Disc material in the corotation region librates with respect to low-mass planets on horseshoe trajectories. The exchange of angular momentum associated with this libration gives rise to the non-linear corotation torque (the horseshoe drag). For the first project described herein, we ran a suite of high-resolution 2D hydrodynamic simulations of low-mass (5 Earth mass) planets, at eccentricities 0 e < 0.3, embedded in both viscous protoplanetary discs with entropy relaxation and inviscid discs without. The attenuation of the corotation torque was obtained from these simulations and found to be well-fitted by an exponential decay with a characteristic ‘e-folding eccentricity’ that scales linearly with disc scale height. These results were tested with different disc scale heights between 0.03 and 0.1 and with a 10 Earth mass planet. In the second project in this thesis we sought to extend on these results by examining the case of an embedded 5 Earth mass planet in three dimensional discs. We found that our scaling relation held in this new case, confirming that it is possible to use 2D simulations with a softening parameter to capture the behaviour of the corotation torque. We investigated the time-averaged horseshoe width as a function of altitude and found that the corotation region extends from the midplane to around three scale heights, changing most near the midplane for eccentric planets. The final project looked at 3D radiative discs, under the influence of stellar irradiation, with more massive embedded planets capable of triggering gap formation. We use the pluto code to simulate a Jupiter mass planet at 5 AU in a protoplanetary disc. We describe our progress in understanding the process of gap formation in a case study of this class of hitherto undescribed disc.

Submitted by Nilton Carlos Santos Araujo null (nilcasr@gmail.com) on 2017-09-06T21:31:14Z No. of bitstreams: 1 teseNilton.pdf: 13643423 bytes, checksum: 0c49d4b6392db7c166aa5c18e501516b (MD5) / Approved for entry into archive by Monique Sasaki (sayumi_sasaki@hotmail.com) on 2017-09-11T19:47:37Z (GMT) No. of bitstreams: 1 araujo_ncs_dr_guara.pdf: 13643423 bytes, checksum: 0c49d4b6392db7c166aa5c18e501516b (MD5) / Made available in DSpace on 2017-09-11T19:47:37Z (GMT). No. of bitstreams: 1 araujo_ncs_dr_guara.pdf: 13643423 bytes, checksum: 0c49d4b6392db7c166aa5c18e501516b (MD5) Previous issue date: 2017-07-07 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Desde 2004, as imagens obtidas pelas câmeras da sonda Cassin têm revelado a existência de vários pequenos satélites no sistema de Saturno. Três desses pequenos satélites estão dentro de arcos de partículas. Enquanto Aegaeon, Methone e Anthe e seus arcos são conhecidos por estarem em ressonância de corrotação 7:6, 14:15 e 10:15, respectivamente, com Mimas, a origem desses arcos é desconhecida. Logo, este trabalho investiga um possível processo de captura em ressonância de corrotação, que envolve o aumento da excentricidade de um satélite perturbador. Assim, através de simulações numéricas e estudos analíticos, nós mostramos um cenário que a excitação da excentricidade de Mimas poderia capturar partículas em ressonância de corrotação 7:6 14:15 e 10:11 com Mimas, fornecendo uma possível explicação para a origem dos arcos de Saturno. Outro objetivo deste trabalho é analisar uma possível região de origem de Aegaeon. Pois, há uma possibilidade de que a pequena lua Aegaeon tenha sido formada em outra região do sistema de Saturno diferente daquela que ela se encontra atualmente. Assim, também através de simulações numéricas e estudos analíticos, verificamos se a perturbação de Jano e Epimeteu através da ressonância de corrotação e Lindblad na borda externa do anel A é responsável pela migração de objetos dessa borda. / Since 2004, the images obtained by the Cassini spacecraft on-board cameras have revealed the existence of several small satellites in Saturn system. Three of these small satellites are embedded in arcs of particles. While Aegaeon, Methone and Anthe and their arcs are known to be in 7:6, 14:15 and 10:11 corotation resonances, respectively with Mimas, their origin remains unknown. This work investigates one possible process for capturing bodies into a corotation resonance, which involves increasing in the eccentricity of the perturbing body. Therefore, through numerical simulations and analytical studies, we showed a scenario in which the excitation of Mimas’ eccentricity could capture particles in 7:6, 14:15 and 10:11 corotation resonance. This is a possible explanation for the origin of the arcs. Another goal of this work is to analyze a region possible of Aegaeon’s origin. Because, there’s a possibility of which Aegaon moonlet has been formed in another region of Saturn’s system different of that Aegaeon finds itself today. Thus, also through numerical simulations and analytical studies, we verified that perturbation of Jano and Epimeteu by corotation and Lindblad resonance in the outer edge of Saturn’s A ring can be responsible by the migration of particles of this edge.

