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This thesis deals with chemical plants constituted by parallel batch-continuous production lines with shared resources. For such plants, it is highly desirable to have optimal operation schedules which determine the starting times of the various batch processes and the flow rates of the continuous processes in order to maximize the average plant productivity and to have a continuous production without interruptions. This optimization problem is constrained by the limitation of the resources that are shared by the reactors and by the capacities of the various devices that constitute the plant. Such plants are "hybrid" by nature because they combine both continuous-time dynamics and discrete-event dynamics. The formalism of "Hybrid Automata" is there fore well suited for the design of plant models. The first contribution of this thesis is the development of a hybrid automaton model of the chemical plant in the Matlab-Simulink-Stateflow environment and its use for the design of an optimal periodic schedule that maximises the plant productivity. Using a sensitivity analysis and the concept of Poincaré; map, it is shown that the optimal schedule is a stable limit cycle of the hybrid system that attracts the system trajectories starting in a wide set of initial conditions. The optimal periodic schedule is valid under the assumption that the hybrid model is an exact description of the plant. Under perturbations on the plant parameters, it is shown that two types of problems may arise. The first problem is a drift of the hybrid system trajectory which can either lead to a convergence to a new stable sub-optimal schedule or to a resource conflict. The second problem is a risk of overflow or underflow of the output buffer tank. The second contribution of the thesis is the analysis of feedback control strategies to avoid these problems. For the first problem, a control policy based on a model predictive control (MPC) approach is proposed to avoid resource conflicts. The feedback control is run on - line with the hybrid Simulink-Stateflow simulator used as an internal model. For the solution of the second problem, a classical PI control is used. The goal is not only to avoid over- or under-filling of the tank but also to reduce the amplitude of outflow rate variations as much as possible. A methodological analysis for the PI controller tuning is presented in order to achieve an acceptable trade-off between these conflicting objectives.

Models of geometry that are intrinsically quantum-mechanical in nature arise from the recoupling theory of space-time symmetry groups. Roger Penrose constructed such a model from SU(2) recoupling in his theory of spin networks; he showed that spin measurements in a classical limit are necessarily consistent with a three-dimensional Euclidian vector space. T. Regge and G. Ponzano expressed the semi-classical limit of this spin model in a form resembling a path integral of the Einstein-Hilbert action in three Euclidian dimensions. This thesis gives new proofs of the Penrose spin geometry theorem and of the Regge-Ponzano decomposition theorem. We then consider how to generalize these two approaches to other groups that give rise to new models of quantum geometries. In particular, we show how to construct quantum models of four-dimensional relativistic space-time from the re-coupling theory of the Poincare group.

La marche occupe un rôle important dans la vie quotidienne. Ce processus apparaît comme facile et naturel pour des gens en bonne santé. Cependant, différentes sortes de maladies (troubles neurologiques, musculaires, orthopédiques...) peuvent perturber le cycle de la marche à tel point que marcher devient fastidieux voire même impossible. Ce projet utilise l'application de Poincaré pour évaluer l'asymétrie de la marche d'un patient à partir d'une carte de profondeur acquise avec un senseur Kinect. Pour valider l'approche, 17 sujets sains ont marché sur un tapis roulant dans des conditions différentes : marche normale et semelle de 5 cm d'épaisseur placée sous l'un des pieds. Les descripteurs de Poincaré sont appliqués de façon à évaluer la variabilité entre un pas et le cycle complet de la marche. Les résultats montrent que la variabilité ainsi obtenue permet de discriminer significativement une marche normale d'une marche avec semelle. Cette méthode, à la fois simple à mettre en oeuvre et suffisamment précise pour détecter une asymétrie de la marche, semble prometteuse pour aider dans le diagnostic clinique. / Gait plays an important part in daily life. This process appears to be very easy and natural for healthy people. However, different kinds of diseases (neurological, muscular, orthopedic...) can impede the gait cycle to such an extent that gait becomes tedious or even infeasible. This project applied Poincare plot analysis to assess the gait asymmetry of a patient from a depth map acquired with a Kinect sensor. To validate the approach, 17 healthy subjects had to walk on a treadmill under different conditions : normal walk and with a 5 cm thick sole under one foot. Poincare descriptors were applied in such a way that they assess the variability between a step and the corresponding complete gait cycle. Results showed that variability significantly discriminates between a normal walk and a walk with a sole. This method seems promising for a clinical use as it is simple to implement and precise enough to assess gait asymmetry.

An integral part of NASA's vision for the coming years is a sustained infrastructure in cislunar space. The current baseline trajectory for this facility is a Near Rectilinear Halo Orbit (NRHO), a periodic orbit in the Circular Restricted Three-Body Problem. One of the goals of the facility is to serve as a proving ground for human spaceflight operations in deep space. Thus, this investigation focuses on transfers between the baseline NRHO and a family of periodic orbits that originate from a period-doubling bifurcation along the halo family. This new family of orbits has been termed the ``butterfly" family. This investigation also provides an overview of the evolution for a large subset of the butterfly family. Transfers to multiple subsets of the family are found by leveraging different design strategies and techniques from dynamical systems theory. The different design strategies are discussed in detail, and the transfers to each of these regions are compared in terms of propellant costs and times of flight.

