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Tropical cellular automata : why urban fires propagate according to polyhedral balls

Stephane Gaubert 1, 2 Daniel Jones 2, 1
2 TROPICAL - TROPICAL
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France
Abstract : In order to analyse the propagation of fire in urban areas, we study a deterministic percolation model on a regular grid in which fire propagates from a point to a bounded neighbourhood of this point, with time constants depending on the jump. Using discrete geometry methods, we obtain an explicit formula for the propagation speed. In particular, we show that for a large time horizon, the wave front is close to the boundary of a ball with respect to a polyhedral weak-Minkowski seminorm, which can be determined analytically from the time constants. We illustrate the model by simulations on data from the Kobe fire following the 1995 Southern Hyogo Prefecture Earthquake, indicating that this deterministic model gives an accurate account of actual urban fires.
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https://hal.inria.fr/hal-01967561
Contributor : Stephane Gaubert <>
Submitted on : Monday, December 31, 2018 - 5:08:26 PM
Last modification on : Friday, April 30, 2021 - 10:00:36 AM
Long-term archiving on: : Monday, April 1, 2019 - 12:49:14 PM

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Stephane Gaubert, Daniel Jones. Tropical cellular automata : why urban fires propagate according to polyhedral balls. AUTOMATA 2018 - Cellular Automata and Discrete Complex Systems, 24th IFIP WG 1.5 International Workshop, Jun 2018, Ghent, Belgium. ⟨hal-01967561⟩

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