347 research outputs found
Scaling of the localization length in linear electronic and vibrational systems with long-range correlated disorder
The localization lengths of long-range correlated disordered chains are
studied for electronic wavefunctions in the Anderson model and for vibrational
states. A scaling theory close to the band edge is developed in the Anderson
model and supported by numerical simulations. This scaling theory is mapped
onto the vibrational case at small frequencies. It is shown that for small
frequencies, unexpectateley the localization length is smaller for correlated
than for uncorrelated chains.Comment: to be published in PRB, 4 pages, 2 Figure
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
Level statistics and eigenfunctions of pseudointegrable systems: dependence on energy and genus number
We study the level statistics (second half moment and rigidity
) and the eigenfunctions of pseudointegrable systems with rough
boundaries of different genus numbers . We find that the levels form energy
intervals with a characteristic behavior of the level statistics and the
eigenfunctions in each interval. At low enough energies, the boundary roughness
is not resolved and accordingly, the eigenfunctions are quite regular functions
and the level statistics shows Poisson-like behavior. At higher energies, the
level statistics of most systems moves from Poisson-like towards Wigner-like
behavior with increasing . Investigating the wavefunctions, we find many
chaotic functions that can be described as a random superposition of regular
wavefunctions. The amplitude distribution of these chaotic functions
was found to be Gaussian with the typical value of the localization volume
. For systems with periodic boundaries we find
several additional energy regimes, where is relatively close to the
Poisson-limit. In these regimes, the eigenfunctions are either regular or
localized functions, where is close to the distribution of a sine or
cosine function in the first case and strongly peaked in the second case. Also
an interesting intermediate case between chaotic and localized eigenfunctions
appears
Components of multifractality in high-frequency stock returns
We analyzed multifractal properties of 5-minute stock returns from a period
of over two years for 100 highly capitalized American companies. The two
sources: fat-tailed probability distributions and nonlinear temporal
correlations, vitally contribute to the observed multifractal dynamics of the
returns. For majority of the companies the temporal correlations constitute a
much more significant related factor, however.Comment: to appear in Physica
Multifractal Detrended Cross-Correlation Analysis of Sunspot Numbers and River Flow Fluctuations
We use the Detrended Cross-Correlation Analysis (DCCA) to investigate the
influence of sun activity represented by sunspot numbers on one of the climate
indicators, specifically rivers, represented by river flow fluctuation for
Daugava, Holston, Nolichucky and French Broad rivers. The Multifractal
Detrended Cross-Correlation Analysis (MF-DXA) shows that there exist some
crossovers in the cross-correlation fluctuation function versus time scale of
the river flow and sunspot series. One of these crossovers corresponds to the
well-known cycle of solar activity demonstrating a universal property of the
mentioned rivers. The scaling exponent given by DCCA for original series at
intermediate time scale, months, is which is almost similar for all underlying rivers at
confidence interval showing the second universal behavior of river
runoffs. To remove the sinusoidal trends embedded in data sets, we apply the
Singular Value Decomposition (SVD) method. Our results show that there exists a
long-range cross-correlation between the sunspot numbers and the underlying
streamflow records. The magnitude of the scaling exponent and the corresponding
cross-correlation exponent are and
, respectively. Different values for scaling
and cross-correlation exponents may be related to local and external factors
such as topography, drainage network morphology, human activity and so on.
Multifractal cross-correlation analysis demonstrates that all underlying
fluctuations have almost weak multifractal nature which is also a universal
property for data series. In addition the empirical relation between scaling
exponent derived by DCCA and Detrended Fluctuation Analysis (DFA), is confirmed.Comment: 9 pages, 8 figures and 1 table. V2: Added comments, references,
figures and major corrections. Accepted for publication in Physica A:
Statistical Mechanics and its Application
Nonextensive statistical features of the Polish stock market fluctuations
The statistics of return distributions on various time scales constitutes one
of the most informative characteristics of the financial dynamics. Here we
present a systematic study of such characteristics for the Polish stock market
index WIG20 over the period 04.01.1999 - 31.10.2005 for the time lags ranging
from one minute up to one hour. This market is commonly classified as emerging.
Still on the shortest time scales studied we find that the tails of the return
distributions are consistent with the inverse cubic power-law, as identified
previously for majority of the mature markets. Within the time scales studied a
quick and considerable departure from this law towards a Gaussian can however
be traced. Interestingly, all the forms of the distributions observed can be
comprised by the single -Gaussians which provide a satisfactory and at the
same time compact representation of the distribution of return fluctuations
over all magnitudes of their variation. The corresponding nonextensivity
parameter is found to systematically decrease when increasing the time
scales.Comment: 14 pages. Physica A in prin
A nonextensive approach to the dynamics of financial observables
We present results about financial market observables, specifically returns
and traded volumes. They are obtained within the current nonextensive
statistical mechanical framework based on the entropy
(). More precisely, we
present stochastic dynamical mechanisms which mimic probability density
functions empirically observed. These mechanisms provide possible
interpretations for the emergence of the entropic indices in the time
evolution of the corresponding observables. In addition to this, through
multi-fractal analysis of return time series, we verify that the dual relation
is numerically satisfied, and being
associated to the probability density function and to the sensitivity to
initial conditions respectively. This type of simple relation, whose
understanding remains ellusive, has been empirically verified in various other
systems.Comment: Invited paper to appear in special issue of Eur. Phys. J. B dedicated
to econophysics, edited by T. Di Matteo and T. Aste. 7 page
Volcanic forcing improves Atmosphere-Ocean Coupled General Circulation Model scaling performance
Recent Atmosphere-Ocean Coupled General Circulation Model (AOGCM) simulations
of the twentieth century climate, which account for anthropogenic and natural
forcings, make it possible to study the origin of long-term temperature
correlations found in the observed records. We study ensemble experiments
performed with the NCAR PCM for 10 different historical scenarios, including no
forcings, greenhouse gas, sulfate aerosol, ozone, solar, volcanic forcing and
various combinations, such as it natural, anthropogenic and all forcings. We
compare the scaling exponents characterizing the long-term correlations of the
observed and simulated model data for 16 representative land stations and 16
sites in the Atlantic Ocean for these scenarios. We find that inclusion of
volcanic forcing in the AOGCM considerably improves the PCM scaling behavior.
The scenarios containing volcanic forcing are able to reproduce quite well the
observed scaling exponents for the land with exponents around 0.65 independent
of the station distance from the ocean. For the Atlantic Ocean, scenarios with
the volcanic forcing slightly underestimate the observed persistence exhibiting
an average exponent 0.74 instead of 0.85 for reconstructed data.Comment: 4 figure
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