mean, we can begin by doing partial means). Once the measure μ is carried by at least three points which are not all localed on the same geodesic, there are different manners to define its barycenter as one of partial barycenters of partial barycenters and so on, in which each elementary operation includes only two points. Thus, we get a whole set of set of points of M, the iterated barycenters of μ. For more general probabilities μ, we call convex barycenter of μ, the set b(μ) of points x of M which are limit of sequence (xn), in which each xn is an iterated barycenter of a finite support probability μn, the measure μn tending to μ
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Monte, Luiz AntÃnio Caetano. "Espectro essencial de uma classe de variedades riemannianas." Universidade Federal do CearÃ, 2012. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=9185.
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Conselho Nacional de Desenvolvimento CientÃfico e TecnolÃgicoCoordenaÃÃo de AperfeiÃoamento de Pessoal de NÃvel Superior
Neste trabalho, provaremos alguns resultados sobre espectro essencial de uma classe de variedades Riemannianas, nÃo necessariamente completas, com condiÃÃes de curvatura na vizinhanÃa de um raio. Sobre essas condiÃÃes obtemos que o espectro essencial do operador de Laplace contÃm um intervalo. Como aplicaÃÃo, obteremos o espectro do operador de Laplace de regiÃes ilimitadas dos espaÃos formas, tais como a horobola do espaÃo hiperbÃlico e cones do espaÃo Euclidiano. Construiremos tambÃm um exemplo que indica a necessidade das condiÃÃes globais sobre o supremo das curvaturas seccionais fora de uma bola para que a variedade nÃo tenha espectro essencial.
In this thesis we consider a family of Riemannian manifolds, not necessarily complete, with curvature conditions in a neighborhood of a ray. Under these conditions we obtain that the essential spectrum of the Laplace operator contains an interval. The results presented in this thesis allow to determine the spectrum of the Laplace operator on unlimited regions of space forms, such as horoball in hyperbolic space and cones in Euclidean space. Also construct an example that shows the need of global conditions on the supreme sectional curvature outside a ball, so that the variety has no essential spectrum.
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Arcostanzo, Marc. "Rigidité et prolongement au disque d'une distance sur le bord." Université Joseph Fourier (Grenoble), 1994. http://www.theses.fr/1994GRE10216.
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Etant donne une distance d sur le bord d'un disque de dimension deux, nous cherchons dans cette these a prolonger d en une distance sur le disque tout entier, de telle sorte que l'espace metrique obtenu soit un espace de longueur, par exemple une metrique riemannienne ou finslerienne. Le prolongement est dit rigide s'il est unique a isometrie pres. Des resultats de rigidite ont ete obtenus par r. Michel, j. P. Otal et c. B. Croke en se restreignant aux metriques riemanniennes. Nous prouvons ici la rigidite des metriques euclidiennes a singularites coniques de courbures negatives. Nous donnons egalement des exemples de metriques riemanniennes non rigides. Nous montrons ensuite qu'un tel prolongement est entierement determine par la donnee de ses courbes geodesiques, ce qui permet de decrire l'ensemble des solutions du probleme. En imposant des conditions sur la distance sur le bord et le systeme de geodesiques, l'espace de longueur obtenu provient en fait d'une metrique finslerienne ou riemannienne. On obtient finalement un critere pour que deux prolongements ne soient pas isometriques
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Silva, Adam Oliveira da. "Rigidez de métricas críticas para funcionais riemannianos." reponame:Repositório Institucional da UFC, 2017. http://www.repositorio.ufc.br/handle/riufc/25969.
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SILVA, Adam Oliveira da. Rigidez de métricas críticas para funcionais riemannianos. 2017. 78 f. Tese (Doutorado em Matemática) – Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2017.Submitted by Andrea Dantas (pgmat@mat.ufc.br) on 2017-09-19T19:08:04Z No. of bitstreams: 1 2017_tese_aosilva.pdf: 481005 bytes, checksum: 2bdfc6ab68b042a5cfd4f67caf1e21e4 (MD5)
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The aim of this work is to study metrics that are critical points for some Riemannian functionals. In the first part, we investigate critical metrics for functionals which are quadratic in the curvature on closed Riemannian manifolds. It is known that space form metrics are critical points for these functionals, denoted by F t,s (g). Moreover, when s = 0, always Einstein metrics are critical to F t (g). We proved that under some conditions the converse is true. For instance, among others results, we prove that if n ≥ 5 and g is a Bach-flat critical metric to F −n/4(n−1) , with second elementary symmetric function of the Schouten tensor σ 2 (A) > 0, then g should be Einstein. Furthermore, we show that a locally conformally flat critical metric with some additional conditions are space form metrics. In the second part, we study the critical metrics to volume functional on compact Riemannian manifolds with connected smooth boundary. We call such critical points of Miao-Tam critical metrics due to the variational study making by Miao and Tam (2009). In this work, we show that the geodesics balls in space forms Rn , Sn and Hn have the maximum possible boundary volume among Miao-Tam critical metrics with connected boundary provided that the boundary be an Einstein manifold. In the same spirit, we also extend a rigidity theorem due to Boucher et al. (1984) and Shen (1997) to n-dimensional static metrics with positive constant scalar curvature, which give us another way to get a partial answer to the Cosmic no-hair conjecture already obtained by Chrusciel (2003).
