Comparison of different numerical methods for the solution of the time-fractional reaction-diffusion equation with variable diffusion coefficient

In this work we perform a comparison of two different numerical schemes for the solution of the time-fractional diffusion equation with variable diffusion coefficient and a nonlinear source term. The two methods are the implicit numerical scheme presented in [M.L. Morgado, M. Rebelo, Numerical approximation of distributed order reaction- diffusion equations, Journal of Computational and Applied Mathematics 275 (2015) 216-227] that is adapted to our type of equation, and a colocation method where Chebyshev polynomials are used to reduce the fractional differential equation to a system of ordinary differential equations

Fractional pennes' bioheat equation: theoretical and numerical studies

In this work we provide a new mathematical model for the Pennes’ bioheat equation, assuming a fractional time derivative of single order. Alternative versions of the bioheat equation are studied and discussed, to take into account the temperature-dependent variability in the tissue perfusion, and both finite and infinite speed of heat propagation. The proposed bioheat model is solved numerically using an implicit finite difference scheme that we prove to be convergent and stable. The numerical method proposed can be applied to general reaction diffusion equations, with a variable diffusion coefficient. The results obtained with the single order fractional model, are compared with the original models that use classical derivatives.

Fractional bioheat equation

In this work we develop a new mathematical model for the Pennes’ bioheat equation assuming a fractional time derivative of single order. A numerical method for the solu- tion of such equations is proposed, and, the suitability of the new model for modelling real physical problems is studied and discussed

External and internal dynamics in the EU's counter-terrorism policy: a political and legal analysis

Tese de Doutoramento em Ciência Política e Relações Internacionais

Media(ted) discourse and society: rethinking the framework of critical discourse analysis

The analysis of journalistic discourse and its social embeddedness has known significant advances in the last two decades, especially due to the emergence and development of Critical Discourse Analysis. However, three important aspects remain under-researched: the time plane in discourse analysis, the discursive strategies of social actors, and the extra- and supra-textual effects of mediated discourse. Firstly, understanding the biography of public matters requires a longitudinal examination of mediated texts and their social contexts but most forms of analysis of journalistic discourse do not account for the time sequence of texts and its implications. Secondly, as the media representation of social issues is, to a large extent, a function of the discursive construction of events, problems and positions by social actors, the discursive strategies that they employ in a variety of arenas and channels ‘‘before’’ and ‘‘after’’ journalistic texts need to be examined. Thirdly, the fact that many of the modes of operation of discourse are extra- or supra-textual calls for a consideration of various social processes ‘‘outside’’ the text. This paper aims to produce a theoretical and methodological contribution to the integration of these issues in discourse analysis by proposing a framework that combines a textual dimension with a contextual one