4
views
0
recommends
+1 Recommend
0 collections
0
shares
• Record: found
• Abstract: found
• Article: found
Is Open Access

# Superdiffusion in a class of networks with marginal long-range connections

Preprint

Bookmark
There is no author summary for this article yet. Authors can add summaries to their articles on ScienceOpen to make them more accessible to a non-specialist audience.

### Abstract

A class of cubic networks composed of a regular one-dimensional lattice and a set of long-range links is introduced. Networks parametrized by a positive integer k are constructed by starting from a one-dimensional lattice and iteratively connecting each site of degree 2 with a $$k$$th neighboring site of degree 2. Specifying the way pairs of sites to be connected are selected, various random and regular networks are defined, all of which have a power-law edge-length distribution of the form $$P_>(l)\sim l^{-s}$$ with the marginal exponent s=1. In all these networks, lengths of shortest paths grow as a power of the distance and random walk is super-diffusive. Applying a renormalization group method, the corresponding shortest-path dimensions and random-walk dimensions are calculated exactly for k=1 networks and for k=2 regular networks; in other cases, they are estimated by numerical methods. Although, s=1 holds for all representatives of this class, the above quantities are found to depend on the details of the structure of networks controlled by k and other parameters.

### Author and article information

###### Journal
24 May 2008
2009-01-09
###### Article
10.1103/PhysRevE.78.066106
0805.3769