O presente trabalho trata do desenvolvimento de uma ferramenta computacional para a análise de sólidos bidimensionais contendo múltiplas fissuras utilizando uma nova estratégia mediante a combinação do método da partição (spliting method) e formulação híbrido-Trefftz de tensão. A primeira consiste em um método de decomposição para a análise de sólidos contendo múltiplas fissuras pela partição do problema original (PG) em três subproblemas: subproblema global (PG(0)), onde o sólido é analisado sem a presença de fissuras, subproblemas locais (PL(k)), onde cada fissura é analisada individualmente e inserida em domínio arbitrário, e subproblemas globais (PG(k)), onde são computados os efeitos de interação entre fissuras. A solução de PG é obtida impondo a condição de nulidade do somatório das tensões nas faces das fissuras de todos os subproblemas. Por simplicidade, os subproblemas PG(0) e PG(k) são analisados via método dos elementos finitos clássico (MEF). Em contrapartida, os PL(k) são analisados via formulação híbrido-Trefftz visando uma alta eficiência na avaliação desses subproblemas contendo fissura. Essa formulação promove a aproximação dos campos de tensão e deslocamento no domínio e contorno do elemento, respectivamente, de maneira independente. As bases aproximativas do campo de tensão são formadas por funções solução da equação de Navier adicionadas às funções analíticas da mecânica da fratura. Assim, essa formulação proporciona uma boa solução do problema utilizando malha grosseira. Além disso, é possível obter os fatores de intensidade de tensão (FIT) da fissura diretamente da solução do sistema linear do problema. Resultados numéricos são apresentados a fim de ilustrar a aplicação da estratégia e sua eficiência ao alcançar soluções precisas aliado a um baixo custo computacional na análise. / This paper presents the development of a computational framework to the analysis of two dimensional solids containing multiple cracks using a new strategy with the combination of splitting method and hybrid-Trefftz stress formulation. The first consists of a decomposition method to the analysis of solids containing multiple cracks through the split of original problem (PG) into three subproblems: global subproblem (PG(0)), where the solid is analyzed without the cracks, local subproblems (PL(k)), where each crack is analyzed individually and insert in an arbitrary domain, and global subproblems (PG(k)), where the effects of the interaction between cracks are evaluated. Solution of PG is obtained using the condition that the sum of tractions on crack faces of all subproblems are null. For simplicity, subproblems PG(0) and PG(k) are analyzed by classical finite element method (FEM). On the other hand, PL(k) are analyzed by hibrid-Trefftz formulation aiming a high efficiency on the evaluation of cracked subproblems. This formulation promote the approximation of stresses and displacements fields on domain and boundary of elements, respectively, on an independent manner. Bases of appoximation of stress field are constructed by functions that solves the Navier equation with the addition of analitical functions of mechanic of fracture. Hence, this formulaition provides good solution of the problem with coarse mesh. Moreover, the stress intensity factors (SIF) of cracks may be obtained directly from the solution of linear system of the problem. Numerical results are presented in order to ilustrate the use of the strategy and its efficiency on the evaluating of accurate solutions with a low computational cost of the analysis.

