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A procedure for computational dosimetry to verify safety standards compliance of mobile communications base stations is presented. Compared with the traditional power density method, a procedure based on more rigorous physics was devised, requiring computation or measurement of the specific absorption rate (SAR) within the biological tissue of a person at an arbitrary distance. This uses a hybrid methd of moments/finite difference time domain (MoM/FDTD) numerical method in order to determine the field or SAR distribution in complex penetrable media, without the computational penalties that would result from a wholly FDTD simulation. It is shown that the transmitted power allowed by the more precise SAR method is, in many cases, between two and five times greater than that allowed by standards implementing the power flux density method.

Obtaining the modal parameters of a deflected and rolling tire represents a challenge due to the complex vibration characteristics that cause the tire's symmetry distortion and the natural frequencies' bifurcation phenomena. The modal parameters are usually extracted using a detailed finite element model. The main issue with full modal models (FEA, for example) is the inability to integrate the tire modal model with the vehicle models to tune the suspension system for optimal ride comfort. An in-plane rigid–elastic-coupled tire model was used to examine the 200 DOF finite difference method (FDM) modal analysis accuracy under non-ground contact and non-rotating conditions. The discrete in-plane rigid–elastic-coupled tire model was modified to include the contact patch restriction, centrifugal force, Doppler, and Coriolis effects, covering a range of 0-300 Hz. As a result, the influence of the contact patch and the rotating tire conditions on the natural frequencies and modes were obtained through modal analysis. The in-plane rigid–elastic-coupled modal model with varying conditions was created that connects any two DOFs around the tire's tread or sidewall as inputs or outputs. The vertical movement of the wheel was incorporated into the in-plane rigid–elastic-coupled tire modal model to extract the transfer function (TF) that connects road irregularities as an input to the wheel's vertical movement as an output. The TF was utilized in a quasi-static manner to obtain the tire's enveloping characteristics rolling over short wavelength obstacles as a direct function of vertical wheel displacement under varying contact patch length constraints. The tire modal model was implemented with the quarter car model to obtain the vehicle response rolling over short wavelength obstacles. Finally, a sensitivity analysis was performed to examine the influence of tire parameters and pretension forces on natural frequencies. / Doctor of Philosophy / The goal of vehicle manufacturers is to predict the vehicle's behavior under various driving conditions using mathematical models and simulation. Automotive companies rely heavily on computational simulation tools instead of real-time tests to shorten the product development cycle and reduce costs. However, the interaction between the tire and the road is one of the most critical aspects to consider when evaluating automobile stability and performance. The tires are responsible for generating the forces and moments that drive and maneuver the vehicle. Tires are complex products due to their intricate design, and their characteristics are affected by many factors such as vertical load, inflation pressure, speed, and a road with an uneven surface profile. Consequently, this project aims to describe the influence of various driving circumstances and load conditions on tire properties, as well as to develop a model that can represent the vertical tire and vehicle behavior while traveling over a cleat under different vehicle loads.

