58 research outputs found
Spatial scaling in fracture propagation in dilute systems
The geometry of fracture patterns in a dilute elastic network is explored
using molecular dynamics simulation. The network in two dimensions is subjected
to a uniform strain which drives the fracture to develop by the growth and
coalescence of the vacancy clusters in the network. For strong dilution, it has
been shown earlier that there exists a characteristic time at which a
dynamical transition occurs with a power law divergence (with the exponent )
of the average cluster size. Close to , the growth of the clusters is
scale-invariant in time and satisfies a dynamical scaling law. This paper shows
that the cluster growth near also exhibits spatial scaling in addition to
the temporal scaling. As fracture develops with time, the connectivity length
of the clusters increses and diverges at as , with . As a result of the scale-invariant
growth, the vacancy clusters attain a fractal structure at with an
effective dimensionality . These values are independent
(within the limit of statistical error) of the concentration (provided it is
sufficiently high) with which the network is diluted to begin with. Moreover,
the values are very different from the corresponding values in qualitatively
similar phenomena suggesting a different universality class of the problem. The
values of and supports the scaling relation with the
value of obtained before.Comment: A single ps file (6 figures included), 12 pages, to appear in Physica
Icequakes coupled with surface displacements for predicting glacier break-off
A hanging glacier at the east face of Weisshorn (Switzerland) broke off in
2005. We were able to monitor and measure surface motion and icequake activity
for 25 days up to three days prior to the break-off. The analysis of seismic
waves generated by the glacier during the rupture maturation process revealed
four types of precursory signals of the imminent catastrophic rupture: (i) an
increase in seismic activity within the glacier, (ii) a decrease in the waiting
time between two successive icequakes, (iii) a change in the size-frequency
distribution of icequake energy, and (iv) a modification in the structure of
the waiting time distributions between two successive icequakes. Morevover, it
was possible to demonstrate the existence of a correlation between the seismic
activity and the log-periodic oscillations of the surface velocities
superimposed on the global acceleration of the glacier during the rupture
maturation. Analysis of the seismic activity led us to the identification of
two regimes: a stable phase with diffuse damage, and an unstable and dangerous
phase characterized by a hierarchical cascade of rupture instabilities where
large icequakes are triggered.Comment: 16 pages, 7 figure
The effect of disorder on the fracture nucleation process
The statistical properties of failure are studied in a fiber bundle model
with thermal noise. We show that the macroscopic failure is produced by a
thermal activation of microcracks. Most importantly the effective temperature
of the system is amplified by the spatial disorder (heterogeneity) of the fiber
bundle. The case of a time dependent force and the validity of the Kaiser
effects are also discussed. These results can give more insight to the recent
experimental observations on thermally activated crack and can be useful to
study the failure of electrical networks.Comment: 22 pages, 11 fgure
Fracture precursors in disordered systems
A two-dimensional lattice model with bond disorder is used to investigate the
fracture behaviour under stress-controlled conditions. Although the cumulative
energy of precursors does not diverge at the critical point, its derivative
with respect to the control parameter (reduced stress) exhibits a singular
behaviour. Our results are nevertheless compatible with previous experimental
findings, if one restricts the comparison to the (limited) range accessible in
the experiment. A power-law avalanche distribution is also found with an
exponent close to the experimental values.Comment: 4 pages, 5 figures. Submitted to Europhysics Letter
Self-Similar Law of Energy Release before Materials Fracture
A general law of energy release is derived for stressed heterogeneous
materials, being valid from the starting moment of loading till the moment of
materials fracture. This law is obtained by employing the extrapolation
technique of the self-similar approximation theory. Experiments are
accomplished measuring the energy release for industrial composite samples. The
derived analytical law is confronted with these experimental data as well as
with the known experimental data for other materials.Comment: Latex, 15 pages, no figure
Artifactual log-periodicity in finite size data: Relevance for earthquake aftershocks
The recently proposed discrete scale invariance and its associated
log-periodicity are an elaboration of the concept of scale invariance in which
the system is scale invariant only under powers of specific values of the
magnification factor. We report on the discovery of a novel mechanism for such
log-periodicity relying solely on the manipulation of data. This ``synthetic''
scenario for log-periodicity relies on two steps: (1) the fact that
approximately logarithmic sampling in time corresponds to uniform sampling in
the logarithm of time; and (2) a low-pass-filtering step, as occurs in
constructing cumulative functions, in maximum likelihood estimations, and in
de-trending, reddens the noise and, in a finite sample, creates a maximum in
the spectrum leading to a most probable frequency in the logarithm of time. We
explore in detail this mechanism and present extensive numerical simulations.
