Made available in DSpace on 2014-06-11T19:35:38Z (GMT). No. of bitstreams: 0 Previous issue date: 2010-04-30Bitstream added on 2014-06-13T20:07:08Z : No. of bitstreams: 1 bertin_mcfg_dr_ift.pdf: 756466 bytes, checksum: ce1f33918fe3aabd6f7ec3c8bae37297 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Neste trabalho apresentaremos o formalismo de Hamilton-Jacobi para sistemas singulares em teorias de campos, com foco em teorias com derivadas de ordem superior. Iniciaremos com uma análise preliminar do cálculo variacional para esses sistemas, que envolve as condições para a extremização de uma integral fundamental múltipla e a análise dos teoremas de Noether. Buscaremos seguir este caminho na construção do formalismo de Hamilton- Jacobi em forma covariante, em que nos utilizaremos da clássica abordagem de Carathéodory adaptada a teorias de campos. No terceiro capítulo, mostraremos como o formalismo pode ser construído dada a escolha de uma dinâmica relativística específica e como esta escolha nos permite tratar de sistemas singulares de forma natural. No quarto capítulo abordaremos o problema das condições de integrabilidade, análise que garantirá um método autoconsistente de análise de vínculos. Nesta análise, seremos capazes de relacionar um conjunto de geradores a simetrias da integral fundamental e um segundo tipo a uma modificação da dinâmica com a introdução de parênteses generalizados. Nos dois últimos capítulos apresentaremos aplicações deste método / In this work we will develop the Hamilton-Jacobi formalism to singular and higher-order derivative field theories. We will begin with a preliminary approach to the variational problem concerning the search for extrema of a given fundamental integral, and the analysis of the Noether’s theorems. Next, we will present a covariant Hamilton-Jacobi theory using the classical approach of Carathéodory applied to field theories. In the third chapter we will show how this formalism can be derived given a choice of relativistic dynamics, and how this choice allows us to deal with singular systems. In the fourth chapter we will address the problem of integrability conditions. This analysis will be the basic tool for a self consistent constraint analysis. We will see that we can relate a certain set of generators to symmetries of the action, as well as a second type of generators to a modification of the dynamics by means of generalized brackets. The two last chapters will be used for applications

abstract: The study of wasp societies (family Vespidae) has played a central role in advancing our knowledge of why social life evolves and how it functions. This dissertation asks: How have scientists generated and evaluated new concepts and theories about social life and its evolution by investigating wasp societies? It addresses this question both from a narrative/historical and from a reflective/epistemological perspective. The historical narratives reconstruct the investigative pathways of the Italian entomologist Leo Pardi (1915-1990) and the British evolutionary biologist William D. Hamilton (1936-2000). The works of these two scientists represent respectively the beginning of our current understanding of immediate and evolutionary causes of social life. Chapter 1 shows how Pardi, in the 1940s, generated a conceptual framework to explain how wasp colonies function in terms of social and reproductive dominance. Chapter 2 shows how Hamilton, in the 1960s, attempted to evaluate his own theory of inclusive fitness by investigating social wasps. The epistemological reflections revolve around the idea of investigative framework for theory evaluation. Chapter 3 draws on the analysis of important studies on social wasps from the 1960s and 1970s and provides an account of theory evaluation in the form of an investigative framework. The framework shows how inferences from empirical data (bottom-up) and inferences from the theory (top-down) inform one another in the generation of hypotheses, predictions and statements about phenomena of social evolution. It provides an alternative to existing philosophical accounts of scientific inquiry and theory evaluation, which keep a strong, hierarchical distinction between inferences from the theory and inferences from the data. The historical narratives in this dissertation show that important scientists have advanced our knowledge of complex biological phenomena by constantly interweaving empirical, conceptual, and theoretical work. The epistemological reflections argue that we need holistic frameworks that account for how multiple scientific practices synergistically contribute to advance our knowledge of complex phenomena. Both narratives and reflections aim to inspire and inform future work in social evolution capitalizing on lessons learnt from the past. / Dissertation/Thesis / Doctoral Dissertation Biology 2016

