Picture of two heads

Open Access research that challenges the mind...

The Strathprints institutional repository is a digital archive of University of Strathclyde research outputs. Strathprints provides access to thousands of Open Access research papers by University of Strathclyde researchers, including those from the School of Psychological Sciences & Health - but also papers by researchers based within the Faculties of Science, Engineering, Humanities & Social Sciences, and from the Strathclyde Business School.

Discover more...

Distributional fixed-point equations for island nucleation in one dimension : a retrospective approach for capture zone scaling

Mulheran, Paul and O'Neill, Kenneth Peter and Grinfeld, Michael and Lamb, Wilson (2012) Distributional fixed-point equations for island nucleation in one dimension : a retrospective approach for capture zone scaling. Physical Review E, 86 (5). ISSN 1539-3755

[img] PDF
DFPE_paper_PRE_V2.pdf - Preprint

Download (602kB)

Abstract

The distributions of inter-island gaps and captures zones for islands nucleated on a one-dimensional substrate during submonolayer deposition are considered using a novel retrospective view. This provides an alternative perspective on why scaling occurs in this continuously evolving system. Distributional fixed point equations for the gaps are derived both with and without a mean field approximation for nearest neighbour gap size correlation. Solutions to the equations show that correct consideration of fragmentation bias justifies the mean field approach which can be extended to provide closed-from equations for the capture zones. Our results compare favourably to Monte Carlo data for both point and extended islands using a range of critical island size i = 0, 1, 2, 3. We also find satisfactory agreement with theoretical models based on more traditional fragmentation theory approaches