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.

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

A hybrid MAC Scheme to improve the transmission performance in body sensor networks

Wireless body sensor networks (WBSNs) constitute a key technology for closing the loop between patients and healthcare providers, as WBSNs provide sensing ability, as well as mobility and portability, essential characteristics for wide acceptance of wireless healthcare technology. However, one important and difficult aspect of WBSNs is to provide data transmissions with quality of service, among other factors due to the antennas being small size and placed close to the body. Such transmissions cannot be fully provided without the assumption of a MAC protocol that solves the problems of the medium sharing. A vast number of MAC protocols conceived for wireless networks are based on random or scheduled schemes. This paper studies firstly the suitability of two MAC protocols, one using CSMA and the other TDMA, to transmit directly to the base station the signals collected continuously from multiple sensor nodes placed on the human body. Tests in a real scenario show that the beaconed TDMA MAC protocol presents an average packet loss ratio lower than CSMA. However, the average packet loss ratio is above 1.0 %. To improve this performance, which is of vital importance in areas such as e-health and ambient assisted living, a hybrid TDMA/CSMA scheme is proposed and tested in a real scenario with two WBSNs and four sensor nodes per WBSN. An average packet loss ratio lower than 0.2 % was obtained with the hybrid scheme. To achieve this significant improvement, the hybrid scheme uses a lightweight algorithm to control dynamically the start of the superframes. Scalability and traffic rate variation tests show that this strategy allows approximately ten WBSNs operating simultaneously without significant performance degradation.

Energy and carbon prices: a comparison of interactions in the European Union Emissions Trading Scheme and the Western Climate Initiative market

We provide a comparative analysis of how short-run variations in carbon and energy prices relate to each other in the emerging greenhouse gas market in California (Western Climate Initiative [WCI], and the European Union Emission Trading Scheme [EU ETS]). We characterize the relationship between carbon, gas, coal, electricity and gasoline prices and an indicator for economic activity, and present a first analysis of carbon prices in the WCI. We also provide a comparative analysis of the structures of the two markets. We estimate a vector autoregressive model and the impulse--response functions. Our main findings show a positive impact from a carbon shock toward electricity, in both markets, but larger in the WCI electricity price, indicating more efficiency. We propose that the widening of carbon market sectors, namely fuels transport and electricity imports, may contribute to this result. To conclude, the research shows significant and coherent relations between variables in WCI, which demonstrate some degree of success for a first year in operation. Reversely, the EU ETS should complete its intended market reform, to allow for more impact of the carbon price. Finally, in both markets, there is no evidence of carbon pricing depleting economic activity.