http://hdl.handle.net/10366/4644 2026-05-01T14:13:08Z http://hdl.handle.net/10366/170945 [ES] La discretización de ecuaciones diferenciales e integrales mediante bases de wavelets constituye una línea de investigación con gran potencial en el análisis numérico. Las técnicas basadas en análisis multirresolución permiten desarrollar métodos eficientes y estables, especialmente adecuados para la aproximación de funciones que presentan estructuras complejas o variaciones significativas a distintas escalas. Las wavelets ofrecen representaciones jerárquicas con distintos niveles de resolución y permiten controlar tanto la localización espacial como la regularidad de la aproximación. De forma paralela, en las últimas décadas ha aumentado el interés por los modelos matemáticos basados en operadores no locales. Estas formulaciones resultan especialmente adecuadas para describir fenómenos en los que la interacción entre regiones alejadas del dominio desempeña un papel esencial y no puede representarse adecuadamente mediante operadores diferenciales clásicos. La difusión no local aparece en numerosos contextos científicos y aplicados, como la epidemiología, la ecología, el análisis de materiales, el procesamiento de imágenes o la propagación de incendios forestales. El objetivo principal de esta tesis es estudiar, desarrollar e implementar esquemas numéricos basados en wavelets para la aproximación de operadores de difusión no local. El trabajo aborda tanto aspectos teóricos como computacionales con el fin de construir discretizaciones eficientes en el marco del método variacional de Galerkin. En particular, se desarrollan herramientas para la construcción de bases wavelet adecuadas, el diseño de algoritmos numéricos eficientes y la aplicación de la metodología propuesta a modelos de interés práctico. Uno de los aspectos centrales del trabajo es el estudio de la discretización de operadores integrales no locales. Aunque estos operadores conducen de forma natural a matrices densas, su representación en bases wavelet presenta propiedades de compresibilidad que permiten obtener matrices con decaimiento rápido de los coeficientes fuera de la diagonal. Esta característica permite reducir significativamente los costes de almacenamiento y computación. La tesis también aborda diversos aspectos computacionales necesarios para la implementación práctica de estos métodos. Entre ellos se incluyen el desarrollo de reglas de cuadratura para la evaluación de integrales, algoritmos eficientes para el cálculo del producto matriz–vector asociados a operadores compresibles y técnicas de aproximación para el tratamiento de términos no lineales. Asimismo, se estudian estrategias de precondicionamiento para mejorar el comportamiento de los métodos iterativos utilizados en la resolución de los sistemas lineales resultantes. Finalmente, la metodología desarrollada se aplica al estudio de distintos modelos de difusión no local. En particular, se consideran problemas de referencia que permiten analizar la estructura de los operadores discretizados, así como aplicaciones en modelos epidemiológicos de propagación espacial de virus y en modelos de propagación de incendios forestales que incluyen términos de radiación no local. 2026-01-01T00:00:00Z http://hdl.handle.net/10366/163832 We present a simplified 2D wildland fire model with some 3D effects, which takes into account convection and radiation. The topography, the fuel load and type and the meteorological data required by the model (temperature, humidity and wind) are provided via GIS. The wind conditions can be considered a given data in all domain, or can be computed by the wind model developed by authors. Given the fire ignition location and time the model provide the state of landscape for several time steps, allowing to establish the perimeter of the fire at different instants. By modifying the fuel load and type raster files, fire suppression tactics can be incorporated in order to adapt the simulation to the real situation, since the simplified model and its numerical solution allow a computational time much less than real time. 2014-10-11T00:00:00Z http://hdl.handle.net/10366/163831 An urban scale Eulerian non-reactive multilayer air pollution model is proposed describing convection, turbulent diffusion and emission. A mass-consistent wind field model developed by authors is included in the air pollution model. An Adaptive Finite Element Method with characteristics in the horizontal directions and Finite Differences in the vertical direction using splitting techniques is proposed to numerically solve the corresponding PDE problem. A parallel version of the algorithm improves the precision of the solution keeping computation time below real time of simulation. A numerical example illustrates the whole problem. 