Made available in DSpace on 2016-04-28T14:16:34Z (GMT). No. of bitstreams: 1 Veranice Canato.pdf: 2119970 bytes, checksum: 0b3e2b259a68a1ec4980cdecd8d345a1 (MD5) Previous issue date: 2008-10-02 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / In the year of 1604, with the objective to produce a theory, that would explain the refraction of light of celestial bodies and solve the existing problems in the observation of solar eclipses through camera obscura, Johannes Kepler published Ad VItellionem Paralipomena, quibus Astronomiae pars Optica Traditvr. Paralipomena has been raising the attention of history of science researchers since the first decades of the twentieth-century, and its classification, as either a continuity or a break with the treatises of optics developed during the Middle Ages, has become a controversial theme. Different aspects in this debate lead to a comprehension of Kepler's work as an appreciation of several studies of optics, astronomy and natural magic available at the end of sixteenth- century. Several studies available in Kepler s times, which probably contributed for his solution of the problems with the camera obscura, are presented in this dissertation in an attempt to show that Kepler s elaboration of his camera obscura theory, presented in chapter second of Paralipomena, is a consequence of this appreciation / Com o objetivo de apresentar teorias capazes de explicar a refração da luz nos corpos celestes e de solucionar problemas nas observações de eclipses solares com câmaras escuras. Johannes Kepler (1571-1630) publicou, em 1604, o seu Ad VItellionem Paralipomena ,quibus Astronomiae pars Optica Traditvr. Esse livro vem despertando a atenção de pesquisadores em história da ciência desde as primeiras décadas do século XX e se constituiu como objeto de um polêmico debate em torno de sua classificação como uma continuidade ou uma ruptura com os tratados ópticos desenvolvidos no medievo. Os diferentes aspectos destacados nesse debate possibilitam uma compreensão do trabalho de Kepler como uma apreensão dos diversos estudos de óptica, de astronomia e de magia natural que circulavam no final do século XVI. Nesta dissertação, procuramos mostrar que a elaboração de sua teoria para a câmara escura, apresentada no segundo capítulo do Paralipomena, é uma conseqüência dessa apreensão. Para tal, procuramos analisar vários trabalhos que circulavam à época de Kepler e que possivelmente contribuíram para a sua solução dos problemas da câmara escura

Hamilton-Jacobi theory provides a powerful method for extracting the equations of motion out of some given systems in classical mechanics. On occasion it allows some systems to be solved by the method of separation of variables. If a system with n degrees of freedom has 2n - 1 constants of the motion that are polynomial in the momenta, then that system is called superintegrable. Such a system can usually be solved in multiple coordinate systems if the constants of the motion are quadratic in the momenta. All superintegrable two dimensional Hamiltonians of the form H = (p_x)sup2 + (p_y)sup2 + V(x,y), with constants that are quadratic in the momenta were classified by Kalnins et al [5], and the coordinate systems in which they separate were found. We discuss Hamilton-Jacobi theory and its development from a classical viewpoint, as well as superintegrability. We then proceed to use the theory to find equations of motion for some of the superintegrable Hamiltonians from Kalnins et al [5]. We also discuss some of the properties of the Poisson algebra of those systems, and examine the orbits.

