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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 Timme1,2,31Max 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[3] J. Nagler, A. Levina, and M. Timme, unpublished (2009).

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