Controlling surface morphologies by time-delayed feedback

TL;DR

This paper introduces a novel time-delayed feedback method to control surface roughness in growth processes, demonstrated on the KPZ equation, allowing stabilization of the growth exponent at desired values, with potential experimental applications.

Contribution

A new general feedback control scheme is developed to manipulate surface growth dynamics, specifically stabilizing the growth exponent in the KPZ model over extended periods.

Findings

Effective control of surface roughness achieved

Growth exponent stabilized at desired values

Method applicable to various growth phenomena

Abstract

We propose a new method to control the roughness of a growing surface, via a time-delayed feedback scheme. As an illustration, we apply this method to the Kardar-Parisi-Zhang equation in 1+1 dimensions and show that the effective growth exponent of the surface width can be stabilized at any desired value in the interval [0.25,0.33], for a significant length of time. The method is quite general and can be applied to a wide range of growth phenomena. A possible experimental realization is suggested.