Il est possible de concevoir un enseignement de la physique qui incorpore l'histoire de la physique sur un mode qui n'est ni anecdotique, ni autonome et qui peut être décliné à différents niveaux de la formation, des élèves de lycée aux enseignants à l'université. L'introduction du manuscrit porte sur une mise en perspective de la démarche proposée avec des recherches antérieures. Le manuscrit est composé de quatre parties. Dans la partie I, après avoir rappelé les objectifs qui ont prévalu à la réalisation du cédérom « Histoire des idées sur la lumière - de l'Antiquité au début du XXe siècle », qui aborde la lumière à travers une approche historique, expérimentale et philosophique, je propose une utilisation de ce cédérom pour l'enseignement de la diffraction par une approche historique (la disparition des franges intérieures dans l'ombre d'un fil). Dans la partie II, je précise l'enjeu que constitue l'utilisation de la figure géométrique de Newton (1684), accompagnée des coordonnées polaires et des vecteurs, pour mettre à la portée d'un large public l'un des grands succès de la pensée scientifique : la détermination des trajectoires elliptiques des planètes (sans utilisation du calcul différentiel). Dans cette partie, je reviens également sur le modèle d'équant de Kepler, souvent assimilé à un échec, alors qu'il peut ouvrir la voie, dans le cadre de la formation des enseignants, à une discussion renouvelée des dynamiques aristotélicienne et newtonienne. La partie III est une analyse historique de "La Dynamique de l'électron" de Henri Poincaré. Après avoir rappelé le point de vue général de Poincaré sur les sciences et leur enseignement, et avoir situé son travail dans la lignée de Lorentz et des connaissances des géomètres, je reviens sur quatre clés que nous avons proposées (avec Jean-Pierre Provost) pour comprendre la logique du Mémoire : l'utilisation de transformations de Lorentz actives, le rôle de l'action et de son invariance, l'origine de la condition de groupe pour éliminer les dilatations (à travers les lettres à Lorentz de mai 1905) et le rôle des modèles d'électron comme théorème d'existence de la nouvelle dynamique. Dans la quatrième et dernière partie, je donne un historique des travaux de Planck et d'Einstein sur les quanta, afin de comparer leurs approches (étude des dépendances énergétique ou volumique de l'entropie du corps noir) et de les replacer dans une perspective moderne où la notion de mode quantique est la notion fondamentale. Je reviens ensuite sur deux questions naturelles que posent les quanta d'Einstein de mars 1905 pour des étudiants abordant la relativité et le quantique : leur vitesse (à laquelle répond le second postulat de la relativité) et leur indépendance (assujettie au retour à loi de Wien de 1896).

Made available in DSpace on 2014-12-17T15:15:01Z (GMT). No. of bitstreams: 1 MariaLC_TESE.pdf: 10138137 bytes, checksum: 77bd9c3c6dc76faa3f4dc70c892af4b1 (MD5) Previous issue date: 2014-04-07 / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior / Stellar differential rotation is an important key to understand hydromagnetic stellar dynamos, instabilities, and transport processes in stellar interiors as well as for a better treatment of tides in close binary and star-planet systems. The space-borne high-precision photometry with MOST, CoRoT, and Kepler has provided large and homogeneous datasets. This allows, for the first time, the study of differential rotation statistically robust samples covering almost all stages of stellar evolution. In this sense, we introduce a method to measure a lower limit to the amplitude of surface differential rotation from high-precision evenly sampled photometric time series such as those obtained by space-borne telescopes. It is designed for application to main-sequence late-type stars whose optical flux modulation is dominated by starspots. An autocorrelation of the time series is used to select stars that allow an accurate determination of spot rotation periods. A simple two-spot model is applied together with a Bayesian Information Criterion to preliminarily select intervals of the time series showing evidence of differential rotation with starspots of almost constant area. Finally, the significance of the differential rotation detection and a measurement of its amplitude and uncertainty are obtained by an a posteriori Bayesian analysis based on a Monte Carlo Markov Chain (hereafter MCMC) approach. We apply our method to the Sun and eight other stars for which previous spot modelling has been performed to compare our results with previous ones. The selected stars are of spectral type F, G and K. Among the main results of this work, We find that autocorrelation is a simple method for selecting stars with a coherent rotational signal that is a prerequisite to a successful measurement of differential rotation through spot modelling. For a proper MCMC analysis, it is necessary to take into account the strong correlations among different parameters that exists in spot modelling. For