Nonlocality in kinetic roughening

We propose a phenomenological equation to describe kinetic roughening of a growing surface in presence of long range interactions. The roughness of the evolving surface depends on the long range feature, and several distinct scenarios of phase transitions are possible. Experimental implications are discussed.Comment: Replaced with the published version (Phys. Rev. Lett 79, 2502 (1997)). Eq. 1 written in a symmetrical form, references update

Flame front propagation I: The Geometry of Developing Flame Fronts: Analysis with Pole Decomposition

The roughening of expanding flame fronts by the accretion of cusp-like 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.Comment: 4 pages, 2 figure