2013-07-24T00:00:00Z http://hdl.handle.net/10366/163830 In this article, we focus on a simplified two-dimensional fire model with some three-dimensional effects. The model takes into account the moisture content and the energy lost in the vertical direction and to radiation from the flames. We couple this model with a local wind model, well adapted to fire modelling. The topography, fuel type, mass fraction of the fuel and the meteorological data required by the model (temperature, humidity and wind) are provided by geographic information systems. We incorporate data assimilation techniques to our fire model in order to improve the approximations obtained with the model. The data assimilated are the temperature of the solid fuel (which is related to the position of the fire front) and the mass fraction of fuel at certain points in the domain. The numerical examples show that this procedure is able to correct the approximations obtained by the model simulations, providing more realistic predictions. The process is implemented using parallel computing. 2014-07-22T00:00:00Z http://hdl.handle.net/10366/163829 A global sensitivity analysis and parameter adjustment of a simplified physical fire model applied to a well measured experimental example is developed in order to validate the model. The fire model is a simplified physical 2D wildland fire model with some 3D effects that takes into account the wind, the slope of the orography, the fuel load and type, the moisture content, the energy lost in the vertical direction and the radiation from the flames. The simplicity of the model and the numerical techniques proposed allow very competitive computational times. 2015-08-25T00:00:00Z http://hdl.handle.net/10366/157893 [EN] In this thesis different aspects of kinks in non-linear Sigma models are studied. Sigma models where families of kinks can be analytically identified will be successfully constructed on different Riemannian manifolds. The stability of these kinks will also be analysed. Moreover, kinks of field theories in Euclidean spaces will be geometrically constricted in a continuous manner by extending its target manifold and choosing interesting families of geometries on it. On the other hand, Sigma models with analytical solutions will be sought for nonsimply connected target manifolds. The different homotopy classes of curves that arise will give rise to the existence of brochosons under certain conditions. This is, these homotopy classes will allow the existence of non-topological kinks that cannot decay into vacuum. This will be accomplished by introducing singularities in the potential in simply connected spaces and by directly considering a non-simply connected manifold like the torus. Furthermore, the methods of deformation of Bazeia et al. will be generalised to the context of Sigma models, also allowing seed-dependent deformations in the process. Lastly, new methods for identifying kinks in new Sigma models are developed. On one hand, procedures for cutting and gluing kinks will allow us to design kink orbits for other Sigma models. In addition to this, Sigma models will be combined to intertwine their dynamics while retaining the original solutions. 2023-01-01T00:00:00Z http://hdl.handle.net/10366/157719 [EN] The purpose of this thesis is two-fold. As already mentioned, we are firstly interested in the geometry of null hypersurfaces. In this context the formalism of hypersurface data becomes a powerful mathematical framework. Our second aim (and actually the starting point of the thesis) is the study of the problem of matching two completely general spacetimes across a null hypersurface, which we address in Chapters 7, 8, 9. Concerning the part of the thesis where we expand the formalism of hypersurface data, the motivations described above have lead us to study how to characterize curvature information at the abstract level. Also, they have allowed us to understand how the data is affected by the existence of a privileged vector field. In particular, this has permitted that we construct abstract notions of Killing horizons of order zero and one which do not require of any ambient space and which generalize the concepts of non-expanding, (weakly) isolated