[ES] La forma más exacta de conocer el desplazamiento de los neutrones a través de un medio material se consigue resolviendo la Ecuación del Transporte Neutrónico. Tres diferentes aproximaciones de esta ecuación se han investigado en esta tesis: Ecuación del transporte neutrónico resuelta por el método de Ordenadas Discretas, Ecuación de la Difusión y Ecuación de Armónicos Esféricos Simplificados. Para resolver estás ecuaciones se estudian diferentes esquemas del Método de Diferencias Finitas. La solución a estas ecuaciones describe la población de neutrones y las reacciones ocasionadas dentro de un reactor nuclear. A su vez, estas variables están relacionadas con el flujo y la potencia, parámetros fundamentales para el Análisis de Seguridad Nuclear. La tesis introduce la definición de las ecuaciones mencionadas y en particular se detallan para el estado estacionario. Se plantea el Método Modal como solución a los problemas de autovalores definidos por dichas ecuaciones. Primero se desarrollan varios algoritmos para la resolución del estado estacionario de la Ecuación del Transporte de Neutrones con el Método de Ordenadas Discretas para la discretización angular y el Método de Diferencias Finitas para la discretización espacial. Se ha implementado una formulación capaz de resolver el problema de autovalores para cualquier número de grupos energéticos con upscattering y anisotropía. Varias cuadraturas utilizadas por este método en su resolución angular han sido estudiadas e implementadas para cualquier orden de aproximación de Ordenadas Discretas. Además, otra formulación se desarrolla para la solución del problema fuente de la ecuación del transporte neutrónico. A continuación, se lleva a cabo un algoritmo que permite resolver la Ecuación de la Difusión de Neutrones con dos variantes del método de diferencias Finitas, una centrada en celda y otra en vértice o nodo. Se utiliza también el Método Modal calculando cualquier número de autovalores para varios grupos de energía y con upscattering. También se implementan los dos esquemas del Método de Diferencias Finitas anteriormente mencionados en el desarrollo de diferentes algoritmos para resolver las Ecuaciones de Armónicos Esféricos Simplificados. Además, se ha realizado un análisis de diferentes aproximaciones de las condiciones de contorno. Finalmente, se han realizado cálculos de la constante de multiplicación, los modos subcríticos, el flujo neutrónico y la potencia para diferentes tipos de reactores nucleares. Estas variables resultan esenciales en Análisis de Seguridad Nuclear. Además, se han realizado diferentes estudios de sensibilidad de parámetros como tamaño de malla, orden utilizado en cuadraturas o tipo de cuadraturas. / [CA] La forma més exacta de conèixer el desplaçament dels neutrons a través d'un mitjà material s'aconsegueix resolent l'Equació del Transport Neutrònic. Tres diferents aproximacions d'esta equació s'han investigat en aquesta tesi: Equació del Transport Neutrònic resolta pel mètode d'Ordenades Discretes, Equació de la Difusió i Equació d'Ármonics Esfèrics Simplificats. Per a resoldre estes equacions s'estudien diferents esquemes del Mètode de Diferències Finites. La solució a estes equacions descriu la població de neutrons i les reaccions ocasionades dins d'un reactor nuclear. Al seu torn, estes variables estan relacionades amb el flux i la potència, paràmetres fonamentals per a l'Anàlisi de Seguretat Nuclear. La tesi introduïx la definició de les equacions mencionades i en particular es detallen per a l'estat estacionari. Es planteja el Mètode Modal com a solució als problemes d'autovalors definits per les dites equacions. Primer es desenvolupen diversos algoritmes per a la resolució de l'estat estacionari de l'Equació del Transport de Neutrons amb el Mètode d'Ordenades Discretes per a la discretiztació angular i el Mètode de Diferències Finites per a la discretització espacial. S'ha implementat una formulació capaç de resoldre el problema d'autovalors per a qualsevol nombre de grups energètics amb upscattering i anisotropia. Diverses quadratures utilitzades per este mètode en la seua resolució angular han sigut estudiades i implementades per a qualsevol orde d'aproximació d'Ordenades Discretes. A més, una altra formulació es desenvolupa per a la solució del problema font de l'Equació del Transport Neutrònic. A continuació, es du a terme un algoritme que permet resoldre l'Equació de la Difusió de Neutrons amb dos variants del mètode de Diferències Finites, una centrada en cel·la i una altra en vèrtex o node. S'utilitza també el Mètode Modal calculant qualsevol nombre d'autovalors per a diversos grups d'energia i amb upscattering. També s'implementen els dos esquemes del Mètode de Diferències Finites anteriorment mencionats en el desenvolupament de diferents algoritmes per a resoldre les Equacions d'Harmònics Esfèrics Simplificats. A més, s'ha realitzat una anàlisi de diferents aproximacions de les condicions de contorn. Finalment, s'han realitzat càlculs de la constant de multiplicació, els modes subcrítics, el flux neutrònic i la potència per a diferents tipus de reactors nuclears. Estes variables resulten essencials en Anàlisi de Seguretat Nuclear. A més, s'han realitzat diferents estudis de sensibilitat de paràmetres com la grandària de malla, orde utilitzat en quadratures o tipus de quadratures. / [EN] The most accurate way to know the movement of the neutrons through matter is achieved by solving the Neutron Transport Equation. Three different approaches to solve this equation have been investigated in this thesis: Discrete Ordinates Neutron Transport Equation, Neutron Diffusion Equation and