DM - Capítulos/Artigos em Livros Internacionais / Chapters in International Works
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- An overview of some mathematical models of blood rheologyPublication . Sequeira, Adélia; Janela, JoãoExperimental investigations over many years reveal that blood flow exhibits non-Newtonian characteristics such as shear-thinning, viscoelasticity and thixotropic behaviour. The complex rheology of blood is influenced by numerous factors including plasma viscosity, rate of shear, hematocrit, level of erythrocytes aggregation and deformability. Hemodynamic analysis of blood flow in vascular beds and prosthetic devices requires the rheological behaviour of blood to be characterized through appropriate constitutive equations relating the stress to deformation and rate of deformation. The objective of this paper is to present a short overview of some macroscopic constitutive models that can mathematically characterize the rheology of blood and describe its known phenomenological properties. Some numerical simulations obtained in geometrically reconstructed real vessels will be also presented to illustrate the hemodynamic behaviour using Newtonian and non-Newtonian inelastic models under a given set of physiological flow conditions.
- Financial econometric modelPublication . Nicolau, JoãoFour recent financial econometric models are discussed. The first aims to capture the volatility created by “chartists”; the second intends to model bounded random walks; the third involves a mechanism where the stationarity is volatility-induced, and the last one accommodates nonstationary diffusion integrated stochastic processes that can be made stationary by differencing.
- From ice to penguins : the role of mathematics in Antarctic researchPublication . Xavier, José C.; Hill, S. L.; Belchier, M.; Lopes, João DiasMathematics underpins all modern Antarctic science as illustrated by numerous activities carried out during the international year “Mathematics for Planet Earth”. Here, we provide examples of some ongoing applications of mathematics in a wide range of Antarctic science disciplines: (1) Feeding and foraging of marine predators; (2) Fisheries management and ecosystem modelling; and (3) Climate change research. Mathematics has allowed the development of diverse models of physical and ecological processes in the Antarctic. It has provided insights into the past dynamics of these systems and allows projections of potential future conditions, which are essential for understanding and managing the effects of fishing and climate change. Highly specific methods and models have been developed to address particular questions in each discipline, from the detailed analyses of remote-sensed predator tracking data to the assessment of the outputs from multiple global climate models. A key issue, that is common to all disciplines, is how to deal with the inherent uncertainty that arises from limited data availability and the assumptions or simplifications that are necessary in the analysis and modeling of interacting processes. With the continued rapid development of satellite-based and remote observation systems (e.g. ocean drifters and automatic weather stations), and of new methods for genetic analyses of biological systems, a step-change is occurring in the magnitude of data available on all components of Antarctic systems. These changes in data availability have already led to the development of new methods and algorithms for their efficient collection, validation, storage and analysis. Further progress will require the development of a wide range of new and innovative mathematical approaches, continuing the trend of world science becoming increasingly international and interdisciplinary.
- Generic Hamiltonian dynamical systems : an overviewPublication . Bessa, Mário; Dias, João LopesWe present for a general audience the state of the art on the generic properties of C² Hamiltonian dynamical systems.
- KAM theory as a limit of renormalizationPublication . Dias, João LopesThis is a brief survey of recent results on the KAM stability of quasiperiodic dynamics using renormalization of vector field
- Mathematical models in financePublication . Grossinho, Maria do RosárioIn this paper we illustrate the interplay between Mathematics and Finance, pointing out the relevance of stochastic calculus and mathematical modelling in some important aspects of modern finance. We present two types of mathematical models: the binomial asset pricing model and continuous-time models. We point out some sensitive points of research.
- Numerical evaluation of continuous time ruin probabilities for a portfolio with credibility updated premiumsPublication . Afonso, Lourdes B.; Reis, Alfredo. D. Egídio dos; Waters, Howard R.The probability of ruin in continuous and finite time is numerically evaluated in a classical risk process where the premium can be updated according to credibility models and therefore change from year to year. A major consideration in the development of this approach is that it should be easily applicable to large portfolios. Our method uses as a first tool the model developed by Afonso et al. (2009), which is quite flexible and allows premiums to change annually. We extend that model by introducing a credibility approach to experience rating. We consider a portfolio of risks which satisfy the assumptions of the B¨uhlmann (1967, 1969) or B¨uhlmann and Straub (1970) credibility models. We compute finite time ruin probabilities for different scenarios and compare with those when a fixed premium is considered.
- Optimal reinsurancePublication . Centeno, M. de Lourdes; Simões, Onofre AlvesIn this article we present a few of the results obtained on optimal reinsurance, since the pioneer work by Bruno de Finetti in 1940. As literature on the subject increased substantially in the last decade, a particular attention was given to these more recent results..
- Periodic solutions of parabolic and telegraph equations with asymmetric nonlinearitiesPublication . Grossinho, Maria do Rosário; Nkashama, M. N.This paper is organized as follows: Introduction, In Section 2, we collect the notation and basic assumptions that we shall suppose fulfilled throughout this paper. Section 3 is devoted to second order nonlinear one-dimensional parabolic and (linearly) damped hyperbolic equations. We compare, in some sense, the nonlinearity g(x, u) with the Fuçik spectrum of the corresponding piecewise linear differential equations with homogeneous Dirichlet boundary conditions, and a resonance condition of Landesman-Lazer type with respect to the forcing term h(x, t). More specifically, we assume that (the asymptotic behavior of) u - ¹ g ( x , u) lies in a rectangle located in what we should call the Fucik -Landesman-Lazer "resolvent" set. In Section 4, we take up the case of second-order multi-dimensional equations, and we prove results on crossing at not necessarily simple (higher) eigenvalues. Finally, in Section 5 we indicate the conditions under which one can extend our results to higher-order multi-dimensional equations.
- Polygonal billiards with a contractive reflection law: a review of some hyperbolic propertiesPublication . Del Magno, Gianluigi; Dias, João Lopes; Duarte, Pedro; Gaivão, José Pedro; Pinheiro, DiogoWe provide an overview of recent results concerning the dynamics of polygonal billiards with a contractive reflection law.