Origin of power-law distributions in deterministic walks: the influence of landscape geometry.
We investigate the properties of a deterministic walk, whose locomotion rule is always to travel to the nearest site. Initially the sites are randomly distributed in a closed rectangular (ALxL) landscape and, once reached, they become unavailable for future visits. As expected, the walker step lengths present characteristic scales in one (L-->0) and two (AL approximately L) dimensions. However, we find scale invariance for an intermediate geometry, when the landscape is a thin striplike region. This result is induced geometrically by a dynamical trapping mechanism, leading to a power-law distribution for the step lengths. The relevance of our findings in broader contexts--of both deterministic and random walks--is also briefly discussed.
Departamento de Física, Universidade Federal do Paraná, 81531-990 Curitiba--PR, Brazil.
M C
MC
Santos
D
D
Boyer
O
O
Miramontes
G M
GM
Viswanathan
E P
EP
Raposo
J L
JL
Mateos
M G E
MG
da Luz