Factorization of elliptic boundary value problems by invariant embedding and application to overdetermined problems

Dissertação para obtenção do Grau de Doutor em Matemática

MASS CONSERVATION ENHANCEMENT OF FREE BOUNDARY FLOWS IN COMPOSITES MANUFACTURING

Undesirable void formation during the injection phase of the liquid composite molding process can be understood as a consequence of the non-uniformity of the flow front progression, caused by the dual porosity of the fiber perform. Therefore the best examination of the void formation physics can be provided by a mesolevel analysis, where the characteristic dimension is given by the fiber tow diameter. In mesolevel analysis, liquid impregnation along two different scales; inside fiber tows and within the spaces between them; must be considered and the coupling between these flow regimes must be addressed. In such case, it is extremely important to account correctly for the surface tension effects, which can be modeled as capillary pressure applied at the flow front. When continues Galerkin method is used, exploiting elements with velocity components and pressure as nodal variables, strong numerical implementation of such boundary conditions leads to ill-posing of the problem, in terms of the weak classical as well as stabilized formulation. As a consequence, there is an error in mass conservation accumulated especially along the free flow front. This article presents a numerical procedure, which was formulated and implemented in the existing Free Boundary Program in order to significantly reduce this error.

Mass Conservation Enhancement of Free Boundary Mesolevel Flows during LCM Processes of Composites Manufacturing

Undesirable void formation during the injection phase of the liquid composite moulding process can be understood as a consequence of the non-uniformity of the flow front progression, caused by the dual porosity of the fibre perform. Therefore the best examination of the void formation physics can be provided by a mesolevel analysis, where the characteristic dimension is given by the fibre tow diameter. In mesolevel analysis, liquid impregnation along two different scales; inside fibre tows and within the open spaces between them; must be considered and the coupling between these flow regimes must be addressed. In such case, it is extremely important to account correctly for the surface tension effects, which can be modelled as capillary pressure applied at the flow front. Numerical implementation of such boundary conditions leads to ill-posing of the problem, in terms of the weak classical as well as stabilized formulation. As a consequence, there is an error in mass conservation accumulated especially along the free flow front. This contribution presents a numerical procedure, which was formulated and implemented in the existing Free Boundary Program in order to significantly reduce this error.

A new approach to the initial value problem

5th Portuguese Conference on Automatic Control, September, 5-7, 2002, Aveiro, Portugal

POST-PROCESSING TECHNIQUES SUITABILITY FOR MESOLEVEL FREE BOUNDARY FLOWS

Reliable flow simulation software is inevitable to determine an optimal injection strategy in Liquid Composite Molding processes. Several methodologies can be implemented into standard software in order to reduce CPU time. Post-processing techniques might be one of them. Post-processing a finite element solution is a well-known procedure, which consists in a recalculation of the originally obtained quantities such that the rate of convergence increases without the need for expensive remeshing techniques. Post-processing is especially effective in problems where better accuracy is required for derivatives of nodal variables in regions where Dirichlet essential boundary condition is imposed strongly. In previous works influence of smoothness of non-homogeneous Dirichlet condition, imposed on smooth front was examined. However, usually quite a non-smooth boundary is obtained at each time step of the infiltration process due to discretization. Then direct application of post-processing techniques does not improve final results as expected. The new contribution of this paper lies in improvement of the standard methodology. Improved results clearly show that the recalculated flow front is closer to the ”exact” one, is smoother that the previous one and it improves local disturbances of the “exact” solution.

Post-processing Techniques in Free Boundary Flows during Liquid Composite Moulding Processes

Post-processing a finite element solution is a well-known technique, which consists in a recalculation of the originally obtained quantities such that the rate of convergence increases without the need for expensive remeshing techniques. Postprocessing is especially effective in problems where better accuracy is required for derivatives of nodal variables in regions where Dirichlet essential boundary condition is imposed strongly. Consequently such an approach can be exceptionally good in modelling of resin infiltration under quasi steady-state assumption by remeshing techniques and with explicit time integration, because only the free-front normal velocities are necessary to advance the resin front to the next position. The new contribution is the post-processing analysis and implementation of the freeboundary velocities of mesolevel infiltration analysis. Such implementation ensures better accuracy on even coarser meshes, which in consequence reduces the computational time also by the possibility of employing larger time steps.