Thin and slender structures are widely occurring both in nature and in human creations. Clever geometries of thin structures can produce strong constructions while requiring a minimal amount of material. Computer modeling and analysis of thin and slender structures have their own set of problems, stemming from assumptions made when deriving the governing equations. This thesis deals with the derivation of numerical methods suitable for approximating solutions to problems on thin geometries. It consists of an introduction and four papers. In the first paper we introduce a thread model for use in interactive simulation. Based on a three-dimensional beam model, a corotational approach is used for interactive simulation speeds in combination with adaptive mesh resolution to maintain accuracy. In the second paper we present a family of continuous piecewise linear finite elements for thin plate problems. Patchwise reconstruction of a discontinuous piecewise quadratic deflection field allows us touse a discontinuous Galerkin method for the plate problem. Assuming a criterion on the reconstructions is fulfilled we prove a priori error estimates in energy norm and L2-norm and provide numerical results to support our findings. The third paper deals with the biharmonic equation on a surface embedded in R3. We extend theory and formalism, developed for the approximation of solutions to the Laplace-Beltrami problem on an implicitly defined surface, to also cover the biharmonic problem. A priori error estimates for a continuous/discontinuous Galerkin method is proven in energy norm and L2-norm, and we support the theoretical results by numerical convergence studies for problems on a sphere and on a torus. In the fourth paper we consider finite element modeling of curved beams in R3. We let the geometry of the beam be implicitly defined by a vector distance function. Starting from the three-dimensional equations of linear elasticity, we derive a weak formulation for a linear curved beam expressed in global coordinates. Numerical results from a finite element implementation based on these equations are compared with classical results.

Orientador: Rafael Sfair de Oliveira / Resumo: A formação de alguns arcos dos anéis planetários pode estar relacionada às colisões de partículas interplanetárias com seus satélites, fragmentando-os e produzindo corpos menores. De modo sucessivo, estes fragmentos podem sofrer novas colisões e eventualmente gerar partículas de poeira. Por outro lado, os corpos macroscópicos (da ordem de metros) imersos no anel podem colidir entre si e aglutinar- se de modo a gerar novos objetos maiores. A existência destes arcos é creditada a presença de um satélite perturbador que os confina em um ressonância de corrotação. No caso do arco do anel G de Saturno, este é confinado por uma uma ressonância excêntrica 7:6 de corrotação com o satélite Mimas. Hedman et al. (2010) citam que o arco do anel G é majoritariamente composto por partículas da ordem de micrômetros. Neste caso, as forças perturbativas, tais como a pressão de radiação e a força eletromagnéticas, são significativas e tendem a reduzir o tempo de vida destas partículas nesta região. Para explicar a estabilidade do arco Hedman et al. (2010) utilizaram o pequeno satélite Aegaeon (imerso no arco) que poderia ser uma fonte do material das partículas micrométricas imersas no arco via colisões de partículas interplanetárias com Aegaeon. Entretanto, Madeira et al. (2018) exploraram o efeito da pressão de radiação solar e mostraram que o tempo de vida das partículas micrométricas no arco é menos de 40 anos e que o satélite Aegaeon não poderia ser fonte de material e manter a quantidade... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: Some planetary rings exhibit denser regions called arcs, and the existence of these arcs is credited by the presence of a disturbing satellite that confines the particles in a corotation resonance. The formation of the planetary ring arc can be related with the collisions between interplanetary particles with an embedded satellite, or the break up of a moon into minor bodies. Successively, these bodies may experience new collisions that eventually create dust particles. Meanwhile, the macroscopic bodies can collide among themselves and merge, resulting in large bodies. For the Saturn’s G ring’s arc, it is confined by a 7:6 corotation resonance with the satellite Mimas. Hedman et al. (2010) showed this arc is composed mostly of micrometers particles, a configuration that perturbative forces are significant and decrease the lifetime of the structure. To explain the stability of this arc, they proposed that the satellite Aegaeon could be a source of the material of the dust by collisions within interplanetary particles. However, Madeira et al. (2018) studied the solar radiation pressure and showed that the lifetime of the particles in less than 40 years and that the satellite Aegaeon cannot be a source. Therefore, another mechanism is necessary to explain the arc. To do so, one can use information derived by the LEMMS (Magnetospheric Imaging Instrument’s LowEnergy), an instrument from that Cassini spacecraft that detected an energy drop from electrons in this region, inferring t... (Complete abstract click electronic access below) / Mestre

