849 research outputs found
Generalized (m,k)-Zipf law for fractional Brownian motion-like time series with or without effect of an additional linear trend
We have translated fractional Brownian motion (FBM) signals into a text based
on two ''letters'', as if the signal fluctuations correspond to a constant
stepsize random walk. We have applied the Zipf method to extract the
exponent relating the word frequency and its rank on a log-log plot. We have
studied the variation of the Zipf exponent(s) giving the relationship between
the frequency of occurrence of words of length made of such two letters:
is varying as a power law in terms of . We have also searched how
the exponent of the Zipf law is influenced by a linear trend and the
resulting effect of its slope. We can distinguish finite size effects, and
results depending whether the starting FBM is persistent or not, i.e. depending
on the FBM Hurst exponent . It seems then numerically proven that the Zipf
exponent of a persistent signal is more influenced by the trend than that of an
antipersistent signal. It appears that the conjectured law
only holds near . We have also introduced considerations based on the
notion of a {\it time dependent Zipf law} along the signal.Comment: 24 pages, 12 figures; to appear in Int. J. Modern Phys
On the influence of time and space correlations on the next earthquake magnitude
A crucial point in the debate on feasibility of earthquake prediction is the
dependence of an earthquake magnitude from past seismicity. Indeed, whilst
clustering in time and space is widely accepted, much more questionable is the
existence of magnitude correlations. The standard approach generally assumes
that magnitudes are independent and therefore in principle unpredictable. Here
we show the existence of clustering in magnitude: earthquakes occur with higher
probability close in time, space and magnitude to previous events. More
precisely, the next earthquake tends to have a magnitude similar but smaller
than the previous one. A dynamical scaling relation between magnitude, time and
space distances reproduces the complex pattern of magnitude, spatial and
temporal correlations observed in experimental seismic catalogs.Comment: 4 Figure
Statistical properties of SGR 1900+14 bursts
We study the statistics of soft gamma repeater (SGR) bursts, using a data
base of 187 events detected with BATSE and 837 events detected with RXTE PCA,
all from SGR 1900+14 during its 1998-1999 active phase. We find that the
fluence or energy distribution of bursts is consistent with a power law of
index 1.66, over 4 orders of magnitude. This scale-free distribution resembles
the Gutenberg-Richter Law for earthquakes, and gives evidence for
self-organized criticality in SGRs. The distribution of time intervals between
successive bursts from SGR 1900+14 is consistent with a log-normal
distribution. There is no correlation between burst intensity and the waiting
times till the next burst, but there is some evidence for a correlation between
burst intensity and the time elapsed since the previous burst. We also find a
correlation between the duration and the energy of the bursts, but with
significant scatter. In all these statistical properties, SGR bursts resemble
earthquakes and solar flares more closely than they resemble any known
accretion-powered or nuclear-powered phenomena. Thus our analysis lends support
to the hypothesis that the energy source for SGR bursts is internal to the
neutron star, and plausibly magnetic.Comment: 11 pages, 4 figures, accepted for publication in ApJ
The Network of Epicenters of the Olami-Feder-Christensen Model of Earthquakes
We study the dynamics of the Olami-Feder-Christensen (OFC) model of
earthquakes, focusing on the behavior of sequences of epicenters regarded as a
growing complex network. Besides making a detailed and quantitative study of
the effects of the borders (the occurrence of epicenters is dominated by a
strong border effect which does not scale with system size), we examine the
degree distribution and the degree correlation of the graph. We detect sharp
differences between the conservative and nonconservative regimes of the model.
