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.

Strain induced edge magnetism at zigzag edge of a graphene quantum dot

We study the temperature dependent magnetic susceptibility of a strained graphene quantum dot by using the determinant quantum Monte Carlo method. Within the Hubbard model on a honeycomb lattice, our unbiased numerical results show that a relative small interaction $U$ may lead to a edge ferromagnetic like behavior in the strained graphene quantum dot, and a possible room temperature transition is suggested. Around half filling, the ferromagnetic fluctuations at the zigzag edge is strengthened both markedly by the on-site Coulomb interaction and the strain, especially in low temperature region. The resultant strongly enhanced ferromagnetic like behavior may be important for the development of many applications.

Evolution of the surface plasmon resonance of Au:TiO2 nanocomposite thin films with annealing temperature

This paper reports on the changes in the structural and morphological features occurring in a particular type of nanocomposite thin-film system, composed of Au nanoparticles (NPs) dispersed in a host TiO2 dielectric matrix. The structural and morphological changes, promoted by in-vacuum annealing experiments of the as-deposited thin films at different temperatures (ranging from 200 to 800 C), resulted in a well-known localized surface plasmon resonance (LSPR) phenomenon, which gave rise to a set of different optical responses that can be tailored for a wide number of applications, including those for optical-based sensors. The results show that the annealing experiments enabled a gradual increase of the mean grain size of the Au NPs (from 2 to 23 nm), and changes in their distributions and separations within the dielectric matrix. For higher annealing temperatures of the as-deposited films, a broad size distribution of Au NPs was found (sizes up to 100 nm). The structural conditions necessary to produce LSPR activity were found to occur for annealing experiments above 300 C, which corresponded to the crystallization of the gold NPs, with an average size strongly dependent on the annealing temperature itself. The main factor for the promotion of LSPR was the growth of gold NPs and their redistribution throughout the host matrix. On the other hand, the host matrix started to crystallize at an annealing temperature of about 500 C, which is an important parameter to explain the shift of the LSPR peak position to longer wavelengths, i.e. a red-shift.