Les ceintures de radiation correspondent à la région de la magnétosphère dans laquelle se trouvent les particules de hautes énergies. Le couplage entre le vent solaire et la magnétosphère donne lieu à des variations des flux de particules sur plusieurs ordres de grandeurs. L’objectif de cette thèse est d’observer et caractériser ces variations de flux d’électrons au passage de différents types d’événements tels que les régions d’interaction en co-rotation (CIRs) et les éjections de masse coronale interplanétaires (ICMEs). Pour cela, nous avons traité et analysé les données de plusieurs types: paramètres du vent solaire, indices géomagnétiques et flux d’électrons dans les ceintures de radiation. Dans les trois premiers chapitres, nous rendons compte de la complexité de l’environnement spatial Terrestre et présentons les différentes données utilisées. Les travaux de thèse sont ensuite organisés en quatre chapitres. Premièrement, nous utilisons les mesures des satellites NOAA-POES afin de caractériser les flux d’électrons dans les ceintures. Nous étudions ensuite les différences de variations de flux causées par les CIRs et les ICMEs en fonction de l’énergie des électrons et du paramètre L*. Après avoir montré le fort lien entre les intensités d’orages magnétiques et les variations de flux, nous nous focalisons sur les ICMEs et la variabilité des orages qu’elles causent. Enfin, nous insistons sur l’importance des enchaînements d’événements. Après avoir quantifié la forte tendance qu’ont les ICMEs à former des séquences, nous réalisons une étude statistique sur les orages qu’elles causent, puis trois études de cas afin d’illustrer leurs effets sur les ceintures. / The radiation belts are the toroidal region within the inner magnetosphere where high energetic particles are located. The coupling between the solar wind and the magnetosphere leads to strong variations of particle fluxes that can therefore increase or decrease over several orders of magnitude. The aim of this thesis is to observe and characterize the variations of fluxes during the crossing of several types of events originating from the sun such as Corotating Interaction Regions (CIRs) and Interplanetary Coronal Mass Ejections (ICMEs). To do so, we processed and analyzed the data of various types : solar wind parameters, geomagnetic indices, and electron fluxes within the radiation belts. In the three first chapters, we report on the complexity of the Terrestrial space environment and we present the Solar-Terrestrial system and the data used. Then, our work is organized around four chapters. First, we characterized the electron fluxes within the radiation belts as measured by the NOAA-POES spacecrafts. Then, we studied the difference between the variations of fluxes caused by the CIRs and the ICMEs depending on the energy and the L* parameter. After establishing strong links between the intensity of magnetic storms and the variations of fluxes, we focused on the ICMEs and the variability of the related magnetic storms. Eventually, we emphasized the importance of the sequences of events. After quantifying the trend of the ICMEs to form sequences, we performed a statistical study on the magnetic storms caused by such sequences. Finally three study cases were performed in order to illustrate the various possible effects on the radiation belts.

Thin and slender structures are widely occurring both in nature and in human creations. Clever geometries of thin structures can produce strong constructions while using a minimal amount of material. Computer modeling and analysis of thin and slender structures has its own set of problems stemming from assumptions made when deriving the equations modeling their behavior from the theory of continuum mechanics. In this thesis we consider two kinds of thin elastic structures; threads and plates. Real-time simulation of threads are of interest in various types of virtual simulations such as surgery simulation for instance. In the first paper of this thesis we develop a thread model for use in interactive applications. By viewing the thread as a continuum rather than a truly one dimensional object existing in three dimensional space we derive a thread model that naturally handles both bending, torsion and inertial effects. We apply a corotational framework to simulate large deformation in real-time. On the fly adaptive resolution is used to minimize corotational artifacts. Plates are flat elastic structures only allowing deflection in the normal direction. In the second paper in this thesis we propose a family of finite elements for approximating solutions to the Kirchhoff-Love plate equation using a continuous piecewise linear deflection field. We reconstruct a discontinuous piecewise quadratic deflection field which is applied in a discontinuous Galerkin method. Given a criterion on the reconstruction operator we prove a priori estimates in energy and L2 norms. Numerical results for the method using three possible reconstructions are presented.