Related papers: Geometric Firefighting in the Half-plane
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…
Early detection of wildfires is essential to prevent large-scale fires resulting in extensive environmental, structural, and societal damage. Uncrewed aerial vehicles (UAVs) can cover large remote areas effectively with quick deployment…
Different one-phase Stefan problems for a semi-infinite slab are considered, involving a moving phase change material as well as temperature dependent thermal coefficients. Existence of at least one similarity solution is proved imposing a…
We build in this paper a numerical solution procedure to compute the flow induced by a spherical flame expanding from a point source at a constant expansion velocity, with an instantaneous chemical reaction. The solution is supposed to be…
The problem of front propagation in a stirred medium is addressed in the case of cellular flows in three different regimes: slow reaction, fast reaction and geometrical optics limit. It is well known that a consequence of stirring is the…
We study the fundamental problem of two gas species in two dimensional velocity space whose molecules collide as hard circles in the presence of a flat boundary and with dependence on only one space dimension. The case of three-dimensional…
This paper concerns compressible subsonic jet flows for a given surrounding pressure from a two-dimensional finitely long convergent nozzle with straight solid wall, which are governed by a free boundary problem for a quasilinear elliptic…
We prove that at least $\Omega(n^{0.51})$ hyperplanes are needed to slice all edges of the $n$-dimensional hypercube. We provide a couple of applications: lower bounds on the computational complexity of parity, and a lower bound on the…
Wildfires are destructive and inflict massive, irreversible harm to victims' lives and natural resources. Researchers have proposed commissioning unmanned aerial vehicles (UAVs) to provide firefighters with real-time tracking information;…
We consider the initial value problem for the thermal-diffusive combustion systems of the form: $u_{1,t}= Delta_{x}u_1 - u_1 u_2^m$, $u_{2,t}= d Delta_{x} u_2 + u_1 u_2^m$, $x in R^{n}$, $n geq 1$, $m geq 1$, $d > 1$, with bounded uniformly…
A geometric model for the computation of the firefront of a forest wildfire which takes into account several effects (possibly time-dependent wind, anisotropies and slope of the ground) is introduced. It relies on a general theoretical…
Extending results of Hershberger and Suri for the Euclidean plane, we show that ball hulls and ball intersections of sets of $n$ points in strictly convex normed planes can be constructed in $O(n \log n)$ time. In addition, we confirm that,…
We propose a method to reconstruct dynamic fire in 3D from a limited set of camera views with a Gaussian-based spatiotemporal representation. Capturing and reconstructing fire and its dynamics is highly challenging due to its volatile…
In this work, we carry out structural and algorithmic studies of a problem of barrier forming: selecting theminimum number of straight line segments (barriers) that separate several sets of mutually disjoint objects in the plane. The…
Recently it was obtained in [Tarzia, Thermal Sci. 21A (2017) 1-11] for the classical two-phase Lam\'e-Clapeyron-Stefan problem an equivalence between the temperature and convective boundary conditions at the fixed face under a certain…
This paper estimates the blow-up time for the heat equation $u_t=\Delta u$ with a local nonlinear Neumann boundary condition: The normal derivative $\partial u/\partial n=u^{q}$ on $\Gamma_{1}$, one piece of the boundary, while on the rest…
In this paper, we discuss existence and finite speed of propagation for the solutions to an initial-boundary value problem for a family of fractional thin-film equations in a bounded domain in $\mathbb{R}^d$. The nonlocal operator we…
Using a new general approach to limits in optical structures that counts orthogonal waves generated by scattering, we derive an upper limit to the number of bits of delay possible in one-dimensional slow light structures that are based on…
A reaction-diffusion model which is called the field-road model was introduced by Berestycki, Roquejoffre and Rossi [9] to describe biological invasion with fast diffusion on a line. In this paper, we investigate this model in a…
We study the speed of propagation of fronts for the scalar reaction-diffusion equation $u_t = u_{xx} + f(u)$\, with $f(0) = f(1) = 0$. We give a new integral variational principle for the speed of the fronts joining the state $u=1$ to…