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DY: Fachverband Dynamik und Statistische Physik

DY 22: Statistical physics of complex networks II

DY 22.3: Vortrag

Mittwoch, 27. Februar 2008, 17:15–17:30, MA 004

Pattern Formation and Efficiency of Reaction-Diffusion Processes on Complex Networks — •Sebastian Weber¹, Marc-Thorsten Hütt², and Markus Porto¹ — ¹Institut für Festkörrperphysik, Technische Universität Darmstadt, Germany — ²Computational Systems Biology, School of Engineering and Science, Jacobs University Bremen, Germany

To understand how the topology of a network influences a given dynamic taking place on it, is a major challenge in many fields of science. We address part of this challenge by studying the impact of topological correlations in complex networks on the pattern formation and the efficiency of the reaction-diffusion process A + B → ∅ [1], the latter serving as a generic dynamic capturing the essentials of many real world examples. We show how to properly compare the states of the dynamics taken place on different ensembles of networks, which allows us to isolate the impact of topological correlations from other effects. The major result is that (i) the pattern formation can by characterized by a single scalar observable directly related to the amount of topological correlations and that (ii) a large amount of pattern formation does not necessarily mean a small efficiency, in contrast to regular d dimensional lattices.

[1] S. Weber, M.-Th. Hütt, and M. Porto, submitted