O presente trabalho trata do desenvolvimento de uma ferramenta computacional para a análise de sólidos bidimensionais contendo múltiplas fissuras utilizando uma nova estratégia mediante a combinação do método da partição (spliting method) e formulação híbrido-Trefftz de tensão. A primeira consiste em um método de decomposição para a análise de sólidos contendo múltiplas fissuras pela partição do problema original (PG) em três subproblemas: subproblema global (PG(0)), onde o sólido é analisado sem a presença de fissuras, subproblemas locais (PL(k)), onde cada fissura é analisada individualmente e inserida em domínio arbitrário, e subproblemas globais (PG(k)), onde são computados os efeitos de interação entre fissuras. A solução de PG é obtida impondo a condição de nulidade do somatório das tensões nas faces das fissuras de todos os subproblemas. Por simplicidade, os subproblemas PG(0) e PG(k) são analisados via método dos elementos finitos clássico (MEF). Em contrapartida, os PL(k) são analisados via formulação híbrido-Trefftz visando uma alta eficiência na avaliação desses subproblemas contendo fissura. Essa formulação promove a aproximação dos campos de tensão e deslocamento no domínio e contorno do elemento, respectivamente, de maneira independente. As bases aproximativas do campo de tensão são formadas por funções solução da equação de Navier adicionadas às funções analíticas da mecânica da fratura. Assim, essa formulação proporciona uma boa solução do problema utilizando malha grosseira. Além disso, é possível obter os fatores de intensidade de tensão (FIT) da fissura diretamente da solução do sistema linear do problema. Resultados numéricos são apresentados a fim de ilustrar a aplicação da estratégia e sua eficiência ao alcançar soluções precisas aliado a um baixo custo computacional na análise. / This paper presents the development of a computational framework to the analysis of two dimensional solids containing multiple cracks using a new strategy with the combination of splitting method and hybrid-Trefftz stress formulation. The first consists of a decomposition method to the analysis of solids containing multiple cracks through the split of original problem (PG) into three subproblems: global subproblem (PG(0)), where the solid is analyzed without the cracks, local subproblems (PL(k)), where each crack is analyzed individually and insert in an arbitrary domain, and global subproblems (PG(k)), where the effects of the interaction between cracks are evaluated. Solution of PG is obtained using the condition that the sum of tractions on crack faces of all subproblems are null. For simplicity, subproblems PG(0) and PG(k) are analyzed by classical finite element method (FEM). On the other hand, PL(k) are analyzed by hibrid-Trefftz formulation aiming a high efficiency on the evaluation of cracked subproblems. This formulation promote the approximation of stresses and displacements fields on domain and boundary of elements, respectively, on an independent manner. Bases of appoximation of stress field are constructed by functions that solves the Navier equation with the addition of analitical functions of mechanic of fracture. Hence, this formulaition provides good solution of the problem with coarse mesh. Moreover, the stress intensity factors (SIF) of cracks may be obtained directly from the solution of linear system of the problem. Numerical results are presented in order to ilustrate the use of the strategy and its efficiency on the evaluating of accurate solutions with a low computational cost of the analysis.

La modélisation du transport réactif dans les milieux poreux implique la simulation de plusieurs processus physico-chimiques : écoulement de phases fluides, transport de chaleur, réactions chimiques entre espèces en phases identiques ou différentes. La résolution du système d'équations qui décrit le problème peut être obtenue par une approche soit totalement couplée soit découplée. Les approches découplées simplifient le système d'équations en décomposant le problème sous-parties plus faciles à gérer. Chacune de ces sous-parties peut être résolue avec des techniques d'intégration appropriées. Les techniques de découplage peuvent être non‑itératives (operator splitting methods) ou itératives (fixed‑point iteration), chacunes ayant des avantages et des inconvénients. Les approches non‑iteratives génèrent une erreur associée à la séparation des sous­-parties couplées, et les approaches itératives peuvent présenter des problèmes de convergence. Dans cette thèse, nous développons un code sous licence libre en langage MATLAB (https://github.com/TReacLab/TReacLab) dédie à la modélisation du la problématique de la carbonatation atmosphérique du béton, dans le cadre du stockage de déchets de moyenne activité et longue vie en couche géologique profonde. Le code propose un ensemble d'approche découplée : classique, comme les approches de fractionnement séquentiel, alternatif ou Strang, et moins classique, comme les approches de fractionnement additif ou par répartition symétrique. En outre, deux approches itératives basées sur une formulation spécifique (SIA CC et SIA TC) ont également été implémentées. Le code été interfacé de manière générique avec différents solveurs de transport (COMSOL, pdepe