Regensburg 2010 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 23: Networks: From Topology to Dynamics III (joint session of BP, DY, SOE)
DY 23.5: Talk
Thursday, March 25, 2010, 11:15–11:30, H44
Discontinuous Phase Transitions in Random Network Percolation — •Jan Nagler1,2, Anna Levina1,3, and Marc Timme1,2,3 — 1Max Planck Institute for Dynamics and Self-Organization, Göttingen — 2Institute for Nonlinear Dynamics, Faculty of Physics, University of Göttingen — 3Bernstein Center for Computational Neuroscience (BCCN) Göttingen
The transition to extensive connectedness upon gradual addition of links,
known as the percolation phase transition, provides a key prerequisite for
understanding networked systems [1]. Until recently, random percolation
processes were thought to exhibit continuous transitions in general, but
now there is numerical evidence for discontinuities changes of the order
parameter in certain percolation processes [2]. Here we present the
concepts of weakly and strongly discontinuous percolation transitions and
explain the microscopic mechanisms underlying them. We study both
numerically and analytically under which conditions the order parameter
may change discontinuously and classify the type of transition in
dependence on the dynamics of cluster joining [3].
[1] G. Grimmett, Percolation (Springer Verlag, Heidelberg,1999).
[2] D. Achlioptas, R. M. D’Souza, J. Spencer, Explosive Percolation in Random Networks, Science 323: 1453 (2009); R. M. Ziff, PRL 103, 045701 (2009); F. Radicchi and S. Fortunato, PRL 103, 168701 (2009); Y. Cho et al., PRL 103, 135702 (2009).
[3] J. Nagler, A. Levina, and M. Timme, unpublished (2009).