Related papers: Geometric Firefighting in the Half-plane
Under the assumption that the initial velocity and outflow velocity are analytic in the horizontal variable, the local well-posedness of the geophysical boundary layer problem is obtained by using energy method in the weighted Chemin-Lerner…
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…
We study the variational problem of finding the fastest path between two points that belong to different anisotropic media, each with a prescribed speed profile and a common interface. The optimal curves are Finsler geodesics that are…
The two-dimensional transient problem that is studied concerns a semi-infinite crack in an isotropic solid comprising an infinite strip and a half-plane joined together and having the same elastic constants. The crack propagates along the…
We consider the online search problem in which a server starting at the origin of a $d$-dimensional Euclidean space has to find an arbitrary hyperplane. The best-possible competitive ratio and the length of the shortest curve from which…
Consider the $(2+1)$D Discrete Gaussian (ZGFF, integer-valued Gaussian free field) model in an $L\times L$ box above a hard floor. Bricmont, El-Mellouki and Fr\"ohlich (1986) established that, at low enough temperature, this random surface…
The steady development of motor vehicle technology will enable cars of the near future to assume an ever increasing role in the decision making and control of the vehicle itself. In the foreseeable future, cars will have the ability to…
Bullets are fired, one per second, with independent speeds sampled uniformly from a discrete set. Collisions result in mutual annihilation. We show that the second fastest bullet survives with positive probability, while a slowest bullet…
Motivated by the numerical investigation by Aoki et al. [1], we study a rarefied gas flow between two parallel infinite plates of the same temperature governed by the Boltzmann equation with diffuse reflection boundaries, where one plate is…
Air curtains are installed in open doorways of a building to reduce buoyancy-driven exchange flows across the doorway. Although an air curtain allows an unhampered passage of humans and vehicles, the interaction of this traffic with an air…
This paper examines the problem of achieving "grace" when controlling dynamical systems for safety, which is defined in terms of providing multi-layered safety assurances. Namely, two safety layers are created: a primary layer that…
This study investigates the critical conditions for flame propagation in channels with cold walls. We analyze the impact of the Lewis number and flow amplitude ($A$) on the minimum channel width required to sustain a premixed flame. Our…
A segment (barrier) is specified on the plane, as well as depots, where the mobile devices (drones) can be placed. Each drone departs from its depot to the barrier, moves along the barrier and returns to its depot, traveling a path of a…
The Volvo burner features the canonical configuration of a bluff-body stabilized premixed flame. This configuration was studied experimentally under the Volvo Flygmotor AB program. Two cases are considered in this study: a non-reacting case…
Given two points in the plane, a set of obstacles defined by closed curves, and an integer $k$, does there exist a path between the two designated points intersecting at most $k$ of the obstacles? This is a fundamental and well-studied…
We consider the energy critical four dimensional semi-linear heat equation \[ \partial_{t}v-\Delta v-v^{3}=0, \quad(t,x)\in \mathbb{R}\times \mathbb{R}^4. \] Formal computation of Filippas et al. (R. Soc. Lond. Proc. 2000) conjectures the…
Semiclassical approximations for tunneling processes usually involve complex trajectories or complex times. In this paper we use a previously derived approximation involving only real trajectories propagating in real time to describe the…
Guided by the duality of turbulence (random versus coherent we seek coherent structures in the turbulent velocity field of molecular clouds, anticipating their importance in cloud evolution. We analyse a large map (40' by 20') obtained with…
The focus of this paper is on a thin obstacle problem where the obstacle is defined on the intersection between a hyper-plane $\Gamma$ in $\mathbb{R}^n$ and a periodic perforation $\mathcal{T}_\varepsilon$ of $\mathbb{R}^n$, depending on a…
We establish the existence of semi-wavefronts solutions for a non-local delayed reaction-diffusion equation with monostable nonlinearity. The existence result is proved for all speeds $c\geq c_\star$, where the determination of $c_\star$ is…