Related papers: Geometric Firefighting in the Half-plane
Thermal decay rate over an edge-shaped barrier at high dissipation is studied numerically through the computer modeling. Two sorts of the stochastic Langevin type equations are applied: (i) the Langevin equations for the coordinate and…
The attempt to gain a theoretical understanding of the concept of time in quantum mechanics has triggered significant progress towards the search for faster and more efficient quantum technologies. One of such advances consists in the…
We consider a reaction-diffusion system for two densities lying in adjacent domains of $\mathbb{R}^N$. We treat two configurations: either a cylinder and its complement, or two half-spaces. Diffusion and reaction heterogeneities for the two…
A fundamental problem in quantum engineering is determining the lowest time required to ensure that all possible unitaries can be generated with the tools available, which is one of a number of possible quantum speed limits. We examine this…
We study the effect of a cut-off on the speed of pulled fronts of the one dimensional reaction diffusion equation. We prove rigorous upper and lower bounds on the speed in terms of the cut-off parameter epsilon. From these bounds we…
In this paper, we consider a problem of covering a straight line segment by equal circles that are initially arbitrarily placed on a plane by moving their centers on a segment or on a straight line containing a segment so that the segment…
The preparation of quantum many-body systems faces the difficulty that in a realistic scenario only few control parameters of the system may be accessible. In this context, an interesting connection between the energy fluctuations during…
Within the standard framework of quasi-steady flight, this paper derives a speed that realizes the maximal obtainable range per unit of fuel. If this speed is chosen at each instant of a flight plan $h(x)$ giving altitude $h$ as a function…
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…
Continuous and discrete models for firefighting problems are well-studied in Theoretical Computer Science. We introduce a new, discrete, and more general framework based on a hexagonal cell graph to study firefighting problems in varied…
A procedure called \textit{graph burning} was introduced to facilitate the modelling of spread of an alarm, a social contagion, or a social influence or emotion on graphs and networks. Graph burning runs on discrete time-steps (or rounds).…
The solution of a boundary-value problem formulated for a modified Kretschmann configuration shows that the phase speed of a surface-plasmon wave guided by the planar interface of a sufficiently thin metal film and a chiral sculptured thin…
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 L\'evy walk process for the lower interval of the time of flight distribution ($\alpha<1$) and with finite resting time between consecutive flights is discussed. The motion is restricted to a region bounded by two absorbing barriers and…
Assessing the desirability of hypersonic glide vehicles (HGVs) requires understanding what capabilities they may provide compared to alternative systems that could carry out the same missions, particularly given the technical difficulties…
In this paper, we share our approach to real-time segmentation of fire perimeter from aerial full-motion infrared video. We start by describing the problem from a humanitarian aid and disaster response perspective. Specifically, we explain…
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…
We study online competitive algorithms for the \emph{line chasing problem} in Euclidean spaces $\reals^d$, where the input consists of an initial point $P_0$ and a sequence of lines $X_1,X_2,...,X_m$, revealed one at a time. At each step…
In the first part of this thesis, we consider an instance of Frechet distance problem in which the speed of traversal along each segment of the curves is restricted to be within a specfied range. This setting is more realistic than the…
Experimental data on the propagation of wildfires show that its short-time spread has a double semi-elliptical shape. Our main goal is to show that this shape can be accurately approximated in polar coordinates by choosing suitable…