[pt] Nesta dissertação iremos analisar de forma pormenorizada os conceitos de espaço, tempo e movimento absolutos de Newton, assim como apresentar uma descrição do método utilizado na elaboração da Física newtoniana, mais precisamente, na confecção dos Princípios Matemáticos de Filosofia Natural. Argumentaremos também que esses conceitos de espaço, tempo e movimento absolutos teriam como origem a controvérsia entre cartesianos e newtonianos sobre os fundamentos da Filosofia Natural e, finalmente, mostraremos que esses conceitos vieram a servir de base para a definição newtoniana de forças e leis do movimento. / [en] In this dissertation we will analyze in detail Newton´s concepts of absolute space, time and movement, as well as present a description of the method used to elaborate Newton´s Physics - more precisely, to create the Mathematical Principles of Natural Philosophy. We will also argue that those concepts of absolute space, time and movement would originate with the controversy between Cartesians and Newtonians about the foundations of Natural Philosophy. We will finally show that those concepts happened to serve as the basis for Newton´s definition of forces and laws of movement.

A partir des années 1730 les succès des prévisions de la gravitation universelle assurent en France la pénétration de l’approche newtonienne de la physique, alors que les concepts cartésiens sont encore bien ancrés dans les esprits. Dans la seconde moitié du Siècle des Lumières, Aimé-Henri Paulian, professeur au collège des jésuites d’Avignon, décide de publier des ouvrages de physique pour un public d’amateurs et d’étudiants. Dans l’esprit du temps, il met en avant la physique de Newton dans un Dictionnaire de physique portatif (1758) puis dans un Dictionnaire de physique (1761) dont les nombreuses éditions durant près de trente ans indiquent le grand succès. Mais, dans un ouvrage plus personnel, il présente une physique impertinente dont on ne peut nier l’originalité : une physique «Newto-Cartésienne» - le Traité de paix entre Descartes et Newton (1763) - issu de son interprétation des physiques de Descartes et de Newton. La comparaison entre le Traité d’optique de Newton et la lecture qu’en fait Paulian révèle son infidélité. L’étude d’articles du Dictionnaire de physique sur la lumière et ses différents effets précise les conceptions souvent masquées de notre auteur. En fait, avec Paulian, l’optique newtonienne est remaniée pour le plus grand profit de sa physique "Newto-Cartésienne". / From the 1730s, successes of universal gravity expectations ensured the spreading of the Newtonian approach of physics in France, while Cartesian concepts were still well established. In the second half of the Age of Enlightenment, Aimé-Henri Paulian, ateacher of the Jesuit College in Avignon, decided to publish works of physics intended for amateurs and students. In line with his time, he highlighted Newton’s physics in the book Dictionnaire de physique portatif (1758) and then in Dictionnaire de physique (1761), whose numerous editions that followed during nearly thirty years point out the great success. However, in a more personalwork, he presented an irrelevant physics, the originality of which cannot be denied: a «Newto-Cartesian» physics – Traité de paix entre Descartes et Newton (1763) – which arose from his interpretation of Descartes’ and Newton’s physics. The comparison between Newton’s Traité d’optique and Paulian’s interpretation reveals his lack of accuracy. The study of articles from the Dictionnaire de physique about light and its different effects clarifies Paulian’s ideas, which are often concealed. Indeed, with Paulian, Newtonian optics is revised for the benefit of his own «Newto-Cartesian» physics.

No description available.

Les méthodes plus avancées d'optimisation avec ou sans contraintes nécessitent le calcul des dérivées de la fonction. En ce sens, la différentiation automatique est devenue un outil primordial. Malgré le fait qu'il soit omniprésent, cet outil est encore en développement et en recherche. Il ne présente pas les inconvénients classiques des méthodes habituelles de dérivation mais reste complexe à utiliser. Ce travail consiste à utiliser un outil de différentiation permettant de calculer des dérivées d'ordres supérieurs afin d'obtenir des directions améliorées. Nous définirons d'abord de manière générale un type d'algorithme d'optimisation à l'aide des directions suffisamment descendantes. Leurs caractéristiques seront analysées pour modifier des méthodes de type Newton afin d'avoir une meilleure fiabilité de convergence. Nous étudierons les opérations critiques et l'ordre du coût de ces méthodes. Dans une deuxième partie, nous verrons les calculs d'algèbre linéaire requis pour nos algorithmes. Ensuite, nous présenterons le fonctionnement de la différentiation automatique et en quoi c'en est un outil indispensable à ce genre de méthode. Puis, nous expliquerons pourquoi nous avons choisi l'outil Tapenade pour la différentiation automatique et la librairie de Moré, Garbow, Hillstrom pour la collection de fonctions tests. Enfin, nous comparerons les méthodes de type Newton.

