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DY: Fachverband Dynamik und Statistische Physik

DY 41: Poster - Pattern/ Nonlinear Dyn./ Fluids/ Granular/ Critical Phen.

DY 41.37: Poster

Donnerstag, 3. April 2014, 17:00–19:00, P3

Percolation threshold on planar Euclidean Gabriel Graphs — •Christoph Norrenbrock — Carl-von-Ossietzky Universität Oldenburg

Planar proximity graphs such as the Gabriel Graph (GG) [1] are of potential interest in the context of wireless ad hoc networks, since the embedded edges provide proximity information regarding their adjacent nodes. Furthermore, the edge-sets ensure that the graph is connected, i.e. nodes are able to communicate to each other via intermediate ones.
Using the highly efficient, union-find based algorithm by Newman and Ziff [2], we simulate the bond and site-percolation problem on planar Gabriel graphs of size N=1024 to N=36864 (N refers to the number of nodes) for Poisson point processes. Previously, it has already been shown that non-trivial percolation thresholds exist and rough estimates for their location has been made [3]. By means of finite-size-scaling techniques, we determine the precise location of the bond and site percolation thresholds and deduce the common percolation critical exponents from the GG data. The associated universality class is that of standard 2D percolation.
Gabriel and Sokal, Systematic Biology 18, 259 (1969)
Newman and Ziff, Phys Rev. Lett. 85, 4104 (2000)
Bertin, Billiot, Drouilhet, Adv. Appl. Prob. 34, 689 (2002)