MATLAB, FVTool, FD scripts) et géochimiques (iPhreeqc, PhreeqcRM). Afin de valider l'implémentations des différentes approches, plusieurs bancs d'essais classiques dans le domaine du transport réactif ont été utilises avec succès. L'erreur associée à la combinaison du fractionnement de l'opérateur et des techniques numériques étant complexe à évaluer, nous explorons les outils mathématiques existants permettant de l'estimer. Enfin, nous structurons le problème de la carbonatation atmosphérique et présentons des simulations préliminaires, en détaillant les problèmes pertinents et les étapes futures à suivre. / Reactive transport modeling in porous media involves the simulation of several physico‑chemical processes: flow of fluid phases, transport of species, heat transport, chemical reactions between species in the same phase or in different phases. The resolution of the system of equations that describes the problem can be obtained by a fully coupled approach or by a decoupled approach. Decoupled approaches can simplify the system of equations by breaking down the problem into smaller parts that are easier to handle. Each of the smaller parts can be solved with suitable integration techniques. The decoupling techniques might be non‑iterative (operator splitting methods) or iterative (fixed‑point iteration), having each its advantages and disadvantages. Non‑iterative approaches have an error associated with the separation of the coupled effects, and iterative approaches might have problems to converge. In this thesis, we develop an open‑source code written in MATLAB (https://github.com/TReacLab/TReacLab) in order to model the problematic of concrete atmospheric carbonation for an intermediate‑level long‑lived nuclear waste package in a deep geological repository. The code uses a decoupled approach. Classical operator splitting approaches, such as sequential, alternating or Strang splitting, and less classical splitting approaches, such as additive or symmetrically weighted splitting, have been implemented. Besides, two iterative approaches based on an specific formulation (SIA CC, and SIA TC) have also been implemented. The code has been interfaced in a generic way with different transport solvers (COMSOL, pdepe MATLAB, FVTool, FD scripts) and geochemical solvers (iPhreeqc, PhreeqcRM). In order to validate the implementation of the different approaches, a series of classical benchmarks in the field of reactive transport have been solved successfully and compared with analytical and external numerical solutions. Since the associated error due to the combination of operator splitting and numerical techniques may be complex to assess, we explore the existing mathematical tools used to evaluate it. Finally, we frame the atmospheric carbonation problem and run preliminary simulations, stating the relevant problems and future steps to follow.

La modélisation et la simulation de la croissance racinaire des plantes en relation avec l'eau et le transfert de nutriments dans le sol constituent un défi majeur permettant des applications dans diverses thématiques de recherche. Les modèles de croissance racinaire ont été classés en SM (Structural Models), FSM (Functional Structural Models) et DBM (Density Based Models). Les modèles basés sur des représentations explicites de la structure du système racinaire simulent des systèmes de manière réaliste. Les modèles basés sur des densités agrègent le développement racinaire et décrivent l'évolution de densités racinaires dans l'espace et le temps. Le principal avantage de ce type de modèles basés sur des formulations continues est le temps de calcul qui est indépendant du nombre de racines, ce qui est particulièrement utile pour des applications à l'échelle d'une population de plantes. De plus, l'utilisation de modèles continus facilite le couplage avec d'autres modèles fonctionnels et physiques qui sont aussi basés sur des équations continues, tels que le transport de nutriments et d'eau dans le sol.Le but de la thèse est de proposer un modèle continu générique (i.e. applicable à une large diversité d'architectures racinaires) et minimal (i.e. avec le moins de paramètres possible), basé sur une équation aux dérivées partielles. Ce modèle est présenté en 3D et considère le nombre d'apex par unité de volume comme étant la variable de sortie. L'équation est composée de trois principaux phénomènes physiques, à savoir l'advection, la diffusion et la réaction, qui agrègent différents processus racinaires de développement et d'architecture, e.g. la croissance primaire, la ramification et la mortalité. Un schéma numérique basé sur la méthode de splitting d'opérateurs est proposée afin de résoudre l'équation en séparant les trois opérateurs physiques. C'est une méthode puissante et numériquement consistante qui permet de choisir des schémas numériques appropriés pour chaque opérateur. Des données observées avec leur variabilité, qui sont codées en utilisant les modèles architecturaux, sont permettent la calibration du modèle continu. Le modèle continu est donc utilisé afin de simuler l'évolution spatio-temporelle de la densité moyenne du nombre d'apex pour des systèmes racinaires dont leurs développements diffèrent. L'évaluation de cette approche de modélisation est traitée sur : 1- des