Refratários são materiais com microestrutura heterogênea constituída de uma fração grosseira, os agregados, e de uma fração mais fina, a matriz, em que ambas exercem papéis fundamentais nas propriedades dos refratários, sendo a resistência ao dano por choque térmico, uma das mais importantes. Para avaliar essa questão crítica dos refratários há necessidade de se conhecer bem seu comportamento à propagação de trinca, principalmente quando submetido a uma tensão. Porém, devido à complexidade da estrutura desses materiais, o comportamento das regiões à frente e atrás da ponta da trinca sempre foi muito discutido, só que essa discussão sempre fez uso de modelos e simulações computacionais, já que é prevista uma zona de processo, em que diferentes mecanismos podem absorver energia aumentando a resistência à propagação da trinca principal. Nesta tese foi proposto o estudo experimental do comportamento da propagação de trinca em refratários, visando entender os mecanismos de resistência à propagação de trinca e o caminho das trincas propagantes, utilizando o método da cunha para propagação estável da trinca, que é o mais adequado para essa classe de materiais. Para isso foram utilizados, dois refratários distintos: tijolo e concreto, ambos de alta alumina. No tijolo, para visualização do caminho da trinca propagante após o ensaio, o caminho da trinca foi infiltrado com cola instantânea para garantir a integridade da mesma, a fim que amostras pudessem ser preparadas para análise de imagens em microscópio eletrônico de varredura. Devido à dificuldade dessa preparação, e de só ser possível observar a trinca após a propagação, um microscópio digital passou a ser utilizado in loco ao ensaio. Esse estudo foi realizado com o concreto, sendo possível associar o comprimento da trinca com a curva carga-deslocamento. A fim de complementar o estudo do processo de fratura, a técnica de emissão acústica (EA) passou a ser utilizada nos ensaios de propagação de trinca, já que quando um material é submetido a uma carga e as trincas se desenvolvem, há liberação de energia de deformação do material, sendo possível capturar os dados de energia dos sinais gerados pela propagação. Sendo assim foi possível correlacionar resultados de energia de fratura, início e tamanho de trinca com as curvas carga-deslocamento, carga-tempo, e inclusive, com a contagem de sinais acumulada-tempo, que foi complementar na estimativa da zona de processo completa, ou seja, os fenômenos produzidos atingiram o estado estacionário. A região em que se encontra o final da zona de processo coincide com o fim do regime estacionário, que é onde a trinca atravessa o corpo de prova. Dessa forma, mostra-se com essa tese, que o corpo de prova utilizado para a propagação estável de trinca pelo método da cunha, nas dimensões atuais, são suficientes para o desenvolvimento de todos os mecanismos de resistência à propagação de trinca em refratários. / Refractories are materials with heterogeneous microstructure, consisting of a coarse fraction, aggregates, and a finer fraction, the matrix, in which both play key roles in the properties of the refractory, and the resistance to thermal shock damage, one of the most important. To examine this critical issue of the refractory is no need to be familiar with their behavior to crack propagation, especially when subjected to a stress. The behavior of the regions ahead of and behind the crack tip has been discussed exhaustively, because a process zone was envisaged in which different mechanisms could absorb energy, thus increasing the propagation resistance of the main crack. However, this discussion has always been based on the use of models and computer simulations. The thesis presented here proposes an experimental study of the behavior of crack propagation in refractories, aiming to understand the mechanisms of crack propagation resistance and the crack propagation path, using the wedge splitting method to achieve stable crack propagation. To this end, two different refractory materials were used: brick and concrete, both high alumina. Based on the stable crack propagation test by the wedge method, techniques were sought that would aid in the visualization of crack propagation. In brick, the crack path was infiltrated with instant glue and infiltrated samples were examined by scanning electron microscopy (SEM); however, in addition to proving laborious, the crack was only visible after its propagation. In the case of concrete, this study was performed in loco during the test, using a digital microscope in combination with the acoustic emission (AE) technique. AE is defined as the generation of stress waves stored energy is suddenly released from localized sources within a material subjected to external loads. By means of the fracture energy data and the AE signals, it was possible to observe the entire fracture process and to correlate the results of fracture energy and crack onset and size with the load-displacement and load-time curves, and even the count of signals accumulated over time. This information was complementary to estimate the complete process zone, i.e., the phenomena produced reached the steady state. This study demonstrated that the dimensions of the test specimen used for stable crack propagation by the wedge splitting method suffice for the development of all the mechanisms of crack propagation resistance in refractories.

