Next: Introduction
Updated: 18th Nov 2005
Two Dimensional Random Walk on a Percolation Cluster
George M Pailey, Shivakumar Jolad, Sangamitra Neogi
Department of Physics,
Abstract
Random walk on lattices of different dimensions has been well studied. The
behavior of Random walks change drastically when you make them to move under
constraints like percolation cluster. Such walks belong to a different set of
Universality class. In this report we illustrate such a behavior by computer
simulations on a 2D lattice percolation cluster (infinite). Through this we
were able to observe the asymptotic behavior of mean square displacement,
return to origin and number of distinct sites visited as a function of time.
Calculation on these asymptotes gives us fracton dimension
, fractal dimension D and exponent 
.
gmp161@psu.edu,
shivkumar@psu.edu, sun114@psu.edu
Pdf
report