We study a new geometric bootstrap percolation model,
This content will become publicly available on October 1, 2025
Cascading structural failures of towers in an electric power transmission line due to straight line winds
- Award ID(s):
- 1751844
- PAR ID:
- 10529065
- Publisher / Repository:
- Reliability Engineering and System Safety
- Date Published:
- Journal Name:
- Reliability Engineering & System Safety
- Volume:
- 250
- Issue:
- C
- ISSN:
- 0951-8320
- Page Range / eLocation ID:
- 110304
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract line percolation , on thed ‐dimensional integer grid. In line percolation with infection parameter r , infection spreads from a subsetof initially infected lattice points as follows: if there exists an axis‐parallel line L withr or more infected lattice points on it, then every lattice point ofon L gets infected, and we repeat this until the infection can no longer spread. The elements of the setA are usually chosen independently, with some densityp , and the main question is to determine, the density at which percolation (infection of the entire grid) becomes likely. In this paper, we determine up to a multiplicative factor of and up to a multiplicative constant as for every fixed . We also determine the size of the minimal percolating sets in all dimensions and for all values of the infection parameter. -
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