Tese de mestrado integrado. Engenharia Electrotécnica e de Computadores. Faculdade de Engenharia. Universidade do Porto. 2012

La séparation photoélectrochimique de l'eau (PEC) est un moyen direct de produire un combustible solaire tel que l'hydrogène à partir de l'eau. Le goulot d'étranglement de ce processus se situe dans la photoanode, qui est responsable du côté oxydation de la réaction1,2. Dans ce travail, l'utilisation de BiVO4 en tant que photoanode a été largement étudiée afin d'améliorer sa photoactivité. L’optimisation de la synthèse de photoanodes BiVO4 par électrodéposition en couche mince sur du FTO a été réalisée. Les facteurs influant sur l'activité photoélectrochimique, tels que le temps d'électrodéposition, le rapport Bi-KI/benzoquinone-EtOH dans le bain de dépôt et la température de calcination, ont été étudiés à l'aide de la conception composite centrale d'expériences. Les états de surface sur la surface de BiVO4 donnent lieu à des niveaux de défaut pouvant induire une recombinaison électron-trou via le mécanisme de Shockley-Read-Hall5. Afin de minimiser les inefficacités dues à la recombinaison électron-trou et passiver les états de surface, des couches de recouvrement ultra-fines d'Al2O3 et de TiO2 ont été déposées sur les électrodes en film mince BiVO4 d'une manière analogue à l'ALD. Cela a également été réalisé afin de protéger la surface de BiVO4 de la photocorrosion et d’augmenter sa stabilité. Une densité de photocourant de 0,54 mA/cm2 à 1,23 V vs RHE a été obtenue pour les 2 cycles de BiVO4 modifié par Al2O3, comme le montre la Figure 2, soit une amélioration de 54% par rapport à la BiVO4 nue qui démontrait une densité de photocourant de 0,35 mA/cm2. à 1,23 V vs RHE. Une augmentation de 15% de la stabilité de l'électrode de BiVO4 modifiée par Al2O3 a également été observée au cours de 7,5 heures d'irradiation continue. De plus, grâce aux mesures de capacité de surface présentées à la Figure 3, il a été montré que la surcouche de Al2O3 passivait effectivement à passiver les états de surface des électrodes de BiVO4. La nature de la surface de BiVO4 a été étudiée en étudiant la réactivité de la poudre de BiVO4 avec un titrant chimique. L’existence de groupes hydroxyle de surface sur BiVO4 a été confirmée et quantifiée (max. 1,5 OH / nm2) par titrage chimique. La réaction de la poudre de BiVO4 avec une impulsion de AlMe3 et une impulsion de H2O a montré qu'il existait 1,2 molécules de CH4 dégagées par Bi-OH. Dans ce travail, nous avons pu mettre en évidence les facteurs importants dans la synthèse de BiVO4 et leur incidence sur la photoactivité résultante. Nous avons également réussi à passiver les états de surface de BiVO4 en utilisant Al2O3, ce qui n’est pas bien exploré dans la littérature. De plus, nous avons pu sonder et discuter de la nature de la surface de BiVO4. Ceci est une connaissance très fondamentale et le premier rapport à ce sujet, à notre connaissance. Une bonne compréhension de cette surface semi-conductrice importante et de ses interactions facilitera la conception d'un photoanode BiVO4 plus efficace / Photoelectrochemical (PEC) water splitting is a direct way of producing a solar fuel like hydrogen from water. The bottleneck of this process is in the photoanode, which is responsible for the water oxidation side of the reaction1,2. In this work, the use of BiVO4 as a photoanode was extensively studied in order to improve its photoactivity. The optimization of BiVO4 photoanode synthesis via thin film electrodeposition on FTO was performed. The factors affecting the photoelectrochemical activity such as the electrodeposition time, ratio of the Bi-KI to benzoquinone-EtOH in the deposition bath, and the calcination temperature, have been investigated by using the Central Composite Design of Experiments.Surface states on the BiVO4 surface give rise to defect levels, which can mediate electron-hole recombination via the Shockley-Read-Hall mechanism5. In order to protect the BiVO4 surface and minimize the inefficiencies due to electron-hole recombination and passivate the surface states, ultrathin overlayers of Al2O3 and TiO2 were deposited to the BiVO4 thin film electrodes in an ALD-like manner. A photocurrent density of 0.54 mA/cm2 at 1.23 V vs RHE was obtained for the 2 cycles Al2O3-modified BiVO4, which was a 54% improvement from the bare BiVO4 that demonstrated a photocurrent density of 0.35 mA/cm2 at 1.23 V vs RHE. A 15% increase in stability of the Al2O3- modified BiVO4 electrode was also observed over 7.5 hours of continuous irradiation. Moreover, through surface capacitance measurements, it was shown that the Al2O3 overlayer was indeed passivating the surface states of the BiVO4 electrodes. The nature of the BiVO4 surface was studied by investigating the reactivity of powder BiVO4 with a chemical titrant. The existence of surface hydroxyl groups on BiVO4 was confirmed and quantified (max 1.5 OH/nm2) via chemical titration. The reaction of the BiVO4 powder with one pulse of AlMe3 and 1 pulse of H2O showed that there were 1.2 molecules of CH4 evolved per Bi-OH. In this work, we were able to highlight which factors are important in the synthesis of BiVO4, and how they affect the resulting photoactivity. We have also achieved the passivation of the BiVO4 surface states using Al2O3, which is not well-explored in literature. Moreover, we were able to probe and discuss the nature of the BiVO4 surface. This is a very fundamental knowledge and the first report of such, to the best of our knowledge. A good understanding of this important semiconductor surface and its interactions will aid in the design of a more efficient BiVO4 photoanode

