Interface dynamics, pole trajectories, and cell size statistics

We demonstrate the possibility to reproduce the experimental evolution of an interface, here a flame front, through the trajectory of a few poles whose position in the complex plane expresses the interface shape. These poles are analytical solutions of the Sivashinsky equation and they evolve according to an ordinary differential equation. The direct comparison with experimental flame fronts propagating in a quasi-two-dimensional configuration is made at the nonlinear but deterministic stages of the front dynamics, reproducing a cell creation and fusion process. At later times, when the front is sensitive to noise as in the Kardar-Parisi-Zhang equation, we demonstrate that the cell size distribution is still ruled by the pole attractive nature.