Accueil du site > Publications > Publications 2006 > Distance traveled by random walkers before absorption in a random medium
Distance traveled by random walkers before absorption in a random medium
David S. Dean, Clément Sire, and Julien Sopik
par - 12 avril 2006
We consider the penetration length 
of random walkers diffusing
in a medium of perfect or imperfect absorbers of number density
. We solve this problem on a lattice and in the continuum in
all dimensions 
, by means of a mean-field renormalization
group. For a homogeneous system in 
, we find that 
, where 
is the absorber
density correlation length. The cases of 
and 
are also
treated. In the presence of long-range correlations, we estimate
the temporal decay of the density of random walkers not yet
absorbed. These results are illustrated by exactly solvable toy
models, and extensive numerical simulations on directed
percolation, where the absorbers are the active sites. Finally, we
discuss the implications of our results for diffusion limited
aggregation (DLA), and we propose a more effective method to
measure in DLA clusters.
Preprint : http://arxiv.org/abs/cond-mat/0604456