Directional wave-field decomposition for heterogeneousanisotropic media with in-stantaneous response is establishedfor both the acoustic and the electromagnetic equations. We derive a sufficient condition for ellipticity of thesystem's matrix in the Laplace domain and show that theconstruction of the splitting matrix via a Dunford-Taylorintegral over the resolvent of the non-compact, non-normalsystem's matrix is well de ned. The splitting matrix also hasproperties that make it possible to construct the decompositionwith a generalized eigenvector procedure. The classical way ofobtaining the decomposition is equivalent to solving analgebraic Riccati operator equation. Hence the proceduredescribed above also provides a solution to the algebraicRiccati operator equation. The solution to the wave-field decomposition for theisotropic wave equation is expressed in terms of theDirichlet-to-Neumann map for a plane. The equivalence of thisDirichlet-to-Neumann map is the acoustic admittance, i.e. themapping between the pressure and the particle velocity. Theacoustic admittance, as well as the related impedance aresolutions to algebraic Riccati operator equations and are keyelements in the decomposition. In the electromagnetic case thecorresponding impedance and admittance mappings solve therespective algebraic Riccati operator equations and henceprovide solutions to the decomposition problem. The present research shows that it is advantageous toutilize the freedom implied by the generalized eigenvectorprocedure to obtain the solution to the decomposition problemin more general terms than the admittance/impedancemappings. The time-reversal approach to steer an acoustic wave eld inthe cavity and half space geometries are analyzed from aboundary control perspective. For the cavity it is shown thatwe can steer the field to a desired final configuration, withthe assumption of local energy decay. It is also shown that thetime-reversal algorithm minimizes a least square error forfinite times when the data are obtained by measurements. Forthe half space geometry, the boundary condition is expressedwith help of the wave-field decomposition. In the homogeneousmaterial case, the response of the time-reversal algorithm iscalculated analytically. This procedure uses the one-wayequations together with the decomposition operator.

There are some nonlinear models for pricing financial derivatives which can improve the linear Black-Scholes model introduced by Black, Scholes and Merton. In these models volatility is not constant anymore, but depends on some extra variables. It can be, for example, transaction costs, a risk from a portfolio, preferences of a large trader, etc. In this thesis we focus on these models. In the first chapter we introduce some important theory of financial derivatives. The second chapter is devoted to the volatility models. We derive three models concerning transaction costs (RAPM, Leland's  and Barles-Soner's model) and Frey's model which assumes a large (dominant) trader on the market. In the third and in the forth chapter we derive portfolio and make numerical experiments with a free boundary. We use the first order additive and the second order Strang splitting methods. We also use approximations of Barles-Soner's model using the identity function and introduce an approximation with the logarithm function of Barles-Soner's model. These models we finally compare with models where the volatility includes constant transaction costs.

