2011/07/06 by Diego Luis Gonzalez Cabrera, Diego Luis González, Alberto Pimpinelli +1
Mathematics · Physics and Astronomy · #Distribution (mathematics) #Geology #Mathematical analysis #Mathematics #Physics #Random Matrices and Applications #Statistical physics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.84.011601
published as Physical Review E 84, 011601 (2011) · 12 pages, 9 figures
openalex publication_date 2011/07/06 · arxiv created 2011/10/18 · arxiv updated 2012/03/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study the configurational structure of the point-island model for epitaxial growth in one dimension. In particular, we calculate the island gap and capture zone distributions. Our model is based on an approximate description of nucleation inside the gaps. Nucleation is described by the joint probability density p(n)(XY)(x,y), which represents the probability density to have nucleation at position x within a gap of size y. Our proposed functional form for p(n)(XY)(x,y) describes excellently the statistical behavior of the system. We compare our analytical model with extensive numerical simulations. Our model retains the most relevant physical properties of the system.