Simplified Spherical Harmonics Equations. In order to solve the equations, different schemes of the Finite Differences Method were studied. The solution of these equations describes the population of neutrons and the occurred reactions inside a nuclear system. These variables are related with the flux and power, fundamental parameters for the Nuclear Safety Analysis. The thesis introduces the definition of the mentioned equations. In particular, they are detailed for the steady state case. The Modal Method is proposed as a solution to the eigenvalue problems determined by the equations. First, several algorithms for the solution of the steady state of the Neutron Transport Equation with the Discrete Ordinates Method for the angular discretization and Finite Difference Method for spatial discretization are developed. A formulation able to solve eigenvalue problems for any number of energy groups, with scattering and anisotropy has been developed. Several quadratures used by this method for the angular discretization have been studied and implemented for any order of approach of the discrete ordinates. Furthermore, an adapted formulation has been developed as a solution of the source problem for the Neutron Transport Equation. Next, an algorithm is carried out that allows to solve the Neutron Diffusion Equation with two variants of the Finite Difference Method, one with cell centered scheme and another edge entered. The Modal method is also used for calculating any number of eigenvalues for several energy groups and upscattering. Both Finite Difference schemes mentioned before are also implemented to solve the Simplified Spherical Harmonics Equations. Moreover, an analysis of different approaches of the boundary conditions is performed. Finally, calculations of the multiplication factor, subcritical modes, neutron flux and the power for different nuclear reactors were carried out. These variables result essential in Nuclear Safety Analysis. In addition, several sensitivity studies of parameters like mesh size, quadrature order or quadrature type were performed. / Me gustaría dar las gracias al Ministerio de Economía, Industria y Competitividad y a la Agencia Estatal de Investigación de España por la concesión de mi contrato predoctoral de formación de personal investigador con referencia BES-2016-076782. La ayuda económica proporcionada por este contrato fue esencial para el desarrollo de esta tesis, así como para el financiamiento de una estancia. / Morato Rafet, S. (2020). Contributions to solve the Multi-group Neutron Transport equation with different Angular Approaches [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/159271

[pt] Para avaliar projetos de investimento florestal, a Teoria de Opções Reais é utilizada com o propósito de incorporar questões relacionadas a incertezas e flexibilidades gerenciais. O objetivo desta dissertação é desenvolver uma modelagem para valoração de um projeto florestal, no qual a variação do estoque de árvores se aproxima do crescimento real de uma floresta, utilizando uma adaptação da equação logística. Desta forma, para um determinado nível de saturação, o estoque se estabiliza. Adicionalmente, o trabalho busca quantificar os benefícios econômicos de uma política ótima de produção a partir do corte de árvores. Para a análise proposta, os resultados são obtidos através do método de diferenças finitas explícitas. O problema apresenta três variáveis independentes - estoque, tempo e preço, sendo este modelado como um Movimento Geométrico Browniano - e duas variáveis dependentes - a taxa de corte e o valor da opção de investimento. É apresentada uma aplicação para uma floresta de eucalipto e os resultados são comparados considerando outras alternativas para a evolução do estoque de árvores, bem como para a decisão da quantidade a ser cortada. Para esta comparação, avalia-se o caso em que o estoque segue um modelo estocástico e o caso em que a taxa de corte é fixa. Os resultados mostram que é vantajoso adotar uma política ótima de corte, corroborando resultados obtidos em trabalhos anteriores de opções reais na área florestal. Além disso, o maior valor da opção é obtido quando o estoque é modelado pela equação logística para o crescimento. / [en] In order to incorporate uncertainty and managerial flexibilities in forestry investment projects, financial literature uses the real options approach. The aim of this work is to develop a model for valuation of a forestry project, in which the inventory growth of trees follows a logistic equation based in the estimated real growth of a forest. Thus, for a given level of saturation, the inventory stabilizes. In addition, this dissertation aims to quantify the economic benefits of an optimal production policy from cutting trees. For the proposal analysis, the results are obtained by the finite difference method in the explicit form. The problem has three independent variables – inventory, time and price, which is modeled as a Geometric Brownian Motion – and two dependent variables – the cutting rate and the value of the investment option. An application for an eucalyptus forest is presented and the results are compared considering other alternatives for the evolution of the inventory and for the decision on the cutting amount. For this purpose, two different assumptions are made, considering a stochastic model for the inventory and a fixed shear rate. The results show that it is advantageous to adopt a optimal cutting policy, confirming results obtained in previous studies of real options in forestry. Moreover, the greatest option value is obtained when the inventory is modeled by logistic equation for growth.

