Abstract
Percolation and non-equilibrium front propagation in a two-dimensional network modeling wildfire spread is studied. The model includes two long-range interactions; a deterministic and a probabilistic one induced by firebrand emis- sion. 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. The dynamical regime is found to belong to the dynamical perco- lation universality class and the static regime to the random deposition class. In the presence of probabilistic interactions, a minimum percolation threshold is found due to the scaling effects. The dynamical exponents belong to a new universality class.
Highlights
IntroductionFor equilibrium and non-equilibrium states (during growing processes or chemical reactions) [1, 2], ranks among the most fascinating phenomena in nature
Phase transition, for equilibrium and non-equilibrium states [1, 2], ranks among the most fascinating phenomena in nature
The dynamical regime is found to belong to the dynamical percolation universality class and the static regime to the random deposition class
Summary
For equilibrium and non-equilibrium states (during growing processes or chemical reactions) [1, 2], ranks among the most fascinating phenomena in nature. It has been extensively studied for several decades, some problems regarding the universality and the dynamics of spreading at the phase transition remain open [6,7,8]. Watts and Strogatz proposed in 1998 a random graph model: Small World Network (SWN) modeling the spread in social networks [5, 9,10,11] It includes both randomly generated long-range connections (shortcuts) and a high connectivity [11]. A weighting process appears due to the ignition energy of the combustible cell and the combustion time of the flame [12]
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