Related papers: A Fire Fighter's Problem
Computed flame motion through and between swirling eddys exhibits a maximum advancement rate which is related to the time duration of flame motion between eddys. This eddy spatial structure effect upon the apparent turbulent flame speed…
The dynamics of two-dimensional thin premixed flames is addressed in the framework of mathematical models where the flow field on either side of the front is piecewise incompressible and vorticity-free. Flames confined in channels with…
Most studies of triple flames in counterflowing streams of fuel and oxidizer have been focused on the symmetric problem in which the stoichiometric mixture fraction is $1/2$. There then exist lean and rich premixed flames of roughly equal…
This work presents a numerical study of a diffusion flame in a reacting, two-dimensional, turbulent, viscous, multi-component, compressible mixing layer subject to a large favorable streamwise pressure gradient. The boundary-layer equations…
One dozen vertically oriented thin rectangular vanes, 62 cm tall and 15.2 cm wide, were placed 27 cm from the center of heptane and ethanol pool fires in continuously fed, floor-flush pans 3.2 cm and 5.1 cm in diameter in the laboratory.…
In this paper, we consider a reaction-diffusion system describing the propagation of flames under the assumption of ignition-temperature kinetics and fractional reaction order. It was shown in [3] that this system admits a traveling front…
The critical dimension necessary for a flame to propagate in suspensions of fuel particles in oxidizer is studied analytically and numerically. Two types of models are considered: First, a continuum model, wherein the individual particulate…
Flickering buoyant diffusion methane flames in weakly rotatory flows were computationally and theoretically investigated. The prominent computational finding is that the flicker frequency nonlinearly increases with the rotational intensity…
There are many wildfire behaviors of increasing relevance that are outside the forecast capabilities of even the most sophisticated operational fire spread and fire behavior model. The limitations of the operational models are due primarily…
A theory of flame propagation in curved channels is developed within the framework of the on-shell description of premixed flames. Employing the Green function appropriate to the given channel geometry, an implicit integral representation…
Reactive flows in confined spaces involve complex flame-wall interaction (FWI). This work aims to gain more insights into the physics of the premixed near-wall flame and the wall heat flux as an important engineering relevant quantity. Two…
We consider the propagation of a flame front in a solid periodic medium. The model is governed by a free boundary system in which the front's velocity depends on the temperature via a kinetic rate which may degenerate. We show the existence…
In this paper we investigate the acceleration of the expansion of premixed spherical flames and evolution of the cellular patterns on their surfaces. An asymptotic model is used for the simulations and a spectral numerical algorithm is…
The current WRF-Fire model starts the fire from a given ignition point at a given time. We want to start the model from a given fire perimeter at a given time instead. However, the fuel balance and the state of the atmosphere depend on the…
We consider a perimeter defense problem in a planar conical environment in which a single vehicle, having a finite capture radius, aims to defend a concentric perimeter from mobile intruders. The intruders are arbitrarily released at the…
The Fighter problem with discrete ammunition is studied. An aircraft (fighter) equipped with $n$ anti-aircraft missiles is intercepted by enemy airplanes, the appearance of which follows a homogeneous Poisson process with known intensity.…
We consider a diffusion process $X_{t}$ and a skeleton curve $x_{t}(\phi)$ and we give a lower bound for $P(\sup_{t\leq T}d(X_{t},x_{t}(\phi))\leq R)$. This result is obtained under the hypothesis that the strong H\"{o}rmander condition of…
In the bullet process, a gun fires bullets in the same direction at independent random speeds, and with independent random time delays between firings. When two bullets collide, they vanish. The critical velocity $v_c$ is the slowest speed…
We prove the existence and uniqueness, up to a shift in time, of curved traveling fronts for a reaction-advection-diffusion equation with a combustion-type nonlinearity. The advection is through a shear flow $q$. This analyzes, for…
This article deals with the variable coefficient thin obstacle problem in $n+1$ dimensions. We address the regular free boundary regularity, the behavior of the solution close to the free boundary and the optimal regularity of the solution…