Hybrid method for simulating front propagation in reaction-diffusion systems

Esteban Moro
Physical Review E, Rapid Communication 69, 060101 (2004). [pdf]

Abstract:

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 Ω. By means of a hybrid simulation scheme, we manage to reach large macroscopic values of Ω, which allows us to show the importance in the dynamics of microscopic pulled fronts of the interplay of microscopic fluctuations and their macroscopic relaxation.

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