We extend to the n-dimensional case a recent theorem establishing the validity of the Huygens' envelope principle for wavefronts in Finsler spaces. Our results have direct applications in analogue gravity models, for which the Fermat's principle of least time naturally gives origin to an underlying Finslerian geometry. For the sake of illustration, we consider two explicit examples motivated by recent experimental results: surface waves in flumes and vortices. For both examples, we have distinctive directional spacetime structures, namely horizons and ergospheres, respectively. We show that both structures are associated with certain directional divergences in the underlying Finslerian (Randers) geometry. Our results show that Finsler geometry may provide a fresh view on the causal structure of spacetime, not only in analogue models but also for General Relativity.

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In this note we discuss a few properties of transnormal Finsler functions, i.e., the natural generalization of distance functions and isoparametric Finsler functions. In particular, we prove that critical level sets of an analytic transnormal function are submanifolds, and the partition of M into level sets is a Finsler partition, when the function is defined on a compact analytic manifold M . d c 1

Every year, the wildfires cause significantly financial damages to the agricultural sector and farmers. Therefore, presenting reliable models which quickly predict the behavior of fire is of great importance to manage and control the progress of wildfire in time. In the present work, by using Randers metric and Huygens' principle, we provide a model for the propagation of wildfire in some agricultural land in the dimension 3, while some wind is blowing across the space. Some example is provided to illustrate the results.

Usually, there are some paths through which the fire spreads faster in wildfire propagation. These paths are called strategic paths here as they play an essential role in improving the fire fighting management strategies. In this work, we find the equations of such paths and the fire fronts' equation. We also calculate the area consumed by the fire. Moreover, implementing the approach in the MATLAB environment, we provide an example to demonstrate the efficiency of our proposed results.