We describe a procedure for classifying 4D N=2 superconformal theories of the type introduced by Davide Gaiotto. Any punctured curve, C, on which the 6D (2,0) SCFT is compactified, may be decomposed into 3-punctured spheres, connected by cylinders. The 4D theories, which arise, can be characterized by listing the ``matter" theories corresponding to 3-punctured spheres, the simple gauge group factors, corresponding to cylinders, and the rules for connecting these ingredients together. Different pants decompositions of C correspond to different S-duality frames for the same underlying family of 4D \mathcal{N}=2 SCFTs. We developed such a classification for the A_{N-1} and the D_N series of 6D (2,0) theories. We outline the procedure for general A_{N-1} and D_N, and construct, in detail, the classification through A_4 and D_4, respectively. / text

Στην συγκεκριμένη διπλωματική εργασία ασχολήθηκα με το φωτοβαρυτικό περιορισμένο πρόβλημα των τριών σωμάτων.Εστίασα στις τρισδιάστατες περιοδικές κινήσεις και περιέγραψα αναλυτικά οικογένειες τρισδιάστατων περιοδικών τροχιών. / At this master I work on the photogravitational restricted 3-orbit problem. Espesially I focus on the 3-dimensional orbits solutions and I describe families of 3-dimensional orbits.

Paper discusses the expected uncertainty of orbital parameters of binary stars as measured by the space-based gravitational wave observatory LISA (Laser Interferometer Space Antenna) and how the inclusion of spin in the model of the binary stars affects the uncertainty. The uncertainties are found by calculating the received gravitational wave from a binary pair and then performing a linear least-squares parameter estimation. The case of a 1500 solar mass black hole that is 20 years from coalescing with a 1000 solar mass black hole--both of which are 50 x 10^6 light years away--is analyzed, and the results show that the inclusion of spin has a negligible effect upon the angular resolution of LISA but can increase the accuracy in mass and distance measurements by factors of 15 and 65, respectively.

Mon travail de thèse a porté sur la compréhension «systèmes dynamiques de la dynamique à grande échelle dans l’écoulement pleinement développé de cisaillement turbulent. Dans le plan écoulement de Couette, simulation des grandes échelles (LES) est utilisée pour modéliser petits mouvements d’échelle et de ne résoudre mouvements à grande échelle afin de calculer non linéaire ondes progressives (SNT) et orbites périodiques relatives (RPO). Artificiel sur-amortissement a été utilisé pour étancher une gamme croissante de petite échelle motions et prouvent que les motions grande échelle sont auto-entretenue. Les solutions d’onde inférieure branche itinérantes qui se trouvent sur le bassin laminaire turbulent limite sont obtenues pour ces simulation sur-amortie et continue encore dans l’espace de paramètre à des solutions de branche supérieure. Cette approche ne aurait pas été possible si, comme supposé dans certains enquêtes précédentes, les mouvements à grande échelle dans le mur bornées flux de cisaillement sont forcée par un mécanisme fondé sur l’existence de structures actives à plus petite échelle. En flux Poseuille, orbites périodiques relatives à décalage réflexion symétrie sur la limite du bassin laminaire turbulent sont calculés en utilisant DNS. Nous montrons que le RPO trouvé sont connectés à la paire de voyager vague (TW) solution via bifurcation mondiale (noeud-col-période infinie bifurcation). La branche inférieure de cette solution TW évoluer dans un état de l’envergure localisée lorsque le domaine de l’envergure est augmentée. La solution de branche supérieure développe plusieurs stries avec un espacement de l’envergure compatible avec des mouvements à grande échelle en régime turbulent. / My thesis work focused on ‘dynamical systems’ understanding of the large-scale dynamics in fully developed turbulent shear flow. In plane Couette flow, large-eddy simulation (L.E.S) is used to model small scale motions and to only resolve large-scale motions in order to compute nonlinear traveling waves (NTW) and relative periodic orbits (RPO). Artificial over-damping has been used to quench an increasing range of small-scale motions and prove that the motions in large-scale are self-sustained. The lower-branch traveling wave solutions that lie on laminar-turbulent basin boundary are obtained for these over-damped simulation and further continued in parameter space to upper branch solutions. This approach would not have been possible if, as conjectured in some previous investigations, large-scale motions in wall bounded shear flows are forced by mechanism based on the existence of active structures at smaller scales. In Poseuille flow, relative periodic orbits with shift-reflection symmetry on the laminar-turbulent basin boundary are computed using DNS. We show that the found RPO are connected to the pair of traveling wave (TW) solution via global bifurcation (saddle-node-infinite period bifurcation). The lower branch of this TW solution evolve into a spanwise localized state when the spanwise domain is increased. The upper branch solution develops multiple streaks with spanwise spacing consistent with large-scale motions in turbulent regime.