and Killing horizons. Finally, we have been able to derive an equation, called generalized master equation, that governs the geometry of null hypersurfaces with an extra null tangent vector field. The analysis of this equation reveals properties about the surface gravity of such vector and about homothetic Killing horizons and Killing horizons of order zero and one. Moreover, it allows us to recover, as particular cases, the well-known near horizon equation of isolated horizons as well as the so-called master equation of multiple Killing horizons. The problem of matching two spacetimes across a null hypersurface constitutes the second part of the thesis. In a spacetime context and by requiring a simple topology of the boundaries, we have been able to encode the whole matching information in a function and a diffeomorphism between the set of null generators of both matching hypersurfaces. We have also derived explicit expressions for the matter-energy content of the shell. Finally, we have exploited the formalism of hypersurface data to address the problem of matching in a completely abstract context and without requiring topological restrictions upon the boundaries. This approach, as we will see, has many advantages that will be discussed later. 2023-01-01T00:00:00Z http://hdl.handle.net/10366/149833 [EN] We use a constituent model to analyze the stability of pentaquark Q qqqq ̄ configurations with a heavy antiquark c ̄ or ̄ b, and four light quarks uuds, ddsu or ssud. The interplay between chromoelectric and chromomagnetic effects is not favorable, and, as a consequence, no bound state is found below the lowest dissociation threshold. 2019-01-01T00:00:00Z http://hdl.handle.net/10366/149831 [EN] Wind speed forecasts obtained by Numerical Weather Prediction models are limited for fine interpretation in heterogeneous terrain, in which different roughnesses and orographies occur. This limitation is derived from the use of low-resolution and grid-box averaged data. In this paper a dynamical downscaling method is presented to increase the local accuracy of wind speed forecasts. The proposed method divides the wind speed forecasting into two steps. In the first one, the mesoscale model WRF (Weather Research and Forecasting) is used for getting wind speed forecasts at specific points of the study domain. On a second stage, these values are used for feeding the HDWind microscale model. HDWind is a local model that provides both a high-resolution wind field that covers the entire study domain and values of wind speed and direction at very located points. As an example of use of the proposed method, we calculate a high-resolution wind field in an urban-interface area from Badajoz, a South-West Spanish city located near the Portugal border. The results obtained are compared with the values read by a weathervane tower of the Spanish State Meteorological Agency (AEMET) in order to prove that the microscale model improves the forecasts obtained by the mesoscale model. 2021-01-01T00:00:00Z http://hdl.handle.net/10366/149532 [EN] In this thesis we study the asymptotic Cauchy problem of general relativity with positive cosmological constant in arbitrary (n + 1)-dimensions. Our aim is to provide geometric characterizations of Kerr-de Sitter and related spacetimes by means of their initial data at conformally flat (n-dimensional) I . In our setting, the conformal Killing vector fields (CKVFs) of I become very relevant because of their relation with the symmetries of the spacetime. In the first part of the thesis, we study the CKVFs ξ of conformally flat n-metrics γ, as well as their equivalence classes [ξ] up to conformal transformations of γ. We do that by analyzing in detail SkewEnd(M1,n+1), the skew-symmetric endomorphisms of the Minkowski space M1,n+1. The cases n = 2, 3 are worked out in special detail. A canonical form that fits every element in SkewEnd(M1,n+1) is obtained along with several applications. Of relevance for the study of asymptotic data is that it gives a canonical form for CKVFs which allows us to determine the conformal classes [ξ] and study the quotient topology associated to these clases. In addition, the canonical form for CKVFs is applied to the n = 3 case to obtain a set of coordinates adapted to an arbitrary CKVF. With these coordinates we provide the set of asymptotic data which generate all conformally extendable spacetimes solving the (Λ > 0)-vacuum field equations and admitting two commuting symmetries, one of which axial. From this, a