254 research outputs found
A simple model for self organization of bipartite networks
We suggest a minimalistic model for directed networks and suggest an
application to injection and merging of magnetic field lines. We obtain a
network of connected donor and acceptor vertices with degree distribution
, and with dynamical reconnection events of size occurring
with frequency that scale as . This suggest that the model is in
the same universality class as the model for self organization in the solar
atmosphere suggested by Hughes et al.(PRL {\bf 90} 131101)
Large Scale Structures, Symmetry, and Universality in Sandpiles
We introduce a sandpile model where, at each unstable site, all grains are
transferred randomly to downstream neighbors. The model is local and
conservative, but not Abelian. This does not appear to change the universality
class for the avalanches in the self-organized critical state. It does,
however, introduce long-range spatial correlations within the metastable
states. We find large scale networks of occupied sites whose density vanishes
in the thermodynamic limit, for d>1.Comment: 4 pages, 5 figures, submitted to Phys. Rev. Let
Comment on "Dynamic Opinion Model and Invasion Percolation"
In J. Shao et al., PRL 103, 108701 (2009) the authors claim that a model with
majority rule coarsening exhibits in d=2 a percolation transition in the
universality class of invasion percolation with trapping. In the present
comment we give compelling evidence, including high statistics simulations on
much larger lattices, that this is not correct. and that the model is trivially
in the ordinary percolation universality class.Comment: 1 pag
Infinite Hierarchy of Exact Equations in the Bak-Sneppen Model
We derive an infinite hierarchy of exact equations for the Bak-Sneppen model
in arbitrary dimensions. These equations relate different moments of temporal
duration and spatial size of avalanches. We prove that the exponents of the BS
model are the same above and below the critical point and express the universal
amplitude ratio of the avalanche spatial size in terms of the critical
exponents. The equations uniquely determine the shape of the scaling function
of the avalanche distribution. It is suggested that in the BS model there is
only one independent critical exponent.Comment: Submitted to PRL, 4 two-column pages (revtex), 1 ps figure included
with epsf, g-zipped, uuencode
Price Variations in a Stock Market With Many Agents
Large variations in stock prices happen with sufficient frequency to raise
doubts about existing models, which all fail to account for non-Gaussian
statistics. We construct simple models of a stock market, and argue that the
large variations may be due to a crowd effect, where agents imitate each
other's behavior. The variations over different time scales can be related to
each other in a systematic way, similar to the Levy stable distribution
proposed by Mandelbrot to describe real market indices. In the simplest, least
realistic case, exact results for the statistics of the variations are derived
by mapping onto a model of diffusing and annihilating particles, which has been
solved by quantum field theory methods. When the agents imitate each other and
respond to recent market volatility, different scaling behavior is obtained. In
this case the statistics of price variations is consistent with empirical
observations. The interplay between ``rational'' traders whose behavior is
derived from fundamental analysis of the stock, including dividends, and
``noise traders'', whose behavior is governed solely by studying the market
dynamics, is investigated. When the relative number of rational traders is
small, ``bubbles'' often occur, where the market price moves outside the range
justified by fundamental market analysis. When the number of rational traders
is larger, the market price is generally locked within the price range they
define.Comment: 39 pages (Latex) + 20 Figures and missing Figure 1 (sorry), submitted
to J. Math. Eco
A Monte Carlo Renormalization Group Approach to the Bak-Sneppen model
A recent renormalization group approach to a modified Bak-Sneppen model is
discussed. We propose a self-consistency condition for the blocking scheme to
be essential for a successful RG-method applied to self-organized criticality.
A new method realizing the RG-approach to the Bak-Sneppen model is presented.
It is based on the Monte-Carlo importance sampling idea. The new technique
performs much faster than the original proposal. Using this technique we
cross-check and improve previous results.Comment: 11 pages, REVTex, 2 Postscript figures include
Solitons in the one-dimensional forest fire model
Fires in the one-dimensional Bak-Chen-Tang forest fire model propagate as
solitons, resembling shocks in Burgers turbulence. The branching of solitons,
creating new fires, is balanced by the pair-wise annihilation of oppositely
moving solitons. Two distinct, diverging length scales appear in the limit
where the growth rate of trees, , vanishes. The width of the solitons, ,
diverges as a power law, , while the average distance between solitons
diverges much faster as .Comment: 4 pages with 2 figures include
Different hierarchy of avalanches observed in the Bak-Sneppen evolution model
We introduce a new quantity, average fitness, into the Bak-Sneppen evolution
model. Through the new quantity, a different hierarchy of avalanches is
observed. The gap equation, in terms of the average fitness, is presented to
describe the self-organization of the model. It is found that the critical
value of the average fitness can be exactly obtained. Based on the simulations,
two critical exponents, avalanche distribution and avalanche dimension, of the
new avalanches are given.Comment: 5 pages, 3 figure
1/f noise from correlations between avalanches in self-organized criticality
We show that large, slowly driven systems can evolve to a self-organized
critical state where long range temporal correlations between bursts or
avalanches produce low frequency noise. The avalanches can occur
instantaneously in the external time scale of the slow drive, and their event
statistics are described by power law distributions. A specific example of this
behavior is provided by numerical simulations of a deterministic ``sandpile''
model.Comment: Completely revised version: 4 pages (revtex), 3 eps figure
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