9623235 Kapila The proposed work is aimed at the modelling and analysis of wave motion that is caused, aided, or provoked by the liberation of chemical energy in exothermically reacting media. The ultimate goal is a mathematical description of the manner in which waves of combustion originate, interact, respond to disturbances, and undergo transitions. Work is proposed in four specific areas: two in which the medium is a single-phase material, i.e., a gaseous mixture, and two in which the medium is a two-phase material, i.e., a mixture of solid particles and gas. In the single-phase context the plan is to study (i) how flames propagate through a stratified mixture in which the scale of stratification is comparable to the natural length of the flame, and (ii) how detonations evolve and propagate (or fail to do so) in regions of temperature, velocity and concentration gradients, especially in nonplanar configurations. In the two-phase portion of the study the objectives are (i) asymptotic reduction of complex models by exploitation of certain natural and realistic limits of rapid equilibration, and (ii) exploration of regularization issues arising in the numerical implementation of reduced models. In all cases the effort will focus largely on unsteady processes. It is anticipated that the problems will be modelled, by and large, by systems of nonlinear partial differential equations. The aim is the construction of explicit solutions, wherever feasible, with strong emphasis on the interplay between analytical techniques (especially asymptotics and singular perturbations) and accurate, well-resolved numerics. %%% Safe and efficient usage, and hazard-free storage and transportation, of combustible and explosive materials demands that the fundamental processes of combustion be precisely understood. This proposal is aimed at achieving such an understanding of certain specific combustion problems, via mathematical modelling, analysis and computation. One c lass of problems under study deals with propagation of flames and detonations in stratified mixtures. This is an area of practical interest in several contexts, including fire safety where stratification may have been caused by an accidental spill, and internal combustion engines where a stratified charge may have been produced intentionally. The second class of problems is concerned with the occurence of explosions in damaged explosives, which can be highly susceptible to low-velocity impacts or relatively mild thermal insults. ***