Orientador: Marco Antonio Teixeira / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-10T12:10:27Z (GMT). No. of bitstreams: 1 Roberto_LuciAnyFrancisco_D.pdf: 627926 bytes, checksum: 0c8cb4e26df805282fa716847859d82f (MD5) Previous issue date: 2008 / Resumo: Neste trabalho estudamos sistemas dinâmicos possuindo estruturas Hamiltonianas e reversíveis( / Abstract: In this work we study dynamical systems possessing Hamiltonian and time-reversible structures. The reversibility concept is de¯ned in terms of an involution. Initially we discuss the dynamics of Hamiltonian vector ¯elds with 2 and 3 degrees of freedom around an elliptic equilibrium in the presence of an involution which preserves the symplectic structure. The main results discuss the existence of one-parameter families of reversible periodic solutions terminating at the equilibrium. The main techniques that are used in the proofs are Belitskii and Birkho® normal forms and the Liapunov-Schmidt Reduction. Next we consider a case of the 3-body restricted problem in rotating coordinates. In this case the two primaries are oving in an elliptic collision orbit. By the continuation method of Poincare we characterize that the periodic circular orbits and the symmetric periodic elliptic orbits from the Kepler problem which can be prolonged to pseudo periodic orbits of the planar restricted 3{body problem in rotating coordinates with the two primaries moving in an elliptic collision orbit / Doutorado / Topologia e Geometria / Doutor em Matemática

Orientador: Marco Antonio Teixeira / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-05T21:55:10Z (GMT). No. of bitstreams: 1 Lima_MauricioFirminoSilva_D.pdf: 1170094 bytes, checksum: 090e81187787a7a96591621e58ae7742 (MD5) Previous issue date: 2006 / Resumo: Neste trabalho tratamos de famílias a um-parâmetro de campos vetoriais R-reversíveis definidos em uma vizinhança de um ponto de equilíbrio ressonante em R2n. Focalizamos a atenção às 0:p:q-ressonâncias. Inicialmente estudamos a existência/bifurcação de órbitas periódicas simétricas para tais sistemas. A existência e rigidez de famílias de órbitas homoclínicas também são discutidas. Além disso, também analisamos, para n = 3, a rigidez de famílias de Cantor¿ de dois-toros invariantes por meio da Teoria KAM / Abstract: In this work we deal with one parameter families of R-reversible vector fields defined around a resonant equilibrium point in R2n. We focus our attention to 0:p:q resonances. First of all we study the existence/bifurcation of symmetric periodic orbits for such systems. The existence and rigidity of families of homoclinic orbits are also discussed. We also analyze for n = 3 the rigidity of ¿Cantor families¿ of invariant two-torus by means of KAM Theory / Doutorado / Sistemas Dinamicos / Doutor em Matemática

