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SOE: Fachverband Physik sozio-ökonomischer Systeme

SOE 12: Networks, From Topology to Dynamics II (joint w. DY)

SOE 12.1: Vortrag

Mittwoch, 28. März 2012, 10:15–10:30, H 0110

Diffusion on random networks with spatial constraints — •Thorsten Emmerich¹, Shlomo Havlin², and Armin Bunde³ — ¹Institut für Theorethische Physik 3, Justus Liebig Universität Giessen, Giessen, Germany — ²Minerva Center and Department of Physiks, Bar Ilan University, Ramat Gan, Israel — ³Institut für Theorethische Physik 3, Justus Liebig Universität Giessen, Giessen, Germany

We consider random networks with spatial constraints. The networks are embedded in a linear chain or in a square lattice with embedding dimension d_e=1 and 2, respectively. Each node has a fixed number of links. The length of the links are chosen with probability p(r) ∼ r^−δ, where r is the Euclidean distance between them. We show how the dimension of those networks can be determined and that it plays a basic role in determining the dynamical properties of the networks. The physical features are determined by δ: For δ < d_e, the spatial constraints are irrelevant, while for δ > 2d_e the network behaves as a regular lattice. In between, for d_e ≤ δ ≤ 2d_e the network shows intermediate behavior and its dimension increases monotonically with decreasing δ.
We show that the dimension obtained from evaluating the structure of the networks appears also in the probability of return to the origin of a diffusing particle as well as in the survival properties of diffusing particles in the chemical reactions A + A → C und A + B → C.