Self-organized criticality and the lattice topology
Abstract
We examine exhaustively the behavior of avalanches in critical height sandpile models based in two- and three-dimensional lattices of various topologies. We get that for two-dimensional lattices the spatial and temporal distributions characterizing bulk avalanches do not depend on the lattice topology. For the three-dimensional case, we detect a small dependence of the topology for the temporal distribution, while the spatial ones are independent. The two-dimensional lattices studied are: the plane (
R
2
), the cylinder (
S
1
×R
), and the Möbius-strip (
M
); and the three-dimensional are:
R
3
,
S
1
×
R
2
,
S
1
×
S
1
×R
,
M×R
,
S
2
×R
,
K×R
, and
RP×R
, where
K
and
RP
are respectively the Klein bottle and the real projective plane.