Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2002-01-07
Physics
Condensed Matter
Statistical Mechanics
10 pages, 10 figures, revtex4. Submitted to PRE
Scientific paper
10.1103/PhysRevE.65.056709
We discuss shortest-path lengths $\ell(r)$ on periodic rings of size L supplemented with an average of pL randomly located long-range links whose lengths are distributed according to $P_l \sim l^{-\xpn}$. Using rescaling arguments and numerical simulation on systems of up to $10^7$ sites, we show that a characteristic length $\xi$ exists such that $\ell(r) \sim r$ for $r<\xi$ but $\ell(r) \sim r^{\theta_s(\xpn)}$ for $r>>\xi$. For small p we find that the shortest-path length satisfies the scaling relation $\ell(r,\xpn,p)/\xi = f(\xpn,r/\xi)$. Three regions with different asymptotic behaviors are found, respectively: a) $\xpn>2$ where $\theta_s=1$, b) $1<\xpn<2$ where $0<\theta_s(\xpn)<1/2$ and, c) $\xpn<1$ where $\ell(r)$ behaves logarithmically, i.e. $\theta_s=0$. The characteristic length $\xi$ is of the form $\xi \sim p^{-\nu}$ with $\nu=1/(2-\xpn)$ in region b), but depends on L as well in region c). A directed model of shortest-paths is solved and compared with numerical results.
de Menezes Marcio Argollo
Moukarzel Cristian F.
No associations
LandOfFree
Shortest paths on systems with power-law distributed long-range connections does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Shortest paths on systems with power-law distributed long-range connections, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Shortest paths on systems with power-law distributed long-range connections will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-321460