Around Hyperbolic Conservation Laws & Vanishing Capillarity-Viscosity Methods

We will comment, review and try to motivate a few issues, perspectives and methods around hyperbolic conservation laws as the open 6th Hilbert problem and physical entropy solutions, smoothing perturbation or non-smooth analysis, and singular vanishing capillarity-viscosity limits

The Hyperbolic Paradigma

As nonlinear hyperbolic partial differential equations have non unique global solutions, I am concerned with two, related, issues: what about physical solutions? and when can we use such a type of equations

Approximation of hyperbolic conservation laws

Tese de doutoramento em Matemática (Análise Matemática), apresentada à Universidade de Lisboa através da Faculdade de Ciências, 2008In a first part, we study the zero diffusion-dispersion limit for a class of nonlinear hyperbolic and multi-dimensional conservation laws regularized in a fashion similar to to the Benjamin-Bona-Mahony-Burgers (BBMB) and Korteweg-deVries-Burgers (KdVB) equations. We establish the strong convergence toward classical entropy solutions by relying DiPerna's theory of entropy measure-valued solutions. Optimal conditions are determined for the balance between diffusion and dispersion coefficients. This allows us to propose criteria for the possible existence or non-existence of nonclassical solutions in the sense investigated by LeFloch. Our analysis distinguishes between several assumptions on the diffusion, the dispersion, and the flux-function and emphasize drastic differences between the BBMB and the KdVB models; distinct convergence behaviors are put in evidence and various energy-type arguments are discussed. In the second part, we study the Riemann problem for nonlinear hyperbolic systems of conservation laws whose flux-function is solely Lipschitz continuous. Typical examples arise in the modelling of multi-phase flows and of elasto-plastic materials. To extend Lax's theory, the main difficulty is to handle possibly discontinuous wave speeds. We revisit certain fundamental notions such as the strict hyperbolicity, the genuine nonlinearity and the entropy inequalities. Our proofs rely on a generalized calculus for Lipschitz continuous mappings and the related Filippov's theory of ordinary differential equations with discontinuous coefficients. We identify here several new features arising in discontinuous solutions of the Riemann problem

CEO compensation as a mechanism to induce firm performance

Over the past few decades, academic literature, specifically on agency theory and executive compensation, has argued that CEO compensation should be aligned to firm performance in order to increase shareholder value. Nevertheless, some studies present the contrary idea, in which no link between performance and compensation can be established. This thesis analyses the relationship between firm performance and CEO compensation regarding Portuguese listed firms in the period of 2008-2013. No statistical evidence was found linking firm performance and CEO compensation, even after introducing governance and financial control variables as well as performing small sampling analysis of the top performers

Philosophy, Science and Social Science

Philosophy, Science and Social Scienc

CEC research activities for the period 2003-2005

The Civil Engineering Research Center of the University of Minho will carry out research at an internationally recognised standard of excellence in the following areas: - Construction Materials, dealing with achieving sustainable materials focussing in durability design, use of eco-efficient materials and techniques for materials repair; - Construction Processes & Management, dealing with construction management, building physics and construction technology focusing on sustainable development and building rehabilitation; - Geotechnics, dealing with properties and modelling of natural ground (soil and rocks) and treated materials, focussing in environmental aspects and structures for transportation infrastructures; - Highways, dealing with pavement materials characterisation, pavement recycling, pavement design and pavement evaluation, both functional and structural; - Hydraulics, dealing with modelling techniques of processes in natural environments and engineered systems and decision support systems for sustainable use of water resources; - Structures, dealing with innovation, safety, strengthening and conservation of structures, focussing in new concrete and masonry structures, FRP, ancient structures and bridges; - Urban and Regional Planning, dealing with land use planning and policy, built environment and urban quality of life, and stressing the evaluation aspects. The management of research is the responsibility of the scientific committee, on which a representative of each group is represented. It is also under the auspicious of the Advisory Committee. The Center provides a core of people with internationally recognised expertise in the areas of Civil Engineering, particularly through PhD programs and post-doctoral training. The dynamism of the staff provides a stimulating atmosphere that will attract research students and professionals assuring excellent academic and technical support of their studies. A financial goal is to attract research funding from industry and other National and European research grants to continue its operation at an excellence research level.Fundação para a Ciência e a Tecnologia (FCT

Nonlinearly perturbed hyperbolic conservation laws

In this presentation we attempt to stress two points of view on hyperbolic conservation laws: modelization and analytical theory. And, how they are sensitively related. While appliers are concerned with reliability, integrity or failure of solutions, mathematcians are concerned with non uniqueness, selection of physically relevant solutions or entropy criteria. In the modeling process, within simplifications, some “spurious terms” are usually discarded from the equations and so, in order to address uniqueness, a crucial information is lost. We discuss here the relevant dissipative or dispersive effect of some of those small scale terms (zero singular limits)

EC2 model applied to the prediction of mechanical properties of soil cement based on test results at early ages

O modelo analítico proposto pelo Eurocódigo 2 (EC2) para a previsão das propriedades mecânicas do betão ao longo do tempo tem mostrado resultados bastante satisfatórios quando adaptado a formulações laboratoriais de Jet Grouting (JG) e de Cutter Soil Mixing (CSM). No entanto, apresenta com principal limitação o facto de estar dependente da realização de ensaios experimentais aos 28 dias de cura para a quantificação das respetivas propriedades, o que limita a sua aplicabilidade em fases mais avançadas do projeto, nomeadamente para fins de controlo de qualidade. No presente artigo o modelo analítico proposto pelo EC2 para a previsão da resistência e rigidez do betão é adaptado a formulações laboratoriais de JG e CSM. Em particular, a abordagem do EC2 é adaptada no sentido de considerar resultados laboratoriais a idades jovens, nomeadamente aos 3, 7 e 14 dias de cura, em substituição dos convencionais 28 dias. Os resultados obtidos mostram que o desempenho do modelo do EC2 aumenta proporcionalmente à idade dos resultados experimentais considerados. Contudo, observou-se também apenas uma ligeira diferença entre o desempenho do modelo do EC2 considerando resultados experimentais aos 14 e aos 28 dias, o que permite fazer um balanceamento entre a precisão do modelo e o tempo/custos totais do projeto.The Eurocode 2 (EC2) approach for strength and stiffness prediction of concrete has been successful adapted to soil-cement laboratory formulations for Jet Grouting (JG) and Cutter Soil Mixing (CSM) technologies. However, its dependence of 28 days test result represents an important limitation. Accordingly, in the present work EC2 approach is modified in order to use laboratory reference data at early ages (e.g. 3, 7 or 14 days) and the achieved results are compared with the conventional 28 days time of cure. As expected, the achieved results show a decrease in EC2 approach performance when reference data at early ages are used. However, it is also observed just a slightly difference in EC2 approach performance when test data at 14 days or 28 days are used. This observation allows us to balance the model prediction accuracy and time consuming in the final project and construction work costs

On Vanishing dissipative-dispersive perturbations of hyperbolic conservation laws

In presence of linear diffusion and non-positive dispersion, we prove well-posedness of the nonlinear conservation equation u_t+f(u)_x=\eps u_xx -\del((u_xx)^2)_x. Then, as the right-hand perturbations vanish, we prove convergence of the previous solutions to the entropy weak solution of the hyperbolic conservation law u_t+f(u)_x=0