165 research outputs found
Evacuation in the Social Force Model is not stationary
An evacuation process is simulated within the Social Force Model. Thousand
pedestrians are leaving a room by one exit. We investigate the stationarity of
the distribution of time lags between instants when two successive pedestrians
cross the exit. The exponential tail of the distribution is shown to gradually
vanish. Taking fluctuations apart, the time lags decrease in time till there
are only about 50 pedestrians in the room, then they start to increase. This
suggests that at the last stage the flow is laminar. In the first stage,
clogging events slow the evacuation down. As they are more likely for larger
crowds, the flow is not stationary. The data are investigated with detrended
fluctuation analysis.Comment: 7 pages, 3 figures; PACS numbers: 89.75.Fb, 05.40.-a, 05.45.Tp,
89.40.B
Discrete charging of a quantum dot strongly coupled to external leads
We examine a quantum dot with levels which is strongly coupled
to leads for varying number of channels in the leads. It is shown both
analytically and numerically that for strong couplings between the dot and the
leads, at least bound states (akin to subradiant states in
optics) remain on the dot. These bound states exhibit discrete charging and,
for a significant range of charging energies, strong Coulomb blockade behavior
as function of the chemical potential. The physics changes for large charging
energy where the same (superradiant) state is repeatedly charged.Comment: 5 pages, 3 figures (accepted for publication in EPL
Generalized Hurst exponent and multifractal function of original and translated texts mapped into frequency and length time series
A nonlinear dynamics approach can be used in order to quantify complexity in
written texts. As a first step, a one-dimensional system is examined : two
written texts by one author (Lewis Carroll) are considered, together with one
translation, into an artificial language, i.e. Esperanto are mapped into time
series. Their corresponding shuffled versions are used for obtaining a "base
line". Two different one-dimensional time series are used here: (i) one based
on word lengths (LTS), (ii) the other on word frequencies (FTS). It is shown
that the generalized Hurst exponent and the derived curves
of the original and translated texts show marked differences. The original
"texts" are far from giving a parabolic function, - in contrast to
the shuffled texts. Moreover, the Esperanto text has more extreme values. This
suggests cascade model-like, with multiscale time asymmetric features as
finally written texts. A discussion of the difference and complementarity of
mapping into a LTS or FTS is presented. The FTS curves are more
opened than the LTS onesComment: preprint for PRE; 2 columns; 10 pages; 6 (multifigures); 3 Tables; 70
reference
Detrended fluctuation analysis for fractals and multifractals in higher dimensions
One-dimensional detrended fluctuation analysis (1D DFA) and multifractal
detrended fluctuation analysis (1D MF-DFA) are widely used in the scaling
analysis of fractal and multifractal time series because of being accurate and
easy to implement. In this paper we generalize the one-dimensional DFA and
MF-DFA to higher-dimensional versions. The generalization works well when
tested with synthetic surfaces including fractional Brownian surfaces and
multifractal surfaces. The two-dimensional MF-DFA is also adopted to analyze
two images from nature and experiment and nice scaling laws are unraveled.Comment: 7 Revtex pages inluding 11 eps figure
Multifractal Properties of Price Fluctuations of Stocks and Commodities
We analyze daily prices of 29 commodities and 2449 stocks, each over a period
of years. We find that the price fluctuations for commodities have
a significantly broader multifractal spectrum than for stocks. We also propose
that multifractal properties of both stocks and commodities can be attributed
mainly to the broad probability distribution of price fluctuations and
secondarily to their temporal organization. Furthermore, we propose that, for
commodities, stronger higher order correlations in price fluctuations result in
broader multifractal spectra.Comment: Published in Euro Physics Letters (14 pages, 5 figures
The Visibility Graph: a new method for estimating the Hurst exponent of fractional Brownian motion
Fractional Brownian motion (fBm) has been used as a theoretical framework to
study real time series appearing in diverse scientific fields. Because its
intrinsic non-stationarity and long range dependence, its characterization via
the Hurst parameter H requires sophisticated techniques that often yield
ambiguous results. In this work we show that fBm series map into a scale free
visibility graph whose degree distribution is a function of H. Concretely, it
is shown that the exponent of the power law degree distribution depends
linearly on H. This also applies to fractional Gaussian noises (fGn) and
generic f^(-b) noises. Taking advantage of these facts, we propose a brand new
methodology to quantify long range dependence in these series. Its reliability
is confirmed with extensive numerical simulations and analytical developments.
Finally, we illustrate this method quantifying the persistent behavior of human
gait dynamics.Comment: 5 pages, submitted for publicatio
Mona Lisa, the stochastic view and fractality in color space
A painting consists of objects which are arranged in specific ways. The art
of painting is drawing the objects, which can be considered as known trends, in
an expressive manner. Detrended methods are suitable for characterizing the
artistic works of the painter by eliminating trends. It means that we study the
paintings, regardless of its apparent purpose, as a stochastic process. We
apply multifractal detrended fluctuation analysis to characterize the
statistical properties of Mona Lisa, as an instance, to exhibit the fractality
of the painting. Our results show that Mona Lisa is long range correlated and
almost behaves similar in various scales.Comment: 16 pages, 5 figures, to appear in Int. J. Mod. Phys.
Characterization of Sleep Stages by Correlations of Heartbeat Increments
We study correlation properties of the magnitude and the sign of the
increments in the time intervals between successive heartbeats during light
sleep, deep sleep, and REM sleep using the detrended fluctuation analysis
method. We find short-range anticorrelations in the sign time series, which are
strong during deep sleep, weaker during light sleep and even weaker during REM
sleep. In contrast, we find long-range positive correlations in the magnitude
time series, which are strong during REM sleep and weaker during light sleep.
We observe uncorrelated behavior for the magnitude during deep sleep. Since the
magnitude series relates to the nonlinear properties of the original time
series, while the signs series relates to the linear properties, our findings
suggest that the nonlinear properties of the heartbeat dynamics are more
pronounced during REM sleep. Thus, the sign and the magnitude series provide
information which is useful in distinguishing between the sleep stages.Comment: 7 pages, 4 figures, revte
Long-term power-law fluctuation in Internet traffic
Power-law fluctuation in observed Internet packet flow are discussed. The
data is obtained by a multi router traffic grapher (MRTG) system for 9 months.
The internet packet flow is analyzed using the detrended fluctuation analysis.
By extracting the average daily trend, the data shows clear power-law
fluctuations. The exponents of the fluctuation for the incoming and outgoing
flow are almost unity. Internet traffic can be understood as a daily periodic
flow with power-law fluctuations.Comment: 10 pages, 8 figure
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