Este trabalho tem como principal objetivo estudar métricas que são pontos críticos de alguns funcionais Riemannianos. Na primeira parte, investigaremos métricas críticas de funcionais que são quadráticos na curvatura sobre variedades Riemannianas fechadas. É de conhecimento que métricas tipo formas espaciais são pontos críticos para tais funcionais, denotados aqui por F t,s (g). Além disso, no caso s = 0, métricas de Einstein são sempre críticas para F t (g). Provamos que sob algumas condições, a recíproca destes fatos são verdadeiras. Por exemplo, dentre outros resultados, provamos que se n ≥ 5 e g é uma métrica Bach-flat crìtica para F−n/4(n−1) com segunda função simétrica elementar do tensor de Schouten σ 2 (A) > 0, então g tem que ser métrica de Einstein. Ademais, mostramos que uma métrica crítica localmente conformemente plana, com algumas hipóteses adicionais, tem que ser tipo forma espacial. Na segunda parte, estudamos as métricas críticas do funcional volume sobre variedades Riemannianas compactas com bordo suave conexo. Chamamos tais pontos críticos de métricas críticas de Miao-Tam, devido ao estudo variacional feito por Miao e Tam (2009). Neste trabalho provamos que as bolas geodésicas das formas espaciais Rn , S n e H n possuem o valor máximo para o volume do bordo dentre todas as métricas críticas de Miao-Tam com bordo conexo, desde que o bordo seja uma variedade de Einstein. No mesmo sentido, também estendemos um teorema de rigidez devido à Boucher et al. (1984) e Shen (1997) para métricas estáticas de dimensão n e com curvatura escalar constante positiva, o qual nos fornece outra maneira para obter uma resposta parcial para a Cosmic no-hair conjecture já obtida por Chrusciel (2003).
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Santambrogio, Filippo. "Variational problems in transport theory with mass concentration." Doctoral thesis, Scuola Normale Superiore, 2006. http://hdl.handle.net/11384/85701.
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Souza, Cristiano Augusto de. "Folheações riemannianas e geodésicas fechadas em orbifolds." Universidade Federal de São Carlos, 2016. https://repositorio.ufscar.br/handle/ufscar/8035.
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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
The present thesis is devoted to the study of closed geodesics in some types of orbifolds. First, we present the notion of Riemannian foliation and their equivalent definitions using foliation atlas and Riemannian submersions. Aiming to understand the leaf space of certain foliations, we introduce the concept of orbifold. Also, the notion of orbifolds will be addressed via pseudogroups. For compact Riemannian good orbifolds, we will prove the existence of non-trivial closed geodesics. The main objective of this work is to obtain closed geodesics in compact Riemannian orbifolds by employing the shortening process with respect to Riemannian foliations. Following the approach of Alexandrino and Javaloyes [5], we also discuss the existence of closed geodesics in the leaf spaces for some classes of singular Riemannian foliations.
A presente dissertação é devotada ao estudo de geodésicas fechadas em alguns tipos de orbifolds. Primeiro, é apresentada a noção de folheação Riemanniana bem como suas equivalentes definições via atlas folheados e submersões Riemannianas. Visando compreender o espaço das folhas de certas folheações, é introduzido o conceito de orbifold. Também será abordada a noção de orbifolds via pseudogrupos. Para orbifolds riemannianos compactos bons, é provada a existência de geodésicas fechadas de comprimento positivo. O principal objetivo deste trabalho é empregar o processo de encurtamento com relação às folheações Riemannianas para obter geodésicas fechadas em orbifolds riemannianos compactos. Seguindo a abordagem de Alexandrino e Javaloyes [5], também discutimos sobre a existência de geodésicas fechadas no espaço das folhas de algumas classes de folheações Riemannianas singulares.
