Related papers: Mathematical modeling the wildfire propagation in …
Climate change is intensifying wildfire risks globally, making reliable forecasting critical for adaptation strategies. While machine learning shows promise for wildfire prediction from Earth observation data, current approaches lack…
The dynamics of a thin Huygens front propagating through turbulent medium is considered. A rigorous asymptotic expression for the effective velocity $v_{F}$ proportional to the front area is derived. The small-scale fluctuations of the…
Level set methods are versatile and extensible techniques for general front tracking problems, including the practically important problem of predicting the advance of a firefront across expanses of surface vegetation. Given a rule,…
Various flame tracking techniques are often used in hydrodynamic simulations. Their use is indispensable when resolving actual scale of the flame is impossible. We show that parameters defining "artificial flame" propagation found from…
Diffuse scattering of electromagnetic waves from natural and artificial surfaces has been extensively studied in various disciplines, including radio wave propagation, and several diffuse scattering models based on different approaches have…
Nonlinear waves are a robust phenomenon observed in complex systems ranging from mechanics to ecology. Fronts are fundamental due to their robustness against perturbations and capacity to propagate one state over another. Controlling and…
We propose here a new model to describe biological invasions in the plane when a strong diffusion takes place on a line. We establish the main properties of the system, and also derive the asymptotic speed of spreading in the direction of…
As an analog model of general relativity, optics on some two-dimensional (2D) curved surfaces has been increasingly paid attention to in the past decade. Here, in light of Huygens-Fresnel principle, we propose a theoretical frame to study…
Electric power infrastructure faces increasing risk of damage and disruption due to wildfire. Operators of power grids in wildfire-prone regions must consider the potential impacts of unpredictable fires. However, traditional wildfire…
The use of pesticides for enhancing crop yield and preventing infestations is a widespread agricultural practice. However, in recent years, there has been a growing shift toward traditional chemical-free organic farming. Regulatory…
We study a model for the destruction of a random network by fire. Suppose that we are given a multigraph of minimum degree at least 2 having real-valued edge-lengths. We pick a uniform point from along the length and set it alight; the…
We are concerned with the persistence of both predator and prey in a diffusive predator-prey system with a climate change effect, which is modeled by a spatial-temporal heterogeneity depending on a moving variable. Moreover, we consider…
The problem of flame propagation is studied as an example of unstable fronts that wrinkle on many scales. The analytic tool of pole expansion in the complex plane is employed to address the interaction of the unstable growth process with…
We consider the propagation of a flame front in a solid medium with a periodic structure. The model is governed by a free boundary system for the pair" temperature-front. "The front's normal velocity depends on the temperature via a…
This paper is concerned with a model for the dynamics of a single species in a one-dimensional heterogeneous environment. The environment consists of two kinds of patches, which are periodically alternately arranged along the spatial axis.…
In 2023, Sicily faced an escalating issue of uncontrolled fires, necessitating a thorough investigation into their spatio-temporal dynamics. Our study addresses this concern through point process theory. Each wildfire is treated as a unique…
We introduce a model of two coupled reaction-diffusion equations to describe the dynamics and propagation of flame fronts in random media. The model incorporates heat diffusion, its dissipation, and its production through coupling to the…
As the impact of wildfires has become increasingly more severe over the last decades, there is continued pressure for improvements in our ability to predict wildland fire behavior over a wide range of conditions. One approach towards this…
Forward propagation of input uncertainties in physics-based wildfire models is computationally prohibitive, limiting the use of high-fidelity simulators in risk assessment workflows. This work introduces a geometry-aligned bi-fidelity…
We introduce new models for Schr\"odinger-type equations, which generalize standard NLS and for which different dispersion occurs depending on the directions. Our purpose is to understand dispersive properties depending on the directions of…