A presente dissertação expõe o ambiente em que o Problema de Merton é construído e, baseando-se na bibliografia apresentada, constrói exemplos em softwares cujas especificidades podem colaborar na clareza da resolução. O software Matlab engloba as soluções numéricas, enquanto o software Maple é responsável pela solução de equações diferenciais ordinárias e parciais de forma simbólica. Apresenta-se modificações do Problema de Merton original como exercícios para melhor esclarecer os diferentes parâmetros abordados. Na seção final é apresentada a solução de viscosidade, uma alternativa quando a função valor não apresenta características desejáveis para a análise apresentada. / This dissertation explicit the environment which Merton’s problem is built, according to the presented bibliography, exemples are built in softwares whose specificity might help to clarify the solution. The Matlab software embraces numeric solutions, while Maple software is appropriate to solve ordinary and parcial differential equations in symbolic form. Some modifications are presented to Merton’s Problem as exercise to improve understanding on the variations adopted. On final section, viscosity solutions are presented as an alternative solution for when the value function does not possess the desirables properties that allow the analysis on focus.

Tese (doutorado)—Universidade de Brasília, Instituto de Física, 2013. / Submitted by Alaíde Gonçalves dos Santos (alaide@unb.br) on 2013-12-06T11:56:34Z No. of bitstreams: 1 2013_FabioFerreiraMonteiro.pdf: 2696614 bytes, checksum: 619da8ca760af24bd24b9970634dde0f (MD5) / Approved for entry into archive by Guimaraes Jacqueline(jacqueline.guimaraes@bce.unb.br) on 2014-08-04T13:11:41Z (GMT) No. of bitstreams: 1 2013_FabioFerreiraMonteiro.pdf: 2696614 bytes, checksum: 619da8ca760af24bd24b9970634dde0f (MD5) / Made available in DSpace on 2014-08-04T13:11:41Z (GMT). No. of bitstreams: 1 2013_FabioFerreiraMonteiro.pdf: 2696614 bytes, checksum: 619da8ca760af24bd24b9970634dde0f (MD5) / O trabalho contido nesta tese apresenta uma nova abordagem numérica computacional para sistemas hidrogenoides, baseada na teoria de Hamilton-Jacobi e nas propriedades de transformação entre os grupos O(3,1) e SU(2) em um espaço plano de Minkowski, cujo desenvolvimento, que parte de uma equação de onda tipo Dirac, porem numa representação bi-dimensional, permite a previsão de autovalores de energia de altíssima precisão, com funções de onda extremamente simples. A partir desta abordagem desenvolvemos o programa computacional DIRAC-LIKE que, no tratamento de sistemas hidrogenoides, se mostrou eficiente, elegante e simples, onde foi possível explorar e se beneficiar do método variacional, sem os desconfortos do chamado colapso variacional. Alem disso, algumas funções de onda geradas pelo programa DIRAC-LIKE foram testadas no calculo de secções de choque diferenciais envolvendo processos de espalhamento fotoelétrico, apresentando excelentes resultados. O sucesso do método para sistemas hidrogenoides sugeriu uma extensão para os sistemas helioides, cujo desenvolvimento já está em andamento. Uma versão preliminar deste método, com abordagem não relativística semelhante à de Hylleraas, e também apresentada neste trabalho e, a partir dela, desenvolvemos o programa computacional HELIUM TEST que oferece valores numéricos de energia para os estados fundamental e excitados, além de suas respectivas funções de onda, atendendo as premissas de simplicidade e razoável precisão. Alguns destes valores, incluindo alguns estados excitados, são apresentados e comentados neste trabalho. _______________________________________________________________________________________ ABSTRACT / The work contained within this thesis presents a new numerical approach for computing hydrogen-like systems, based on Hamilton-Jacobi theory and the transformation properties between O(3,1) and SU(2) groups in a Minkowski flat space, whose development, starting form a Dirac-like equation, but in a bi-dimensional representation, allows the prediction of high precision energy eigenvalues, with extremely simple wave functions. From this approach we have developed the DIRACLIKE program that, in the treatment of hydrogen-like systems, has proved to be efficient, elegant and simple, and where it was possible to explore the benefits of using the variational method, without the discomforts of the so-called variational collapse. Besides that, some wave functions generaded by the DIRAC-LIKE program were tested in the calculation of photoelectric effect differential cross sections, with excellent results. The success of the method for the hydrogen-like systems has suggested an extension to helium-like systems, whose development is already in progress. A preliminary version of this method in a non-relativistic approach, similar to that of Hylleraas, is also presented in this work and, based on it, we have developed the HELIUM TEST program for calculating numerical values of energy from ground and excited states, and their respective wave functions, taking into account the assumptions of simplicity and reasonable accuracy. Some of these values, including some excited states are presented and discussed in this work.