Factorization by invariant embedding of elliptic problems: circular and star-shaped domains

Dissertação apresentada para obtenção do grau de Doutor em Matemática na especialidade de Equações Diferenciais, pela Universidade Nova de Lisboa,Faculdade de Ciências e Tecnologia

Numerical Method to Predict Void Formation during The Liquid Composite Molding Process

Void formation during the injection phase of the liquid composite molding process can be explained as a consequence of the non-uniformity of the flow front progression. This is due to the dual porosity within the fiber perform (spacing between the fiber tows is much larger than between the fibers within in a tow) and therefore the best explanation can be provided by a mesolevel analysis, where the characteristic dimension is given by the fiber tow diameter of the order of millimeters. In mesolevel analysis, liquid impregnation along two different scales; inside fiber tows and within the open spaces between the fiber tows must be considered and the coupling between the flow regimes must be addressed. In such cases, it is extremely important to account correctly for the surface tension effects, which can be modeled as capillary pressure applied at the flow front. Numerical implementation of such boundary conditions leads to illposing of the problem, in terms of the weak classical as well as stabilized formulation. As a consequence, there is an error in mass conservation accumulated especially along the free flow front. A numerical procedure was formulated and is implemented in an existing Free Boundary Program to reduce this error significantly.

What is the value of value-at-risk after all?: A conditional approach using quantile regressions

A Work Project, presented as part of the requirements for the Award of a Masters Degree in Finance from the NOVA – School of Business and Economics

Business model analysis of Mobitto: How to solve the chicken and egg problem of a multi-sided platform?

A Work Project, presented as part of the requirements for the Award of a Masters Degree in Management from the NOVA – School of Business and Economics

Malnutrição em idosos na admissão hospital actuação perante a sua elevado prevalência

