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 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
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 + A → C und A + B → C.