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On the fractional Yamabe problem with isolated singularities and related issues

  • Torre Pedraza, Azahara de la
Premi Extraordinari de Doctorat, promoció 2016-2017. Àmbit de Ciències, My research is based on non-local elliptic semilinear equations in conformal geometry. The fractional curvature is defined from the conformal fractional Laplacian and it is a non-local version of some of the classical local curvatures such as the scalar curvature, the fourth-order Q-curvature or the mean curvature. This new notion of non-local curvature has good conformal properties that allow to treat classical problems from a more general convexity point of view. Note that the fractional curvature in my research is different from the one defined by Caffarelli, Roquejoffre and Savin . In particular, I have worked on the fractional singular Yamabe problem and related issues. This problem arises in conformal geometry when we try to find a conformal metric to a given one having constant fractional curvature and prescribed singularities. The precise problem I considered in my thesis was to find solutions for the fractional Yamabe problem in the Eucliden space of dimension bigger than 2¿, 0<¿<1, with prescribed isolated singularities: first, I just considered radial solutions when there is an isolated singularity and, later, the problem of removing a finite number of points. This thesis consists of nine chapters. First, we give is a brief introduction and summary of the thesis. Next, provide some background, notation and known results. Later, we show the main results, i.e, Chapters 3, 4, 5 and 6. After this, we introduce the research plan to come. The thesis also has two appendixes with useful computations. I started my research focusing on the geometric interpretation of the problem for an isolated singularity (Chapter 3). This study is based on an extension problem for the computation of the conformal fractional Laplacian. This is a Dirichlet-to-Neumann problem for a degenerate elliptic, but local, equation, which gives an example of a boundary reaction problem where the nonlinearity is of power type with the critical Sobolev exponent. Later, I treated the problem as an integro-differential equation, facing two main difficulties: the lack of compactness and the fact that we are dealing with a non-local ODE (Chapter 4) . Our study is carried out using variational methods and it proves the existence of Delaunay-type solutions for the problem. These are radially symmetric metrics with constant fractional curvature. Finally, I applied some gluing methods together with a Lyapunov reduction to construct solutions for the singular fractional Yamabe problem when the singular set consists of a given finite number of points (Chapter 5). At the moment, I am working on the fractional Caffarelli-Kohn-Nirenberg inequality, which is an interpolation between the Hardy and Sobolev fractional inequalities. In particular, I am looking at the radial symmetry or symmetry breaking of the minimizers (Chapter 6). I have collaborated with Weiwei Ao (University of British Columbia), María del Mar González (Universidad Autónoma de Madrid), Manuel del Pino (Universidad de Santiago, Chile) and Juncheng Wei (University of British Columbia)., Mi investigación se basa en ecuaciones no-locales elípticas semilineales que surgen en la geometría conforme. La curvatura fraccionaria se define partir del Laplaciano fraccionario conforme y es una versión no local de algunas de las curvaturas locales clásicas tales como la curvatura escalar, la Q-curvatura (operador de orden 4) o la curvatura media. Esta nueva noción de curvatura no-local tiene buenas propiedades conformes que permiten tratar problemas clásicos desde un punto de vista de convexidad más general. Debemos tener en cuenta que se trata de una curvatura fraccionaria distinta a la definida por Caffarelli, Roquejoffre y Savin . En particular, he trabajado en el problema de Yamabe singular fraccionario y problemas relacionados. Se trata de un problema que aparece en la geometría conforme cuando intentamos encontrar una métrica conforme a la dada en una variedad, que tenga curvatura fraccionaria constante y singularidades prescritas. Más concretamente, el problema que he considerado para mi tesis es encontrar soluciones para el problema de Yamabe fraccionario en el espacio Euclídeo de dimensión mayor que 2¿, 0<¿<1, con singularidades aisladas prescritas: en primer lugar, consideré sólo soluciones radiales para una singularidad aislada y más adelante, soluciones para este problema cuando el conjunto singular consta de un número finito de puntos. La tesis está compuesta por nueve capítulos. En primer lugar, hacemos una introducción a modo de sumario de la tesis. Después, hay un capítulo conocimientos básicos, notación, historia del problema y resultados previos. En los capítulos 3,4,5 y 6 presentamos los principales resultados de la tesis, que resumimos más abajo. Finalmente, presentamos brevemente la idea de trabajo para el futuro cercano. En la tesis podemos encontrar también, dos apéndices con cálculos y resultados que serán útiles en la lectura de la tesis. El comienzo de mi investigación se basó en la interpretación geométrica del problema para un singularidad aislada (Capítulo 3). Este estudio parte del problema de extensión para calcular el Laplaciano fraccionario conforme. Se trata de un problema Dirichlet-to-Neumann para una ecuación elíptica, pero local, que proporciona un ejemplo del problema de reacción con borde en el que la no-linearidad es del tipo exponente crítico de Sobolev. Más adelante, traté el mismo problema pero desde el punto de vista de una ecuación integro diferencial. Este método presenta dos dificultades principales: la pérdida de compacidad y el hecho de que estamos tratando con una ODE( ecuación diferencial ordinaria ) no local (Capítulo 4). Nuestro estudio es llevado a cabo utilizando el método variacional y prueba la existencia de soluciones ¿del tipo Delaunay¿ para nuestro problema. Estas soluciones son radialmente simétricas y tienen curvatura fraccionaria constante. Por último, he utilizado métodos de "gluing" (o pegado) junto con el método de reducción de Lyapunov para la construcción de soluciones para el problema de Yamabe singular fraccionario cuando el conjunto singular dado está formado por un número finito de puntos (Capítulo 5). Actualmente, estoy trabajando en la generalización de la desigualdad de Caffarelli-Kohn-Nirenberg al caso fraccionario; se trata de una interpolación entre las desigualdades de Hardy y Sobolev fraccionarias. En particular, estoy estudiando la simetría o pérdida de simetría de los minimizantes (Capítulo 6). En la investigación presentada en esta tesis he colaborado con Weiwei Ao (University of British Columbia), María del Mar González (Universidad Autónoma de Madrid), Manuel del Pino (Universidad de Santiago, Chile) y Juncheng Wei (University of British Columbia)., Award-winning
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An extremely thin and robust interconnecting layer providing 76% fill factor in a tandem polymer solar cell architecture