Ce travail de thèse est consacré à la mise en œuvre d’une méthode de décomposition de domaine appliquée à l’équation du transport. L’objectif de ce travail est l’accès à des solutions déterministes haute-fidélité permettant de correctement traiter les hétérogénéités des réacteurs nucléaires, pour des problèmes dont la taille varie d’un motif d’assemblage en 3 dimensions jusqu’à celle d’un grand cœur complet en 3D. L’algorithme novateur développé au cours de la thèse vise à optimiser l’utilisation du parallélisme et celle de la mémoire. La démarche adoptée a aussi pour but la diminution de l’influence de l’implémentation parallèle sur les performances. Ces objectifs répondent aux besoins du projet APOLLO3, développé au CEA et soutenu par EDF et AREVA, qui se doit d’être un code portable (pas d’optimisation sur une architecture particulière) permettant de réaliser des modélisations haute-fidélité (best estimate) avec des ressources allant des machines de bureau aux calculateurs disponibles dans les laboratoires d’études. L’algorithme que nous proposons est un algorithme de Jacobi Parallèle par Bloc Multigroupe. Chaque sous domaine est un problème multigroupe à sources fixes ayant des sources volumiques (fission) et surfaciques (données par les flux d’interface entre les sous domaines). Le problème multigroupe est résolu dans chaque sous domaine et une seule communication des flux d’interface est requise par itération de puissance. Le rayon spectral de l’algorithme de résolution est rendu comparable à celui de l’algorithme de résolution classique grâce à une méthode d’accélération non linéaire par la diffusion bien connue nommée Coarse Mesh Finite Difference. De cette manière une scalabilité idéale est atteignable lors de la parallélisation. L’organisation de la mémoire, tirant parti du parallélisme à mémoire partagée, permet d’optimiser les ressources en évitant les copies de données redondantes entre les sous domaines. Les architectures de calcul à mémoire distribuée sont rendues accessibles par un parallélisme hybride qui combine le parallélisme à mémoire partagée et à mémoire distribuée. Pour des problèmes de grande taille, ces architectures permettent d’accéder à un plus grand nombre de processeurs et à la quantité de mémoire nécessaire aux modélisations haute-fidélité. Ainsi, nous avons réalisé plusieurs exercices de modélisation afin de démontrer le potentiel de la réalisation : calcul de cœur et de motifs d’assemblages en 2D et 3D prenant en compte les contraintes de discrétisation spatiales et énergétiques attendues. / This thesis is devoted to the implementation of a domain decomposition method applied to the neutron transport equation. The objective of this work is to access high-fidelity deterministic solutions to properly handle heterogeneities located in nuclear reactor cores, for problems’ size ranging from colorsets of assemblies to large reactor cores configurations in 2D and 3D. The innovative algorithm developed during the thesis intends to optimize the use of parallelism and memory. The approach also aims to minimize the influence of the parallel implementation on the performances. These goals match the needs of APOLLO3 project, developed at CEA and supported by EDF and AREVA, which must be a portable code (no optimization on a specific architecture) in order to achieve best estimate modeling with resources ranging from personal computer to compute cluster available for engineers analyses. The proposed algorithm is a Parallel Multigroup-Block Jacobi one. Each subdomain is considered as a multi-group fixed-source problem with volume-sources (fission) and surface-sources (interface flux between the subdomains). The multi-group problem is solved in each subdomain and a single communication of the interface flux is required at each power iteration. The spectral radius of the resolution algorithm is made similar to the one of a classical resolution algorithm with a nonlinear diffusion acceleration method: the well-known Coarse Mesh Finite