5,675 research outputs found

### 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 $n$ neighboring sites is occupied by a given configuration of trees.
The critical exponent describing the size distribution of forest clusters is
exactly $\tau = 2$ 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/

### Platelet Collapse Model of Pulsar Glitches

A platelet collapse model of starquakes is introduced. It displays
self-organized criticality with a robust power-law behavior. The simulations
indicate a near-constant exponent, whenever scaling is present.Comment: Figures available by sending request to Ivan Schmidt:
[email protected]

### 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

### 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

### d_c=4 is the upper critical dimension for the Bak-Sneppen model

Numerical results are presented indicating d_c=4 as the upper critical
dimension for the Bak-Sneppen evolution model. This finding agrees with
previous theoretical arguments, but contradicts a recent Letter [Phys. Rev.
Lett. 80, 5746-5749 (1998)] that placed d_c as high as d=8. In particular, we
find that avalanches are compact for all dimensions d<=4, and are fractal for
d>4. Under those conditions, scaling arguments predict a d_c=4, where
hyperscaling relations hold for d<=4. Other properties of avalanches, studied
for 1<=d<=6, corroborate this result. To this end, an improved numerical
algorithm is presented that is based on the equivalent branching process.Comment: 4 pages, RevTex4, as to appear in Phys. Rev. Lett., related papers
available at http://userwww.service.emory.edu/~sboettc

### 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

### Spatial-temporal correlations in the process to self-organized criticality

A new type of spatial-temporal correlation in the process approaching to the
self-organized criticality is investigated for the two simple models for
biological evolution. The change behaviors of the position with minimum barrier
are shown to be quantitatively different in the two models. Different results
of the correlation are given for the two models. We argue that the correlation
can be used, together with the power-law distributions, as criteria for
self-organized criticality.Comment: 3 pages in RevTeX, 3 eps figure

### 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

### 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

### 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

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