  • Martinez Otero, Alberto
  • Liu, Quansheng
  • Mantilla Perez, Paola
  • Montes Bajo, Miguel
  • Martorell Pena, Jordi
We report a thin and robust interconnecting layer (ICL) for polymer tandem solar cells. This ICL shows low absorption, good electrical contacts, large work function contrast and robustness. Its use yields tandem cells with a very high fill factor of 76%, making this ICL a promising component of future highly efficient multijunction organic solar cells., Peer Reviewed
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Avaliação da formação de ilhas de calor em Goiás / GO

  • Gonçalves, Pedro Henrique
  • Cardoso, Carina Folena
Os estudos climáticos assumem uma importância estratégica no diagnóstico e na proposição de diretrizes para se alcançar um planejamento de cidades mais confortáveis e eficientes. No rol dos fenômenos climáticos frequentemente estudados nas cidades está a ilha de calor. A hipótese lançada neste trabalho é a possibilidade de ocorrência do fenômeno da ilha de calor em uma cidade de pequeno porte, devido à insuficiência de vegetação, à caracterização dos materiais que compõem seu ambiente construído, à sua geometria urbana e aos usos do solo. A cidade contemplada no estudo é Goiás - GO, com um enfoque específico em seu centro histórico. O método utilizado na pesquisa consiste dos seguintes tópicos de análise: superfícies que compõem a área urbanizada do centro histórico da cidade, geometria urbana e usos do solo. Os resultados mostraram qualitativamente que as características do centro histórico de Goiás possivelmente contribuem para a formação da ilha de calor., Climate studies are strategically important in diagnosing and proposing planning guidelines for achieving more comfortable and efficient cities. In the list of climatic phenomena frequently studied in cities is the heat island. The hypothesis presented in this work is related with the possibility of occurrence of heat island phenomenon in a small city due to its insufficient vegetation, the characterization of the materials that compose its built environment, its urban geometry and land uses. The city contemplated in this study is Goiás-GO, with a specific focus in its historical center. The method used in this research consists of the following analysis topics: surfaces that integrate the urbanized area of the city’s historical center, urban geometry and land uses. The results qualitatively showed that the characteristics of the historical center of Goiás possibly contribute to the formation of heat island.
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Estudi i propostes de millora de la xarxa de bicicleta al municipi de Manresa