characterization of Kerr-de Sitter and related spacetimes follows. Our study provides in principle a good arena to test definitions of mass and angular momentum for positive cosmological constant. In the second part of this thesis we focus in the asymptotic Cauchy problem in arbitrary dimensions. For this we use the Fefferman-Graham formalism. We carry out an study of the asymptotic initial data in this picture and extend an existing geometric characteri- zation of them, in the conformally flat I case, to arbitrary signature and cosmological constant. We discuss the validity of this geometric characterization of data beyond the conformally flat I case. We provide a KID equation for asymptotic analytic data (which comprise Kerr-de Sitter). This equation being satisfyied by the data amounts to the existence of a Killing vector field in the corresponding spacetime. With the above results in hand we provide a geometric characterization of Kerr-de Sitter by means of its asymptotic initial data, which happen to be determined by the conformally flat class of metrics [γ] and one particular conformal class of CKVFs [ξ] of [γ]. These data admit a generalization, keeping [γ] conformally flat, by allowing [ξ] to be an arbitrary confor- mal class. This extends the so-called Kerr-de Sitter-like class with conformally flat I , defined in previous works in four spacetime dimensions, to arbitrary dimensions. We study this class and prove that the corresponding spacetimes are contained in the set of (Λ > 0)-vacuum Kerr-Schild spacetimes, which share (conformally flat) I with their background metric (de Sitter). We name these Kerr-Schild-de Sitter spacetimes. The proof largely relies on our study of the space of classes of CKVFs and in particular on the properties of its quotient topology. In addition, we prove the converse inclusion, providing a full characterization of the Kerr-de Sitter-like class as the Kerr-Schild-de Sitter spacetimes. 2021-01-01T00:00:00Z http://hdl.handle.net/10366/139591 [ES]El presente trabajo tiene por objeto sentar las bases teóricas para el diseño de dispositivos de irradiación de células mediante haces de rayos X generados por láser con energías características aproximadamente en el rango 20–50 keV, así como el desarrollo de métodos de medición y caracterización de las radiaciones implicadas, en atención a sus singulares características temporales. Entre los hallazgos en la descripción del sistema destacan un análisis del efecto de los parámetros del conjunto láser-blanco sobre la temperatura de los electrones acelerados, un modelo de producción de rayos X por distribuciones de electrones que mejora varios aspectos de los preexistentes en el campo y un estudio espacial de la deposición de dosis en tejido que estas fuentes pueden generar, mostrando que este aspecto es similar al de las fuentes convencionales. Los métodos de detección especializados aportados son un refinamiento de un detector basado en la curva de distancia-dosis de los electrones en el aire, un modelo del apilamiento en detectores de estado sólido que ha permitido demostrar la presencia de éste en resultados experimentales sin picos de repetición y un estudio formal de los mal llamados parámetros de temperatura en las distribuciones de rayos X, revelando que las supuestas evidencias de una mezcla de temperaturas de electrones en el espectro de emisión resultante son potencialmente engañosas. 2018-01-01T00:00:00Z http://hdl.handle.net/10366/137259 [ES]El objetivo de esta tesis doctoral es estudiar la desigualdad de Penrose en el caso luminoso, es decir, aquellos casos en que la superficie atrapada genera un cono de luz pasado que se extiende de manera regular hasta infinito pasado luminoso. La desigualdad de Penrose en este caso involucra la demonimada masa de Bondi del espacio-tiempo. Este contexto tiene interés, además de por ser el más sencillo compatible con un proceso de colapso realista, porque incluye como caso particular la construcción originalmente propuesta por Penrose y que consiste en una capa delgada de materia que se propaga a la velocidad de la luz en el espacio-tiempo de Minkowski. En este caso la desigualdad de Penrose se convierte en una desigualdad geométrica para superficies espaciales convexas (más precisamente "espacio-temporalmente convexas") en el espacio-tiempo de Minkowski. Esta situación particular, pero de especial interés, es objeto de estudio pormenorizado en esta tesis doctoral. La desigualdad de Penrose en ese caso se denomina "desigualdad de Penrose para capas". 