Interface dynamics from experimental data

Abstract

A novel algorithm is envisaged to extract the coupling parameters of the Kardar-Parisi-Zhang (KPZ) equation from experimental data. The method hinges on the Fokker-Planck equation combined with a classical least-square error procedure. It takes properly into account the fluctuations of surface height through a deterministic equation for space correlations. We apply it to the 1+1 KPZ equation and carefully compare its results with those obtained by previous investigations. Unlike previous approaches, our method does not require large sizes and is stable under a modification of sampling time of observations. Shortcomings associated to standard discretizations of the continuous KPZ equation are also pointed out and possible future perspectives are finally analyzed.