  • Forné Muntaner, Carles
Manresa es tracta d’un municipi amb una morfologia geogràfica complicada, amb un relleu ondulat degut a les petites elevacions que hi ha, per una banda, i la depressió que el riu Cardener provoca al seu pas per la part oest i sud del municipi, per l’altre. A més, la infraestructura ferroviària dels FGC actua com a barrera física en el centre de la ciutat. Com a conseqüència, la gran majoria de trajectes que es realitzen dins de Manresa són en vehicle privat, causant problemes de trànsit en hores punta i augmentant la contaminació atmosfèrica i acústica que això comporta. Per tal de solucionar aquests inconvenients, l’Ajuntament de Manresa va instal·lar la primera fase d’un sistema de carril bici, que a la llarga havia de completar una gran xarxa de circulació sostenible per tota la ciutat, connectant el Parc de l’Agulla i la Zona Esportiva El Congost (dos dels principals nuclis d’oci de la ciutat) passant pel centre del municipi. Encara que per part dels usuaris habituals del carril la proposta va ser ben rebuda, els no usuaris van ser molt crítics amb l’actuació, defensant que aquest carril treia places d’aparcament a vehicles privats a canvi de que casi ningú l’utilitzés. Aquest enfrontament va provocar que l’Ajuntament modifiqués o, en algun cas, retirés algun tram del carril que s’havia instal·lat fins llavors. El següent treball consta de dues parts, la primera d’elles, és una anàlisi de la mobilitat sostenible del municipi de Manresa a partir del planejament que es disposa, dins del marc geogràfic i històric tan important en el nostre cas. La segona part del treball serà un seguit de propostes de millora de la xarxa de carril bici existent tenint en compte l’ampliació que ja té planejada l’Ajuntament. A més, aquest treball també té en consideració la futura Via Cicloturística Intercatalunya, un projecte de la Generalitat de Catalunya que té per objectiu construir una via per a ciclistes que connecti Lleida amb Girona, passant per Manresa. Aquest treball farà una proposta d’adequació d’aquesta futura via amb la xarxa municipal de bicicletes per tal d’unir el sistema urbà amb l’interurbà., Manresa es un municipio con una morfología geográfica complicada, con un relieve ondulado debido a las pequeñas elevaciones que hay, por un lado, y la depresión que el río Cardener provoca a su paso por la parte oeste y sur del municipio, por el otro. Además, la infraestructura ferroviaria de los FGC actúa como barrera física en el centro de la ciudad. Como consecuencia, la gran mayoría de trayectos que se realizan dentro de Manresa son en vehículo privado, causando problemas de tráfico en horas punta y aumentando la contaminación atmosférica y acústica que esto conlleva. Para solucionar estos inconvenientes, el Ayuntamiento de Manresa instaló la primera fase de un sistema de carril bici, que a la larga tenía que completar una gran red de circulación sostenible por toda la ciudad, conectando el Parc de l’Agulla y la Zona Deportiva El Congost (dos de los principales núcleos de ocio de la ciudad) pasando por el centro del municipio. Aunque por parte de los usuarios habituales del carril la propuesta fue bien recibida, los no usuarios fueron muy críticos con la actuación, defendiendo que este carril eliminaba plazas de aparcamiento a vehículos privados a cambio de que casi nadie lo utilizara. Este enfrentamiento provocó que el Ayuntamiento modificara o, en algún caso, retirara algún tramo del carril que se había instalado hasta entonces. El siguiente trabajo consta de dos partes, la primera de ellas, es un análisis de la movilidad sostenible del municipio de Manresa a partir del planeamiento que se dispone, todo dentro del marco geográfico e histórico tan importante en nuestro caso. La segunda parte del trabajo será una serie de propuestas de mejora de la red de carril bici existente teniendo en cuenta la ampliación que ya tiene planeada el Ayuntamiento. Además, este trabajo también tiene en consideración la futura Vía Cicloturística Intercatalunya, un proyecto de la Generalitat de Catalunya que tiene por objetivo construir una vía para ciclistas que conecte Lleida con Girona, pasando por Manresa. Este trabajo hará una propuesta de adecuación de esta futura vía con la red municipal de bicicletas para unir el sistema urbano con el interurbano., Manresa is a town with a complex geographical morphology, with an undulating relief due to, on the one hand, its low elevations and, on the other hand, the depression the river Cardoner causes on its way through the west and south of the town. Furthermore, the railway infrastructure of the FGC acts as a physical barrier in the town centre. As a consequence, most of the routes that are followed in town are in a private vehicle, bringing on traffic problems in the rush hours, with the atmospheric and acoustic pollution it provokes. In order to solve these inconviniences, l’Ajuntament de Manresa had the first phase of a system of bicycle track built, which in the long turn had to complete a larger one of substainable movement of traffic in the whole of the town, connecting the Parc de l’Agulla and the Zona Esportiva El Congost (both of the main leisure areas in town), therefore crossing its centre. Even though the habitual users of the track welcomed the proposal, the non-users were very critical against it, claiming that the track limited the amount of public parking places and substituted it for a track that very few people were likely to use. This confrontation made the Ajuntament have it modified or, in some cases, it had some sections of the track that had been built so far removed. The first part of this project will consist of an analysis of the substainable mobility in the town of Manresa, starting with the available planning within such an important geographic and historic environment as ours. The second part of the project will propose some measures of improvement of the existing net of bicycle track , taking into account the expansion the Ajuntament has already planned. Moreover, this project also takes into consideration the future Via Cicloturística Intercatalunya, a project designed by the Generalitat de Catalunya, whose objective is creating a cycling route to connect Lleida and Girona, going through Manresa. This project will try to make a proposal of adequacy of this future way to the local bicycle net, so as to join the urban and interurban system.
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Temperature control of open-cathode PEM fuel cells

