Hybrid method for simulating front propagation in reaction-diffusion systems

Hybrid method for simulating front propagation in reaction-diffusion systems.

We study the propagation of pulled fronts in the A<--> A+A microscopic reaction-diffusion process using Monte Carlo simulations. In the mean field approximation the process is described by the deterministic Fisher-Kolmogorov-Petrovsky-Piscounov equation. In particular, we concentrate on the corrections to the deterministic behavior due to the number of particles per correlated volume Omega. By ...

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...

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...

Reaction-Diffusion Systems for Hypothesis Propagation

This paper describes a technique for determining a classiication map or a hypothesis selection map using a system of reaction-diiusion equations. The reaction term of the equations is a replicator equation and provides a mutually exclusive solution. The diffusion term exploits the local consistency of the solution. The technique is eecient for problems with a small labeling space compared to an...

Large scale reaction front dynamics in anisotropic reaction-diffusion systems