This report explores the effect of interactive visualizations on the advancement of mathematics understanding. Not only do interactive visualizations aid mathematicians to expand the body of knowledge of mathematics but it also allows students an efficient way to process the information taught in schools. There are many concepts in mathematics that utilize interactive visualizations and examples of such concepts are illustrated within this report. / text

In this thesis, X-ray observations of four accretion powered pulsars are presented. Using RXTE observations of 4U 1907+09, we found three new pulse periods of the source. We found that the source spun-down almost at a constant rate of $dot nu$ = (-3.54 $pm 0.02) times 10^{-14}$ Hz s$^{-1}$ for more than 15 years. Using RXTE observations, X-ray flux related spectral and timing features in 2S 1417-62 were, in general, interpreted as a sign of a disc accretion with a similar geometry with a varying mass accretion rate, whereas spectral and timing features of the low X-ray flux regions were interpreted as a sign of possible temporary accretion geometry change prior to the next periastron. Using XMM-Newton and RXTE observations of SAX J2103.5+4545, we discovered quasi periodic oscillations around 0.044 Hz (22.7 sec) while the source was spinning-up with a rate of $(7.4pm0.9)times10^{-13}$Hz s$^{-1}$. In the X-ray spectrum, we also found a soft component consistent with a blackbody emission with ${rm{kT}}sim1.9$keV. Using RXTE observations, we also studied spectral evolution of Her X-1

[Special characters cannot be displayed. Please see the pdf version of the Abstract for an accurate reproduction.] We studied the circumstellar discs, the initial mass function (IMF), mass distribution, binarity and the fundamental properties of the [special character] 9 Myr-old pre-main sequence (PMS) [special character] Chamaeleontis cluster. Using JHKL colour-colour and colour-excess diagrams, we found the circumstellar disc fraction to be [special character] 0.60 among the late-type members. Four stars with [special character] (K - L) > 0.4 were identified as experiencing ongoing accretion which was later confirmed by high-resolution spectroscopic study. Quantitative analysis of the H[special character] profiles found accretion in these four stars at rates comparable to that of two members of the similarly-aged TW Hydrae Association (TWA); rates 1 - 3 orders of magnitude lower than in younger classical T Tauri stars. Together these results suggest that, while the mass accretion rate decreases with age, PMS stars can retain their inner discs for [special character] 10 Myr. An optical photometric survey spanning 1.3 ?? 1.3 pc added two low-mass stars to the cluster inventory. Together with other recent surveys the population is likely to be significantly complete for primaries with masses M > 0.15M[special character]. The cluster now consists of 18 primaries and 9 confirmed and candidate secondaries, with [special character] 2-4 times higher multiplicity than seen in field dwarfs. The cluster IMF is consistent with that of rich young clusters and field stars. By extending the IMF to lower masses, we predict 20-29 low-mass stars and brown dwarfs may remain undiscovered. From study of the cluster???s spatial and mass distribution, we find the [special character] Cha cluster has significant mass segregation, with > 50 per cent of the stellar mass residing within the central 0.17 pc. Lastly we classified members of the cluster with low-resolution spectra, providing information about the fundamental properties of the PMS stars by comparison to standard dwarfs. Broadband VRI colours and pseudocontinuum indices derived for the cluster stars are indistinguishable from dwarfs at visual and red wavelengths. This suggests the temperature sequence for the PMS [special character] Cha cluster is similar to that of the dwarf sequence. Narrow-band spectral indices for the [special character] Cha cluster possibly indicate higher metallicity and strongly indicate lower surface gravity than the dwarf indices.

