Related papers: Modelling wildfire spread and spotfire merger usin…

We consider a multidimensional reaction-diffusion equation of either ignition or monostable type, involving periodic heterogeneity, and analyze the dependence of the propagation phenomena on the direction. We prove that the (minimal) speed…

Wave propagation in one-dimensional heterogeneous bistable media is studied using the Schl\"ogl model as a representative example. Starting from the analytically known traveling wave solution for the homogeneous medium, infinitely extended,…

Spreading of bacteria in a highly advective, disordered environment is examined. Predictions of super-diffusive spreading for a simplified reaction-diffusion equation are tested. Concentration profiles display anomalous growth and…

The transfer matrix formalism is widely used in modeling heat diffusion in layered structures.Due to an intrinsic numerical instability issue, which has not yet drawn enough attention to the heat transfer community,this formalism fails at…

We developed a conformal map technique to analyze the attenuation of edge modes propagating along imperfect boundaries. In systems where the potential energy exhibits conformal invariance, the conformal transformation can straighten the…

The understanding and prediction of large wildland fire events around the world is a growing interdisciplinary research area advanced rapidly by development and use of computational models. Recent models bidirectionally couple computational…

Different approaches to the nonlinear dynamics of premixed flames exist in the literature: equations based on developments in a gas ex- pansion parameter, weak nonlinearity approximation, potential model equation in a coordinate-free form.…

This chapter is a pedagogical review of methods and results for studying wave propagation in one-dimensional complex structures. We describe and compare the tight-binding, scattering matrix, transfer matrix and Riccati formalisms. We…

One of the most elementary spreading models on graphs can be described by a fire spreading from a burning vertex in discrete time steps. At each step, all neighbors of burning vertices catch fire. A well-studied extension to model fire…

First-principles Markov Chain Monte Carlo sampling is used to investigate uncertainty quantification and uncertainty propagation in parameters describing hydrogen kinetics. Specifically, we sample the posterior distribution of thirty-one…

Inspired by recent studies associating shifting temperature conditions with changes in the efficiency of predator species in converting their prey to offspring, we propose a predator-prey model of reaction-diffusion type to analyze the…

Wildfire spread is strongly influenced by the transport and ignition of embers. While long-range spotting driven by plume lofting has received significant attention, embers transported near the surface by turbulent winds can also influence…

Wildland fire dynamics is a complex turbulent dimensional process. Cellular automata (CA) is an efficient tool to predict fire dynamics, but the main parameters of the method are challenging to estimate. To overcome this challenge, we…

We study analytically and numerically a model describing front propagation of a KPP reaction in a fluid flow. The model consists of coupled one-dimensional reaction-diffusion equations with different drift coefficients. The main rigorous…

This work surveys an r-adaptive moving mesh finite element method for the numerical solution of premixed laminar flame problems. Since the model of chemically reacting flow involves many different modes with diverse length scales, the…

Reactive Rayleigh-Taylor systems are characterized by the competition between the growth of the instability and the rate of reaction between cold (heavy) and hot (light) phases. We present results from state-of-the-art numerical simulations…

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…

We investigate three different methods for systematically approximating the diffusion coefficient of a deterministic random walk on the line which contains dynamical correlations that change irregularly under parameter variation. Capturing…

We present a fast adaptive method for the evaluation of heat potentials, which plays a key role in the integral equation approach for the solution of the heat equation, especially in a non-stationary domain. The algorithm utilizes a…

Diffusion in inhomogeneous materials can be described by both the Fick and Fokker--Planck diffusion equations. Here, we study a mixed Fick and Fokker-Planck diffusion problem with coefficients rapidly oscillating both in space and time. We…