Numerical study for controlling surface roughening in KPZ growth process

The Kardar-Parisi-Zhang (KPZ) equation has been used to describe growth processes in a variety of systems, and the corresponding exponents have been shown to prevail in both numerical models and experiments. Our objective in this work is to control the surface roughening for the KPZ growth process in (1+1) dimensions. We aim to saturate the surface roughness to the desired value using feedback control and try to understand the effect of the feedback control on the underlying dynamics. To this end, we apply a numerical integration scheme of the KPZ equation (with and without control) using the pseudo-spectral method. The numerical results show that controlling only a few small wave numbers leaves the system in the KPZ universality class. However, perturbing the wave numbers beyond a certain threshold changes the underlying kinetics, depending on the specific type of implemented (linear or nonlinear) control.