Role of weighting in the dynamics of front propagation

Role of weighting and long-range connections on the dynamics of front propagation

“…It includes also a time weighting process. Three weight-dependent regimes were found previously; dynamical, static, and non-propagative regime [12]. In the absence of probabilistic interaction, the percolation threshold dependence on the weight does not depend on the deterministic interaction.…”

“…For weights R ≤ 1 (saturation regime), the percolation threshold saturates at a minimum value independently of the exponent β (Fig.2) [12]. In this regime, the burning cell can ignite all cells located in its influence zone, and the number of burned cells will be independent of the weighting procedure.…”

“…The propagation exhibits thus a weighting process corresponding to the ratio of the ignition energy to the energy produced by the burning cell during its residence time / [12]. As this procedure depends on the distance to the burning cell , the weighting parameter R is defined as this ratio for cells located at the border of the influence zone 4 For =2, three propagation regimes were found depending on the values of R; a dynamical regime for , a static regime for and no propagation for .…”

“…Recently, the SWN model was adapted to forest fire spread [11][12][13]. In this model, in addition to the probabilistic long-range interactions representing the firebrands emission, deterministic long-range connections due to the ignition by flame radiations are introduced [12,13].…”

“…In this model, in addition to the probabilistic long-range interactions representing the firebrands emission, deterministic long-range connections due to the ignition by flame radiations are introduced [12,13]. A weighting process appears due to the ignition energy of the combustible cell and the combustion time of the flame [12].…”