Related papers: A Fire Fighter's Problem
Various flame tracking techniques are often used in hydrodynamic simulations. Their use is indispensable when resolving actual scale of the flame is impossible. We show that parameters defining "artificial flame" propagation found from…
We consider very natural "fence enclosure" problems studied by Capoyleas, Rote, and Woeginger and Arkin, Khuller, and Mitchell in the early 90s. Given a set $S$ of $n$ points in the plane, we aim at finding a set of closed curves such that…
Katz & Zingale (2019, KZ19) recently studied a one-dimensional test problem, intended to mimic the process of detonation ignition in head-on collisions of two carbon--oxygen (CO) white dwarfs. They do not obtain ignition of a detonation in…
Understanding how intrinsically fast hydrogen-air premixed flames can be rendered much faster in turbulence is crucial for systematically developing hydrogen-based gas turbines and spark ignition engines. Here, we present fundamental…
Consider a fully connected network where up to $t$ processes may crash, and all processes start in an arbitrary memory state. The self-stabilizing firing squad problem consists of eventually guaranteeing simultaneous response to an external…
This article investigates a mathematical model for bushfire propagation, focusing on the existence and properties of translating solutions. We obtain quantitative bounds on the environmental diffusion coefficient and ignition kernels,…
We consider a deterministic discrete-time model of fire spread introduced by Hartnell [1995] and the problem of minimizing the number of burnt vertices when deploying a limited number of firefighters per timestep. We consider the process…
We investigate a forest-fire model with the density of empty sites as control parameter. The model exhibits three phases, separated by one first-order phase transition and one 'mixed' phase transition which shows critical behavior on only…
Thermal-diffusional pulsation behaviors in planar as well as outwardly and inwardly propagating white dwarf carbon flames are systematically studied. In the 1D numerical simulation, the asymptotic degenerate equation of state and simplified…
This paper is concerned with the analysis of speed-up of reaction-diffusion-advection traveling fronts in infinite cylinders with periodic boundary conditions. The advection is a shear flow with a large amplitude and the reaction is…
In this paper we propose an algorithm for stabilizing circular formations of fixed-wing UAVs with constant speeds. The algorithm is based on the idea of tracking circles with different radii in order to control the inter-vehicle phases with…
Fronts, propagating into an unstable state $\phi=0$, whose asymptotic speed $v_{\text{as}}$ is equal to the linear spreading speed $v^*$ of infinitesimal perturbations about that state (so-called pulled fronts) are very sensitive to changes…
We study forest fire processes in two dimensions. On a given planar lattice, vertices independently switch from vacant to occupied at rate $1$ (initially they are all vacant), and any connected component "is burnt" (its vertices become…
The burning number is a recently introduced graph parameter indicating the spreading speed of content in a graph through its edges. While the conjectured upper bound on the necessary numbers of time steps until all vertices are reached is…
The renormalization ideas of self-similar dynamics of a strongly turbulent flame front are applied to the case of a flame with realistically large thermal expansion of the burning matter. In that case a flame front is corrugated both by…
A high-pressure hydrogen micromix combustor has been investigated using direct numerical simulation with detailed chemistry to examine the flame structure and stabilisation mechanism. The configuration of the combustor was based on the…
Motion of a rigid body immersed in a semi-infinite expanse of gas in a $d$-dimensional region bounded by an infinite plane wall is studied for free molecular flow on the basis of the free Vlasov equation under the specular boundary…
Flame propagation through a non-volatile solid-fuel suspension is studied using a simplified, time-dependent numerical model that considers the influence of both diffusional and kinetic rates on the particle combustion process. It is…
Increasing wildfire occurrence has spurred growing interest in wildfire spread prediction. However, even the most complex wildfire models diverge from observed progression during multi-day simulations, motivating need for data assimilation.…
We consider the propagation of a flame front in a solid medium with a periodic structure. The model is governed by a free boundary system for the pair" temperature-front. "The front's normal velocity depends on the temperature via a…