Campus Units

Physics and Astronomy, Mathematics, Ames Laboratory

Document Type

Article

Publication Version

Published Version

Publication Date

1988

Journal or Book Title

Physical Review A

Volume

38

Issue

8

First Page

4186

Last Page

4197

DOI

10.1103/PhysRevA.38.4186

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.

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.

Copyright Owner

American Physical Society

Language

en

File Format

application/pdf

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