Fluctuations and scaling in models for particle aggregation

TL;DR

This paper compares two particle deposition models, analyzing how different fluctuation levels affect surface growth, island formation, and scaling behavior, revealing a steady-state regime with properties similar to more complex models.

Contribution

It introduces and analyzes a Sequential Diffusion model that incorporates intermediate fluctuations, bridging simpler and more complex deposition models for surface growth.

Findings

Sequential Diffusion exhibits a steady-state with scaling island size distribution

Island density increases over time in the steady-state regime

The model provides insights into the role of fluctuations in particle aggregation

Abstract

We consider two sequential models of deposition and aggregation for particles. The first model (No Diffusion) simulates surface diffusion through a deterministic capture area, while the second (Sequential Diffusion) allows the atoms to diffuse up to \ell steps. Therefore the second model incorporates more fluctuations than the first, but still less than usual (Full Diffusion) models of deposition and diffusion on a crystal surface. We study the time dependence of the average densities of atoms and islands and the island size distribution. The Sequential Diffusion model displays a nontrivial steady-state regime where the island density increases and the island size distribution obeys scaling, much in the same way as the standard Full Diffusion model for epitaxial growth. Our results also allow to gain insight into the role of different types of fluctuations.