2017-01-01T00:00:00Z http://hdl.handle.net/10366/127879 [EN]The starting point of this thesis is the calculation of the five-point amplitude for the scattering of two distinct scalars with the emission of one graviton in the final state for Einstein-Hilbert gravity. We find that the result, expressed in Sudakov variables, corresponds to the sum of two gauge invariant contributions written in terms of a new two scalar - two graviton effective vertex. A similar calculation is carried out in Quantum Chromodynamics (QCD) for the scattering of two distinct quarks with one extra gluon in the final state. The effective vertices which appear in both cases are then evaluated in the multi-Regge limit (where the emitted on-shell graviton is well separated in rapidity from the scalar particles) reproducing the well-known result obtained by Lipatov where the Einstein-Hilbert graviton emission vertex from two off-shell gravitons can be related to the product of two QCD gluon emission vertices. After this we investigate tree-level five-point amplitudes in scalar-QCD (sQCD) expressed in terms of Sudakov variables and find the equivalent “gravitational” counterparts using the so-called color-kinematics duality proposed by Bern, Carrasco, and Johannson. Taking the multi-Regge limit in the gravitational amplitudes, we show that those pieces in the coupling of two Reggeized gravitons to one on-shell graviton directly stemming from the double copy of the vertex for two Reggeized gluons to one on-shell gluon are universal and properly reproduced by the duality.In the second part of the thesis we study the applicability of the colorkinematics duality to the scattering of two now distinguishable scalar matter particles with gluon emission in QCD, or graviton emission in Einstein gravity. Our previous analysis suggested that a direct use of the Bern-Carrasco-Johansson double-copy prescription to matter amplitudes does not reproduce the gravitational amplitude in multi-Regge kinematics. However, minimal extensions of thecalculation eliminate this obstacle. Here we present two approaches: introduction of a scalar contact interaction, or relaxing distinguishibility of the scalars. In both cases new diagrams allow for a full reconstruction of the correct multi-Regge limit on the gravitational side. Both modifications correspond to pure theories obtained by dimensional reduction from higher-dimensional gauge theories.; [ES]El punto de partida la tesis es el cálculo de la amplitud de dispersión a cinco puntos de dos escalares de diferentes sabores con la emisión de un gravitón en la teoría de Einstein. El resultado corresponde a la suma de dos contribuciones invariantes gauge escritas en términos de un nuevo vértice efectivo para dos escalares y dos gravitones. Un cálculo similar se lleva a cabo en Cromodinámica Cuántica (QCD) para la amplitud de dispersión de dos quarks distinguibles con la emisión de un gluón. Los vértices efectivos que aparecen en ambos casos son evaluado en el llamado límite de cinemática multi-Regge, reproduciendo el conocido resultado obtenido por Lipatov en el que el vértice de emisión del graviton se puede relacionar con el producto de dos vértices de emisión de un gluón. En la segunda parte de la tesis se estudia la aplicabilidad de la dualidad color-cinemática (color-kinematics duality) a la dispersión de dos partículas escalares distinguibles con emisión de gluones en QCD, o emisión de gravitones en gravedad de Einstein. Nuestro análisis indica que un uso directo de laprescripción de doble copia Bern-Carrasco-Johansson a amplitudes con materia no reproduce la amplitud gravitacional en la cinemática de multi-Regge. Sin embargo, extensiones mínimas del cálculo eliminan este obstáculo. Aquí se presentan dos enfoques: la introducción de una interacción de contacto escalar, o la relajación de la distinguibilidad de los escalares. En ambos casos nuevos diagramas permiten una reconstrucción completa del límite correcto de Regge en la amplitud gravitacional. Ambas modificaciones se corresponden con teorías obtenidas por reducción dimensional de teorías de gauge puras en dimensiones superiores. 