Dresden 2014 – wissenschaftliches Programm
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DY: Fachverband Dynamik und Statistische Physik
DY 46: Stochastic Dynamics of Growth Processes in Biological and Social Systems (joint session SOE/BP)
DY 46.10: Vortrag
Freitag, 4. April 2014, 12:15–12:30, GÖR 226
Discrete scale invariance in growing networks — Wei Chen1,2,3, •Malte Schröder4, Raissa M. D'Souza3, Didier Sornette5, and Jan Nagler5,4 — 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.