Numerical studies on control of surface roughness in the KPZ equation

Kardar-Parisi-Zhang (KPZ) equation has been used in determining the growth process in a wide variety of particle interacting systems and experiments. Our objective in this work is to control the surface roughening in one and two dimensions using the KPZ equation. We aim to saturate the surface roughening to the desired value and try to understand its effect on the growth of mean and fluctuations. We perform the numerical simulation of the KPZ equation with and without control using the pseudospectral method. The Family-Vicsek scaling of numerical data shows that the linear feedback control does not affect the underlying process and leaves the system in the same KPZ universality class.