Difference. In this way an ideal scalability is achievable when the calculation is parallelized. The memory organization, taking advantage of shared memory parallelism, optimizes the resources by avoiding redundant copies of the data shared between the subdomains. Distributed memory architectures are made available by a hybrid parallel method that combines both paradigms of shared memory parallelism and distributed memory parallelism. For large problems, these architectures provide a greater number of processors and the amount of memory required for high-fidelity modeling. Thus, we have completed several modeling exercises to demonstrate the potential of the method: 2D full core calculation of a large pressurized water reactor and 3D colorsets of assemblies taking into account the constraints of space and energy discretization expected for high-fidelity modeling.

Le domaine du photovoltaïque en couches minces s’attache à réduire le coût de l’énergie photovoltaïque, en réduisant considérablement la quantité de matières premières utilisées. Dans le cas du silicium cristallin en couches minces, la réduction de l’épaisseur de la cellule s’accompagne d’une baisse drastique de l’absorption, notamment pour les plus fortes longueurs d’onde. Nombreuses sont les techniques aujourd’hui mises en œuvre pour lutter contre cette baisse de performance, dont l’utilisation des effets plasmoniques induits par des nanostructures métalliques qui permettent un piégeage de la lumière accru dans la couche absorbante. Dans ces travaux, nous étudions l’influence de nanostructures d’argent organisées suivant un réseau périodique sur l’absorption d’une couche de silicium. Ces travaux s’articulent autour de deux axes majeurs. L’influence de ces effets plasmoniques sur l’absorption est d’abord mise en évidence à travers différentes simulations numériques réalisées par la méthode FDTD. Nous étudions ainsi les cas de réseaux périodiques finis et infinis de nanostructures d’argent situés sur la face arrière d’une couche mince de silicium. En variant les paramètres du réseau, nous montrons que l’absorption au sein du silicium peut être améliorée dans le proche infrarouge, sur une large plage de longueurs d’onde. Le second volet de la thèse concerne la réalisation des structures modélisées. Pour cela, deux voies de fabrication ont été explorées et développées. Pour chacune d’entre elles, trois briques élémentaires ont été identifiées : (i) définition du futur motif du réseau grâce à un masque, (ii) réalisation de pores dans le silicium et (iii) remplissage des pores par de l’argent pour former le réseau métallique. La première voie de fabrication développée fait appel à un masque d’alumine, réalisé par l’anodisation électrochimique d’une couche d’aluminium, pour définir les dimensions du réseau métallique. Une gravure chimique assistée par un métal est ensuite utilisée pour former les pores, qui seront alors comblés grâce à des dépôts d’argent par voie humide. La seconde voie de fabrication utilise un masque réalisé par lithographie holographique, une gravure des pores par RIE et un remplissage des pores par dépôt d’argent electroless. Les substrats plasmoniques fabriqués sont caractérisés optiquement, au moyen d’une sphère intégrante, par des mesures de transmission, réflexion et absorption. Pour tous les substrats plasmoniques caractérisés, les mesures optiques montrent une baisse de la réflexion et de la transmission et une hausse de l’absorption pour les plus grandes longueurs d’onde. / Thin-film photovoltaics focus on lowering the cost reduction of photovoltaic energy through the significant reduction of raw materials used. In the case of thin-films crystalline silicon, the reduction of the thickness of the cell is linked to a drastic decrease of the absorption, particularly for the higher wavelengths. This decrease of the absorption can be fought through the use of several different light trapping methods, and the use of plasmonic effects induced by metallic nanostructures is one of them. In