Le processus d'accrétion joue un rôle crucial dans le scénario de formation stellaire. Il régit l'interaction des étoiles jeunes avec leurs disques, en régulant l'échange de masse et de moment cinétique; ainsi, il a un impact durable sur leur évolution. De plus, l'accrétion est un ingrédient essentiel de la physique des systèmes étoile-disque à l'époque de formation planétaire. Selon le modèle d'accrétion magnétosphérique, une cavité de quelques rayons stellaires s'étend de la surface de l'étoile au bord interne du disque. L'interaction se produit donc par le champ magnétique stellaire, qui pénètre le disque interne et l'attèle à l'objet central. Des colonnes d'accrétion se développent du disque interne suivant les lignes de champ, et atteignent l'étoile à des vitesses presque de chute libre. L'impact à la surface crée des chocs localisés, qui sont responsables de l'excès de luminosité UV distinctif des systèmes accrétants par rapport aux objets non-accrétants. L'évolution temporelle intrinsèque et l'effet d'alternance du côté visible des objets au cours de leur rotation se mélangent dans la variabilité photométrique typique des étoiles jeunes, révélée par les campagnes de suivi.Durant ma thèse, j'ai mené une étude statistique du processus d'accrétion et de sa variabilité dans la région NGC 2264 (3 Myr). Cet amas contient plus de 700 membres, repartis entre étoiles avec disque (45%) et sans disque. J'ai qualifié l'accrétion par la diagnostique de l'excès UV; les étoiles de l'amas privées de disque définissent le niveau d'émission de référence au-dessus duquel l'excès UV provenant du choc d'accrétion est décelé et mesuré. Mon étude se base sur un jeu de données photométriques obtenues au télescope Canada-France-Hawaii (CFHT), comprenant un relevé profond en 4 filtres (u,g,r,i) et un suivi simultané de variabilité optique (bande r) et UV (bande u) d'une durée de 2 semaines et avec échantillonnage de l'ordre des heures. Dans une première étape de cette étude, je convertis les excès UV en taux d'accrétion pour obtenir une image globale du processus à travers l'amas et examiner sa dépendance envers les paramètres stellaires. Le taux d'accrétion moyen corrèle avec la masse de l'étoile, bien qu'une dispersion significative autour de cette tendance moyenne soit observée à chaque masse. Je montre que cet étalement ne peut pas être justifié par la variabilité des objets; une diversité de mécanismes d'accrétion et de stades évolutifs dans l'amas pourrait contribuer à la vaste gamme de régimes d'accrétion décelés. Ensuite, j'explore les signatures dans l'UV propres à des types distincts d'étoiles jeunes variables. Je montre que les étoiles accrétantes présentent en général une variabilité plus prononcée que les objets sans disque, et que les respectives variations de couleur sont cohérentes avec une origine différente de la variabilité associée aux deux groupes. Pour le premier groupe, ce sont les chocs d'accrétion à dominer, alors que le deuxième est dominé par des taches froides à la surface, dérivant de l'activité magnétique stellaire. Je compare les variations photométriques mesurées sur bases de quelques heures, quelques jours et quelques années, afin de déterminer quelles soient les composantes de variabilité les plus importantes. L'échelle de temps de quelques jours prévaut sur les autres délais investigués dans la variabilité enregistrée pour ces étoiles jeunes, avec une contribution majeure provenant de l'effet de modulation rotationnelle. Enfin, j'analyse les propriétés de rotation des étoiles de l'amas à partir d'un jeu de courbes de lumière optiques, d'une durée de 38 jours, obtenues avec le satellite CoRoT près de la campagne d'observation au CFHT. Je reconstruis la distribution de périodes de l'amas et montre que les objets sans disque tournent statistiquement plus vite que les objets accrétants. Cette connexion entre les propriétés d'accrétion et celles de rotation peut être interprétée dans le scénario de disk-locking. / Disk accretion plays a most important role in the star formation scenario. It governs the interaction of young stars with their disks, with a long-lasting impact on stellar evolution, by providing both mass and angular momentum regulation. Accretion is also a central ingredient in the physics of star-disk systems at the epoch when planets start to form. In the picture of magnetospheric accretion, a cavity of a few stellar radii extends from the star surface to the inner disk rim. The star-disk interaction is then mediated by the stellar magnetic field, whose lines thread the inner disk and couple it to the central object. Material from the inner disk