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

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

2012-02-23

arxiv.org/abs/1202.5327v1

Physics

Condensed Matter

Statistical Mechanics

4 pages, 4 figures (including 2 colour figures) and 1 table

Scientific paper

The distribution of the capture zones of point islands nucleated in one dimension are considered using a retrospective view, providing an alternative perspective on why scaling occurs in this continuously evolving system. Distributional fixed point equations for the capture zones are derived through a mean field approximation for nearest neighbour size correlation. Solutions of these equations compare favourably to Monte Carlo data for a range of critical island size $i=0,1,2,3$, and to theoretical models based on more traditional fragmentation theory approaches.

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