racines horizontales d'eucalyptus, chacune contrôlée par un apex principal ; 2- des systèmes centralisés, e.g. les systèmes du maïs, et 3- des systèmes décentralisés, e.g. les systèmes de chiendent. Les résultats de la méthode de calibration sont satisfaisants et ont permis de définir et simuler diverses stratégies de croissance racinaire. / Modelling and simulating plant root growth in connection with soil water and nutrient transfer is an important challenge that finds applications in many fields of research. Root growth models have been classified into SM (Structural Models), FSM (Functional Structural Models) and DBM (Density Based Models). Models based on explicit representations of root system structures simulate realistic patterns. Density based models aggregate root development and describe the evolution of root densities in space and time. The main advantage of this kind of models based on continuous formulation is that the computational time is independent of the number of roots, which is especially useful for applications at the plant stand scale. Moreover, the use of continuous models facilitates coupling with other functional and physical models that are also based on continuous equations such as water and nutrient transport.The aim of the thesis is to propose a minimal (i.e. involving a minimum number of parameters) and generic (i.e. applicable to a wide range of root architectures) continuous model based on a partial differential equation. This model is presented in a 3D form and considers the number of apices per unit volume of soil as output variable. The equation includes three main physical phenomena, namely advection, diffusion andreaction, which aggregate different aspects of root architectural and developmental rules, e.g. primary growth, branching and mortality. A numerical scheme based on an operator splitting method is proposed to solve the equation by separating the three different processes. It is a powerful and consistent numerical method that allows the use of appropriate numerical scheme for each operator. Observed data with their variability, which are encoded using architectural models, are used to calibrate the continuous model. The continuous model is then used to simulate the spatio-temporal evolution of the mean density of apex number for root systems with different developmental rules. The evaluation of this modelling approach is carried out on : 1- horizontal roots of eucalyptus that are controlled by a main apex ; 2- centralizedsystems, e.g. maize root systems, and 3- decentralized root systems, e.g. couch grass root systems.The results of the calibration method were satisfactory and allowed us to define and simulate different root growth strategies.

Cette thèse est une contribution à la problématique de la simulation d'événements rares. A partir de l'étude des méthodes de Splitting, un nouveau cadre théorique est développé, indépendant de tout algorithme. Ce cadre, basé sur la définition d'un processus ponctuel associé à toute variable aléatoire réelle, permet de définir des estimateurs de probabilités, quantiles et moments sans aucune hypothèse sur la variable aléatoire. Le caractère artificiel du Splitting (sélection de seuils) disparaît et l'estimateur de la probabilité de dépasser un seuil est en fait un estimateur de la fonction de répartition jusqu'au seuil considéré. De plus, les estimateurs sont basés sur des processus ponctuels indépendants et identiquement distribués et permettent donc l'utilisation de machine de calcul massivement parallèle. Des algorithmes pratiques sont ainsi également proposés.Enfin l'utilisation de métamodèles est parfois nécessaire à cause d'un temps de calcul toujours trop important. Le cas de la modélisation par processus aléatoire est abordé. L'approche par processus ponctuel permet une estimation simplifiée de l'espérance et de la variance conditionnelles de la variable aléaoire résultante et définit un nouveau critère d'enrichissement SUR adapté aux événements rares / This thesis address the issue of extreme event simulation. From a original understanding of the Splitting methods, a new theoretical framework is proposed, regardless of any algorithm. This framework is based on a point process associated with any real-valued random variable and lets defined probability, quantile and moment estimators without any hypothesis on this random variable. The artificial selection of threshold in Splitting vanishes and the estimator of the probability of exceeding a threshold is indeed an estimator of the whole cumulative distribution function until the given threshold. These estimators are based on the simulation of independent and identically distributed replicas of the point process. So they allow for the use of massively parallel computer cluster. Suitable practical algorithms are thus proposed.Finally it can happen that these advanced statistics still require too much samples. In this context the computer code is considered as a random process with known distribution. The point process framework lets handle this additional source of uncertainty and estimate easily the conditional expectation and variance of the resulting random variable. It also defines new SUR enrichment criteria designed for extreme event probability estimation.

