Hybrid method for simulating front propagation in reaction-diffusion systems

We study the propagation of pulled fronts in the $A<->\leftrightarrow A+A$ microscopic reaction-diffusion process using Monte Carlo (MC) simulations. In the mean field approximation the process is described by the deterministic Fisher-Kolmogorov-Petrovsky-Piscounov (FKPP) equation. In particular we concentrate on the corrections to the deterministic behavior due to the number of particles per site $\mathrm{\Omega }$. By means of a new hybrid simulation scheme, we manage to reach large macroscopic values of $\mathrm{\Omega }$ which allows us to show the importance in the dynamics of microscopic pulled fronts of the interplay of microscopic fluctuations and their macroscopic relaxation.