Removing border effects, the conservative regime exhibits a Poisson-like degree
statistics and is uncorrelated, while the nonconservative has a broad
power-law-like distribution of degrees (if the smallest events are ignored),
which reproduces the observed behavior of real earthquakes. In this regime the
graph has also a unusually strong degree correlation among the vertices with
higher degree, which is the result of the existence of temporary attractors for
the dynamics: as the system evolves, the epicenters concentrate increasingly on
fewer sites, exhibiting strong synchronization, but eventually spread again
over the lattice after a series of sufficiently large earthquakes. We propose
an analytical description of the dynamics of this growing network, considering
a Markov process network with hidden variables, which is able to account for
the mentioned properties.Comment: 9 pages, 10 figures. Smaller number of figures, and minor text
corrections and modifications. For version with full resolution images see
http://fig.if.usp.br/~tpeixoto/cond-mat-0602244.pd
Memory in Self Organized Criticality
Many natural phenomena exhibit power law behaviour in the distribution of
event size. This scaling is successfully reproduced by Self Organized
Criticality (SOC). On the other hand, temporal occurrence in SOC models has a
Poisson-like statistics, i.e. exponential behaviour in the inter-event time
distribution, in contrast with experimental observations. We present a SOC
model with memory: events are nucleated not only as a consequence of the
instantaneous value of the local field with respect to the firing threshold,
but on the basis of the whole history of the system. The model is able to
reproduce the complex behaviour of inter-event time distribution, in excellent
agreement with experimental seismic data
Dynamics of Elastic Excitable Media
The Burridge-Knopoff model of earthquake faults with viscous friction is
equivalent to a van der Pol-FitzHugh-Nagumo model for excitable media with
elastic coupling. The lubricated creep-slip friction law we use in the
Burridge-Knopoff model describes the frictional sliding dynamics of a range of
real materials. Low-dimensional structures including synchronized oscillations
and propagating fronts are dominant, in agreement with the results of
laboratory friction experiments. Here we explore the dynamics of fronts in
elastic excitable media.Comment: Int. J. Bifurcation and Chaos, to appear (1999
Renormalization group theory for finite-size scaling in extreme statistics
We present a renormalization group (RG) approach to explain universal
features of extreme statistics, applied here to independent, identically
distributed variables. The outlines of the theory have been described in a
previous Letter, the main result being that finite-size shape corrections to
the limit distribution can be obtained from a linearization of the RG
transformation near a fixed point, leading to the computation of stable
perturbations as eigenfunctions. Here we show details of the RG theory which
exhibit remarkable similarities to the RG known in statistical physics. Besides
the fixed points explaining universality, and the least stable eigendirections
accounting for convergence rates and shape corrections, the similarities
include marginally stable perturbations which turn out to be generic for the
Fisher-Tippett-Gumbel class. Distribution functions containing unstable
perturbations are also considered. We find that, after a transitory divergence,
they return to the universal fixed line at the same or at a different point
depending on the type of perturbation.Comment: 15 pages, 8 figures, to appear in Phys. Rev.
A Complexity View of Rainfall
We show that rain events are analogous to a variety of nonequilibrium
relaxation processes in Nature such as earthquakes and avalanches. Analysis of
high-resolution rain data reveals that power laws describe the number of rain
events versus size and number of droughts versus duration. In addition, the
accumulated water column displays scale-less fluctuations. These statistical
properties are the fingerprints of a self-organized critical process and may
serve as a benchmark for models of precipitation and atmospheric processes.Comment: 4 pages, 5 figure
Extreme value distributions and Renormalization Group
In the classical theorems of extreme value theory the limits of suitably
rescaled maxima of sequences of independent, identically distributed random
variables are studied. So far, only affine rescalings have been considered. We
show, however, that more general rescalings are natural and lead to new limit
distributions, apart from the Gumbel, Weibull, and Fr\'echet families. The
problem is approached using the language of Renormalization Group
transformations in the space of probability densities. The limit distributions
are fixed points of the transformation and the study of the differential around
them allows a local analysis of the domains of attraction and the computation
of finite-size corrections.Comment: 16 pages, 5 figures. Final versio
Earthquake networks based on similar activity patterns
Earthquakes are a complex spatiotemporal phenomenon, the underlying mechanism
for which is still not fully understood despite decades of research and
analysis. We propose and develop a network approach to earthquake events. In
this network, a node represents a spatial location while a link between two
nodes represents similar activity patterns in the two different locations. The
strength of a link is proportional to the strength of the cross-correlation in
activities of two nodes joined by the link. We apply our network approach to a
Japanese earthquake catalog spanning the 14-year period 1985-1998. We find
strong links representing large correlations between patterns in locations
separated by more than 1000 km, corroborating prior observations that
earthquake interactions have no characteristic length scale. We find network
characteristics not attributable to chance alone, including a large number of
network links, high node assortativity, and strong stability over time.Comment: 8 pages text, 9 figures. Updated from previous versio
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