Dresden 2014 – scientific programme

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SOE: Fachverband Physik sozio-ökonomischer Systeme

SOE 23: Stochastic Dynamics of Growth Processes in Biological and Social Systems (session accompanying symposium SYGP, joint with DY and BP)

SOE 23.10: Talk

Friday, April 4, 2014, 12:15–12:30, GÖR 226

Discrete scale invariance in growing networks — Wei Chen^1,2,3, •Malte Schröder⁴, Raissa M. D'Souza³, Didier Sornette⁵, and Jan Nagler^5,4 — ¹Chinese Academy of Sciences, Beijing — ²Peking University, Beijing — ³University of California, Davis — ⁴MPI DS Göttingen — ⁵ETH Zürich

Discrete scale invariance (DSI) arises in systems where the usual (continuous) scale invariance (for example at phase transitions) is partially broken, leading to a remarkable discrete hierarchy of resonances in the system order parameter. DSI has broad technical, physical and biological relevance, penetrating statistical physics (Potts model, Singularities), hydrodynamics, turbulence, astronomy, evolution, fracture and economics. (D. Sornette, Phys. Rep. 297, 239 (1998)).

A hierarchy of discrete micro-transitions leading up to the transition to global connectivity in models of continuous and discontinuous percolation is observed. These transitions can in some cases be observed in the relative variance of the size of the largest cluster even in the thermodynamic limit.

Depending on the model these cascades exhibit either genuine discrete scale-invariance or a generalized (novel) form. In contrast to average values, the size of the largest cluster before the phase transition is limited to integer values. This leads to a family of scaling relations that describe the behavior of the micro-transition cascade (Chen, Schröder, D'Souza, Sornette, Nagler (under review)). Our findings open up the possibility for the prediction of tipping in complex systems that are dominated by large-scale disorder.