RESUMO: Ao longo das últimas décadas a redistribuição etária da população mundial tem vindo a apresentar um aumento do número de pessoas com 65 ou mais anos, integrando um grupo populacional comummente designado por população idosa. Importa aprofundar mecanismos fisiológicos que conduzem ao envelhecimento e de que forma podem condicionar não só aspetos clínicos, como também nutricionais, entre outros, com a perspetiva da sua origem no aparecimento de doenças crónicas. Com esse enfoque, a desnutrição na pessoa idosa é hoje considerada pela European Nutrition for Health Alliance(ENHA) um problema de saúde pública. Está descrito que a sua prevalência ronda os 60% a nível de instituições hospitalares, 40% em unidades residenciais e 5 a 10% na pessoa idosa a residir em domicílio próprio ou de familiares, e na sua maioria permanece por diagnosticar e tratar. Assim, foi objetivo deste estudo caracterizar e estimar a prevalência da desnutrição e do risco de desnutrição na pessoa idosa, nas primeiras 72 horas de admissão hospitalar. Aplicou-se um estudo observacional, analítico, transversal, quantitativo e correlacional, cujos dados foram recolhidos por entrevista ao próprio e por observação. O estudo desenvolveu-se em duas vertentes de investigação, uma focada na caracterização da desnutrição em pessoas idosas institucionalizadas em hospitais portugueses da zona centro e sul do Continente e Madeira, nos períodos de julho/agosto de 2009, abril/junho de 2010, maio/julho de 2011, através do MNA®. A outra, uma avaliação nutricional detalhada, efetuada no Centro Hospitalar de Lisboa Central – Hospital de Santa Marta, EPE, entre o início de janeiro de 2009 e o fim de janeiro de 2010, sendo a amostra recrutada de entre os idosos de ambos os sexos, internados. Foram estudados dados sociodemográficos, de saúde e feita uma avaliação nutricional extensa. A avaliação nutricional constou de colheita de parâmetros laboratoriais (hematológicos e bioquímicos) e antropométricos (índice de massa corporal (IMC), prega cutânea tricipital(PCT), prega cutânea subescapular (PCSE), perímetro braquial (PB), adequação do perímetro braquial (APB), área muscular braquial (AMB) e perímetro Geminal (PG), análise da composição corporal (Massa Gorda Corporal (MGC), Massa Isenta de Gordura (MIG)),caracterização de um dia alimentar tipo e questionário Mini Nutritional Assessment Long Form®– MNA LF®. Dos dados obtidos em hospitais portugueses, destaca-se que dos 402 idosos avaliados, 53% eram do sexo masculino, tinham uma idade média de 75,8 + 6,52 (65 – 100) e segundo o MNA® 57,5% encontravam-se Desnutridos ou em Risco de Desnutrição.Na amostra, dos dados obtidos, a nível sociodemográfico salienta-se que 50% dos doentes eram do sexo masculino, a idade média rondava os 75,5 + 7,22 (65 – 100) anos, 55% eram naturais de Lisboa e 80% residiam em Lisboa e Vale do Tejo, 38% não tiveram estudos formais e 43% fizeram-no apenas até ao 4º ano de escolaridade. Em relação aos dados de saúde, a maioria dos doentes foi admitida através do Serviço de Urgência do Centro Hospitalar de Lisboa Central – Hospital de São José e foram internados no Serviço de Medicina (38%) e no Serviço de Cardiologia (30%), por patologia médica (38%) e patologia do sistema circulatório (56%). Nos hábitos de vida, quanto à mobilidade, um terço dos doentes estavam acamados e os restantes deambulavam ou tinham uma mobilidade normal, 74% não apresentaram hábitos etanólicos regulares, 19% apresentavam um consumo elevado (> 30g de etanol/dia); 95% dos doentes não apresentavam hábitos tabágicos. Relativamente à caracterização nutricional, os valores médios encontrados em relação aos parâmetros laboratoriais revelaram-se inferiores aos valores padrão para a idade e sexo e eram inferiores no sexo feminino. Na caracterização antropométrica verificaram-se os seguintes achados: o cálculo do IMC mostrou-se pouco sensível na identificação de doentes desnutridos; a PCT e a PCSE revelaram valores de massa gorda dentro do intervalo considerado normal;segundo o PB, 88% não apresentavam valor indicativo de desnutrição e 8% estavam desnutridos; a APB identificou 50% de doentes desnutridos; a AMB, revelou que 97% dos homens e 95% das mulheres apresentavam deficit da massa magra e segundo o PG, 18% apresentavam um valor inferior a 31cm descritor de desnutrição. Na análise da composição corporal verificou-se que ambos os sexos apresentavam uma percentagem de MGC classificada como demasiado alta e que esta era superior nas mulheres em relação aos homens. Ao analisar a ingestão nutricional verificou-se que esta era inferior às Dietary Reference Intakes (DRIs) para a ingestão hídrica (p=0,00), energética (p=0,00), proteica (p=0,00), lipídica (p=0,01), MUFA (p=0,00), PUFA (p=0,00), e glícidos (p=0,00), fibra (p=0,02), potássio (p=0,00), cálcio (p=0,00), magnésio (p=0,00), fósforo (p=0,00), zinco (p=0,00), vitamina D (p=0,00), vitamina E (p=0,00) e folato (p=0,00). No que diz respeito ao MNA®, a sua aplicação permitiu identificar 62% de situações de risco nutricional ou de desnutrição já instalada. Valores de MNA® indicativos de desnutrição ou risco estavam associados a níveis de escolaridade mais baixos (r=0,32; p=0,00). Verificou-se correlação entre o MNA® e a PCT (r=0,30;p=0,00), PCSE (r=0,19;p=0,03) e PG (r=0,27;p=0,00). Na análise da amostra por sexo e escalão etário, apenas se distinguiram as mulheres mais velhas, que apresentaram situação de IMC indicador de risco de desnutrição (IMC <23,5 + 2,9, (r=0,42;p=0,02)), e de valores médios de PB de 25,6+3,84cm (r=0,42;p=0,01), em situações de menor mobilidade caraterizados pelo MNA®. Os homens maisvelhos apresentaram correlação entre o MNA® e PCSE (r=0,41;p=0,02), APMB (r=0,57;p=0,00)e PG (r=0,55;p=0,00), e as mulheres mais velhas apenas com a PCT (r=0,39;p=0,02). A análise multivariada do MNA® em função do sexo e do escalão etário, revelou que estes são independentes. Os homens apresentaram valores médios de MNA® superiores às mulheres e à medida que a idade aumenta, os valores de MNA® em ambos os sexos diminuem, sendo indicativos de risco de desnutrição. Consideramos que, tendo em conta a natureza e objetivos do presente estudo, foi possível caracterizar e estimar a prevalência da desnutrição e do risco de desnutrição em pessoas idosas nas primeiras 72 horas de admissão hospitalar. Os resultados obtidos sinalizam a sua elevada prevalência e alertam para a necessidade de procedimentos protocolados de avaliação e intervenção nutricional da população idosa na admissão hospitalar. Para este efeito a aplicação do MNA® provou a sua aplicabilidade, assim como a medição e cálculo da AMB, que poderão ser muito precocemente aplicados e contribuir para potenciar melhorias do estado de saúde e diminuir o tempo de internamento, nomeadamente de pessoas idosas. Em relação ao padrão alimentar, este estudo contribuiu para uma chamada de atenção dos profissionais de saúde que a população idosa pode apresentar carências nutricionais na admissão, e que estas se não forem devidamente sinalizadas e colmatadas tendem a agravar-se durante o internamento podendo contribuir para o aumento da morbilidade.