A presente dissertação expõe o ambiente em que o Problema de Merton é construído e, baseando-se na bibliografia apresentada, constrói exemplos em softwares cujas especificidades podem colaborar na clareza da resolução. O software Matlab engloba as soluções numéricas, enquanto o software Maple é responsável pela solução de equações diferenciais ordinárias e parciais de forma simbólica. Apresenta-se modificações do Problema de Merton original como exercícios para melhor esclarecer os diferentes parâmetros abordados. Na seção final é apresentada a solução de viscosidade, uma alternativa quando a função valor não apresenta características desejáveis para a análise apresentada. / This dissertation explicit the environment which Merton’s problem is built, according to the presented bibliography, exemples are built in softwares whose specificity might help to clarify the solution. The Matlab software embraces numeric solutions, while Maple software is appropriate to solve ordinary and parcial differential equations in symbolic form. Some modifications are presented to Merton’s Problem as exercise to improve understanding on the variations adopted. On final section, viscosity solutions are presented as an alternative solution for when the value function does not possess the desirables properties that allow the analysis on focus.

Les dimensions des satellites spatiaux tendent à croître fortement alors que le volume disponible dans la coiffe des lanceurs est limité. L'utilisation de structures déployables permet de résoudre cette contradiction. Afin de développer l'offre disponible, le département Recherche de Thales Alenia Space étudie les mètres rubans comme solution innovante de déploiement. La première structure envisagée est un télescope déployé par le déroulement de six mètres rubans assurant également le positionnement du miroir secondaire. D'autres structures déployables utilisant les propriétés des mètres rubans sont également en cours d'étude : mât, panneaux solaires, etc.Il convient alors de se doter d'outils de modélisation spécifiques pour modéliser les scénarios de déploiement et multiplier les configurations envisagées. Deux précédentes thèses ont conduit à l'élaboration de modèles énergétiques de poutre à section flexible, rendant compte du comportement plan des rubans ([Guinot2011]) puis de leur comportement tridimensionnel ([Picault2014]). Cette thèse présente différentes contributions autour de ces modèles de poutre à section flexible. Les hypothèses du modèle ont été améliorées. Le re-positionnement de la ligne de référence sur le barycentre des sections conduit à des résultats plus proches des scénarios physiques (apparition et disparition des plis sur le ruban). A ce jour, les hypothèses et les équations du modèle sont définitivement formalisées. Nous avons établi les équations locales 1D (équilibre, comportement) dans le cas des comportements tridimensionnels avec le souci de la plus grande généralité. Établir ensuite les équations dans des cas dérivés simplifiés (restriction aux comportements 2D, section faiblement courbée) nous a permis d'obtenir un certain nombre de solutions analytiques et les équations à implémenter dans l'outil métier.Nous avons développé sur le logiciel de continuation ManLab les premiers éléments d'un outil métier performant dédié à la modélisation des mètres rubans. Nous avons ainsi pu réaliser deux contributions principales :- Un outil généraliste, performant en temps de calcul, permettant d'étudier les systèmes différentiels 1D (BVP, Boundary Value Problems). Les équations locales des modèles de poutre à section flexible ont été implémentées dans cet outil, avec une discrétisation par interpolation polynomiale et collocation orthogonale.- Un élément fini spécifique pour les poutres à section flexible et son implémentation dans ManLab.Ces éléments ont permis de réaliser différentes simulations numériques conduisant à une meilleure compréhension du comportement des mètres rubans grâce aux diagrammes de bifurcation associés à plusieurs essais significatifs. / Dimensions of spatial satellites tend to grow bigger and bigger, whereas the volume in launchers remains very limited. Deployable structures must be used to meet this contradiction. To expand the offer of possible solutions, the Research Department of Thales Alenia Space is currently studying tape springs as an innovative deployment solution. The first structure to be considered is a telescope that is deployed by the uncoiling of six tape springs that also ensure the positioning of the secondary mirror. Other deployable structures that use the properties of tape springs are under investigation : mast, solar panels,...Specific modeling tools then appear compulsory to model deployment scenarios and multiply the tested configurations. Two previous PhD thesis lead to the development of energetic rod models with flexible cross-sections that account for planar ([Guinot2011])and three dimensional behavior of tape springs ([Picault2014]). This PhD thesis presents several contributions on these rod models with flexible cross-sections. The hypotheses of the model were improved. Re-positioning the reference rod line so that it passes through the sections' centroids leads to results that are closer to experimental scenarios (creation and disappearance of folds in the spring). The hypotheses and equations of the model are now definitively formalized.We have derived the 1D local equations in the three-dimensional behavior case in the most generalist way. Then, the derivation of the equations in simplified cases (restriction to 2D behavior, shallow cross-section) enabled us to obtain several analytic solutions and the equations to implement in the specific modeling tool.We have developed on the continuation software ManLab the first elements towards a home made, efficient modeling tool dedicated to the modeling of tape springs. Two main contributions can be listed :- A generalist tool, efficient in calculus times, to study 1D differential problems (BVP, Boundary Value Problems). The local equations of the rod models with flexible cross sections were implemented in this tool, with a discretization based on polynomial interpolation and orthogonal collocation.- A specific finite element for rods with flexible cross sections and its implementation in ManLab.These elements enabled us to perform several numerical simulations and have a better understanding of the behavior of tape springs thanks to full bifurcation diagrams obtained for significant tests.

