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

Light responsive multilayer surfaces with controlled spatial extinction capability

Multilayer systems obtained using the Layer-by-Layer (LbL) technology have been proposed for a variety of biomedical applications in tissue engineering and regenerative medicine. LbL assembly is a simple and highly versatile method to modify surfaces and fabricate robust and highly-ordered nanostructured coatings over almost any type of substrates and with a wide range of substances. The incorporation of polyoxometalate (POM) inorganic salts as constituents of the layers presents a possibility of promoting light-stimuli responses in LbL substrates. We propose the design of a biocompatible photo-responsive multilayer system based on a Preyssler-type POM ([NaP5W30O110]14â ) and a natural origin polymer, chitosan, using the LbL methodology. The photo-reduction properties of the POM allow the spatially controlled disruption of the assembled layers due to the weakening of the electrostatic interactions between the layers. This system has found applicability in detaching devices, such as the cell sheet technology, which may solve the drawbacks actually found in other cell treatment proposals.

Blow-up and finite time extinction for p(x, t)-curl systems arising in electromagnetism

"Available online 22 March 2016"