-------------ABSTRACT:Over the last decades the age redistribution group of the population worldwide has been presenting an increasing number of people aged 65 years or more, incorporating a population group commonly referred to as the elderly population. It´s important to further analyze the physiological mechanisms that lead to aging and how they might influence not only clinical aspects, but also nutritional, among others, with the perspective of their origin in the onset of chronic diseases. With this approach, malnutrition in the elderly is now considered by the European Nutrition for Health Alliance (ENHA) a public health problem. It is reported that its prevalence is around 60% at the level of hospital units, 40% in residential units and 5 to 10% in the elderly living in their own home or family's, and mostly remains to diagnose and treat. The aim of this study was to characterize and estimate the prevalence of malnutrition and risk of malnutrition in the elderly, in the first 72 hours of hospital admission. We applied an observational, analytical, cross-sectional and correlacional quantitative type of study and data were collected by interview and observation itself. The study was developed in two lines of research: one focused on the characterization of malnutrition in elderly institutionalized in Portuguese hospitals, in the central and southern mainland and Madeira, in the periods between July - August 2009, April - June 2010, May - July 2011, through the MNA®; and the other: a detailed nutritional assessment, conducted in Hospital Lisbon Center - Hospital de Santa Marta, EPE, between early January 2009 and late January 2010, and the sample was recruited from among the elderly of both sexes at hospital admission. We studied intensively sociodemographic, health and nutritional assessment done extensive. Nutritional evaluation consisted of harvesting different parameters: hematological, biochemical and anthropometric (body mass index (BMI), triceps skinfold (TSF), sub-scapular skinfold (SSF), arm circumference (AC), arm muscle area (AMA), geminal perimeter (GP), analysis of body composition (Fat Mass (FM), Fat Free Mass (FFM)), characterization of a daily food type and Mini Nutritional Assessment Long Form® questionnaire - MNA LF®. Form the data obtained in Portuguese hospitals, it is noteworthy that of the 402 patients included, 53% were male, had a mean age of 75,8 + 6,52 (65 - 100) and, according to the MNA®, 57,5% were malnourished or at risk of malnutrition. In the sample, from the sociodemographic data obtained, we saw that 50% of patients were male, the average age was around 75,5 + 7,22 years (65-100), 55% were from Lisbon and 80 %lived in Lisbon, 38% had no formal education and 43% did so only until the 4th grade. Regarding health data, the majorities of patients were admitted through the ER of Hospital Lisbon Center - S. José Hospital - and were admitted to the Medicine Unit (38%) and to the Cardiology Unit (30%), by medical pathology (38%) and circulatory system disease (56%). In regard to lifestyle, and considering mobility, one third of patients were bedridden and the rest were ambulating or had a normal mobility. 74% had no regular ethanol habits, 19% had a high intake (> 30 g ethanol / day); 95% of the patients had no smoking habits. Regarding nutritional assessment, the mean values for laboratory parameters proved inferior to standard values for age and sex and were lower in females. In anthropometric assessment these were the findings: BMI calculation showed to be scarcely sensitive in the identification of undernourished patients; the TSF and SSF revealed values of fat mass within the normal range; in AC, 88% did not have an indicative value of malnutrition and 8% were malnourished; in AMA, 97% of men and 95% women had a deficit of lean mass and in GP, 18% had a value of less than the 31cm malnutrition descriptor. In body composition analysis found that both sexes showed a percentage of FM ranked too high and this was higher in women compared to men. By analyzing the nutritional intake was found that this was less than the Dietary Reference Intakes (DRIs) for water intake (p=0,00), energy (p=0,00), protein (p=0,00), lipid (p=0,01), MUFA (p=0,00), PUFA (p=0,00), carbohydrates (p=0,00), fiber (p=0,02), potassium (p=0,00), calcium (p=0,00), magnesium (p=0,00), phosphorus (p=0,00), zinc (p=0,00), vitamin D (p=0,00), vitamin E (p=0,00) and folate (p=0,00). Regarding MNA®, its application identified 62% of cases of nutritional risk or malnutrition already installed. MNA® values indicative of malnutrition or risk were associated with lower levels of education (r=0,32; p=0,00). There was a correlation between the MNA ® and TSF (r =0,30, p = 0,00), SFF (r = 0,19, p = 0,03) and GP (r=0,27, p = 0,00). In the analysis of the sample by gender and age group, the highlight was in older women who had BMI status indicator of malnutrition risk (BMI <23,5 + 2,9 (r=0,42;p=0,02)) and mean values of AC 25,6 +3,84cm (r=0,42; p=0,01), in situations characterized by low mobility MNA®. Older men showed a correlation between the MNA® and SFF (r = 0,41; p = 0,02), AMA (r = 0,57; p = 0,00) and GP (r=0,55;p=0,00), and in older women only TSF showed a correlation(r = 0,39; p =0,02). Multivariate analysis of the MNA® by gender and age group, revealed that they are independent. The men had MNA® mean superior to women, and as the age increases, the values of MNA® in both sexes declined, being indicative of risk of malnutrition. We believe that, given the nature and objectives of the present study, it allowed us to characterize and estimate the prevalence of risk of malnutrition and malnutrition in older people during the first 72 hours of hospital admission. The results indicate a high prevalence and point to the need for protocol procedures of nutritional assessment and intervention in the elderly population at hospital admission. For this purpose the application of MNA® has proved its applicability, as well as measuring and calculating AMA, which may be applied in early stages thus contributing to enhance health state improvements and to shorten the time of hospitalization, particularly in elderly people. In relation to dietary pattern, this study contributed to call of attention from health professionals that the elderly may have nutritional deficiencies on admission, and that these are not properly marked and addressed tend to worsen during hospitalization may contribute to increased morbidity.

