Related papers: Gielis superformula and wildfire models

We develop a wildfire simulation model that evolves the temperature scalar field using an energy balance equation accounting for heat generation, transport, and loss. For these equations, we develop quasi-implicit time integration schemes…

In recent years, advances in computational power and spatial data analysis (GIS, remote sensing, etc) have led to an increase in attempts to model the spread and behvaiour of wildland fires across the landscape. This series of review papers…

Forecasting bushfire spread is an important element in fire prevention and response efforts. Empirical observations of bushfire spread can be used to estimate fire response under certain conditions. These observations form rate-of-spread…

In a recent paper, we have introduced a new model to describe front propagation in bushfires. This model describes temperature diffusion in view of an ignition process induced by an interaction kernel, the effect of the environmental wind…

This paper focuses on the statistical properties of wild-land fires and, in particular, investigates if spread dynamics relates to simple invasion model. The fractal dimension and lacunarity of three fire scars classified from satellite…

We present an analytical closed form expression, which gives a good approximate propagator for diffusion on the sphere. Our formula is the spherical counterpart of the Gaussian propagator for diffusion on the plane. While the analytical…

Understanding the dynamics of wildfire is crucial for developing management and intervention strategies. Mathematical and computational models can be used to improve our understanding of wildfire processes and dynamics. This paper presents…

A wildfire model is formulated based on balance equations for energy and fuel, where the fuel loss due to combustion corresponds to the fuel reaction rate. The resulting coupled partial differential equations have coefficients that can be…

This work demonstrates the possibilities for improving wildfire and air quality management in the western United States by leveraging the unprecedented hourly data from NASA's TEMPO satellite mission and advances in self-supervised deep…

The increasing frequency and severity of wildfires highlight the need for accurate fire and plume spread models. We introduce an approach that effectively isolates and tracks fire and plume behavior across various spatial and temporal…

This paper presents the development of a new continuous forest fire model implemented as a weighted local small-world network approach. This new approach was designed to simulate fire patterns in real, heterogeneous landscapes. The wildland…

We introduce the heat method for computing the shortest geodesic distance to a specified subset (e.g., point or curve) of a given domain. The heat method is robust, efficient, and simple to implement since it is based on solving a pair of…

We study the problem of locating fire suppression resources in a burning landscape in order to minimise the total area burned. The landscape is modelled as a directed graph, with nodes representing regions of the landscape, and arcs…

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…

Wildfire is an important system process of the earth that occurs across a wide range of spatial and temporal scales. A variety of methods have been used to predict wildfire phenomena during the past century to better our understanding of…

Accurate prediction of wildfire spread is crucial for effective risk management, emergency response, and strategic resource allocation. In this study, we present a deep learning (DL)-based framework for forecasting the final extent of…

We propose a discrete two-dimensional mathematical model for forest fires and we derive certain results describing its limiting behavior. We also pose a relevant open question.

Motivated by models of signaling pathways in B lymphocytes, which have extremely large nuclei, we study the question of how reaction-diffusion equations in thin $2D$ domains may be approximated by diffusion equations in regions of smaller…

Models for wildfires must be stochastic if their ability to represent wildfires is to be objectively assessed. The need for models to be stochastic emerges naturally from the physics of the fire, and methods for assessing fit are…

In this paper we consider a classical model of gasless combustion in a one dimensional formulation under the assumption of ignition temperature kinetics. We study the propagation of flame fronts in this model when the initial distribution…