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Critical Stretching of Mean-Field Regimes in Spatial Networks

Ivan Bonamassa, Bnaya Gross, Michael M. Danziger, and Shlomo Havlin
Phys. Rev. Lett. 123, 088301 – Published 22 August 2019
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Abstract

We study a spatial network model with exponentially distributed link lengths on an underlying grid of points, undergoing a structural crossover from a random, Erdős-Rényi graph, to a d-dimensional lattice at the characteristic interaction range ζ. We find that, whilst far from the percolation threshold the random part of the giant component scales linearly with ζ, close to criticality it extends in space until the universal length scale ζ6/(6d), for d<6, before crossing over to the spatial one. We demonstrate the universal behavior of the spatiotemporal scales characterizing this critical stretching phenomenon of mean-field regimes in percolation and in dynamical processes on d=2 networks, and we discuss its general implications to real-world phenomena, such as neural activation, traffic flows or epidemic spreading.

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  • Received 12 February 2019

DOI:https://doi.org/10.1103/PhysRevLett.123.088301

© 2019 American Physical Society

Physics Subject Headings (PhySH)

Interdisciplinary PhysicsStatistical Physics & ThermodynamicsNetworks

Authors & Affiliations

Ivan Bonamassa1, Bnaya Gross1, Michael M. Danziger2, and Shlomo Havlin1

  • 1Department of Physics, Bar Ilan University, Ramat Gan 52900, Israel
  • 2Network Science Institute, Northeastern University, Boston, Massachusetts, 02115, USA

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Issue

Vol. 123, Iss. 8 — 23 August 2019

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