this work, we study the influence of a periodic array of silver nanostructures on the absorption of a silicon layer. This work is decomposed into two main axes. First, the influence of the plasmonic effects on the silicon absorption is highlighted through different numerical simulations performed by the FDTD method. Both finite and infinite arrays of silver nanostructures, located at the rear side of a thin silicon layer, are studied. By varying the parameters of the array, we show that the silicon absorption can be improved in the near infrared spectral region, over a wide range of wavelengths. The second part of the thesis is dedicated to the fabrication of such modeled structures. Two different approaches have been explored and developed inside the lab. For each of these two strategies, three major building blocks have been identified: (i) definition of the future array pattern through a mask, (ii) etching of the pattern in the silicon layer and (iii) filling of the pores with silver in order to form the metallic array of nanostructures. In the first fabrication method, an anodic alumina mask, produced by the electrochemical anodization of an aluminium layer, is used in order to define the dimensions of the metallic array. A metal assisted chemical etching is then performed to produce the pores inside the silicon, which will then be filled with silver through a wet chemical process. The second fabrication method developed involves the use of holographic lithography to produce the mask, the pores in silicon are formed by reactive ion etching and they are filled during an electroless silver deposition step. The fabricated plasmonic substrates are optically characterized using an integrating sphere, and transmission, reflection and absorption are measured. All the characterized plasmonic substrates shown a decrease of their reflection and transmission and an absorption enhancement at the largest wavelengths.

This thesis develops the methodology for solving initial boundary value problems with the use of summation-by-parts discretizations. The combination of high orders of accuracy and a systematic approach to construct provably stable boundary and interface procedures makes this methodology especially suitable for scientific computations with high demands on efficiency and robustness. Most classes of high order methods can be applied in a way that satisfies a summation-by-parts rule. These include, but are not limited to, finite difference, spectral and nodal discontinuous Galerkin methods. In the first part of this thesis, the summation-by-parts methodology is extended to the time domain, enabling fully discrete formulations with superior stability properties. The resulting time discretization technique is closely related to fully implicit Runge-Kutta methods, and may alternatively be formulated as either a global method or as a family of multi-stage methods. Both first and second order derivatives in time are considered. In the latter case also including mixed initial and boundary conditions (i.e. conditions involving derivatives in both space and time). The second part of the thesis deals with summation-by-parts discretizations on multi-block and hybrid meshes. A new formulation of general multi-block couplings in several dimensions is presented and analyzed. It collects all multi-block, multi-element and  hybrid summation-by-parts schemes into a single compact framework. The new framework includes a generalized description of non-conforming interfaces based on so called summation-by-parts preserving interpolation operators, for which a new theoretical accuracy result is presented.

本文的主要內容為評價JPMorgan Chase & Co.（美國摩根大通銀行）及UBS（瑞士銀行）所發行的兩檔結構型票券，共同的特色是票券為保本型且不付息，報酬條款中附有雙重界限觸及失效選擇權，其價值對於標的資產的波動程度相當敏感。一旦標的資產價格觸及任一界限，具有額外收益的選擇權將失效，投資人僅能拿回原始投資本金，相當於損失了原本可能獲得的無風險利息。 　　針對雙重界限觸及失效選擇權，我們使用顯式、隱式以及Crank-Nicolson三種有限差分法來進行評價，並比較蒙地卡羅模擬和封閉解的結果，藉以了解各種方法的準確性及效率。接著我們求算避險參數Greeks，分析發行商所面臨的風險。同時根據市場未來的情況，分析投資人的預期收益，進而了解這種商品在市場上廣為流通的原因，以及此類新奇結構型商品對於風險的重分配方式，如何締造買方賣方雙贏的局面。