Molecular dynamics (MD) computations aim to simulate materials at the atomic level by approximating molecular interactions classically, relying on the Born-Oppenheimer approximation and semi-empirical potential energy functions as an alternative to solving the difficult time-dependent Schrodinger equation. An approximate solution is obtained by discretization in time, with an appropriate algorithm used to advance the state of the system between successive timesteps. Modern MD simulations simulate complex systems with as many as a trillion individual atoms in three spatial dimensions. Many applications use MD to compute ensemble averages of molecular systems at constant temperature. Langevin dynamics approximates the effects of weakly coupling an external energy reservoir to a system of interest, by adding the stochastic Ornstein-Uhlenbeck process to the system momenta, where the resulting trajectories are ergodic with respect to the canonical (Boltzmann-Gibbs) distribution. By solving the resulting stochastic differential equations (SDEs), we can compute trajectories that sample the accessible states of a system at a constant temperature by evolving the dynamics in time. The complexity of the classical potential energy function requires the use of efficient discretization schemes to evolve the dynamics. In this thesis we provide a systematic evaluation of splitting-based methods for the integration of Langevin dynamics. We focus on the weak properties of methods for confiurational sampling in MD, given as the accuracy of averages computed via numerical discretization. Our emphasis is on the application of discretization algorithms to high performance computing (HPC) simulations of a wide variety of phenomena, where configurational sampling is the goal. Our first contribution is to give a framework for the analysis of stochastic splitting methods in the spirit of backward error analysis, which provides, in certain cases, explicit formulae required to correct the errors in observed averages. A second contribution of this thesis is the investigation of the performance of schemes in the overdamped limit of Langevin dynamics (Brownian or Smoluchowski dynamics), showing the inconsistency of some numerical schemes in this limit. A new method is given that is second-order accurate (in law) but requires only one force evaluation per timestep. Finally we compare the performance of our derived schemes against those in common use in MD codes, by comparing the observed errors introduced by each algorithm when sampling a solvated alanine dipeptide molecule, based on our implementation of the schemes in state-of-the-art molecular simulation software. One scheme is found to give exceptional results for the computed averages of functions purely of position.

Bounded Verification is an effective technique for finding subtle bugs in object-oriented programs. Given a program, its correctness specification and bounds on the input domain size, scope bounded checking translates bounded code segments into formulas in boolean logic and uses off the shelf satisfiability solvers to search for correctness violations. However, scalability is a key issue of the technique, since for non-trivial programs, the formulas are often complex and can choke the solvers. This thesis describes approaches which aim to scale scope bounded checking by utilizing syntactic and semantic information from the code to split a program into sub-programs which can be checked incrementally. It presents a thorough evaluation of the approaches and compares their performance with existing bounded verification techniques. Novel ideas for future work, specifically a specification slicing driven splitting approach, are proposed to further improve the scalability of bounded verification. / text

<p>This licentiate thesis comprises two complementary studiesdealing with the sheet-fed offset printing of paper. The firststudy addresses the further development of a practical methodto acoustically monitor and analyse the film splitting ofoffset inks. This method was tested on laboratory printingequipment, specifically monitoring the continuous ink splittingin the nip of an IGT ink distribution unit and the short-timeink splitting in the inked print disc-paper nip of the printingunit of an ISIT instrument. The study verified that the inksplitting component of the acoustic signal contributes to thehigher frequency range (10-20 kHz) of the audible spectrum, andcan thus be separated from the lower frequency machine noise.Furthermore, the film splitting component is sensitive tochanges in the ink and printing conditions, thus enabling itsuse in probing the fundamental mechanisms occurring during inktransfer and also suggesting its applicability fornon-intrusive monitoring of industrial printing presses. Anincrease in film thickness during ink distribution correspondsto an increased acoustic power, with the exception of very lowink amounts, which give reduced acoustic emission due to alubricating effect. The effect of the presence of fountainsolution was simulated by adding emulsion-forming, butnon-evaporative, ethylene glycol. This produces an increase inacoustic power at low amounts, due to resistance to glycol dropdeformation, followed by a decrease at higher amounts owing toexcess glycol lining the rolls. During test printing on paper,increasing ink amounts also display an increased acousticresponse.