Related papers: Gielis superformula and wildfire models
Front propagation described by Huygens' principle is a fundamental mechanism of spatial spreading of a property or an effect, occurring in optics, acoustics, ecology and combustion. If the local front speed varies randomly due to…
Predicting the extent of massive wildfires once ignited is essential to reduce the subsequent socioeconomic losses and environmental damage, but challenging because of the complexity of fire behaviour. Existing physics-based models are…
In recent years wildfires have caused havoc across the world, especially aggravated in certain regions, due to climate change. Remote sensing has become a powerful tool for monitoring fires, as well as for measuring their effects on…
The aim of this paper is to develop stable and accurate numerical schemes for boundary integral formulations of the heat equation with Dirichlet boundary conditions. The accuracy of Galerkin discretisations for the resulting boundary…
Accurate information on the distribution of vegetation species is used as a proxy for the health of an ecosystem, a currency of international environmental treaties, and a necessary planning tool for forest preservation and rehabilitation,…
The level-set method is a prominent approach to modelling the evolution of a fire over time based on a characterised rate of spread. It however does not provide a direct means for assimilating new data and quantifying uncertainty. Fire…
The forest fire model is a reaction-diffusion model where energy, in the form of trees, is injected uniformly, and burned (dissipated) locally. We show that the spatial distribution of fires forms a novel geometric structure where the…
We study the propagation properties of the solutions of the finite-difference space semi-discrete wave equation on an uniform grid of the whole Euclidean space. We provide a construction of high frequency wave packets that propagate along…
A vertical slice model is developed for the Euler-Boussinesq equations with a constant temperature gradient in the direction normal to the slice (the Eady-Boussinesq model). The model is a solution of the full three-dimensional equations…
We devise a new geometric approach to study the propagation of disturbance - compactly supported data - in reaction diffusion equations. The method builds a bridge between the propagation of disturbance and of almost planar solutions. It…
The aim of this paper is to develop the theory of distributions, not necessarily of compact support, in a topos model of Synthetic Differential Geometry, the so-called "Cahiers Topos". As an application, we study the evolution through time…
We consider a nonlinear dielectric medium surrounding a static, charged and spherically symmetric compact body which gravitational field is driven by General Relativity (GR). Considering the propagating waves on the dielectric medium, we…
This paper addresses the pattern of damage, and investigates its properties, of a theoretical hail storm which gathers in intensity before subsiding, and which travels linearly across the landscape at constant velocity. We start by assuming…
This simulation study compares statistical approaches for estimating extreme quantile regression, with a specific application to fire risk forecasting. A simulation-based framework is designed to evaluate the effectiveness of different…
Finslerian extensions of Special and General Relativity -- commonly referred to as Very Special and Very General Relativity -- necessitate the development of a unified Lorentz-Finsler geometry. However, the scope of this geometric framework…
Spherical radial basis functions are used to define approximate solutions to strongly elliptic pseudodifferential equations on the unit sphere. These equations arise from geodesy. The approximate solutions are found by the Galerkin and…
Spider pulsars are binary systems containing an energetic millisecond pulsar that intensely irradiates a closely orbiting low-mass companion. Modelling their companion's optical light curves is essential to the study of the orbital…
Rapid detection and well-timed intervention are essential to mitigate the impacts of wildfires. Leveraging remote sensed data from satellite networks and advanced AI models to automatically detect hotspots (i.e., thermal anomalies caused by…
The method of geodesic deviations has been applied to derive accurate analytic approximations to geodesics in Schwarzschild space-time. The results are used to construct analytic expressions for the source terms in the Regge-Wheeler and…
Because most natural phenomena exhibit dependence at multiple scales like locations of earthquakes or forest fire occurrences, spatio-temporal single-scale point process models are unrealistic in many applications. This motivates us to…