4,805 research outputs found
Formation of Space-Time Structure in a Forest-Fire Model
We present a general stochastic forest-fire model which shows a variety of
different structures depending on the parameter values. The model contains
three possible states per site (tree, burning tree, empty site) and three
parameters (tree growth probability , lightning probability , and
immunity ). We review analytic and computer simulation results for a
quasideterministic state with spiral-shaped fire fronts, for a percolation-like
phase transition and a self-organized critical state. Possible applications to
excitable systems are discussed.Comment: 20 pages REVTEX, 9 figures upon reques
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
Exact equqations and scaling relations for f-avalanche in the Bak-Sneppen evolution model
Infinite hierarchy of exact equations are derived for the newly-observed
f-avalanche in the Bak-Sneppen evolution model. By solving the first order
exact equation, we found that the critical exponent which governs the
divergence of the average avalanche size, is exactly 1 (for all dimensions),
confirmed by the simulations. Solution of the gap equation yields another
universal exponent, denoting the the relaxation to the attractor, is exactly 1.
We also establish some scaling relations among the critical exponents of the
new avalanche.Comment: 5 pages, 1 figur
Exact Results for the One-Dimensional Self-Organized Critical Forest-Fire Model
We present the analytic solution of the self-organized critical (SOC)
forest-fire model in one dimension proving SOC in systems without conservation
laws by analytic means. Under the condition that the system is in the steady
state and very close to the critical point, we calculate the probability that a
string of neighboring sites is occupied by a given configuration of trees.
The critical exponent describing the size distribution of forest clusters is
exactly and does not change under certain changes of the model
rules. Computer simulations confirm the analytic results.Comment: 12 pages REVTEX, 2 figures upon request, dro/93/
Replicating financial market dynamics with a simple self-organized critical lattice model
We explore a simple lattice field model intended to describe statistical
properties of high frequency financial markets. The model is relevant in the
cross-disciplinary area of econophysics. Its signature feature is the emergence
of a self-organized critical state. This implies scale invariance of the model,
without tuning parameters. Prominent results of our simulation are time series
of gains, prices, volatility, and gains frequency distributions, which all
compare favorably to features of historical market data. Applying a standard
GARCH(1,1) fit to the lattice model gives results that are almost
indistinguishable from historical NASDAQ data.Comment: 20 pages, 33 figure
Crossover from Percolation to Self-Organized Criticality
We include immunity against fire as a new parameter into the self-organized
critical forest-fire model. When the immunity assumes a critical value,
clusters of burnt trees are identical to percolation clusters of random bond
percolation. As long as the immunity is below its critical value, the
asymptotic critical exponents are those of the original self-organized critical
model, i.e. the system performs a crossover from percolation to self-organized
criticality. We present a scaling theory and computer simulation results.Comment: 4 pages Revtex, two figures included, to be published in PR
Celebrating the Physics in Geophysics
As 2005, the International Year of Physics, comes to an end, two physicists
working primarily in geophysical research reflect on how geophysics is not an
applied physics. Although geophysics has certainly benefited from progress in
physics and sometimes emulated the reductionist program of mainstream physics,
it has also educated the physics community about some of the generic behaviors
of strongly nonlinear systems. Dramatic examples are the insights we have
gained into the ``emergent'' phenomena of chaos, cascading instabilities,
turbulence, self-organization, fractal structure, power-law variability,
anomalous scaling, threshold dynamics, creep, fracture, and so on. In all of
these examples, relatively simple models have been able to explain the
recurring features of apparently very complex signals and fields. It appears
that the future of the intricate relation between physics and geophysics will
be as exciting as its past has been characterized by a mutual fascination.
Physics departments in our universities should capitalize on this trend to
attract and retain young talent motivated to address problems that really
matter for the future of the planet. A pressing topic with huge impact on
populations and that is challenging enough for both physics and geophysics
communities to work together like never before is the understanding and
prediction of extreme events.Comment: 6 pages, final version to appear in EOS-AGU Transactions in November
200
Stochastic modeling of Congress
We analyze the dynamics of growth of the number of congressmen supporting the
resolution HR1207 to audit the Federal Reserve. The plot of the total number of
co-sponsors as a function of time is of "Devil's staircase" type. The
distribution of the numbers of new co-sponsors joining during a particular day
(step height) follows a power law. The distribution of the length of intervals
between additions of new co-sponsors (step length) also follows a power law. We
use a modification of Bak-Tang-Wiesenfeld sandpile model to simulate the
dynamics of Congress and obtain a good agreement with the data
Word Processors with Line-Wrap: Cascading, Self-Organized Criticality, Random Walks, Diffusion, Predictability
We examine the line-wrap feature of text processors and show that adding
characters to previously formatted lines leads to the cascading of words to
subsequent lines and forms a state of self-organized criticality. We show the
connection to one-dimensional random walks and diffusion problems, and we
examine the predictability of catastrophic cascades.Comment: 6 pages, LaTeX with RevTeX package, 4 postscript figures appende
Randmoness and Step-like Distribution of Pile Heights in Avalanche Models
The paper develops one-parametric family of the sand-piles dealing with the
grains' local losses on the fixed amount. The family exhibits the crossover
between the models with deterministic and stochastic relaxation. The mean
height of the pile is destined to describe the crossover. The height's
densities corresponding to the models with relaxation of the both types tend
one to another as the parameter increases. These densities follow a step-like
behaviour in contrast to the peaked shape found in the models with the local
loss of the grains down to the fixed level [S. Lubeck, Phys. Rev. E, 62, 6149,
(2000)]. A spectral approach based on the long-run properties of the pile
height considers the models with deterministic and random relaxation more
accurately and distinguishes the both cases up to admissible parameter values.Comment: 5 pages, 5 figure
- …