the planethosting star Kepler-30, we derive a lower limit to the relative amplitude of the differential rotation. We confirm that the Sun as a star in the optical passband is not suitable for a measurement of the differential rotation owing to the rapid evolution of its photospheric active regions. In general, our method performs well in comparison with more sophisticated procedures used until now in the study of stellar differential rotation / A rota??o diferencial superficial ? um importante par?metro para a compreens?o do d?namo hidromagn?tico estelar, instabilidades e processos de transportes no interior estelar, bem como fornece subs?dios para um melhor tratamento das mar?s em bin?rias pr?ximas e sistemas estrela-planeta. As miss?es espaciais MOST, CoRoT e Kepler t?m fornecido uma grande e homog?nea quantidade de dados fotom?tricos. O que permite, pela primeira vez, o estudo da rota??o diferencial em amostras estatisticamente robustas cobrindo quase todos os est?gios da evolu??o estelar. Nesta tese, n?s desenvolvemos e apresentamos um m?todo para medir o limite inferior para a amplitude da rota??o diferencial a partir de s?ries fotom?tricas igualmente espa?adas, tais como aquelas obtidas pelas miss?es espaciais supracitadas. O modelo foi concebido para ser aplicado em estrelas do tipo solar cuja modula??o ?tica ? dominada pelo efeito das manchas estelares. As estrelas s?o selecionadas a partir de uma autocorrela??o das s?ries temporais, o que permite uma determina??o precisa dos per?odos de rota??o das manchas. Um modelo simples de duas manchas ? aplicado juntamente com crit?rios de informa??o bayesiana para selecionar, preliminarmente, os intervalos das s?ries temporais que mostram evid?ncias de rota??o diferencial com manchas de ?rea quase constante. A signific?ncia da rota??o diferencial detectada e as medidas de sua amplitude e incertezas s?o obtidas por an?lise a posteriori bayesiana, em uma aproxima??o Monte Carlo via cadeias de Markov (MCMC). Aplicamos nosso m?todo para o Sol e outras oito estrelas para as quais a modelagem de manchas foi anteriormente realizada. As estrelas selecionadas s?o de tipo espectral F, G e K. Obtivemos ent?o a rota??o diferencial e comparamos os resultados obtidos pelo nosso m?todo com aqueles j? conhecidos na literatura. Entre os principais resultados deste trabalho, encontramos que autocorrela??o ? um m?todo simples e eficaz para sele??o de estrelas com um sinal rotacional coerente, pr?-requisito para uma medida de rota??o diferencial por meio de modelagem de manchas. Para uma an?lise adequada de MCMC ? necess?rio levar em considera??o a forte correla??o entre diferentes par?metros existentes na modelagem de manchas. Para a estrela hospedeira de planeta Kepler-30, encontramos um baixo limite para uma amplitude relativa de rota??o diferencial. Tamb?m, confirmamos ainda que o nosso modelo n?o ? adequado para medir a rota??o diferencial do Sol como uma estrela, na banda ?tica, devido ? r?pida evolu??o de suas regi?es fotosf?ricas ativas. Em geral, o nosso modelo funciona bem em compara??o com os mais sofisticados procedimentos at? agora utilizados no estudo da rota??o diferencial estelar

Mysterium Cosmographicum is a musical chronicle of an astronomy treatise by the German astronomer Johannes Kepler (1571-1630). Kepler's Mysterium cosmographicum (Tubingen, 1596), or "Secret of the Universe," was a means by which he justified the existence of the six planets discovered during his lifetime. Kepler, through flawless a priori reasoning, goes to great lengths to explain that the reason there are six and only six planets (Mercury, Venus, Earth, Mars, Jupiter, and Saturn) is because God had placed one of the five regular solids (tetrahedron, cube, octa-, dodeca-, and icosahedron) around each orbiting body. Needless to say, the publication was not very successful, nor did it gain much comment from Kepler's peers, Galileo Galilei (1564-1642) and Tycho Brahe (1546-1601). But hidden within the Mysterium cosmographicum. almost like a new planet waiting to be discovered, is one of Kepler's three laws of planetary motion, a law that held true for planets discovered long after Kepler's life-time. Mysterium Cosmographicum is a monologue with music in three parts for orchestra, narrator/actor, and computer music on tape. All musical data structures ape generated via an interactive Pascal computer program that computes latitudinal and longitudinal coordinates For each of the nine planets as seen From a Fixed point on Earth For any given time Frame. These coordinates are then mapped onto selected musical parameters as determined by the composer. Whenever Kepler reads From his treatise or From a lecture or correspondence, the monologue is supported by orchestral planetary data generated From the exact place, date, and time oF the treatise, lecture, or correspondence. To the best oF my knowledge, Mysterium Cosmographicum is the First composition ever written that employs planetary data as a supporting chronology to action and monologue.

