SCALING, PROPAGATION, AND KINETIC ROUGHENING OF FLAME FRONTS IN RANDOM-MEDIA

We introduce a model of two coupled reaction-diffusion equations to de scribe the dynamics and propagation of flame fronts in random media. T he model incorporates heat diffusion, its dissipation, and its product ion through coupling to the background reactant density. We first show analytically and numerically that there is a finite critical value of the background density below which the front associated with the temp erature field stops propagating. The critical exponents associated wit h this transition are shown to be consistent with mean-field theory of percolation. Second, we study the kinetic roughening associated with a moving planar flame front above the critical density. By numerically calculating the time-dependent width and equal-time height correlatio n Function of the Gent, we demonstrate that the roughening process bel ongs to the universality class of the Kardar-Parisi-Zhang interface eq uation. Finally, we show how this interface equation can be analytical ly derived from our model in the limit of almost uniform background de nsity.