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Restoring site percolation on damaged square lattices
Serge Galam1, Krzysztof Malarz
1Centre de Recherche en Epistémologie Appliquée, CNRS UMR 7656, CREA--Ecole Polytechnique, 1 rue Descartes, F-75005 Paris, France. galam@shs.polytechnique.fr
Summary
This study explores restoring site percolation on damaged square lattices. Two strategies involving adding longer-range links (N3, N4) were analyzed to recover percolation thresholds.
Area of Science:
- Statistical Mechanics
- Complex Systems
- Network Science
Background:
- Site percolation theory models the connectivity of random networks.
- Damaged lattices lose connectivity, impacting system function.
- Nearest-neighbor (N2) interactions are fundamental in many lattice models.
Purpose of the Study:
- To investigate methods for restoring site percolation on damaged square lattices.
- To compare two distinct strategies for re-establishing network connectivity.
- To quantify the effectiveness of new links (N3, N4) in recovery.
Main Methods:
- Utilizing Monte Carlo simulations to model lattice damage and restoration.
- Implementing two strategies: creating new sites with longer links or adding longer links to existing sites.
- Calculating critical densities (y(c), v(c)) required for percolation recovery.
Main Results:
- Quantified the critical densities (y(c), v(c)) needed for percolation restoration under both strategies.
- Evaluated the impact of N3 and N4 links on restoring connectivity.
- Obtained results across the full range of site destruction (0 to p(c)(N2)).
Conclusions:
- Both investigated strategies can effectively restore site percolation on damaged lattices.
- The required densities for restoration depend on the specific strategy and link types used.
- This research provides insights into network resilience and repair mechanisms.
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