Persisting roughness when deposition stops

TL;DR

This paper modifies classical surface growth theories to account for persistent surface roughness after deposition stops, revealing that the steady state becomes history-dependent and differs from traditional predictions.

Contribution

It introduces modifications to the Edwards-Wilkinson and KPZ models to better reflect physical constraints, showing the emergence of history-dependent steady states after deposition ceases.

Findings

Steady state in the modified model is similar to EW in the long wavelength limit.

Surface rearrangement halts once gradients are below the angle of repose.

Post-deposition, the surface exhibits history-dependent steady state distributions.

Abstract

Useful theories for growth of surfaces under random deposition of material have been developed by several authors. The simplest theory is that introduced by Edwards and Wilkinson (EW), which is linear and soluble. Its non linear generalization by Kardar, Parisi and Zhang (KPZ), resulted in many subsequent studies. Yet both theories EW and KPZ contain an unphysical feature. When deposition of material is stopped both theories predict that as time tends to infinity, the surface becomes flat. In fact, of course, the final surface is not flat, but simply has no gradients larger than the gradient related to the angle of repose. We modify the EW and KPZ to accommodate this feature and study the consequences for the simpler system which is a modification of the EW equation. In spite of the fact that the equation describing the evolution of the surface is not linear, we find that the steady state in the presence of noise is not very different in the long wave length limit from that of the linear EW. The situation is quite different from that of EW when deposition stops. Initially there is still some rearrangement of the surface but that stops as everywhere on the surface the gradient is less than that related to the angle of repose. The most interesting feature observed after deposition stops is the emergence of history-dependent steady state distributions.