Pulled fronts: sampling the microscopics

During the last years several studies of wave-like solutions of reaction- diffusion systems have stressed the different nature of what are known as pulled and pushed fronts. While the later ones are the usual type of solutions on which different perturbative techniques can be applied to study different phenomena, the former exhibit no typical time and length scales, a fact which in turn becomes apparent in different dynamic anomalies. Interestingly enough, this lack of typical length and time scales separating between macroscopic and microscopic scales makes pulled fronts sensible to microscopic details.

To understand this sensibility, we study pulled front propagation in the so called stochastic Fisher-Kolmogorov-Petrovsky-Piscounov (sFKPP) equation by means of numerical simulations. To this end, new numerical algorithms are proposed which handle correctly the behavoir around the unstable phase. We find that, while the front velocity is universally corrected by the introduction of the noise, the front diffusion correction does depend on the microscopic details and, in particular, on the precise way the numerical algorithm works at very low densities. Our results do confirm recently observed scalings in diffusion and velocity corrections in a particle model whose mesoscopic description is given by the sFKPP equation.