4,219 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
Money and Goldstone modes
Why is ``worthless'' fiat money generally accepted as payment for goods and
services? In equilibrium theory, the value of money is generally not
determined: the number of equations is one less than the number of unknowns, so
only relative prices are determined. In the language of mathematics, the
equations are ``homogeneous of order one''. Using the language of physics, this
represents a continuous ``Goldstone'' symmetry. However, the continuous
symmetry is often broken by the dynamics of the system, thus fixing the value
of the otherwise undetermined variable. In economics, the value of money is a
strategic variable which each agent must determine at each transaction by
estimating the effect of future interactions with other agents. This idea is
illustrated by a simple network model of monopolistic vendors and buyers, with
bounded rationality. We submit that dynamical, spontaneous symmetry breaking is
the fundamental principle for fixing the value of money. Perhaps the continuous
symmetry representing the lack of restoring force is also the fundamental
reason for large fluctuations in stock markets.Comment: 7 pages, 3 figure
Intelligent systems in the context of surrounding environment
We investigate the behavioral patterns of a population of agents, each controlled by a simple biologically motivated neural network model, when they are set in competition against each other in the Minority Model of Challet and Zhang. We explore the effects of changing agent characteristics, demonstrating that crowding behavior takes place among agents of similar memory, and show how this allows unique `rogue' agents with higher memory values to take advantage of a majority population. We also show that agents' analytic capability is largely determined by the size of the intermediary layer of neurons.
In the context of these results, we discuss the general nature of natural and artificial intelligence systems, and suggest intelligence only exists in the context of the surrounding environment (embodiment).
Source code for the programs used can be found at http://neuro.webdrake.net/
Disorder-induced phase transition in a one-dimensional model of rice pile
We propose a one-dimensional rice-pile model which connects the 1D BTW
sandpile model (Phys. Rev. A 38, 364 (1988)) and the Oslo rice-pile model
(Phys. Rev. lett. 77, 107 (1997)) in a continuous manner. We found that for a
sufficiently large system, there is a sharp transition between the trivial
critical behaviour of the 1D BTW model and the self-organized critical (SOC)
behaviour. When there is SOC, the model belongs to a known universality class
with the avalanche exponent .Comment: 10 pages, 7 eps figure
Conformal field theory correlations in the Abelian sandpile mode
We calculate all multipoint correlation functions of all local bond
modifications in the two-dimensional Abelian sandpile model, both at the
critical point, and in the model with dissipation. The set of local bond
modifications includes, as the most physically interesting case, all weakly
allowed cluster variables. The correlation functions show that all local bond
modifications have scaling dimension two, and can be written as linear
combinations of operators in the central charge -2 logarithmic conformal field
theory, in agreement with a form conjectured earlier by Mahieu and Ruelle in
Phys. Rev. E 64, 066130 (2001). We find closed form expressions for the
coefficients of the operators, and describe methods that allow their rapid
calculation. We determine the fields associated with adding or removing bonds,
both in the bulk, and along open and closed boundaries; some bond defects have
scaling dimension two, while others have scaling dimension four. We also
determine the corrections to bulk probabilities for local bond modifications
near open and closed boundaries.Comment: 13 pages, 5 figures; referee comments incorporated; Accepted by Phys.
Rev.
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
Abrupt transition in a sandpile model
We present a fixed energy sandpile (FES) model which, by increasing the
initial energy,undergoes, at the level of individual configurations, a
discontinuous transition.The model is obtained by modifying the toppling
procedure in the BTW rules: the energy transfer from a toppling site takes
place only to neighbouring sites with less energy (negative gradient
constraint) and with a time ordering (asynchronous). The model is minimal in
the sense that removing either of the two above mentioned constraints (negative
gradient or time ordering) the abrupt transition goes over to a continuous
transition as in the usual BTW case. Therefore the proposed model offers an
unique possibility to explore at the microscopic level the basic mechanisms
underlying discontinuous transitions.Comment: 7 pages, 5 figure
Unified Scaling Law for Earthquakes
We show that the distribution of waiting times between earthquakes occurring
in California obeys a simple unified scaling law valid from tens of seconds to
tens of years, see Eq. (1) and Fig. 4. The short time clustering, commonly
referred to as aftershocks, is nothing but the short time limit of the general
hierarchical properties of earthquakes. There is no unique operational way of
distinguishing between main shocks and aftershocks. In the unified law, the
Gutenberg-Richter b-value, the exponent -1 of the Omori law for aftershocks,
and the fractal dimension d_f of earthquakes appear as critical indices.Comment: 4 pages, 4 figure
Scaling of impact fragmentation near the critical point
We investigated two-dimensional brittle fragmentation with a flat impact
experimentally, focusing on the low impact energy region near the
fragmentation-critical point. We found that the universality class of
fragmentation transition disagreed with that of percolation. However, the
weighted mean mass of the fragments could be scaled using the pseudo-control
parameter multiplicity. The data for highly fragmented samples included a
cumulative fragment mass distribution that clearly obeyed a power-law. The
exponent of this power-law was 0.5 and it was independent of sample size. The
fragment mass distributions in this regime seemed to collapse into a unified
scaling function using weighted mean fragment mass scaling. We also examined
the behavior of higher order moments of the fragment mass distributions, and
obtained multi-scaling exponents that agreed with those of the simple biased
cascade model.Comment: 6 pages, 6 figure
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