We use the social force model to study the behaviour of two crowds of pedestrians in a bi-directional flow. There are two main goals of the project. The first goal is to study the effects of perception anisotropy on lane formation of the two crowds. The perception anisotropy models the fact that people actually do not perceive their surroundings equally well in all directions, i.e they have a field of vision. The second goal is to develop pedestrian viscosity indices to characterize the motion of the crowds. Our concepts of viscosity indices estimate how fluid the motion of the crowds are. We develop two viscosity indices. A lane viscosity index which gives information of the flow on large timescales, and a space-dependent viscosity index which can pinpoint where in space the motion is less fluid. Our results indicate that there is a small correlation between the perception anisotropy and the lane formation of the two crowds. The two viscosity indices work as intended but more refinement is needed to cope with simultaneous space-time changes.

published_or_final_version / abstract / Mathematics / Master / Master of Philosophy

In the generalized Nash equilibrium problem not only the cost function of a player depends on the rival players' decisions, but also his constraints. This thesis presents different iterative methods for the numerical computation of a generalized Nash equilibrium, some of them globally, others locally superlinearly convergent. These methods are based on either reformulations of the generalized Nash equilibrium problem as an optimization problem, or on a fixed point formulation. The key tool for these reformulations is the Nikaido-Isoda function. Numerical results for various problem from the literature are given. / Das verallgemeinerte Nash-Gleichgewichtsproblem ist ein Lösungskonzept für Spiele, in denen neben der Kostenfunktion eines Spielers auch dessen Strategiemenge von den Entscheidungen der anderen Spieler abhängt. In dieser Arbeit werden global konvergente und lokal superlinear konvergente Verfahren zur numerischen Berechnung eines verallgemeinerten Nash-Gleichgewichts vorgestellt. Die Verfahren basieren entweder auf einer Umformulierung des verallgemeinerten Nash-Gleichgewichtsproblems als Optimierungsproblem oder als Fixpunktproblem. Für diese Umformulierungen wird die Nikaido-Isoda Funktion verwendet. Es werden numerische Ergebenisse für einige Probleme aus der Literatur widergegeben.

An investigation of transforming people' lives regarding their achievements into design processes of making textilesCase studies: Isaac Newton and Andy Warhol / Program: Master Programme in Fashion and Textile Design

One of the most fundamental problems in classical general relativity is the measure of e↵ective mass of a pure gravitational field. The principle of equivalence prohibits a purely local measure of this mass. This thesis critically examines the most recent quasi-local measure by Wang and Yau for a maximally rotating black hole spacetime. In particular, it examines a family of spacelike 2-surfaces with constant radii in Boyer-Lindquist coordinates. There exists a critical radius r* below which, the Wang and Yau quasi-local energy has yet to be explored. In this region, the results of this thesis indicate that the Wang and Yau quasi-local energy yields complex values and is essentially equivalent to the previously defined Brown and York quasi-local energy. However, an application of their quasi-local mass is suggested in a dynamical setting, which can potentially give new and meaningful measures. In supporting this thesis, the development of a novel adiabatic isometric mapping algorithm is included. Its purpose is to provide the isometric embedding of convex 2-surfaces with spherical topology into Euclidean 3-space necessary for completing the calculation of quasilocal energy in numerical relativity codes. The innovation of this algorithm is the guided adiabatic pull- back routine. This uses Ricci flow and Newtons method to give isometric embeddings of piecewise simplicial 2-manifolds, which allows the algorithm to provide accuracy of the edge lengths up to a user set tolerance. / Includes bibliography. / Dissertation (Ph.D.)--Florida Atlantic University, 2017. / FAU Electronic Theses and Dissertations Collection

Este trabalho tem por objetivo estudar e analisar a influência do parâmetro de barreira e de seu fator de correção no processo de convergência dos métodos de pontos interiores primal-dual, primal-dual barreira modificada e primal-dual barreira modificada com as técnicas preditor-corretor e Newton composto. A grande motivação para o desenvolvimento desta pesquisa está relacionada com a busca de métodos eficientes para resolver problemas de otimização de programação não-linear, existentes na área de engenharia elétrica mais especificamente na operação de sistemas elétricos de potência. Esses métodos foram aplicados a um problema de programação não-linear e aos sistemas elétricos de três e de trinta barras para analisar a sensibilidade em relação ao parâmetro de barreira e ao seu fator de correção. / This work has for objective to study and to analyze the influence of the barrier parameter and its correction factor in the convergence process of the methods primal-dual interior point, primal-dual modified barrier and primal-dual barrier modified with the techniques predictor-corrector and composed Newton. The great motivation for the development of this research is related with the search of efficient methods to solve nonlinear programming optimization problems, existent in the area of electric engineering more specifically in the operation of power systems. Those methods were applied to a nonlinear programming problem and the electric systems of three and thirty buses to analyze the sensibility in relation to the barrier parameter and its correction factor.