In this dissertation, we present two research projects, namely finite-state mean-field games and the Hughes model for the motion of crowds. In the first part, we describe finite-state mean-field games and some applications to socio-economic sciences. Examples include paradigm shifts in the scientific community and the consumer choice behavior in a free market. The corresponding finite-state mean-field game models are hyperbolic systems of partial differential equations, for which we propose and validate a new numerical method. Next, we consider the dual formulation to two-state mean-field games, and we discuss numerical methods for these problems. We then depict different computational experiments, exhibiting a variety of behaviors, including shock formation, lack of invertibility, and monotonicity loss. We conclude the first part of this dissertation with an investigation of the shock structure for two-state problems. In the second part, we consider a model for the movement of crowds proposed by R. Hughes in [56] and describe a numerical approach to solve it. This model comprises a Fokker-Planck equation coupled with an Eikonal equation with Dirichlet or Neumann data. We first establish a priori estimates for the solutions. Next, we consider radial solutions, and we identify a shock formation mechanism. Subsequently, we illustrate the existence of congestion, the breakdown of the model, and the trend to the equilibrium. We also propose a new numerical method for the solution of Fokker-Planck equations and then to systems of PDEs composed by a Fokker-Planck equation and a potential type equation. Finally, we illustrate the use of the numerical method both to the Hughes model and mean-field games. We also depict cases such as the evacuation of a room and the movement of persons around Kaaba (Saudi Arabia).

The aim of this thesis is to study a class of left-invariant optimal control problems on the matrix Lie group SE(2). We classify, under detached feedback equivalence, all controllable (left-invariant) control affine systems on SE(2). This result produces six types of control affine systems on SE(2). Hence, we study six associated left-invariant optimal control problems on SE(2). A left-invariant optimal control problem consists of minimizing a cost functional over the trajectory-control pairs of a left-invariant control system subject to appropriate boundary conditions. Each control problem is lifted from SE(2) to T*SE(2) ≅ SE(2) x se (2)*and then reduced to a problem on se (2)*. The maximum principle is used to obtain the optimal control and Hamiltonian corresponding to the normal extremals. Then we derive the (reduced) extremal equations on se (2)*. These equations are explicitly integrated by trigonometric and Jacobi elliptic functions. Finally, we fully classify, under Lyapunov stability, the equilibrium states of the normal extremal equations for each of the six types under consideration.

Uruguay is a pioneer in the use of renewable sources of energy and can usually satisfy its total demand from renewable sources. Control and optimization of the system is complicated by half of the installed power - wind and solar sources - be- ing non-controllable with high uncertainty and variability. In this work we present a novel optimization technique for efficient use of the production facilities. The dy- namical system is stochastic, and we deal with its non-Markovian dynamics through a Lagrangian relaxation. Continuous-time optimal control and value function are found from the solution to a sequence of Hamilton-Jacobi-Bellman partial differential equations associated with the system. We introduce a monotone scheme to avoid spurious oscillations in the numerical solution and apply the technique to a number of examples taken from the Uruguayan grid. We use parallelization and change of variables to reduce the computational times. Finally, we study the usefulness of extra system storage capacity offered by batteries.

京都大学 / 0048 / 新制・課程博士 / 博士(農学) / 甲第22488号 / 農博第2392号 / 新制||農||1076(附属図書館) / 学位論文||R2||N5268(農学部図書室) / 京都大学大学院農学研究科地域環境科学専攻 / (主査)教授 藤原 正幸, 教授 村上 章, 准教授 宇波 耕一 / 学位規則第4条第1項該当 / Doctor of Agricultural Science / Kyoto University / DFAM