Anomalous critical and supercritical phenomena in explosive percolation

Abstract

The emergence of large-scale connectivity on an underlying network or lattice, the so-called percolation transition, has a profound impact on the system’s macroscopic behaviours. There is thus great interest in controlling the location of the percolation transition to either enhance or delay its onset and, more generally, in understanding the consequences of such control interventions. Here we review explosive percolation, the sudden emergence of large-scale connectivity that results from repeated, small interventions designed to delay the percolation transition. These transitions exhibit drastic, unanticipated and exciting consequences that make explosive percolation an emerging paradigm for modelling real-world systems ranging from social networks to nanotubes.

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Figure 1: Schematic of explosive percolation.
Figure 2: Classes of explosive percolation.
Figure 3: Explosive percolation with stochastic staircases.
Figure 4: Non-self-averaging in explosive percolation.
Figure 5: Multiple giant components and the ‘powder keg’.

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Acknowledgements

We thank M. Schröder and A. Witt for valuable discussions and assistance in the preparation of the figures, and C. D’Souza and L. Nagler-Deutsch for invaluable input. R.M.D’S. gratefully acknowledges support from the US Army Research Office MURI Award No. W911NF-13-1-0340 and Cooperative Agreement No. W911NF-09-2-0053 and the Defense Threat Reduction Agency Basic Research Award HDTRA1-10-1-0088.

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Correspondence to Raissa M. D’Souza or Jan Nagler.

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D’Souza, R., Nagler, J. Anomalous critical and supercritical phenomena in explosive percolation. Nature Phys 11, 531–538 (2015). https://doi.org/10.1038/nphys3378

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