Two-Front Traveling Waves in Filtration Combustion

Historical perspective and contribution of US researchers into the field of self-propagating high-temperature synthesis (SHS)/combustion synthesis (CS): Personal reflections

“…Theoretical research describing combustion front stability and bifurcation analysis was done by Matkowsky from Northwestern University, and Margolis, Armstrong and Koszykowski from Lawrence Livermore National Laboratory. Professor Matkowsky has published numerous theoretical papers on the subject of gasless and gas-solid reactions [38][39][40][41][42][43][44][45][46][47][48][49][50][51][52]. His pioneering work with Margolis, Kaper, and Leaf on bifurcation on pulsating and spinning reactions in condensed twophase combustion belongs to very fundamental classics of combustion synthesis [39].…”

Nonlinear Waves and Polarization in Diffusive Directed Particle Flow

“…The resulting solution was comprised of two humps of particles moving outward from the center at the critical velocity specified above, growing in width so that their rear flank moves at the particle velocity 1, and leaving behind a central region devoid of any particles. This emergence of multiple wave fronts of different velocities has been known for a long time (e.g., [11]) but it is remarkable that complicated patterns of this type are observed in a rather minimal system of two equations.…”

A two-dimensional model for large-scale bushfire spread

“…A great many numerical solutions has been computed, using the difference scheme of Section 3, and a good understanding of the behaviour of the model (9)- (10) has been developed for a one-dimensional fire. In particular, the fact that the present model does not automatically predict a fire growing in intensity is regarded as one of its considerable successes.…”

“…Norbury and Stuart [9] have investigated such waves in a porous medium, and show that there are two types of behaviour, depending upon whether the temperature at each end of the combustion wave falls below some ignition temperature, or else if there is complete exhaustion of the fuel upstream. A similar model, but one which is more complex, has been presented recently by Shkadinsky et al [10], and permits two-fronted travelling waves. A model in which the speed of the combustion wave is approximately constant is discussed for a similar system by Booty and Matkowsky [1]; in this case there is a gradual change to the shape of the wave front as it propagates.…”