Invariant manifolds and transport in a Sun-perturbed Earth-Moon system

[eng] This dissertation is devoted to the analysis of the motion of small bodies, like asteroids, in the neighbourhood of the Earth-Moon system from a celestial mechanics approach. This is an extensive area of research where probably, the most extended simplified mathematical model is the well-known autonomous Hamiltonian system the Restricted Three-Body Problem (RTBP). Many modifications to this model have been proposed, looking for a more accurate description of the system. One of the simplest ways of introducing additional physical effects is through time-periodic perturbations, such that such that the new non-autonomous system is close to the autonomous one, and it has many periodic or quasi-periodic solutions. If these solutions are hyperbolic, they have stable/unstable invariant manifolds, such that stable manifolds approach the quasi-periodic solutions forward in time, meanwhile unstable manifolds do it backward in time, constituting the skeleton for the dynamical transport phenomena we are interested in. Notice that one dimension can be reduced by defining a suitable temporal Poincar´e map. Therefore, our aim is to compute the quasi-periodic solutions and their manifolds in this map. Most of the effort of this dissertation is addressed to the Bicircular Problem (BCP), in which the Earth and Moon are treated as the primaries in the RTBP and the gravitational field of the Sun is introduced as a time-periodic forcing of the RTBP. In particular, we have extensively analysed the horizontal family of two dimensional quasi-periodic solutions in the neighbourhood of the collinear unstable equilibrium point L3. We found that diverse trajectories connecting the Earth, the Moon and the outside Earth-Moon system are governed by L3 dynamics. Big attention is paid to the trajectories coming from the Moon towards the Earth, since they may give an insight of the travel that lunar meteorites perform before landing in our planet. These results have been translated and compared with those of a realistic model based on JPL (Jet Propulsion Laboratory) ephemeris, showing a good agreement between the results obtained. We also have proposed and carried out a strategy for capturing a Near Earth Asteroid (NEA) using the stable invariant manifolds of the horizontal family of quasi-periodic orbits around L3 in the BCP. To this aim the high order parametrization of the stable/unstable invariant manifolds is introduced, for which computation we have employed the jet transport technique. Finally, the strategy is applied to the NEA 2006 RH120. The contributions to the BCP presented in this dissertation include two other applications. The first one is devoted to the study of the unstable behaviour near the triangular points, meanwhile the second is devoted to a family of stable invariant curves around the Moon that are close to a resonance, promoting the appearance of chaotic motion. The last part of the dissertation is focused on the effective computation of the high or- der parametrization of the stable and unstable invariant manifolds associated with reducible invariant tori of any high dimension. To this aim, we resort on the reducible system, that offers a high degree of parallelization of the computations. Besides, we explain how to com- bine the presented methods with multiple shooting techniques to accurately compute highly unstable invariant objects. Finally, we apply the developed algorithms to compute the high order parametrization of the manifolds associated to L1 and L2 in an Earth-Moon system that includes five time-periodic forcings regarded to four physical features of the system, besides the solar gravitational field.[spa] Esta tesis analiza el movimiento de pequeños cuerpos, como asteroides, en el sistema Tierra­ Luna desde el marco de la mecánica celeste. El modelo que hemos empleado en mayor profundidad es el Problema Bicircular (PBC), el cual se puede entender como una perturbación periódica en el tiempo del conocido Problema Restringido de Tres Cuerpos (PRTC), dado que en el PBC se incluye el campo gravitatorio de un tercer cuerpo masivo que rota en movimiento circular alrededor de la configuración del PRTC. El cuerpo que causa la perturbación es para nosotros el Sol de tal forma que los objetos invariantes del PRTC adquieren una dimensión angular debida a la frecuencia del movimiento relativo entre el Sol y el baricentro Tierra-Luna. En el marco del PBC hemos analizado los fenómenos de transporte gobernados por la familia horizontal de soluciones cuasi-periódicas dos dimensionales (toros 2D) alrededor punto inestable colinear L3. Estas soluciones tienen asociadas variedades invariantes estables e inestables que constituyen el esqueleto de los fenómenos que queremos estudiar. Las trayectorias encontradas conectan la Tierra y la Luna y también el exterior/interior del sistema Tierra-Luna. Hemos prestado especial atención a las trayectorias que van de la Luna a la Tierra ya que podrían explicar el viaje que realizan los meteoritos lunares encontrados en nuestro planeta. Estos resultados han sido testeados en un modelo más realista basado en las efemérides del JPL (Jet Propulsion Laboratory). Otra de las aplicaciones propuestas es la de capturar un asteroide cercano a la Tierra usando la parametrización a orden alto de las variedades invariantes asociadas a los toros 2D alrededor de L3. La parte final trata del desarrollo de algoritmos para el cálculo preciso de la parametrización a orden alto de variedades invariantes estables/inestables asociadas a toros reducibles de cualquier dimensión alta. Además, se explica cómo combinar dichos algoritmos con métodos de tiro múltiple para aquellos objetos invariantes que sean muy inestables. Finalmente, aplicamos la metodología al cálculo de las variedades asociadas a L1 y L2 de un sistema Tierra-Luna que incluye cinco perturbaciones periódicas en el tiempo