  • Costa Castelló, Ramon
  • Strahl, Stephan
Proper temperature control of Proton Exchange Membrane (PEM) Fuel Cells is a crucial factor for optimizing fuel cell performance. A robust temperature controller is required for optimal water management of PEM fuel cells. This paper describes a model-based characterization of the equilibrium points of an open-cathode fuel cell system as the baseline for proper controller design, highlighting the relation between fuel cell temperature, humidification and performance. Phase plane analysis of the nonlinear model versus a linearized model around different points of operation shows the potential of approximating the nonlinear system behavior with a linear model. The methodology for the system analysis presented in this paper finally serves for the development of control schemes using robust control techniques. The designed controller is validated in simulation with the nonlinear plant model.
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The city of the future: The challenge of the ECHORD++ Project

  • Grau Saldes, Antoni
  • Bolea Monte, Yolanda
  • Sanfeliu Cortés, Alberto
  • Puig-Pey Clavería, Ana María
Focussed on application-oriented research and development, ECHORD++ (E++) is being funded by the European Comission in the 7PM for five years to improve and increase the innovation in robotic technology. Activities include small-scale projects and a “structured dialogue” incorporating public entities and citizens. Three instruments and processes are being developed under the ECHORD++ project: experiments (EXP), Research Innovation Facilities (RIF) and Public end-user Driven Technological Innovation (PDTI), all of them aimed at improving and increasing the innovation in robotic technology within SMEs companies and addressing answers to societal and industrial needs in different scenarios. This paper describes the outcomes and results of the project, the tasks of communication and dissemination and the structured dialogue between all the involved stakeholders., Peer Reviewed
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Modeling tuberculosis transmission in urban cities through agent-based simulation: the case of Barcelona