A type system for value-dependent information flow analysis

Information systems are widespread and used by anyone with computing devices as well as corporations and governments. It is often the case that security leaks are introduced during the development of an application. Reasons for these security bugs are multiple but among them one can easily identify that it is very hard to define and enforce relevant security policies in modern software. This is because modern applications often rely on container sharing and multi-tenancy where, for instance, data can be stored in the same physical space but is logically mapped into different security compartments or data structures. In turn, these security compartments, to which data is classified into in security policies, can also be dynamic and depend on runtime data. In this thesis we introduce and develop the novel notion of dependent information flow types, and focus on the problem of ensuring data confidentiality in data-centric software. Dependent information flow types fit within the standard framework of dependent type theory, but, unlike usual dependent types, crucially allow the security level of a type, rather than just the structural data type itself, to depend on runtime values. Our dependent function and dependent sum information flow types provide a direct, natural and elegant way to express and enforce fine grained security policies on programs. Namely programs that manipulate structured data types in which the security level of a structure field may depend on values dynamically stored in other fields The main contribution of this work is an efficient analysis that allows programmers to verify, during the development phase, whether programs have information leaks, that is, it verifies whether programs protect the confidentiality of the information they manipulate. As such, we also implemented a prototype typechecker that can be found at http://ctp.di.fct.unl.pt/DIFTprototype/.