Development of a battery of tests for a numerical optimal control library

One of the two objectives of this bachelor thesis is the development of a set of problems to be solved with an optimal control numerical method and evaluate the obtained results. The problems to be solved have been selected from the literature, which from now on are going to be named ’canonical problems’. These problems are used by authors in the field of optimal control in order to compare their results between them and assess the strength of the optimization method they are using. The second objective of this thesis is the development of four problems, related with climb, cruise and descend performance of a general twin turbofan airliner, applying the numerical method in question, and evaluating the results. This is then a manner to apply optimal control into more common problems in the aerospace field.Ingeniería Aeroespacia

Dynamics of water entry and descent along a flexible beam

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2009.Cataloged from PDF version of thesis.Includes bibliographical references (p. 117-123).This thesis has two parts. In Part I, we present the results of a combined experimental and theoretical investigation of the vertical impact of spheres on a water surface. Particular attention is given to characterizing the shape of the resulting air cavity in the limit where cavity collapse is strongly influenced by surface tension. A parameter study reveals the dependence of the cavity structure on the governing dimensionless groups. A theoretical description is developed to describe the evolution of the cavity shape and yields an analytical solution for the pinch-off time and depth. We also examine low-density spheres that decelerate substantially following impact, and characterize the deceleration rate and resulting change in behavior of the associated water-entry cavities. Theoretical predictions compare favorably with our experimental observations. Finally, we present a theoretical model for the evolution of the splash curtain formed at high speeds, and couple it to the underlying cavity dynamics. In Part II, we present the results of a combined experimental and theoretical investigation of the motion of a sphere on an inclined flexible beam. A theoretical model based on Euler-Bernoulli beam theory is developed to describe the dynamics, and in the limit where the beam reacts instantaneously to the loading, we obtain exact solutions for the sphere trajectory and descent time. For the case of an initially horizontal beam, we calculate the period of the resulting oscillations. Theoretical predictions compare favorably with our experimental observations in this quasi-static regime. Inertial effects are also addressed.(cont.) The time taken for descent along an elastic beam, the elastochrone, is shown to always exceed the classical brachistochrone, the shortest time between two points in a gravitational field.by Jeffrey Michael Aristoff.Ph.D

Steps towards "Quantum Gravity" and the practice of science: will the merger of mathematics and physics work?

The author recalls general tendencies of the "mathematization" of the sciences and derives challenges and tentative obstructions for a successful merger of mathematics and physics on fancied steps towards "Quantum Gravity". This is an edited version of the author's opening words to an international workshop "Quantum Gravity: An Assessment", Denmark, May 17-18, 2008. It followed immediately after the Quantum Gravity Summer School 2008, see http://QuantumGravity.ruc.dk/Comment: To appear as part of a Springer Lecture Notes in Physics publication: "Quantum Gravity - New Paths towards Unification" (B. Booss-Bavnbek, G. Esposito, M. Lesch, Eds.