We use this insight to analyze the 27 best aftershock sequences studied by
Kisslinger and Jones [1991] to search for traces of genuine log-periodic
corrections to Omori's law, which states that the earthquake rate decays
approximately as the inverse of the time since the last main shock. The
observed log-periodicity is shown to almost entirely result from the
``synthetic scenario'' owing to the data analysis. From a statistical point of
view, resolving the issue of the possible existence of log-periodicity in
aftershocks will be very difficult as Omori's law describes a point process
with a uniform sampling in the logarithm of the time. By construction, strong
log-periodic fluctuations are thus created by this logarithmic sampling.Comment: LaTeX, JGR preprint with AGU++ v16.b and AGUTeX 5.0, use packages
graphicx, psfrag and latexsym, 41 eps figures, 26 pages. In press J. Geophys.
Re
Stochastics theory of log-periodic patterns
We introduce an analytical model based on birth-death clustering processes to
help understanding the empirical log-periodic corrections to power-law scaling
and the finite-time singularity as reported in several domains including
rupture, earthquakes, world population and financial systems. In our
stochastics theory log-periodicities are a consequence of transient clusters
induced by an entropy-like term that may reflect the amount of cooperative
information carried by the state of a large system of different species. The
clustering completion rates for the system are assumed to be given by a simple
linear death process. The singularity at t_{o} is derived in terms of
birth-death clustering coefficients.Comment: LaTeX, 1 ps figure - To appear J. Phys. A: Math & Ge
Log-periodic corrections to scaling: exact results for aperiodic Ising quantum chains
Log-periodic amplitudes of the surface magnetization are calculated
analytically for two Ising quantum chains with aperiodic modulations of the
couplings. The oscillating behaviour is linked to the discrete scale invariance
of the perturbations. For the Fredholm sequence, the aperiodic modulation is
marginal and the amplitudes are obtained as functions of the deviation from the
critical point. For the other sequence, the perturbation is relevant and the
critical surface magnetization is studied.Comment: 12 pages, TeX file, epsf, iopppt.tex, xref.tex which are joined. 4
postcript figure
Evidence of Intermittent Cascades from Discrete Hierarchical Dissipation in Turbulence
We present the results of a search of log-periodic corrections to scaling in
the moments of the energy dissipation rate in experiments at high Reynolds
number (2500) of three-dimensional fully developed turbulence. A simple
dynamical representation of the Richardson-Kolmogorov cartoon of a cascade
shows that standard averaging techniques erase by their very construction the
possible existence of log-periodic corrections to scaling associated with a
discrete hierarchy. To remedy this drawback, we introduce a novel ``canonical''
averaging that we test extensively on synthetic examples constructed to mimick
the interplay between a weak log-periodic component and rather strong
multiplicative and phase noises. Our extensive tests confirm the remarkable
observation of statistically significant log-periodic corrections to scaling,
with a prefered scaling ratio for length scales compatible with the value gamma
= 2. A strong confirmation of this result is provided by the identification of
up to 5 harmonics of the fundamental log-periodic undulations, associated with
up to 5 levels of the underlying hierarchical dynamical structure. A natural
interpretation of our results is that the Richardson-Kolmogorov mental picture
of a cascade becomes a realistic description if one allows for intermittent
births and deaths of discrete cascades at varying scales.Comment: Latex document of 40 pages, including 18 eps figure
Possibility between earthquake and explosion seismogram differentiation by discrete stochastic non-Markov processes and local Hurst exponent analysis
The basic purpose of the paper is to draw the attention of researchers to new
possibilities of differentiation of similar signals having different nature.
One of examples of such kind of signals is presented by seismograms containing
recordings of earthquakes (EQ's) and technogenic explosions (TE's). We propose
here a discrete stochastic model for possible solution of a problem of strong
EQ's forecasting and differentiation of TE's from the weak EQ's. Theoretical
analysis is performed by two independent methods: with the use of statistical
theory of discrete non-Markov stochastic processes (Phys. Rev. E62,6178 (2000))
and the local Hurst exponent. Time recordings of seismic signals of the first
four dynamic orthogonal collective variables, six various plane of phase
portrait of four dimensional phase space of orthogonal variables and the local
Hurst exponent have been calculated for the dynamic analysis of the earth
states. The approaches, permitting to obtain an algorithm of strong EQ's
forecasting and to differentiate TE's from weak EQ's, have been developed.Comment: REVTEX +12 ps and jpg figures. Accepted for publication in Phys. Rev.
E, December 200
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