is channeled along the field lines in accretion columns that reach the star at near free-fall velocities. The impact produces localized hot shocks at the stellar surface, which determine the distinctive UV excess emission of accreting objects relative to non-accreting sources. Intrinsic time evolution, and varying visibility of surface features during stellar rotation, combine in the characteristic photometric variability of young stars, revealed by monitoring surveys.In this thesis, I investigate the statistical properties of disk accretion and of its variability in the young open cluster NGC 2264 (3 Myr). This comprises a population of over 700 objects, about similarly distributed between disk-bearing (45%) and disk-free sources. I characterize accretion from the UV excess diagnostics; disk-free cluster members define the reference emission level over which the UV excess linked to accretion is detected and measured. The study is based on a homogeneous photometric dataset obtained at the Canada-France-Hawaii Telescope (CFHT), composed of a deep mapping of the region in four different bands (u,g,r,i) and of simultaneous optical (r-band) and UV (u-band) monitoring on timescales from hours to days for a period of 2 weeks. In the first part of the study, UV excesses are converted to accretion luminosities and mass accretion rates to derive a global picture of the accretion process across the cluster, and to investigate the dependence of the typical accretion properties on stellar parameters such as mass and age. A robust correlation is detected between the average accretion rate and stellar mass, but a significant dispersion in accretion rates is observed around this average trend at any given mass. I show that the extent of this spread cannot be accounted for by typical variability on week timescales; I discuss several aspects, including a diversity in accretion mechanisms and a non-negligible evolutionary spread among cluster members, which may contribute to the broad range of accretion regimes detected. In the second part of the study, I explore the variability signatures in the UV that pertain to different types of variable young stars. I show that accreting objects typically exhibit stronger variability than non-accreting objects, and that the color properties associated with the two groups are consistent with a statistically distinct origin of the variability features in the two cases. These are dominated, in the first case, by hot accretion spots, and in the second, by cold spots linked to magnetic activity. I compare the amounts of variability on timescales of hours, days and years, to assess the dominant components. The mid term (days) appears to be the leading timescale for variability in young stars up to years, with a major contribution from rotational modulation. In the third part of the study, I use a set of 38 day-long optical light curves obtained with the CoRoT satellite, close to the epoch of the CFHT survey, to investigate periodicity and rotation properties in NGC 2264. I derive the period distribution for the cluster and show that accreting and non-accreting objects exhibit statistically distinct properties: the second rotate on average faster than the first. I then illustrate the connection between accretion and rotation properties in the disk-locking scenario.

This thesis contains spectroscopic analyses of two unusual binaries with circum- stellar disks - β Lyr and ǫ Aur. Several hundred optical spectra were processed and analyzed for both binaries which led to several original findings. For β Lyr, it was a discovery of a weak shell spectrum originating in a disk pseudophotosphere and a hidden satellite spectrum, present only during eclipses, which arise from additional absorption of the primary light passing through the gaseous envelope around the secondary. For ǫ Aur, it led to the discovery of the apparent multiperiodic line vari- ability occuring during the current eclipse with a dominant and common period of 66d .21 and to an explanation of complex Hα line profiles during the eclipse which is again caused by an additional absorption of a primary light in an atmosphere of a dark disk around a secondary. Also rich series of radial velocity measurements and photometric observations were collected and used to determine a new precise orbital solution for ǫ Aur. Further, a hydrodynamical and a radiative modeling of a discontinuous mass transfer in a close binary system was carried out which resulted in a formation of an elongated disk with a slow prograde revolution, demonstrated itself by double emission Hα line profiles that exhibit V/R variations.

