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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

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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

Item type: Article
ID code: 42130
Keywords: gap size distribution, capture zone distribution, distributional , fixed-point equations , island nucleation , one dimension , retrospective approach , capture-zone scaling, Chemical engineering, Mathematics, Statistical and Nonlinear Physics, Statistics and Probability, Condensed Matter Physics
Subjects: Technology > Chemical engineering
Science > Mathematics
Department: Faculty of Engineering > Chemical and Process Engineering
Faculty of Science > Mathematics and Statistics
Depositing user: Pure Administrator
Date deposited: 19 Nov 2012 14:01
Last modified: 06 Oct 2017 00:10
Related URLs:
URI: https://strathprints.strath.ac.uk/id/eprint/42130
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