Correlated percolation in island-forming processes: Analysis of cooperative filling on a square lattice.

Percolation transitions are analyzed for correlated distributions of occupied sites created by irreversible cooperative filling on a square lattice. Filling can be either autocatalytic, corresponding to island formation, or autoinhibitory. Here percolation problems for occupied and unoccupied clusters are generally distinct. Our discussion focuses on the influence of island formation (associated with correlation lengths of many lattice vectors), and of island perimeter roughness, on percolation. We also discuss the transition to continuum percolation problems as the ratio of island growth to nucleation rates, and thus the average island size, diverges. Some direct analysis of occupied cluster structure is provided, the connection with correlated animals is made, and correlated spreading and walking algorithms are suggested for direct generation of clusters and their perimeters. Disciplines Atomic, Molecular and Optical Physics | Physics Comments This article is published as Sanders, D. E., and J. W. Evans. "Correlated percolation in island-forming processes: Analysis of cooperative filling on a square lattice." Physical Review A 38, no. 8 (1988): 4186, doi:10.1103/ PhysRevA.38.4186. Posted with permission. This article is available at Iowa State University Digital Repository: http://lib.dr.iastate.edu/physastro_pubs/412 PHYSICAL REVIE%' A VOLUME 38, NUMBER 8 OCTOBER 15, 1988 Correlated percolation in island-forming processes: Analysis of cooperative filling on a square lattice D. E. Sanders and J. W. Evans Ames Laboratory and Department of Chemistry, Iowa State University, Ames, Iowa 50011 4,'Received 12 February 1988} Percolation transitions are analyzed for correlated distributions of occupied sites created by irreversible cooperative filling on a square lattice. Filling can be either autocatalytic, corresponding to island formation, or autoinhibitory. Here percolation problems for occupied and unoccupied clusters are generally distinct. Our discussion focuses on the influence of island formation (associated with correlation lengths of many lattice vectors}, and of island perimeter roughness, on percolation. We also discuss the transition to continuum percolation problems as the ratio of island growth to nucleation rates, and thus the average island size, diverges. Some direct analysis of occupied cluster structure is provided, the connection with correlated animals is made, and correlated spreading and walking algorithms are suggested for direct generation of clusters and their perimeters.