Role of weighting in the dynamics of front propagation

Non-equilibrium front propagation in a two-dimensional network modelling wildfire propagation was studied. The model includes deterministic long-range interactions due to radiation and a time weighting procedure. Three weight-dependent propagation regimes were found: dynamical, static, and non-propagative. The dynamical regime shows saturation for small weight values and a percolation transition area depending on the weight and size of the interaction domain. From the scaling interface exponents, the model seems to belong to the dynamical percolation universality class. In the limit of static regime it belongs to the random deposition class.

► Percolation model used includes the weighting procedure and long-range interactions (an interaction domain). The interaction strength is chosen to decrease inversely with the square distance.
► There is a weight threshold RcRc above which the front cannot propagate.
► At RcRc the percolation is static (usual percolation), and below this threshold it becomes dynamic.
► A generalized dependence of the percolation threshold on both the interaction size nyny and the weight parameter R is proposed.
► A further study of the front dynamic scaling is added to this version and dynamic exponents determined.