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BP: Fachverband Biologische Physik
BP 57: Networks: From Topology to Dynamics II (Joint Session DY/BP/SOE)
BP 57.3: Vortrag
Donnerstag, 23. März 2017, 15:30–15:45, ZEU 147
Scaling Laws in Spatial Network Formation — •Nora Molkenthin1,2 and Marc Timme1,2 — 1Network Dynamics, Max Planck Institute for Dynamics and Self-Organization (MPIDS), 37077 Göttingen, German — 2Institute for Nonlinear Dynamics, Faculty of Physics, University of Göttingen, 37077 Göttingen, Germany
Geometric constraints strongly impact the formation of networked systems. Examples range from amino acid chains folding to proteins structures to rearranging particle aggregates. The dynamical self-organization of the interaction network in such systems is far from fully understood. Here, we analyze a class of spatial network formation processes by introducing a mapping from geometric to graph-theoretic constraints. Combining stochastic and mean field analyses yields an algebraic scaling law for the extent (graph diameter) of the resulting networks with system size, in contrast to logarithmic scaling known for networks without constraints. Intriguingly, the exponent falls between that of self-avoiding random walks and that of space filling arrangements, consistent with experimentally observed scaling (of the spatial radius of gyration) for protein tertiary structures.