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Updated: May 16, 2026

Visually Based Characterization of the Incipient Particle Motion in Regular Substrates: From Laminar to Turbulent Conditions
Published on: February 22, 2018
Distributional fixed-point equations for island nucleation in one dimension: a retrospective approach for
P A Mulheran1, K P O'Neill, M Grinfeld
1Department of Chemical and Process Engineering, University of Strathclyde, Glasgow. paul.mulheran@strath.ac.uk
Abstract:
The distributions of interisland 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 neighbor 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 favorably 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.
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