Lab RTVE. Transmedia Storytelling in fiction series

El creciente consumo multipantalla de contenidos de ficción es clave en la transformación de los medios audiovisuales. La búsqueda de estrategias de comunicación no lineal para captar la audiencia a través de múltiples plataformas fomenta el mensaje transmedia. La transmedialidad no se limita a la forma de narrar, sino también al modo de producir y difundir una historia. El Laboratorio de Radio Televisión Española, Lab RTVE, destaca en España por su impulso innovador en la producción de contenidos audiovisuales experimentando y desarrollando nuevas narrativas y formatos, así como detectando tendencias. Ejemplo de ello son series como El Caso, Águila Roja o El Ministerio del Tiempo. Este texto valora el uso de la narrativa transmedia de los contenidos de ficción de Lab RTVE en el 2015 y 2016. Se elabora una rúbrica con elementos que constituyen que un producto sea narrativamente transmedia. Además, cada ítem se analiza cualitativamente estableciendo el grado de transmedialidad del producto. Destaca la transmedialidad apoyada en la inmersividad del usuario como estrategia de difusión de las series de ficción y la innovación en cuanto al modo de expandir historias. Además, se obtiene una herramienta de análisis extrapolable a otros productos audiovisuales.The growing multiscreen consumption of fiction content is key in the transformation of audiovisual media. The search for non-linear communication strategies to capture the audience through multiple platforms promotes the transmedia message. Transmediality is not limited to the way of narrating, but also to the way of producing and disseminating a story. The Laboratory of Radio Televisión Española, Lab RTVE, stands out in Spain for its innovative impulse in the production of audiovisual content, experimenting and developing new narratives and formats, as well as detecting trends. Examples of this are series such as El Caso, Águila Roja or El Ministerio del Tiempo. This text assesses the use of the transmedia storytelling of fiction contents of Lab RTVE in 2015 and 2016. A rubric is elaborated with elements that make a product narratively transmedia. In addition, each item is analyzed qualitatively establishing the degree of transmediality of the product. It emphasizes the transmediality supported by the user's immersiveness as a strategy to disseminate fiction series and innovation in the way of telling stories. In addition, an analysis tool extrapolated to other audiovisual products is obtained

Transport and invariant manifolds near L3 in the Earth-Moon Bicircular model

This paper focuses on the role of $\mathrm{L}_3$ to organise trajectories for a particle going from Earth to Moon and viceversa, and entering or leaving the Earth-Moon system. As a first model, we have considered the planar Bicircular problem to account for the gravitational effect of the Sun on the particle. The first step has been to compute a family of hyperbolic quasi-periodic orbits near $\mathrm{L}_3$. Then, the computation of their stable and unstable manifolds provides connections between Earth and Moon, and also generates trajectories that enter and leave the Earth-Moon system. Finally, by means of numerical simulations based on the JPL ephemeris we show that these connections can guide the journey of lunar ejecta towards the Earth

