Related papers: Geometric Firefighting in the Half-plane
We consider a wave equation with a time-dependent propagation speed, whose potential oscillations are controlled through bounds on its first and second derivatives and by limiting the integral of the difference with a fixed constant. We…
An "edge guard set" of a plane graph $G$ is a subset $\Gamma$ of edges of $G$ such that each face of $G$ is incident to an endpoint of an edge in $\Gamma$. Such a set is said to guard $G$. We improve the known upper bounds on the number of…
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…
The Firefighter problem and a variant of it, known as Resource Minimization for Fire Containment (RMFC), are natural models for optimal inhibition of harmful spreading processes. Despite considerable progress on several fronts, the…
We derive a new quantum speed limit (QSL) for open quantum systems governed by Markovian dynamics. By analyzing the time derivative of the Bures angle between the initial pure state and its time-evolved state, we obtain an analytically…
We investigate numerically the blocking of two-dimensional bistable reaction diffusion fronts by geometric obstacles. Our goal is to derive quantitative criteria for front propagation in the presence of spatial heterogeneities. Using a…
Wild-land fire fighting is a hazardous job. A key task for firefighters is to observe the "fire front" to chart the progress of the fire and areas that will likely spread next. Lack of information of the fire front causes many accidents.…
We establish rigorous upper and lower bounds for the speed of pulled fronts with a cutoff. We show that the Brunet-Derrida formula corresponds to the leading order expansion in the cut-off parameter of both the upper and lower bounds. For…
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 effects of initial pressure and temperature on the laminar burning speed of n-hexane-air mixtures were investigated experimentally and numerically. The spherically expanding flame technique with a nonlinear extrapolation procedure was…
The main goal of this paper is to understand finer properties of the effective burning velocity from a combustion model introduced by Majda and Souganidis [19]. Motivated by results in [4] and applications in turbulent combustion, we show…
In this paper, we propose a feedback control strategy to protect vulnerable areas from wildfires. We consider a system of coupled partial differential equations (PDEs) that models heat propagation and fuel depletion in wildfires and study…
For two points $p$ and $q$ in the plane, a straight line $h$, called a highway, and a real $v>1$, we define the \emph{travel time} (also known as the \emph{city distance}) from $p$ and $q$ to be the time needed to traverse a quickest path…
Unmanned aerial vehicles are now becoming increasingly accessible to amateur and commercial users alike. A safety air traffic management system is needed to help ensure that every newest entrant into the sky does not collide with others.…
We have studied the fully nonlinear behavior of pre-mixed flames in a gravitationally stratified medium, subject to the Boussinesq approximation. Key results include the establishment of criterion for when such flames propagate as simple…
Air-bridges play a critical role in the performance of microwave circuits integrated with superconducting quantum bits, and their mechanical stability is predominant for reliable operation. This study is devoted to the technological issues…
In this work, we study the finite time blow-up phenomenon of three types of semilinear wave systems with multiple speeds, posed on asymptotically Euclidean manifolds. We establish the upper bound estimates for the lifespan of solutions when…
The mean first-passage time (MFPT) for a Brownian particle to surmount a potential barrier of height $\Delta U$ is a fundamental quantity governing a wide array of physical and chemical processes. According to the Arrhenius Law, the MFPT…
We investigate how many hyperplanes with independent standard Gaussian directions one needs to produce a $\delta$-uniform tessellation of a subset $S$ of the Euclidean sphere, meaning that for any pair of points in $S$ the fraction of…
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…