No description available.

In this thesis, central configurations, regularization of Simultaneous binary collision, linear stability of Kepler orbits, and index theory for symplectic path are studied. The history of their study is summarized in section 1. Section 2 deals with the following problem: given a collinear configuration of 4 bodies, under what conditions is it possible to choose positive masses which make it central. It is always possible to choose three positive masses such that the given three positions with the masses form a central configuration. However, for an arbitrary configuration of 4 bodies, it is not always possible to find positive masses forming a central configuration. An expression of four masses is established depending on the position x and the center of mass u, which gives a central configuration in the collinear four body problem. Specifically it is proved that there is a compact region in which no central configuration is possible for positive masses. Conversely, for any configuration in the complement of the compact region, it is always possible to choose positive masses to make the configuration central. The singularities of simultaneous binary collisions in collinear four-body problem is regularized by explicitly constructing new coordinates and time transformation in section 3. The motion in the new coordinates and time scale across simultaneous binary collision is at least C^2. Furthermore, the behavior of the motion closing, across and after the simultaneous binary collision, is also studied. Many different types of periodic solutions involving single binary collisions and simultaneous binary collisions are constructed. In section 4, the linear stability is studied for the Kepler orbits of the rhombus four-body problem. We show that, for given four proper masses, there exists a family of periodic solutions for which each body with the proper mass is at the vertex of a rhombus and travels along an elliptic Kepler orbit. Instead of studying the 8 degrees of freedom Hamilton system for planar four-body problem, we reduce this number by means of some symmetry to derive a two degrees of freedom system which then can be used to determine the linear instability of the periodic solutions. After making a clever change of coordinates, a two dimensional ordinary differential equation system is obtained, which governs the linear instability of the periodic solutions. The system is surprisingly simple and depends only on the length of the sides of the rhombus and the eccentricity e of the Kepler orbit. In section 5, index theory for symplectic paths introduced by Y.Long is applied to study the stability of a periodic solution x for a Hamiltonian system. We establish a necessary and sufficient condition for stability of the periodic solution x in two and four dimension.

Thomas Hobbes est sans doute mieux connu comme philosophe politique que comme homme de science et ses longues querelles avec John Wallis en mathématiques et Robert Boyle en physique n’ont guère encouragé les historiens des sciences à prêter attention à son œuvre scientifique. Pourtant, Hobbes conçut la philosophie comme une science et se considérait comme le fondateur non seulement d’une science nouvelle : la philosophie civile, mais aussi de la science de l’optique - récemment renouvelée à la faveur de la découverte du télescope - et même des mathématiques. Mais à quoi Hobbes pense-t-il quand il parle de science ? Aux mathématiques qu’il admire tant ? A la philosophie naturelle de Galilée ? Ou à la médecine de Harvey ? En quel sens la philosophie civile est-elle une science et quel est le statut des mathématiques ? Telles sont les questions que nous abordons à partir d’une analyse du De Corpore et des dix premiers chapitres du De Homine traduits du latin. L’interprétation proposée ici consiste à réaffirmer l’unité du système des Éléments de la philosophie et à souligner la dimension matérialiste et réaliste de la science hobbesienne. Bien que Noel Malcolm ait définitivement établi que Hobbes n’est pas l’auteur du Short Tract on first principles, nous montrons que le tournant scientifique de Hobbes est profondément marqué par son intérêt pour l’optique qu’il renouvela sur la base d’une ontologie matérialiste et des principes du mécanisme hérités de Galilée. / Thomas Hobbes is perhaps best known as a political philosopher than as a scientist and his too long quarrels with John Wallis in mathematics and Robert Boyle in physics did little to encourage historians of science to pay attention to his scientific work. Yet Hobbes conceived of philosophy as a science and considered himself the founder not only of a new science: civil philosophy, but also the science of optics - recently renewed thanks to the discovery of the telescope - even mathematics. But what Hobbes has in mind when he talks about science? Mathematics he so admires? Galileo’s natural philosophy? Or Harvey’s medicine? In what sense civil philosophy is a science and what is the status of mathematics? These are the issues we discuss from an analysis of De Corpore and the first ten chapters of De Homine translated from Latin. The interpretation proposed here is to underline the unity of the system of the Elements of philosophy and emphasize the materialistic and realistic nature of Hobbesian science. Although Noel Malcolm has definitively established that Hobbes is not the author of Short Tract on First Principles, we show that Hobbes’s shift to science was deeply marked by his interest in the science of optics he renewed on the basis of a materialist ontology and principles inherited from Galilee mechanism.

