Kinetic-growth self-avoiding walks on small-world networks
- 60 Downloads
Kinetically-grown self-avoiding walks have been studied on Watts-Strogatz small-world networks, rewired from a two-dimensional square lattice. The maximum length L of this kind of walks is limited in regular lattices by an attrition effect, which gives finite values for its mean value 〈L 〉. For random networks, this mean attrition length 〈L 〉 scales as a power of the network size, and diverges in the thermodynamic limit (system size N ↦∞). For small-world networks, we find a behavior that interpolates between those corresponding to regular lattices and randon networks, for rewiring probability p ranging from 0 to 1. For p < 1, the mean self-intersection and attrition length of kinetically-grown walks are finite. For p = 1, 〈L 〉 grows with system size as N1/2, diverging in the thermodynamic limit. In this limit and close to p = 1, the mean attrition length diverges as (1-p)-4. Results of approximate probabilistic calculations agree well with those derived from numerical simulations.
PACS.89.75.Fb Structures and organization in complex systems 89.75.Hc Networks and genealogical trees 87.23.Ge Dynamics of social systems 05.40.Fb Random walks and Levy flights
Unable to display preview. Download preview PDF.
- S.N. Dorogovtsev, J.F.F. Mendes, Evolution of Networks: From Biological Nets to the Internet and WWW (Oxford University, Oxford, 2003) Google Scholar
- L. da F. Costa, F.A. Rodrigues, G. Travieso, P.R. Villas Boas, e-print arXiv:cond-mat/0505185 Google Scholar
- B. Bollobás, Modern Graph Theory (Springer-Verlag, New York, 1998) Google Scholar
- D.J. Watts, Small Worlds (Princeton University Press, Princeton, 1999) Google Scholar
- P.G. de Gennes, Scaling Concepts in Polymer Physics (Cornell University, Ithaca, NY, 1979) Google Scholar
- V. Privman, P.C. Hohenberg, A. Aharony, in Phase Transitions and Critical Phenomena, edited by C. Domb, J.L. Lebowitz (Academic Press, London, 1991), Vol. 14 Google Scholar
- A.D. Sokal, in Monte Carlo and Molecular Dynamics Simulations in Polymer Science, edited by K. Binder (Oxford University, Oxford, 1995), pp. 47–124 Google Scholar