Gauge transformations in the Lagrangian and Hamiltonian formalisms of generally covariant theories

We study spacetime diffeomorphisms in Hamiltonian and Lagrangian formalisms of generally covariant systems. We show that the gauge group for such a system is characterized by having generators which are projectable under the Legendre map. The gauge group is found to be much larger than the original group of spacetime diffeomorphisms, since its generators must depend on the lapse function and shift vector of the spacetime metric in a given coordinate patch. Our results are generalizations of earlier results by Salisbury and Sundermeyer. They arise in a natural way from using the requirement of equivalence between Lagrangian and Hamiltonian formulations of the system, and they are new in that the symmetries are realized on the full set of phase space variables. The generators are displayed explicitly and are applied to the relativistic string and to general relativity.Comment: 12 pages, no figures; REVTeX; uses multicol,fancyheadings,eqsecnum; to appear in Phys. Rev.

Noether's theorem and gauge transformations. Application to the bosonic string and CP(2,n-1) model

New results on the theory of constrained systems are applied to characterize the generators of Noethers symmetry transformations. As a byproduct, an algorithm to construct gauge transformations in Hamiltonian formalism is derived. This is illustrated with two relevant examples

Sistemes d’adquisició d’imatges aèries

Es tracta de dissenyar un sistema per realitzar la gestió de l’adquisició d’imatges des d’una càmera embarcada en un UAV. Per un costat el sistema ha de poder identificar amb un cert grau de precisió la posició i orientació de la càmera en el moment d’adquirir la imatge; i per un altre la imatge s’ha de codificar en algun format digital sense pèrdua d’informació pel seu posterior processament. El sistema d’adquisició es realitzarà amb una càmera PAL mentre que per identificar la posició i orientació s’utilitzarà una Unitat de Mesura Inercial (IMU). Utilitzant una placa FPGA de la Xilinx (la XUPV2P) primer s’estudien els dos elements per separat i es creen unes aplicacions individuals, llavors, finalment, s’integren per formar el sistema final. El sistema final es crea en dues versions diferents, una utilitzant un Sistema Operatiu GNU/Linux encastat (embedded) i l’altre sense. Aquest SO encastat es construeix directament a partir de les fonts del kernel 2.6

Optimization of electrolytic anodization of Ti-6Al-7Nb surfaces

Treballs Finals de Grau d'Enginyeria Biomèdica. Facultat de Medicina i Ciències de la Salut. Universitat de Barcelona. Curs: 2021-2022. Director: Javier Fernández González. Tutora: Raisha Lorena García Cadme.Increased life expectancy leads to the increasing use of metallic prostheses. Titanium and its alloys are the most widely used materials for metallic prostheses thanks to their biocompatibility, but further work still necessary to improve bioactivity and reduce osseointegration problems. Developing nanostructured titanium dioxide (TiO2) coatings increases the biocompatibility of titanium prostheses. Using the electrolytic anodizing process, nanostructures can be achieved easily and economically. This project aims to optimize the voltage and anodizing time conditions to obtain titanium dioxide nanotubes on the surface of Ti-6Al-7Nb alloy, as well as to propose ideas for industrial implementation of the project. To this purpose, a market study, a project implementation plan and a technical and economic feasibility analysis were carried out. An electron microscope image processing method and a rigorous statistical analysis have been studied to obtain an average pore diameter quantify the effect of the studied variables. Potentials of 15, 30 and 60 volts and anodizing times of 15 and 30 minutes were studied. The effect of the concentration of fluoride ions and the type of cathode used in anodizing has also been studied. The optimum conditions for the smallest pore size we have found are anodizing at 15V and 15 minutes, with a grid cathode. With these conditions, an average pore diameter of 0,48 ± 0,05 μm was obtained