(in English): The thesis deals with the topic of social criticism across the genre of detective stories from the 1960s in Sweden. The theoretical part describes how social criticism is constituted in this genre and how it contributes to its specificity. Based on a selected cross-section of five works, it presents not only the various topics which these authors work with, but also the changes in this critique over time. The analyzed works are: The Man on the Balcony (1968) by Sjöwall and Wahlöö, who establish this genre with clear social criticism, the first part of the trilogy Millennium The Girl with the Dragon Tattoo (2008) by Stieg Larsson, who, according to many experts, successfully completes this era, The Stone Cutter (2008) by Camilla Läckberg, The Sandman (2012) by Lars Kepler and Those Who Failed (2015) by the duo Hjorth and Rosenfeldt, that is the works by three contemporary authors of this genre.

[ES] Esta tesis trata sobre la integración numérica de sistemas hamiltonianos con potenciales explícitamente dependientes del tiempo. Los problemas de este tipo son comunes en la física matemática, porque provienen de la mecánica cuántica, clásica y celestial. La meta de la tesis es construir integradores para unos problemas relevantes no autónomos: la ecuación de Schrödinger, que es el fundamento de la mecánica cuántica; las ecuaciones de Hill y de onda, que describen sistemas oscilatorios; el problema de Kepler con la masa variante en el tiempo. El Capítulo 1 describe la motivación y los objetivos de la obra en el contexto histórico de la integración numérica. En el Capítulo 2 se introducen los conceptos esenciales y unas herramientas fundamentales utilizadas a lo largo de la tesis. El diseño de los integradores propuestos se basa en los métodos de composición y escisión y en el desarrollo de Magnus. En el Capítulo 3 se describe el primero. Su idea principal consta de una recombinación de unos integradores sencillos para obtener la solución del problema. El concepto importante de las condiciones de orden se describe en ese capítulo. En el Capítulo 4 se hace un resumen de las álgebras de Lie y del desarrollo de Magnus que son las herramientas algebraicas que permiten expresar la solución de ecuaciones diferenciales dependientes del tiempo. La ecuación lineal de Schrödinger con potencial dependiente del tiempo está examinada en el Capítulo 5. Dado su estructura particular, nuevos métodos casi sin conmutadores, basados en el desarrollo de Magnus, son construidos. Su eficiencia es demostrada en unos experimentos numéricos con el modelo de Walker-Preston de una molécula dentro de un campo electromagnético. En el Capítulo 6, se diseñan los métodos de Magnus-escisión para las ecuaciones de onda y de Hill. Su eficiencia está demostrada en los experimentos numéricos con varios sistemas oscilatorios: con la ecuación de Mathieu, la ec. de Hill matricial, las ecuaciones de onda y de Klein-Gordon-Fock. El Capítulo 7 explica cómo el enfoque algebraico y el desarrollo de Magnus pueden generalizarse a los problemas no lineales. El ejemplo utilizado es el problema de Kepler con masa decreciente. El Capítulo 8 concluye la tesis, reseña los resultados y traza las posibles direcciones de la investigación futura. / [CAT] Aquesta tesi tracta de la integració numèrica de sistemes hamiltonians amb potencials explícitament dependents del temps. Els problemes d'aquest tipus són comuns en la física matemàtica, perquè provenen de la mecànica quàntica, clàssica i celest. L'objectiu de la tesi és construir integradors per a uns problemes rellevants no autònoms: l'equació de Schrödinger, que és el fonament de la mecànica quàntica; les equacions de Hill i d'ona, que descriuen sistemes oscil·latoris; el problema de Kepler amb la massa variant en el temps. El Capítol 1 descriu la motivació i els objectius de l'obra en el context històric de la integració