Geometry of developing flame fronts: Analysis with pole decomposition

The roughening of expanding flame fronts by the accretion of cusplike singularities is a fascinating example of the interplay between instability, noise, and nonlinear dynamics that is reminiscent of self-fractalization in Laplacian growth patterns. The nonlinear integro-differential equation that describes the dynamics of expanding flame fronts is amenable to analytic investigations using pole decomposition. This powerful technique allows the development of a satisfactory understanding of the qualitative and some quantitative aspects of the complex geometry that develops in expanding flame fronts.