From the 2nd Law of Thermodynamics to AC–Conductivity Measures of Interacting Fermions in Disordered Media

Abstract

Wildfire propagation modelling is a challenging problem due to its complex multi-scale multi-physics nature. This process can be described by a reaction- diffusion equation based on the energy balance principle. Alternative technique is the so-called level-set method (LSM), used in wildfire modelling as well as in many other fields. In the present study a methodology for fire propagation modelling that reconciles these approaches is proposed. This methodology is distinguishable and significant from both academical and industrial point of view because of the inclusion of the ran- dom effects by preserving the existing algorithms and direct implementation as a post-processing numerical routine. The random behaviour of the fire front is caused, for example, by the turbulence and the fire-spotting phenomenon. A probability density function (PDF) is employed in order to describe the random process. In earlier studies it has been shown that new independent ignitions can increase the rate of spread (ROS) of fire and therefore should be carefully studied. In this respect, a physical parametrization of the fire-spotting distribution was proposed. Special attention in the present study is paid to the atmospheric stability conditions. The parametrization proposed in previous works is completed by the multiple fire-spotting modelling. Afterwards special attention is paid to the study of uniqueness of the PDF and consistency with the energy balance equation. Numerical results and discussions complete the study.