4,048 research outputs found
Renormalization group approach to an Abelian sandpile model on planar lattices
One important step in the renormalization group (RG) approach to a lattice
sandpile model is the exact enumeration of all possible toppling processes of
sandpile dynamics inside a cell for RG transformations. Here we propose a
computer algorithm to carry out such exact enumeration for cells of planar
lattices in RG approach to Bak-Tang-Wiesenfeld sandpile model [Phys. Rev. Lett.
{\bf 59}, 381 (1987)] and consider both the reduced-high RG equations proposed
by Pietronero, Vespignani, and Zapperi (PVZ) [Phys. Rev. Lett. {\bf 72}, 1690
(1994)] and the real-height RG equations proposed by Ivashkevich [Phys. Rev.
Lett. {\bf 76}, 3368 (1996)]. Using this algorithm we are able to carry out RG
transformations more quickly with large cell size, e.g. cell for
the square (sq) lattice in PVZ RG equations, which is the largest cell size at
the present, and find some mistakes in a previous paper [Phys. Rev. E {\bf 51},
1711 (1995)]. For sq and plane triangular (pt) lattices, we obtain the only
attractive fixed point for each lattice and calculate the avalanche exponent
and the dynamical exponent . Our results suggest that the increase of
the cell size in the PVZ RG transformation does not lead to more accurate
results. The implication of such result is discussed.Comment: 29 pages, 6 figure
Boussinesq Solitary-Wave as a Multiple-Time Solution of the Korteweg-de Vries Hierarchy
We study the Boussinesq equation from the point of view of a multiple-time
reductive perturbation method. As a consequence of the elimination of the
secular producing terms through the use of the Korteweg--de Vries hierarchy, we
show that the solitary--wave of the Boussinesq equation is a solitary--wave
satisfying simultaneously all equations of the Korteweg--de Vries hierarchy,
each one in an appropriate slow time variable.Comment: 12 pages, RevTex (to appear in J. Math Phys.
Chaos in Sandpile Models
We have investigated the "weak chaos" exponent to see if it can be considered
as a classification parameter of different sandpile models. Simulation results
show that "weak chaos" exponent may be one of the characteristic exponents of
the attractor of \textit{deterministic} models. We have shown that the
(abelian) BTW sandpile model and the (non abelian) Zhang model posses different
"weak chaos" exponents, so they may belong to different universality classes.
We have also shown that \textit{stochasticity} destroys "weak chaos" exponents'
effectiveness so it slows down the divergence of nearby configurations. Finally
we show that getting off the critical point destroys this behavior of
deterministic models.Comment: 5 pages, 6 figure
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
Order Parameter and Scaling Fields in Self-Organized Criticality
We present a unified dynamical mean-field theory for stochastic
self-organized critical models. We use a single site approximation and we
include the details of different models by using effective parameters and
constraints. We identify the order parameter and the relevant scaling fields in
order to describe the critical behavior in terms of usual concepts of non
equilibrium lattice models with steady-states. We point out the inconsistencies
of previous mean-field approaches, which lead to different predictions.
Numerical simulations confirm the validity of our results beyond mean-field
theory.Comment: 4 RevTex pages and 2 postscript figure
Universality Classes in Isotropic, Abelian and non-Abelian, Sandpile Models
Universality in isotropic, abelian and non-abelian, sandpile models is
examined using extensive numerical simulations. To characterize the critical
behavior we employ an extended set of critical exponents, geometric features of
the avalanches, as well as scaling functions describing the time evolution of
average quantities such as the area and size during the avalanche. Comparing
between the abelian Bak-Tang-Wiesenfeld model [P. Bak, C. Tang and K.
Wiensenfeld, Phys. Rev. Lett. 59, 381 (1987)], and the non-abelian models
introduced by Manna [S. S. Manna, J. Phys. A. 24, L363 (1991)] and Zhang [Y. C.
Zhang, Phys. Rev. Lett. 63, 470 (1989)] we find strong indications that each
one of these models belongs to a distinct universality class.Comment: 18 pages of text, RevTeX, additional 8 figures in 12 PS file
Mean-field behavior of the sandpile model below the upper critical dimension
We present results of large scale numerical simulations of the Bak, Tang and
Wiesenfeld sandpile model. We analyze the critical behavior of the model in
Euclidean dimensions . We consider a dissipative generalization
of the model and study the avalanche size and duration distributions for
different values of the lattice size and dissipation. We find that the scaling
exponents in significantly differ from mean-field predictions, thus
suggesting an upper critical dimension . Using the relations among
the dissipation rate and the finite lattice size , we find that a
subset of the exponents displays mean-field values below the upper critical
dimensions. This behavior is explained in terms of conservation laws.Comment: 4 RevTex pages, 2 eps figures embedde
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