Interdependent Networks: Novel Physical Phase Transitions

by Shlomo Havlin (Bar-Ilan University, Israel)

Monday 16 Jan 2023, 14:30 → 16:00 Europe/Rome

Aula Conversi (Dipartimento di Fisica - Ed. Marconi)

A framework for studying the percolation theory of interdependent networks will be presented. In interdependent networks, such as infrastructures, when nodes in one network fail, they cause dependent nodes in other networks to also fail. This may happen recursively and can lead to a cascade of failures and to a sudden abrupt fragmentation of the system of interdependent systems. This is in contrast to a single network where the fragmentation percolation transition due to failures is continuous. I will present analytical solutions based on percolation theory, for the critical thresholds, cascading failures, and the giant functional component of a network of n interdependent networks. I will show, that the general theory shows many novel processes and features that are not present in the percolation theory of single networks.
I will also show that interdependent networks embedded in space are significantly more vulnerable and the phase transition is much richer compared to non-embedded networks. In particular, small localized attacks of zero fraction but above a critical size may lead to cascading failures that dynamically propagate and yield an abrupt phase transition. I will finally discuss the consequences of the behavior of percolation of interdependent networks on phase transitions in real physical interdependent systems. I will discuss the recent theory and experiments on interdependent superconducting networks where we identified a novel abrupt transition although each isolated system shows a continuous transition.
References:
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[5] M. Danziger et al, Nature Physics 15(2), 178 (2019)
[6] I Bonamassa et al, Interdependent superconducting networks, preprint arXiv:2207.01669 (2022)
[7] B. Gross et al, arXiv:2208.00440, PRL, in press (2022)