Using invariant manifolds to capture an asteroid near the L3 point of the Earth-Moon Bicircular model

This paper focuses on the capture of Near-Earth Asteroids (NEAs) in a neighbourhood of the $\mathrm{L}_{3}$ point of the Earth-Moon system. The dynamical model for the motion of the asteroid is the planar Earth-Moon-Sun Bicircular problem (BCP). It is known that the $\mathrm{L}_{3}$ point of the Restricted Three-Body Problem is replaced, in the BCP, by a periodic orbit of centre $\times$ saddle type, with a family of mildly hyperbolic tori that is born from the elliptic direction of this periodic orbit. It is remarkable that some pieces of the stable manifolds of these tori escape (backward in time) the Earth-Moon system and become nearly circular orbits around the Sun. In this work we compute this family of invariant tori and also high order approximations to their stable/unstable manifolds. We show how to use these manifolds to compute an impulsive transfer of a NEA to an invariant tori near $\mathrm{L}_{3}$. As an example, we study the capture of the asteroid $2006 \mathrm{RH} 120$ in its approach of 2006. We show that there are several opportunities for this capture, with different costs. It is remarkable that one of them requires a $\Delta v$ as low as 20 $\mathrm{m} / \mathrm{s}$

Alternative channels of access to the Spanish media on the internet. News without the newspaper

We analyze the systems inside an online newspaper that allow access to news outside their own online media. It is important to know how mass media are using these tools because of the sparse documentation and its constant evolution. We propose a model of analysis applied to seven Spanish national newspapers to know how the information services, alternatives to navigation or search, are being used. Spanish newspapers distribution systems incorporate information based on interactivity and personalization: the kind of information you receive, how, when and where. We also emphasize the integration of social tools for sharing and disseminating news outside of the newspaper

Numerical simulation of the shear stress produced by the hot metal jet on the blast furnace runner

During steel casting process a jet of molten metal runs out of the blast furnace hearth and strikes the runner. The continuous impact of hot fluids causes significant damage to its surface, which is made of refractory concrete. In particular, the initial impact on the dry runner is expected to be critical. This work deals with the analysis of the mechanical impact on the runner through the numerical simulation of the process. We propose an incompressible turbulent isothermal Navier-Stokes model, where turbulence is modelled considering two models (standard and SST). The interface dynamics is described by applying the Volume of Fluid (VOF) method, while the surface tension vector is provided by the Continuum Surface model (CSF). Their numerical results are performed in 2D. A comparative analysis of the most suitable transient turbulent multiphase model is presented by simulating benchmark physical experiments. The shear stress arising from the impact of the jet on the runner is also analyzed. An improvement of the classical analytical expression given in [1] is proposed. Both, the chosen turbulence model, and the formulas to compute the shear stress are validated using two benchmark laboratory tests and three numerical experiments. Numerical results are given for the impact of the jet on the dry runner of the blast furnaceThis work was supported by FEDER and Xunta de Galicia [grant number ED431C 2017/60, ED431C 2021/15], the Ministry of Economy, Industry and Competitiveness through the Plan Nacional de I+D+i [grant number MTM2015-68275-R], Agencia Estatal de Investigación [PID2019-105615RB-I00/AEI/10.13039/501100011033] and by the Vicerreitoría de Investigación e Innovación da Universidade de Santiago de Compostela via the Programa de Becas de Colaboración en Investigación 2016S

A Reflection on the Class Teaching Sequence with Particular Reference to History Classes in Spain

This contribution reflects empirical data arising from a study based on the testimony of 1523 students referring to the time when they studied history in secondary school. It forms part of an on-going inter-disciplinary research project. By means of open activities, information was compiled on the History classes received by students studying Bachillerato (two-year pre-university course) in Spanish secondary schools. The data, therefore, reflect students’ views of the subject and the way in which it was imparted. The article will analyse the sequence of actions followed by teachers in the classroom (initial phase, development or application phase, and final phase). For each stage we shall analyse the information received and study the aspects into which the teacher, seemed to put most effort. The results show that the most frequently used teaching model in the classroom was the traditional rote learning approach, with little student participation

