Front Dynamics in Reaction-Diffusion Systems with Levy Flights: A Fractional Diffusion Approach

Front dynamics in reaction-diffusion systems with Levy flights: a fractional diffusion approach.

The use of reaction-diffusion models rests on the key assumption that the diffusive process is Gaussian. However, a growing number of studies have pointed out the presence of anomalous diffusion, and there is a need to understand reactive systems in the presence of this type of non-Gaussian diffusion. Here we study front dynamics in reaction-diffusion systems where anomalous diffusion is due to...

Large scale reaction front dynamics in anisotropic reaction-diffusion systems

Fluctuation-regularized front propagation dynamics in reaction-diffusion systems.

We introduce and study a new class of fronts in finite particle-number reaction-diffusion systems, corresponding to propagating up a reaction-rate gradient. We show that these systems have no traditional mean-field limit, as the nature of the long-time front solution in the stochastic process differs essentially from that obtained by solving the mean-field deterministic reaction-diffusion equat...

A Reaction-Diffusion System with Periodic Front Dynamics

A reaction-diffusion model motivated by Proteus mirabilis swarm colony development is presented and analyzed in this work. The principal variables are the concentrations of swarm cells and swimmer cells, which are multicellular and single-cell forms, respectively, of the Proteus mirabilis bacteria. The kinetic terms model the growth and division process of the swimmer cells, as well as the form...

Front propagation in hyperbolic fractional reaction-diffusion equations.

From the continuous-time random walk scheme and assuming a Lévy waiting time distribution typical of subdiffusive transport processes, we study a hyperbolic reaction-diffusion equation involving time fractional derivatives. The linear speed selection of wave fronts in this equation is analyzed. When the reaction-diffusion dimensionless number and the fractional index satisfy a certain condition...