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Orientador: Patricio A. Letelier Sotomayor / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-13T05:26:41Z (GMT). No. of bitstreams: 1 Steklain_AndreFabiano_D.pdf: 11096709 bytes, checksum: 482e5ffb56f964f7786da54ec1791864 (MD5) Previous issue date: 2009 / Resumo: Neste trabalho a dinâmica do problema de Hill é analisada utilizando-se duas metodologias diferentes. Na primeira metodologia, ainda no contexto da mecânica newtoniana, utilizamos potenciais que reproduzem efeitos da relatividade geral. Foram utilizados os potenciais de Paczynski-Wiita e um dos potenciais de Artemova, Bjornsson e Novikov (ABN). Estes potenciais reproduzem os efeitos que surgem no contexto da métrica de Schwarzschild (horizonte de eventos) e da métrica de Kerr (efeito Lense-Thirring), respectivamente. Na segunda metodologia as equações de movimento são obtidas a partir da relatividade geral, utilizando a métrica aproximada de um sistema binário obtida a partir de uma expansão pós-newtoniana de primeira ordem (1PN). A análise da dinâmica envolveu o estudo da estabilidade das órbitas fechadas, utilizando ferramentas clássicas como seções de Poincaré e expoentes de Lyapunov. Foram estudadas também trajetórias não limitadas utilizando escape fractal. Dentre os resultados obtidos destacam-se dois fatos. No caso do potencial ABN, existe uma influência da rotação na estabilidade das órbitas. No caso relativístico existe um limite para o qual o sistema, em geral caótico, se torna estável, diferentemente do que se poderia esperar de acordo com os potenciais pseudo-Newtonianos, em particular considerando o potencial de Paczynski-Wiita. / Abstract: In this work the Hill problem dynamics is analyzed using two different approaches. In the first approach, still in the realm of Newtonian mechanics, we use potentials that reproduce General Relativity effects. We use the Paczynski-Wiita and one of the Artemova, Bj¨ornsson e Novikov (ABN) potentials. These potentials reproduce effects that arise in the context of the Schwarzschild metric (event horizon) and of the Kerr metric (Lense-Thirring effect), respectively. On the second approach the equations of motion are obtained using general relativity, from the approximate metric of a binary system obtained from post-Newtonian expansions up to first order (1PN). In the analysis of the dynamics we study the stability of bounded orbits using classical tools, like Poincare sections and Lyapunov exponents. We also study open trajectories using Fractal Escape analysis. From our results we remark that two features. For the ABN potential there is an influence of the rotations on the stability of the orbits. In general relativity there is a limit where the system, in general chaotic, become stable, in disagreement with the pseudo-Newtonian potentials, in particular the Paczy'nski-Wiita potential. / Doutorado / Doutor em Matemática Aplicada

This thesis examines the relation between classical and quantum mechanics from philosophical, mathematical and physical standpoints. It first presents arguments in support of "conjectural realism" in scientific theories distinguished by explicit contextual structure and empirical testability; and it analyses intertheoretic reduction in terms of weakly equivalent theories over a domain of applicability. Familiar formulations of classical and quantum mechanics are shown to follow from a general theory of mechanics based on pure states with an intrinsic probability structure. This theory is developed to the stage where theorems from quantum logic enable expression of the state geometry in Hilbert space. Quantum and classical mechanics are then elaborated and applied to subsystems and the measurement process. Consideration is also given to spacetime geometry and the constraints this places on the dynamics. Physics and Mathematics, it is argued, are growing apart; the inadequate treatment of approximations in general and localization in quantum mechanics in particular are seen as contributing factors. In the description of systems, the link between localization and lack of knowledge shows that quantum mechanics should reflect the domain of applicability. Restricting the class of states provides a means of achieving this goal. Localisation is then shown to have a mathematical expression in terms of compactness, which in tum is applied to yield a topological theory of bound and scattering states: Finally, the thesis questions the validity of "classical limits" and "quantisations" in intertheoretic reduction, and demonstrates that a widely accepted classical limit does not constitute a proof of reduction. It proposes a procedure for determining whether classical and quantum mechanics are weakly equivalent over a domain of applicability, and concludes that, in this restricted sense, classical mechanics reduces to quantum mechanics.

This diploma thesis is focused on use of polarization mode dispersion for measurement of temperature. It also deals with representation of polarization mode dispersion in Poincaré sphere and a mathematical description of polarization mode dispersion by using Stokes and Jones vectors. Here are described basic alternatives of settings, selected temperature relationships and dependence and relationship between coherency and polarization. The practical portion of the diploma thesis examines behavior of the temperature sensor at different temperatures for wavelength 1550 nm and 633 nm.