  • Montañola Sales, Cristina
  • Prats Soler, Clara
  • Cardona, Pere-Joan
  • Gilabert, Joan-Francesc
  • López Codina, Daniel
  • Vilaplana, Cristina
  • Casanovas Garcia, Josep
  • Valls Ribas, Joaquim
Tuberculosis remains one of the world’s deadliest infectious diseases. About one-third of the world’s population is infected with tuberculosis bacteria. Understanding the dynamics of transmission at different spatial scales is critical to progress in its control. We present an agent-based model for tuberculosis epidemics in Barcelona, which has an observatory on this disease. Our model considers high heterogeneity within the population, including risk factors for developing an active disease, and it tracks the individual behavior once diagnosed. We incorporated the immunodeficiency and smoking/alcoholism, as well as the individual’s origin (foreigner or not) for its contagion and infection as risks factors. We implemented the model in Netlogo, a useful tool for interaction with physicians. However, the platform has some computational limitations, and we propose a solution to overcome them., Peer Reviewed
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DJSB: Dynamic Job Scheduling Benchmark

  • López Herrero, Víctor
  • Jokanovic, Ana
  • D'Amico, Marco
  • Garcia Gasulla, Marta
  • Sirvent Pardell, Raül
  • Corbalán González, Julita
High-performance computing (HPC) systems are very big and powerful systems, with the main goal of achieving maximum performance of parallel jobs. Many dynamic factors influence the performance which makes this goal a non-trivial task. According to our knowledge, there is no standard tool to automatize performance evaluation through comparing different configurations and helping system administrators to select the best scheduling policy or the best job scheduler. This paper presents the Dynamic Job Scheduler Benchmark (DJSB). It is a configurable tool that compares performance metrics for different scenarios. DJSB receives a workload description and some general arguments such as job submission commands and generates performance metrics and performance plots. To test and present DJSB, we have compared three different scenarios with dynamic resource management strategies using DJSB experiment-driven tool. Results show that just changing some DJSB arguments we can set up and execute quite different experiments, making easy the comparison. In this particular case, a cooperative-dynamic resource management is evaluated compared with other resource management approaches., This work is supported by the Spanish Government through Programa Severo Ochoa (SEV-2015-0493), by the Spanish Ministry of Science and Technology (project TIN2015-65316-P), by the Generalitat de Catalunya (grant 2014-SGR-1051), by the European Union’s Horizon 2020 research and innovation program under grant agreement No. 720270 (HBP SGA1)., Peer Reviewed
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Hardware design of an electronic tag for marine wildlife

  • Vallés Tomàs, Javier
This thesis is a summary of the process of design of the hardware and firmware associated of an electronic tracking tag for marine wildlife. It includes the aspects of analysing the tags already existing and its main features. Then, proposing a design that fulfils the requirements of these devices. Assemble a first prototype, designing the PCB previously and test its functionality using the firmware designed for the tasks it has to perform as a real product. Finally, proposing a second version of the hardware, attempting to provide a final solution that can be used in a next stage of the project of designing a completely functional electronic tag.
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Hierarchical representations in machine learning and many-body quantum physics, Deep Learning in Quantum Physics

  • Blázquez García, Raúl
En col·laboració amb la Universitat Autònoma de Barcelona (UAB) i la Universitat de Barcelona (UB), Over the past few years a number of proofs have emerged revealing the many connections between the methods used in quantum-many body physics and those in machine learning. In particular, much attention has been given to tensor networks (TNs) and deep learning architectures which exhibit striking similarities. Finding those similarities has helped us gain a better understanding on why deep learning architectures have so much expressive efficiency. Recently, machine learning techniques have been used to approximate many-body physics problems. Conversely, TNs have been used for machine learning tasks. For example, state-of-the-art research has used one-dimensional TNs to solve image recognition problems with very limited scalability. The scalability problem, however, can be overcomed by using a two-dimensional hierarchical TNs and a training algorithm derived from the multipartite entanglement renormalization ansatz (MERA). Here we give further analysis of the inner structural resemblance between such hierarchical tensor networks (TNs) and pretrained convolutional neural networks (CNNs): this was achieved by analyzing their abstraction power layer by layer.
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