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Title: Vulnerability and cosusceptibility determine the size of network cascades

Abstract

In a network, a local disturbance can propagate and eventually cause a substantial part of the system to fail in cascade events that are easy to conceptualize but extraordinarily difficult to predict. Furthermore, we develop a statistical framework that can predict cascade size distributions by incorporating two ingredients only: the vulnerability of individual components and the cosusceptibility of groups of components (i.e., their tendency to fail together). Using cascades in power grids as a representative example, we show that correlations between component failures define structured and often surprisingly large groups of cosusceptible components. Aside from their implications for blackout studies, these results provide insights and a new modeling framework for understanding cascades in financial systems, food webs, and complex networks in general.

Authors:
 [1];  [1];  [1]
  1. Northwestern Univ., Evanston, IL (United States)
Publication Date:
Research Org.:
Northwestern Univ., Evanston, IL (United States)
Sponsoring Org.:
USDOE Advanced Research Projects Agency - Energy (ARPA-E)
OSTI Identifier:
1369629
Alternate Identifier(s):
OSTI ID: 1341322
Grant/Contract Number:
AR0000702
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Physical Review Letters
Additional Journal Information:
Journal Volume: 118; Journal Issue: 4; Journal ID: ISSN 0031-9007
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING

Citation Formats

Yang, Yang, Nishikawa, Takashi, and Motter, Adilson E. Vulnerability and cosusceptibility determine the size of network cascades. United States: N. p., 2017. Web. doi:10.1103/PhysRevLett.118.048301.
Yang, Yang, Nishikawa, Takashi, & Motter, Adilson E. Vulnerability and cosusceptibility determine the size of network cascades. United States. doi:10.1103/PhysRevLett.118.048301.
Yang, Yang, Nishikawa, Takashi, and Motter, Adilson E. Fri . "Vulnerability and cosusceptibility determine the size of network cascades". United States. doi:10.1103/PhysRevLett.118.048301. https://www.osti.gov/servlets/purl/1369629.
@article{osti_1369629,
title = {Vulnerability and cosusceptibility determine the size of network cascades},
author = {Yang, Yang and Nishikawa, Takashi and Motter, Adilson E.},
abstractNote = {In a network, a local disturbance can propagate and eventually cause a substantial part of the system to fail in cascade events that are easy to conceptualize but extraordinarily difficult to predict. Furthermore, we develop a statistical framework that can predict cascade size distributions by incorporating two ingredients only: the vulnerability of individual components and the cosusceptibility of groups of components (i.e., their tendency to fail together). Using cascades in power grids as a representative example, we show that correlations between component failures define structured and often surprisingly large groups of cosusceptible components. Aside from their implications for blackout studies, these results provide insights and a new modeling framework for understanding cascades in financial systems, food webs, and complex networks in general.},
doi = {10.1103/PhysRevLett.118.048301},
journal = {Physical Review Letters},
number = 4,
volume = 118,
place = {United States},
year = {Fri Jan 27 00:00:00 EST 2017},
month = {Fri Jan 27 00:00:00 EST 2017}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 3works
Citation information provided by
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  • The understanding of cascading failures in complex systems has been hindered by the lack of realistic large-scale modeling and analysis that can account for variable system conditions. By using the North American power grid, we identified, quantified, and analyzed the set of network components that are vulnerable to cascading failures under any out of multiple conditions. We show that the vulnerable set consists of a small but topologically central portion of the network and that large cascades are disproportionately more likely to be triggered by initial failures close to this set. These results elucidate aspects of the origins and causesmore » of cascading failures relevant for grid design and operation and demonstrate vulnerability analysis methods that are applicable to a wider class of cascade-prone networks.« less
    Cited by 1
  • No abstract prepared.
  • The standard theoretical treatment of collisional cascades derives a steady-state size distribution assuming a single constant velocity dispersion for all bodies regardless of size. Here we relax this assumption and solve self-consistently for the bodies' steady-state size and size-dependent velocity distributions. Specifically, we account for viscous stirring, dynamical friction, and collisional damping of the bodies' random velocities in addition to the mass conservation requirement typically applied to find the size distribution in a steady-state cascade. The resulting size distributions are significantly steeper than those derived without velocity evolution. For example, accounting self-consistently for the velocities can change the standard qmore » = 3.5 power-law index of the Dohnanyi differential size spectrum to an index as large as q = 4. Similarly, for bodies held together by their own gravity, the corresponding power-law index range 2.88 < q < 3.14 of Pan and Sari can steepen to values as large as q = 3.26. Our velocity results allow quantitative predictions of the bodies' scale heights as a function of size. Together with our predictions, observations of the scale heights for different-sized bodies for the Kuiper belt, the asteroid belt, and extrasolar debris disks may constrain the mass and number of large bodies stirring the cascade as well as the colliding bodies' internal strengths.« less