In the thesis we consider two types of problems. In Paper 1, we study small solutions to a time-independent nonlinear elliptic partial differential equation of Emden-Fowler type in a semi-infnite cylinder. The asymptotic behaviour of these solutions at infnity is determined. First, the equation under the Neumann boundary condition is studied. We show that any solution small enough either vanishes at infnity or tends to a nonzero periodic solution to a nonlinear ordinary differential equation. Thereafter, the same equation under the Dirichlet boundary condition is studied, the non-linear term and right-hand side now being slightly more general than in the Neumann problem. Here, an estimate of the solution in terms of the right-hand side of the equation is given. If the equation is homogeneous, then every solution small enough tends to zero. Moreover, if the cross-section is star-shaped and the nonlinear term in the equation is subject to some additional constraints, then every bounded solution to the homogeneous Dirichlet problem vanishes at infnity. In Paper 2, we study asymptotics as t → ∞ of solutions to a linear, parabolic system of equations with time-dependent coefficients in Ωx(0,∞), where Ω is a bounded domain. On δΩ(0,∞) we prescribe the homogeneous Dirichlet boundary condition. For large values of t, the coefficients in the elliptic part are close to time-independent coefficients in an integral sense which is described by a certain function κ(t). This includes in particular situations when the coefficients may take different values on different parts of Ω and the boundaries between them can move with t but stabilize as t → ∞. The main result is an asymptotic representation of solutions for large t. As a corollary, it is proved that if κєL1(0,∞), then the solution behaves asymptotically as the solution to a parabolic system with time-independent coefficients.

The upper mantle structure of Swedish part of Baltic Shield with its isotropic and anisotropic seismic velocity characteristics is investigated using telesesismic body waves (i.e. P waves and shear waves) recorded by the Swedish National Seismological Network (SNSN). Nonlinear high-resolution P and SV and SH wave isotropic tomographic inversions reveal velocity perturbations of ± 3 % down to at least 470 km below the network. Separate SV and SV models indicate several consistent major features, many of which are also consistent with P-wave results. A direct cell by cell comparison of SH and SV models reveals velocity differences of up to 4%. Numerical tests show that differences in the two S-wave models can only be partially caused by noise and limited resolution, and some features are attributed to the effect of large scale anisotropy. Shear-wave splitting and P-travel time residual analyses also detect anisotropic mantle structure. Distinct back-azimuth dependence of SKS splitting excludes single-layer anisotropy models with horizontal symmetry axes for the whole region. Joint inversion using both the P and S data reveals 3D self-consistent anisotropic models with well-defined mantle lithospheric domains. These domains of differently oriented anisotropy most probably retain fossil fabric since the domains' origin, supporting the idea of the existence of an early form of plate tectonics during formation of continental cratons already in the Archean. The possible disturbing effects of anisotropy on seismic tomography studies are investigated, and found to be potentially significant. P-wave arrival times were adjusted based on the estimates of mantle anisotropy, and re-inverted. The general pattern of the velocity-perturbation images was similar but changed significantly in some places, including the disappearance of a slab-like structure identified in the inversion with the original data. Thus the analysis demonstrates that anisotropy of quite plausible magnitude can have a significant effect on the tomographic images, and should not be ignored. If, as we believe, our estimates of anisotropy are reasonably correct, then the model based on the adjusted data should give a more robust and correct image of the mantle structure.

