Volume 53, Number 5, March 2001
|Page(s)||693 - 699|
|Section||Interdisciplinary physics and related areas of science and technology|
|Published online||01 December 2003|
Small-world behaviour in a system of mobile elements
Max Planck Institute for Colloids and Interfaces, Theory
Division 14424 Potsdam, Germany
2 Departament de Llenguatges i Sistemes Informàtics, Universitat Politècnica de Catalunya - Campus Nord, Mòdul C6, 08034 Barcelona, Spain
3 Centro de Astrobiología (CAB), INTA - Carretera de Ajalvir Km. 4 28850 Torrejón de Ardoz, Madrid, Spain
Accepted: 11 December 2000
We analyze the propagation of activity in a system of mobile automata. A number of elements move as random walkers on a lattice of dimension d, while with a small probability p they can jump to any empty site in the system. We show that this system behaves as a Dynamic Small World (DSW) and present analytic and numerical results for several quantities. Our analysis shows that the persistence time T* (equivalent to the persistence size L* of small-world networks) scales as , with .
PACS: 87.23.Ge – Dynamics of social systems / 05.10.-a – Computational methods in statistical physics and nonlinear dynamics / 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion
© EDP Sciences, 2001
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