Estudamos o comportamento dinâmico de séries temporais experimentais obtidas de um circuito de Chua quando dois parâmetros de controle, $Delta R_1$ e $Delta R_2$, são variados.Investigamos os comportamentos caótico e periódico, analisando as séries temporais ao redor e no interior de duas janelas periódicas presentes no espaço de parâmetros $(Delta R_1,Delta R_2)$ do circuito. Na vizinhança da janela de período três, analisamos como a dinâmica simbólica se altera quando construída em diferentes seções de Poincaré de um mesmo atrator, e investigamos a dimensão dos mapas de retorno, uni ou bidimensional, para diferentes atratores caóticos presentes nessa região do espaço de parâmetros. Ainda nessa vizinhança, empregamos técnicas de caracterização topológica para confirmar a existência de fibras caóticas, que são curvas de codimensão um no espaço de parâmetros onde as propriedades caóticas dos atratores são preservadas.Ao redor da janela de período quatro, investigamos a transição entre os três comportamentos caóticos para os quais construímos os respectivos moldes topológicos. Propusemos também um molde topológico para o regime caótico após a crise por fusão ocorrer no circuito. Finalizando, investigamos as bifurcações e a estrutura topológica das órbitas periódicas que formam as janelas de período três e de período quatro, construindo um espaço de parâmetros topológico, baseado em um mapa bi-modal, para descrever as duas janela periódicas. / We have studied the dynamical behavior of experimental time series obtained from a Chua's circuit by variation of two parameter control, $Delta R_1$ and $Delta R_2$. We investigated the chaotic and periodic behaviors of the circuit, analyzing temporal series around and inside of two periodic windows in the two-parameter space $(Delta R_1,Delta R_2)$. In the period-three window neighborhood, we analyzed how the symbolic dynamics changes when it is built by different Poincaré sections of an attractor, and we studied the dimension of return map, one- or two-dimensional, for many chaotic attractors in this region of the parameter space. In this neighborhood, we also applied topological techniques to confirm the existence of chaotic fibers: codimension one curves where the chaotic properties of the attractors remain unchanged in the two-parameter space.Around the period-four window, we investigated, by template analysis, the transition between three chaotic attractors found in the Chua's circuit. We proposed a template for chaotic regime of the circuit after merge-crisis. Finally, we investigated the bifurcations and topological structure of periodic orbits in period-three and period-four windows and also proposed a topological parameter space, based in a bimodal map model, that describe these two periodic windows.

<div>Over the past twenty years, ridesharing opportunities for smallsats, i.e., secondary payloads, has increased with the introduction of Evolved Expendable Launch Vehicle (EELV) Secondary Payload Adapter (ESPA) rings. However, the orbits available for these secondary payloads is limited to Low Earth Orbits (LEO) or Geostationary Orbits (GEO). By incorporating a propulsion system, propulsive ESPA rings offer the capability to transport a secondary payload, or a collection of payloads, to regions beyond GEO. In this investigation, the ridesharing scenario includes a secondary payload in a dropped-off Geosynchronous Transfer Orbit (GTO) and the region of interest is the vicinity near the Sun-Earth Lagrange points. However, mission design for secondary payloads faces certain challenges. A significant mission constraint for a secondary payload is the drop-off orbit orientation, as it is dependent on the primary mission. To address this mission constraint, strategies leveraging dynamical structures within the Circular Restricted Three-Body Problem (CRTBP) are implemented to construct efficient and flexible transfers from GTO to orbits near Sun-Earth Lagrange points. First, single-maneuver ballistic transfers are constructed from a range of GTO departure orientations. The ballistic transfer utilize trajectories within the stable manifold structure associated with periodic and quasi-periodic orbits near the Sun-Earth L1 and L2 points. Numerical differential corrections and continuation methods are leveraged to create families of ballistic transfers. A collection of direct ballistic transfers are generated that correspond to a region of GTO departure locations. Additional communications constraints, based on the Solar Exclusion Zone and the Earth’s penumbra shadow region, are included in the catalog of ballistic transfers. An integral-type path condition is derived and included throughout the differential corrections process to maintain transfers outside the required communications restrictions. The ballistic transfers computed in the CRTBP are easily transitioned to the higher-fidelity ephemeris model and validated, i.e., their geometries persist in the ephemeris model. To construct transfers to specific orbits near Sun-Earth L1 or L2, families of two-maneuver transfers are generated over a range of GTO departure locations. The two-maneuver transfers consist of a maneuver at the GTO departure location and a Deep Space Maneuver (DSM) along the trajectory. Families of two-maneuver transfers are created via a multiple- shooting differential corrections method and a continuation process. The generated families of transfers aid in the rapid generation of initial guesses for optimized transfer solutions over a range of GTO departure locations. Optimized multiple-maneuver transfers into halo and Lissajous orbits near Sun-Earth L1 and L2 are included in this analysis in both the CRTBP model and the higher-fidelity ephemeris model. Furthermore, the two-maneuver transfer strategy employed in this analysis are easily extended to other Three-Body systems. </div>