És difícil dibuixar una frontera, dins la Teoria de Sistemas Dinàmics, entre lleis de conservació i simetries doncs, sovint, les seves característiques es confonen. Un clar exemple d'aquest fenómen el constitueixen els sistemes Hamiltonians i els sistemes reversibles.Breument, un sistema dinàmic es diu temps-reversible (o, per nosaltres, simplement reversible) si és invariant sota l'acció d'un difeomorfisme involutiu a l'espai i una inversió en el sentit del temps. és en aquest marc on cal situar aquesta memòria. Concretament, ens centrem en dos punts molt particulars: la Teoria de Formes Normals i el fenómen del trencament de separatrius, tots dos introduïts per Poincaré a la seva tesi (1890).Respecte al primer d'aquests punts, en aquesta tesi s'introdueix el concepte de Pseudo Forma Normal (breument PNF), inspirat en idees d'en Moser, i que permet transformar, sota certes hipotesis, un sistema analític en un d'equivalent d'aspecte el més simple possible. Aquesta PNF és una generalització de la coneguda Forma Normal de Birkhoff amb la qual coincideix si el sistema considerat és Hamiltonià o reversible. Com a conseqüència, s'obté, en determinats casos, l'equivalència local entre aquests dos tipus de sistemes. Aquesta PNF pot esdevenir una eina útil per estudiar la dinàmica d'un sistema analític a l'entorn d'un equilibri (un punt, una òrbita periòdica o un tor).El segon punt, l'escissió de separatrius, fa referència a l'intersecció transversal de varietats invariants procedent del trencament d'una certa connexió homoclínica a l'afegir al sistema una petita pertorbació. Un dels motius d'interés sobre aquest fenòmen és que és un dels principals causants de comportament estocàstic en sistemes Hamiltonians.Un problema relacionat amb aquest trencament de separatrius és el de mesurar-lo, sigui a partir del càlcul de l'angle amb el que es troben aquestes varietats per primer cop, per l'àrea que tanquen entre elles, etc. El mètode habitualment utilitzat per a estimar-lo és l'anomenat mètode de Poincaré-Melnikov. Malhauradament, si la pertorbació és ràpidament oscil-latòria els termes que proporciona aquest mètode són exponencialment petits en el paràmetre pertorbador, fet que dificulta el seu càlcul. En aquesta tesi s'ha demostrat, tal i com passa en el cas Hamiltonià, que en el cas d'un sistema reversible, respecte a una involució lineal, 2-dimensional i pertorbat de manera ràpidament periòdica i reversible, el mètode de Poincaré-Melnikov és correcte i dóna en primer ordre l'anomenada funció de Melnikov. / It is difficult, in the Theory of Dynamical Systems, to draw a boundary line between conservation laws and symmetries because often their effects on the dynamics are very similar. This is the case of the Hamiltonian and the Reversible systems.Briefly, a dynamical system is called time-reversible (or, simply, reversible) if it is invariant under the action of an involutive spatial diffeomorphism and a reversion in time's arrow. This is the frame where this work must be placed. Precisely, we focus our attention in two particular points: the Theory of Normal Forms and the phenomenon of the splitting of separatrices, both introduced by Poincare in his thesis (1890).Regarding the first one of this topics, we introduce the concept of Pseudo-normal Form (PNF in short). It comes from ideas of Moser and allows to transform, under suitable conditions, an analytic system around an equilibrium in another equivalent one having a quite simple form. This PNF is a generalization of the celebrated Birkhoff Normal Form and both coincide if the system is Hamiltonian or reversible. Consequently, the local equivalence between both types of systems is derived in some cases. This PNF can become a useful tool to study the dynamics of an analytic system in a neighborhood of an equilibrium (a fixed point, a periodic orbit or a torus).The second topic, the splitting of separatrices, is related to the transversal intersection of invariant manifolds derived from the splitting of a given homoclinic connection when some small perturbation is considered. One of the reasons that makes this phenomenon interesting is that it seems to be one of the main causes of the stochastic behavior in Hamiltonian systems.One problem related to this splitting of separatrices becomes to measure it, studying, for instance, some angle the form when they meet for the first time, the area of the first lobe, etc. The standard method to estimate this size is the celebrated Poincaré-Melnikov method. Unfortunately, if the perturbation oscillates rapidly the terms provided by this method are exponentially small in the perturbation parameter, and this fact makes this computation more involved. In this work we prove, like it happens in the Hamiltonian case, that in the case of a 2-dimensional analytic reversible system (reversible with respect to a linear spatial involution) perturbed by a rapidly periodic reversible perturbation, the Poincaré-Melnikov method works and it provides, at first order, the well known Melnikov Function.

This work deals with the bearing capacity of wood based I-joists Finite element models were analyzed to determine the bearing capacity of I-joists, using the finite element software Abaqus CAE. The purpose of this study is to compare the results from the developed FE-models with experimental results, and with a previously proposed design formula. To perform the analyses finite element models were created. The model consists of three parts:, the web (made of shell element), the flanges and steel plates used at the supports and loading points (made of solid elements) To determine the bearing capacity of the I-joist two types of analyses were performed, a linear buckling analysis to check the risk of web buckling and a static (stress) analysis to check the risk of splitting of the flanges. This study shows that the steel plate length, in some cases, has little or no impact on primarily the splitting load. Furthermore, the buckling load decreases as the depth of the beam increases, the influence of the depth being proportional to 1/h2. The depth of the beam has no impact on the risk of splitting of the flange.

In this thesis we investigate Asian oating strike options. We particu-larly focus on options with early exercise - American options. This typeof options are very lucrative to the end-users of commodities or ener-gies who are tend to be exposed to the average prices over time. Asianoptions are also very popular with corporations, who have ongoing cur-rency exposures. The main idea of the pricing is to examine the freeboundary position on which the value of the option is depending. Wefocus on developing a ecient numerical algorithm for this boundary.In the rst Chapter we give an informative description of the nancialderivatives including Asian options. The second Chapter is devoted tothe analytical derivation of the corresponding partial dierential equa-tion coming from the original Black - Scholes equation. The problemis simplied using transformation methods and dimension reduction. Inthe third and fourth Chapter we describe important numerical methodsand discretize the problem. We use the rst order Lie splitting and thesecond order Strang splitting. Finally, in the fth Chapter we makenumerical experiments with the free boundary and compare the resultwith other known methods.