</p><p>The second study further developed a theoretical model toexplain and predict the evolution of ink tack in terms of inksetting directly after offset printing on coated paper. Asmeasured by the ISIT, the tack of the printed ink rises duringshorter time periods, attains a maximum, and then falls atlonger times. The proposed model described how the ink tack,characterised by the impulse during disc pull-off, dependsdynamically on the viscoelastic properties of the ink, thecontact with paper and disc, and the flow geometry. The inksetting was modelled as a diffusion-limited transport of theoil vehicle through the ink film and into the pores of thecoated paper. The coupling of the tack and setting models,compared to the ISIT experimental measurements, then provided adiffusion coeffcient for ink setting during the tack riseperiod. This coeffcient decreases with time, and increasinglyrapidly with decreasing ink amounts due to theconcentration-dependent diffusion. For an accurate descriptionthe elasticity and adhesion effects also have to be considered,at least for explaining the tack fall period.</p>

Spectrum-splitting is a multijunction photovoltaic technology that can effectively improve the conversion efficiency and reduce the cost of photovoltaic systems. Microscale PV design integrates a group of microconcentrating photovoltaic (CPV) systems into an array. It retains the benefits of CPV and obtains other benefits such as a compact form, improved heat rejection capacity, and more versatile PV cell interconnect configurations. We describe the design and performance of a two-junction holographic spectrum-splitting micro-CPV system that uses GaAs wide bandgap and silicon narrow bandgap PV cells. The performance of the system is simulated with a nonsequential raytracing model and compared to the performance of the highest efficiency PV cell used in the micro-CPVarray. The results show that the proposed system reaches the conversion efficiency of 31.98% with a quantum concentration ratio of 14.41x on the GaAs cell and 0.75x on the silicon cell when illuminated with the direct AM1.5 spectrum. This system obtains an improvement over the best bandgap PV cell of 20.05%, and has an acceptance angle of +/- 6 deg allowing for tolerant tracking. (C) 2017 Society of Photo-Optical Instrumentation Engineers (SPIE)

In a progressive income tax system with an individual tax unit, high-rate taxpayers have an incentive to split income with lower-rate family members to minimise the family’s total tax burden. This raises equity and neutrality concerns. Adopting a spousal tax unit limits the gains from income splitting, but the individual is the better choice on privacy, autonomy, equality, definitional, marriage neutrality and work incentive grounds. Once the individual is chosen as the income tax unit, the control model provides a strong policy basis for attributing both earned and unearned income to individuals. Income splitting, however, undermines this model as well as the individual tax unit. This thesis focuses on the UK’s approach to income-splitting in family businesses. The relevant UK income tax rules, particularly the settlements provisions, are inadequate for the task. Various possible reforms are examined. Incorporating a transfer pricing or ‘reasonableness’ test into the settlements provisions would strengthen these rules, but would make taxpayer compliance with an uncertain regime even more difficult. Another option is to expand the scope of employment tax by moving the borderline between employees and the self-employed or companies. Deeper structural reforms could be made to enhance the neutrality of taxation on different legal forms of economic activity. This would reduce the incentives to incorporate for tax savings, including from income splitting. Integration of income tax and NICs is one such option; a dual income tax is another. A TAAR or GAAR also could be pursued. Ultimately, some combination of these various reform options could provide a partial solution to this challenging issue.