numèrica. En Capítol 2 s'introdueixen els conceptes essencials i unes ferramentes fonamentals utilitzades al llarg de la tesi. El disseny dels integradors proposats es basa en els mètodes de composició i escissió i en el desenvolupament de Magnus. En el Capítol 3, es descriu el primer. La seua idea principal consta d'una recombinació d'uns integradors senzills per a obtenir la solució del problema. El concepte important de les condicions d'orde es descriu en eixe capítol. El Capítol 4 fa un resum de les àlgebres de Lie i del desenvolupament de Magnus que són les ferramentes algebraiques que permeten expressar la solució d'equacions diferencials dependents del temps. L'equació lineal de Schrödinger amb potencial dependent del temps està examinada en el Capítol 5. Donat la seua estructura particular, nous mètodes quasi sense commutadors, basats en el desenvolupament de Magnus, són construïts. La seua eficiència és demostrada en uns experiments numèrics amb el model de Walker-Preston d'una molècula dins d'un camp electromagnètic. En el Capítol 6 es dissenyen els mètodes de Magnus-escissió per a les equacions d'onda i de Hill. El seu rendiment està demostrat en els experiments numèrics amb diversos sistemes oscil·latoris: amb l'equació de Mathieu, l'ec. de Hill matricial, les equacions d'onda i de Klein-Gordon-Fock. El Capítol 7 explica com l'enfocament algebraic i el desenvolupament de Magnus poden generalitzar-se als problemes no lineals. L'exemple utilitzat és el problema de Kepler amb massa decreixent. El Capítol 8 conclou la tesi, ressenya els resultats i traça les possibles direccions de la investigació futura. / [EN] The present thesis addresses the numerical integration of Hamiltonian systems with explicitly time-dependent potentials. These problems are common in mathematical physics because they come from quantum, classical and celestial mechanics. The goal of the thesis is to construct integrators for several import ant non-autonomous problems: the Schrödinger equation, which is the cornerstone of quantum mechanics; the Hill and the wave equations, that describe oscillating systems; the Kepler problem with time-variant mass. Chapter 1 describes the motivation and the aims of the work in the historical context of numerical integration. In Chapter 2 essential concepts and some fundamental tools used throughout the thesis are introduced. The design of the proposed integrators is based on the composition and splitting methods and the Magnus expansion. In Chapter 3, the former is described. Their main idea is to recombine some simpler integrators to obtain the solution. The salient concept of order conditions is described in that chapter. Chapter 4 summarises Lie algebras and the Magnus expansion ¿ algebraic tools that help to express the solution of time-dependent differential equations. The linear Schrödinger equation with time-dependent potential is considered in Chapter 5. Given its particular structure, new, Magnus-based quasi-commutator-free integrators are build. Their efficiency is shown in numerical experiments with the Walker-Preston model of a molecule in an electromagnetic field. In Chapter 6, Magnus-splitting methods for the wave and the Hill equations are designed. Their performance is demonstrated in numerical experiments with various oscillatory systems: the Mathieu equation, the matrix Hill eq., the wave and the Klein-Gordon-Fock eq. Chapter 7 shows how the algebraic approach and the Magnus expansion can be generalised to non-linear problems. The example used is the Kepler problem with decreasing mass. The thesis is concluded by Chapter 8, in which the results are reviewed and possible directions of future work are outlined. / Kopylov, N. (2019). Magnus-based geometric integrators for dynamical systems with time-dependent potentials [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/118798 / TESIS