Les disques de débris orbitant dans l'environnement des étoiles proches constituent un indicateur très important des propriétés des systèmes planétaires extra-solaires. Depuis l'espace et au sol, les moyens observationnels actuels permettent de déterminer dans divers domaines de longueurs d'ondes les propriétés spatiales de ces disques et celles des grains de poussières circumstellaires. Cette thèse aborde le sujet de la modélisation des disques de débris, à partir de données fournies par de multiples instruments, en premier lieu les télescopes spatiaux Hubble et Herschel, et les interféromètres infrarouges du VLTI, CHARA, et KIN. Mes premiers projets ont pris place dans le cadre de deux programmes-clés de l'Observatoire Spatial Herschel dédiés à l'étude des disques circumstellaires autour des étoiles proches. Au sein du projet GASPS, j'ai obtenu des observations spectro-photométriques de HD 181327, une jeune étoile (12+8-4 millions d'années, Ma) de type solaire entourée d'un anneau de débris massif de 90 unités astronomique (UA) de rayon vu aussi en lumière diffusée par le télescope spatial Hubble. La bonne détermination de la géométrie de l'anneau permet de se concentrer sur la modélisation de la distribution spectrale d'énergie, afin de mieux caractériser les propriétés des poussières. J'ai utilisé le code de transfert radiatif GRaTer et démontré que le système héberge une population de planétésimaux glacés, qui pourrait représenter une source d'eau et de volatils susceptible d'être libérée sur des planètes telluriques encore en formation. Je discute quelques résultats additionnels obtenus avec Herschel à propos de disques de débris jeunes, notamment HD 32297, et d'analogues faibles de la Ceinture de Kuiper. Les disques exo-zodiacaux (exozodis), analogues du nuage Zodiacal du Système Solaire, représentent une contrepartie chaude (ou tiède) aux disques de débris, résidant proche de la zone habitable (moins de quelques unités astronomiques) et encore mal connue. Ils sont révélés par leur émission proche et moyen infrarouge et peuvent être étudiés avec la précision et la résolution requises grace à l'interférométrie optique. Dans le cas de l'étoile Beta Pictoris (12+8-4 Ma), dont le disque est vu par la tranche, une fraction significative du disque externe diffuse de la lumière vers le champ de vue des interféromètres ; une composante interne chaude doit tout de même être invoquée pour justifier de l'excès mesuré dans l'infrarouge proche. En m'appuyant sur l'exemple de l'étoile Véga (440±40 Ma), je présente la méthodologie employée et démontre que les exozodis chauds se caractérisent par une abondance de poussières sub-microniques, près de la distance de sublimation de l'étoile. D'un point de vue théorique, le mécanisme de production de ces petits grains non-liés est encore incompris. J'aborde plus en détails le cas du disque exozodiacal à deux composantes (chaude et tiède) de Fomalhaut (440±40 Ma). Je développe une nouvelle méthode de calcul des distances de sublimation et recense les processus variés qui peuvent affecter un grain de poussière afin de fournir un cadre pour l'interprétation : l'exozodi chaud à ~0.1 - 0.2 UA serait la signature indirecte d'une ceinture d'astéroïdes située à 2 UA à l'activité dynamique particulièrement intense. Finalement, je dresse un bilan des propriétés des disques de débris et de ce qu'ils peuvent nous apprendre quand on les compare au Système Solaire, et propose de futures directions de recherche pour explorer davantage les systèmes planétaires et leur dynamique. / Debris disks orbiting in the environment of nearby stars are a very important indicator of extrasolar planetary systems properties. From space and from the ground, current observational facilities enable a multi-wavelength determination of the disks structures and of the dust properties. This thesis addresses the topic of debris disks modelling, based on data from multiple instruments including first of all the Herschel and Hubble space telescopes, and the VLTI, CHARA and KIN infrared interferometers. My first research pro jects took place in the framework of two key programs from the Herschel Space Observatory dedicated to the study of circumstellar disks around nearby stars. As part of the GASPS pro ject, I obtained Herschel far-infrared spectro-photometric observations of HD 181327, a young (12+8−4 Myr) Sun-like star surrounded by a massive, 90 AU-wide debris belt, also imaged in scattered light by the Hubble Space Telescope. Proper determination of the belt geometry allows one to focus on modelling the dust properties. I used the GRaTer radiative transfer code to demonstrate that the system hosts a population of icy planetesimals that may be a source for the future delivery of water and volatiles onto forming terrestrial planets. I discuss additional results obtained with Herschel related to young debris disks, in particular HD 32297, and to faint Kuiper-Belt analogues. Exo-zodiacal disks (exozodis), those analogues to the Solar System Zodiacal cloud, represent a little known hot (or warm) counterpart of debris disks located close the habitable zone (inside of a few AUs). They are revealed by their near- to mid-infrared emission and can be assessed with the required accuracy and resolution with optical interferometers. In the case of the near edge-on star β Pictoris (12+8−4 Myr), I show that a significant fraction of the outer disk scatters light towards the small field-of-view of the interferometers; an inner hot component must nonetheless be invoked to explain the measured near-infrared excess. Based on the example of the star Vega (440 ± 40 Myr), I introduce a methodology to study inner dust disks and I show that hot exozodis are characterized by an abundance of submicron-sized grains, close to the star sublimation distance. From a theoretical point-of-view, the production mechanism for these small, unbound grains is not understood. I go into more details on the case of the Fomalhaut (440 ± 40 Ma) double-component (warm and hot) exozodiacal disk. I develop a new model for the calculation of the dust sublimation distances, and I address the various processes that can affect a dust grain in order to provide a framework for interpreting the exozodi: the hot exozodiacal disk may be the indirect signature of an asteroid belt with a particularly high dynamical activity. Lastly I draw up a summary of the properties of dusty debris disks and of what they can teach us when compared to the Solar System. I propose possible future research directions for further investigations of planetary systems and their dynamics.

