1202.5327 (Paul A. Mulheran et al.)

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

Paul A. Mulheran, Kenneth P. O'Neill, Michael Grinfeld, Wilson Lamb

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.

View original: http://arxiv.org/abs/1202.5327