Deterministic walks in random media: evidence of generic scale invariance

Details Deterministic walks in random media: evidence of generic scale invariance Deterministic walks in random media: evidence of generic scale invariance

2000-05-25

arxiv.org/abs/cond-mat/0005446v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

Scientific paper

Deterministic walks over a random set of points in one and two dimensions (d=1,2) are considered. Points (``cities'') are randomly scattered in R^d following a uniform distribution. A walker (a ``tourist''), at each time step, goes to the nearest neighbor city that has not been visited in the past \tau steps. Each initial city leads to a trajectory composed of a transient part and a final p-cycle attractor. The distribution of transient times, p-cycles and number of cities per attractor are studied. It is shown numerically that transient times (for d=1,2) follow a Poisson law with a $\tau$ dependent decay but the density of p-cycles follows a power law D(p) \propto p^{-\alpha(\tau)} for d=2. For large \tau, the expoent tends to \alpha ~ 5/2. Some analytical results are given for the d=1 case. Since the power law is robust and does not depend on free parameters, this system presents ``generic scale invariance''. Applications to animal exploratory behavior and other local minimization problems are suggested.

Affiliated with

Also associated with

No associations

Rating

Deterministic walks in random media: evidence of generic scale invariance 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 Deterministic walks in random media: evidence of generic scale invariance, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Deterministic walks in random media: evidence of generic scale invariance will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-200622