From Graph theory to Novel Physics
Seminar
Speaker
Shlomo Havlin (Bar-Ilan University)
Date
09/11/2025 - 13:00 - 12:00Add to Calendar
2025-11-09 12:00:00
2025-11-09 13:00:00
From Graph theory to Novel Physics
Phase transitions (PTs) are fundamental phenomena in statistical physics and condensedmatter, manifesting as abrupt or continuous changes in system properties.I will show that it is possible to generalize the single graph theory to interdependent graphs (networks) and obtain novel typesof physical processes that can be observed in experiments.Interdependent networks appear in all aspects of nature and technology. Examples include thephysiological systems in our body and in infrastructures. A theoretical framework for percolationtheory of interdependent networks will be presented. In interdependent networks, such asinfrastructures, when nodes in one network fail, they cause dependent nodes in other networksto also fail. This may happen recursively and can lead to a cascade of failures and to a suddenfragmentation of the system. This contrasts with a single network where the networkbreakdown due to failures is continuous. I will present analytical solutions based on thepercolation theory, for the functional network and cascading failures, for a network of ninterdependent networks. Our analytical results show that the percolation theory of a singlegraph studied in mathematics and physics for over 90 years is just a limited case, n=1, of the general and significantlyricher case of n>1. I will also show that interdependent networks embedded in space areextremely vulnerable and have significantly richer behavior compared to non-embeddednetworks. I will finally show that the abstract interdependent percolation theory and its novel behavior in networks ofnetworks can be realized and proven in controlled experiments performed by Aviad Frydman oninterdependent superconducting networks and by Patrick Sebbah on coupled laser systems. ReferencesS. Buldyrev, G. Paul, H.E. Stanley, S. Havlin, Nature, 464, 08932 (2010)J. Gao, S. Buldyrev, H. E. Stanley, S. Havlin, Nature Physics, 8, 40 (2012)A. Bashan et al, Nature Physics, 9, 667 (2013)B. Gross et al, PRL 129, 268301 (2022)I. Bonamassa et al, Interdependent superconducting networks, Nature Physics 19, 1163 (2023) J. Wang, Coupled Lasers phase transitions arXiv preprint arXiv:2508.21786
(201) Math Seminar room
אוניברסיטת בר-אילן - המחלקה למתמטיקה
mathoffice@math.biu.ac.il
Asia/Jerusalem
public
Place
(201) Math Seminar room
Abstract
Phase transitions (PTs) are fundamental phenomena in statistical physics and condensed
matter, manifesting as abrupt or continuous changes in system properties.
matter, manifesting as abrupt or continuous changes in system properties.
I will show that it is possible to generalize the single graph theory to interdependent graphs (networks) and obtain novel types
of physical processes that can be observed in experiments.
Interdependent networks appear in all aspects of nature and technology. Examples include the
physiological systems in our body and in infrastructures. A theoretical framework for 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
fragmentation of the system. This contrasts with a single network where the network
breakdown due to failures is continuous. I will present analytical solutions based on the
percolation theory, for the functional network and cascading failures, for a network of n
interdependent networks. Our analytical results show that the percolation theory of a single
graph studied in mathematics and physics for over 90 years is just a limited case, n=1, of the general and significantly
richer case of n>1. I will also show that interdependent networks embedded in space are
extremely vulnerable and have significantly richer behavior compared to non-embedded
networks. I will finally show that the abstract interdependent percolation theory and its novel behavior in networks of
networks can be realized and proven in controlled experiments performed by Aviad Frydman on
interdependent superconducting networks and by Patrick Sebbah on coupled laser systems.
References
S. Buldyrev, G. Paul, H.E. Stanley, S. Havlin, Nature, 464, 08932 (2010)
J. Gao, S. Buldyrev, H. E. Stanley, S. Havlin, Nature Physics, 8, 40 (2012)
A. Bashan et al, Nature Physics, 9, 667 (2013)
B. Gross et al, PRL 129, 268301 (2022)
I. Bonamassa et al, Interdependent superconducting networks, Nature Physics 19, 1163 (2023)
physiological systems in our body and in infrastructures. A theoretical framework for 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
fragmentation of the system. This contrasts with a single network where the network
breakdown due to failures is continuous. I will present analytical solutions based on the
percolation theory, for the functional network and cascading failures, for a network of n
interdependent networks. Our analytical results show that the percolation theory of a single
graph studied in mathematics and physics for over 90 years is just a limited case, n=1, of the general and significantly
richer case of n>1. I will also show that interdependent networks embedded in space are
extremely vulnerable and have significantly richer behavior compared to non-embedded
networks. I will finally show that the abstract interdependent percolation theory and its novel behavior in networks of
networks can be realized and proven in controlled experiments performed by Aviad Frydman on
interdependent superconducting networks and by Patrick Sebbah on coupled laser systems.
References
S. Buldyrev, G. Paul, H.E. Stanley, S. Havlin, Nature, 464, 08932 (2010)
J. Gao, S. Buldyrev, H. E. Stanley, S. Havlin, Nature Physics, 8, 40 (2012)
A. Bashan et al, Nature Physics, 9, 667 (2013)
B. Gross et al, PRL 129, 268301 (2022)
I. Bonamassa et al, Interdependent superconducting networks, Nature Physics 19, 1163 (2023)
J. Wang, Coupled Lasers phase transitions arXiv preprint arXiv:2508.21786
תאריך עדכון אחרון : 01/11/2025
