Moving boundary problems governed by anomalous diffusion.

An Unusual Moving Boundary Condition Arising in Anomalous Diffusion Problems

Anomalous diffusion governed by a fractional diffusion equation and the electrical response of an electrolytic cell.

The electrical response of an electrolytic cell in which the diffusion of mobile ions in the bulk is governed by a fractional diffusion equation of distributed order is analyzed. The boundary conditions at the electrodes limiting the sample are described by an integro-differential equation governing the kinetic at the interface. The analysis is carried out by supposing that the positive and neg...

A numerical scheme for axisymmetric solutions of curvature driven free boundary problems, with applications to the Willmore flow

We present a numerical scheme for axisymmetric solutions to curvature driven moving boundary problems governed by a local law of motion, e.g. the mean curvature flow, the surface diffusion flow, and the Willmore flow. We then present several numerical experiments for the Willmore flow. In particular, we provide numerical evidence that the Willmore flow can develop singularities in finite time.

The two-dimensional reaction-diffusion Brusselator system: a dual-reciprocity boundary element solution

The dual-reciprocity boundary element method is applied for the numerical solution of a class of two-dimensional initial-boundary value problems governed by a non-linear system of partial differential equations. The system, known as the reaction-diffusion Brusselator, arises in the modeling of certain chemical reaction-diffusion processes. Numerical results are presented for some specific probl...

Anomalous kinetics in diffusion limited reactions linked to non-Gaussian concentration probability distribution function.

We investigate anomalous reaction kinetics related to segregation in the one-dimensional reaction-diffusion system A + B → C. It is well known that spatial fluctuations in the species concentrations cause a breakdown of the mean-field behavior at low concentration values. The scaling of the average concentration with time changes from the mean-field t(-1) to the anomalous t(-1/4) behavior. Usin...