3 research outputs found
Sandpile Model with Activity Inhibition
A new sandpile model is studied in which bonds of the system are inhibited
for activity after a certain number of transmission of grains. This condition
impels an unstable sand column to distribute grains only to those neighbours
which have toppled less than m times. In this non-Abelian model grains
effectively move faster than the ordinary diffusion (super-diffusion). A novel
system size dependent cross-over from Abelian sandpile behaviour to a new
critical behaviour is observed for all values of the parameter m.Comment: 11 pages, RevTex, 5 Postscript figure
An Exactly Solvable Anisotropic Directed Percolation Model in Three Dimensions
We solve exactly a special case of the anisotropic directed bond percolation
problem in three dimensions, in which the occupation probability is 1 along two
spatial directions, by mapping it to a five-vertex model. We determine the
asymptotic shape of the ininite cluster and hence the direction dependent
critical probability. The exponents characterising the fluctuations of the
boundary of the wetted cluster in d-dimensions are related to those of the
(d-2)-dimensional KPZ equation.Comment: 4 pages, RevTex, 4 figures. 1 reference added, minor change
Evaluation of effective resistances in pseudo-distance-regular resistor networks
In Refs.[1] and [2], calculation of effective resistances on distance-regular
networks was investigated, where in the first paper, the calculation was based
on the stratification of the network and Stieltjes function associated with the
network, whereas in the latter one a recursive formula for effective
resistances was given based on the Christoffel-Darboux identity. In this paper,
evaluation of effective resistances on more general networks called
pseudo-distance-regular networks [21] or QD type networks \cite{obata} is
investigated, where we use the stratification of these networks and show that
the effective resistances between a given node such as and all of the
nodes belonging to the same stratum with respect to
(, belonging to the -th stratum with respect
to the ) are the same. Then, based on the spectral techniques, an
analytical formula for effective resistances such that
(those nodes , of
the network such that the network is symmetric with respect to them) is given
in terms of the first and second orthogonal polynomials associated with the
network, where is the pseudo-inverse of the Laplacian of the network.
From the fact that in distance-regular networks,
is satisfied for all nodes
of the network, the effective resistances
for ( is diameter of the network which
is the same as the number of strata) are calculated directly, by using the
given formula.Comment: 30 pages, 7 figure