Les vingt-cinq dernières années ont connu une véritable révolution dans notre connaissance des systèmes planétaires avec plus de 1800 planètes extrasolaires connues à ce jour. L'étude observationnelle des disques de débris constitue l'approche proposée dans ce travail de thèse pour éclairer les processus de formation et d'évolution des systèmes planétaires. Ces disques circumstellaires sont constitués de particules de poussière générées par des collisions de petits corps appelés planétésimaux, en orbite autour d'une étoile de la séquence principale. La lumière stellaire qu'elles diffusent représente une observable particulièrement riche en informations sur l'architecture du système, mais difficile d'accès en raison du contraste élevé et de la faible séparation angulaire avec leur étoile. Le développement récent de nouveaux instruments à haut contraste équipés d'optique adaptative extrême représente un formidable potentiel pour l'étude de ces systèmes. Cette thèse se place dans le cadre de ces nouveaux développements et porte sur la caractérisation des disques de débris grâce à deux instruments qui équipent le VLT (Very Large Telescope) : NaCo et SPHERE (Spectro Polarimetric High contrast Exoplanet REsearch). NaCo est en opération depuis plus de 10 ans et a connu plusieurs améliorations successives. SPHERE a été conçu et développé dans la même période, testé intensivement en laboratoire en 2013 et est actuellement en cours de vérification opérationnelle sur le télescope. Le caractère novateur de ce travail consiste à associer à l'étude des propriétés physiques des disques de débris, une expertise instrumentale poussée pour tirer le meilleur profit des observations. La première partie vise à développer et caractériser des méthodes de réduction de données innovantes adaptées aux observations de disques en lumière diffusée et au comportement de l'instrument. En particulier les atouts, performances et biais des techniques d'imagerie différentielle angulaire, polarimétrique et de soustraction de référence sont quantifiés. Ces méthodes sont appliquées, dans une seconde partie, à l'étude et la caractérisation de deux prototypes de disques de débris entourant les étoiles beta Pictoris et HR 4796A. Elles permettent une analyse poussée de la morphologie de ces disques et révèlent de nouvelles asymétries, interprétées en terme de perturbateurs gravitationnels ou de propriétés de diffusion de la lumière par la poussière. Enfin une évaluation prospective des performances attendues et observées avec l'instrument SPHERE est détaillée dans la dernière section, basée sur des simulations et des mesures en laboratoire ou sur le ciel. Une comparaison avec NaCo révèle les points forts de SPHERE avant de conclure sur les questions scientifiques auxquelles les observations de disques de débris avec SPHERE pourront apporter des réponses. / Over the last two and a half decades, the discovery of more than 1800 exoplanets has been a major breakthrough in our understanding of planetary systems. To shed light on the formation and evolution processes of such systems, I have chosen an observational approach based on the study of debris discs. These circumstellar discs are composed of dust particles constantly generated by collisions of small rocky bodies called planetesimals, orbiting a main-sequence star. The stellar light they scatter can be studied from the Earth and reveal a wealth of information on the architecture of the system. These observations are challenging because of the high contrast and the small angular separation between the disc and the star. The recent developments of new high-contrast instruments with extreme adaptive optic systems are therefore bringing new expectations for the study of these systems and set the framework of this PhD thesis. My work aims at characterising debris discs thanks to two instruments installed on the Very Large Telescope: NaCo and SPHERE (Spectro Polarimetric High contrast Exoplanet REsearch). NaCo has been in operation for more than a decade and has undergone many improvements. SPHERE has been designed and assembled in the same period, was intensively tested in laboratory in 2013, and is currently being commissioned on the telescope. The innovative approach of this PhD work is to combine the study of debris discs with strong instrumental expertise to get the best science results from the observations. The first part of the study aims at developing innovative data reduction techniques adapted to the observations of discs in scattered light and to the behaviour of the instrument. I quantify in particular the performances, advantages, and biases of the angular, polarimetric and reference-star differential imaging technique. In a next step, I apply those techniques to characterise two prototypes of debris discs, around the stars beta Pictoris and HR 4796A. A detailed analysis of the morphology is carried out, which reveals new asymmetries interpreted in terms of gravitational perturbers or of dust scattering properties. Lastly, I detail the expected and measured performances of SPHERE, from simulations, laboratory and on-sky measurements. A comparison with NaCo reveals the assets of SPHERE and I conclude with the scientific questions SPHERE will be able to answer with new debris disc observations.

