Consistent local projection stabilized finite element methods

This work establishes a formal derivation of local projection stabilized methods as a result of an enriched Petrov-Galerkin strategy for the Stokes problem. Both velocity and pressure finite element spaces are enhanced with solutions of residual-based local problems, and then the static condensation procedure is applied to derive new methods. The approach keeps degrees of freedom unchanged while gives rise to new stable and consistent methods for continuous and discontinuous approximation spaces for the pressure. The resulting methods do not need the use of a macro-element grid structure and are parameter-free. The numerical analysis is carried out showing optimal convergence in natural norms, and moreover, two ways of rendering the velocity field locally mass conservative are proposed. Some numerics validate the theoretical results

A symmetric nodal conservative finite element method for the Darcy equation

This work introduces and analyzes novel stable Petrov-Galerkin EnrichedMethods (PGEM) for the Darcy problem based on the simplest but unstable continuous P1/P0 pair. Stability is recovered inside a Petrov-Galerkin framework where element-wise dependent residual functions, named multi-scale functions, enrich both velocity and pressure trial spaces. Unlike the velocity test space that is augmented with bubble-like functions, multi-scale functions correct edge residuals as well. The multi-scale functions turn out to be the well-known lowest order Raviart-Thomas basis functions for the velocity and discontinuous quadratics polynomial functions for the pressure. The enrichment strategy suggests the way to recover the local mass conservation property for nodal-based interpolation spaces. We prove that the method and its symmetric version are well-posed and achieve optimal error estimates in natural norms. Numerical validations confirm claimed theoretical results

O impacto das pastilhas elásticas na área orofacial

Dissertação para obtenção do grau de Mestre no Instituto Universitário Egas MonizA mastigação de produtos não alimentares é um hábito que já existe há milénios. Actualmente, este fenómeno encontra-se através da mastigação de pastilhas elásticas que se tornou uma prática popular. Mas este hábito, às vezes considerado como um hábito parafuncional, têm consequências a nível orofacial dos consumidores. O uso frequente de pastilhas elásticas pode ser considerado como um fator de risco na amplificação de algumas patologias articulares, mas, por outro lado, a mastigação regularizada destas pastilhas pode ser incluída num esquema terapêutico das dores oraofaciais. O objetivo é de realizar um state of the art das repercuções da mastigação de pastilhas elásticas; avaliar a influência das pastilhas elásticas na área orofacial, os seus benefícios e os seus danos provocados. O consumo de pastilhas elásticas permite também aumentar a secreção de saliva pelo fenómeno de estimulação mecânica e gustativa. Uma saliva estimulada neutraliza os ácidos produzidos pelos microrganismos acidogénicos da placa bacteriana e permite reduzir o risco de cárie. Também ocorre uma modificação da composição salivar com aumento da concentração dos iões constituintes do cristais de hidroxiapatita, o que facilita a remineralização do esmalte e previne desmineralização. Esta estimulação da secreção salivar pela mastigação das pastilhas elásticas permite proteger os dentes contra a desmineralização erosiva A mastigação regular de pastilhas elásticas sem açúcar permite também a redução do número de compostos sulfurados volátéis, refrescando assim o hálito. Permite também reduzir a coloração extrínseca dos dentes. Os fármacos podem ser incorporados na pastilha elástica que representa neste sentido uma alternativa aos outros sistemas de administração oral de medicamento. O consumo de pastilhas elásticas sem açúcar pode ser uma ajuda para superar aos inconvenientes do tratamento ortodôntico fixo mas nunca poderá substituir a escovagem dos dentes.Chewing non-food products is a habit that has been around for millennia. Today, this phenomenon is found through chewing gum, which has become a popular practice. But this habit, sometimes considered a parafunctional habit, has orofacial consequences for consumers. The frequent use of chewing gum can be considered a risk factor in the amplification of some joint pathologies, but, on the other hand, the regularized chewing of these chewing gum can be included in a therapeutic scheme of oraofacial pain. The objective is to conduct a state of the art of the repercutions of mastication of chewing gum; assess the influence of chewing gum on the orofacial area, its benefits and damage. The consumption of chewing gum also allows increasing the secretion of saliva by the phenomenon of mechanical and gustatory stimulation. A stimulated saliva neutralizes the acids produced by the acidogenic microorganisms of plaque and reduces the risk of caries. There is also a modification of the salivary composition with an increase in the concentration of the constituent ions of the hydroxyapatite crystals, which facilitates the remineralization of the enamel and prevents demineralization. This stimulation of salivary secretion by chewing gum protects the teeth against erosive demineralisation. Regular chewing of sugar-free chewing gum also reduces the number of volatile sulfur compounds, thus refreshing the breath. It also reduces the extrinsic staining of the teeth. The drugs can be incorporated into the chewing gum, which in this sense represents an alternative to other systems of oral administration of medication. The consumption of sugar-free chewing gum can also be an aid to overcome the inconveniences of fixed orthodontic treatment but can never replace tooth brushing

Studying the joint role of partial observability and channel reliability in emergent communication

International audienceMulti-Agent Reinforcement Learning (MARL) provides a powerful conceptual and computational framework for modeling emergent communication as a way to solve complex problems in sequential environments. However, despite the recent advances in this field, there is still a need to better understand the role of heterogeneous factors, e.g. partial observability and channel reliability, in the emergence of communication systems. An important step has recently been done in this direction by proposing new information-theoretic measures of emergent communication. As of yet, very few contributions have taken advantage of these new measures to perform detailed quantitative studies analyzing how different environmental and cognitive factors can foster the emergence of communication systems. This work quantitatively measures the joint role of partial observability and channel reliability in the emergence of communication systems. To this end, we performed experiments in a simulated multi-agent grid-world environment where agents learn how to solve different cooperative tasks through MARL

Radiatively limited dephasing and exciton dynamics in MoSe2 monolayers revealed with four-wave mixing microscopy

By implementing four-wave mixing (FWM) microspectroscopy, we measure coherence and population dynamics of the exciton transitions in monolayers of MoSe2. We reveal their dephasing times T2 and radiative lifetime T1 in a subpicosecond (ps) range, approaching T2 = 2T1 and thus indicating radiatively limited dephasing at a temperature of 6 K. We elucidate the dephasing mechanisms by varying the temperature and by probing various locations on the flake exhibiting a different local disorder. At the nanosecond range, we observe the residual FWM produced by the incoherent excitons, which initially disperse toward the dark states but then relax back to the optically active states within the light cone. By introducing polarization-resolved excitation, we infer intervalley exciton dynamics, revealing an initial polarization degree of around 30%, constant during the initial subpicosecond decay, followed by the depolarization on a picosecond time scale. The FWM hyperspectral imaging reveals the doped and undoped areas of the sample, allowing us to investigate the neutral exciton, the charged one, or both transitions at the same time. In the latter, we observe the exciton–trion beating in the coherence evolution indicating their coherent coupling

Stabilization arising from PGEM : a review and further developments

The aim of this paper is twofold. First, we review the recent Petrov-Galerkin enriched method (PGEM) to stabilize numerical solutions of BVP's in primal and mixed forms. Then, we extend such enrichment technique to a mixed singularly perturbed problem, namely, the generalized Stokes problem, and focus on a stabilized finite element method arising in a natural way after performing static condensation. The resulting stabilized method is shown to lead to optimal convergences, and afterward, it is numerically validated