9,262 research outputs found
Avalanches in Breakdown and Fracture Processes
We investigate the breakdown of disordered networks under the action of an
increasing external---mechanical or electrical---force. We perform a mean-field
analysis and estimate scaling exponents for the approach to the instability. By
simulating two-dimensional models of electric breakdown and fracture we observe
that the breakdown is preceded by avalanche events. The avalanches can be
described by scaling laws, and the estimated values of the exponents are
consistent with those found in mean-field theory. The breakdown point is
characterized by a discontinuity in the macroscopic properties of the material,
such as conductivity or elasticity, indicative of a first order transition. The
scaling laws suggest an analogy with the behavior expected in spinodal
nucleation.Comment: 15 pages, 12 figures, submitted to Phys. Rev. E, corrected typo in
authors name, no changes to the pape
25 Years of Self-Organized Criticality: Numerical Detection Methods
The detection and characterization of self-organized criticality (SOC), in
both real and simulated data, has undergone many significant revisions over the
past 25 years. The explosive advances in the many numerical methods available
for detecting, discriminating, and ultimately testing, SOC have played a
critical role in developing our understanding of how systems experience and
exhibit SOC. In this article, methods of detecting SOC are reviewed; from
correlations to complexity to critical quantities. A description of the basic
autocorrelation method leads into a detailed analysis of application-oriented
methods developed in the last 25 years. In the second half of this manuscript
space-based, time-based and spatial-temporal methods are reviewed and the
prevalence of power laws in nature is described, with an emphasis on event
detection and characterization. The search for numerical methods to clearly and
unambiguously detect SOC in data often leads us outside the comfort zone of our
own disciplines - the answers to these questions are often obtained by studying
the advances made in other fields of study. In addition, numerical detection
methods often provide the optimum link between simulations and experiments in
scientific research. We seek to explore this boundary where the rubber meets
the road, to review this expanding field of research of numerical detection of
SOC systems over the past 25 years, and to iterate forwards so as to provide
some foresight and guidance into developing breakthroughs in this subject over
the next quarter of a century.Comment: Space Science Review series on SO
25 Years of Self-Organized Criticality: Solar and Astrophysics
Shortly after the seminal paper {\sl "Self-Organized Criticality: An
explanation of 1/f noise"} by Bak, Tang, and Wiesenfeld (1987), the idea has
been applied to solar physics, in {\sl "Avalanches and the Distribution of
Solar Flares"} by Lu and Hamilton (1991). In the following years, an inspiring
cross-fertilization from complexity theory to solar and astrophysics took
place, where the SOC concept was initially applied to solar flares, stellar
flares, and magnetospheric substorms, and later extended to the radiation belt,
the heliosphere, lunar craters, the asteroid belt, the Saturn ring, pulsar
glitches, soft X-ray repeaters, blazars, black-hole objects, cosmic rays, and
boson clouds. The application of SOC concepts has been performed by numerical
cellular automaton simulations, by analytical calculations of statistical
(powerlaw-like) distributions based on physical scaling laws, and by
observational tests of theoretically predicted size distributions and waiting
time distributions. Attempts have been undertaken to import physical models
into the numerical SOC toy models, such as the discretization of
magneto-hydrodynamics (MHD) processes. The novel applications stimulated also
vigorous debates about the discrimination between SOC models, SOC-like, and
non-SOC processes, such as phase transitions, turbulence, random-walk
diffusion, percolation, branching processes, network theory, chaos theory,
fractality, multi-scale, and other complexity phenomena. We review SOC studies
from the last 25 years and highlight new trends, open questions, and future
challenges, as discussed during two recent ISSI workshops on this theme.Comment: 139 pages, 28 figures, Review based on ISSI workshops "Self-Organized
Criticality and Turbulence" (2012, 2013, Bern, Switzerland
Avalanches, thresholds, and diffusion in meso-scale amorphous plasticity
We present results on a meso-scale model for amorphous matter in athermal,
quasi-static (a-AQS), steady state shear flow. In particular, we perform a
careful analysis of the scaling with the lateral system size, , of: i)
statistics of individual relaxation events in terms of stress relaxation, ,
and individual event mean-squared displacement, , and the subsequent load
increments, , required to initiate the next event; ii) static
properties of the system encoded by , the distance of local
stress values from threshold; and iii) long-time correlations and the emergence