Orientador: Patricio Anibal Letelier Sotomayor / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Fisica "Gleb Wataghin" / Made available in DSpace on 2018-08-14T18:55:47Z (GMT). No. of bitstreams: 1 Coimbra-Araujo_CarlosHenrique_D.pdf: 1401888 bytes, checksum: ea7cff271a9dd2f1aba347507e316ac1 (MD5) Previous issue date: 2009 / Resumo: Neste trabalho é apresentada uma nova abordagem teórica e semifenomenológica acerca do que dimensões extras poderiam representar na explicação do que é a matéria escura. Aqui mostra-se que a gravitação baseada numa ação de Einstein-Hilbert para espaços-tempo com dimensão acima de quatro, produz um termo de força extra nas equações de movimento de um sistema de partículas teste, o que pode ser aplicado ao problema do campo gerado por alguma estrutura autogravitante, como clusters esféricos ou discos, por exemplo. Tal resultado é explorado no cálculo de configurações que possam mimetizar uma galáxia real. As configurações calculadas são o disco fino - a partir do método de imagens - e também a distribuição isotrópica de Miyamoto-Nagai - que reproduz o comportamento idealizado de uma galáxia espiral graças à estratificação de matéria num bojo central mais um disco galático. Para tais configurações são calculadas as curvas de rotação bem como a sua estabilidade, perfis de densidade e pressão, e mostra-se que no domínio onde as curvas são estáveis há a possibilidade de se reproduzir os resultados observacionais usualmente relacionados à incidência de um halo escuro. Nos modelos apresentados, no entanto, não há inclusão de matéria escura. O cálculo de lentes gravitacionais para clusters esféricos também é desenvolvido, indicando que as dimensões extras promovem desvios capazes de explicar as anomalias nas observações astronômicas de aglomerados de galáxias. Os resultados são amplamente discutidos e algumas comparações fenomenológicas são feitas. Dos resultados em estruturas autogravitantes, conclui-se que a presença de dimensões extras (sem matéria escura) é equivalente ao procedimento usual de se adicionar matéria escura às configurações calculadas, o que poderia levar à interpretação de que a matéria escura é apenas o produto de um desconhecimento acerca da natureza do espaço-tempo / Abstract: In the present work it is showed a new theoretical and semiphenomenological approach concerning what extra dimensions could represent to explain the nature of dark matter. Here the gravitation based on an multidimensional Einstein-Hilbert action reveals that an extra force term appears in the equations of motion for a system of test particles, that can be applied for the problem of the field produced by a self gravitating structure, as for instaure spherical clusters or disks. Such results are explored in the calculation of configurations that mimic real galaxies. The computed configurations are the thin disk - from the inverse method - and also the isotropic distribution of Miyamoto-Nagai - that reproduces the idealized behavior of a disk galaxy thanks to the stratification of matter in a central bulge plus a disk. The rotation curves, the stability, density and pressure profiles are calculated. In the domain where the curves are stable it is possible to reproduce observational results usually related to a dark halo. In present models, however, there is no inclusion of dark matter. It is also presented the calculation for gravitationallensing of spherical clusters, indicating that extra dimensions promote deviations capable to explain anomalies in the astronomical observation of many galaxy clusters. The results are widely discussed and some phenomenological comparisons are made. From results for self gravitating objects, one concludes that the presence of extra dimensions (without dark matter) is equivalent to the effect due to addition of dark matter in the calculated configurations. This could lead to the interpretation where dark matter concerns to an unfamiliarity related to the real structure of spacetime / Doutorado / Relatividade e Gravitação / Doutor em Física

