一维岛形核的分布不动点方程：捕获区标度的回溯方法
Distributional fixed point equations for island nucleation in one dimension: a retrospective approach for capture zone scaling
摘要：
在亚单层沉积过程中，岛间的间隙和捕获区的分布被认为是使用一种新的回顾性的观点在一维衬底上成核的岛屿。这为为什么在这个不断发展的系统中发生缩放提供了另一种视角。间隙的分布不动点方程推导出与最近邻间隙尺寸相关的平均场近似和不近似。方程的解决方案表明，正确的考虑碎片的偏见证明了平均场的方法，可以扩展到提供封闭的捕获区的方程。我们的研究结果相比有利的Monte Carlo数据点和扩展的岛屿，使用一系列的临界岛屿大小$i=0,1,2,3$。我们也发现令人满意的协议与理论模型的基础上更传统的碎裂理论的方法。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
