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Conference Papers Year : 2018

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

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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Dates and versions

hal-01967561 , version 1 (31-12-2018)

Identifiers

  • HAL Id : hal-01967561 , version 1

Cite

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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