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

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

Gd2O3: Eu Nanoparticle-Based Poly(vinylidene fluoride) Composites for Indirect X-ray Detection

Polymer based scintillator composites have been fabricated by combining poly(vinylidene fluoride) (PVDF) and Gd2O3:Eu nanoparticles (50nm). PVDF has been used since it is a flexible and stable binder matrix and highly resistance to thermal and light deterioration. Gd2O3:Eu has been selected as scintillator material due to its wide band gap, high density and suitable visible light yield. The structural, mechanical, thermal and electrical characteristics of the composites were studied as a function of filler content, together with their performance as scintillator material. The introduction of Gd2O3:Eu nanoparticles into the PVDF matrix does not influence the morphology of the polymer or the degree of crystallinity. On the other hand, an increase of the Young´s modulus with respect to PVDF matrix is observed for filler contents of 0.1-0.75 wt.%. The introduction of Gd2O3:Eu into the PVDF matrix increases dielectric constant and DC electrical conductivity as well as the visible light yield in the nanocomposite, being this increase dependent upon Gd2O3:Eu content and X-ray input power. In this way, Gd2O3:Eu/PVDF composites shows suitable characteristics to be used as X-ray radiation transducers, in particular for large area applications.