title: Asymptotic shape of the region visited by an Eulerian walker.
abstract: We study an Eulerian walker on a square lattice, starting from an initial randomly oriented background using Monte Carlo simulations. We present evidence that, for a large number of steps N , the asymptotic shape of the set of sites visited by the walker is a perfect circle. The radius of the circle increases as N1/3, for large N , and the width of the boundary region grows as Nalpha/3, with alpha=0.40+/-0.06 . If we introduce stochasticity in the evolution rules, the mean-square displacement of the walker, <RN2> approximately <RN2> approximately N2nu, shows a crossover from the Eulerian (nu=1/3) to a simple random-walk (nu=1/2) behavior.
authors.affiliation: Department of Theoretical Physics, Tata Institute of Fundamental Research, 1 Homi Bhabha Road, Colaba, Mumbai 400 005, India. rkapri@theory.tifr.res.in
authors.forename: Rajeev
authors.initials: R
authors.lastname: Kapri
authors.forename: Deepak
authors.initials: D
authors.lastname: Dhar
mesh_terms: D003102:Colloids / Q000737:chemistry*; D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D008956:Models, Chemical; D015233:Models, Statistical
chemical_list: D003102:Colloids