2,027 research outputs found
Evolution in complex systems
What features characterise complex system dynamics? Power laws and scale
invariance of fluctuations are often taken as the hallmarks of complexity,
drawing on analogies with equilibrium critical phenomena[1-3]. Here we argue
that slow, directed dynamics, during which the system's properties change
significantly, is fundamental. The underlying dynamics is related to a slow,
decelerating but spasmodic release of an intrinsic strain or tension. Time
series of a number of appropriate observables can be analysed to confirm this
effect. The strain arises from local frustration. As the strain is released
through "quakes", some system variable undergoes record statistics with
accompanying log-Poisson statistics for the quake event times[4]. We
demonstrate these phenomena via two very different systems: a model of magnetic
relaxation in type II superconductors and the Tangled Nature model of
evolutionary ecology, and show how quantitative indications of ageing can be
found.Comment: 8 pages, 5 figures all in one fil
Universal local versus unified global scaling laws in the statistics of seismicity
The unified scaling law for earthquakes, proposed by Bak, Christensen, Danon
and Scanlon, is shown to hold worldwide, as well as for areas as diverse as
Japan, New Zealand, Spain or New Madrid. The scaling functions that account for
the rescaled recurrence-time probability densities show a power-law behavior
for long times, with a universal exponent about (minus) 2.2. Another decreasing
power law governs short times, but with an exponent that may change from one
area to another. This is in contrast with a spatially independent,
time-homogenized version of Bak et al's procedure, which seems to present a
universal scaling behavior.Comment: submitted to Per Bak's memorial issue of Physica
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.
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
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