Roughening of the (1+1) interfaces in two-component surface growth with an admixture of random deposition

TL;DR

This paper investigates how adding random deposition to a KPZ-type surface growth model affects interface scaling, revealing a universal scaling function and implications for parallel computing synchronization.

Contribution

It derives a universal scaling function for mixed growth models and demonstrates the dilatation effect of random deposition on KPZ correlations.

Findings

Random deposition acts as a dilatation mechanism for interface scales.

The universal scaling function describes the interface width behavior.

Existence of an early non-scaling phase in interface evolution.

Abstract

We simulate competitive two-component growth on a one dimensional substrate of $L$ sites. One component is a Poisson-type deposition that generates Kardar-Parisi-Zhang (KPZ) correlations. The other is random deposition (RD). We derive the universal scaling function of the interface width for this model and show that the RD admixture acts as a dilatation mechanism to the fundamental time and height scales, but leaves the KPZ correlations intact. This observation is generalized to other growth models. It is shown that the flat-substrate initial condition is responsible for the existence of an early non-scaling phase in the interface evolution. The length of this initial phase is a non-universal parameter, but its presence is universal. In application to parallel and distributed computations, the important consequence of the derived scaling is the existence of the upper bound for the desynchronization in a conservative update algorithm for parallel discrete-event simulations. It is shown that such algorithms are generally scalable in a ring communication topology.