858 research outputs found
Nonstationary dynamics of the Alessandro-Beatrice-Bertotti-Montorsi model
We obtain an exact solution for the motion of a particle driven by a spring
in a Brownian random-force landscape, the Alessandro-Beatrice-Bertotti-Montorsi
(ABBM) model. Many experiments on quasi-static driving of elastic interfaces
(Barkhausen noise in magnets, earthquake statistics, shear dynamics of granular
matter) exhibit the same universal behavior as this model. It also appears as a
limit in the field theory of elastic manifolds. Here we discuss predictions of
the ABBM model for monotonous, but otherwise arbitrary, time-dependent driving.
Our main result is an explicit formula for the generating functional of
particle velocities and positions. We apply this to derive the
particle-velocity distribution following a quench in the driving velocity. We
also obtain the joint avalanche size and duration distribution and the mean
avalanche shape following a jump in the position of the confining spring. Such
non-stationary driving is easy to realize in experiments, and provides a way to
test the ABBM model beyond the stationary, quasi-static regime. We study
extensions to two elastically coupled layers, and to an elastic interface of
internal dimension d, in the Brownian force landscape. The effective action of
the field theory is equal to the action, up to 1-loop corrections obtained
exactly from a functional determinant. This provides a connection to
renormalization-group methods.Comment: 18 pages, 3 figure
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
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
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.
noise and avalanche scaling in plastic deformation
We study the intermittency and noise of dislocation systems undergoing shear
deformation. Simulations of a simple two-dimensional discrete dislocation
dynamics model indicate that the deformation rate exhibits a power spectrum
scaling of the type . The noise exponent is far away from a
Lorentzian, with . This result is directly related to the
way the durations of avalanches of plastic deformation activity scale with
their size.Comment: 6 pages, 5 figures, submitted to Phys. Rev.
Brownian forces in sheared granular matter
We present results from a series of experiments on a granular medium sheared
in a Couette geometry and show that their statistical properties can be
computed in a quantitative way from the assumption that the resultant from the
set of forces acting in the system performs a Brownian motion. The same
assumption has been utilised, with success, to describe other phenomena, such
as the Barkhausen effect in ferromagnets, and so the scheme suggests itself as
a more general description of a wider class of driven instabilities.Comment: 4 pages, 5 figures and 1 tabl
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
Energy constrained sandpile models
We study two driven dynamical systems with conserved energy. The two automata
contain the basic dynamical rules of the Bak, Tang and Wiesenfeld sandpile
model. In addition a global constraint on the energy contained in the lattice
is imposed. In the limit of an infinitely slow driving of the system, the
conserved energy becomes the only parameter governing the dynamical
behavior of the system. Both models show scale free behavior at a critical
value of the fixed energy. The scaling with respect to the relevant
scaling field points out that the developing of critical correlations is in a
different universality class than self-organized critical sandpiles. Despite
this difference, the activity (avalanche) probability distributions appear to
coincide with the one of the standard self-organized critical sandpile.Comment: 4 pages including 3 figure
The origin of power-law distributions in self-organized criticality
The origin of power-law distributions in self-organized criticality is
investigated by treating the variation of the number of active sites in the
system as a stochastic process. An avalanche is then regarded as a first-return
random walk process in a one-dimensional lattice. Power law distributions of
the lifetime and spatial size are found when the random walk is unbiased with
equal probability to move in opposite directions. This shows that power-law
distributions in self-organized criticality may be caused by the balance of
competitive interactions. At the mean time, the mean spatial size for
avalanches with the same lifetime is found to increase in a power law with the
lifetime.Comment: 4 pages in RevTeX, 3 eps figures. To appear in J.Phys.G. To appear in
J. Phys.
Rain: Relaxations in the sky
We demonstrate how, from the point of view of energy flow through an open
system, rain is analogous to many other relaxational processes in Nature such
as earthquakes. By identifying rain events as the basic entities of the
phenomenon, we show that the number density of rain events per year is
inversely proportional to the released water column raised to the power 1.4.
This is the rain-equivalent of the Gutenberg-Richter law for earthquakes. The
event durations and the waiting times between events are also characterised by
scaling regions, where no typical time scale exists. The Hurst exponent of the
rain intensity signal . It is valid in the temporal range from
minutes up to the full duration of the signal of half a year. All of our
findings are consistent with the concept of self-organised criticality, which
refers to the tendency of slowly driven non-equilibrium systems towards a state
of scale free behaviour.Comment: 9 pages, 8 figures, submitted to PR
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