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

Fundamental studies on natural deep eutectic solvents: physico-chemical, thermal and rheological properties

When combined at particular molar fractions, sugars, aminoacids or organic acids a present a high melting point depression, becoming liquids at room temperature. These are called Natural Deep Eutectic Solvents – NADES and are envisaged to play a major role on the chemical engineering processes of the future. Nonetheless, there is a significant lack of knowledge of its fundamental and basic properties, which is hindering their industrial applications. For this reason it is important to extend the knowledge on these systems, boosting their application development [1]. In this work, we have developed and characterized NADES based on choline chloride, organic acids, amino acids and sugars. Their density, thermal behavior, conductivity and polarity were assessed for different compositions. The conductivity was measured from 0 to 40 °C and the temperature effect was well described by the Vogel-Fulcher-Tammann equation. The morphological characterization of the crystallizable materials was done by polarized optical microscopy that provided also evidence of homogeneity/phase separation. Additionally, the rheological and thermodynamic properties of the NADES and the effect of water content were also studied. The results show these systems have Newtonian behavior and present significant viscosity decrease with temperature and water content, due to increase on the molecular mobility. The anhydrous systems present viscosities that range from higher than 1000Pa.s at 20°C to less than 1Pa.s at 70°C. DSC characterization confirms that for water content as high as 1:1:1 molar ratio, the mixture retains its single phase behavior. The results obtained demonstrate that the NADES properties can be finely tunned by careful selection of its constituents. NADES present the necessary properties for use as extraction solvents. They can be prepared from inexpensive raw materials and tailored for the selective extraction of target molecules. The data produced in this work is hereafter importance for the selection of the most promising candidates avoiding a time consuming and expensive trial and error phase providing also data for the development of models able to predict their properties and the mechanisms that allow the formation of the deep eutectic mixtures.

Safety classification using GIS in decision-making process to define priority road interventions

Given the current economic situation of the Portuguese municipalities, it is necessary to identify the priority investments in order to achieve a more efficient financial management. The classification of the road network of the municipality according to the occurrence of traffic accidents is fundamental to set priorities for road interventions. This paper presents a model for road network classification based on traffic accidents integrated in a geographic information system. Its practical application was developed through a case study in the municipality of Barcelos. An equation was defined to obtain a road safety index through the combination of the following indicators: severity, property damage only and accident costs. In addition to the road network classification, the application of the model allows to analyze the spatial coverage of accidents in order to determine the centrality and dispersion of the locations with the highest incidence of road accidents. This analysis can be further refined according to the nature of the accidents namely in collision, runoff and pedestrian crashes.

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

Fundamental concepts in multibody dynamics

In this chapter, the fundamental ingredients related to formulation of the equations of motion for multibody systems are described. In particular, aspects such as degrees of freedom, types of coordinates, basic kinematics joints and types of analysis in multibody systems are briefly characterized. Illustrative examples of application are also presented to better clarify the fundamental issues for spatial rigid multibody systems, which are of crucial importance in the formulation development of mathematical models of mechanical systems, as well as its computational implementation.

O direito fundamental à proteção na velhice através dos impostos

Dissertação de mestrado em Direito das Crianças, Família e Sucessões

Investigação das dificuldades na memória de trabalho em alunos do 2º ano do Ensino Fundamental em Manaus: um estudo com a Working Memory Rating Scale

Dissertação de mestrado em Educação Especial (área de especialização em Dificuldades de Aprendizagem Específicas)

Participação de fisioterapeutas em equipes multidisciplinares que atuam junto a alunos com necessidades educativas especiais: um estudo quantitativo em escolas de ensino fundamental da rede pública de Manaus

Dissertação de mestrado em Educação Especial (área de especialização em Dificuldades de Aprendizagem Específicas)

As fontes jornalísticas na era digital: relações e encenação

Dissertação de mestrado em Ciências da Comunicação (área de especialização em Informação e Jornalismo)

Formação de professores no programa nacional para a alfabetização na idade certa com uso das TIC: um estudo de caso no ensino fundamental

Dissertação de mestrado em Ciências da Educação (área de especialização em Tecnologia Educativa)