Volume 93, Number 6, March 2011
|Number of page(s)||5|
|Section||Interdisciplinary Physics and Related Areas of Science and Technology|
|Published online||23 March 2011|
Percolation of spatially constraint networks
Minerva Center and Department of Physics, Bar-Ilan University - Ramat-Gan 52900, Israel
2 Center for Polymer Studies, Department of Physics, Boston University - 590 Commonwealth Avenue, Boston, MA 02215, USA
3 Physics Department and Network Operations Center, Aristotle University of Thessaloniki 54124 Thessaloniki, Greece, EU
4 Institut für Theoretische Physik III, Justus-Liebig-Universität Giessen - 35392 Giessen, Germany, EU
Accepted: 27 February 2011
We study how spatial constraints are reflected in the percolation properties of networks embedded in one-dimensional chains and two-dimensional lattices. We assume long-range connections between sites on the lattice where two sites at distance r are chosen to be linked with probability p(r) ∼ r− δ. Similar distributions have been found in spatially embedded real networks such as social and airline networks. We find that for networks embedded in two dimensions, with 2 < δ < 4, the percolation properties show new intermediate behavior different from mean field, with critical exponents that depend on δ. For δ < 2, the percolation transition belongs to the universality class of percolation in Erdös-Rényi networks (mean field), while for δ > 4 it belongs to the universality class of percolation in regular lattices. For networks embedded in one dimension, we find that, for δ < 1, the percolation transition is mean field. For 1 < δ <2, the critical exponents depend on δ, while for δ > 2 there is no percolation transition as in regular linear chains.
PACS: 89.75.-k – Complex systems / 89.75.Da – Systems obeying scaling laws / 05.10.Ln – Monte Carlo methods
© EPLA, 2011
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.