Correlated percolation in island-forming processes: Analysis of cooperative filling on a square lattice
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Ames National Laboratory is a government-owned, contractor-operated national laboratory of the U.S. Department of Energy (DOE), operated by and located on the campus of Iowa State University in Ames, Iowa.
For more than 70 years, the Ames National Laboratory has successfully partnered with Iowa State University, and is unique among the 17 DOE laboratories in that it is physically located on the campus of a major research university. Many of the scientists and administrators at the Laboratory also hold faculty positions at the University and the Laboratory has access to both undergraduate and graduate student talent.
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Abstract
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.
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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.