Front Propagation and Local Ordering in One-Dimensional Irreversible Autocatalytic Reactions

We consider the irreversible $A+B\to 2A$ autocatalytic reaction via Monte Carlo simulations in 1D. Contrary to mean-field-type predictions, the simulations show that only a unique, stable front propagates. Its structure is time independent and the spatial correlations turn out to be universal functions of the dimensionless interparticle distances. These findings are due to the discrete character (particles) of the model and to the 1D topological constraints. The temporal changes of the averaged front form stem from velocity fluctuations and are not a sign of unstable propagation.