Damage and fracture algorithm using the screened Poisson equation and local remeshing

We propose a crack propagation algorithm which is independent of particular constitutive laws and specific element technology. It consists of a localization limiter in the form of the screened Poisson equation with local mesh refinement. This combination allows the cap- turing of strain localization with good resolution, even in the absence of a sufficiently fine initial mesh. In addition, crack paths are implicitly defined from the localized region, cir- cumventing the need for a specific direction criterion. Observed phenomena such as mul- tiple crack growth and shielding emerge naturally from the algorithm. In contrast with alternative regularization algorithms, curved cracks are correctly represented. A staggered scheme for standard equilibrium and screened equations is used. Element subdivision is based on edge split operations using a given constitutive quantity (either damage or void fraction). To assess the robustness and accuracy of this algorithm, we use both quasi-brittle benchmarks and ductile tests.

CO2 utilization and alternative solvents: effective tools for sustainable applications

The growing concentration of CO2 in the atmosphere and its harmful consequences has led the scientific community to direct its efforts towards sustainable processes. Among the possible approaches, the use of CO2 and alternative solvents are two strategies that are having widespread diffusion. In this work the reuse of CO2 is expressed by using it as a reaction reagent and as trigger to change the physical properties of a catalyst thus facilitating its recovery. As regards the CO2 use as reagent, two catalytic systems have been developed for the conversion of CO2 and epoxides into cyclic carbonates, used in the synthesis of polymers and as aprotic solvents. Homogeneous catalysts made by choline-based eutectic mixtures and heterogeneous catalysts made from biopolymers and waste pyrolysis have been synthesized and tested on this reaction. The carbonate interchange reaction (CIR) of a diol with a linear carbonate (as dimethyl carbonate) is an interesting alternative, for the synthesis of cyclic carbonates; as the second application of CO2 as polarity trigger, it was used for catalyst recovery. In fact DBU, here used as catalyst, is part of the so called “switchable solvents”: they can pass from a less-polar to a more-polar form (and from being soluble to non-soluble in the reaction mixture) when reacting with CO2 in presence of water or alcohols. Also in this case, heterogeneous catalysts made from biopolymers and waste pyrolysis have been synthesized and tested on CIR. As for the use of alternative solvents, this work focuses on the use of Deep Eutectic Solvents (DESs). They are a new generation of solvents composed by a mixture of two or more substances, liquid at room temperature, and non-volatile. New and biobased DESs were here used: i) as reaction media to carry out chemoenzymatic epoxidation; ii) in the extraction of astaxanthin from microalgae culture.

A Unified Model for XVA, including Interest Rates and Rating

We start in Chapter 2 to investigate linear matrix-valued SDEs and the Itô-stochastic Magnus expansion. The Itô-stochastic Magnus expansion provides an efficient numerical scheme to solve matrix-valued SDEs. We show convergence of the expansion up to a stopping time τ and provide an asymptotic estimate of the cumulative distribution function of τ. Moreover, we show how to apply it to solve SPDEs with one and two spatial dimensions by combining it with the method of lines with high accuracy. We will see that the Magnus expansion allows us to use GPU techniques leading to major performance improvements compared to a standard Euler-Maruyama scheme. In Chapter 3, we study a short-rate model in a Cox-Ingersoll-Ross (CIR) framework for negative interest rates. We define the short rate as the difference of two independent CIR processes and add a deterministic shift to guarantee a perfect fit to the market term structure. We show how to use the Gram-Charlier expansion to efficiently calibrate the model to the market swaption surface and price Bermudan swaptions with good accuracy. We are taking two different perspectives for rating transition modelling. In Section 4.4, we study inhomogeneous continuous-time Markov chains (ICTMC) as a candidate for a rating model with deterministic rating transitions. We extend this model by taking a Lie group perspective in Section 4.5, to allow for stochastic rating transitions. In both cases, we will compare the most popular choices for a change of measure technique and show how to efficiently calibrate both models to the available historical rating data and market default probabilities. At the very end, we apply the techniques shown in this thesis to minimize the collateral-inclusive Credit/ Debit Valuation Adjustments under the constraint of small collateral postings by using a collateral account dependent on rating trigger.

SUS: estrutura, competências e serviços

Em SUS: Estrutura, Competências e Serviços, analisa-se o Sistema Único de Saúde (SUS) e sua estrutura abrangendo a organização em regiões de saúde, a hierarquização, em níveis de complexidade de serviços, a competência constitucional e as desigualdades entre os entes federativos e as instâncias de decisão – CIT, CIB e CIR. Por fim, trata-se da integralidade da assistência à saúde atendida pelo SUS por meio do rol de ações, serviços e medicamentos previstos na RENASES e RENAME.

SUS: estrutura, competências e serviços

Em SUS: Estrutura, Competências e Serviços, analisa-se o Sistema Único de Saúde (SUS) e sua estrutura abrangendo a organização em regiões de saúde, a hierarquização, em níveis de complexidade de serviços, a competência constitucional e as desigualdades entre os entes federativos e as instâncias de decisão – CIT, CIB e CIR. Por fim, trata-se da integralidade da assistência à saúde atendida pelo SUS por meio do rol de ações, serviços e medicamentos previstos na RENASES e RENAME.