A numerical solution of the problem of crown forest fire initiation and spread

Mathematical model of forest fire was based on an analysis of known experimental data and using concept and methods from reactive media mechanics. The study takes in to account the mutual interaction of the forest fires and three-dimensional atmosphere flows. The research is done by means of mathematical modeling of physical processes. It is based on numerical solution of Reynolds equations for chemical components and equations of energy conservation for gaseous and condensed phases. It is assumed that the forest during a forest fire can be modeled as a two-temperature multiphase non-deformable porous reactive medium. A discrete analog for the system of equations was obtained by means of the control volume method. The developed model of forest fire initiation and spreading would make it possible to obtain a detailed picture of the variation in the velocity, temperature and chemical species concentration fields with time. Mathematical model and the result of the calculation give an opportunity to evaluate critical conditions of the forest fire initiation and spread which allows applying the given model for of means for preventing fires

A review of wildland fire spread modelling, 1990-present, 1: Physical and quasi-physical models

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 behaviour of wildland fires across the landscape. This series of review papers endeavours to critically and comprehensively review all types of surface fire spread models developed since 1990. This paper reviews models of a physical or quasi-physical nature. These models are based on the fundamental chemistry and/or physics of combustion and fire spread. Other papers in the series review models of an empirical or quasi-empirical nature, and mathematical analogues and simulation models. Many models are extensions or refinements of models developed before 1990. Where this is the case, these models are also discussed but much less comprehensively.Comment: 31 pages + 8 pages references + 2 figures + 5 tables. Submitted to International Journal of Wildland Fir

A review of wildland fire spread modelling, 1990-present 3: Mathematical analogues and simulation models

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 endeavours to critically and comprehensively review all types of surface fire spread models developed since 1990. This paper reviews models of a simulation or mathematical analogue nature. Most simulation models are implementations of existing empirical or quasi-empirical models and their primary function is to convert these generally one dimensional models to two dimensions and then propagate a fire perimeter across a modelled landscape. Mathematical analogue models are those that are based on some mathematical conceit (rather than a physical representation of fire spread) that coincidentally simulates the spread of fire. Other papers in the series review models of an physical or quasi-physical nature and empirical or quasi-empirical nature. Many models are extensions or refinements of models developed before 1990. Where this is the case, these models are also discussed but much less comprehensively.Comment: 20 pages + 9 pages references + 1 page figures. Submitted to the International Journal of Wildland Fir

A review of wildland fire spread modelling, 1990-present 2: Empirical and quasi-empirical models

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 behaviour of wildland fires across the landscape. This series of review papers endeavours to critically and comprehensively review all types of surface fire spread models developed since 1990. This paper reviews models of an empirical or quasi-empirical nature. These models are based solely on the statistical analysis of experimentally obtained data with or without some physical framework for the basis of the relations. Other papers in the series review models of a physical or quasi-physical nature, and mathematical analogues and simulation models. The main relations of empirical models are that of wind speed and fuel moisture content with rate of forward spread. Comparisons are made of the different functional relationships selected by various authors for these variables.Comment: 22 pages + 7 pages references + 2 pages tables + 2 pages figures. Submitted to International Journal of Wildland Fir

Reducing wildland fire hazard exploiting complex network theory. A case study analysis

We discuss a new systematic methodology to mitigate wildland fire hazard by appropriately distributing fuel breaks in space. In particular, motivated by the concept of information flow in complex networks we create a hierarchical allocation of the landscape patches that facilitate the fire propagation based on the Bonacich centrality. Reducing the fuel load in these critical patches results to lower levels of fire hazard. For illustration purposes we apply the proposed strategy to a real case of wildland fire. In particular we focus on the wildland fire that occurred in Spetses Island, Greece in 1990 and burned the one third of the forest. The efficiency of the proposed strategy is compared against the benchmark of random distribution of fuel breaks for a wide range of fuel breaks densities

A reaction-diffusion model of cholinergic retinal waves

Prior to receiving visual stimuli, spontaneous, correlated activity called retinal waves drives activity-dependent developmental programs. Early-stage waves mediated by acetylcholine (ACh) manifest as slow, spreading bursts of action potentials. They are believed to be initiated by the spontaneous firing of Starburst Amacrine Cells (SACs), whose dense, recurrent connectivity then propagates this activity laterally. Their extended inter-wave intervals and shifting wave boundaries are the result of the slow after-hyperpolarization of the SACs creating an evolving mosaic of recruitable and refractory cells, which can and cannot participate in waves, respectively. Recent evidence suggests that cholinergic waves may be modulated by the extracellular concentration of ACh. Here, we construct a simplified, biophysically consistent, reaction-diffusion model of cholinergic retinal waves capable of recapitulating wave dynamics observed in mice retina recordings. The dense, recurrent connectivity of SACs is modeled through local, excitatory coupling occurring via the volume release and diffusion of ACh. In contrast with previous, simulation-based models, we are able to use non-linear wave theory to connect wave features to underlying physiological parameters, making the model useful in determining appropriate pharmacological manipulations to experimentally produce waves of a prescribed spatiotemporal character. The model is used to determine how ACh mediated connectivity may modulate wave activity, and how the noise rate and sAHP refractory period contributes to critical wave size variability.Comment: 38 pages, 10 figure

Mathematical modelling of the spread of contamination during fires in forests exposed to radioactive contamination

The paper suggested in the context of the general mathematical model of forest fires [1] gives a new mathematical setting and method of numerical solution of a problem of a radioactive spread above the forest region. Numerical solution of problems of radioactive smoke spread during crown fire in exemplified heat energy release in the forest fire front was found. Heat energy release in the forest fire front was found to cause further radioactive particles spread by the action of wind. In the absence of wind, radioactive smoke particles deposit again on the underlying surface after a time. As a wind velocity increases, these particles are transferred in the ground layer over distances proportional to a wind velocity