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Berlin 2012 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 18: Networks II (with SOE)

DY 18.1: Talk

Wednesday, March 28, 2012, 10:15–10:30, H 0110

Diffusion on random networks with spatial constraints — •Thorsten Emmerich1, Shlomo Havlin2, and Armin Bunde31Institut 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 de=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 < de, the spatial constraints are irrelevant, while for δ > 2de the network behaves as a regular lattice. In between, for de ≤ δ ≤ 2de 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 + AC und A + BC.

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