Applications of Randers geodesics for wildfire spread modelling

An account on links between Finsler and Lorentz Geometries for Riemannian Geometers

“…Markvorsen was the first to propose the use of these metrics for wildfire modelling, transforming Richards' PDE into an ODE (the geodesic equations of the Randers metric; see [61]) and even developing a rheonomic Lagrangian viewpoint to include the time dependence (see [62]). For further developments using Randers metrics see [34]. Our work including Lorentz-Finsler metrics completes this theoretical framework and provides a full geometrical picture of the evolution of the wildfire in the most general situation.…”

On the paths through which the fire progress faster

“…( 5) we find 3 the Riemannian metric. Next, one applies Theorem 3.2 and Proposition 3.2 of [2] to establish the following results.…”

“…where θ is the rotational angle around the origin, and a and b are the ellipse axes determined from the experimental data [2]. Once we have the ellipse equation, the Riemannian metric is…”

“…Every year the wildfires become harsher, and more complex mathematics is needed to study their behavior more efficiently and to present a more reliable model for their propagation. Randers geometry is a strong tool for investigating complex phenomena and has been recently used to analyze waves propagation and wildfire spreading [2][3][4][5][6]. In [2] it is shown that the paths of fire particles are geodesics of the Randers metric associated with the propagation.…”

“…Randers geometry is a strong tool for investigating complex phenomena and has been recently used to analyze waves propagation and wildfire spreading [2][3][4][5][6]. In [2] it is shown that the paths of fire particles are geodesics of the Randers metric associated with the propagation. The authors found the Randers metric from the equation of an ellipse on the space.…”