of diffusive behavior. For the event statistics, we find that the distribution
of is similar to, but distinct from, the distribution of . We find a
strong correlation between and for any particular event, with with . completely determines the scaling exponents
for given those for . For the distribution of local thresholds, we
find is analytic at , and has a value which scales with lateral system length as . Extreme value statistics arguments lead to a scaling relation
between the exponents governing and those governing . Finally, we
study the long-time correlations via single-particle tracer statistics. The
value of the diffusion coefficient is completely determined by and the scaling properties of (in particular from
) rather than directly from as one might have naively
guessed. Our results: i) further define the a-AQS universality class, ii)
clarify the relation between avalanches of stress relaxation and diffusive
behavior, iii) clarify the relation between local threshold distributions and
event statistics
A damage model based on failure threshold weakening
A variety of studies have modeled the physics of material deformation and
damage as examples of generalized phase transitions, involving either critical
phenomena or spinodal nucleation. Here we study a model for frictional sliding
with long range interactions and recurrent damage that is parameterized by a
process of damage and partial healing during sliding. We introduce a failure
threshold weakening parameter into the cellular-automaton slider-block model
which allows blocks to fail at a reduced failure threshold for all subsequent
failures during an event. We show that a critical point is reached beyond which
the probability of a system-wide event scales with this weakening parameter. We
provide a mapping to the percolation transition, and show that the values of
the scaling exponents approach the values for mean-field percolation (spinodal
nucleation) as lattice size is increased for fixed . We also examine the
effect of the weakening parameter on the frequency-magnitude scaling
relationship and the ergodic behavior of the model
Self-organized criticality as an absorbing-state phase transition
We explore the connection between self-organized criticality and phase
transitions in models with absorbing states. Sandpile models are found to
exhibit criticality only when a pair of relevant parameters - dissipation
epsilon and driving field h - are set to their critical values. The critical
values of epsilon and h are both equal to zero. The first is due to the absence
of saturation (no bound on energy) in the sandpile model, while the second
result is common to other absorbing-state transitions. The original definition
of the sandpile model places it at the point (epsilon=0, h=0+): it is critical
by definition. We argue power-law avalanche distributions are a general feature
of models with infinitely many absorbing configurations, when they are subject
to slow driving at the critical point. Our assertions are supported by
simulations of the sandpile at epsilon=h=0 and fixed energy density (no drive,
periodic boundaries), and of the slowly-driven pair contact process. We
formulate a field theory for the sandpile model, in which the order parameter
is coupled to a conserved energy density, which plays the role of an effective
creation rate.Comment: 19 pages, 9 figure
Discrete Fracture Model with Anisotropic Load Sharing
A two-dimensional fracture model where the interaction among elements is
modeled by an anisotropic stress-transfer function is presented. The influence
of anisotropy on the macroscopic properties of the samples is clarified, by
interpolating between several limiting cases of load sharing. Furthermore, the
critical stress and the distribution of failure avalanches are obtained
numerically for different values of the anisotropy parameter and as a
function of the interaction exponent . From numerical results, one can
certainly conclude that the anisotropy does not change the crossover point
in 2D. Hence, in the limit of infinite system size, the crossover
value between local and global load sharing is the same as the one
obtained in the isotropic case. In the case of finite systems, however, for
, the global load sharing behavior is approached very slowly
Driving rate dependence of avalanche statistics and shapes at the yielding transition
We study stress time series caused by plastic avalanches in athermally
sheared disordered materials. Using particle-based simulations and a mesoscopic
elasto-plastic model, we analyze size and shear-rate dependence of the
stress-drop durations and size distributions together with their average
temporal shape. We find critical exponents different from mean-field
predictions, and a clear asymmetry for individual avalanches. We probe scaling
relations for the rate dependency of the dynamics and we report a crossover
towards mean-field results for strong driving.Comment: 5 pages, 3 figures, 1 table, supplementary material to be found at
http://www-liphy.ujf-grenoble.fr/pagesperso/martens/documents/liu2015-sm.pd
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