2015-09-01T00:00:00Z http://hdl.handle.net/10366/121164 [ES] En el trabajo se presenta un estudio de la dinámica de sistemas multiquark utilizando un modelo de quarks constituyentes. Se analizan los sistemas mesón-antimesón, mesón-barión y barión-antibarión en diferentes procesos. Para ello se utiliza el Método del Grupo Resonante para describir la interacción a nivel hadrónico en base a interacciones entre quarks, el modelo $^3P_0$ para conectar el espectro de mesones con el sistema mesón-antimesón, y la resolución de la ecuación de Lippmann-Schwinger para describir los estados de scattering. La dinámica del sistema barión-antibarión se centra en la producción de extrañeza en colisiones protón-antiprotón. También se comprueba la validez de la interaccion nucleón-antinucleón en la región de producción de hiperones, mucho mayor que la región para la que el modelo fue propuesto. El estudio del sistema mesón-antimesón y mesón-barión se centra en la busqueda de estados moleculares que contribuyan al espectro de mesones y bariones, respectivamente. Para el sistema mesón-antimesón se desarrolla un formalismo que permite acoplar los sectores de dos y cuatro quarks, planteando el efecto del espectro mesónico en la dinámica de estados moleculares. Este nuevo planteamiento permite obtener estados ligados adicionales en el espectro, como las particulas $X(3872)$, $D_{s1}(2460)$ o $\Lambda_c(2940)^+$, modificando a su vez los estados originales mesónicos debido a la existencia de canales hadrónicos intermedios. Finalmente se plantea un mecanismo que permite obtener resonancias y estados ligados provinientes del acoplamiento de forma no perturbativa, con posibilidad de obtener resultados no triviales capaces de describir muchos aspectos novedosos del espectro mesónico, como puede ser la inversion de estados en la región de energia de 4 GeV en el sector $1^{--}$.; [EN] The paper presents a study of the dynamics of multiquark systems using a constituent quark model. Systems are analyzed to anti-meson, meson-baryon and baryon-antibaryon in different processes. It uses the Resonant Group Method for describing hadronic level interaction based on interactions between quarks, the model $ ^ $ 3P_0 to connect the spectrum of mesons to anti-meson system, and the resolution of the Lippmann equation to describe-Schwinger scattering states. The dynamics of baryon-antibaryon system focuses on strangeness production in proton-antiproton collisions. It also checks the validity of nucleon-anti-nucleon interaction in the region of production of hyperons, much larger than the region for which the model was proposed. The study of the meson-meson to anti-baryon and focuses on the search for molecular states contribute to the spectrum of mesons and baryons, respectively. For the system to anti-meson formalism is developed for attaching sections of two four quarks, considering the effect of meson spectrum in the dynamics of molecular states. This new approach allows for additional bound states in the spectrum, as the particles $ X (3872) $, $ D_ {s1} (2460) $ or $ \ Lambda_c (2940) ^ + $, in turn modifying the original states meson due to the existence of intermediate hadronic channels. Finally it proposes a mechanism that allows for resonances and bound states provinientes coupling non-perturbatively, with the possibility of nontrivial results can describe many novel aspects of the meson spectrum, such as the inversion of states in the energy region of 4 GeV in the sector $ 1 ^ {-} $. 2012-01-01T00:00:00Z http://hdl.handle.net/10366/22464 The aim of the paper is twofold. First, some results of Shiota and Plaza-Martín on Prym varieties of curves with an involution are generalized to the general case of an arbitrary automorphism of prime order. Second, the equations defining the moduli space of curves with an automorphism of prime order as a subscheme of the Sato Grassmannian are given. 2003-01-01T00:00:00Z http://hdl.handle.net/10366/56038 Se presenta una estimación a posteriori del error para el problema parabólico lineal, y se diseña el correspondiente algoritmo de adaptación de malla y paso de tiempo. Para la discretización espacial se utiliza el elemento de Raviart-Thomas de menor orden y para la integración temporal la aproximación de Galerkin discontinua con paso variable. Se aplican los métodos numéricos desarrollados a variosproblemas significativos que muestran la eficiencia del algoritmodesarrollado.; In this paper we present an a-posteriori error estimator for the mixed formulation of a linear parabolic problem, used for designing an efficient adaptive algorithm. Our space-time discretization consists of lowest order Raviart-Thomas finite element over graded meshes and discontinuous Galerkin method with variable time step. Finally, several examples show that the proposed method is efficient and reliable. 2006-04-26T00:00:00Z