Use and credibility of news sources 2.0 in Portugal and Spain

Internet ha cambiado las rutinas de producción en el periodismo. La búsqueda de información ha sido una de las áreas más afectadas, con la aparición de fuentes 2.0 como blogs y redes sociales. A pesar del aparente valor añadido de estas nuevas fuentes de información, ¿qué utilización práctica les dan los periodistas portugueses y españoles y qué credibilidad les atribuyen? Se intenta responder a estas dos cuestiones, definiendo las aplicaciones que pueden considerarse fuentes 2.0 y en qué medida los periodistas las estiman creíbles y fiables. Los resultados muestran que los periodistas de ambos países siguen utilizando internet diariamente para buscar material para su trabajo, documentarse, recibir y enviar información y verificarla, pero aún confían poco en las fuentes 2.0

Los antecedentes de la pedagogía vocal contemporánea: el caso del Dr. Ricardo Botey

En los estudios históricos sobre Pedagogía Vocal suele situarse al año 1950 como inicio del período de la Pedagogía Vocal Contemporánea, pues ese fue el momento histórico en que diferentes profesionales (maestros de canto, médicos, ingenieros y psicólogos, entre otros) confluyeron en una única voluntad interdisciplinaria que tomó como eje la necesidad de dilucidar los mecanismos fisiológicos subyacentes a la producción vocal cantada. De esta forma, al interior de los aportes académicos actuales es aceptado que este año constituye un quiebre respecto de las modalidades tradicionales de enseñanza y aprendizaje del canto. Sin embargo, pocos estudios se han ocupado de problematizar esta fecha y de trazar, en cambio, una trayectoria disciplinar que avance desde la Pedagogía Vocal Tradicional hasta la Contemporánea de modo progresivo. Como resultado de esta perspectiva, el período contemporáneo en Pedagogía Vocal aparece, usualmente, como un movimiento de emergencia repentina desvinculado de los desarrollos anteriores, y sólo posibilitado por el avance tecnológico que habilitó a los profesionales a explorar en detalle y a niveles microanalíticos el aparato fonador. En este artículo, analizamos la obra del Dr. Ricardo Botey planteando que sus desarrollos resultan vanguardistas en su contexto de producción, y que ellos constituyen antecedentes importantes de investigaciones contemporáneas posteriores, ampliamente difundidas

El Dr. Ricard Botey i la pedagogia del cant.

El Dr. Ricard Botey i Ducoing (1855-1927) s'inclinà cap a l'estudi de la veu per la seva afició al cant. Botey, junt amb altres estudiosos de la seva època anomenats "laringòlegs", va estar profundament interessat en veure com es comportaven les cordes vocals durant la producció dels diferents sons. En 1886 publicà el seu primer llibre dedicat a la veu titulat "Higiene, desarrollo y conservación de la voz".Aquesta primera edició no ens parla de les patologies vocals, sinó de la fisiologia de la veu i els seus mecanismes de producció en relació a la laringe. L'any 1899, publicà el treball pioner "Les maladies de la voix chez les chanteurs et leur traitement", a la revista Annales des maladies de l'oreille, du larynx, du nez et du pharynx. En la tercera edició del seu llibre d'Higiene de 1914 incorporà un apèndix on també tractà les patologies laríngies en els cantants: "Las enfermedades de la voz en los cantantes". Botey, com els seus companys laringòlegs, creia que els cantants havien de conèixer com és el seu cos, i, en concret, la seva laringe per tal d'evitar patologies derivades del seu mal ús. Aquestes idees, s'avançaren molt en el temps al que succeí en el camp de la pedagogia vocal, ja que no fou fins als anys 50 del segle XX que la pedagogia incorporà com a paradigma la necessitat de conèixer la anatomia i fisiologia del òrgans de la fonació