Discrete-Event Analytic Technique for Surface Growth Problems

TL;DR

This paper presents a novel discrete-event analytical method for calculating non-universal properties of rough surfaces in surface growth problems, effectively bridging the gap between discrete events and surface configurations.

Contribution

It introduces a new approach that maps local surface configurations to discrete events, enabling analytical predictions of surface properties that align well with numerical simulations.

Findings

Analytical probability distributions match simulation results.

Method effectively predicts surface growth properties.

Neglecting temporal correlations still yields accurate results.

Abstract

We introduce an approach for calculating non-universal properties of rough surfaces. The technique uses concepts of distinct surface-configuration classes, defined by the surface growth rule. The key idea is a mapping between discrete events that take place on the interface and its elementary local-site configurations. We construct theoretical probability distributions of deposition events at saturation for surfaces generated by selected growth rules. These distributions are then used to compute measurable physical quantities. Despite the neglect of temporal correlations, our approximate analytical results are in very good agreement with numerical simulations. This discrete-event analytic technique can be particularly useful when applied to quantification problems, which are known to not be suited to continuum methods.