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Picaud, Jean-Claude. "Un aspect géométrique du deuxième groupe de cohomologie bornée réelle des surfaces." Université Joseph Fourier (Grenoble), 1995. http://www.theses.fr/1995GRE10174.
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M. Gromov, dans un article publie au debut des annees 80, met en evidence la notion de cohomologie bornee dans un contexte geometrique. Depuis, un certain nombre de travaux ont revele la complexite et la richesse de cette notion. Precisement, l'objet de ce travail est de rendre compte de la geometrie contenue dans le deuxieme groupe de cohomologie bornee reelle des surfaces. Lorsqu'une surface admet une metrique hyperbolique, ce groupe, qui est muni d'une structure d'espace de banach, est de dimension infinie. Nous proposons d'interpreter certaines de ses classes (de nature geometrique mais aussi algebriques) en termes de classes de mesures sur le bord du revetement universel de la surface. Nous montrons egalement que cette construction apparait naturellement dans le contexte de la dynamique symbolique
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Tholozan, Nicolas. "Uniformisation des variétés pseudo-riemanniennes localement homogènes." Thesis, Nice, 2014. http://www.theses.fr/2014NICE4079/document.
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Ce travail étudie les variétés pseudo-riemanniennes compactes localement homogènes à travers le prisme des (G,X)-structures, introduites par Thurston dans son programme de géométrisation. Nous commençons par présenter la problématique générale et discutons notamment du rapport entre la complétude géodésique de ces variétés et une autre notion de complétude propre aux (G,X)-structures. Nous donnons également dans le chapitre 1 une nouvelle preuve d’un théorème de Bromberg et Medina qui classifie les métriques lorentziennes invariantes à gauche sur SL(2,R) dont le flot géodésique est complet. Conjecturalement, toute (G,X)-structure pseudo-riemannienne sur une variété compacte est complète. Nous prouvons ici que cela est vrai pour certaines géométries, sous l’hypothèse que la (G,X)-structure est a priori kleinienne. On en déduit que, pour ces géométries, la complétude est une condition fermée. Lorsque X est un groupe de Lie de rang 1 muni de sa métrique de Killing, ce résultat complète un théorème de Guéritaud–Guichard–Kassel–Wienhard selon lequel la complétude est une condition ouverte. Nous nous tournons ensuite vers l’étude des représentations d’un groupe de surface à valeurs dans les isométries d’une variété riemannienne M complète simplement connexe de courbure sectionnelle inférieure à -1. Étant donnée une telle représentation ρ, nous montrons que l’ensemble des représentations fuchsiennes j telles qu’il existe une application (j,ρ)-équivariante et contractante de H2 dans M est un ouvert non vide et contractile de l’espace de Teichmüller (sauf lorsque ρ est elle-même fuchsienne). Ce résultat nous permet de décrire l’espace des métriques lorentziennes de courbure constante -1 sur un fibré en cercle au-dessus d’une surface compacte. Nous montrons que cet espace possède un nombre fini de composantes connexes classifiées par un invariant que nous appelons longueur de la fibre. Nous prouvons également que le volume total de ces métriques ne dépend que de la topologie du fibré et de la longueur de la fibreIn this work, we study closed locally homogeneous pseudo-Riemannian manifolds through the notion of (G,X)-structure, introduced by Thurston in his geometrization program. We start by presenting the general problem. In particular, we discuss the link between geodesical completeness of those manifolds and another notion of completeness specific to (G,X)-structures. In chapter 1, we also give a new proof of a theorem by Bromberg and Medina which classifies left invariant Lorentz metrics on SL(2,R) that are geodesically complete. Conjecturally, every pseudo-riemannian (G,X)-structure on a closed manifold is complete. Here we prove that it holds for certain geometries, provided that the (G,X )-structure is a priori Kleinian . This implies that, for such geometries, completeness is a closed condition. When X is a Lie group of rank 1 handled with its Killing metric, this result complements a theorem of Guéritaud–Guichard–Kassel–Wienhard, acording to which completeness is an open condition. We then turn to the study of representations of surface groups into the isometry group of a complete simply connected Riemannian manifold M of curvature less than or equal to -1. Given such a representation ρ, we prove that the set of Fuchsian representations j for which there exists a (j,ρ)-equivariant contracting map from H2 to M is a non-empty open contractible subset of the Teichmüller space (unless ρ itself is Fuchsian). This result allows us to describe the space of Lorentz metrics of constant curvature -1 on a circle bundle over a closed surface. We show that this space has finitely many connected components, classified by an invariant that we call the length of the fiber. We also prove that the total volume of those metrics only depends on the topology of the bundle and on the length of the fiber