Point island dynamics under fixed rate deposition

TL;DR

This paper investigates the behavior of point islands during submonolayer deposition, incorporating island fragmentation, and applies advanced mathematical methods to analyze the asymptotic dynamics and compare different modeling assumptions.

Contribution

It introduces a comprehensive mathematical framework for analyzing point island dynamics with fragmentation, extending previous models by including subcritical island behavior and using centre manifold theory.

Findings

Derived asymptotic solutions for island size distributions.

Compared quasi-steady state assumptions with full dynamical models.

Provided insights into the long-term behavior of island growth and fragmentation.

Abstract

In this paper we consider the dynamics of point islands during submonolayer deposition, in which the fragmentation of subcritical size islands is allowed. To understand asymptotics of solutions, we use methods of centre manifold theory, and for globalisation, we employ results from the theories of compartmental systems and of asymptotically autonomous dynamical systems. We also compare our results with those obtained by making the quasi-steady state assumption.