<div> <div> <div> <p>Resonant orbits in a multi-body environment have been investigated in the past to aid the understanding of perceived chaotic behavior in the solar system. The invariant manifolds associated with resonant orbits have also been recently incorporated into the design of trajectories requiring reduced maneuver costs. Poincaré sections are now also extensively utilized in the search for novel, maneuver-free trajectories in various systems. This investigation employs dynamical systems techniques in the computation and characterization of resonant orbits in the higher-fidelity Circular Restricted Three-Body model. Differential corrections and numerical methods are widely leveraged in this analysis in the determination of orbits corresponding to different resonance ratios. The versatility of resonant orbits in the design of low cost trajectories to support exploration for several planet-moon systems is demonstrated. The efficacy of the resonant orbits is illustrated via transfer trajectory design in the Earth-Moon, Saturn-Titan, and the Mars-Deimos systems. Lastly, Poincaré sections associated with different resonance ratios are incorporated into the search for natural, maneuver-free trajectories in the Saturn-Titan system. To that end, homoclinic and heteroclinic trajectories are constructed. Additionally, chains of periodic orbits that mimic the geometries for two different resonant ratios are examined, i.e., periodic orbits that cycle between different resonances are determined. The tools and techniques demonstrated in this investigation are useful for the design of trajectories in several different systems within the CR3BP. </p> </div> </div> </div>

Forest fires cause a significant amount of damage and destruction each year. Optimally dispatching resources reduces the amount of damage a forest fire can cause. Models predict the fire spread to provide the data required to optimally dispatch resources. However, the models are only as accurate as the data used to build them. Satellites are one valuable tool in the collection of data for the forest fire models. Satellites provide data on the types of vegetation, the wind speed and direction, the soil moisture content, etc. The current operating paradigm is to passively collect data when possible. However, images from directly overhead provide better resolution and are easier to process. Maneuvering a constellation of satellites to fly directly over the forest fire provides higher quality data than is achieved with the current operating paradigm. Before launch, the location of the forest fire is unknown. Therefore, it is impossible to optimize the initial orbits for the satellites. Instead, the expected cost of maneuvering to observe the forest fire determines the optimal initial orbits. A two-stage stochastic programming approach is well suited for this class of problem where initial decisions are made with an uncertain future and then subsequent decisions are made once a scenario is realized. A repeat ground track orbit provides a non-maneuvering, natural solution providing a daily flyover of the forest fire. However, additional maneuvers provide a second daily flyover of the forest fire. The additional maneuvering comes at a significant cost in terms of additional fuel, but provides more data collection opportunities. After data are collected, ground stations receive the data for processing. Optimally selecting the ground station locations reduce the number of built ground stations and reduces the data fusion issues. However, the location of the forest fire alters the optimal ground station sites. A two-stage stochastic programming approach optimizes the selection of ground stations to maximize the expected amount of data downloaded from a satellite. The approaches of selecting initial orbits and ground station locations including uncertainty will provide a robust system to reduce the amount of damage caused by forest fires.