Control of the surface roughness during a growth process described by the Kardar-Parisi-Zhang equation

Control theory is a widely used tool in engineering to develop controlled, stable models of dynamical systems. The control of deterministic models has been extensively studied; however, investigations of the control of non-equilibrium systems are less explored due to combined nonlinearity and noise. I will focus on understanding the effect of both linear and nonlinear control processes on the intrinsic dynamics and stationary properties of non-equilibrium systems. In particular, I will discuss how to achieve the saturation of the mean surface roughness to a prescribed value in a stochastic growth process described by the (1+1)-dimensional Kardar-Parisi-Zhang (KPZ) equation, by means of a non-linear feedback control scheme that manipulates a subset of Fourier modes. The control process limits the time and length scales within which the system behaves according to its intrinsic stochastic dynamics. These time and length scales show scaling behavior with the control parameter, and the associated scaling exponents are related to those of the unperturbed KPZ model.