Orientador: Samuel Rocha de Oliveira / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica / Made available in DSpace on 2018-08-24T16:31:57Z (GMT). No. of bitstreams: 1 Garcia_RaphaeldeOliveira_D.pdf: 5512062 bytes, checksum: a2805b263757b93de5fb67b8cc3aba15 (MD5) Previous issue date: 2013 / Resumo: Neste trabalho foi desenvolvido um novo programa computacional em Fortran 90, com o objetivo de obter soluções numéricas de um sistema de equações diferenciais parciais de Magnetohidrodinâmica Relativística, com gravitação pré-determinada (GRMHD), capaz de simular a formação de jatos relativísticos desde a acreção de disco de matéria até sua ejeção. De início fez-se um estudo sobre métodos numéricos de Volumes Finitos Unidimensionais, a saber método Lax-Friedrichs, Lax-Wendroff, Nessyahu-Tadmor e métodos de Godunov dependentes de problemas de Riemann, aplicados nas equações de Euler com o intuito de verificar as suas principais características e de efetuar comparações entre aqueles métodos. Em seguida implementou-se os métodos de Volumes Finitos Centrados Lax-Friedrichs e Nessyahu-Tadmor, que são esquemas numéricos que possuem uma formulação sem separação dimensional e livres de resolvedores de problemas de Riemann, mesmo em duas ou mais dimensões espaciais; neste ponto, já aplicados nas equações de GRMHD. Um método Lax-Wendroff com Runge-Kutta de ordem 3, com a propriedade de ser Valor Total Decrescente (TVD) no tempo e com separação dimensional, também foi aplicado no mesmo problema. Por fim, com o método Nessyahu-Tadmor foi possível obter soluções numéricas estáveis - sem oscilações espúrias nem dissipação excessiva - desde o processo de acreção do disco magnetizado, em rotação com relação a um buraco negro central (BH) de Schwarzschild e imerso a uma magnetosfera, até a ejeção de matéria em forma de jato ao longo de uma distância de quatorze vezes o raio do BH, um recorde em termos de simulação astrofísica / Abstract: We have developed a new computer program in Fortran 90, in order to obtain numerical solutions of a system of partial differential equations of Relativistic Magnetohydrodynamics with predetermined gravitation (GRMHD), capable of simulate the formation of relativistic jets from the accretion disk of matter up to his ejection. Initially we carried out a study on numerical methods of Unidimensional Finite Volume, namely Lax-Friedrichs, Lax-Wendroff, Nessyahu-Tadmor method and Godunov methods dependent on Riemann problems, applied to equations Euler in order to verify their main features and make comparisons among those methods. It was then implemented the methods of Finite Volume Centered Lax-Friedrichs and Nessyahu-Tadmor, which are numerical schemes that have a formulation free and without dimensional separation Riemann problem solvers, even in two or more spatial dimensions, at this point, already applied in equations GRMHD. A Lax-Wendrof Runge-Kutta method of order 3, with the property of Total Value Descending (TVD) in time and size separation, was also applied to the same problem. Finally, with Nessyahu - Tadmor method was possible to obtain solutions stable numerical - without spurious oscillations or excessive dissipation - from the process of magnetized accretion disk, in rotation with respect to a central black hole (BH) Schwarzschild and immersed in a magnetosphere, to the ejection of matter in the form of jet over a distance of fourteen times the radius of the BH, a record in terms of astrophysical simulation / Doutorado / Matematica / Doutor em Matemática Aplicada

[pt] Coberturas de um disco quadriculado com buracos D são contados de acordo com volume (na variável formal q) e fluxo (em p1, p2, ..., pN). Consideramos propriedades algébricas dos resultados gerados pela função F (p1, p2, ..., pN, q). Para números fixos p2, ..., pN, q > 0 o polinômio f(p1) = F(p1, p2, ..., pN, q) tem todas as raízes reais (e negativas). / [en] Tilings of a quadriculated disk with holes D are counted according to vol- ume (in the formal variabel q) and flux (in p1; p2;... pN). We consider algebraic properties of the resulting generating function D (p1; p2; ...; pk; q). For p1; p2; ...; bpi; ...; pn; q > 0 the polynomial f(pi) = D (p1; p2; ... ; pi; ...; pn; q) has all roots real numbers (and negative).